An Innovative Investigation of the Thermal Environment Inside the Reconstructed Caldaria of Two Ancient Roman Baths Using Computational Fluid Dynamics

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2013-01-18 An Innovative Investigation of the Thermal Environment inside the Reconstructed Caldaria of Two Ancient Roman Baths Using Computational Fluid Dynamics

Oetelaar, Taylor

Oetelaar, T. (2013). An Innovative Investigation of the Thermal Environment inside the Reconstructed Caldaria of Two Ancient Roman Baths Using Computational Fluid Dynamics (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/24900 http://hdl.handle.net/11023/435 doctoral thesis

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An Innovative Investigation of the Thermal Environment inside the Reconstructed

Caldaria of Two Ancient Roman Baths Using Computational Fluid Dynamics

Taylor Anthony Oetelaar

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE

DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING

CALGARY, ALBERTA

JANUARY, 2013

The overarching premise of this dissertation is to use engineering principles and classical archaeological data to create knowledge that benefits both disciplines: transdisciplinary research. Specifically, this project uses computational fluid dynamics (CFD) to analyze the thermal environment inside one room of two Roman bath buildings. By doing so, this research reveals the temperature distribution and velocity profiles inside the room of interest.

One of the first preliminary necessities was an accurate measure of the heat input into the room from the radiant heating system. The best way to do this was experimentally. The results showed no dependence on the plenum temperature. The measured convective heat transfer coefficient was between 6.2 and 7.6W/m2·°C, with an average of 7.0W/m2·°C.

The CFD analyses begin with a 2-D assessment of the relationship between the windows and doorways of the rooms of interest and their heat retention. The former reinforced the standpoint that the windows had to have glazing to maintain an adequate bathing temperature. The latter suggested that the reason why many doorways were narrow was thermal.

The first of two 3-D case studies is a replica small bath for the television series NOVA.

The results illustrated that the vault traps the hottest air leaving the region inhabited by the patrons cooler than the average of 35°C. The data also showed that the open doorway heavily influenced the environment of the room. This influence seemed misleading and

ii the best way to test this was to add the adjoining room and observe the flow patterns. The results of this revealed that the exchange between rooms decreased and the temperature in the room of interest rose to 44°C. The addition of a cloth door increased the temperature to 49°C.

The second case study—the Baths of Caracalla in Rome—is significantly larger making the simulation of the entire volume impossible. The results showed a greater transitory phase which is due to the self-contained nature of the model. The data also demonstrated a minimal response to the change of season but a dramatic shift with a change to the representation of the sun.

iii Preface

This dissertation merges the two seemingly opposing fields of mechanical engineering and classical archaeology. I am a mechanical engineer by training but have attempted to balance and explain the terminology, methodology, and results in such a way that scholars from both fields can understand them.

iv Acknowledgements

I begin by thanking my co-supervisors Dr. Clifton Johnston, Dr. Daryl Caswell (2006-

2010), and Dr. David Wood (2010-2013). When I first approached Drs. Johnston and

Caswell with this idea of joining engineering with classical archaeology, they did not slam their doors. Instead they sat down and encouraged me to find a way to make this unique topic work. When Dr. Caswell had to step down because of health issues and Dr.

Johnston transferred to Dalhousie University, Dr. Wood was gracious enough to take over the supervisory role even though he had not met me. All three gave me enough latitude and freedom to explore many issues but were there if I needed assistance.

The next people I thank are my Greek and Roman Studies committee members, Dr. Lisa

Hughes and Dr. John Humphrey. When I took Dr. Hughes’ Greek Art and Architecture class in my fourth year of undergrad, she always answered my (many) questions. She never stopped. Dr. Humphrey was patient with me as I struggled with my Latin translations. Both helped as I grappled with a new field and tried to gain fluency. Plus they were never afraid to ask me to clarify something if I started using too much engineering jargon.

This project would not have been possible without the funding support of the Natural

Sciences and Engineering Research Council of Canada and the Alberta Ingenuity Fund.

I thank Dr. Alexandra Lesk, her husband Paul Blomerus, and Dr. Marcelo Epstein for their encouragement in the early stages of this project. When I started asking if there was

v need for applying engineering to classical archaeology, they were steadfast in their answer: yes. I also thank Dr. Richard Levy, Dr. Milo Nikolic, and Dr. Michael Roth for their continued support throughout this process.

Much thanks to the staff of Mechanical Engineering—particularly Jim McNeely, Steven

Crocker, Ann Tikk, and Nareeza Khan—and Kent Paulson for all the technical and administrative support. I thank the faculty, staff, and graduate students of Greek and

Roman Studies for welcoming an engineer into their midst. A great deal of this dissertation would not have been possible without WestGrid, the High Performance

Computing at the University of Calgary and the technical staff running these systems, particularly Doug Phillips and Anne Traynor. Thank you for putting up with my sometimes idiotic questions. I would be remised if I did not thank the people of the

Disability Resource Centre—specifically Merlin Keillor and Judy Smith—and my aide

Dmitry Mekinulov.

Finally, but certainly most importantly, a huge thank you to my family: my brothers,

Garrett and Matt, and my parents, Gerald and Joy. Without their constant support and encouragement, this entire endeavour would not have been possible. With the seemingly never-ending delays and setbacks that plagued this project, it was always nice to know that I had such a loving family at home. I have to give additional recognition to my parents for instilling the belief in me that nothing is beyond my capabilities.

vi Dedication

Inspired by LdV

vii Table of Contents

Abstract ...... ii Preface...... iv Acknowledgements ...... v Dedication ...... vii Table of Contents ...... viii List of Tables ...... xi List of Figures and Illustrations ...... xii List of Symbols, Abbreviations and Nomenclature ...... xx Epigraph ...... xxi

CHAPTER 1 — INTRODUCTION ...... 1

CHAPTER 2 — THE FOUNDATIONS ...... 7 2.1 Background Information ...... 7 2.1.1 Introduction to Computational Fluid Dynamics (CFD) ...... 7 2.1.2 Introduction to Ancient Roman Baths ...... 10 2.1.2.1 The Heating System of Roman Baths ...... 13 2.1.2.2 The NOVA Baths ...... 15 2.1.2.3 The Baths of Caracalla ...... 16 2.2 Literature Reviews ...... 22 2.2.1 Transdisciplinary Literature Review ...... 23 2.2.2 Engineering Literature Review ...... 26 2.2.3 Classical Archaeology Literature Review on Baths ...... 35 2.2.4 Gaps in the Knowledge Base ...... 45

CHAPTER 3 — RECONSTRUCTING THE BATHS OF CARACALLA ...... 48 3.1 Introduction ...... 48 3.2 Software ...... 49 3.3 General Structure and Broad-Spectrum Assumptions ...... 50 3.4 Specific Alterations and Assumptions ...... 53 3.5 Windows and Window Glazing ...... 56 3.6 Texturing the Model ...... 60 3.7 Benefits of Digital Reconstruction ...... 63 3.8 Conclusion ...... 66

CHAPTER 4 — DETERMINATION OF THE CONVECTIVE HEAT TRANSFER COEFFICIENT OF THE TUBULI ...... 69 4.1 Introduction ...... 69 4.2 Experimental Setup ...... 70 4.2.1 Calibration ...... 73 4.3 Results ...... 74 4.3.1 Mass Flow Rate ...... 76 4.4 Calculation of Coefficients ...... 77 4.5 Discussion ...... 85

viii 4.6 Conclusion ...... 88

CHAPTER 5 — THE DESIGN OF CALDARIA, WINDOWS, AND DOORWAYS AND ITS IMPACT ON HEAT FLOW ...... 89 5.1 Introduction ...... 89 5.2 Theory and Fact Based Simulations ...... 90 5.3 Case Study I: Caldaria Windows ...... 91 5.3.1 Location and Design of Windows ...... 91 5.3.2 Evidence for Glazing in Caldaria Windows ...... 92 5.3.3 CFD Model of Caldaria Windows ...... 94 5.3.4 The CFD Results ...... 96 5.3.4.1 Summer State ...... 96 5.3.4.2 Winter State ...... 103 5.4 Case Study II: Caldaria Doorways ...... 107 5.4.1 The Design of Caldaria Doorways ...... 107 5.4.2 The CFD Model of the Caldarium Doorways ...... 109 5.4.3 The CFD Results ...... 109 5.5 Conclusions ...... 112 5.6 Appendix 5A ...... 115 5.7 Appendix 5B ...... 116

CHAPTER 6 — PRELIMINARY CFD ANALYSES ...... 117 6.1 Introduction ...... 117 6.2 Methodology ...... 117 6.2.1 Meshing the NOVA Bath Air Volume ...... 117 6.2.2 Configuring the Model ...... 119 6.2.3 The Boundary Conditions ...... 120 6.3 Results and Discussion ...... 122 6.4 Conclusions ...... 154

CHAPTER 7 — ENHANCING THE NOVA MODEL ...... 156 7.1 Introduction ...... 156 7.2 Methodology ...... 156 7.2.1 Grid ...... 156 7.2.2 Sub-Models ...... 157 7.2.3 Boundary Conditions ...... 158 7.3 Results and Discussion ...... 160 7.4 Conclusions ...... 181

CHAPTER 8 — MODELLING NOVA WITH THE TEPIDARIUM ...... 183 8.1 Introduction ...... 183 8.2 Brief Review of Previous Results ...... 183 8.3 Changes to this Model ...... 187 8.3.1 Grid ...... 188 8.3.2 Sub-Models ...... 188 8.3.3 Boundary Conditions ...... 189 8.4 Results and Discussion ...... 191

ix 8.5 Conclusions ...... 222

CHAPTER 9 — SIMULATING THE CALDARIUM OF THE BATHS OF CARACALLA ...... 224 9.1 Introduction ...... 224 9.2 Methodology ...... 227 9.2.1 Grid ...... 227 9.2.2 Sub-Models ...... 229 9.2.3 Boundary Conditions ...... 229 9.3 Results and Discussion ...... 231 9.4 Conclusion ...... 249

CHAPTER 10 — CONCLUSION ...... 251 10.1 Summary of the Results ...... 251 10.2 Recommendations for Future Work ...... 256

REFERENCES ...... 259

APPENDIX 1 — THE ANCIENT SOURCES ...... 294 A1.1 A Short Glossary of Latin Terms ...... 294 A1.2 Passages about Glazing ...... 296 Seneca the Younger — Epistulae 86.8-11 ...... 296 Seneca the Younger — Epistulae 86.6 ...... 299 A1.3 Passages about Heating ...... 299 Seneca the Younger — Epistulae 90.25 ...... 299 Seneca the Younger — Naturales Quaestiones 3.24.2-3 ...... 301 Pliny the Younger — Epistulae 3.14 ...... 303 A1.4 Passages about Bathing Time ...... 303 Martial — Epistulae 10.48.3-4 ...... 303 Scriptores Historiae Augustae — Severus Alexander 24.5-6 ...... 305 A1.5 Passages about Bath Construction ...... 306 Vitruvius — De Architectura 5.10.1-5 ...... 306 Cetus Faventinus — De Diversis Fabricis Architectonicae 16 ...... 313 Cetus Faventinus — De Diversis Fabricis Architectonicae 17 ...... 315 Palladius — De Re Rustica 1.39.1-5 ...... 316

x List of Tables

Table 2.1: Dimensions of Tubuli along the Northeast Pier of the Baths of Caracalla ...... 21

Table 3.1: Breakdown of the Windows of the Baths of Caracalla...... 59

Table 4.1: Summary of Inlet Velocities and Mass Flow Rates...... 77

Table 4.2: Breakdown of Heat Fluxes ...... 78

Table 4.3: Average CHTC for Both Clusters...... 84

Table 4.4: Rayleigh and Nusselt Numbers for the Bottom Cluster Based on the Average CHTCs ...... 87

Table 5.1: The Grid Details for the Window Case Study ...... 115

Table 5.2: The Basic Operating Parameters for the Window Case Study ...... 115

Table 5.3: The Grid Details for the Doorway Case Study ...... 116

Table 5.4: The Basic Operating Parameters for the Doorway Case Study ...... 116

Table 6.1: Discretization Methods ...... 119

Table 6.2: The Boundary Conditions for the Caldarium Wall Sections ...... 122

Table 6.3: The Case Setup ...... 123

Table 6.4: Case Setup, Part 2 ...... 146

Table 7.1: The Boundary Conditions for the Wall Sections ...... 159

Table 7.2: Case Breakdown ...... 160

Table 7.3: Comparison of Heat Fluxes Calculated by FLUENT ...... 171

Table 8.1: Porous Zone Values ...... 189

Table 8.2: The Boundary Conditions for the Caldarium Wall Sections ...... 190

Table 8.3: The Boundary Conditions for the Tepidarium Wall Sections ...... 190

Table 9.1: The Boundary Conditions for the Wall Sections ...... 230

Table 9.2: Case Setup ...... 231

xi List of Figures and Illustrations

Figure 2.1: Diagram of a pipe showing the mesh and boundary conditions. (Model created by Taylor Oetelaar.)...... 9

Figure 2.2: Layout of the Baths of Caracalla. (Model created by Taylor Oetelaar.) ...... 12

Figure 2.3: Diagram of the hypocaust heating system. (Model created by Taylor Oetelaar.) ...... 14

Figure 2.4: CAD reconstruction of the NOVA baths. (Model created by Taylor Oetelaar.) ...... 16

Figure 2.5: CAD reconstruction of the Baths of Caracalla. (Model created by Taylor Oetelaar.) ...... 18

Figure 2.6: Tubuli remnants from NW pool of the caldarium of the Baths of Caracalla (Photo by Joy Oetelaar)...... 20

Figure 2.7: Tubuli remnants from NE pier of the caldarium of the Baths of Caracalla (Photo by Joy Oetelaar)...... 20

Figure 2.8: Projected tubuli locations. (Model created by Taylor Oetelaar.) ...... 21

Figure 2.9: Size distribution of the tubuli along the northeast pier of the Baths of Caracalla...... 22

Figure 3.1: (a) A preliminary model showing a flat-topped frigidarium. (b) A preliminary model showing a gabled frigidarium. (Model created by Taylor Oetelaar.) ...... 52

Figure 3.2: Sketch of a sample window showing the different parts. (Model created by Taylor Oetelaar.) ...... 58

Figure 3.3: Reconstructed opus sectile floors of the Baths of Caracalla. (Model created by Taylor Oetelaar.)...... 62

Figure 3.4: A view from the northeast of the reconstructed Baths of Caracalla. (Model created by Taylor Oetelaar.)...... 67

Figure 3.5: A view from the southwest of the reconstructed Baths of Caracalla. (Model created by Taylor Oetelaar.) ...... 67

Figure 4.1: (a) Picture of experimental setup (Photo by Matt Oetelaar). (b) Picture looking down the rightmost flue showing the layers of the wall (Photo by Matt Oetelaar)...... 70

xii Figure 4.2: (a) Cross-section diagram of the setup (Dimensions: mm; Arrows indicate air flow direction). (b) Magnified view of the wall cross-section showing thickness dimensions and the approximate depth of the thermocouples...... 71

Figure 4.3: Temperature distribution of bottom cluster...... 75

Figure 4.4: Temperature distribution of top cluster...... 75

Figure 4.5: Heat fluxes from bottom cluster with the surface temperature as the reference point...... 79

Figure 4.6: Heat fluxes from top cluster with the surface temperature as the reference point...... 79

Figure 4.7: Heat fluxes from bottom cluster with the mid-marble temperature as the reference point...... 80

Figure 4.8: Heat fluxes from top cluster with the mid-marble temperature as the reference point...... 80

Figure 4.9: CHTCs using heat fluxes from bottom cluster with the surface temperature as the reference point...... 82

Figure 4.10: CHTCs using heat fluxes from top cluster with the surface temperature as the reference point...... 83

Figure 4.11: CHTCs using heat fluxes from bottom cluster with the mid-marble temperature as the reference point...... 83

Figure 4.12: CHTCs using heat fluxes from top cluster with the mid-marble temperature as the reference point...... 84

Figure 5.1: Layout for the window case study: (a) open; (b) glazed...... 96

Figure 5.2: Temperature distribution for the open summer case (Units: °C)...... 98

Figure 5.3: Temperature distribution for the glazed summer case (Units: °C)...... 99

Figure 5.4: Temperature versus time of all four window cases...... 100

Figure 5.5: Temperature distribution for the glazed summer case after one hour (Units: °C)...... 101

Figure 5.6: Magnified temperature distribution for the summer glazed case after one hour (Units: °C)...... 102

Figure 5.7: Temperature distribution for the open winter case (Units: °C)...... 104

Figure 5.8: Temperature distribution for the glazed winter case (Units: °C)...... 105

xiii Figure 5.9: Temperature distribution for the glazed winter case after one hour (Units: °C)...... 106

Figure 5.10: Temperature distribution for a colonnaded doorway (Units: °C)...... 110

Figure 5.11: Temperature distribution for a doorway with a pier (Units: °C)...... 111

Figure 6.1: The final unstructured mesh...... 118

Figure 6.2: Placement of the display planes...... 124

Figure 6.3: Temperature distribution in the x-mid-plane for Case #6.1 (Units: °C)...... 126

Figure 6.4: Temperature distribution in the z-mid-plane for Case #6.1 (Units: °C)...... 127

Figure 6.5: Velocity vectors in the x-mid-plane for Case #6.1 (Units: m/s)...... 128

Figure 6.6: Velocity vectors in the z-mid-plane for Case #6.1 (Units: m/s)...... 129

Figure 6.7: Temperature distribution in the x-mid-plane for Case #6.2 (Units: °C)...... 130

Figure 6.8: Temperature distribution in the z-mid-plane for Case #6.2 (Units: °C)...... 131

Figure 6.9: Velocity vectors in the x-mid-plane for Case #6.2 (Units: m/s)...... 132

Figure 6.10: Velocity vectors in the z-mid-plane for Case #6.2 (Units: m/s)...... 133

Figure 6.11: Temperature distribution in the x-mid-plane for Case #6.3 (Units: °C). ... 134

Figure 6.12: Temperature distribution in the z-mid-plane for Case #6.3 (Units: °C). .... 135

Figure 6.13: Velocity vectors in the x-mid-plane for Case #6.3 (Units: m/s)...... 136

Figure 6.14: Velocity vectors in the z-mid-plane for Case #6.3 (Units: m/s)...... 137

Figure 6.15: Temperature distribution in the x-mid-plane for Case #6.4 (Units: °C). ... 138

Figure 6.16: Temperature distribution in the z-mid-plane for Case #6.4 (Units: °C). .... 139

Figure 6.17: Velocity vectors in the x-mid-plane for Case #6.4 (Units: m/s)...... 140

Figure 6.18: Velocity vectors in the z-mid-plane for Case #6.4 (Units: m/s)...... 141

Figure 6.19: Temperature distribution in the x-mid-plane for Case #6.5 (Units: °C). ... 142

Figure 6.20: Temperature distribution in the z-mid-plane for Case #6.5 (Units: °C). .... 143

Figure 6.21: Velocity vectors in the x-mid-plane for Case #6.5 (Units: m/s)...... 144

Figure 6.22: Velocity vectors in the z-mid-plane for Case #6.5 (Units: m/s)...... 145 xiv Figure 6.23: Temperature distribution in the x-mid-plane for Case #6.6 (Units: °C). ... 147

Figure 6.24: Velocity vectors in the x-mid-plane for Case #6.6 (Units: m/s)...... 148

Figure 6.25: Temperature distribution in the x-mid-plane for Case #6.7 (Units: °C). ... 149

Figure 6.26: Velocity vectors in the x-mid-plane for Case #6.7 (Units: m/s)...... 150

Figure 6.27: Temperature distribution in the x-mid-plane for Case #6.8 (Units: °C). ... 151

Figure 6.28: Velocity vectors in the x-mid-plane for Case #6.8 (Units: m/s)...... 152

Figure 6.29: Temperature distribution in the x-mid-plane for Case #6.9 (Units: °C). ... 153

Figure 6.30: Velocity vectors in the x-mid-plane for Case #6.9 (Units: m/s)...... 154

Figure 7.1: The structured grid of the caldarium with the pool...... 157

Figure 7.2: Temperature distribution in the x-mid-plane for Case #7.1 (Units: °C)...... 161

Figure 7.3: Temperature distribution in the z-mid-plane for Case #7.1 (Units: °C)...... 162

Figure 7.4: Velocity vectors in the x-mid-plane for Case #7.1 (Units: m/s)...... 163

Figure 7.5: Velocity vectors in the z-mid-plane for Case #7.1 (Units: m/s)...... 164

Figure 7.6: Temperature distribution in the x-mid-plane for Case #7.2 (Units: °C)...... 166

Figure 7.7: Temperature distribution in the z-mid-plane for Case #7.2 (Units: °C)...... 167

Figure 7.8: Velocity vectors in the x-mid-plane for Case #7.2 (Units: m/s)...... 168

Figure 7.9: Velocity vectors in the z-mid-plane for Case #7.2 (Units: m/s)...... 169

Figure 7.10: Water vapour distribution in the z-mid-plane for Case #7.2 (Units: kg of water vapour/kg of dry air)...... 170

Figure 7.11: Temperature distribution in the x-mid-plane for Case #7.3 (Units: °C). ... 172

Figure 7.12: Temperature distribution in the z-mid-plane for Case #7.3 (Units: °C). .... 173

Figure 7.13: Velocity vectors in the x-mid-plane for Case #7.3 (Units: m/s)...... 174

Figure 7.14: Velocity vectors in the z-mid-plane for Case #7.3 (Units: m/s)...... 175

Figure 7.15: Water vapour distribution in the z-mid-plane for Case #7.3 (Units: kg of water vapour/kg of dry air)...... 176

Figure 7.16: Temperature distribution in the x-mid-plane for Case #7.4 (Units: °C). ... 177

xv Figure 7.17: Temperature distribution in the z-mid-plane for Case #7.4 (Units: °C). .... 178

Figure 7.18: Velocity vectors in the x-mid-plane for Case #7.4 (Units: m/s)...... 179

Figure 7.19: Velocity vectors in the z-mid-plane for Case #7.4 (Units: m/s)...... 180

Figure 8.1: Temperature distribution in the x-mid-plane for Case #7.3 (Units: °C)...... 184

Figure 8.2: Temperature distribution in the z-mid-plane for Case #7.3 (Units: °C)...... 185

Figure 8.3: Velocity vectors in the x-mid-plane for Case #7.3 (Units: m/s)...... 186

Figure 8.4: Velocity vectors in the z-mid-plane for Case #7.3 (Units: m/s)...... 187

Figure 8.5: Temperature distribution in the x-mid-plane for Case #8.1 (Units: °C)...... 193

Figure 8.6: Temperature distribution in the z-mid-plane for Case #8.1 (Units: °C)...... 194

Figure 8.7: Velocity vectors in the x-mid-plane for Case #8.1 (Units: m/s)...... 195

Figure 8.8: Velocity vectors in the z-mid-plane for Case #8.1 (Units: m/s)...... 196

Figure 8.9: Temperature distribution in the x-mid-plane for Case #8.2 (Units: °C)...... 197

Figure 8.10: Temperature distribution in the z-mid-plane for Case #8.2 (Units: °C). .... 198

Figure 8.11: Velocity vectors in the x-mid-plane for Case #8.2 (Units: m/s)...... 199

Figure 8.12: Velocity vectors in the x-mid-plane for Case #8.2 (Units: m/s)...... 200

Figure 8.13: Temperature distribution in the x-mid-plane for Case #8.3 (Units: °C). ... 201

Figure 8.14: Temperature distribution in the z-mid-plane for Case #8.3 (Units: °C). .... 202

Figure 8.15: Velocity vectors in the x-mid-plane for Case #8.3 (Units: m/s)...... 203

Figure 8.16: Velocity vectors in the z-mid-plane for Case #8.3 (Units: m/s)...... 204

Figure 8.17: Temperature distribution in the x-mid-plane for Case #8.4 (Units: °C). ... 205

Figure 8.18: Temperature distribution in the z-mid-plane for Case #8.4 (Units: °C). .... 206

Figure 8.19: Velocity vectors in the x-mid-plane for Case #8.4 (Units: m/s)...... 207

Figure 8.20: Velocity vectors in the z-mid-plane for Case #8.4 (Units: m/s)...... 208

Figure 8.21: Temperature distribution in the x-mid-plane for Case #8.5 (Units: °C). ... 209

Figure 8.22: Temperature distribution in the z-mid-plane for Case #8.5 (Units: °C). .... 210

xvi Figure 8.23: Velocity vectors in the x-mid-plane for Case #8.5 (Units: m/s)...... 211

Figure 8.24: Velocity vectors in the z-mid-plane for Case #8.5 (Units: m/s)...... 212

Figure 8.25: Temperature distribution in the x-mid-plane for Case #8.6 (Units: °C). ... 213

Figure 8.26: Temperature distribution in the z-mid-plane for Case #8.6 (Units: °C). .... 214

Figure 8.27: Velocity vectors in the x-mid-plane for Case #8.6 (Units: m/s)...... 215

Figure 8.28: Velocity vectors in the z-mid-plane for Case #8.6 (Units: m/s)...... 216

Figure 8.29: Temperature distribution in the x-mid-plane for Case #8.7 (Units: °C). ... 217

Figure 8.30: Temperature distribution in the z-mid-plane for Case #8.7 (Units: °C). .... 218

Figure 8.31: Velocity vectors in the x-mid-plane for Case #8.7 (Units: m/s)...... 219

Figure 8.32: Velocity vectors in the z-mid-plane for Case #8.7 (Units: m/s)...... 220

Figure 9.1: Comparing the NOVA baths to the Baths of Caracalla. (Model created by Taylor Oetelaar.) ...... 225

Figure 9.2: Comparing caldarium air volume of the NOVA baths to one of the Baths of Caracalla. (Model created by Taylor Oetelaar.) ...... 225

Figure 9.3: The volume breakdown for meshing purposes. The clear represents the structured mesh; the dark grey, the semi-structured; and the medium grey, the unstructured. (Model created by Taylor Oetelaar.) ...... 228

Figure 9.4: The final mesh...... 228

Figure 9.5: Temperature distribution for Case #9.1 after ten minutes (Units: °C)...... 232

Figure 9.6: Velocity vectors for Case #9.1 after ten minutes (Units: m/s)...... 233

Figure 9.7: Temperature distribution for Case #9.1 after twenty minutes (Units: °C). .. 234

Figure 9.8: Temperature distribution for Case #9.1 after thirty minutes (Units: °C). .... 234

Figure 9.9: Temperature distribution for Case #9.1 after forty minutes (Units: °C)...... 234

Figure 9.10: Temperature distribution for Case #9.1 after fifty minutes (Units: °C). .... 234

Figure 9.11: Temperature distribution for Case #9.1 after sixty minutes (Units: °C). ... 235

Figure 9.12: Temperature distribution for Case #9.1 after seventy minutes (Units: °C).235

Figure 9.13: Temperature distribution for Case #9.1 after eighty minutes (Units: °C). . 235

xvii Figure 9.14: Temperature distribution for Case #9.1 after ninety minutes (Units: °C). . 235

Figure 9.15: Temperature distribution for Case #9.1 after one-hundred-and-twenty minutes (Units: °C)...... 236

Figure 9.16: Velocity vectors for Case #9.1 after one-hundred-and-twenty minutes (Units: m/s)...... 236

Figure 9.17: Temperature distribution for Case #9.1 after one-hundred-and-eighty minutes (Units: °C)...... 237

Figure 9.18: Velocity vectors for Case #9.1 after one-hundred-and-eighty minutes (Units: m/s)...... 237

Figure 9.19: Temperature distribution for Case #9.1 after two-hundred-and-forty minutes (Units: °C)...... 237

Figure 9.20: Velocity vectors for Case #9.1 after two-hundred-and-forty minutes (Units: m/s)...... 237

Figure 9.21: Temperature distribution for Case #9.2 after ten minutes (Units: °C)...... 239

Figure 9.22: Velocity vectors for Case #9.2 after ten minutes (Units: m/s)...... 240

Figure 9.23: Temperature distribution for Case #9.2 after twenty minutes (Units: °C). 241

Figure 9.24: Temperature distribution for Case #9.2 after thirty minutes (Units: °C). .. 241

Figure 9.25: Temperature distribution for Case #9.2 after forty minutes (Units: °C). ... 241

Figure 9.26: Temperature distribution for Case #9.2 after fifty minutes (Units: °C). .... 241

Figure 9.27: Temperature distribution for Case #9.2 after sixty minutes (Units: °C). ... 242

Figure 9.28: Temperature distribution for Case #9.3 after ten minutes (Units: °C)...... 243

Figure 9.29: Temperature distribution for Case #9.4 after ten minutes (Units: °C)...... 243

Figure 9.30: Temperature distribution for Case #9.3 after twenty minutes (Units: °C). 243

Figure 9.31: Temperature distribution for Case #9.4 after twenty minutes (Units: °C). 243

Figure 9.32: Temperature distribution for Case #9.3 after forty minutes (Units: °C). ... 244

Figure 9.33: Temperature distribution for Case #9.4 after forty minutes (Units: °C). ... 244

Figure 9.34: Temperature distribution for Case #9.3 after sixty minutes (Units: °C). ... 244

Figure 9.35: Temperature distribution for Case #9.4 after sixty minutes (Units: °C). ... 244

xviii Figure 9.36: Temperature distribution for Case #9.3 after ninety minutes (Units: °C). . 245

Figure 9.37: Temperature distribution for Case #9.4 after ninety minutes (Units: °C). . 245

Figure 9.38: Temperature distribution for Case #9.3 after one-hundred-and-twenty minutes (Units: °C)...... 245

Figure 9.39: Temperature distribution for Case #9.4 after one-hundred-and-twenty minutes (Units: °C)...... 245

Figure 9.40: Temperature distribution for Case #9.5 after ten minutes (Units: °C)...... 246

Figure 9.41: Temperature distribution for Case #9.5 after twenty minutes (Units: °C). 246

Figure 9.42: Temperature distribution for Case #9.5 after thirty minutes (Units: °C). .. 247

Figure 9.43: Temperature distribution for Case #9.5 after forty minutes (Units: °C). ... 247

Figure 9.44: Temperature distribution for Case #9.5 after fifty minutes (Units: °C). .... 247

Figure 9.45: Temperature distribution for Case #9.5 after sixty minutes (Units: °C). ... 247

xix

List of Symbols, Abbreviations and Nomenclature

Symbol Definition

BCE Before Common Era; prior to year 1 CE Common Era; after year 1 CFD computational fluid dynamics CHTC convective heat transfer coefficient Dt thread diameter E east g gravity h convective heat transfer coefficient HVAC heating, ventilation, and air conditioning keff effective thermal conductivity L characteristic length Nu Nusselt number Q solar irradiation q”con conductive heat flux Ra Rayleigh number RNG k-ε renormalized group k-ε turbulence model SST k-ω shear stress transport k-ω turbulence model Ts temperature of the model sun Tw wall temperature T∞ bulk fluid temperature T0 outdoor temperature T1 temperature at point 1 T2 temperature at point 2 VOF volume of fluid (multi-phase) model W west Δx horizontal distance difference α thermal diffusivity β thermal expansion coefficient ν kinematic viscosity ϵ void fraction

xx Epigraph

Those who cannot remember the past are condemned to repeat it.

(Santayana, 1905)

xxi

CHAPTER 1 — INTRODUCTION

This project will utilize a technique of transdisciplinary scholarship known as

"knowledge integration" which, in this case, involves a synthesis of engineering (more specifically, computational fluid dynamics or CFD) and classical archaeology. The purpose of this study is to develop a more sophisticated understanding of ancient Roman public baths in order to determine the thermal atmosphere1 inside. This better understanding of Roman baths will possibly, in turn, lead to new advances for modern heating, ventilation, and air conditioning (HVAC) design and sustainability.

"Knowledge integration" is a difficult phrase to define precisely. In educational theory, there are three main ways to approach a problem that encompasses multiple fields: multidisciplinarity, interdisciplinarity, and transdiciplinarity. The first involves bringing together insights from the various disciplines without integration. The second, according to Repko (2008), is “a process of answering a question, solving a problem, or addressing a topic that is too broad or complex to be dealt with adequately by a single discipline and draws on disciplinary perspectives and integrates their insights to produce a more comprehensive understanding or cognitive advancement” (p12). The last, according to Lattuca (2001), is “the application of theories, concepts, or methods across disciplines with the intent of developing an overarching synthesis” (p83). None of these is easy to undertake because modern academia has its foundations in the uniqueness of its disciplines. Transdisciplinary research, of which this project is an example, somewhat

1 The thermal environment of a room includes its temperature, humidity, velocity profiles, etc. 1

overcomes this rigidness by creating a new body of knowledge from which all disciplines concerned can extract what they find useful.

The results of this project, for example, will provide engineers with a new way to investigate building heating and perhaps to be able to conceive of a new application for this new expertise, while classicists and classical archaeologists will improve their understanding of the thermal environment inside of Roman baths. From an engineering perspective, this study will enhance the understanding of many modern phenomena, including modeling large volume heating systems with CFD, determining convective heat transfer coefficients in ducts, simulating multi-phase flow, and studying hydronic radiation floor heating (a process that is similar to how the ancients heated their baths).

Archaeologically, on the other hand, the surviving primary physical and documentary evidence is sketchy at best, even though, according to a catalogue in the 4th century CE, there were nearly 900 baths within Rome itself. To put this number in perspective, according to Starbucks™ (2009), there are 102 of their coffee shops in Calgary, which is just over one-ninth the number of baths in Rome. Despite the prominence of baths within

Roman society, there are still many questions that scholars have not answered, particularly regarding the heat and air flow within the bath. The biggest of these is what the thermal atmosphere in the hot rooms was like. The answer to this, however, heavily depends on whether or not the windows were glazed, another ongoing debate in this field and key issue, which this project will address. Furthermore, these unanswered questions not only limit the understanding of the running of the bath, but lead to gaps in the social commentary of bathing and the wider Roman society (for instance, cleanliness).

Two sites served as case studies to investigate these areas of research. The first is a bath constructed by a team led by Fikret Yegül for the American television series

NOVA: termed the NOVA baths. Initially, this building was a validation model for the second case study because an article (Yegül and Couch, 2003) gives the exact dimensions of this building and data collection is possible. However, the intricacies of this bath proved to be sufficient for this to become the core of the research. The results of the

NOVA bath agreed with the data from the article and demonstrated some interesting flow patterns. The second case study is of the Baths of Caracalla (212-216 CE). As the second largest and most complete complex in Rome, it is well documented, eliminating some of the archaeological uncertainty. The intent of the inclusion of the Baths of Caracalla was to provide more insight into how the large Roman bathing complexes operated. Despite only completing a limited number of simulations, the results show interesting aspects for both fields.

This dissertation is broken down into nine subsequent chapters and three major sections: the introductory and preliminary work, the CFD studies, and the conclusion.

The first section contains four chapters; the second section, five; and the last section, one.

The introductory and preliminary work section continues in Chapter 2 which focuses on establishing, in more detail, the foundations of this unique project. Since this research incorporates two drastically different fields, one of the most important founding aspects is to define terms and methodologies unique to each field. The other aspect of the groundwork is to situate this project in the scholastic landscape by surveying the relevant previous research and identifying the potential gaps in both engineering and classical archaeology.

Chapters 3 and 4 diverge from the overall transdisciplinary theme briefly with topics that are primarily of interest to the individual fields. The third chapter looks at the process behind the digital reconstruction of the Baths of Caracalla, which started as a way of obtaining the geometry necessary for the simulation but grew to encompass the entire building. The process includes solutions for confusing or under-documented rooms, the determination of the window glass size, and a description of the completed texturing.

Chapter 4, the last of the preliminary section, is about the convective heat transfer coefficient or CHTC on the inside of the wall heating system which is the last major unknown for the CFD analyses. The chosen way to determine the CHTC is experimentally by building and measuring a section of heated wall. The results show that the CHTC is 7 W/m2·°C which is almost double the accepted standard value of air rising past a vertical surface.

Chapter 5 begins the CFD section of the dissertation. Its purpose is two-fold: first, it adds to the debate about whether the windows of heated bath rooms were glazed.

Second, it explores how the configuration of doorways affected heat flow between rooms.

The two studies use nonspecific two-dimensional (2-D) models of baths to investigate these two topics. These simulations suggest that glazing was almost certainly necessary to maintain high temperatures and that doorway design played a critical role in the thermal environment. This chapter provides a perfect example of transdisciplinarity because the question is archaeological in nature and the methodology is engineering but the results encompass both fields.

Chapters 6, 7, and 8 switch the CFD analyses from 2-D to 3-D (three- dimensional) with the introduction of the NOVA baths case study. Chapter 6 explains

some of the aspects unique to 3-D simulations and creates the skeleton of the model. The key decisions include what density and turbulence models are best and whether or not the solution showed any dependency on time. The results show that switching turbulence models has essentially no effect but changing density can have a significant impact.

Chapters 7 and 8 examine the established model of the NOVA baths in more detail. The former deals with a single room while the latter deals with two rooms and the interplay between them. The purpose of the simulations in Chapter 7 is to expand upon the basic setup by testing the effect of the addition of humidity and variation of the CHTC of the heated surfaces. While these have minimal impact on the stratified temperature profile, the biggest influence came from the doorway to the next room. The magnitude of the influence suggested that the computational conditions for the doorway may be misrepresentative of the actual conditions. This realization led to the second set of simulations of the NOVA baths in Chapter 8. When the second room was added, the temperature profiles and velocity vectors changed considerably and, as suspected, the flow from and into the adjoining room decreased thereby making the temperature in the room of interest higher. In the end, though, both sets of results demonstrate the transdisciplinary approach by generating data that combine knowledge from both fields.

The results match Yegül and Couch's data (2003) and again show the importance of the doorway; echoing the results from the Chapter 5.

Chapter 9 introduces the results from the Baths of Caracalla and concludes the

CFD section. The NOVA baths are relatively small and are therefore easy to model, however, since they exist in their entirety, they could be the subject of experimentation.

Modelling the Baths of Caracalla provide a way to simulate a complex that is too large to

be reconstructed and experimented on. Even though the maximum computational volume was 1/14th of the total, the results that did complete show a striking similarity to the ones from the NOVA baths. Once the results stabilized, they demonstrated the same stratification as the NOVA baths and a similar invariance to seasonal change as seen in

Chapter 5. The first unique aspect present in the Baths of Caracalla is the long and unusual transitory phase. The hot air in the Baths of Caracalla, because of the self- contained nature of the model, rose in a spire in the centre of the room that eventually flattened out after two hours of simulation time. The second aspect was the radical difference in the results when an external radiation temperature replaced the solar load representing the sun. The temperature in the room was almost uniform over its height.

Finally, Chapter 10 summarizes the entire project from both engineering and classical archaeological perspectives.

CHAPTER 2 — THE FOUNDATIONS

This chapter is broken down into two major sections: background information and the literature reviews. Since this is a transdisciplinary project, there is terminology that needs some explanation to assist the potentially varied audience. Within the background information, there are two cornerstones: an introduction to computational fluid dynamics or CFD and an introduction to ancient Roman baths. While the former is in one part, the latter is in three. The introduction to baths begins by defining what an ancient bath was and what the major rooms were. The second part is an explanation of how the Romans heated their baths. The cornerstone concludes by giving specific data on the case study sites: the NOVA baths and the Baths of Caracalla. Three categories make up the literature reviews: transdisciplinary (articles that bridge the two fields); engineering; and classical archaeology on baths. An analysis of the gaps in the knowledge base follow these.

2.1 Background Information

2.1.1 Introduction to Computational Fluid Dynamics (CFD)

Since computational fluid dynamics is the cornerstone of this project, this section presents the basics of the field for those who may be unfamiliar with it. CFD is a branch of fluid mechanics that uses computers to solve problems with no easy analytical or exact solution. Since the governing equations for the flow of a fluid, either gas or liquid, are impossible to solve explicitly (i.e., to find functions that can describe the flow fully) except for very simplistic regimes, CFD uses numerical approximations to solve them. A

numerical approximation uses a discrete collection of points to describe a function instead of an infinite stream which means there are gaps in the data.

In CFD, the first step is to break the volume of fluid down into small, regularly- shaped pieces and assign each corner a ‘node’ value, which is a process known as meshing. These nodes are where the program calculates the approximation. The quality of the mesh dramatically influences the accuracy of the results. Normally, the finer the grid—that is, smaller pieces and closer nodes—the better the results will represent the actual conditions. The problem is that closer nodes mean more nodes, which in turn mean higher memory demands and longer computing times, so there is a careful balance.

Once the modeller has created the mesh, the geometry is complete. In order to solve the problem two more items of information are necessary: conditions at the spatial boundary and the initial conditions at the beginning of the process. For example, the flow of water inside a pipe (Figure 2.1), the mesh represents the volume of water inside the pipe while the boundary conditions specify the parameters at the three exterior faces (the pipe wall, the inlet, and the outlet). The initial conditions indicate whether the flow started from rest or was in motion at the start of the simulation. The CFD software then solves the governing equations iteratively and generates a solution in terms of physical flow properties.

Figure 2.1: Diagram of a pipe showing the mesh and boundary conditions. (Model created by Taylor Oetelaar.)

In CFD, there are many variables and sub-models that need manipulating in order to get an accurate result. The few that need explanation for this project are density models, turbulence models, species modeling, and multiphase modeling. Calculating density (mass per unit volume) is dependent on what the fluid is but if it is a gas, there are multiple options and the level of accuracy and computing time varies for each.

Turbulence is a complicated concept because it results from the random fluctuations in fluid flow. As such, modeling turbulence is extremely difficult and yet is vital to an accurate solution. Species and multiphase modeling are very similar conceptually but radically different in application due to the physics involved. The first simulates two or more fluids of the same phase such as air and propane or water and oil while the second simulates two fluids of different phases such as water and air (Chung, 2010).

2.1.2 Introduction to Ancient Roman Baths

During Roman times, there were two major classes of bath buildings: the balnea2 and the thermae. The balnea were smaller buildings that were often privately owned, whereas the thermae, according to Yegül, “embraced a variety of secondary functions— sportive, educational, and social—besides bathing” (Yegül, 1995, p494) and were state owned. The number of each type of bath in Rome is given in the Notitia Urbis Regionum, a catalogue written approximately between 334 CE and 357 CE, which tallied 11 thermae and 856 balnea. Scholars know relatively little about the balnea in Rome since only a handful has survived to modern times. There is a relatively large amount of information on the thermae in Rome, on the other hand, because of their impressive size and survivability. The Baths of Caracalla are one such building.

Most thermae in Rome3 are very symmetrical, with a shorter axis running approximately northeast-southwest. The Baths of Caracalla will provide an example of the layout of the thermae (Figure 2.2). The alignment of the four rooms in the middle of the bath—the natatio, the frigidarium, the tepidarium, and the caldarium—comprise the axis mentioned above. These four rooms represent the major bathing components of the complex. The natatio was a vast swimming pool (1300m2)4 originally thought to have a roof (Iwanoff and Hülsen, 1898; shown in Yegül, 1995, p158) but now believed to be open to the atmosphere (DeLaine, 1997). The frigidarium was a giant, typically high

2 Balneum is a neuter noun of which the plural is balnea. Caldarium, tepidarium, frigidarium, and apodyterium follow the same rule. Palaestra, suspensura, and pila are feminine nouns whose plural form is palaestrae, suspensurae, and pilae, respectively. Finally, tubulus is a masculine noun for which the plural is tubuli. For a glossary of terms, refer to Appendix 1. 3 The notable exception is the early Baths of Agrippa (26-19 BCE). 4 Areas given are for the Baths of Caracalla. 10

vaulted, room (1960m2) that housed the unheated baths.5 The tepidarium was a smaller room (360m2) containing the warm baths. The caldarium was another large room

(1300m2) which contained hot pools. The two very important off-axis rooms are 3E/W, the apodyteria, and 12E/W, the palaestrae. The two apodyteria were rooms (540m2 each) where patrons changed into their bathing attire (which, many times, consisted of sandals and nothing else) and store their clothes. The two palaestrae, large, probably open-aired,6 rooms (2000m2 each) where the patrons would exercise, represented the major sportive component of the baths. The specific purposes of the remaining rooms are largely unknown though there are some speculations.7 Rooms 19E/W to 22E/W were a form of hot rooms since excavators found evidence of heating structures (to be discussed in detail later) in them. Rooms 14E/W, 17E/W, and possibly 19E/W had smaller pools, above ground in the case of 14E/W and below ground in the case of 17E/W and 19E/W.

5 The term frigidarium technically implies an association with cold water; however, since artificial cooling was impossible in Roman times, cold baths were simply baths with unheated water. 6 Brödner (1951) suggests that the palaestrae were roofed but most others (DeLaine, 1997; Yegül, 1995, Nielsen, 1992) maintain they were open-aired. 7 Ripostelli (1916) lists 2E/W as rooms for conversation; 8-10E/W as schools for the gymnasia; 17E/W as small sudatoria; 19E/W as baths for the palaestra; and 20E/W as open rooms for exercise. Krencker et al. (1929) specifically state that they were not trying to identify room function but they do speculate that 19E/W might have been ancillary frigidaria. Lugli (1970) lists 8-10E/W as schools; 14E/W as sudatoria; and 20E/W as halls. Nielsen (1993) lists Room 19E/W as unctoria or frigidaria, 20E/W as tepidaria, and 21E/W and 22E/W as sudatoria. DeLaine (1997) suggests that 17E/W may have been massage rooms, 20E/W were very hot, and, on page 46, she gives a schematic breakdown of the rooms (1-3E/W: dressing; 4-6E/W: entrance; 7-12E/W: palaestra; 13-14E/W, 17E/W: social; 15-16E/W, 18E/W, 23E/W: services, 19- 22E/W: hot rooms. Piranomonte (2008) lists 1E/W as a vestibula and 20E/W as lanconia. 11

Figure 2.2: Layout of the Baths of Caracalla. (Model created by Taylor Oetelaar.)

Outside the complex there was a garden-like area surrounded by a large external wall. In this wall there were libraries, small shops, eateries, a theatre, and massive cisterns that held the water for the baths. In the garden just south of the hot rooms there was an intricate network of underground passageways that slaves primarily used for the day-to-day workings of the bath, such as storing wood and boiling water for the hot baths

(Piranomonte, 2008).

2.1.2.1 The Heating System of Roman Baths

The heating system (Figure 2.3), or hypocaust—Greek for “heating from below”—consisted of three major components: the praefurnium, the suspensura supported by pilae, and the tubuli. The praefurnium was either a wood- or charcoal- burning furnace that supplied the heat and hot exhaust gases. Roman engineers would typically locate the furnaces underground on the foundations on the outside of the heated rooms. The suspensura or ‘suspended floor’ was a false floor above the sunken floor of the foundation. The gap between the suspensura and the foundation floor was 0.65-1.00m but could reach as much as 1.70m (Yegül, 1995, p357). To support the suspensura there were usually pilae or pillars at regular intervals. Lining the walls of the room above the suspensura were tubuli or inlayed rectangular terracotta tubes8 that may have been connected to a chimney that protruded from the roof.

8 The size and shape of the tubuli had a large degree of variability demonstrated by the difference between ones in the NOVA baths and the Baths of Caracalla. There was also an alternative method of wall heating called tegulae mammatae. These were flat tiles with protrusions on each corner that created a small air gap for the air to rise through. Yegül (1995) has a nice description on pages 363-365. 13

Figure 2.3: Diagram of the hypocaust heating system. (Model created by Taylor Oetelaar.)

The premise behind the hypocaust was simple but very effective. The praefurnium burned fuel and converted it into hot exhaust gases. These exhaust gases circulated between the suspensura and the foundation floor, up through the tubuli, and eventually exited out the chimney. During their movement, the gases heated up the surfaces and by extension the room inside. Seneca the Younger, an early-1st-century-CE

Roman writer, makes reference to how even the heat distribution was in vaulted baths

heated by the hypocaust,9 which suggests that the temperature gradients were fairly small within a room: a key note for this project. Furthermore, to place the hypocaust in a modern context, this irradiative heat transfer is similar to the recently adopted radiation slab cooling used in the heating, ventilation, and air-conditioning (HVAC) of buildings.

2.1.2.2 The NOVA Baths

With the basics of Roman baths and their heating systems outlined, a more detailed look at the two case study sites—the NOVA baths and the Baths of Caracalla—is necessary to establish not only the historical time line of the complex, but also to give quantified data for key features. These data will prove invaluable when it comes time to model the caldarium using CFD.

The NOVA baths (Figure 2.4) is a small balneum (37.7m2) consisting of three rooms: a frigidarium (19.7m2), a tepidarium (5.8m2), and a caldarium (12.2m2). The fire that heats the water for the caldarium pool—located to the south of the pool—also feed the hypocaust. The tubuli line the east, west, and north walls of the caldarium and the west wall of the tepidarium. They extend 2.57m above the floor or 0.21m below the springing of the barrel vault that covers the rooms. The tubuli themselves are rectangular with holes on the short sides to allow the exhaust gases to move between adjoining columns of tubuli. There are also twelve small windows—totalling about 8m2—in the east and west walls of the building: three under each end of the two barrel vaults. Finally,

9 The passage–“ima simul ac summa foveret aequaliter” (Ep. 90.25)–means “ensuring an even temperature in the lowest part as well as the highest.” 15

the pool of the caldarium covers an area of 2.4m2 and has a volume of approximately

1.6m3.

Figure 2.4: CAD reconstruction of the NOVA baths. (Model created by Taylor Oetelaar.)

2.1.2.3 The Baths of Caracalla

The Romans constructed the Baths of Caracalla (formally the Thermae

Antoninianae) between 212 CE and 216 CE and dedicated them in 216 CE. The Emperor

Septimius Serverus (193-211 CE) commissioned their construction but his son, Marcus

Aurelius Antoninus Bassianus (popularly known as Caracalla; 211-217 CE), completed them. The baths remained in use until the Goths severed the aqueducts to Rome in 537

CE. During the Middle Ages the garden area was used as a cemetery for the nearby SS

Nereus and Achilles church and much of the marble revetment was pilfered for use

elsewhere. Excavations began at the Baths of Caracalla during the Renaissance, at which point much of the remaining statuary was removed for display in private collections and museums. Today it is a park and the site for the summer performances of L’Opera di

Roma.

From the plan above (Figure 2.2) it is hard to comprehend the size of the Baths of

Caracalla (Figure 2.5). The main building itself covers just over 2.4ha and, with the garden and perimeter walls, the complex occupies just under 9ha. The beginning of 2.1.2 gave the basic layout as well as areas of the key rooms but this section provides more detailed information. The largest room, the frigidarium, measures 60m by 25m and the top of the vaulted roof, based on the reconstruction in the next chapter, was 35m above the floor. The architects of the old Pennsylvania Station in New York City (Ballon, 2002, p65) based their design on this room because of the number of people it could accommodate. The frigidarium had four 91m2 pools—one in each corner—and one 50m2 circular pool near the doorway to the natatio. It also had eight sets of three windows— each set totalling 64m2—on each end of the barrel vaults and two 117m2 windows in the south wall of each the south pool alcoves. The tepidarium measures 17m by 15m and the groin vault sprung from a height of 16m. It has two 55m2 pools and two 134m2 windows: one set on the west side and the other on the east. The caldarium measures 35m in diameter on the inside and the dome that covered the room sprang from the wall at 28m above the floor. It has seven pools averaging 38m2 each: one in each direction except site north. The caldarium also had fourteen massive windows—each measuring approximately 90m2—two above each pool. With the caldarium facing southwest, these

windows allowed for maximum passive solar heating. There is, however, as mentioned above, great debate on whether or not the windows were glazed.10

Figure 2.5: CAD reconstruction of the Baths of Caracalla. (Model created by Taylor Oetelaar.)

Few publications exist (Piranomonte, 2008) on the caldarium hypocaust for the

Baths of Caracalla since only the northeast and northwest piers of the caldarium remain to any considerable height. This leaves uncertain many of the parameters necessary for accurate simulation of the thermal environment inside. One of these is information on the tubuli, such as, placement, size, and height. Fortunately some tubuli do still exist, so

10 For a further discussion on glazing, see section 2.2.3, Chapter 5 and Appendix I. This project will provide more evidence on this issue. 18

determining the location of the remaining tubuli relies heavily their position and on the principles of symmetry. The remaining tubuli are in two areas: around the northwest pool

(Figure 2.6) and on the southwest corner of the northeast pier (Figure 2.7).11 Figure 2.8 shows a reconstruction of a possible layout of the tubuli. In terms of size, however, there is a considerable level of variance. Table 2.1 provides the complete list of tubuli dimensions from along the northeast pier taken with a laser distance meter and Figure 2.9 shows the size distribution. The average of the tubuli is 7.7±0.89 cm by 12.6±1.78 cm.

These are comparable to the sizes recorded by Thatcher (1956) at the Terme del Foro at

Ostia (mid 2nd century CE) but are considerably smaller than those found by Yegül

(1986) at the Bath-gymnasium complex at Sardis (1st to 2nd century CE); and, unlike the tubuli at these two baths, the tubuli at the Baths of Caracalla have mortar between the columns. This means the exhaust gas in one column is not allowed to move to the one beside it and vice versa. The separation alters the convective heat-transfer properties between the exhaust gases and the tubuli wall and thus affects the heat transfer between the wall and the air inside the caldarium.

11 I thank Professoressa M. Piranomonte and the Soprintendenza Archeologica di Roma for allowing me to gain access to the caldarium at the Baths of Caracalla and take photographs and measurements in May 2008. 19

Figure 2.6: Tubuli remnants from NW pool of the caldarium of the Baths of Caracalla (Photo by Joy Oetelaar).

Figure 2.7: Tubuli remnants from NE pier of the caldarium of the Baths of Caracalla (Photo by Joy Oetelaar).

Figure 2.8: Projected tubuli locations. (Model created by Taylor Oetelaar.)

Table 2.1: Dimensions of Tubuli along the Northeast Pier of the Baths of Caracalla Tubulus (L to R in Fig 2.7) Interior Length (cm) Interior Width (cm) 1 9.8 12.2 2 6.9 9.1 3 7.3 13.9 4 6.6 12.2 5 8.2 13.0 6 7.6 12.6 7 8.5 13.8 8 8.1 12.4 9 6.7 13.6 10 7.1 12.1 11 7.5 13.4

Figure 2.9: Size distribution of the tubuli along the northeast pier of the Baths of Caracalla.

2.2 Literature Reviews

As mentioned in the beginning of the previous section, the second foundation for the project is the literature reviews. The purposes of a literature review are, first, to search out all previously published scholarship in the field, then to determine the gaps in the knowledge base (as well as the errors of the previous scholars), and finally to identify those deficiencies that this project can address. Since this is a transdisciplinary venture, there are three sets of literature which need addressing: the transdisciplinary, the engineering,12 and the classical archaeological. Much like the edge of a coin, the

12 Many engineering theses involving CFD have sections that describe its mathematical and numerical underpinnings. Since this project is focused on the application of CFD and uses a commercial package for its analyses, such an in-depth review is unwarranted. If more information is needed, refer to Anderson (1995), Wilcox (1998), Lomax et al. (2004), and Chung (2010). 22

transdisciplinary literature provides the connection that links the two facets—engineering and classical archaeology—of this project.

2.2.1 Transdisciplinary Literature Review

Seven earlier researchers have applied their knowledge from engineering and used it to investigate problems in the understanding of Roman baths. The first two, Thatcher and Ring, explore the troublesome debate surrounding the windows in baths: both of which are key for the discussion in Chapter 5. Thatcher performs a very detailed sun study of the Terme del Foro at Ostia to determine whether it would have been possible to comfortably bathe without glazing (Thatcher, 1956). He derives the values for the solar radiation from a climatic housing design handbook (Olgyay and Olgyay, 1954) and the

ASHRAE Guide (1953) and assumes that the floor temperatures are 37.8°C. Working from these, he determines the wall and vault temperatures, then the bulk indoor air temperature, then the human heat loss, and finally combines these into a room performance. Based on his calculations, he concludes that it would have been possible to bathe nude at the Terme del Foro at Ostia.

Ring (1996), on the other hand, along with Meiggs (1960) and Yegül (1995), doubts the validity of Thatcher’s conclusion and sets about to disprove it. He follows

Thatcher and uses the same assumptions but uses data from Rook (1978) and Kretschmer

(1953) as inputs. Using standard conductive and convective equations, he calculates the heat inflow and outflow through the various surfaces of the caldarium. Ring, however, comes to the opposite conclusion from Thatcher and states that it would not have been possible to comfortably bathe nude.

The remaining articles concentrate on the workings of the hypocaust and its fuel consumption. While these establish the overall context of the state of research with baths, since this project focuses on the caldarium itself, they will not be an apt comparator. The additional problem with these two articles is that they deal with only the big picture (i.e., average temperatures) and give no indication of details (i.e., distribution). Jorio (1978-

79) provides detailed information about the hypocausts of the Pompeian baths (Stabian,

2nd century BCE;13 Forum, early 1st century CE; and Central, 62-79 CE) as well as comparable domestic settings. He also considers the effect of wall thickness and of the restoration after the earthquake of 62 CE on the heat flow in the Stabian Baths. He uses temperatures from a previous work (Schween, 1937)14 to analyze the heat losses from four rooms (the men’s and women’s caldaria and tepidaria) in the Stabian Baths. Based on his calculations, for a heat flow of 513Mcal (2.15GJ) per day, he estimates that the fuel consumption was 7kg/hr of wood.

Rook (1978) utilizes thermodynamic equations to estimate the fuel consumption of the Welwyn Roman bath (3rd century CE). He uses the heat flow balance (i.e., heat in is equal to the heat out) to solve for the average room temperature. He then uses this to calculate the heat generated by the hypocaust and then the amount of wood needed. This turns out to be 13kg/hr or 114tonnes/yr which, interestingly, is almost double what Jorio estimated for the larger Stabian Baths.

13 The original building dates back to the 5th century BCE but it was rebuilt in the 2nd century BCE (Nielsen, 1993). 14 These temperatures are as follows: 100°C in the chimneys; 16°C for the outdoors; 35°C for the caldaria; and 30°C for the tepidaria. 24

Kretschmer (1953), Hüser (1979), and Baatz (1979) perform experiments on a replica hypocaust to analysis its thermodynamic characteristics. Kretschmer’s experiments provide detailed temperature profiles of various surfaces given different conditions over several days. Hüser continued to perform experiments on Kretschmer’s replica focusing on the suspensura and analyzing the modern applicability of the hypocaust. Baatz, on the other hand, is interested in the canal-heating system. He concludes that canal-heating is not as effective as the typical hypocaust, particularly for large rooms, due to its high thermal inertia.

The applications of computational methods to a bath are few and all led by Tahsin

Basaran formerly of Dokuz Eylül University in Turkey. The first (Basaran and Ilken,

1998) did not use CFD but rather numerical heat transfer15 to investigate the heating system of the Small Baths at Phaselis16 in Turkey. Their simulations suggested a number of key conclusions, including: 1) the bath only had limited use in the winter; 2) the input heat was less than the heat lost; 3) the fuel required was massive. The second (Basaran et al., 2005) used CFD to analyze the heating system of a bath house in Metropolis (early

2nd century CE). Like the study of Phaselis, it shows an inefficiency of the hypocaust design and that the fuel requirements were substantial though a suitable environment was achievable. The third and final (2007) is, in essence, a summary of the first two and again demonstrates the inefficiency of the heating system and high fuel costs. All, however,

15 The difference is that CFD integrates fluid mechanics and heat transfer whereas numerical heat transfer only looks at the movement of heat. Interestingly, the only use of CFD in classical archaeology comes in the study of aqueducts, see Ortloff (1998; 2005); Ortloff and Crouch (2001); Ortloff and Kassinos (2003); Nikolic (2008); and Haut and Viviers (2007a; 2007b). Clearly, with so few studies being done with CFD, there are many unexplored avenues for this project to advance the transdisciplinary knowledge base and benefit both fields. 16 Basaran and Ilken do not give the date of this bath. 25

deal with the temperature in the hypocaust and not in the room above which they acknowledge in the 2005 article. Furthermore, like all studies done before, the focus is on balnea. Both of these points mean that Basaran’s work, while significant, leaves unanswered the principal questions that this project is trying to address.

Briefly, to summarize, the previous transdisciplinary research has primarily focused on balnea and the hypocaust. The techniques used have answered the questions that scholars have been asking but provide limited detailed analysis of the thermal environment inside caldaria. This leaves many avenues open for the application of CFD to baths such as was there a difference between the average temperature and the actual temperature where the patrons were.

2.2.2 Engineering Literature Review

On one side, from an engineering perspective, this project is, in essence, the study of the HVAC of a building. Most HVAC designers, however, analyze problems using a process called building simulation (BS) instead of CFD. For building simulation (Wang and Wong, 2009):

...tools basically include two fundamental modules: thermal simulation and airflow network to solve the heat and mass transfer and airflow in the building systems. These tools greatly facilitate energy-efficient sustainable building designs by providing rapid predictions of facade thermal behaviors, indoor airflow of the building and better understanding of the consequences of various design decisions. However, BS assumes the indoor air is well mixed. It can only provide the uniform results for targeted spaces, which normally does not meet the requirements for detailed indoor environment analyses. The simple flowpressure governing equations for various components limit the accuracy of the airflow model.

Despite these inadequacies, the reason for using BS over CFD is that most projects in HVAC design do not require the level of detail that CFD can provide, so CFD is computationally unnecessary. Zhai, though, does identify five areas of application of

CFD in building design17 and six trends in modifying CFD codes for better integration into the design process (Zhai et al., 2002).18 With the rapid improvements in both computers and CFD modelling techniques, more emphasis is being put on CFD, especially in the areas that Zhai et al. identified. To help modellers develop their CFD simulations, Chen and Srebric (2002) created a guide with validating and reporting directed specifically at the HVAC industry. This can be complemented further by reading

Stamou and Katsiris (2006) and (AIAA, 1998). Recently, however, Li and Nielsen (2011) have seen an increased collaboration between CFD and other HVAC methodologies, specifically experimentation. They state that CFD has two major hurdles—turbulence

‘modelling’ and the fact that it is an approximation by nature—but present new opportunities: solution multiplicity, inverse CFD modelling, near-body micro- environments, and disease transmission.

One of the trends named by Zhai et al. (2002) is combining CFD and BS methodologies. Though Negrão (1998), Bartak et al. (2002) and Zhai et al. (2002; 2003) published conference papers and articles around this time, the topic appeared to draw little interest over the next few years. Recently, a revival has taken place. As Wang and

17 These are "the predicted mean vote (PMV), the percentage of people dissatisfied (PPD) due to discomfort, the percentage dissatisfied (PD) due to draft, ventilation effectiveness, and the mean age of air" (Zhai, 2002). 18 For static coupling, there is 'One Step' and 'Two Step'. For dynamic coupling, there is 'One-Time-Step Dynamic Coupling', 'Quasi-Dynamic Coupling,' 'Full Dynamic Coupling,' and 'Virtual Dynamic Coupling' (Zhai, 2002). 27

Wong noted, “the integration of BS and CFD programs can eliminate a few assumptions employed in the separate applications, dramatically reduce computation time of CFD, and result in accurate and quick predictions of building performance” (Wang and Wong,

2009). Lee (2007) proposed a design that united general algorithms and CFD to optimize

HVAC design. Zuo and Chen (2009) follow a similar vein of programming but, instead of combining BS and CFD, they look at the use of fast fluid dynamics (FFD): a blend of

CFD and nodal models. Zhai (2006) suggested uses for CFD in building design: site planning, natural ventilation studies, HVAC system design, and pollution and particulate dispersion. Fan and Ito (2012) performed energy consumption analyses comparing building energy simulation (BES), coupled BES-CFD, and experimental methodologies.

They found that there was minimal difference between the BES and coupled BES-CFD and that there was basic agreement between coupled BES-CFD and the experimental measurements though there were issues with the boundary layer that require further investigation.

As for pure CFD applied to building design, a large number of the studies deal with particulate and gaseous toxin flow patterns in small rooms or offices. According to

Ladeinde and Nearon (1997), some of the major questions that CFD can help answer with respect to HVAC in buildings are:

- Where should the flow inlets and/or outlets be located? - What kinds of velocities are expected at a specified portion of the system? - What does the flow pattern look like? - What is the heat transfer coefficient (or Nusselt number) on a specified portion of the system surface? - What is the temperature distribution in a specified portion of the system? - What is the drag on a specified portion of the system surface? - What is the response time of the system with respect to heat transfer and flow development?

- How is a species or chemical reactant or product transported by the flow?

While this article is now 15 years old, all of these questions are still valid since not all configurations have been modelled using CFD. This is particularly true with large, open enclosures. The answer to the second to last question is still very much an unknown, especially when dealing with radiation slab methods of heating and cooling, which is very similar to how the Romans heated their baths.

One of the major debates when dealing with CFD in the context of HVAC applications has been over the choice of turbulence model. There are two models that appear to be favoured: the renormalized group (RNG) k- and the shear-stress transport

(SST) k-.19 Some scholars, including Kuznik et al. (2007) and Ramponi and Blocken

(2012), state that the SST k- agrees with the experimental data the best, while others, including Zhai et al. (2007) and Zhang et al. (2007), maintain that the RNG k-ε model is superior. Interestingly, when modelling a large train station, Li et al. (2009) used the

RNG k-ε model and got accurate results.

The hypocaust of the Roman bath is very similar to the modern radiant slab or hydronic heating (Moe, 2010; Siegenthaler, 2004). Radiant slab heating or cooling is a

HVAC method where pipes are shallowly buried in a concrete floor and water is circulated in these pipes to either absorb heat from or emit heat into the room. These systems are slow to react to temperature changes in the room so they are usually combined with a smaller air circulatory system. In one interesting article, Golkafard et al

(2012) simulate a floor heating system, though not hydronic heating specifically, with

19 In these models, k is a measure of the turbulent kinetic energy and ε and ω are measures of the turbulent dissipation or the scale of the turbulence: ω being the specific dissipation. 29

CFD and investigate the impact of building height on the thermal environment. Their results show a unique draft in the middle of the room instead of the typical stratification one expects with buoyancy. This draft is very similar to the one seen in the early results from the Baths of Caracalla presented in Chapter 9, which means that this conical uprising may not be erroneous but rather a trait of that configuration. Tye-Gingras and

Gosselin (2012) recently published an article that analyzes this system using CFD. They model a 2-D cross-section with multiple configurations of wall and ceiling sections to find the optimum method. They instead find a family of solutions and that the fluid temperature control is the most important aspect for energy efficiency. Gao et al. (2011) used CFD to investigate the impact of pipe spacing and layout on the interior air temperature. While the differences between their five cases were small, the most uniform temperature came from the most uniform layout. Causone et al. (2010) compared experimental results of a hydronically-floor-heated test room with CFD simulations and found that the agreement was close and the CFD was useful in visualizing the flow patterns that occurred. Though not hydronic, Hami et al. (2012) investigate the impact of a solar wall on the temperature of a room and the results show that the structure provides a similar rising flow pattern as the tubuli.

The remaining articles deal with the radiant slab system itself. Sattari and

Farhanieh (2006) do a parametric analysis of a radiant slab system to see the effect of different factors (pipe diameter, pipe wall thickness, etc.) on the performance of the system. Zaheer-Uddin et al. (1997) look at how to control these systems optimally.

Bozkir and Canbazolu (2004) analyse an interesting variant of the radiant slab: one that uses hot air instead of water, which is very similar to the heating system of the Roman

bath. Athienitis and Chen (2000) study the effect of solar radiation of heated floors and showed that solar radiation greatly reduced the heating energy consumption. An interesting complement of the radiant slab system is the use of hollow brick walls to ease the cooling load in hot climates. The two articles on this topic ((Li et al, 2008) and (Al-

Hazmy, 2006)) examine the viability of this wall structure and both proved to have an increased thermal efficiency.

Another key aspect addressed by the literature is the importance of correctly determining the convective heat transfer coefficients (CHTCs) for the hypocaust. The closest example, geometrically speaking, is Hmouda et al. (2010) who analyze a water heater that uses hot gas as the heat source. Even though this is very similar to the hypocaust, they do not determine the CHTC but rather focus on the temperature distribution of the water as it cools. The next closest include analyses of enclosures, pipes, and ducts. All of these, however, deal with heating the air by passing it by a hot surface and not heating the surface with hot air so cannot really be comparative. Hatami and Bahadorinejad (2008), Rao (2007) and Cruz-Peragon et al (2012) look at fluid heaters: Hatami and Bahadorinejad, a vertical flat-plate solar air heater;20 Rao, a vertical channel air heater; and Cruz-Peragon et al., a flat-plate solar water heater. Fossa et al.

(2008) use a vertical air channel to examine the possibility of convection to cool photovoltaic modules.21 Calay et al. (1998),22 Boukendil et al. (2009), and Terekhov et al.

20 Nusselt numbers (Nu) ranged from 2.9×102 to 3.7×102 (1.2×1010

(2011) look at heat transfer within enclosures. Terekhov and Terekhov (2008),23

Terekhov and Ekaid (2011) and Khandelwal and Bera (2012) model heat transfer in vertical containers or channels. Gosselin and Chen (2008) compare numerical simulations of a dual-airflow window to experimental data. Elshazly et al. (2005; 2006), Ko (2006;

2007), Mikhailov et al. (2007), Ali (2009), Arshad et al. (2011), and Heo and Chung

(2012) all investigate convective heat transfer from ducts or pipes but again, the surface is heated and not the fluid. Then there are the studies which are more closely tied to the

HVAC industry. Awbi (1998), Awbi and Hatton (1999; 2000), Wallentén (2001), Gao et al. (2008), Karadaet al. (2007) Karada and Teke (2008), Novoselac et al. (2006), Pires et al. (2005) all discuss heat transfer coefficients for various configurations of heated or cooled walls, ceilings, and floors. Liu et al (2011) investigate the impact heat and mass diffusion coefficient ratios, solid wall thickness and thermal Rayleigh numbers (Ra) of a wall on the air flow in a room. Medved and Novak (1998), Manz (2003), and Pappas and

Zhai (2008) all look at the flow patterns inside facade elements to determine how heat moves from outside to inside. Some articles ((Beausoleil-Morrison, 2002); (Davies et al.,

2005); (Fohanno and Polidori, 2006); (Karada and Akgbek, 2008)) describe new methodologies for analysing or calculating heat transfer coefficients in HVAC design.

Finally, there are articles that generally describe heat transfer coefficients with no connection to the HVAC industry. Khalifa provides two summaries of basic shapes. The first (Khalifa, 2001a) looks at isolated horizontal and vertical surfaces while the second

22 Nusselt numbers ranged from 7.8 at a Ra of 3.9×108 for one configuration to a high of 74.5 at a Ra of 6.5×109 for another configuration. 23 Nusselt numbers ranged from a low of 1 with no fins and a Ra of 4×103 to a high of 4.5 with 20 fins and a Ra of 1×105. 32

(Khalifa, 2001b) summarizes simple and well-documented surfaces in two- and three- dimensional spaces. While none of these studies is directly related to the determination of the CHTC of the tubuli, they do expose a hole in CHTC research: the heating of a solid by a fluid.

The study of thermal comfort or the thermal environment in a certain region is a significant aspect of HVAC design and is the aim of this project. However, most of the

CFD analyses focus on small enclosures such as offices ((Hien et al., 2005), (Lin et al.,

2006), (Myhren and Holmberg, 2008), (Abantoa et al., 2004) or (Manz and Frank, 2004)) or generic rooms ((Kim et al., 2001), (Teodosi et al., 2003), (Mak et al., 2007), or

(Stavrakakis et al., 2012)). There are, however, some important exceptions. Lepska et al.

(2012) extensively investigated a proposed redesign of the air conditioning system for a large historic auditorium at the University of Wroclaw using CFD. Stavrakakis et al.

(2008) demonstrated the impact of cross-ventilation on thermal comfort by simulating a small building with two doors. Papakonstantinou et al. (2002) modelled a simple, yet large, auditorium and showed that the peak temperature was near the roof while the peak

CO2 concentration was near the floor. Kavgic et al. (2008) perform a more advanced analysis of another theatre where they look at thermal comfort and air quality.

Papakonstantinou et al. (2000) explored the main hall of the National Archaeological

Museum of Athens and accounted for a variety of aspects including blockages, people, internal heat loads, and the weather. Sreshthaputra et al. (2004) looked at the unique case of air flow through and around a 100-year-old Buddhist temple in Bangkok, Thailand.

Stamou et al. (2008) developed a CFD model of the Galatsi Arena in Athens which envelopes a large volume of air. Song (2007) investigates the effect of glazing methods

on the temperature inside a large atrium. Examining a different atrium, Lau and Niu

(2003) study the temperature stratification using both CFD and experimental methods.

Liu et al. (2009), using both CFD and reduced-scale models of a large atrium, demonstrate a number of key points, including the ineffectiveness of the venting stacks during hot weather. Walker et al. (2011) performed a similar analysis of a different atrium and found, among other things, that ventilation stacks dramatically affected both the temperature and airflow inside. Lin and Zmeureanu (2008) look at the temperature distribution inside a large dome. Balocco’s analysis (2007) of the Salone dei Duecento di

Palazzo Vecchio in Florence models the interior environment to help with tapestry preservation. Ayata and Yildiz (2006) propose a new way of incorporating natural ventilation for buildings in Turkey through optimal placement of windows in the façade.

Rohdin and Moshfegh (2011) compared experiments with the simulation of an industrial room to determine if displacement or mixed ventilation was better suited and found displacement performs superiorly. Finally, there is the distinctive study of the external thermal environment of three regions in Kyoto city by Takahashi et al. (2004).

Another element of this study is the integration of multi-phase flows, evaporation from the water in the bath, and subsequent dispersion of the vapour throughout the room.

While dispersion of particulate matter and vapour has been covered extensively, it is surprising that there has not been much published on the multi-phase aspect within the bounds of HVAC. The two most important are Caruso et al.’s work (2007) on the Halls of the "Città dello Sport" and Bellache et al.’s work (2005) on an ice rink. Interestingly, though both mention the importance of their respective other phase (water for Caruso and ice for Bellache), neither models them. For models that include two phases, one needs to

look outside the HVAC industry. There are two major proponents for multi-phase CFD: geology/hydrology and chemical engineering. Even within these categories, the methodology for multi-phase modelling is not agreed upon. For instance, Hardy et al.

(2005) noted that when modelling rivers common practice is to use a symmetry plane to capture the water surface, usually called a “free surface.” Ma et al. (2002) analysed a river channel in England and they incorporated the free surface in their model; however, by doing so they were able to simulate only a small section of the channel. The most useful articles for this present project come from the chemical engineering sector. Akbar and Ghiaasiaan (2006) worked on the rise of bubbles in a liquid, which is the reverse of the situation in this project (gas in liquid instead of liquid in gas). Nguyen and Evans

(2006) wrote an article on gas jets impinging on liquid surfaces, for which the commercial CFD software FLUENT was used. Venetsanos and Bartzis (2007) published an article on liquid hydrogen spills, which not only contained multi-phase modelling but also the evaporation and dispersion of the hydrogen gas.

2.2.3 Classical Archaeology Literature Review on Baths

On the other side, from the classical archaeological perspective, the topic of

Roman baths is now over two thousand years old. There is a distinction between works written at the time (primary accounts) and research done after the baths fell out of use

(secondary sources). The primary accounts vary from graffiti on walls to passages by well-known authors. Due to the large volume of graffiti, they are not part of this discussion but Fagan (2002) has a sample.

The primary accounts predominantly commented on the social aspects and impressive opulence of the structures,24 however, some writers provide significant information. The discussion of the pertinent primary sources here is brief but Appendix 1 provides a full listing including translation and commentary. Seneca the Younger, while bemoaning the luxury of the baths in his time as compared to the simplistic elegance of those that existed in the mid-second century BCE (Ep. 86.8-12), mentions that the caldaria windows of his time had “latis specularibus,” a phrase that indicates some kind of glazing, either thin sheets of mica or glass. This ambiguity has an impact because the light and heat transmissibility is different for mica than it is for glass, which would influence the temperature distribution, especially in the Baths of Caracalla with its grand windows. Seneca further comments on the baths having an even vertical temperature distribution which gives a qualitative measure to compare with the computational results.

It is important to note, though, that this passage is in relation to a balneum and not thermae so it might not hold true for the Baths of Caracalla. Pliny the Younger makes an intriguing comment in one of his letters about a searing hot pavement used to test if a person was still alive (Ep. 14). This could be, though, highly speculative, the floor of a villa bath and if it is, this would give a guide for the floor temperature. Two passages give indications about the time of day when bathing took place. The first comes from

Martial, a late-first-century Latin poet. He informs us that the best time for a bath is the eighth hour (shortly after the mid-day meal) and that the sixth hour (just prior to mid-day)

24 These include Martial (Ep. 6.42), Lucian, a 2nd-century-CE Greek satirist (Hippias 4-8), Statius, a late- 1st-century-CE Latin poet (Poems 1.5), Petronius, a mid-1st-century Latin poet (Sat. 28), and Sidonius Apollinaris, a 5th-century Roman writer (Letters 2.2.4-9). These, though interesting, are not pertinent to this study. 36

is too hot for it (Ep. 10.48).25 The second does not state hours but rather implies night usage. The Historia Augusta, a 4th-century-CE compilation of biographies, tells of a tax plan implemented by Severus Alexander to pay for oil for lamps for the baths (Severus

Alexander 24.5-6), which suggests that bathing at night was popular.

In addition to the above segments, there are three passages that deal with the architecture of the buildings. These are valuable for the general understanding of the construction of the bath and, more importantly, the hypocaust. As with most things architectural, the major primary resource is De Architectura by Vitruvius, a late-1st- century-BCE Roman architect. In Book V, Chapters 10 and 11, he outlines the proper construction of the baths. The problem with Vitruvius’ account is that, when he wrote at the end of the first century BCE, the largest bath was the atypical Baths of Agrippa.26 The other two notes are by later authors: the 4th century CE Cetus Faventinus and the 5th- century-CE Palladius. Both follow the blueprint laid out by Vitruvius, and, even though the technology had progressed far beyond the small baths of Vitruvius’ time, neither significantly updates the knowledge base. Palladius does mention the use of pool overflow being used to water gardens and of baths as heat sources for apartments. It is clear, however, that both are referring to balnea rather than thermae given the maximum

25 The Romans relied on the sun for daylight time-keeping and, as such, had seasonally variable hours (that is, the period of daylight was divided into 12 equal segments). This means the length of an hour depended on the time of year. For the example above, the “sixth hour” will always end at noon, but the “eighth hour” could fall between 13:20 in the winter and 14:40 in the summer. 26 The earliest imperial thermae, whose layout is highly speculative; however, even from the limited evidence available–namely, the Forma Urbis representation (Yegül 1995, 134)–it is clear that they were radically different from the later Imperial thermae of Rome. 37

bath size in time period that Vitruvius wrote27 and the fact that Palladius refers to the head of the household when describing water usage, implying a smaller building.

After bathing practices changed when the Roman Empire collapsed, 28 the primary accounts dissipate and the secondary research begins. During the Middle Ages, many large complexes in Rome succumbed to the ravages of both nature and humans for many reasons. Some, like the Baths of Diocletian—now the Basilica di Santa Maria degli

Angeli e dei Martiri—were later converted to churches, while others were almost entirely destroyed. The Baths of Caracalla were somewhat spared as the church owned the land and it used the grounds for burials as well as markets, vineyards, and orchards (DeLaine,

1997, p40-41). The Renaissance marked a renewal of interest in things classical. A few architects, most famously Andrea Palladio (1732), drew the Imperial thermae as they existed at the time and postulated their grandeur when they were in use. Others, like L. B.

Alberti (1485/1955), were more conservative in their evaluations. In Chapter 10 of his eighth book on architecture, Alberti discusses the large public baths; however, it is clear from his nondescript depictions that, even in 1485 when the series was published, the baths were somewhat of a mystery. Some excavations, at least at the Baths of Caracalla, also began here: the most notable for the purposes here being the one conducted by Pope

Paul III (Alessandro Farnese) which saw the removal of sculpture and marble (Lanciani,

1902). The excavations of the Baths of Caracalla from the sixteenth to the early

27 One of the largest baths in late 1st-century-BCE Rome was the Baths of Agrippa which covered an area of between 0.8-1.2ha: small in comparison to later thermae. 28 Bathing in general, however, did not die out as shown by Caskey (1999). In the west, the buildings shrunk and were usually associated with a domestic context as the officials of the church came to object to public bathing. Many elements, such as the hypocaust, survived the transition. In the Middle East, cultural reform, guided primarily by the tenets of Islam, transformed the baths into hamams: which exist to this day. 38

nineteenth centuries were primarily for “the greater glory of the church” (DeLaine, 1997, p42), making its preservation, for the most part, a beneficial consequence.

During the 19th and early 20th centuries, some people began to examine these buildings in greater detail. Visitors to the sites extolled their architectural beauty and grandeur, in particular, the Baths of Caracalla and of Diocletian. John Stoddard, a renowned 19th-century lecturer and world traveller, exclaimed (Stoddard, 1898, p305-

308):

There is nothing now in the world that corresponds to the magnificent establishments of ancient Rome, which her Emperors founded to contribute to the cleanliness, pleasures, and luxuries of the people. … The ruins of the Baths of Caracalla are now carefully preserved under the supervision of the Government; but, alas! both time and man have injured them so greatly that it is difficult to form more than a vague idea of what their stupendous arches and enormous areas signify.

This sentiment is echoed by C. R. Cockerell, a prominent 19th-century English neo-classical architect, who said that the Imperial thermae of ancient Rome were “the most remarkable buildings the world has ever seen” (Watkin, 1974, p117). Despite this intrigue and amazement from sections of the public, baths played a very minor role in classical studies. As stated by Janet DeLaine, “altogether, the baths are something of an embarrassment to those who take their ancient world seriously” (DeLaine, 1988) and there has been a “(false) assumption that nothing new could be said about them”

(DeLaine, 1988). The modern research, on the whole, began in the 20th-century. Three major categories are key: surveys and overviews, site-specific research, and articles that focus on a certain aspect of baths or bathing.

The first category—surveys and overviews—encompasses a broad spectrum of sites, both geographically and temporally. The first major survey publication was Die

Trierer Kaiserthermen by Krencker et al. (1929), in which they categorized the Roman baths into different types.29 Their designations have formed the basis for most of the typology of baths since. Krencker’s student, Erika Brödner, followed this with her own book, Die römischen Thermen und das antike Badewesen (1983), which expanded

Krencker et al.’s typology to include more buildings, though, each is discussed only briefly. Heinz (1983) focuses on the chronological evolution of the bath and the hygiene of the baths. The next, Inge Nielsen’s Thermae et Balnea (1993),30 is a two-volume compilation of many of the known bath buildings from the Roman Empire, organizing them into five regions. For each region, she analyzes the available sources and provides an overview of the baths within. Fikret Yegül’s Baths and Bathing in Classical Antiquity

(1995)31 follows a similar layout to Nielsen’s book, describing trends in baths based on regionalism and historical periods. He has more emphasis, though, on the Greek gymnasia and the thermo-mineral baths of the Mediterranean. Garrett Fagan’s Bathing in

Public in the Roman World (2002) takes a much broader approach, looking at the socioeconomic impacts of baths based on literary and inscriptional evidence. Finally, Bouet

(2003b) surveys, though more limited in geographical scope, the baths in Gaule

Narbonnaise (what is now southeast France) and he groups buildings with similar key room designs (for example, those with rectangular caldaria).32

29 These are the row type, the ring type, the half-axial type, the “Small Imperial Type,” and the “Large Imperial Type.” Yegül (1995) provides a nice pictorial representation of these types on pages 131 and 132. 30 DeLaine (1993) provides a review of both Nielsen’s (1993) and Yegül’s (1995) work. 31 Ibid. 32 Other noteworthy works are Manderscheid’s compilation of bibliography on baths (2004) and the proceedings of the First International Conference on Roman Baths (DeLaine and Johnston, 1999). 40

The second category—site-specific research—includes hundreds of books and articles but only those that pertain to the Baths of Caracalla are important for this project.

Considering that these are the best preserved thermae in Rome, there are only three major scholarly monographs on the Baths of Caracalla. The first is Restauration des Thermes d’Antonin Caracalla à Rome by Abel Blouet (1828). This book is the first archaeological study of this complex and is extremely rare. It provides a glimpse of some aspects that have disappeared over the last 150 years, such as the mosaic patterns. The second is

Untersuchungen an den Caracallathermen by Erika Brödner (1951). This small manuscript looks at the architectural features of the building, but her focus is on the palaestrae and the terraces above. She suggests that a large vault covered the palaestrae instead of being open to the air. Lastly, there is the most recent and most often referenced book, Janet DeLaine’s Baths of Caracalla (1997). Primarily an architectural account of the Baths with particular interest in the building process, it does discuss decoration and some socioeconomic issues, and provides an extensive, but incomplete, table of dimensions as well.

There are four smaller guides on the Baths that provide a good overview of the site. They start with a very old one by Ripostelli (1916) which has a romanticized feel to it. Lugli’s book (1970) is by far the smallest at 35 pages but covers all the key features, though he does call the frigidarium the tepidarium. Iacopi’s (1977) couples the Baths of

Caracalla with the Arch of Constantine, which is interesting as the two are not close spatially or temporally. The most in-depth is Piranomonte’s The Baths of Caracalla

Guide (2008). She covers the site history, the architecture, the mythraeum and underground levels, the decoration, the Emperor Caracalla, and what it was like to bathe

here. While the subjects of these four books are similar, they provide different and complementary information. Each has a piece of data that might help with the digital reconstruction of Chapter 3, such as, Piranomonte’s description of the sublevels. There are also two books published that survey the complex and the surrounding area to ascertain the viability of holding the opera here in the summer (Commissione reale per la zona mommentale di Roma, 1910; Baccelli, 1914). These provide a cultural context for the Baths as well as some incredible imagery.

There are also sections of more general books, which provide quick synopses of the Baths of Caracalla and previous scholarly work. As expected, the two most famous topographical dictionaries of Rome (Platner and Ashby, 1926; and Richardson, 1992) are among these. John H. Middleton has quite an extensive discussion of the site and its history in his book The Ruins of Ancient Rome (Middleton, 2005). Lanciani, in his book

Storia degli Scavi di Roma (1902), summarizes the excavations between 1546 and 1583, including the removal of the Farnese bull.

Finally, there are a number of articles on the Baths of Caracalla. Iwanoff and

Hulsen’s Aus den Caracalla-Thermen (1898) focuses on the decoration and inscriptions in the complex. Ghislanzoni (1912) published an article in Notizie degli Scavi di Antichità on the finds in the garden to ascertain the viability of holding the opera on site. Iacopi

(1985) and Cecchini (1985) excavated the perimeter walls and their teams’ finds are published in Roma: Archeologia nel Centro. DeLaine, aside from her book, has published two articles on the Baths of Caracalla, of which the first (DeLaine, 1985) looks at the construction techniques used in the complex while the second (DeLaine, 1987) tries to determine the location of the so-called ‘cella solearis’. Conforto (1991) summarizes the

research and the general state of the Baths in her article. Manderscheid (1991) published an article on water management in the Baths, an essential, but surprisingly often overlooked, aspect of their operation.

The third category—articles that focus on a certain aspect of baths or bathing— covers topics ranging from historical aspects to sanitation to case studies. In one, Fagan

(1996) sets out to uncover whether Sergius Orata can be positively identified as the inventor of the heating system. Based on an examination of the ancient sources he concludes that the pensiles balineae or ‘hanging baths’ mentioned by Pliny the Elder,

Cicero, and Valerius Maximus and linked to Orata are not the heating system. Fagan

(2000) tries to address the ‘cleanliness’ of the baths by looking at the number of bathers who could fit into caldaria pools in a number of different baths, to assess the deposition of dirt and mud in these pools. Interestingly, though, most of the scholarship has dealt with the architectural details of the buildings and some of the accompanying social issues while the heating and water distribution systems have been seemingly relegated to a few sentences.

The development of thermodynamic theories in the mid-nineteenth century filtered somewhat into classical archaeology about 100 years later, spurring the renewed interest in hypocausts as seen above (Forbes, 1966, p43). Three further articles illustrate this renewal. Forbes (1966) describes the heating system and its components and he gives average dimensions for each. Sandklef and Selling (1976) discuss the heating system of thermae and fuel usage. Blyth (1999) uses epigraphic evidence to estimate fuel consumption at a variety of small balnea; the Stabian Baths are an example.

A subcategory that needs introducing is those articles that present evidence of glazing at balnea sites as the window issue is important for this project. Foy and Fontaine

(2008), Allen (2002), Whitehouse (2001), Ortiz and Paz Peralta (1997), Charlesworth

(1977), and Boon (1966) all provide overviews of Roman window glazing in many different environments. Almost all of the articles that deal with glazing in baths are site reports of various excavations across the Mediterranean. Therefore explanations will not be included except for special cases. Many scholars found glass panes and fragments at a number of sites dated primarily between the 1st and 2nd centuries CE.33 Other finds, though, better indicate the nature of Roman bath window construction. Zienkiewicz

(1986, p1:337) came across glass fragments and the remnants of putty which supposedly held the glass into the frames at the legionary fortress baths at Caerleon (ca 75 CE). In the

Forum Baths at Pompeii (62 CE), Nissen (1877, p135) uncovered remainders of bronze frames along with pieces of sheet glass. Martini (1984, p199-200) unearthed complete marble-framed windows in the Roman baths at Samos (ca 2nd century CE). In the caldarium of the Constantinian Baths (ca mid-3rd century CE) at Arles, excavators discovered not only glass, but evidence for wooden shutters (Formige, 1922, p253-254).

This evidence implies that ancient windows were not of one pane, like modern windows,

33 These are the Taurine Baths at Civitavecchia (Bastianelli, 1933, p407, 420), the Hadrianic Baths at Leptis Magna (ca 2nd century CE; Bartoccini, 1929, p60-61), the small baths of the Middle City in Pergamon (ca 2nd century CE; Radt, 1980, p412), the Great Bath on the Lechaion Road in Corinth (ca late 2nd century CE; Biers, 1985, p17), the baths at Chassenon (ca 2nd century CE; Hourcade, 1999), the public baths at Caesaraugusta in Zaragozza (ca 1st century CE; Ortiz Palomar and Paz Peralta, 1997, p442), the baths at Labitolosa (ca 1st century CE; Ortiz and Paz, Peralta 1997, p442), the baths at Uncastillo (ca 1st century CE; Beltrán Lloris, 1996, p76), the baths at Bilbilis (ca 1st century CE; Ortiz and Paz Peralta, 1997, p440), the baths at Saint-Jean-Le-Vieux (ca 1st century CE; Bouet and Tobie, 2003, p160), the bath-house at Garden Hill, Hartfield, Sussex (ca 2nd century CE; Harden, 1974), and the baths at Barzan (ca 1st century BCE; Bouet, 2003a, p187-188). 44

but were multi-paned.34 The multi-paned window has an impact on the thermodynamics and light transmission. If one thinks about the difference between open and slightly angled venetian blinds, this effect will be apparent and needs incorporation. Furthermore, the muntins separating each pane are metallic and as such transmit more heat than the glass panes. Modeling each pane and muntin, however, is computationally impractical so an analog is necessary.

2.2.4 Gaps in the Knowledge Base

Stepping back to observe the whole picture again, there are many lacunae that this project can fill. This section outlines where these are.

While the engineering research of HVAC and related systems is extensive, it is by no means complete. The absence of CFD analyses of the radiant slab heating technique is striking, and this project may provide some new insight here. From the convective heat transfer coefficient side, there are two possible avenues that this project could address.

One is the influence of hot air and the capacity of the air to heat the boundary. The other is the absence of heat transfer coefficients from radiant slab floors and similar constructions. Finally, multi-phase modelling is quite unexplored, especially when dealing with HVAC processes, which makes the inclusion of pools a new contribution.

From an archaeological perspective, there are substantial areas that the previous works on baths either did not cover or only briefly did so. The most glaring is the lack of information on the heating and water distribution systems as these are the biggest

34 In fact, it was not until after the Industrial Revolution that large plate glass became available. (Douglas and Frank, 1972) 45

differences between a bath and any other building. The earlier studies that deal with the heating of the baths, mentioned previously, have two major failings. First, they deal with only the smaller baths, and second, they treat the air inside uniformly and ignore stratification due to buoyancy. The latter means that, while the results are accurate, the entire story cannot be told. For instance, the average temperature may be 35°C but, because of buoyancy, the temperature in the region occupied by patrons may only be

27°C. This becomes even more problematic when the large baths are considered, where the ceiling may be over forty metres above the floor.

CFD is a tool that can help improve the understanding of the thermal environment inside these unique rooms. No one, though, has looked at the temperature inside one of the heated rooms with the help of CFD, especially not of one of the large Imperial baths.

One advantage of CFD is that the temperature at every point in the entire volume is calculated instead of an average temperature. With this, one can determine the uniformity of the temperature distribution, whether any hot spots exist, and if so, where they are.

This can provide a great deal of information about the operation of the baths. The major other advantage of CFD is it is possible to test the larger baths on which experimentation is not feasible. The scale of the rooms of the grand baths could produce unique air flow patterns and operating conditions inside, such as dramatic temperature differentials between floor and ceiling, which can be detected using CFD.

This project sets out to address some of these gaps. As Chapter 3 covers a disparate but necessary topic for completion of the CFD model of the Baths of Caracalla, it does not fill a gap. The first major engineering impact appears in Chapter 4, which discusses the experimentation of the CHTC of the tubuli. Chapter 5 switches disciplines

and adds to the debate surrounding window glazing mentioned in Section 2.2.1. The remaining chapters on CFD contribute to both fields.

CHAPTER 3 — RECONSTRUCTING THE BATHS OF CARACALLA35

3.1 Introduction

What began as a digital reconstruction of the caldarium for the purpose of creating the mesh for the CFD model for the Baths of Caracalla quickly morphed into an interesting, yet difficult, reconstruction of the entire bathing complex for the IATH project, Rome Reborn.36 This project relies on detailed models of strategic complexes, such as the Flavian Amphitheatre (or Colosseum), in a panorama of apartment blocks, shops, and private homes. The details of these key buildings create a semblance of life in the enormous model of Rome around 320 CE. Since it is the most intact thermae in

Rome, the Baths of Caracalla are important to reproduce as accurately as possible. So its reconstruction required careful attention to many different facets, from room dimensions to mosaic patterns. Even though much of the structure still exists, the published, publicly available data are surprisingly sparse. This led to gaps in the knowledge base that make reconstruction exceedingly difficult. To offset these lacunae, the best approach was to survey all the evidence and make well-educated estimates. Given the complexity of the

Baths of Caracalla, I decided to use a parametric modeling suite, which necessitated the use of a second program for the application of textures. This chapter provides a

35 Versions of this chapter were presented at the VAST Conference in Prato, Italy in October 2011 and the Computer Applications and Quantitative Methods in Archaeology Conference in Southampton, England in April 2012. 36 Rome Reborn is a project of the Institute for Advanced Technology in the Humanities (IATH) that is rebuilding the city of Rome digitally as it existed in the fourth century CE. The aim is to provide another tool for classicists to look at the spatial distribution and urban landscape of Rome. With a 3-D digital model of Rome, scholars can better investigate debated questions such as the visibility of monuments from different vantage points or how the setting changed under different Imperial building plans. 48

methodological overview that chronicles the software programs used, the overarching issues that arose, the room specific adjustments made, the intricate insertion of window glazing, and the application of textures. In so doing, the chapter will make apparent the major benefits and stumbling blocks of digitally modeling the Baths of Caracalla.

3.2 Software

Because of its parametric capabilities, I chose to use the engineering computer- aided design (CAD) program, Dassault Systèmes’ SolidWorks (Dassault Systmes, 2012), for the geometrical portion of the reconstruction. In parametric design, as the name suggests, the researcher creates features by drawing shapes and defining modifiable parameters to hold the shapes in place. This allows for easy manipulation of pieces of the design if new information becomes available. However, the program is based on mathematical formulae, which limits the creativity of the researcher. Since parametric programs are based on mathematical formulae, forming intricate curves, such as a

Corinthian capital, can be time-consuming and frustrating if not impossible. This is why parametric programs are almost always engineering-based. Therefore, for the artistic finishing details, such as texture application, Autodesk’s 3ds MAX (Autodesk, 2012) was more appropriate. However, the use of McNeel’s Rhino 4 (McNeel, 2012) was necessary to ensure a smooth transition between these two programs because Rhino 4 can open a native SolidWorks file and export it to a Autodesk file format.

3.3 General Structure and Broad-Spectrum Assumptions

DeLaine’s Appendix 1 (1997), which contains measurements of wall lengths, door widths and heights, window widths and heights, window-sill heights and niche widths and heights of most rooms, served to provide the preliminary data. This revealed the first stumbling block, that is, the incomplete nature of the data. In some cases,

DeLaine could not provide a particular dimension, either due to access issues or, more often, because it simply did not exist anymore. For these cases, fortunately, the mirror image dimension did exist. For example, the N window of Room 1E (Fig 2.2) is missing but DeLaine listed the N window dimensions of Room 1W so both windows used the same dimensions. While she gave many key dimensions, she omitted some, most noticeably the placement of the doors, windows, and niches. For dimensions not given in the appendix, where possible measurements from DeLaine’s scale drawings provided approximations.

The reconstruction process involved many assumptions and modifications. To make the process easier, averaging opposing wall lengths modified the rooms from quadrilateral to rectangular: meaning all corners met at ninety degrees. In actuality, since opposing walls were not the same length, no room corners were perfectly square. In most cases, though, the difference was two or three centimetres, which, over a wall measuring up to twenty metres, was relatively insignificant. The key reason for modification was because it substantially decreased the complexity of the reconstruction of the vaults. The parallel walls allowed for a simple extrusion to create the vaults instead of using a

complicated, somewhat unpredictable loft.37 More importantly, it simplified the whole process because then all walls were either vertical or horizontal and angles were not involved.

The vault heights required a similar adjustment. Like the wall lengths, the distance from the floor to the springing of the vault varied depending on where DeLaine took the initial measurements. As the finishing piece, structurally speaking, these differences were not as critical and could be incorporated without jeopardizing subsequent components. The vaults themselves were easy to create but their thickness is a point of debate due to the uncertainty surrounding the existence of rooftop terraces. Some reconstructions have gabled roofs on many of the major rooms while others (including

DeLaine's) have all flat roofs. Based on site observations that I made in 2008, my current reconstruction is somewhere in the middle. The presence of stairs above Room 11E/W and from 18E/W to the roof of the portico above 12E/W intimated that there were terraces on Rooms 4E/W-11E/W. There were also the well-lit staircases that ascend from the floor of Room 3c to the top of Room 4; presumably if the Roman designers had meant these for only the maintenance staff, the light wells would not be present.38 The

37 An extrusion converts a 2-D sketch into a 3-D object by expanding it along a straight line perpendicular to the sketch. A loft creates a 3-D object by connecting two or more sketches, perhaps following a curve known as a guide path. A sweep takes a sketch and moves it along a path thereby making a 3-D object. 38 This is similar to the windowed stairwell inside the Column of Trajan. As Wilson Jones points out, “that the stair was meant to be used by visitors, and not just for maintenance purposes, is confirmed by the presence of forty windows, ten on each cardinal axis, sufficient to ensure an adequate illumination throughout the climb” (Wilson Jones, 2003, p165). Given the size differential (0.15m by 0.3m in the Column of Trajan and 0.5m by 1.25m in the Baths of Caracalla), it is safe to assume that the same principle applies. 51

presence of a gabled roof on the Basilica di Santa Maria degli Angeli e dei Martiri,39 formerly the frigidarium of the Baths of Diocletian, the sister complex to the Baths of

Caracalla in ancient Rome, suggests that there was gabling on the roof of the Caracalla frigidarium. Gabling on the frigidarium does make the room appear visually impressive, especially when the remaining roofs are flat-topped (Fig 3.1).

Figure 3.1: (a) A preliminary model showing a flat-topped frigidarium. (b) A preliminary model showing a gabled frigidarium. (Model created by Taylor Oetelaar.)

Considering the size of the complex, it was not necessary to make many assumptions like those described above. This decreased the amount of introduced uncertainty associated with this reconstruction. The squaring of the rooms and equalling

39 Etchings by Palladio in 1550 (Cameron, 1772), Dosio in 1564 (Siebenhüner, 1955, p181), and Dupérac in 1575 (Siebenhüner, 1955, p181) suggest that the vaults were largely intact when construction on the basilica began. Though it is difficult to tell from these drawings whether the gabling existed in the 1500s, it is hard to believe that the architects would have risked collapse to convert the roof. 52

of the springing heights reduced the complexity of the reconstructive process considerably without affecting the overall accuracy too much. All of this means that the base of the model stayed true to the site and the surviving evidence.

3.4 Specific Alterations and Assumptions

There were also room-by-room alterations and assumptions. Ten of the fifty rooms—Rooms 15E/W, 16E/W, 18E/W, 20E/W, the tepidarium, and the caldarium— required some special interpretation and/or modification, due to either complex geometry or a lack of information. Rooms 20E/W, for example, had the most complicated ground plan of any room aside from the caldarium. An accurate reconstruction, therefore, required measurements from the floor plan—some of which were extremely difficult to obtain—in concert with the standard dimensions given by DeLaine. However, the intricacy of the floor plan made it necessary to assume that the apses that contained doorways were indeed semi-circular. The other major problem with these two rooms was the intricacy of the roofs. The doorways, which were not straight conduits, open into small apses that in turn are in larger apses (see Fig. 2.2). Lofts created the doorways but that produced a flat face in the middle of the curved surface, so cutting out the extraneous material re-established the curved apse. Then revolves40 created the semi-dome ceilings of the smaller apses, but this in turn created an anomaly in the surface in the larger apse.

The removal of the excess material permitted the addition of the semi-dome. Finally, the flat-roof completed the structure of the room.

40 A revolve is a sketch that is rotated about a central axis to create a 3-D body. 53

The next room that required special attention was the tepidarium because no dimensions have been recorded. The dimensions of the tepidarium came from measuring the floor plan and scale elevation drawings. Fortunately, the tepidarium was a very small rectangular room. The most difficult aspect was the semi-circular doorway to the caldarium; however, after dealing with Rooms 20E/W, this was straightforward.

The caldarium also requires interpretation since the entire southern half exists only to half a metre in height and DeLaine’s data on the caldarium were therefore minimal. The structure of the caldarium, after measuring the scale drawings established the floor plan, was an extrusion with a revolved dome on top.41 The simplicity of the main structure, however, was severely outweighed by the complexity of the arched recesses that surrounded the pools and the decorative moulding around the windows.

Given the intricate geometry, lofts created all of these features. The major problem was that the walls are circular, which meant that the planes that help make the lofts had to be tangent to the curved surface at the midpoint of the opening. It was more practical to create the arches above the pools first, as all lofts in SolidWorks have to start and end with a flat sketch. This means that the outer face of the inner arches (in the middle of the wall) is flat when it needs to be round. To counter this, adding the outer arches after the inner arches covered the flat ends of the inner arches. The top bay outer mouldings added another degree because the loft was straight along the sides but concave in the middle.

The use of multiple guide curves solved this.

41 It is important to note, however, that some reconstructions such as Le Duc’s (1867; given in Piranomonte, 2008) show the caldarium as having an oculus on top. This could have a dramatic impact of the thermal environment inside and on its controllability. This, though, introduces another aspect of uncertainty which is beyond the scope of the CFD work later so I did not include it in this reconstruction. 54

The final six rooms—Rooms 15E/W, 16E/W, and 18E/W—required attention because they were geometrically difficult and the publically available documentation is sparse.42 Rooms 15E/W and 16E/W most likely were places for servants and maintenance people as the doorways were extremely small when compared to the others. There appeared to be remains of a hanging staircase in 15E/W leading to the window sill in the central wall that separated 15E/W and 23E/W and the second floor of 16E/W. It may have been that the ground floor of 16E/W led to the subterranean maze under the baths.

From unpublished pictures provided by DeLaine, it appeared that the roof of 16E/W connects to the terrace system which eventually led to the central wall of 15E/W mentioned above. Room 18E/W was a mystery because even DeLaine had to guess its contents. Her drawings indicated a staircase leading up to the terrace level. Blouet (1828), however, suggested that it was just a connecting room between 12E/W, 17E/W, and

20E/W with a mosaic floor. If there was a staircase in 18E/W, it would have to lead to the second floor of 16E/W because there was no break in the roof structure of 16E/W. While this staircase is not improbable, it would seem rather futile unless the Romans used it to transport bathing accoutrements to the hot rooms. The most curious aspect of 18E/W, however, was the terrace floor, because it appears that the designers raised the terrace walkway above the structural vaulting, leaving an air gap. What was the purpose of this gap? Heating? The reconstruction of these six rooms was, therefore, tenuous and highly speculative.

42 DeLaine states, in a personal communication, that she was not allowed in these rooms during her research so this discrepancy is not surprising. 55

Most of the room-by-room modifications dealt with problems that arose from a lack of data, the notable exception being the caldarium window arches, which were also difficult to create. The recreation of Rooms 20E/W, the tepidarium, and the caldarium, however, was as accurate as the evidence allowed. The reconstruction of Rooms 15E/W,

16E/W, and 18E/W, on the other hand, was interpretive given the extreme absence of data and their apparent complexity. Overall, the recreation of these complicated rooms took more resourceful thinking but was not unrealistic.

3.5 Windows and Window Glazing

One of the more challenging and time-consuming aspects of the model construction was the creation of the glazing for the windows. This was for two reasons: one, the number and size of the windows in the complex, and two, nothing remains of them, archaeologically. There are 130 windows in DeLaine’s reconstruction and the smallest measures 2.5m wide by 3.25m high. This meant that, considering the state of glass manufacturing practices at the time,43 the Roman designers would have most likely made the inserts from compilations of smaller panes. Therefore all windows had to be split into two parts: the glass and the frame. Instead of making the individual panes of glass, it was easier to make one sheet of glass fill the window opening and then overlay the frames.

One major question remains: how big were the panes, muntins, stiles, and rails

(Fig 3.2)? For clues one has to turn to sites outside Rome. The evidence, though, was

43 See Foy and Fontaine, 2008; Allen, 2002; Whitehouse, 2001; Ortiz and Paz Peralta, 1997; Charlesworth, 1977; Boon, 1966 or refer to the end of section 2.2.3 of Chapter 2. 56

limited as shown earlier, so one must appeal to practicality. The panes of glass were most likely in multiples of Roman feet (1 Roman foot or pes (p) is 0.297m) and assuming that the muntins are 5cm wide, a starting point presents itself. To determine the size of the panes, I created a spreadsheet giving the dimensions of each window and the multiple of each 1p, 1.5p, 2p, 2.5p, and 3p panes (see Table 3.1) that would fit in each window, to see if a pattern appeared from these data. Somewhat counter-intuitively, though, there has to be some leeway in the fit to allow for the space for the frames (i.e., the muntins, rails, and stiles). Interestingly, a pattern emerged. The columns in bold (number of 2p panes that fit in height-wise and number of 2.5p panes that fit in width-wise) have values that are all just above multiples of 5 and 4 respectively. This means that the best fit comes from arranging panes 2.5p wide by 2p high into panels 4 panes wide by 5 high, and making the rails and stiles adjustable. There are two exceptions—the windows in Room

13 and the smaller windows in the frigidarium—where the best fit is 1.5p wide panes.

However, it should be noted that these were completely based on DeLaine’s drawings as nothing remains. The caldarium windows were different because the openings that they cover were curved. Since curved glass panes were difficult to manufacture and the radius of the curve is so large, I decided to break these windows down into three equal flat sections and then paned them. Interestingly, though, the size of the window differed depending on its orientation and thus each window had a different number of panes per panel and even a different sized pane. The site northeast and northwest windows (Fig 2.2) were the smallest, each section with three 2.5p wide by 2p high panes across the bottom; the site east, west, southeast, and southwest windows each had four 2p wide by 2.5p high panes; and the largest were the site south windows, with six 1.5p wide by 2p high panes.

Figure 3.2: Sketch of a sample window showing the different parts. (Model created by Taylor Oetelaar.)

Table 3.1: Breakdown of the Windows of the Baths of Caracalla Width Height Number of Roman feet per dimension (first: width; second: height) Window (cm) (cm) 1p 1p 1.5p 1.5p 2p 2p 2.5p 2.5p 3p 3p 1N 501 1303 16.9 44.0 11.3 29.3 8.5 22.0 6.8 17.6 5.6 14.7 2W 595 726 20.1 24.5 13.4 16.4 10.1 12.3 8.0 9.8 6.7 8.2 3NE 529 717 17.9 24.2 11.9 16.1 8.9 12.1 7.1 9.7 6.0 8.1 3NW 533 680 18.0 23.0 12.0 15.3 9.0 11.5 7.2 9.2 6.0 7.7 3SE 530 683 17.9 23.1 11.9 15.4 9.0 11.5 7.2 9.2 6.0 7.7 3SW 528 719 17.8 24.3 11.9 16.2 8.9 12.1 7.1 9.7 5.9 8.1 3W 456 683 15.4 23.1 10.3 15.4 7.7 11.5 6.2 9.2 5.1 7.7 4N 660 714 22.3 24.1 14.9 16.1 11.1 12.1 8.9 9.6 7.4 8.0 4S 650 333 22.0 11.3 14.6 7.5 11.0 5.6 8.8 4.5 7.3 3.8 5N 497 879 16.8 29.7 11.2 19.8 8.4 14.8 6.7 11.9 5.6 9.9 5S 1000 247 33.8 8.3 22.5 5.6 16.9 4.2 13.5 3.3 11.3 2.8 6N 634 733 21.4 24.8 14.3 16.5 10.7 12.4 8.6 9.9 7.1 8.3 6S 700 334 23.6 11.3 15.8 7.5 11.8 5.6 9.5 4.5 7.9 3.8 7W 442 297 14.9 10.0 10.0 6.7 7.5 5.0 6.0 4.0 5.0 3.3 11W 353 314 11.9 10.6 8.0 7.1 6.0 5.3 4.8 4.2 4.0 3.5 13W 250 200 8.4 6.8 5.6 4.5 4.2 3.4 3.4 2.7 2.8 2.3 Tier 1 13W 250 316 8.4 10.7 5.6 7.1 4.2 5.3 3.4 4.3 2.8 3.6 Tier 2 14S 300 444 10.1 15.0 6.8 10.0 5.1 7.5 4.1 6.0 3.4 5.0 Tier 1 14S 300 572 10.1 19.3 6.8 12.9 5.1 9.7 4.1 7.7 3.4 6.4 Tier 2 17E 725 741 24.5 25.0 16.3 16.7 12.2 12.5 9.8 10.0 8.2 8.3 17W 747 306 25.2 10.3 16.8 6.9 12.6 5.2 10.1 4.1 8.4 3.4 17S 425 477 14.4 16.1 9.6 10.7 7.2 8.1 5.7 6.4 4.8 5.4 19W 425 575 14.4 19.4 9.6 13.0 7.2 9.7 5.7 7.8 4.8 6.5 19S 375 600 12.7 20.3 8.4 13.5 6.3 10.1 5.1 8.1 4.2 6.8 20S 375 600 12.7 20.3 8.4 13.5 6.3 10.1 5.1 8.1 4.2 6.8 Frig N 200 978 6.8 33.0 4.5 22.0 3.4 16.5 2.7 13.2 2.3 11.0 Frig S 200 978 6.8 33.0 4.5 22.0 3.4 16.5 2.7 13.2 2.3 11.0 Frig E 200 1014 6.8 34.3 4.5 22.8 3.4 17.1 2.7 13.7 2.3 11.4 Frig W 200 1020 6.8 34.5 4.5 23.0 3.4 17.2 2.7 13.8 2.3 11.5 Frig SE 962 1127 32.5 38.1 21.7 25.4 16.3 19.0 13.0 15.2 10.8 12.7 Frig SW 900 1198 30.4 40.5 20.3 27.0 15.2 20.2 12.2 16.2 10.1 13.5 Tep E 996 926 33.6 31.3 22.4 20.9 16.8 15.6 13.5 12.5 11.2 10.4 Tep W 1022 913 34.5 30.8 23.0 20.6 17.3 15.4 13.8 12.3 11.5 10.3

3.6 Texturing the Model

With the geometry complete, the next step in the reconstruction was texturing.

This is where the major drawback of SolidWorks becomes apparent. As an engineering design program, models generated by SolidWorks look metallic and the program’s rendering capability is limited. As mentioned earlier, to enhance its appearance, I chose the more artistic Autodesk 3ds MAX. The transition process, however, was not easy as

3ds MAX cannot open SolidWorks files directly and IGES—a CAD interchange file format—did not provide adequate results. The best alternative was to open the

SolidWorks files directly in another program, McNeel’s Rhino 4, and then save the model as a 3D Studio file. In essence, a tertiary program was necessary to ensure the best results. The problem then became the large mesh size and the limitations associated with high memory demands. For instance, instead of a cylindrical surface that has three faces, the model would import a cylindrical mesh containing many polygons or polyfaces. As with CFD, smaller grids produce smoother images but rendering times go up dramatically and some displays can only handle a limited number polyfaces. The intricacy of the Baths of Caracalla turned into a drawback because creating the mesh of the entire building required more computer memory than was available. Instead of importing the entire model, it was better to import groups: superstructure, frames, glazing, mosaic floors, subfloor, columns, terrace and tiled roofs, and pool water. This also made applying the texture simpler because, for example, applying the bronze texture to all the frames at once is easier than applying it to each frame individually. To create the mesh of the superstructure, though, it was necessary to break the complex down further into three

blocks: the two wings and the central rooms. Since their coordinate system origins were the same, the reassembly of the groups required only a simple importation.

For the most part, in the prototype model, the textures themselves were generic.44

This was because the details of the decorative scheme are largely unknown. However, I did attempt a reconstruction of the opus sectile floors using drawings from Blouet published in 1828. I only had access to the microform version that was black and white so I extrapolated the colour scheme based on the fragments of opus sectile still in situ; however, the assumption that the colour scheme remains similar throughout the baths is questionable as evident by the remnants. Room 3E and its subsidiaries (a-d) were all black with white detailing but Room 12W had white, tan, green, and maroon with some sea green accents. This version used the colours of Room 12W and tried to ensure some degree of continuity; however, this was just one of many interpretations. The completed design is shown in Figure 3.3. There is one omission, the semi-circular Rooms 13E/W that held the Mosaics of the Athletes now in Rome's Vatican Museums.45 I did not attempt to reproduce these rooms as they are much more intricate and require much more expertise than I possess.

44 Texture application is critical to the appearance of a reconstruction because, as a visual medium, the ‘skin’ is the first thing that the eye catches. As an engineer, I have limited practical knowledge of Roman art, so recreating the actual design motif is exceedingly difficult and outside the scope of this project. 45 For a picture of this, refer to Fig 71 in Dunbabin (1999). 61

Figure 3.3: Reconstructed opus sectile floors of the Baths of Caracalla. (Model created by Taylor Oetelaar.)

The decorative motifs of the walls and vaults were considerably more difficult to reconstruct. DeLaine provided line drawings of her interpretation of the marble revetment on one wall of two rooms. These mosaics of large rectangular tiles appeared inconsistent with what little remains in a corner of Room 8E, which indicated intricate multi-layer decoration. However, if one remembers that Romans often painted marble, these two images can merge and create an extremely complicated picture. This becomes even more complex with the suggestion that the walls could have glass tesserae, as contended by

Sear (1977). As such, I decided not to attempt to reconstruct the wall and vault treatments. For this model, the best option to cover the superstructure was a simple stone material which mimicked travertine.

Initially I used two tones of greenish marble to cover the columns, or more specifically, column placeholders:46 dark green for the large columns and light for the others. Later iterations may have more specific colours of marble and ideally detailed columns will replace the placeholders. The window frames imitated bronze and the glass had a slight blue tinge to match many examples of panes from that period.

With the geometry completed, attention turned to the more intricate details, namely texture application. For this, it was necessary to switch to Autodesk 3ds MAX.

Picking the most appropriate texture was exceedingly difficult considering the state of preservation of the veneers and mosaics. The arrangement presented in this model was a simplified one and not a completely accurate appearance of the Baths of Caracalla when they opened in 216 CE.

3.7 Benefits of Digital Reconstruction

There are many benefits to digitally reconstructing the Baths of Caracalla. The first and foremost is to visualize the building while in use. Even though drawings and physical models can offer the same view into the past, digital models have another degree of freedom. To see a different perspective with the older mediums, an artist would need to create a new drawing or the model might need to be cut, whereas one can rotate a digital model to capture any view. Also, a digital model allows a walk through the reconstruction, which is all but impossible with the previous mediums. However, there is a problem with perception. With a drawing and a physical model there is the

46 A column placeholder is a cylinder which has the same dimensions as the column but lacks the base, capitol, and fluting. 63

understanding that they are artistic renditions but with a computer model there can be an unwarranted assumption of definiteness.

One of the major benefits of digital reconstructions, particularly those using parametric programs like SolidWorks, goes against this air of definiteness. Since it is parametric (i.e., the dimensions are parameters instead of hard numbers) SolidWorks allows the researcher to make changes easily without having to redo entire pieces. This is particularly helpful when not all the data are available at the time. For example, in the case of Rooms 15E/W, 16E/W, and 18E/W, the initial data suggested one design but after visiting the site and discovering new information I changed my vision.

The other benefit of digital reconstruction is that one can easily try new ideas that may challenge long-standing beliefs. The perfect example of this is the south façade of the hot rooms (19E/W-22E/W). Every known model exhibits a columnar veil in the southern openings of these rooms, which, thermodynamically, does not make sense because any heat generated by the hypocaust would dissipate outside very quickly. Since the doorways47 leading into and among these rooms were among the smallest in the complex, the Romans were obviously aware that large doors let heat out faster than small doors; so why would they locate a huge opening on one side (two, in the case of 19E/W)?

DeLaine recognized this fact but she did not have an answer. The archaeological record and architectural drawings going back to Palladio (1732)48 support the existence of columns, but this does not preclude a secondary paned glass wall. The jambs on either

47 Chapter 5 discusses the importance of doorways in more detail. 48 These columnar veils are present in both his drawings of the existing state (ca. mid 1500s) and his reconstructed view. 64

side of these openings are intricate, which might support such a design. The problem with this idea, though, is the amount of material that would be necessary to cover these openings. It would take approximately 1600 kg of bronze to make the frames and 2000 kg of glass for the south facade of Room 20W. Another possibility is window coverings, such as shades, but this cancels the main reason for the southern exposure: the solar heating. While these two ideas have their flaws, the point is that one can test these methods digitally and easily separate the chaff from the wheat as it were.

As shown previously, parametric design provides both advantages and drawbacks.

One additional benefit of using SolidWorks is Dassault Systèmes’ eDrawings, a free downloadable program that allows the user to view and manipulate files created in

SolidWorks. One can rotate parts, pan, zoom in or out, and take select cross-section views. These allow the user to view a particular model from almost any vantage point, which is particularly useful when disseminating information to a lay audience. One of the most valuable features for scholarly applications is the ability to measure anything on the model. With this, one can share in one file a catalog of dimensions in the context of the overall building. This eliminates some of the uncertainty associated with many tabular catalogs, including DeLaine’s, as they need more dimensions than they logistically have room for. With the ability to take any dimension, the onus then falls on the creator of the model to ensure accuracy. The main downside of eDrawings is that, since it was designed for engineering use, its rendering capabilities are limited so texturing is not advised.

However, a monochrome model can efficiently show the geometry and, by using

SolidWorks, eDrawings provides another way to easily and cost-effectively share raw data with both other scholars and the general public.

3.8 Conclusion

This digital reconstruction of the Baths of Caracalla (Figs 3.4, 3.5) relied heavily on the work done by DeLaine. Her composite of dimensions, in combination with her scale drawings, provide its foundation. However, there were perplexing aspects and missing elements that necessitated assumptions and, because of these, the recreation is not static. As new data come to light, it may be necessary to update the model. The two main areas of uncertainty are the six rooms that required the most interpretation (Rooms

15E/W, 16E/W, and 18E/W) and the texturing. The data surrounding Rooms 15E/W,

16E/W, and 18E/W were incomplete and problematic and so the recreation is highly speculative. The decorative scheme chosen does not truly reflect the opulence of the

Baths as they existed in antiquity. This model hopefully still gives the impression of immensity that an Imperial thermae possessed.

Figure 3.4: A view from the northeast of the reconstructed Baths of Caracalla. (Model created by Taylor Oetelaar.)

Figure 3.5: A view from the southwest of the reconstructed Baths of Caracalla. (Model created by Taylor Oetelaar.)

In the context of the entire project, while this reconstruction started as a way to obtain the geometry for the CFD simulation of the Baths of Caracalla of Chapter 9, it surpassed the goal and evolved into a separate research thread. However, the questions 67

raised about the hot rooms (19-22E/W) give further credence to the study in Chapter 5.

This reconstruction, for the most part, though, has been engineering-based and gives scholars a basic test bed to investigate further aspects of the Baths of Caracalla. One immediate transdiciplinary opportunity is to use the model to improve the wall texturing and, thus, the opulence of the complex. Ideally, this digital replica could expand to include the perimeter wall and thereby establish context for the main building.

CHAPTER 4 — DETERMINATION OF THE CONVECTIVE HEAT TRANSFER

COEFFICIENT OF THE TUBULI49

4.1 Introduction

The last foundation is an accurate assessment of the boundary condition for the subsequent CFD models since the tubuli are the driving force behind the air circulation.

This chapter describes an experiment to investigate how much heat the air transferred to the wall (Fig 4.1). The aim is to determine the convective heat transfer coefficient

(CHTC) of the air rising through a representation of the tubuli of the NOVA baths. The results gave an average CHTC of 7W/m2·°C and showed that there was no relationship between the Nusselt and Rayleigh numbers for this configuration. Given the variability of tubuli size and shape mentioned in Chapter 2, another design might have different results.

49 A version of this chapter has been accepted for publication in the Transactions of the Canadian Society of Mechanical Engineers under the title “Determination of the Convective Heat Transfer Coefficient of Hot Air Rising through Terracotta Flues”. 69

Figure 4.1: (a) Picture of experimental setup (Photo by Matt Oetelaar). (b) Picture looking down the rightmost flue showing the layers of the wall (Photo by Matt Oetelaar).

4.2 Experimental Setup

The basic setup for this experiment (Fig 4.2a) was a section of wall placed above a plenum which houses the heater. A wooden box faced with cement board on the inside and covered with both batt and rigid insulation encased these. A volume of air above the plenum and next to the wall section was meant as a faux room to prevent the direct conduction between the wall and the outside. It was important to maintain material consistency as much as possible between this case study and the NOVA wall. The tubuli used in the bath were custom made and thus unattainable. Superior Clay terracotta flue liners were similar in size, shape, and material to the tubuli in the replica bath. The tubuli were prismatic and were 200mm wide by 120mm deep by 250 mm high. The flues were

216mm wide by 114mm deep by 607mm high but the shorter edges were semi-circular instead of straight. Both the tubuli and the flues are of modern terracotta, however, the specific composition is most likely not the same. Six of the flues in an array three wide by two high with the rounded sides facing each other made up the main wall component.

Lime mortar and marble tiles then covered the side facing the room substitute.

Figure 4.2: (a) Cross-section diagram of the setup (Dimensions: mm; Arrows indicate air flow direction). (b) Magnified view of the wall cross-section showing thickness dimensions and the approximate depth of the thermocouples.

The initial heater was a Watlow 300W finned strip heater. A thermocouple located above and behind the heater, measuring what will be referred to as the plenum temperature, was attached to a controller. The peak temperature with the 300W heater was 40°C which was insufficient. A larger 750W finned strip heater was more appropriate as its peak temperature was 160°C.

It was necessary to make one final set of adjustments to keep the mass flow rate steady. A 31.8mm hole was drilled in the front door of the plenum and the outside two flues were capped with rigid foam. This ensured that the heater drew in a manageable amount of air or, in other words, had the correct draw weight.

There were 16 K-type (Chromel-Alumel) thermocouples used for measurement.

The best placement was to locate the thermocouples in the centre two flue liners to minimize the effect of the edges. Localizing the thermocouples into two groups of eight—one cluster located half way up the lower flue liner (referred to as the bottom cluster) and the other half way up the upper flue liner (referred to as the top cluster)— minimized spatial variation. In each group, the spread was about 50.8mm but the depths varied. The eight depths were: the middle of the flue (capturing the air temperature), on the inner surface of the flue, one-third of the flue wall thickness, two-thirds of the flue wall thickness, on the outer flue surface, half way through the mortar, on the inner surface of the marble, and finally, half way through the marble (refer to Fig. 4.2b).

The thermocouple placement was difficult because, unlike in many experiments, their insertion tool place during construction. This posed two major problems. The first was ensuring that the thermocouples did not move without drastically affecting the thermal properties. A combination of silicone and tape helped, however, some of the thermocouples may have moved slightly even with this procedure. The second was ensuring that no two thermocouples were directly on top of one another while still ensuring a tight clustering. Since all the materials were opaque and each layer erases the landmarks, the chosen technique was to employ an approximately circular pattern.

An unexpected problem arose with the thermocouples on the inner surface of the flue next to the rising air. Even though the thermocouples were encased in concrete, the readings indicated that they were measuring the air temperature because they mirrored the fluctuations in the free stream readings. To test this hypothesis, a FLIR infrared camera took a sample of temperature readings. The infrared measurements proved to be drastically different from the bare wire thermocouple readings and closer to the expected results, so a K-type infrared thermocouple mounted on a rod in the middle of the flue replaced the surface thermocouple.

The data acquisition setup was uncomplicated. After the thermocouples measured the signals, they passed through an AD595 amplifier and captured by a NI PCI-6024E

DAQ. The long time frame of this experiment, however, made continuous data sampling challenging. A custom LabVIEW virtual instrument (VI) program sampled 30 seconds worth of data at 200 Hz every 5 minutes. The VI then averaged the data and plotted these points on a continuous graph.

4.2.1 Calibration

It was necessary to complete the thermocouple calibration in situ. The lower point was ascertained by allowing the system to reach room temperature. The best way to obtain a higher point was to place insulation over the marble and seal the inlet and outlet with insulation. A fan then drew air from one flue and blew it back down another. The result was that the temperature equalized throughout the thickness of the wall. This provided the second point which allowed for the calculation of the linear calibration.

4.3 Results

Once the methodology and equipment were satisfactory, the experimental procedure consisted of running the setup on five plenum temperatures (60°C, 70°C, 80°C,

90°C, and 100°C) for each thermocouple cluster. The best test for repeatability was to duplicate a sample of temperatures: two for the bottom cluster and one for the top. The plenum temperature was the only controllable variable. Most experiments measuring

CHTCs use the wall temperature or heat flux as their reference but neither are applicable here. The wall temperature is constantly changing as it is warming up and there is no external heat flux outside of the heat from the rising air.

Since data collection took over twelve hours, the system did not have the opportunity to cool completely between runs. To compensate, on cool days, the data collection only began after the system warmed up. Even with this precaution, though, the starting temperatures of the individual thermocouples were never the same. However, the resulting CHTC values differed by a maximum of 4.7% between comparative runs.

Each run produced eight data curves: one for each thermocouple in one of the two clusters. Simultaneous measurement of the two data clusters was not possible because of technical limitations of the setup.

For the temperature measurements there were three sources of error: the thermocouples themselves, the amplifier, and the DAQ. The standard K-type thermocouple had an accuracy of ±1.1°C, and the infrared had an accuracy of 2% or a maximum of ±1.2°C. According to the literature, the amplifier used had an error of ±1°C, while the DAQ had a maximum error of ±3.8764mV which converts to ±0.38°C.

Therefore the maximum total error, using the root-sum-square methodology, was

±1.53°C for the K-type thermocouple and ±1.61°C for the infrared thermocouple.

Figure 4.3: Temperature distribution of bottom cluster.

Figure 4.4: Temperature distribution of top cluster.

Figure 4.3 shows the temperature data from the bottom cluster when the plenum was 90°C and Figure 4.4 shows the temperature data from the top cluster at the same plenum set point. The first thing that immediately becomes apparent is the difference 75

between both the individual temperatures and their trend. With the bottom cluster, the air temperature reached a fairly steady value after approximately three hours whereas, the top cluster never stabilizes but rather keeps increasing throughout the entire 7 hour time period. This was most likely because the top cluster was only 305mm from the exit so there was a competing downdraft from the room which would cause turbulence. Another interesting difference between the top and bottom clusters is the surface temperature. In the bottom cluster the surface temperature is less than 1°C hotter than the next thermocouple reading whereas with the top cluster the surface temperature is more than

4°C away and only just over 2°C from the air temperature. This happened with all the top cluster tests and, given the fact that the surface temperature readings started at roughly the same point, it cannot be a systematic sensor error. This disparity, as seen below, caused a significant increase in the CHTC as it raises flux values and, more importantly, decreases the temperature difference on which the CHTC is based.

The radiation heat transfer to the room might be a partial reason for the discrepancy between the surface temperatures of the top and bottom clusters. The best way to test the plausibility of this was to run the system with the flues closed from external influences. While sealing the flues changes the fluid dynamics, the heat transfer mechanism is essentially the same. The results were definitive. With the flue sealed, the surface temperature was less than a degree from the next thermocouple in the wall.

4.3.1 Mass Flow Rate

Although the mass flow rate is not necessary to determine the CHTC, its approximate determination is useful for future comparative purposes. The best way to

calculate the mass flow rate of the system was to use a hot-wire anemometer and measure the velocity of the air at the inlet. Since the probe nearly covered the entire inlet, only one measurement was necessary. The initial transitional flow dictated that the most appropriate time to take a reading was when the flow had stabilized. Also, it was important to take measurements at the different plenum temperatures to see if there was any change. Interestingly, the velocity increased almost proportionally to the plenum temperature but remains low. The error of the Testo anemometer was 5% of 20ft/min

(1ft/min) or 0.005m/s. Using the area of the inlet, the velocity supplies the volumetric flow rate which, in turn, provides the mass flow rate factoring in the density given the air temperature of the room. Table 4.1 summarizes the data.

Table 4.1: Summary of Inlet Velocities and Mass Flow Rates Plenum Temperature Measured Converted Velocity Mass Flow Rate (°C) Velocity (ft/min) (m/s) (×10-4kg/s) 60 250 ± 1 1.27 ± 0.005 10.6 ± 0.043 70 260 ± 1 1.32 ± 0.005 11.1 ± 0.043 80 270 ± 1 1.37 ± 0.005 11.5 ± 0.043 90 300 ± 1 1.52 ± 0.005 12.8 ± 0.043 100 315 ± 1 1.60 ± 0.005 13.4 ± 0.043

4.4 Calculation of Coefficients

The equation for convective heat transfer is (Eq. 4.1):

The raw data provide the undisturbed fluid temperature, T∞, and the wall temperature, Tw, which leaves q, the heat flux. There are two negative heat fluxes: conduction through the wall and radiation from the interior wall of the flue. Assuming that the thermal

conductivities are uniform throughout their thickness, the transverse one-dimensional

Fourier equation is (Eq. 4.2):

In this equation, keff is the effective thermal conductivity of the section of the wall, T is the temperature at a specified point, and Δx is the distance between the two points. To palliate the possible random error from using only two points, the best alternative was to calculate multiple fluxes. Table 4.2 gives the classification of the eleven sets of data points used for the heat transfer: six using the surface as a reference and five using the marble as a reference.

Table 4.2: Breakdown of Heat Fluxes Surface-Referenced Heat Fluxes: Marble-Referenced Heat Fluxes: Surface to 1/3 Terracotta 1/3 Terracotta to Mid-Marble Surface to 2/3 Terracotta 2/3 Terracotta to Mid-Marble Surface to Terracotta/Mortar Interface Terracotta/Mortar Interface to Mid-Marble Surface to Mid-Mortar Mid-Mortar to Mid-Marble Surface to Mortar/Marble Interface Mortar/Marble Interface to Mid-Marble Surface to Mid-Marble

Figure 4.5: Heat fluxes from bottom cluster with the surface temperature as the reference point.

Figure 4.6: Heat fluxes from top cluster with the surface temperature as the reference point.

Figure 4.7: Heat fluxes from bottom cluster with the mid-marble temperature as the reference point.

Figure 4.8: Heat fluxes from top cluster with the mid-marble temperature as the reference point.

To ensure completeness, the chosen methodology was to calculate the conduction heat fluxes for each time increment. Figure 4.5 shows the results for the bottom cluster using the surface as the reference in the same sample plenum temperature above and

Figure 4.7, using marble as the reference. Figures 4.6 and 4.8 show the fluxes for the top cluster. First thing to note for both cases is how quickly the conduction steadies compared to the temperature. By 500 minutes, the flux in both clusters had stopped fluctuating appreciably. This means that, while the temperature was still climbing, the amount of heat going into the wall remained constant.

With the uncertainty in the temperature being high relative to the temperature differences in the wall, the uncertainty in the heat flux is large, despite the fact that two of the three variables are actually constants. For both clusters, therefore, the scattering of the heat fluxes can be attributed to experimental error. This is most readily apparent in

Figures 4.5 and 4.7 where the 1/3 TC curve is separated from the remaining curves. The distance between this thermocouple and the wall surface is just over 4mm and is the smallest of any of the surface-referenced calculations. This means that the heat flux calculation magnifies any error in the 1/3 TC thermocouple reading and gives the appearance of an alternate heat flux value. In addition, there is no discernable pattern to the spread, however, the closer together the thermocouples are, the more likely it is for the resulting fluxes to be more askew because the random error grows relative to the temperature difference.

The radiative heat transfer was not easy to estimate. In the hypocaust, a horizontal pipe would cover each flue which would take the exhaust gas to a chimney and vent it outside. In the experimental setup, on the other hand, the flue was open to the room. This presents two possibilities for the radiation from the inner wall. In the bath, the radiation contained within the flue would not transfer much heat as the walls are within 2°C of

each other and there would be little radiation. In the experiment, however, the radiation could scatter throughout the room thereby cooling the surface.

For the purposes of this setup, the initial course was to ignore the heat transfer due to radiation. Therefore, dividing the heat flux by the difference between the surface temperature and the bulk temperature using Eq. 4.1 provided the CHTC. The next step was to calculate an average, excluding those CHTCs that were obviously skewed, namely the one calculated from the heat flux between the mortar/marble interface and the mid- marble thermocouples. Figure 4.9 shows the results from the bottom cluster for a plenum temperature of 90°C using the surface-referenced heat fluxes and Figure 4.11 the marble- referenced heat fluxes. Figures 4.10 and 4.12 display the CHTC breakdown for the top cluster. The patterns were nearly identical as those for the fluxes above, particularly when the results steadied. The fluctuations in the CHTC came from the fact that the bulk temperature was never constant.

Figure 4.9: CHTCs using heat fluxes from bottom cluster with the surface temperature as the reference point.

Figure 4.10: CHTCs using heat fluxes from top cluster with the surface temperature as the reference point.

Figure 4.11: CHTCs using heat fluxes from bottom cluster with the mid-marble temperature as the reference point.

Figure 4.12: CHTCs using heat fluxes from top cluster with the mid-marble temperature as the reference point.

There is a considerable difference in the CHTCs from the bottom and top clusters: nearly a factor of ten. Table 4.3 shows the average of the averages for various plenum temperatures:

Table 4.3: Average CHTC for Both Clusters Plenum Bottom Cluster CHTC Top Cluster CHTC Temperature (W/m2·°C) (W/m2·°C) 60°C 7.2 ± 10.0 63.6 ± 138 70°C 7.0 ± 8.9 64.6 ± 104 80°C 7.6 ± 8.6 69.8 ± 140 90°C 6.8 ± 9.2 63.2 ± 131 100°C 6.2 ± 8.4 60.2 ± 86.2

The uncertainty determined for the CHTC (and Nu latter) appears to be significant. While theoretically correct, however, it is not an accurate portrayal of the experimental results. The uncertainty arises largely from the fact that the small temperature differentials in the heat flux calculations are of the order of the thermocouple errors, as mentioned earlier. The standard deviation of the temperature data of multiple 84

runs for the same conditions was less than 0.24°C. Given these runs, done on different days, have this small a standard deviation suggests good experimental repeatability and that the calculated errors, while possible, were not realized.

The CHTCs for the bottom cluster are close to other values for natural CHTCs for air,50 however, the values from the top are considerably higher. When compared with the sealed flue mentioned above for which the average CHTC was 7.7 W/m2·°C for a trial when the plenum temperature was 90°C, the data from the top cluster become suspect.

Also, for the case under investigation, it is a safe assumption that most of the tubuli were in scenarios much like the lower cluster or the sealed top cluster and not to the open top cluster. For this reason, the data from the bottom cluster is accurate within the narrow confines of the initial question.

Furthermore, generally, it should be noted that the CHTCs do not vary as a function of plenum temperature. This is somewhat surprising as the expectation is for the

CHTC to increase somewhat as the air temperature and turbulence level rise. In fact, if anything, the CHTC peaks when the plenum temperature is 80°C.

4.5 Discussion

In order to compare these results to the studies mentioned in Section 2.2.2, it is necessary to compute the Nusselt number (Eq. 4.3):

50 For more data on natural convection, refer to Holman (2002). 85

In this equation, h is the CHTC, L is the characteristic length, and k is the thermal conductivity of the air at, in this case, the bulk temperature. For this particular setup, the best choice for the characteristic length is the height of one flue or 607mm. This is for a number of reasons. One, this arrangement is most similar to channel flow which uses height as the length scale. Two, since there are two clusters of thermocouples, each centred on a flue, it is the natural divisor in the system. Three, that distance allows the

Nusselt number to be typical of the flue. The other key comparator is the Rayleigh number (Eq. 4.4):

In this equation, g is the gravitational acceleration, β is the thermal expansion coefficient for air, Tw is the surface temperature, T∞ is the bulk temperature of the air, L is the characteristic length, ν is the kinematic viscosity of the air, and α is the thermal diffusivity of the air. All air properties were taken at the bulk temperature. Since, however, for this case the wall temperature is lower than the bulk temperature so the

Rayleigh number is negative. Another notable difference is the reference temperature for the calculation of the thermal properties. Unlike most studies, the driving force of this study is the air so the film temperature is not applicable. Therefore, the chosen datum temperature was the bulk temperature. Table 4.4 gives the Rayleigh and Nusselt numbers for the bottom cluster:

Table 4.4: Rayleigh and Nusselt Numbers for the Bottom Cluster Based on the Average CHTCs Plenum Temperature Rayleigh Number Nusselt Number 60°C -1.65×108 ± 3.1×107 154 ± 216 70°C -1.49×108 ± 3.0×107 146 ± 190 80°C -1.64×108 ± 2.8×107 162 ± 182 90°C -1.45×108 ± 2.7×107 142 ± 193 100°C -1.65×108 ± 2.5×107 130 ± 175

The first thing that becomes clear is that there is no relationship between the

Rayleigh and Nusselt numbers. This is most likely because the Rayleigh, or more specifically the Grashof,51 number is a comparative measure between buoyancy and viscous forces and, since the air is actually cooled by the walls, it does not capture the mechanics of this setup even though it is a natural convection system.

If one just looks at the Nusselt numbers, however, there are a few things to note.

The pattern of peaking at 80°C present in the CHTCs is more exaggerated here. These

Nusselt numbers are more than double the values in all but one of the cases mentioned in

Chapter 2, Section 2.2.2. Interestingly, the one case (the channel flow studied by Hatami and Bahadorinejad, 2008) that is higher is the closest comparison. When compared to these, the Nusselt numbers here are about half. This setup, which is approximately two millennia old in design, is, therefore, half way between the comparable modern equivalents which may be surprising. In essence, the system of terracotta pipes is not only incredibly effective for its age, it matches modern counterparts.

51 The Grashof number is the ratio between buoyancy and viscosity and defined as:

4.6 Conclusion

The goal of this chapter was to determine the convective heat transfer coefficient

(CHTC) for terracotta flues designed to replicate the heating system inside an ancient

Roman bath. The unique aspect about these experiments was that a heater warmed the air before being exposed to the faux wall and then the air rose through the flues, thereby warming the flue walls. The experiment tested five plenum temperatures (60°C, 70°C,

80°C, 90°C, 100°C) and the data showed that the CHTC was relatively insensitive to plenum temperature. The average CHTC was 7.0 W/m2·°C. Furthermore, there was no relationship established connecting the Nusselt number which ranged from 1.3×102 to

1.6×102 with the Rayleigh number which ranged from -1.7×108 to -1.5×108.

In the context of the entire dissertation, even though this chapter is about the thermodynamics of tubuli, the results will be pivotal for the transdisciplinary CFD studies in the forthcoming chapters. As mentioned earlier, the CHTC of the tubuli is necessary for an accurate simulation. However, it is important to note that the experiments done here only focused on one configuration of tubuli and that there are many more.

CHAPTER 5 — THE DESIGN OF CALDARIA, WINDOWS, AND DOORWAYS

AND ITS IMPACT ON HEAT FLOW

5.1 Introduction

Chapter 5 begins the CFD section of the dissertation with two 2-D case studies on

Imperial thermae— one on caldaria windows52 and the other on caldaria doorways.53

These are the two main perforations in the wall of the caldarium and, as will be shown, constitute the largest influence on the movement of heat. These will, in turn, further the presently incomplete understanding of the temperature distribution and heat flow in thermae and of the rationale behind key design features.

The first case study uses two-dimensional CFD analyses to explore the impact of the seasons. Seasonal changes play a very important, but often little discussed, role in the use of a bath, especially those in the northern provinces. In previous endeavors to address this issue, scholars have offered diverse theories in order to reconstruct the design of windows in the caldaria of the Imperial thermae (Thatcher, 1956; Ring, 1996); however, the seasonal uses of the baths have not been explicitly discussed.54 Both Thatcher and

Ring have started their investigations by suggesting that unglazed windows would make the room too cool in the winter, whereas glazed windows would make the room unbearably hot in the summer. Earlier research has looked to prove or disprove the former without investigating the latter, most likely, because the effects of glazing are

52 For convenience, I refer to the following definitions. A window is an opening in the wall that starts above the floor. A glazed window is a window with some type of semi-transparent material in the opening, whereas an unglazed window is one without this material and that is open to the atmosphere. 53 A doorway is an entrance to a room whereas a door is the barrier used to open or close a doorway. 54 For further discussion on these articles, see Section 2.2.1. 89

difficult to assess with the techniques available at the time. With the help of CFD, it is now possible to examine how glazing would have affected the caldarium in both winter and summer.

The second case study analyzes the under-examined doorway design. CFD can demonstrate that the design of caldaria doorways had an influence on the heating of air and heat flow inside the baths. These effects become more relevant depending on the results of the window composition. If, for instance, the windows were glazed, the doorways would be the only conduit for air moving in and out of a caldarium. Thus, the doorway design would dramatically affect the heat retention of the room and, therefore, the heat distribution in the bath as a whole.

Both of these topics tie into the overall heating of the baths. If the caldarium had glazed windows the bath would have contained the heat within, thus making it easier to maintain the hot atmosphere. Depending on how the doorways were configured, the hot air of the caldarium could have been used to help in the heating of the adjoining rooms or largely kept within the confines of the room. This difference affects the manner of heat distribution in the bath and thus the fuel requirement for each area.

5.2 Theory and Fact Based Simulations

The general application of CFD as seen in Section 2.1.1 raises an important point.

CFD tackles two distinct sets of problems, which are fact and theory based. Fact-based simulations are those where the investigator models a specific and well-defined scenario, for example, the simulation of an airplane during flight. These are primarily used to check the performance of an object without the expense of a physical experiment.

Theory-based simulations, on the other hand, are almost always done in academia and cannot be linked directly to a specific scenario. This generality is meant to help prove a hypothesis and allows the results to be applied to a wide range of circumstances. As such, the simulations presented in this paper are theory-based.

5.3 Case Study I: Caldaria Windows

5.3.1 Location and Design of Windows

In many baths, particularly the Imperial thermae, the number, size, and placement of windows are highly speculative, since most buildings survive only in foundations or low walls. Windows are primarily known from the existence of a raised sill, and when this is missing (or in a multistoried building), it is exceedingly difficult to determine how many existed, where they were, and their dimensions, all of which requires a great deal of guess work. Certainly the most significant heating criterion for windows is not their size

(in many caldaria they are enormous), but their covering. There are four possible scenarios: they were open, they were glazed, they had shutters only, or they were glazed and had shutters.

These four cases merit comment. First, regional discrepancies—both location and cultural—mean that Romans might have used all four variants in different capacities throughout the Empire. Second, it should be clear that a major problem with using only shutters is that they would severely reduce the positive impact of passive solar heating— heat coming directly from the sun—and thus make the orientation of the caldarium almost irrelevant. A large proportion of thermae, especially in Rome, faced southwest,

which is the optimal orientation for passive solar heating,55 so clearly solar heat must have played some role in the design of the buildings.56 It is true that shutters could be opened to allow for solar heating during the summer, but, as will be shown, even if the outside temperature were 20°C, without a barrier separating the hot room from the outside, the room would be about 20°C as well. This raises another problem with shutters, their size. In the Baths of Caracalla, the windows in the caldarium measured roughly 5m by 6m.57 Shutters on these would have enormous weight: a shutter

2.5x6x0.05m (WxHxT) made of an average wood could weigh as much as 375kg. As demonstrated by the colossal doors in the Pantheon, though, the Romans were capable of making shutters such as these easily moveable. Clearly, the inclusion of shutters adds another level of complexity and will require further investigation. Without shutters, two distinct possibilities remain: glazed and unglazed windows.

5.3.2 Evidence for Glazing in Caldaria Windows

Is there any proof, though, for glazing in bath complexes, particularly the Imperial thermae? There is no direct evidence pointing to this in Imperial thermae, for which there are two possible explanations. First, only one ancient author discusses the use of windows in the baths, and second, there is no complete caldarium among the Imperial thermae, meaning that glazing, if present in antiquity, has disappeared.

55 Vitruvius (De Arch. 5.10.1) states that the ideal orientation is southwest. 56 Based on measurements of the thermae in Rome (taken from plan drawings), only the Baths of Diocletian, oriented at approximately 130 degrees from north, was not facing between southwest and due south. Outside Rome, this pattern becomes less definite, with only thirty-five percent of baths oriented between southwest and south. 57 These are based on DeLaine’s recreation drawings (1997) and the reconstruction in Chapter 3. 92

The one literary commentary comes from Seneca the Younger when he makes a passing reference to what could be glazing in Letter 86. While comparing baths in Scipio

Africanus’ time (ca. two centuries earlier than his own), Seneca states that his baths are less rustic because his caldaria are designed with “latis specularibus” (Ep. 86.11). The word specularia is mentioned seven other times in Latin literature—none of which have any connection to baths—and appears to have varied meaning but generally implying a mica pane or glass.58 Vitruvius makes no reference to glass in his discussion of bath construction in Book 5 of De Architectura. It must be remembered, though, that Vitruvius was writing before the age of the large Imperial thermae, during the late 1st century

BCE,59 when, perhaps, as in Scipio’s age, builders did not implement glazing. In short, the ancient authors provide no definite answers on whether the caldaria of Imperial thermae were glazed or not.

The archaeological remains provide no conclusive indication of whether or not the caldaria of Imperial thermae had glazing60. In Rome, no glass or frames (the physical evidence that indicates the presence of glazed windows) were found at any of the

Imperial thermae, but this absence could reflect the poor state of preservation of the caldaria of these thermae. The two most complete thermae in Rome demonstrate this discrepancy. First, much of the caldarium of the Baths of Caracalla survives only to half

58 Refer to Appendix 1 for more details. 59 Although the Thermae Agrippae existed during Vitruvius’ time, its layout is highly speculative, especially when discussing the caldarium. However, even from the limited evidence available–namely, the Forma Urbis representation (Yegül 1995, 134) –it is clear that the Thermae Agrippae were radically different from the later Imperial thermae of Rome. 60 For more information on glazing, refer back to Section 2.2.3. 93

a metre in height and, second, nothing remains of the caldarium of the Baths of

Diocletian (298-305/6 CE).61

5.3.3 CFD Model of Caldaria Windows

The chosen methodology was to create two 2-D simulations—one that included an open window and one that included a glazed window—using a CFD package, ANSYS

FLUENT v13. These are generic and simplistic representations and do not simulate any particular building. In order to ensure a high degree of accuracy from the perspective of fluid dynamics, the models of the windows are in section view.62 In both scenarios

(Figure 5.4), the bottom wall of the caldarium—shown with the dashed line—represents the suspensura and the left wall, also in the dashed line, represents the tubuli. Both have a convective boundary condition: meaning that the program models them as a fluid moving past the wall.63 The roof was also convective.64 The two protrusions on the right side of the caldarium represent the physical wall of the room while the rectangle in the middle represents the separator between the upper and lower windows. The walls between the outside and the caldarium are incorporated into the simulation as solid pieces and do not need boundary conditions. The remaining walls, including the ground outside, are set as

61 Yegul 1995, 163-169. The Piazza della Repubblica covers much of where the ancient caldarium once stood. 62 There are two mains reasons behind using the section view. First, it allows for buoyancy effects. Second, in section, the simulation minimizes the harsher, more direct, impact of the wind. 63 There are two key inputs for a convective boundary: the fluid gas temperature and the convective heat transfer coefficient or CHTC. I took the fluid gas temperature from Yegül and Couch’s article (2003) on a replica bath that they built. I chose a mid-range value of 70°C. The CHTC is a relative measure of the amount of heat that the fluid gives to (or takes away from) the wall. The calculated value for the CHTC for the tubuli is 7 W/m2·°C (see Ch. 4). 64 The CHTC is 4 W/m2·°C (a standard natural CHTC; Holman, 2002) and the fluid gas temperature is the same as the outside air temperature. 94

insulating: that is, no heat was permitted to flow through them. A vast open area was created on the right of the test room to simulate the outside. The reason this region is so large is to reduce the effects of the wind and to make the model more realistic. As shown

65 in Figure 5.1a, the simulation discharges air at a specified temperature, T0, into the right of the system at 4.5m/s or 16.2km/h—a gentle breeze—and allows it to exit at the top and at the left of the open region. There is also a special heat source representing the sun, with temperature Ts, which also varies with the season. The sun is modeled as a blackbody. 66 In Figure 5.1b, which illustrates the glazed window, the only addition made was a semi-transparent wall to separate the open region and the caldarium. For a more complete description of the setup, refer to Appendix 5A.

65 This temperature will be varied to match the conditions in summer and winter. The reason for this is because the glazing argument is two pronged. One aspect is that, in winter, without glass, the caldarium would be too cold while the other is that in summer, with glass, the caldarium would be too hot. 66 A blackbody heat source emits radiation perfectly and obeys Planck’s Law (Holman, 2002). Radiation is, in essence, rays of energy. It does not affect the temperature of the air because air can only absorb a small fraction of this energy. Instead, radiation heats the surfaces it impacts which in turn heat the air. 95

Figure 5.1: Layout for the window case study: (a) open; (b) glazed.

5.3.4 The CFD Results

5.3.4.1 Summer State

In this case, T0 is 35°C (the air temperature on an hot summer day in the

Mediterranean), Ts is 87°C (to reproduce the average summer solar intensity for Rome’s latitude according to the ASHRAE, 1997).

The results are intriguing. Without glass, the room temperature varies between

35°C and 40°C (Fig. 5.2) whereas with glazing, the temperatures range from 55°C to

60°C (Fig. 5.3), so it is clear that the glazing contains the heat. However, the one issue to consider is the difference in convergence time, that is, the time for the temperature to stabilize. Figure 5.4 shows that, for the open case, this is about 1800 seconds or half an hour, but for the closed case, the temperature is still climbing after five hours. This 96

assumes that everything (hypocaust temperature, solar radiation, wind speed and temperature, etc.) remains constant during the five hours, which is unrealistic. This is because, for example, five hours is almost half of the entire daylight period, sunrise to sunset, but, in this model, the sun does not move and is shining into the window for five hours straight. It would be realistic, though, that these factors could remain relatively constant for one hour. After one hour of time, the temperature distribution ranges from

45°C to 50°C (Fig. 5.5). This might seem low, and it is, but if the hypocaust was started in the morning or if it ran twenty-four hours, by the late afternoon the temperature could have reached 55°C in the summer. It is interesting to note though that the difference between the glazed and unglazed cases at the extremes is 5°C. Whether or not this extra five degrees would have made the caldarium intolerable to ancient Romans is speculative. The modern sauna is over 70°C (Johnson and Miller, 1977) while the modern Turkish bath can reach 60°C (Goksugur et al. 2006).

Figure 5.2: Temperature distribution for the open summer case (Units: °C).

Figure 5.3: Temperature distribution for the glazed summer case (Units: °C).

Figure 5.4: Temperature versus time of all four window cases.

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Figure 5.5: Temperature distribution for the glazed summer case after one hour (Units: °C).

The actual temperatures of the rooms aside, the distributions are also quite telling.

In both cases, the distributions are fairly uniform, with the top and bottom of the caldarium differing by only six or seven degrees. The key point is, however, that the difference is related to height. The hottest air is near the roof, as shown by Figure 5.6.67

This effect has not been incorporated into previous analyses because with the techniques

67 Note that the scale is different for this figure. 101

used by Ring and Thatcher this would have been exceedingly difficult and time consuming. With CFD, however, this level of detail is inherent and provides a further example of the benefit of this type of analysis.

Figure 5.6: Magnified temperature distribution for the summer glazed case after one hour (Units: °C).

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5.3.4.2 Winter State

In this case, T0 is 10°C (the air temperature on a cold winter day in the

68 Mediterranean), Ts is 107°C (to reproduce the average winter solar intensity for Rome’s latitude according to the ASHRAE, 1997), and the hypocaust floor and wall is 42°C.

Without glass, the temperature distribution is between 10°C and 15°C (Fig. 5.7).

This is rather cool and, considering that the outside temperature is 10°C, the hypocausts appear to have little effect. Furthermore, the warm temperatures are near the roof. Down where the bathers are, it is between 10°C and 11°C. With glazing, on the other hand, the temperature of the room ranges from 50°C to 60°C (Fig. 5.8). However, as above, the average temperature is still climbing after five hours which, again, is an unrealistic timeframe (see Fig. 5.4). After an hour, the temperature distribution is between 35°C and

50°C (Fig. 5.9). As with the glazed summer case, depending on whether the hypocaust started in the morning or ran all the time, the temperature could have surpassed this by the late afternoon and reached 45°C, which is considerable.

68 In winter, because the sun is lower in the sky, there is more radiation, thus giving the higher temperature. 103

Figure 5.7: Temperature distribution for the open winter case (Units: °C).

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Figure 5.8: Temperature distribution for the glazed winter case (Units: °C).

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Figure 5.9: Temperature distribution for the glazed winter case after one hour (Units: °C).

In the distributions in the room with the open window, the temperature gradients form ripples starting from the window and proceeding to the left wall, whereas in the glazed case the gradients form horizontal bands going from bottom to top. The bathing space is somewhat cooler than near the roof in both winter scenarios because hot air rises.

While this may seem obvious, it may help explain how the Romans managed the temperature inside the caldarium with glazed windows. If there is a high ceiling, the hottest air will tend to rise to the top, leaving the cooler air at the bottom. While this

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would be a detriment in the winter because the hot air would be near the roof and would not benefit the bathers, it would keep the temperature at floor level bearable in the summer.

These results prove that without glass the caldarium would have been too cold to serve its purpose as a hot room in the winter, and with glass the caldarium would not have been unbearable in the summer. Interestingly, in both seasons, without glass, the temperature is only slightly warmer than the ambient temperature so if it is 20°C outside, it would be a maximum 25°C inside. The models used here, however, are simplistic in nature. There are a number of aspects that are omitted, including, but not limited to, the movement of the sun, the intermittent nature of the wind, the absence of people, and doorways. To incorporate these changes would have made the models very complicated and their effects require further investigation. The design of the doorway, though, will have the greatest influence of these three aforementioned factors on the amount of the heat that can be retained in a glazed room.

5.4 Case Study II: Caldaria Doorways

5.4.1 The Design of Caldaria Doorways

In the design of a caldarium, the number and style of doorways are very important elements because they connect the caldarium to the other rooms in the thermae and thus are the main passages for people. Also, based on the results from the windows study, doorways were almost certainly the only opening for air circulation. Therefore, doorways become a key design feature when dealing with the movement of heat in and out of the caldaria.

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Archaeological plans generally show details of doorways at ground level.

Doorway heights are often unknown due to the poor state of preservation of the buildings. It is logical that the size of a doorway influences the flow of heat from one room to another, but the design of the opening is significant too. There are three basic kinds of doorway in thermae in Rome: a clear (and relatively narrow) passage from one room to another, a passage marked off by a row of columns, or a passage divided by a pier.69 In the Baths of Caracalla, an example of a single passage is the doorway between the caldarium and Room 22E; of a pier-divided passage the doorway between the caldarium and main tepidarium; of the colonnaded passage, the doorway between the

14W and frigidarium. Colonnaded passageways are prevalent in most Imperial thermae in Rome but none that scholars currently know about were doorways to the caldaria.70

Furthermore, the doorways are narrow considering the size of the room. Why is this? By the time thermae became popular, the Greco-Roman construction techniques were well tested and so it seems unlikely that the narrow doorways were necessary for structural integrity. This leaves contemporary social reasons and the impact of doorway design on heat flow. The latter is the focus of this study. Could the Roman architects and engineers have realized this influence?

69 This delineation was determined by the author after looking at the floor plans of the thermae in Rome. 70 Palladio (1732) indicates that there were columns in the Baths of Titus (dedicated in 80 CE) but Caruso (1989-90) and Caruso et al. (1988-89; 1990) have challenged the accuracy of the plan and suggested that the building Palladio drew was of a much later date. 108

5.4.2 The CFD Model of the Caldarium Doorways

Like the analysis of the windows, the models presented here do not describe actual bath designs but rather generalized doorways. Unlike the study of windows, though, a plan view of these models will better represent the doorway designs. Also, unlike the previous examination, seasonality will not be considered because the doorway modeled connects two interior rooms (the caldarium and tepidarium) and does not have any direct contact with the outside air. In both cases, the opening is the same at 8m but the actual doorways are different sizes, similar to the arrangements found in the remaining thermae. The columns are 0.88m in diameter and the spacing is 3.25m on centre. In the design with the pier, the two doorways are 2.5m, making the pier itself 3m wide. Both are an indeterminate height above the floor, however, since the heat escaping is of interest, the assumption of the plane being in the top half of the doorway is safe. For the Baths of Caracalla, this would be from 2m to 3.95m above the floor. On the caldarium side of both doorways, the air comes in at a low velocity of 0.1m/s and on the tepidarium side there was a pressure outlet, or a type of neutral boundary, allowing for the expulsion of air. The incoming air is at 42°C and the air in the tepidarium is at 25°C.

Further details are in Appendix 5B.

5.4.3 The CFD Results

The results prove that the design of the doorway dramatically affected the flow of heat out of the caldarium. Colonnaded doorways allow for easy air and heat flow between the rooms (Figure 5.10). A pier (Figure 5.11), in contrast, acts as a buffer between the two rooms, minimizing heat and air flow in the same way as two separate

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doorways. The reason for this difference lies in the fact that a pier greatly restricts the air flow. The principle is similar to the slow, single-file entry of spectators to a theatre or stadium. The square edges of the pier also inhibit the flow of air between the two rooms.

This phenomenon is slightly more difficult to explain, but square edges create more turbulence than round columns and decelerate the flow.

Figure 5.10: Temperature distribution for a colonnaded doorway (Units: °C).

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Figure 5.11: Temperature distribution for a doorway with a pier (Units: °C).

Based on these results, one can suggest that the Romans did have an understanding, however simple, of the fact that by using piered doorways, the caldarium would retain its heat better than if they used columns.71 This may be why doorway design in thermae changed in Rome between the Baths of Nero (dedicated in 62 CE; Yegül,

1995) and the Baths of Trajan (104-109 CE; Yegül, 1995). The Baths of Nero have one

71 It is possible that narrower doorways also aided in fire prevention and containment as these would slow fire much like the heat. However, unlike heat, the spread of fire is dependent on the decoration and revetments covering the walls and floor so it is possible that these narrower doors might have encouraged fire by providing more fuel. 111

rather large unobstructed opening, ca. four metres wide, on the north side of the caldarium (Yegül, 1995; Nielsen, 1993). The Baths of Trajan, on the other hand, have a passageway with a pier creating two small doorways on the north side of its caldarium and two single doorways on the northeast and northwest corners of the caldarium. This design remained relatively unchanged in the later thermae such the Baths of Caracalla, of

Diocletian, and of Constantine (ca 315 CE; Yegül, 1995).

There are two final observations about doorways. First, in both single passages and passages with a dividing pier it is possible to install actual doors;72 whereas in colonnaded passages such a measure is not practicable. A door would allow for maximum heat retention, since when the door is closed almost no air is permitted to escape. Second, the doorways in most Imperial thermae in Rome are extremely narrow.

The four doorways of the caldarium in the Baths of Caracalla, for example, do not exceed three metres across. This narrow width also inhibits the movement of heat as smaller doorways allow less air to move through. The doorway design, then, was chosen partly for structural reasons, but also in consideration of whether the principal room would be used to heat adjacent spaces.

5.5 Conclusions

All of the observations on the windows, firstly, confirm Ring’s original conclusion that unglazed windows would not have been suitable for use in the caldarium.

72 While there is no direct evidence for doors in the caldaria of the thermae of Rome, the size of the doorways are much smaller than that of places, like the Pantheon, which are known to have had bronze doors in their openings. I am not suggesting that there were doors in caldaria doorways but, merely that there could have been. 112

Secondly, they also show that, with glazing, the caldarium would not have been unbearable in the summer. Thirdly, the unglazed results demonstrate that the temperature inside the caldarium would have been dependent on the season. This can be generalized further, with caution, to the atmosphere inside the baths. Without glazing or a hypocaust, the unheated portion of the bath would, in all probability, have been very susceptible to the effects of the changing seasons; however, more specific statements would require further research. As mentioned previously, though, even the examples given here do not paint the entire picture, since they are presented in two dimensions and there may be phenomena that become apparent only in three dimensions.

The CFD models of the different doorway types reveal the importance of their design in terms of heat flow. They indicate that the Roman designers may have realized the problem with colonnaded doorways in caldaria and may explain the change from the open passageways in the Baths of Nero to the piered passageways in the Baths of Trajan.

They also suggest that the air inside the caldarium was not used to heat other rooms but instead was retained for maximum heat preservation.

Finally, and most importantly, both case studies demonstrate the viability of CFD for applications in classical archaeology. While not meant to replace either literary or physical evidence, CFD can help understand the rationale behind certain phenomena in the absence of sufficient conventional evidence. Many more avenues can be explored with CFD, even within the brief period in Roman history when thermae were popular.

Overall, Chapter 5 introduces CFD as a transdisciplinary tool and serves as a catalyst for the more in-depth studies of NOVA and the Baths of Caracalla. Many of the phenomena seen here, like stratification, are also present in the 3-D simulations.

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Interestingly, however, the Baths of Caracalla do not demonstrate the same temperature ranges that are in the 2-D simulations. This could be for a number of reasons: most notably the addition of the third dimension.

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5.6 Appendix 5A

Table 5.1: The Grid Details for the Window Case Study Maximum x Dimension 100m Maximum y Dimension 100m Maximum Caldarium x Dimension 35m Maximum Caldarium y Dimension 25m Number of Cells 179461 Number of Nodes 180685

Table 5.2: The Basic Operating Parameters for the Window Case Study Solver Pressure-based Solver Gradient Option Green-Gauss Cell-Based Time Dependency 1st Order Implicit Unsteady Turbulence Model RNG k-ε with Full Buoyancy Effects Radiation Model Discrete Ordinates Type Incompressible Ideal Gas Density R 286.9 J/kg.K Pressure-Velocity Coupling SIMPLE Pressure Body-Force-Weighted Momentum First Order Upwind Turbulent Kinetic Energy Second Order Upwind Discretization Turbulent Dissipation Second Order Upwind Method Rate Energy First Order Upwind Discrete Ordinates First Order Upwind

The boundary conditions are as in the paper. The radiation temperature was determined using the following equation (5.1):

Q T  4  T 4 s  0

In the above equation, Q is the solar irradiation as given in the ASHRAE Applications

Handbook Section 34 (1997), σ is the Stefan-Boltzmann constant, and T0 is the temperature outside temperature.

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5.7 Appendix 5B

Table 5.3: The Grid Details for the Doorway Case Study Maximum x Dimension 10m Maximum y Dimension 10m Maximum Caldarium x Dimension 10m Maximum Caldarium y Dimension 4.5m Number of Cells in Column Version 6905 Number of Nodes in Column Version 6526 Number of Cells in Pier Version 6080 Number of Nodes in Pier Version 6288

Table 5.4: The Basic Operating Parameters for the Doorway Case Study Solver Pressure-based Solver Gradient Option Green-Gauss Cell-Based Time Dependency 1st Order Implicit Unsteady Turbulence Model RNG k-ε Density Constant Pressure-Velocity Coupling SIMPLE Pressure Standard Momentum First Order Upwind Discretization Turbulent Kinetic Energy Second Order Upwind Method Turbulent Dissipation Second Order Upwind Rate Energy First Order Upwind

All walls are set as insulating. The sides of the rooms are pressure outlets. For the caldarium, the backflow temperature is 42°C and for the tepidarium, it is 25°C. This is to eliminate the influence of the room walls.

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CHAPTER 6 — PRELIMINARY CFD ANALYSES

6.1 Introduction

This chapter describes the choices of the sub-models and the results from changing these in the NOVA bath simulation. These sub-models include, but are not limited to, the modelling of turbulence and the calculation73 of the physical properties.74

While not a sub-model, an influential aspect of the solver is the dependency on time.

Each of these can have dramatic impacts on the accuracy of the final solution and different combinations can have unanticipated results. The computer model may converge but give physically erroneous results. The data provided by experimenting with the sub-models will give a basic skeletal model of the NOVA baths which future, more in-depth simulations—including the subsequent NOVA baths and the Baths of

Caracalla—can use.

6.2 Methodology

6.2.1 Meshing the NOVA Bath Air Volume

The ideal mesh is a structured mesh, that is, one that is created from regular hexahedral (six-sided) or rectangular elements. The nodes in a structured mesh are less random in their placement, which reduces the computational intensity required. An unstructured mesh, on the other hand, consists of mainly tetrahedral (four-sided) elements. This type of mesh is much easier to create and adapt to complex geometry. The

73 That is, whether they are constant or dependent on a parameter, such as temperature. 74 For example, density or thermal conductivity. 117

trade-off is that the solution becomes more dependent on the element size and shape, requiring increased computational time. The complex geometry of the air volume, specifically the barrel vault and windows, made an unstructured mesh the best choice for the preliminary simulations of the NOVA bath. The final result (Fig. 6.1) was a mesh with 1976183 cells and no cells above 80% skewness.75

Figure 6.1: The final unstructured mesh.

75 Skewness is a measure of how contorted an cell is with respect to its native shape. The native shape of a tetrahedral element is a three-sided pyramid with its apex directly above the center of its base. If, for example, the apex was outside of its base, the cell is skewed and how far it is outside is its skewness. 118

6.2.2 Configuring the Model

The procedure, then, is to start with an initial setup, change sub-models, and examine the results. Thus, there are two categories of sub-models: those that do not alter between cases76—the base configurations—and those that do: the case-specific changes.

The major base configurations are the solver settings77 and discretization methods.78

Since the model will not deal with supersonic flow, the pressure-based solver was the best option. As mentioned in the introduction, the cases in this chapter test the time dependency of the simulation. For the unstructured mesh here, the Green-Gauss node- based gradient evaluation was optimal but, for the structural meshes later, the Green-

Gauss cell-based gives a computational advantage. For the cases in this and subsequent chapters, the discretization methods in Table 6.1 remained the same.

Table 6.1: Discretization Methods Quantity Method Pressure Interpolation Body-force-weighted Momentum Second Order Upwind Turbulence First Order Upwind Energy Second Order Upwind Pressure-Velocity Coupling SIMPLE

76 Cases are variations of the initial model.

77 There are two major solver settings: the basis of the solver and the time dependency. The solver can either be pressure-based or density-based: low-speed compressible flows use the former while high-speed compressible flows use the latter. For time dependency, the solver can be either steady state (disregarding temporal information) or unsteady (varies with time). 78 Discretization is essentially the mathematical approach of how the program solves the approximation equations describing the flow of air, the temperature distribution, etc. 119

The cases in this chapter did not employ species79 or multiphase80 models and the solar load function represented the radiation from the sun.

All of the physical properties of the air, with the exception of density, were kept constant; that is, they were not dependent on an aspect of the flow, such as temperature.

The other properties of concern are those of the walls and pool. The walls were a mixture of concrete, marble, and terracotta, but the selection in the standard FLUENT database of solid materials was minimal. Therefore, for the initial cases here, using dolomite to mimic the wall material was a reasonable, albeit crude, assumption because dolomite has similar insulating properties as the actual materials. The windows, however, used glass supplied in the FLUENT tutorial (Fluent, Inc.). Because the initial models did not include the liquid water of the pool, a solid with the properties of water was an apt substitute. All properties of all solid materials were kept constant.

6.2.3 The Boundary Conditions

The only face that was not a solid wall was the doorway to the tepidarium which was a pressure outlet. The major concern with the boundary conditions was thermal, that is, what was the heat input at the walls. In FLUENT, there are four useful types of thermal boundary conditions: constant temperature, heat flux, convective, and mixed convective and radiation.

79 Species modelling is a way of incorporating multiple fluids of the same phase (i.e. gas or liquid).

80 Multiphase modelling is a way of incorporating multiple fluids of different phases.

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There are six sections of wall, or zones, which require attention: windows, external walls, heated walls, heated floor, walls connected to the tepidarium, the pool interface, and walls connected to nothing. The walls connected to nothing are small sections which if drilled through one would either hit the air volume or the earth. The chosen alternative was to give these a zero heat flux (insulating) condition and specify as dolomite. The remaining boundary conditions are in Table 6.2.

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Table 6.2: The Boundary Conditions for the Caldarium Wall Sections External Heated Heated Tepidarium Pool Property Glazing Wall Floor Wall Wall Interface Constant Type Mixed Mixed Convective Convective Convective Temperature Material Glass Dolomite Dolomite Dolomite Dolomite Water Thickness 0.01m 0.40m 0.20m 0.06m 0.40m 0.50m Heat Transfer 4 W/m2.°C 4 W/m2.°C 2 W/m2.°C 2 W/m2.°C 4 W/m2.°C -- Coefficient Free Stream 15°C 15°C 60°C 60°C 27°C -- Temperature External 0.49 0.91 ------Emissivity Radiation -273.15°C 50°C ------Temperature Surface ------42°C Temperature

The convective three zones require specification of the convective heat transfer coefficient (CHTC) as defined in Chapter 5. For the tepidarium wall, the most suitable estimate was 4W/m2·°C (Holman, 2002). For the heated walls and floor, the preliminary estimate was 2 W/m2·°C.

6.3 Results and Discussion

As mentioned above, the aspects that changed between cases were the time dependency, the density model, the turbulence model, and whether or not species modelling was employed. Table 6.3 provides an overview of the setup for each case.

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Table 6.3: The Case Setup Time Case Density Model Turbulence Model Dependency Boussinesq #6.1 Steady State RNG k-ε with viscous heating Approximation81 #6.2 Unsteady Incompressible Ideal Gas RNG k-ε with viscous heating #6.3 Unsteady Incompressible Ideal Gas RNG k-ε without viscous heating #6.4 Unsteady Incompressible Ideal Gas SST k-ω without viscous heating #6.5 Unsteady Incompressible Ideal Gas SST k-ω with viscous heating

Case #6.1 followed the FLUENT HVAC tutorial (Fluent, Inc.). In Case #6.2, after observing that the pressure changed only minimally, the better choice density model was the incompressible ideal gas because it is more accurate than the Boussinesq approximation.82 Also, to help convergence of the buoyancy-driven flow, the unsteady solver83 was more appropriate. Case #6.3 checked the effect of viscous heating: heating due to friction. Cases #6.4 and #6.5 tested the impact of changing the turbulence model to

SST k-ω without and with viscous heating.

81 The Boussinesq approximation is a simple linear function. It is only valid for natural convection problems that involve small temperature changes. It essentially uses a known density and temperature to extrapolate densities for other temperatures. The formula is:

In this, ρ0 is the reference density, T0 is the reference temperature, and β is the thermal expansion 3 -1 coefficient. In this simulationρ0 was 1.18kg/m , T0 was 25C, and β was 0.00335K . 82 Ibid. 83 There is one puzzling aspect about the unsteady formulation. It assumes that the walls and floors have reached their maximum output already at time zero. In essence, it would be like taking all of the air out of the room, allowing the hypocaust to run for a long time, putting the air back into the room, and then starting the calculation. This is opposed to the real scenario of allowing the hypocaust and the room to heat up at the same time. For a more accurate assessment, the alternative is to input the unsteady CHTC and time- dependent flue gas temperature: both of which are extremely difficult to determine. 123

Displaying meaningful results from a 3-D model is somewhat difficult as there are only two possibilities: flat slices—the chosen methodology—or iso-surfaces.84 The problem with slices is they may miss data but the mid-planes of both the x- and z- directions capture the major features of the NOVA baths.85 For a diagram showing the placement of the two planes (x-mid-plane and z-mid-plane) within the volume, refer to

Figure 6.2.

Figure 6.2: Placement of the display planes.

84 Iso-surfaces are surfaces on which a variable (velocity, temperature, pressure, etc.) does not change. The problem with iso-surfaces is that their shapes can be quite confusing depending on the complexity of them, leaving the reader trying to decipher it. 85 These are the hypocausted walls, the hypocausted floor, the windows, the pool, and the doorway to the tepidarium. 124

The temperature distribution of Case #6.1 (Figs. 6.3-6.4) shows thermal stratification that is what is anticipated when dealing with buoyancy-driven flows, as there is no external input to stir the flow. The stratification, however, disappears as the air gets closer to both the walls and floor as shown by both figures. The influence of the tubuli height and the tepidarium on the caldarium is considerable since the bulk of the stratification takes place where the patrons would be. Having said this, however, the temperature within the occupied space is still quite warm, between 25C and 30C. The x-mid-plane temperature distribution (Fig 6.3) has three interesting features: the cool region by the window in the top left corner, the cool protrusions near the left wall, and the absence of stratification above the height of the tubuli. Since glass is not a good insulator the former is logical while the latter are evidence of the convective currents that drive the air because the cooler air is rising, thus creating these protrusions. The z-mid- plane temperature distribution (Fig. 6.4) illustrates the same protrusions; however, it is apparent which walls are not heated by the absence of the warmer region near the right walls.

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Figure 6.3: Temperature distribution in the x-mid-plane for Case #6.1 (Units: °C).

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Figure 6.4: Temperature distribution in the z-mid-plane for Case #6.1 (Units: °C).

The general velocity profiles (Fig. 6.5-6.6) are as expected: air coming in the bottom of the doorway and leaving at the top and a circular convective current above the pool. There are, however, a few interesting currents. One is the cool air from next to the window coming down and exiting out the top of the doorway in Figure 6.5. In comparison with the surrounding velocity, this current is quite fast, making it almost draft-like. The other unique aspect is how far and fast the air from the tepidarium comes in to the caldarium without dissipating. The air entering nearly reaches the far wall with

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almost no loss in speed. This dramatically influences the dynamics of the room because with this speed the air introduces more cold temperatures than a slower flow would, hence the cooler temperatures near the floor.

Figure 6.5: Velocity vectors in the x-mid-plane for Case #6.1 (Units: m/s).

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Figure 6.6: Velocity vectors in the z-mid-plane for Case #6.1 (Units: m/s).

What is immediately apparent from Figures 6.7 and 6.8 is the difference in temperature between Case #6.2 and the previous one. The stratification is still present, but the temperature goes from 30ºC to 35ºC. Interestingly, a warm region near the window replaced the previously cool area (Fig. 6.7). The reason for this is that for the simulations in this chapter the application of the solar load was only to the closest cells to the window and not to the adjacent cells. Broadening the solar load out reduces the probability of getting anomalously high wall temperatures (Fluent, Inc.). Plus, the grid

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next to the windows is relatively coarse. The simulations in subsequent chapters corrected these errors.

Figure 6.7: Temperature distribution in the x-mid-plane for Case #6.2 (Units: °C).

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Figure 6.8: Temperature distribution in the z-mid-plane for Case #6.2 (Units: °C).

As expected the velocities (Figs. 6.9-6.10) are low, with the highest velocity coming from the bottom of the tepidarium doorway as air rushes in. What is intriguing, though, are the differences between these profiles and the ones from Case #6.1. Unlike the previous one, the air from the tepidarium comes in at the top of the door and exits abruptly out the bottom of the doorway (Fig. 6.9). Furthermore, in comparison with the velocities of the rest of the volume, this circulation path has a high velocity. This flow pattern, by its nature, limits the amount of cold air that enters the room thereby keeping

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the room warmer. Fortunately, the addition of the humidity in the next chapter negates this flow and causes the flow to revert to as it was in Case #6.1.

Figure 6.9: Velocity vectors in the x-mid-plane for Case #6.2 (Units: m/s).

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Figure 6.10: Velocity vectors in the z-mid-plane for Case #6.2 (Units: m/s).

The results from Case #6.3 are not very different from Case #6.2 (Figs. 6.11-

6.14), which proves that viscous heating has little effect on the overall flow. The 35°C interface is higher than with the viscous heating, however, the change is minimal. There is no noticeable difference in any of the velocity profiles.

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Figure 6.11: Temperature distribution in the x-mid-plane for Case #6.3 (Units: °C).

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Figure 6.12: Temperature distribution in the z-mid-plane for Case #6.3 (Units: °C).

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Figure 6.13: Velocity vectors in the x-mid-plane for Case #6.3 (Units: m/s).

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Figure 6.14: Velocity vectors in the z-mid-plane for Case #6.3 (Units: m/s).

The temperature distribution of Case #6.4 (Figs. 6.15-6.16) is not appreciably different from Case #6.3. With the SST k-ω, the room is somewhat cooler as the 35°C break is slightly lower and the air from the tepidarium encroaches a little further. The difference in the height of the 35°C break is clearer on the z-mid-plane (Figs. 6.12 and

6.16). The velocity profiles (Figs. 6.17-6.18) are remarkably similar between the Cases

#6.4 and #6.3 with the only major difference being that the current going from the bottom of the doorway to the top is wider and is deeper. These results are unexpected because the

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SST k-ω turbulence model supposedly has superior blending between near-wall and far field areas when compared to the RNG k-ε model, the assumption being that the heat from the hypocaust would have heated a larger volume of air. Overall, though, the difference is small, which means that the turbulence model does not affect the results.

The results in Chapter 8 echo this.

Figure 6.15: Temperature distribution in the x-mid-plane for Case #6.4 (Units: °C).

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Figure 6.16: Temperature distribution in the z-mid-plane for Case #6.4 (Units: °C).

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Figure 6.17: Velocity vectors in the x-mid-plane for Case #6.4 (Units: m/s).

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Figure 6.18: Velocity vectors in the z-mid-plane for Case #6.4 (Units: m/s).

The comparison between Cases #6.4 and #6.5 (Figs. 6.19-6.22) is very similar to that of between Cases #6.2 and #6.3 with the differences being analogous. The difference between Cases #6.4 and #6.5 is, however, much smaller than between Cases #6.2 and

#6.3, which indicates that viscous heating plays even less of a role in the SST k-ω model than it did in the RNG k-ε model. The variation between the x-mid-plane temperature profiles (Figs. 6.16 and 6.20) is not noticeable. The deviation in the other two profiles is visible only by the enlarged 25ºC to 30ºC region. Like Case #6.3 in comparison with

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Case #6.2, the velocity profiles (Figs. 6.20-6.21) do not diverge noticeably from Case

#6.4.

Figure 6.19: Temperature distribution in the x-mid-plane for Case #6.5 (Units: °C).

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Figure 6.20: Temperature distribution in the z-mid-plane for Case #6.5 (Units: °C).

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Figure 6.21: Velocity vectors in the x-mid-plane for Case #6.5 (Units: m/s).

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Figure 6.22: Velocity vectors in the z-mid-plane for Case #6.5 (Units: m/s).

Cases #6.2-#6.5 have two peculiar traits that are absent from Case #6.1. First are the velocity profiles near the doorway (e.g. Fig. 6.9). In the latter cases, the air comes in at the top of the door to the tepidarium and almost immediately rises and exits out the bottom. In Case #6.1 (Fig. 6.5), the air comes in at the bottom and moves across the floor to the opposite wall and, quite separately, the air exits out the top. This is more like what is expected for the scenario presented. Second, the temperature distribution next to the

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window (e.g. Fig. 6.7) shows a decidedly hot region, which is due to the solar load calculator as explained above.

Between Cases #6.1 and #6.2, the density model and the time dependency changed. Since both the RNG k-ε and SST k-ω models demonstrate the above two traits, this proves that the turbulence model is not a factor, which in turn means that the cause has to be either the density model or the time dependency. Table 6.4 gives the subsequent trial cases.

Table 6.4: Case Setup, Part 2 Time Case Density Model Turbulence Model Dependency Boussinesq #6.6 Unsteady RNG k-ε with viscous heating Approximation #6.7 Steady State Incompressible Ideal Gas RNG k-ε with viscous heating #6.8 Unsteady Ideal Gas RNG k-ε without viscous heating Boussinesq #6.9 Steady State RNG k-ε with viscous heating Approximation

The Boussineq approximation in Case #6.6 uses the same reference values as

Case #6.1. Here the velocity profile has reverted to that of Case #6.1 (Fig. 6.24), but the temperature distribution (Fig. 6.23) shows the same warm region near the windows as later cases, though not to the same extent. This means that while the time dependency does not affect the velocity profiles, it does affect the temperature, at least in part.

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Figure 6.23: Temperature distribution in the x-mid-plane for Case #6.6 (Units: °C).

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Figure 6.24: Velocity vectors in the x-mid-plane for Case #6.6 (Units: m/s).

Case #6.7 confirmed that the incompressible ideal gas density model was the reason for the dramatic shift in the velocity profile (Fig. 6.26) and a compounding reason for the temperature (Fig. 6.25) change around the window, as both show the same patterns as Case #6.2. If the incompressible ideal gas creates false results, this presents a problem because, in order to do species modelling (i.e. incorporating humidity), the

FLUENT code does not allow the use of the Boussinesq approximation for density. This is why Case #6.8 tests the results of the remaining density model: the ideal gas.

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Figure 6.25: Temperature distribution in the x-mid-plane for Case #6.7 (Units: °C).

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Figure 6.26: Velocity vectors in the x-mid-plane for Case #6.7 (Units: m/s).

With the ideal gas model, the results of Case #6.8 (Figs. 6.27-6.28) have a similar velocity profile as in Case #6.2 and thus a comparable temperature distribution. Because the higher order density models agree and the Boussinesq method is an approximation, this means that these apparent aberrations are the simulated characteristics of the flow regime within the caldarium of the NOVA baths at this time.

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Figure 6.27: Temperature distribution in the x-mid-plane for Case #6.8 (Units: °C).

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Figure 6.28: Velocity vectors in the x-mid-plane for Case #6.8 (Units: m/s).

It is clear that the Boussinesq approximation gave different results from the more accurate density models but is there a way to reconcile these variations. In Cases #6.1 and

#6.6, the reference data was below the average temperature of the fluid. This means that

FLUENT was extrapolating only from one side and the further away the calculation takes place from the reference point, the weaker the approximation. For Case #6.9, ρ0 was

3 -1 1.12kg/m , T0 was 32C, and β was 0.00335K . The results (Figs. 6.29-6.30) are interesting because like Cases #6.2-#6.5 and #6.7-#6.8, the air from the tepidarium comes

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in at the top of the door and leaves from the bottom. Unlike these cases but similar to

Cases #6.1 and #6.6, though, some of the air breaks and flows further into the caldarium.

Consequently, the temperature distribution is a mixture of these two very distinct scenarios. These results prove, however, that the reference data have a significant influence on the accuracy of the Boussinesq approximation—at least when dealing with this air volume—and thereby nullifying its applicability here.

Figure 6.29: Temperature distribution in the x-mid-plane for Case #6.9 (Units: °C).

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Figure 6.30: Velocity vectors in the x-mid-plane for Case #6.9 (Units: m/s).

6.4 Conclusions

The preliminary simulations of the NOVA baths in this chapter compared the options for the sub-models of time-dependency, turbulence, and density. It is clear from the data that the simulation was invariant with respect to time-dependency; however, the time-dependent results were more computationally efficient. The results of the turbulence models of RNG k-ε and SST k-ω had minimal differences and, thus, the simulation can use them interchangeably. Further, the viscous heating did not affect the results. The

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higher order density models—incompressible ideal gas and ideal gas—had a similar relationship as the two turbulence models but since the former is less computationally intensive, this is the preferred choice. However, there was a dramatic difference between the Boussinesq approximation and incompressible ideal gas. The results using the

Boussinesq approximation were substantially cooler because the air from the tepidarium entered at the bottom of the door and came much further into the room. Using the more accurate incompressible ideal gas, the air from the tepidarium comes in at the top and immediately leaves at the bottom. For the subsequent chapters, therefore, the most appropriate combination is time-dependent, incompressible ideal gas, and either turbulence model.

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CHAPTER 7 — ENHANCING THE NOVA MODEL86

7.1 Introduction

This chapter builds a more complete thermal simulation of the caldarium of the

NOVA baths. It begins by briefly reviewing the skeletal model from Chapter 6. The next step is to enhance the model with the addition of the pool and humidity, and the adjustment of the convective heat transfer coefficient (CHTC) to the experimentally- determined value of Chapter 4. Finally, the chapter tests how the addition of a surface-to- surface radiation model affects the results. The average temperature is 35°C; however, the hottest air is trapped in the high vault leaving the region inhabited by the patrons significantly cooler than the average. The data suggest a relative insensitivity to changes in the convective heat transfer coefficient and addition of humidity or radiation simulation to the model.

7.2 Methodology

7.2.1 Grid

The initial mesh was the same unstructured mesh that the simulations in Chapter

6: 1976183 cells with no cells above 80% skewness. Prior to including the effects of the heated pool, the development of a structured mesh was necessary. To ensure continuity, the chosen path was to compare results from a structured mesh without the pool with the results from the unstructured mesh. After establishing congruency between the results

86 A version of this chapter has been submitted to Energy and Buildings under the title “A Computational Investigation of a Radiantly Heated Room – A Case Study of a Replica Roman Bath.” 156

from the two mesh types, it was rational to perform a grid refinement test with different cell sizes (100mm, 50mm, 37.5mm, and 25mm with a corresponding change in the total number of cells). A cell size of 37.5mm attained grid independence with minor fluctuations near the window. Therefore, the final structured mesh used 37.5mm cells with 10mm cells near the window and had 990143 cells without the pool and 1164501 cells with the pool (Fig. 7.1).

Figure 7.1: The structured grid of the caldarium with the pool.

7.2.2 Sub-Models

Again, these simulations used the CFD package FLUENT 6.3/ANSYS FLUENT

13.0. As mentioned in Chapter 6, the important sub-models are: time-dependency, density, turbulence, multi-phase, and species. The cases here were time-dependent

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because this stabilized the multi-phase calculations. As stated in Chapter 6, the incompressible ideal gas law density model accommodated humidity whereas the

Boussinesq approximation did not. Finally, the difference between the RNG k-ε and SST k-ω was small but the simulations here use the SST k-ω method due to its slightly warmer results.

The new sub-models in this chapter are for multi-phase and species: essential for the addition of humidity. Only the implicit volume of fluid (VOF) and the “Transport &

Reaction” models were applicable for multi-phase and species simulation, respectively.

All other multi-phase and species models did not meet the minimum requirements.

However, the difficult part is modeling the evaporation of the water from the pool to the air. A user-defined function (UDF)87 accomplished this. The UDF first identifies the interface between the two phases where the evaporation is taking place through an area function and then calculates the mass transfer rate on this interface. The final case also included FLUENT’s surface-to-surface88 (S2S) radiation model.

7.2.3 Boundary Conditions

The boundary conditions have not changed much from Chapter 6; however, with the addition of the pool, there are two new zones: the water inlet to the pool and the water outlet. Table 7.1 summarizes the conditions for the walls.

87 A user-defined function is essentially a piece of code written to perform a certain task much like a macro in Excel. 88 Much like the radiation model used in Chapter 5, the S2S model simulates the heat transferred specifically between surfaces by electromagnetic radiation. Unlike the DO model in Chapter 5, though, the S2S model is simpler and essentially uses the geometry to triangulate where the heat goes. 158

Table 7.1: The Boundary Conditions for the Wall Sections External Connecting Property Glazing Heated Floor Heated Wall Wall Wall Type Mixed Mixed Convective Convective Convective Material Glass Custom Custom Custom Custom Thickness 0.005 m 0.40 m 0.20 m 0.06 m 0.40 m Convective Heat See Table See Table 4 W/m2·°C 4 W/m2·°C 4 W/m2·°C Transfer 7.2 7.2 Coefficient Free Stream 15°C 15°C 90°C 90°C 27°C Temperature External 0.49 0.94 ------Emissivity External Radiation -273.15°C 50°C ------Temperature

Like before, the heated walls were convective and Yegül and Couch’s readings

(2003) gave the free stream temperature. The heated surfaces used the maximum recorded flue gas temperature. The initial cases in this chapter used the estimate of

2W/m2·°C from Chapter 6, however, the penultimate simulation utilized the experimentally determined value of 7 W/m2·°C from Chapter 4. The free stream temperatures for all other surfaces came from the data in Yegül and Couch (2003) and the external radiation temperature came from the FLUENT tutorial (Fluent, Inc.). The emissivity for the glass came from the FLUENT tutorial (Fluent, Inc.) on HVAC testing and the entry for rough concrete on the Engineering Toolbox website (2012) supplied the emissivity for the external wall.

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The water inlets and outlets are uncomplicated. The water comes in at 40°C and an arbitrary low velocity of 0.1 m/s and the backflow temperature of the outlet is 39°C.

This is a common temperature for many hot tub tests (Harvey et al., 1981).

7.3 Results and Discussion

Table 7.2 designates the three important cases that demonstrate the progression of the simulation. As in Chapter 6, the mid-planes of both the x- and z-directions display the temperature distributions and velocity vectors. These slices capture the major features of the NOVA bath—the hypocausted walls, the hypocausted floor, the windows, the pool, and the doorway to the adjoining room—and represent the three Cartesian directions.

Table 7.2: Case Breakdown Heated Time- Multi- Wall Radiation Case Turbulence Species Dependency Phase CHTC Model (W/m2·°C) #7.1 Unsteady SST k-ω N/A N/A 2 N/A (#6.4) #7.2 Unsteady SST k-ω VOF S&T 2 N/A #7.3 Unsteady SST k-ω VOF S&T 7 N/A #7.4 Unsteady SST k-ω VOF S&T 7 S2S

Case #7.1 is the base case for this chapter and provides the basis of comparison for the subsequent cases. It is the same as Case #6.4 of Chapter 6 but is represented here to eliminate any potential confusion. Case #7.2 presents the addition of the pool and humidity and, thus, multi-phase and species modeling, respectively. Case #7.3 changes the CHTC of the heated walls from the preliminary estimate to the experimentally- determined value of Chapter 4. Finally, Case #7.4 adds the S2S radiation model.

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Figures 7.2-7.5 show the temperature distribution and velocity vector profile of

Case #7.1. Overall, the temperature ranges from 27C to 38C and the velocity magnitudes are low with most of the room being largely stagnant. From a comfort perspective, the stratification has a drawback. It means that the region occupied by the patrons (i.e., the volume of air below the height of the door or 1.88m) is only between

30C and 35C, which is only slightly warmer than the tepidarium. Therefore, while the average temperature of the room might be 30C, much of the heat from the hypocaust is lost to the vault.

Figure 7.2: Temperature distribution in the x-mid-plane for Case #7.1 (Units: °C).

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Figure 7.3: Temperature distribution in the z-mid-plane for Case #7.1 (Units: °C).

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Figure 7.4: Velocity vectors in the x-mid-plane for Case #7.1 (Units: m/s).

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Figure 7.5: Velocity vectors in the z-mid-plane for Case #7.1 (Units: m/s).

The other significant factor seen from both the temperature and velocity vector profiles is the doorway. The cooler air from the tepidarium creates an envelope which acts as a barrier. The flow pattern is unique and, as mentioned in Chapter 6, almost counter-intuitive because it is coming in the top and leaving the bottom. Moving away from the doorway, there is a thin film of warm air above the floor and next to the heated walls showing the effect of these surfaces. The pool stand-in does not appear to have

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much impact on the overall temperature distribution but there is a draft coming off the surface which indicates that it is perturbing the flow.

With the addition of humidity and the pool the flow pattern changes dramatically as seen in Figures 7.6-7.9. It all, however, stems from the reversal of the doorway flow.

In Case #7.1, the air from the tepidarium came in from the top and exited out the bottom thereby limiting the effect of its cooler nature. In Case #7.2, though, the air enters at the bottom and exits at the top, which means the cooler air comes into the room further. This flow reversal completely changes the environment within the room. The entire room is colder, particularly the occupied region, and the velocities are higher in the room. This pattern though is more likely than the one from Case #7.1 because of the more accurate modeling. The heating system has the same effect: it creates an updraft and a layer of warm air next to the walls.

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Figure 7.6: Temperature distribution in the x-mid-plane for Case #7.2 (Units: °C).

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Figure 7.7: Temperature distribution in the z-mid-plane for Case #7.2 (Units: °C).

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Figure 7.8: Velocity vectors in the x-mid-plane for Case #7.2 (Units: m/s).

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Figure 7.9: Velocity vectors in the z-mid-plane for Case #7.2 (Units: m/s).

There are two new smaller drafts in Case #7.2. One from the windows, which is due to an adjustment in the solar load calculator. As mentioned in Chapter 6, inadvertently, Case #7.1 did not include a feature that spread the solar heating to adjacent cells. Without this feature enabled, the solar heat would create unrealistic hot spots. Case

#7.2 corrected this oversight. The more significant draft is the one originating from the pool. In Case #7.1, the stand-in for the pool did not affect the flow regime greatly, but the addition of the water warmed the alcove by 10C and impeded the flow of cool air from

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the tepidarium. However, the temperature effects of the pool remains localized to the alcove, further showing the influence of the doorway.

The humidity profile in Figure 7.10 illustrates the effect of the pool well. There is a definite stream of water vapour rising from the water/air interface with the vapour culminating at the apex of the alcove vault before dispersing into the room. The humidity itself does not have a noticeable effect on the room temperature. This is not surprising since the room is dominated by the tepidarium door boundary condition which means most of the room is at the tepidarium humidity.

Figure 7.10: Water vapour distribution in the z-mid-plane for Case #7.2 (Units: kg of water vapour/kg of dry air). 170

The only change with Case #7.3 was that the convective heat transfer coefficient

(CHTC) of the heated walls was raised from the early estimate of 2 W/m2·°C to the experimentally derived value of 7 W/m2·°C. The results (Figs. 7.11-7.15) illustrate the resulting changes. A comparison of Figures 7.7 and 7.11 illustrates an increase in temperature along the heated wall from the 30-35°C to the 35-40°C, indicating that the increased CHTC is generating more heat. There is a similar trend with the z-mid-plane temperature distribution (Fig. 7.12). The cooling effect of the air coming in from the tepidarium is significantly reduced. These changes result in the room being generally warmer with the experimentally derived CHTC. However, the temperature has not increased significantly in proportion to the increase in the CHTC. The value of the CHTC increased 350% but the volume-averaged temperature in the room only increased 2°C

(32.8°C to 34.8°C), which is less than seven percent. This suggests that while the CHTC of the heated walls is a drives the simulation the temperature distribution in the room is relatively insensitive to changes in CHTC. In fact, the heat from the heated walls only increases by between 139% and 189% with an average of 168% as seen in the Table 7.3:

Table 7.3: Comparison of Heat Fluxes Calculated by FLUENT Case #7.2 Input Heat Case #7.3 Input Heat Zone % Increase (W) (W) Tubuli next to 51.1 96.6 189.0 Doorway North Tubuli 460.7 787.4 170.9 NE Tubuli 149.9 253.6 169.2 SE Tubuli 170.7 283.3 166.0 W Tubuli 535.6 934.0 174.4 Top of Tubuli 70.2 97.6 139.0 Average 168.1

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Part of this decreased response to CHTC is possibly due to the insulating nature of the wall material. Because of its lower thermal conductivity, a ceramic wall such as this requires more heat to make a set temperature increase than a metallic or modern composite wall. This could be by design as a safety feature, but is more likely an inherent benefit of the materials available to Romans. With 90°C exhaust gases only 6 cm from the surface of the wall, someone leaning against it could be seriously burned without this type of wall.

Figure 7.11: Temperature distribution in the x-mid-plane for Case #7.3 (Units: °C).

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Figure 7.12: Temperature distribution in the z-mid-plane for Case #7.3 (Units: °C).

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Figure 7.13: Velocity vectors in the x-mid-plane for Case #7.3 (Units: m/s).

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Figure 7.14: Velocity vectors in the z-mid-plane for Case #7.3 (Units: m/s).

The velocity vector profiles are very similar. The velocities in Case #7.3 are slightly lower than the other cases. However, this is only a marginal change. The main currents are almost identical in the two cases.

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Figure 7.15: Water vapour distribution in the z-mid-plane for Case #7.3 (Units: kg of water vapour/kg of dry air).

The water vapour reaches a higher concentration in the corner of the alcove above the pool in the humidity distribution in Case #7.3 (Fig. 7.15). It does not reach as far into the main room. This change is due to the minor alteration in the air current above the pool.

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Figure 7.16: Temperature distribution in the x-mid-plane for Case #7.4 (Units: °C).

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Figure 7.17: Temperature distribution in the z-mid-plane for Case #7.4 (Units: °C).

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Figure 7.18: Velocity vectors in the x-mid-plane for Case #7.4 (Units: m/s).

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Figure 7.19: Velocity vectors in the z-mid-plane for Case #7.4 (Units: m/s).

The addition of the radiation model in Case #7.4 (Figs. 7.16-7.19) does not affect the results significantly, especially in the occupied region. The average temperature by volume only differs by approximately 0.1°C (34.8°C for Case #7.3 versus 34.7°C for

Case #7.4). The flow patterns are similar with the only important change at the top of the vault where the temperature breaches the next temperature contour. Based on these data, the change resulting from addition of radiation model is negligible.

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Case #7.3 appears to compare well to the data from Yegül and Couch (2003). The average temperature of the caldarium given is 35°C and the volume-averaged temperature from the computational model is 34.8°C. However, one potential limitation of the simulation is that it used the maximum temperature Yegul and Couch listed for the exhaust gases. The estimation of the doorway to the tepidarium is the most likely cause.

In these cases above, the door is an outlet with a constant temperature of 27°C based on the tepidarium temperature reported by Yegül and Couch. In actuality, the temperature across the length of the two rooms will vary since there is no wall separating them. The exchange between these two rooms should be gradual. In fact, Yegül states that he designed the baths so that the caldarium would heat, at least partially, the tepidarium.

Chapter 8 assesses the accuracy of the doorway boundary condition. Nonetheless these three case studies still illustrate the effectiveness of the heating system as well as the impact, or lack thereof, of the addition of humidity.

7.4 Conclusions

This chapter has emphasized that without the constant influx of new air though ventilation, stratification becomes prominent and any opening in the envelope of the room becomes extremely important to the air circulation patterns. The addition of the multi-phase and species modeling reversed the flow from the doorway to the tepidarium.

In Case #7.2, the air from the tepidarium cools the occupied region considerably, almost negating the heating system. The difference between a wall with the same thermal properties as water and a simulated pool is remarkable. The pool had a much greater impact on the flow by creating a draft of warmer air. Interestingly, however, the CHTC of

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the heated walls and floor has little impact on the overall temperature. The volume- averaged temperature rose by 2°C even though the CHTC increased by three hundred and fifty percent from 2W/m2·°C to 7W/m2·°C. The addition of the S2S radiation model did not change the results appreciably, particularly in the occupied region where the temperature distributions are near identical. In the broader scope of the dissertation, this chapter investigated how three enhancements impacted the skeletal model of Chapter 6.

The data suggest that the supplement of humidity does not affect the overall temperature distribution by a noticeable margin. This is purely a quantitative measure though and does not take into account the perception of the patron. The results again underscore the importance of the doorway as stated in Chapter 5.

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CHAPTER 8 — MODELLING NOVA WITH THE TEPIDARIUM

8.1 Introduction

This continuation of research of Chapter 7 creates a more complete model of the thermal environment of the NOVA baths. In the previous simulations, the temperature distribution of the caldarium was dominated by the flow coming in from the tepidarium through a combination pressure inlet/pressure outlet boundary condition. This chapter investigates the accuracy of the doorway boundary condition and of the resulting thermal environment by including the tepidarium in the simulation. The advantage of including the tepidarium is that between it and the next room, the frigidarium, there was a wooden door which provides a definite boundary condition.

8.2 Brief Review of Previous Results

The previous chapter considered only the caldarium and had a mixed pressure inlet/outlet for the doorway to the next room called the tepidarium. This boundary condition produced a significant draft, which dominated both the temperature and velocity profile as shown by Figs 8.1-8.4. As a result, the region occupied by the patrons was considerably cooler than the air in the vault. Furthermore, the velocities at the doorway were much higher than the rest of the room. Both of these factors indicated that the boundary condition needs further investigation.

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Figure 8.1: Temperature distribution in the x-mid-plane for Case #7.3 (Units: °C).

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Figure 8.2: Temperature distribution in the z-mid-plane for Case #7.3 (Units: °C).

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Figure 8.3: Velocity vectors in the x-mid-plane for Case #7.3 (Units: m/s).

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Figure 8.4: Velocity vectors in the z-mid-plane for Case #7.3 (Units: m/s).

8.3 Changes to this Model

The major modification was to include the tepidarium in the simulation, as mentioned earlier, to test the aptness of the doorway boundary condition. The tepidarium measures 3.2m by 1.8m with tubuli on the west wall and three small windows on the east.

There is a wooden door in the north wall leading to the frigidarium. For the purposes of this simulation the assumption that this door makes a perfect air-tight seal and it behaves as a wall was necessary. This is acceptable since the amount of air entering the

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tepidarium is very small and will not affect the caldarium, the room of interest. The addition of the tepidarium allowed testing of the effect of adding a cloth door between the caldarium and tepidarium as seen in the television special (Linde and Linde, 2000).

This gave rise to three separate test cases: a clear doorway, a doorway completely blocked by a cloth, and a doorway mostly blocked by cloth but with gaps above and below. This chapter considers these test cases in turn.

8.3.1 Grid

The grid contained structured 37.5mm cells with 10mm cells near the window.

For the runs with the cloth, a 1 mm slice was cut into the doorway and this was meshed with 0.1mm cells. The final structured mesh had 1729903 cells without the cloth,

1755553 cells with the cloth, and 1755553 cells with the partial cloth.

8.3.2 Sub-Models

Like before, the investigation of the thermal environment used the CFD package

ANSYS FLUENT 13. Most of the sub-models were unchanged from the previous chapter: the incompressible ideal gas law for the air density, the implicit volume of fluid

(VOF) multi-phase method for the pool water, the ‘species-transport’ for the water vapour content in the air. A user-defined function (UDF) managed the interaction between these two, namely the evaporation and creation of humidity. The UDF first identifies the interface between the two phases where the evaporation is taking place through an area function and then calculates the mass transfer rate on this interface.

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Based on technical advice89 which stated that the renormalized group (RNG) k-ε model is better suited the multi-phase model than the shear-stress transport (SST) k-ω dictated a switch of turbulence models.

Setting up the properties for the cloth door was the intricate aspect. While it could be modelled as a solid wall, like a true door, all fabric has some degree of permeability, which is critical for a study on velocity currents. Therefore, the best choice was to model the region as porous. Using Ogulata’s study (2006) on woven fabrics, an estimate of the void fraction was obtained which then led to values for porosity and the inertial and viscous resistance coefficients.90 Table 8.1 tabulates the values.

Table 8.1: Porous Zone Values Void Fraction 0.0922 Viscous Resistance Coefficient (m-2) 2.456E+12 Inertial Resistance Coefficient (m-1) 1.598E+07 Porosity 0.0845

8.3.3 Boundary Conditions

Table 8.2 reviews the boundary conditions for the caldarium. The tepidarium has key zones: the exterior walls, the window glass, the heated floor, the heated walls, the

89 The original impetus for this switch came from a forum post (Xarvarin, 2008) but the survey of turbulence models in Ramponi and Blocken (2012) corroborated this even though Ramponi and Blocken themselves disagreed. 90 Though not exactly accurate, the chosen option was to model the fabric as a packed bed like a sand substrate. Under this assumption, the void fraction of the material is the volumetric percentage of the fabric that is open. The formula for the viscous resistance coefficient is essentially a measure of how the porous material affects the shear forces of the fluid and its formula is:

The formula for the inertial resistance coefficient is essentially a measure of how the porous material affects the inertia of the fluid and its formula is:

Porosity is a measure of how much air space there is in the fabric and its formula is:

In the above formulae, Dt is the thread diameter and ϵ is the void fraction. 189

wall connecting to the caldarium, the wall connecting to the frigidarium, and the door to the frigidarium. Most of these are the same as the caldarium boundary conditions but

Table 8.3 summarizes those unique to the tepidarium.

Table 8.2: The Boundary Conditions for the Caldarium Wall Sections External Tepidarium Property Glazing Heated Floor Heated Wall Wall Wall Type Mixed Mixed Convective Convective Convective Material Glass Custom Custom Custom Custom Thickness 0.005 m 0.40 m 0.20 m 0.06 m 0.40 m Heat Transfer 4 W/m2.°C 4 W/m2.°C 7 W/m2.°C 7 W/m2.°C 4 W/m2.°C Coefficient Free Stream 15°C 15°C 90°C 90°C 27°C Temperature External 0.49 0.91 ------Emissivity Radiation -273.15°C 50°C ------Temperature

Table 8.3: The Boundary Conditions for the Tepidarium Wall Sections Property Frigidarium Door Frigidarium Wall Caldarium Wall Type Convective Convective Convective Material Wood Custom Custom Thickness 0.05 m 0.40 m 0.40 m Heat Transfer 4 W/m2.°C 4 W/m2.°C 4 W/m2.°C Coefficient Free Stream 21°C 21°C 35°C Temperature

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8.4 Results and Discussion

As in the previous chapter, only two slices of the caldarium were chosen to display the temperature distributions and velocity vector profiles: the mid-planes of both the x- and z-directions. These slices were chosen because they capture the major features of the NOVA bath: the hypocausted walls, the hypocausted floor, the windows, the pool, and the doorway to the tepidarium. Table 8.4 shows the tested scenarios.

Table 8.4: Case Summary Doorway Floor Gas Wall Gas Turbulence Simulation Case Type Temperature Temperature Model Time #8.1 Open 90°C 90°C RNG k-ε 3600s #8.2 Full Cloth 90°C 90°C RNG k-ε 3600s #8.3 Partial Cloth 90°C 90°C RNG k-ε 3600s #8.4 Full Cloth 80°C 60°C RNG k-ε 3600s #8.5 Full Cloth 60°C 60°C RNG k-ε 3600s #8.6 Full Cloth 60°C 60°C SST k-ω 3600s #8.7 Full Cloth 60°C 60°C RNG k-ε 10800s

With the addition of the tepidarium in Case #8.1, the flow regime changes dramatically as shown by Figs 8.5-8.8. The first thing that is immediately apparent is the increase in temperature in comparison to Figures 8.1 and 8.2. Without the influence of the 27°C breeze, the temperature increases by 10°C, however, it is intriguing to note that the basic distribution is the same in the x-mid-plane. The distribution in the z-mid-plane has changed substantially because the influence of the tepidarium has disappeared. It now looks very similar to the x-mid-plane with the pronounced stratification.

The velocity profiles (Figs 8.7-8.8), though, displayed the most change when compared to Figures 8.3 and 8.4. The surges of air coming into and going out of the room present in Case 7.3 have subsided tremendously. These have been replaced with weaker

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currents. This means, however, that the exchange between the two rooms is still valid which makes sense because Yegül says he designed the caldarium to partially heat the tepidarium. The path of the air current leaving the caldarium is interesting because it is almost like a funnel in that the hotter air is squeezing through a narrow region at the top of the doorway. This would seem to indicate a degree of low pressure as, once inside the tepidarium, the air goes almost directly up and does not linger at that level. On the bottom, the current is reversed, however, unlike Case 7.3, the incoming air is much slower and less of a draft. In fact, most of the air in the doorway is stagnant. The only major difference in the z-mid-plane velocity profile is that the draft off the pool has vanished although this can be attributed to the fact that the air is roughly the same temperature as the water so the impact of the pool is lessened significantly.

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Figure 8.5: Temperature distribution in the x-mid-plane for Case #8.1 (Units: °C).

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Figure 8.6: Temperature distribution in the z-mid-plane for Case #8.1 (Units: °C).

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Figure 8.7: Velocity vectors in the x-mid-plane for Case #8.1 (Units: m/s).

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Figure 8.8: Velocity vectors in the z-mid-plane for Case #8.1 (Units: m/s).

The results from Case #8.2 with the addition of the full cloth door are shown in

Figs 8.9-8.12. There is a definite break in the temperature distribution in the x-mid-plane and the caldarium is about 5°C warmer than the case with the open doorway. This increase is readily apparent in the z-mid-plane temperature distribution where the pool at

~40°C is actually cooler than the air above it. This also means, though thin, the full cloth door retains more heat in the caldarium than the open doorway. The retention might not be surprising but what is surprising is the tepidarium is warmer which means the full

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cloth door makes both rooms hotter. The reason for this can be seen in the x-mid-plane velocity profile. Instead of passing unhindered through the doorway, the hot air partially rebounds thereby making the caldarium warmer while the air that does pass through the door is hotter which makes the tepidarium warmer.

Figure 8.9: Temperature distribution in the x-mid-plane for Case #8.2 (Units: °C).

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Figure 8.10: Temperature distribution in the z-mid-plane for Case #8.2 (Units: °C).

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Figure 8.11: Velocity vectors in the x-mid-plane for Case #8.2 (Units: m/s).

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Figure 8.12: Velocity vectors in the x-mid-plane for Case #8.2 (Units: m/s).

Somewhat surprisingly the difference between the partial cloth door results (Case

#8.3; Figs 8.13-8.16) and full cloth door is minimal. There are only minor variations in the x- and z-mid-plane temperature distributions. Even the velocity profiles, excluding the draft from the window in the partial cloth door case which is cyclical in nature, are nearly the same. The only measurable difference is at the bottom of the doorway in the x- mid-plane where, in the partial cloth door case, there is no break in the draft coming in

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from the tepidarium. All together, though, these results show that gaps in the top and bottom of the doorway do not affect the results in a discernible way and are insignificant.

Figure 8.13: Temperature distribution in the x-mid-plane for Case #8.3 (Units: °C).

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Figure 8.14: Temperature distribution in the z-mid-plane for Case #8.3 (Units: °C).

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Figure 8.15: Velocity vectors in the x-mid-plane for Case #8.3 (Units: m/s).

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Figure 8.16: Velocity vectors in the z-mid-plane for Case #8.3 (Units: m/s).

It is evident that with the addition of the tepidarium the temperature increases dramatically. In fact, it goes well above the recorded temperature. The most obvious computational remedy for this inaccuracy is to reduce the heat input by decreasing the flue gas temperature. The previous runs used the maximum flue gas temperature recorded by Couch (Yegül and Couch, 2003). Consequently for Case #8.4 the first option was to reduce the tubuli flue gas to the average and slightly decrease the floor flue gas temperature. The results (Figs 8.17-8.20) demonstrate a dramatic shift in the thermal

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environment. The temperature drops two full contour levels and the room becomes more uniform. The velocity vectors, however, remain the same which means the change in the flue temperature only affects the temperature profiles.

Figure 8.17: Temperature distribution in the x-mid-plane for Case #8.4 (Units: °C).

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Figure 8.18: Temperature distribution in the z-mid-plane for Case #8.4 (Units: °C).

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Figure 8.19: Velocity vectors in the x-mid-plane for Case #8.4 (Units: m/s).

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Figure 8.20: Velocity vectors in the z-mid-plane for Case #8.4 (Units: m/s).

The results from decreasing the floor flue gas temperatures (Case #8.5; Figs 8.21-

8.24) show the importance of the floor. Without the higher floor temperature, the cooler region that was beginning to form in Case #8.4 has grown substantially and now covers the bottom of both rooms. However, interestingly, the velocity vectors are the same which implies that the temperature changes are small enough not to influence the fluid properties.

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Figure 8.21: Temperature distribution in the x-mid-plane for Case #8.5 (Units: °C).

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Figure 8.22: Temperature distribution in the z-mid-plane for Case #8.5 (Units: °C).

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Figure 8.23: Velocity vectors in the x-mid-plane for Case #8.5 (Units: m/s).

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Figure 8.24: Velocity vectors in the z-mid-plane for Case #8.5 (Units: m/s).

Switching turbulence models (Case #8.6; Figs 8.25-8.28) reduces the temperature more which is peculiar because without the tepidarium, the SST k-ω turbulence generated slightly warmer results. The difference between the two turbulence methods arises because with the SST k-ω method, the pool and humidity has a much greater effect as seen by comparing Fig 8.26 to Fig 8.22. Given the limited size of the pool and the results from without the tepidarium, the decision to adopt the RNG k-ε method seems validated. Despite the change in the temperature profiles, the velocity vectors do not

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which again displays the invariability of the overall flow pattern with respect to the temperature of the room.

Figure 8.25: Temperature distribution in the x-mid-plane for Case #8.6 (Units: °C).

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Figure 8.26: Temperature distribution in the z-mid-plane for Case #8.6 (Units: °C).

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Figure 8.27: Velocity vectors in the x-mid-plane for Case #8.6 (Units: m/s).

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Figure 8.28: Velocity vectors in the z-mid-plane for Case #8.6 (Units: m/s).

The results from Case #8.7 (Figs 8.29-8.32) show that, after two more hours of simulated time, the temperature stratification in the caldarium has disappeared. The uniformity illustrates the final effect of a radiantly heated room without air recirculation which is a saturation of heat. This staleness means that the cooler air from the window has a more pronounced effect as seen in Fig 8.29 but particularly in the velocity vectors

Fig 8.31. The window draft in turn creates flow in the vault not present in the earlier time.

Interestingly, the z-mid-plane velocity vectors (Fig 8.32) do not change appreciably. The

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circular pattern in the vault has developed and now goes across the entire span which is not surprising considering that one wall is heated while the other is not.

Figure 8.29: Temperature distribution in the x-mid-plane for Case #8.7 (Units: °C).

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Figure 8.30: Temperature distribution in the z-mid-plane for Case #8.7 (Units: °C).

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Figure 8.31: Velocity vectors in the x-mid-plane for Case #8.7 (Units: m/s).

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Figure 8.32: Velocity vectors in the z-mid-plane for Case #8.7 (Units: m/s).

The addition of the tepidarium dramatically affected the thermal environment inside the caldarium. The two drafts that were present at the doorway of the original model, though they did not disappear, decreased in magnitude. Since these dominated both the temperature profiles and velocity vectors by bringing ‘cold’ air into the room, with the tepidarium, the caldarium is much hotter. In fact, using the maximum flue gas temperature as in the original simulation produced an average air temperature that exceeded the temperature that Yegül and Couch measured by 14°C. The best option was

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to reduce the flue gas temperature to the average recorded by Couch which reduced the average temperature 9°C. However, like the results from increasing in the convective heat transfer coefficient (CHTC) in the previous simulation, the resulting change from decreasing the flue gas temperature was decisively less than the drop in the flue gas temperature. This shows the effect of using materials with a low thermal conductivity but medium heat capacity in the wall construction. Equally as interesting, though, was the fact that the velocity vectors remained nearly constant when the flue gas temperature changed. This indicates that the general flow structure is stable and does not depend greatly on the air temperature.

The most intriguing part of these simulations was the effect of the introduction of the cloth door. Even though it is narrow and breathable, the cloth door turned back a large proportion of the air that escaped the caldarium without it. The result is that the caldarium is 6.4°C warmer with the cloth than without. In addition, there is a new draft created near the floor from the ‘reflected’ air. Interestingly, the gaps at the top and bottom with the partial cloth door do not affect either the temperature profile or velocity vectors appreciably. In fact, the partial cloth door results are marginally hotter (0.2°C).

Comparing the final result from Case #8.7 to the measured temperature in Yegül and Couch (2003) shows that the simulation, even with the lowered flue gas temperature, is still 6°C hotter. This means that the simulation still is awry. From the data collected by

Couch, there is one aspect that is missing from the present model. They recorded a large amount of variability in the flue gas temperature, both spatially and temporally. The lowest value was 21.6°C while the highest was 96.3°C. This randomness means that, unlike this simulation where the input heat is always constant, the real building had hot

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and cool spots in the heating system that move around throughout its operation. While it might be possible to mimic this varying heat flux with an UDF, the computational requirements for this would be high even for a relatively small volume such as the

NOVA baths and it would still not accurately represent the data. What is left, however, is the idealized scenario if the heat was constant which shows us the threshold for the hypocaust heating system in the NOVA baths.

8.5 Conclusions

In this study, to test the aptness of the previous doorway boundary condition, the sound option was to add a second room to an existing computational fluid dynamic model of a room of a modern replica of an ancient Roman bath. The effect is dramatic as the cooling draft from the tepidarium dissipated greatly with an open doorway and all but disappeared with the cloth and partial cloth doors separating the two rooms. This means that the caldarium is hotter, rising from an average temperature of 35°C to a maximum of

49.4°C with the partial cloth door. Realizing that this was much too high, the rational choice was to reduce the flue gas temperature by 30°C to the approximate average recorded value. Surprisingly, however, the average air temperature only decreased by

9°C, from 49°C to 40°C, which again shows the unique response of the hypocaust to change. All of this emphasizes the importance of the doorway, as the main interchange of air, to the thermal environment of a purely radiantly heated room. This study adds to the methodological starting point for future studies on Roman baths established in Chapters 6 and 7 and reemphasizes the importance of doorways as per Chapter 5. Finally, the results suggest that the sensorial transition between rooms of a bath was gradual but also

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depended on the door separating the rooms. With a cloth door, the temperature gradient was greater than the open case but still not highly perceptible.

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CHAPTER 9 — SIMULATING THE CALDARIUM OF THE BATHS OF

CARACALLA

9.1 Introduction

This chapter explores the results from the CFD model of the caldarium of the

Baths of Caracalla. As shown in Chapter 2, the Baths of Caracalla cover 2.4ha or nearly five hundred times the size of the NOVA baths in Chapter 6. The area of the caldarium of the Baths of Caracalla is approximately 1100m2 and its volume is 45000m3: both of which are substantially larger than the NOVA baths. To get an idea of the difference in scale, Figure 9.1 shows the two buildings next to one another and Figure 9.2, the air volumes. In words, the caldarium of the Baths of Caracalla is over a thousand times larger than the NOVA bath’s. The other major difference is the proportion of the Baths of

Caracalla that is windowed. In the NOVA bath, the windows are small and relatively insignificant to the overall thermal environment. In the Baths of Caracalla, on the other hand, the windows take up nearly half of the outer wall area. This means that while the hypocaust drove the temperature in the NOVA, the hypocaust here will only be one of the heat inputs: the other being the large amount of solar radiation.

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Figure 9.1: Comparing the NOVA baths to the Baths of Caracalla. (Model created by Taylor Oetelaar.)

Figure 9.2: Comparing caldarium air volume of the NOVA baths to one of the Baths of Caracalla. (Model created by Taylor Oetelaar.)

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The size of the volume means that it is not possible to mesh its entirety. To counter the enormity of the volume, the approximate rotational symmetry of the caldarium gives an advantage in that modelling a 1/14th ‘slice’ which contained 3405m3 is possible. Although not ideal, this portion captures three of the four major zones of the room—the heated floor, the tubuli, and the windows—and omitting the doorways leading to the adjoining rooms. Using a 2D model is not possible because, given the placement of all the key zones, there was no one plane that did not skew the data. The only alternative for the faces that connect to the remainder of the room was to model them as being a mathematical mirror.

The size of the volume is not the only issue. Despite being the best preserved thermae, the ravages of the millennia have arguably affected the caldarium the most of the rooms in the main building. As mentioned by DeLaine (1997), the entire southern half only stands to half a metre in height. From the remaining fragmentary evidence, the extrapolated placement of the tubuli in the floor plan (Fig. 2.8) is credible, but how high they reached is still a mystery.91 For the runs presented here, the tubuli along the inner circle reach the dome and the tubuli next to pool reach to the springing of the arch. It is also important to note that the window glass is one pane unlike the reconstruction presented in Chapter 3. This assumption simplified the meshing procedure considerably; hopefully, without detracting too much from the accuracy.

91 See Section 2.1.2.3 for further discussion of the placement and the reasoning behind the layout. 226

9.2 Methodology

9.2.1 Grid

Even with the dramatic cut in volume, gridding still proved exceedingly difficult.

This was mainly due to the dome and its circular shape. The aim was to use a structured mesh to ease computation but the geometry only permitted a composite of structured, semi-structured and unstructured92 as per Figure 9.3. The structured portion consisted of the volume next to the tubuli and windows and the pools. The only way to mesh the sub- volumes with next to the windows was to approximate the curves over the windows with steps. Once the structured sections were complete, the dome was next using tetrahedral elements. Continuing the triangular face mesh down the apex of the slice formed the semi-structured portion. The final mesh (Fig. 9.4) was 2564893 elements or more than double the structured mesh of the NOVA bath caldarium. The element size was not ideal at 150mm and grid refinement proved to be computationally too expensive.

92 To refresh, hexahedral elements compose the structured mesh; a mix of pentahedral and hexahedral elements, the semi-structured mesh; and tetrahedral elements, the unstructured mesh. 227

Figure 9.4: The final mesh.

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9.2.2 Sub-Models

In this simulation there are five important sub-models: time-dependency, density, turbulence, multi-phase, and species. None had changed from the runs in Chapter 8. The runs were unsteady, used the incompressible ideal gas law, RNG k-ε turbulence model, implicit volume of fluid (VOF) multi-phase, and the “Transport & Reaction” species models. Given the limited surface area and the limited impact on the NOVA baths, the radiation model was unnecessary.

9.2.3 Boundary Conditions

In this simulation there are a number of key zones: the exterior walls, the window glass, the heated floor, the heated walls, the water inlet to the pool, the water outlet, and the walls that do not have thermal significance (i.e., the walls separating the upper and lower windows). Like with NOVA, giving the zones with no thermal significance a zero heat flux (insulating) condition was the chosen alternative. The one additional boundary condition unique to these simulations are the symmetry ones where the room ‘reflects’ around the central axis. These have no variables to fill. The conditions for the remaining walls are summarized in Table 9.1.

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Table 9.1: The Boundary Conditions for the Wall Sections Property Glazing External Wall Heated Floor Heated Wall Type Mixed Mixed Convective Convective

Material Glass Custom Custom Custom

Thickness 0.005 m 2 m 0.20 m 0.06 m

Convective Heat Transfer 4 W/m2·°C 4 W/m2·°C 7 W/m2·°C 7 W/m2·°C Coefficient

Free Stream See Table 9.2 See Table 9.2 90°C 90°C Temperature

External 0.49 0.94 -- -- Emissivity

External Radiation See Table 2 50°C -- -- Temperature

The convective heat transfer coefficients (CHTC) remained unchanged from

Chapter 5, 7, and 8. Even though the tubuli in the Baths of Caracalla were smaller and squarer than the ones in the NOVA baths, for these simulations, the assumption that the

CHTC is the same was necessary. The free stream temperatures came from the data in

(Yegül and Couch, 2003) and the external radiation temperature came from the tutorial

(Fluent, Inc.). The heated surfaces used the maximum recorded flue gas temperature.

The water inlets and outlets are uncomplicated. Like NOVA, the water comes in at 40°C and an arbitrary low velocity of 0.1 m/s and the backflow temperature of the outlet is 39°C.

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9.3 Results and Discussion

Unlike the NOVA bath where the simulations were of one time of year, the cases for the Baths of Caracalla modelled summer and winter. Table 9.2 shows the different cases. The first two cases simulate the two extremes in season: #9.1 being summer and

#9.2 being winter. Cases #9.3-#9.5 stem from the early results from Case #9.1. The purpose was to see what effect the solar loading model and external radiation temperature had on the simulation.

Table 9.2: Case Setup Free Stream Temperature for External Radiation Case Solar Loading Glass and External Wall (°C) Temperature for Glass (°C) #9.1 30 Yes -273.15 #9.2 10 Yes -273.15 #9.3 30 No 50 #9.4 30 No 30 #9.5 30 No 87

For Case #9.1, unlike the NOVA baths in which the transitory flow patterns were brief and similar to the final patterns, the early results are dramatically different from the latter ones. Figures 9.5 and 9.6 show the temperature profile and velocity vectors, respectively, of Case #9.1 after ten minutes of simulated time.93 Both are extremely perplexing as there is a spire of hot air rising from the centre of the room instead of the expected layered stratification. Golkafard et al. (2012) found a similar pattern when they modelled a room heated from the floor. This model, like Golkafard et al.’s and unlike the

NOVA bath, does not have an exit for the air. Therefore, since the outer wall has a lower

93 Simulated time is the time that the simulation has run. The variability in length of computation means that there is no correlation between simulated time and real time. 231

temperature and cools the air, the air can only rise in the middle at the outset. Under this scenario, the flow— which continues for approximately seventy more minutes as shown by the temperature profiles (one every ten minutes; Figs. 9.7-9.14)—makes sense.

Figure 9.5: Temperature distribution for Case #9.1 after ten minutes (Units: °C).

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Figure 9.6: Velocity vectors for Case #9.1 after ten minutes (Units: m/s).

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Figure 9.7: Temperature distribution for Figure 9.8: Temperature distribution for Case #9.1 after twenty minutes (Units: Case #9.1 after thirty minutes (Units: °C). °C).

Figure 9.9: Temperature distribution for Figure 9.10: Temperature distribution Case #9.1 after forty minutes (Units: °C). for Case #9.1 after fifty minutes (Units: °C).

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Figure 9.11: Temperature distribution Figure 9.12: Temperature distribution for Case #9.1 after sixty minutes (Units: for Case #9.1 after seventy minutes °C). (Units: °C).

Figure 9.13: Temperature distribution Figure 9.14: Temperature distribution for Case #9.1 after eighty minutes (Units: for Case #9.1 after ninety minutes (Units: °C). °C).

The progression of the temperature distribution through the first ninety minutes of the simulation is very intriguing. The centre region heats up first and as it does, the hot air rises and fills the room. The bulk of the air, however, never reaches 55°C even though there is air reaching at least 65°C at the centre. At eighty minutes, there is a temperature spike about halfway across the radius as a shift in the room dynamics takes place. By

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ninety minutes of simulation time, the central temperature spire has all but disappeared, and is replaced by the anticipated stratification. The temperature distributions and velocity vectors do not show significant change from the one-hundred-and-twentieth minute on (Figs. 9.15-9.20). However, in the occupied region (the first 2.5m in height), the temperature does drop consistently as the system stabilizes. By the four hour mark, the temperature is between 35°C and 40°C.

Figure 9.15: Temperature distribution Figure 9.16: Velocity vectors for Case for Case #9.1 after one-hundred-and- #9.1 after one-hundred-and-twenty twenty minutes (Units: °C). minutes (Units: m/s).

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Figure 9.17: Temperature distribution Figure 9.18: Velocity vectors for Case for Case #9.1 after one-hundred-and- #9.1 after one-hundred-and-eighty eighty minutes (Units: °C). minutes (Units: m/s).

Figure 9.19: Temperature distribution Figure 9.20: Velocity vectors for Case for Case #9.1 after two-hundred-and- #9.1 after two-hundred-and-forty forty minutes (Units: °C). minutes (Units: m/s).

The results from 120min onward are a bit perplexing. While the stratified structure is expected, the temperatures seem cool. Considering that the outdoor temperature is 30°C, the volume near the floor where the patrons are at between 35°C and 40°C is not that much warmer and certainly not modern sauna temperature. Having said that, the air near in the dome is between 60°C and 65°C which indicates that there is

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a substantial amount of heat entering the system. This suggests that the design of the room acts as a type of regulator. If the ceiling were lower, the temperature distribution would be squashed vertically, making the occupied region hotter.

The results also reaffirm the conclusions from the 2D simulations in Chapter 5.

Case #9.1 models summer conditions, which are the hottest time of year and include an accurate representation of the effect of the sun. With these two specifications and glazed windows, the temperature is definitely bearable and even tepid in comparison with expectations. Furthermore, this model does not contain any doorways which, as shown in both Chapter 5 and the NOVA results, subtract heat.

The velocity profiles give an explanation for why the room appears to be cooling down. There are clear downdrafts that form near the window that have more control over the general flow pattern after the initial central updraft disappeared. However, it is interesting to note that the lower window draft stops about two metres above the floor.

The most probable reason for this is that the hot mass near the floor creates a pocket of rising air which counteracts the cooler air from the window.

Another intriguing aspect from the velocity vectors is the decrease of the air movement in the dome. In Figure 9.6, the arrows, while not long, indicating slower speeds, are apparent and erratic in nature. By 120min (Fig. 9.16), a large portion of the dome is still but there is a very distinct pattern that follows the roof line until the centre, where it curls under and goes back down. Two hours later (Fig. 9.20) that pattern is all but gone and almost all the air in the dome is motionless.

Case #9.2 has the general structure as Case #9.1, but is cooler, which is expected.

Comparing Figure 9.5 to Figure 9.21, the spire in Case #9.2 is much lower and narrower

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but the shape is almost identical. In Case #9.2, the hypocaust has to overcome a much greater temperature differential to start so this is not surprising. The velocity vectors

(Figs. 9.6, 9.22) are similar. Like with the temperature distribution, the updraft in Case

#9.2 is narrower but that is the only significant difference.

Figure 9.21: Temperature distribution for Case #9.2 after ten minutes (Units: °C).

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Figure 9.22: Velocity vectors for Case #9.2 after ten minutes (Units: m/s).

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Figure 9.23: Temperature distribution Figure 9.24: Temperature distribution for Case #9.2 after twenty minutes (Units: for Case #9.2 after thirty minutes (Units: °C). °C).

Figure 9.25: Temperature distribution Figure 9.26: Temperature distribution for Case #9.2 after forty minutes (Units: for Case #9.2 after fifty minutes (Units: °C). °C).

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Figure 9.27: Temperature distribution for Case #9.2 after sixty minutes (Units: °C).

While there is a difference between the temperature distributions of Case #9.1 and

#9.2, the difference is minimal. When Figures 9.25 and 9.9 are compared, surprisingly the bulk of the volume is at the same temperature: between 40°C and 45°C. This consistency between seasons suggests that the external temperature has a nominal effect on the system. However, it is still clear that Figure 9.9 represents the summer case and

9.25 the winter because the band between 45°C and 50°C in the spire of Figure 9.9 extends much higher than in Figure 9.25. Plus, in Figure 9.9, there is a band between

45°C and 50°C in the top of the bottom alcove which is not present in Figure 9.25.

The results from Cases #9.3 and #9.4 (Figs. 9.28-9.39) are completely different and there are many things to note. While there is a spire in the middle of the room, it is very small and disappears before twenty minutes have elapsed. Unlike the results from

Case #9.1, the results from Cases #9.3 and #9.4 are amazingly uniform: both top-to-

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bottom and side-to-side. However, they are not that warm as both only reach between

35°C and 40°C.

Figure 9.28: Temperature distribution Figure 9.29: Temperature distribution for Case #9.3 after ten minutes (Units: for Case #9.4 after ten minutes (Units: °C). °C).

Figure 9.30: Temperature distribution Figure 9.31: Temperature distribution for Case #9.3 after twenty minutes (Units: for Case #9.4 after twenty minutes (Units: °C). °C).

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Figure 9.32: Temperature distribution Figure 9.33: Temperature distribution for Case #9.3 after forty minutes (Units: for Case #9.4 after forty minutes (Units: °C). °C).

Figure 9.34: Temperature distribution Figure 9.35: Temperature distribution for Case #9.3 after sixty minutes (Units: for Case #9.4 after sixty minutes (Units: °C). °C).

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Figure 9.36: Temperature distribution Figure 9.37: Temperature distribution for Case #9.3 after ninety minutes (Units: for Case #9.4 after ninety minutes (Units: °C). °C).

Figure 9.38: Temperature distribution Figure 9.39: Temperature distribution for Case #9.3 after one-hundred-and- for Case #9.4 after one-hundred-and- twenty minutes (Units: °C). twenty minutes (Units: °C).

When comparing Figures 9.34 and 9.35, it is apparent that the extra 20°C on the external radiation temperature in Case #9.3 does not affect the temperature distribution.

However, thirty minutes later (Figs. 9.36 and 9.37), there is a dramatic difference. The lower region of Case #9.3—where the patrons would be—reaches the temperature division that is in the top half of Case #9.4 necessitating that Case #9.3 is hotter.

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Having said all of this, the accuracy of Cases #9.3 and #9.4 is suspect because of the uniformity of the temperature distribution. The apex of the dome is 45m above the floor and it is highly unlikely that this volume is all within 5°C: especially without an agitating or mixing device. This point becomes more evident when these cases are compared with Case #9.1 where the temperature gradation between the top and bottom is at least 20°C. The reason for this uniformity is still unknown, however, further investigation might provide clarification.

The results from Case #9.5 (Figs. 9.40-9.45) show a similar pattern to those of

Cases #9.3 and #9.4 in that the spire from Cases #9.1 and #9.2 has undergone a reduction.

The temperatures are slightly warmer than those in Case #9.3 but that is appropriate given the 37°C increase in the external radiation temperature.

Figure 9.40: Temperature distribution Figure 9.41: Temperature distribution for Case #9.5 after ten minutes (Units: for Case #9.5 after twenty minutes (Units: °C). °C).

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Figure 9.42: Temperature distribution Figure 9.43: Temperature distribution for Case #9.5 after thirty minutes (Units: for Case #9.5 after forty minutes (Units: °C). °C).

Figure 9.44: Temperature distribution Figure 9.45: Temperature distribution for Case #9.5 after fifty minutes (Units: for Case #9.5 after sixty minutes (Units: °C). °C).

Another confusing aspect about the latter three cases is the apparent decreased influence of the hypocaust floor. In Cases #9.1 and #9.2, the majority of the heat is coming from the floor given the temperature spire in the centre of the room. In Cases

#9.3, #9.4, and #9.5, on the other hand, the main heat source is the windows even though nothing has changed with the hypocaust. This might explain the uniformity of these

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temperature distributions. Further investigation by turning off the hypocaust in Cases

#9.1 and #9.3 might provide some answers.

The results from the first five cases demonstrate the complexities of simulating a volume the size of the Baths of Caracalla. The seemingly diametrically opposing temperature distributions and velocity vectors of Cases #9.1 and #9.3 illustrate how changing one sub-model can affect the entire system. However, even the assumed more accurate results of the first two cases do not reach the temperatures of modern sauna and

Turkish bath as mentioned in Chapter 5. Interestingly, the air temperature where the patrons are in Case #9.1 is slightly cooler than that of the NOVA bath in Case #7.4 even though the flue gas was 30°C hotter. The extreme height of the caldarium plays a significant role here as all the hottest air is in the dome. Scholars have not addressed the impact of height in previous studies which raises the question as to why the Romans constructed the hot rooms in such a manner. The height might be a passive thermal regulator.

The temperature distributions from the first two cases were comparable indicating that the season change does not have a significant impact; echoing the results from

Chapter 5. Practically, this similarity also suggests that the thermal design was very effective. Given the thickness of the walls, this makes sense.

A notable point to remember is that all of these simulations used data from the

NOVA baths for the hypocaust values. While the CHTC might not vary much when moving from the rectangular tubuli of the NOVA bath to the squarer ones of the Baths of

Caracalla, the flue gas temperature might be very different. The NOVA baths had one furnace to operate the entire system, the Baths of Caracalla, based on my on-site

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observations, had a minimum of seven furnaces—one behind each pool—for the caldarium alone. Therefore, a flue gas temperature of 90°C might be extremely conservative. If the flue gas temperatures were higher, the temperature distribution might change radically.

9.4 Conclusion

This chapter switched to the second case study of the Baths of Caracalla. The dramatic increase in volume brought computational challenges and simulation of a slice was all that was possible. In so doing, the model became self-contained and had no entrances or exits for air exchange. This produced unique transitional flow conditions in the first two cases which had a spire of hot air about the axis. After two hours of simulation time for Case #9.1, the temperature distribution showed the stratification seen in the NOVA baths. Surprisingly, though, the region where the patrons are had similar conditions to the one in the NOVA bath. This suggests that the height of the caldarium was a passive temperature regulator. Another key finding was that the temperature difference between the summer and winter is minimal despite a 20°C difference in the external temperature. Finally, replacing the solar load with an external radiation temperature caused a dramatic shift in the temperature distribution. The uniformity of the results with the external radiation temperature indicates that these are erroneous.

In the context of the entire project, the results from this chapter show how temperature can vary with time. The similarity of the temperature distribution when comparing the two seasons reaffirm the results from Chapter 5. The results also demonstrate some of the issues with simulating a volume as large as the caldarium of the

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Baths of Caracalla. Finally, it opens the door for future avenues of research as these results are by no means complete.

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CHAPTER 10 — CONCLUSION

10.1 Summary of the Results

This dissertation has introduced many varied topics from the two fields throughout its nine previous chapters and has synthesized this information into new transdisciplinary knowledge. Now it is time to take a step back and see how this new knowledge fits into the scholastic landscape. The overall aim of this project was to provide an enhanced understanding of the thermal environment inside of ancient Roman baths using computational fluid dynamics (CFD). Mainly this includes the temperature distribution and air velocities in the bathing areas. In order to obtain an accurate representation, however, many preliminary steps—contained in the first four chapters— from both disciplines were necessary.

Chapter 2 established the two foundations of this project. It introduced the main principles and sub-models of computational fluid dynamics. The chapter explained the key terminology that the dissertation used including the layout of an ancient Roman bath and its heating system: the hypocaust. Details of the two case studies—the NOVA baths and the Baths of Caracalla—concluded the first foundation. The second foundation comprised the literature reviews.

Chapter 3 presented the processes behind the digital reconstruction of the Baths of

Caracalla. Relying heavily on the data provided by DeLaine, the initial purpose of this reconstruction was to provide the basis for the geometry for the computational fluid dynamics model. In the end, however, it had transitioned to a scholastic interpretation of the entire complex which included complete geometry and some initial textural

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interpretations. From an engineering perspective, this chapter did not have any significant impact. Archaeologically, the questions raised about the hot rooms (19-22E/W) are important to the understanding of their thermal environments. Even though this reconstruction was engineering-based, it gives scholars a basic test bed to investigate further aspects of the Baths of Caracalla: most immediately being the wall texturing.

Chapter 4 determines the convective heat transfer coefficient (CHTC) for the inside surface of the tubuli using a simplified laboratory reconstruction of them that the author designed and built. The procedure was to test five plenum temperatures (60°C,

70°C, 80°C, 90°C, 100°C) and the data demonstrated that the average convective heat transfer coefficient was 7.0 W/m2·°C. The subsequent computational fluid dynamics simulations required the accurate convective heat transfer coefficient for the boundary conditions of the heated surfaces. From an engineering perspective, these experiments were unique in that it was the air heating the surface instead of the inverse which is the norm. Archaeologically, these experiments did not create any new knowledge.

Chapter 5 had two purposes: to contribute to the debate about whether or not caldaria windows had glazing; and to investigate the design and development of caldaria doorways from a thermodynamic point of view. The results from the window simulation showed that, with glass, the caldarium would not have been too hot in the summer, and, without glass, it would have been too cool in the winter. The results from the doorway analyses prove that the design of caldaria doorways affected the amount of heat that escaped to adjoining rooms and a piered doorway is better at retaining heat than a columned one. From an engineering perspective, these simulations demonstrate the effect of a radiant floor/wall heating system on the temperature distribution of a large open

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room. Archaeologically, this chapter is quite significant and the results help address some of the main outcomes of the project.

Chapter 6 introduced the 3-D model of the NOVA baths as well as some of the unique aspects of three-dimensional simulation. It compared the available density models and two common turbulence models: RNG k-ε and SST k-ω. Since density was a driving factor of the flow and viscosity was constant, the cases with small temperature changes all had similar velocity profiles. The results show that the difference between the density models can be drastic while between the turbulence closures was minimal. Furthermore, the addition of viscous heating did not alter the results by any appreciable margin.

Finally, the data of this chapter proved that the solution was independent of time. This chapter explained the rationale behind the creation of the skeleton of the NOVA baths model used in the subsequent two chapters.

Chapter 7 examined the set of runs with the established model of the caldarium: testing the effect of adding humidity and modifying the convective heat transfer coefficient of the heated surfaces. Interestingly, neither had a significant impact on either the temperature distribution or the velocity vectors. In all runs, however, the doorway to the tepidarium did have the greatest influence on the thermal environment, which suggested the boundary condition was inadequate. For all simulations, the volume- averaged temperature was different from the temperature where the patrons are due to stratification. From an engineering perspective, these simulations detailed the unique scenario of a room heated only by a radiant heating system instead of the standard mixed air air-conditioning system. Unlike Chapter 5, these results were in three dimensions and incorporated more aspects. Archaeologically, these simulations prove the importance of

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stratification: a point that is often ignored with previous studies. The importance of the doorway also echoes the conclusion of Chapter 5.

Chapter 8 addresses one of the questionable elements of Chapter 7—the doorway boundary condition—by adding the tepidarium. The results are dramatically different from the data of the previous chapters. The resulting temperature change proved large enough to affect the velocity field. The caldarium temperature increased considerably and the flux from the tepidarium severely decreased. This shift gave rise to the idea of trying adding two cloth ‘doors’: one that covered the entire opening and the other partially. The results from the two doors were similar and both made the caldarium even hotter. Since the temperature increased significantly, the best option was to lower the flue gas temperature; however, the resulting drop in room temperature was proportionally much less. From an engineering perspective, this chapter added more complexity to the

NOVA bath model by introducing an adjoining room and a porous zone. The addition of the tepidarium demonstrated the fallibility of the door boundary condition and stresses the importance of ensuring the accuracy of boundary conditions. Archaeologically, the data again reiterates the importance of doorways but also how a simple cloth door can affect the thermal environment.

Chapter 9 switches case studies and presents the results from the Baths of

Caracalla. As seen, the major difficulty with this case study was the volume of the caldarium. It was too large to simulate as a whole so the best option was to model a vertical1/14th slice, taking advantage of the rotational symmetry. This meant, however, that there were no openings for the exchange of air like in the NOVA baths. The self- contained nature of the simulation produced a unique temperature spire in the centre of

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the room as the hot air rose. This eventually dissipated and gave way to the stratified layers that were in the NOVA baths. Interestingly, the temperature in the occupied region was less than 40°C even though the maximum temperature was greater than 60°C. This dispersion suggests that the height of the caldarium might provide a form of passive thermal regulation. The results also show a similar invariance to seasonal change as seen in Chapter 5. The other unusual aspect was the uniformity of the temperature distribution that occurred when an external radiation temperature replaced the solar load representing the sun. From an engineering perspective, the data in this chapter showed how a large volume reacts to a radiant heating system without a mixing device. Archaeologically, the results have begun to illustrate the thermal environment inside the caldarium of a large

Imperial thermae.

This project has shown that by combining engineering and archaeology, the resulting knowledge generated is insightful for both fields. The data have shown how a radiantly-heated room behaves and, with the absence of fans to stir the air, buoyancy and openings in the envelope are crucial. Buoyancy makes the hotter air rise and the cooler air sink; meaning, for the caldarium of the Baths of Caracalla, for example, the average temperature may be 47°C but the region where the patrons were may only be 35°C. This puts a new spin on previous studies that used average temperatures. Overall, though, this project has shown the utility of transdisciplinary research involving computational fluid dynamics and ancient bathing complexes.

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10.2 Recommendations for Future Work

While this project has explored some areas dealing with a transdisciplinary approach to ancient Roman baths, there are still many areas worth further exploration:

 Use the hypocaust to improve modern radiant floor heating

methodologies. In the present energy-conscious society, any advantage the

public can gain will be beneficial in the long-term.

 An expansion of the convective heat transfer coefficient study to include

other variations of the tubuli design to see what effect the shape or size

has. In the NOVA baths, for example, the tubuli have holes in their sides

which permit the movement of the gases between adjoining tubuli. This

could affect the heat inflow as well as show potential better designs for

heating systems.

 A comparison of the convective heat transfer coefficient and, thus, the

effectiveness of tubuli to that of the tegulae mammatae or tiles with pegs

on each corner. Since tegulae mammatae rely on corner pegs to provide

the gap for the hot gases to rise between, the gap is smaller but there is

much more lateral movement possible. This means that the convective

heat transfer coefficient may not differ by a considerable amount and

could have similar impacts as the previous suggested study.

 The calculation of the convective heat transfer coefficient of the underside

of the suspensura. This project assumed that this value was the same as

the one for the tubuli. The pilae might affect the effectiveness of the heat

transfer dramatically because of highly turbulent flow.

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 A more general simulation of the suspensura and tubuli emphasizing the

calculation of the convective heat transfer coefficient. There may be a

significant impact on the coefficient values because of the interplay

between these two sections of the hypocaust

 A more detailed model of the NOVA bath, as mentioned at the end of

Chapter 7. At present, the exhaust gases have no time variation which

would account for the natural fluctuations in temperature. Also, the above

simulations treated the heated walls as being homogeneous instead of

composed of separate tubuli. Both of these simplifications produce

unusually large and consistent heat influxes which affect the thermal

environment indeterminately.

 An expanded NOVA bath model. It would be interesting to expand the

simulation to include the frigidarium and the walls separating the rooms.

Both of these inclusions would help complete the current understanding of

the computational fluid dynamics model of the complex.

 A refined grid model of the current slice of the Baths of Caracalla. The

mesh size of the present simulation is exceedingly large as compared to

the NOVA bath. An improved mesh might show some different results

and change the present interpretation of the thermal environment.

 A multi-paned window in the Baths of Caracalla. The muntins, stiles, and

rails may affect the heat influx from the sun but also from the exterior air.

 A complete model of the caldarium of the Baths of Caracalla. The current

slice is an approximation of the scenario and does not include doorways to 257

the adjoining rooms. The complete simulation might produce radically

different results. Furthermore, a full model could show the impact of the

doorways which might be substantial.

 A 3-D model of the caldarium of the Baths of Caracalla capable of

conclusively addressing the glazing debate. With this, scholars could test

the true effect of the solar radiation, glass, and shutters on the thermal

environment.

 A computational fluid dynamics model of a caldarium that included

people or analogs of people. A person would add heat to the environment

so it would be interesting to see how this new source would affect the

temperature distribution or whether motion of the occupants affected the

temperature distribution.

 Test the impact of an oculus on the thermal environment. If the oculus had

a movable lens like Vitruvius says were present in some buildings

(Section A1.5 in Appendix 1), this could have a dramatic impact on the

degree of control the Romans had over the temperature.

 Computational fluid dynamics models of other rooms in the Baths of

Caracalla or of other bathing complexes. This is the most expansive

suggestion as scholars could test different configurations of bath and

different climates. The caldarium of the Baths of Caracalla is cylindrical

whereas most other caldaria were prismatic. The variation in shape alone

might cause some interesting thermal phenomena to occur.

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APPENDIX 1 — THE ANCIENT SOURCES

A1.1 A Short Glossary of Latin Terms

Apodyterium (pl. -ia) – A changing room

Balneum (pl. -ea) – A small bathing complex, usually privately-owned.

Caldarium (pl. -ia) – Generally, something used for hot water; a tank or boiler; or, in

terms of a bath plan, a large room which contained hot pools.

Frigidarium (pl. -ia) – Generally, something used for unheated water; or, in terms of a

bath plan, a giant, typically high vaulted, room that housed the unheated baths.

Hypocausis (pl. -ia) – Originally, the fire chamber for heating the baths; subsequently

applied to the Roman system of under floor heating. Often modernized and

expanded to hypocaust.

Laconicum (pl. -a) – A dry-steam room.

Natatio (pl. -iones) – A vast swimming pool.

Opus sectile – A form of floor or wall decoration made by placing coloured stones

(usually marble) in geometric patterns.

Palaestra (pl. -ae) – A large, probably open-aired, room where the patrons would

exercise, represented the major sportive component of the baths.

Pila (pl. -ae) – A part of the hypocaust. A support pillar for the suspensura.

Praefurnium (pl. -ia) – Either a wood- or charcoal-burning furnace that supplied the heat

and hot air.

Specularia (pl. -iae) – A translucent material, possibly mica, used in caldarium windows

according to Seneca the Younger.

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Sudatorium (pl. -ia) – A ‘wet’ steam room.

Suspensura (pl. -ae) – A part of the hypocaust. The ‘suspended’ floor above the sunken

floor of the foundation under which the exhaust gases flowed. The gap between

the suspensura and the foundation floor was 0.65-1.00m but could reach as much

as 1.70m (Yegül, 1995, p357).

Tegula mammatae (pl. tegulae mammatae) – A part of the hypocaust. Tiles with small

protrusions on each corner that, when placed on the interior of the structural wall,

created an air gap for the exhaust gases to rise through. An alternative to the

tubulus.

Tepidarium (pl. -ia) – Generally, something used for warm water; or, in terms of a bath

plan, a smaller room containing the warm baths.

Thermae (sc. aquae) – Large, state-owned complexes that included a number of functions

besides bathing; namely, sportive, educational, and social.

Tubulus (pl. - i) – A part of the hypocaust. A box flue on the inside of the structural wall

through which the exhaust gases rose. An alternative to the tegula mammatae.

Vitrum (pl. -a) – Glass.

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A1.2 Passages about Glazing

Seneca the Younger — Epistulae 86.8-11

In hoc balneo Scipionis minimae In the balneum of Scipio, there are sunt rimae magis quam fenestrae muro tiny slits rather than windows cut out of the lapideo exsectae, ut sine iniuria munimenti stone wall so that they admit light without lumen admitterent: at nunc blattaria vocant damaging the building. Even now, they call balnea, si qua non ita aptata sunt ut totius baths places fit for moths if they are not so diei solem fenestris amplissimis recipiant, arranged that they receive sunshine all day nisi et lavantur simul et colorantur, nisi ex long through extraordinarily large solio agros ac maria prospiciunt.... Non windows, and unless people can bathe and suffundebatur aqua nec recens semper suntan simultaneously, unless they can velut ex calido fonte currebat, nec referre look out from their bathtub on fields and credebant in quam pellucida sordes seas.... [In past times] water was not poured deponerent. Sed, di boni, quam iuvat illa over people, nor did it always run fresh as balnea intrare obscura et gregali tectorio if from a hot spring and they did not think inducta,... Nam hoc quoque nobilissimi it mattered how clear the water was in aediles fungebantur officio, intrandi ea which they deposited their grime. But, loca quae populum receptabant good gods, how pleasant it is to enter baths exigendique munditias et utilem ac that are dark and covered by common salubrem temperaturam—non hanc quae plaster work.... For the noblest aediles used nuper inventa est similis incendio, adeo to assume this duty also, of entering these quidem ut convictum in aliquo scelere places which accommodated the people

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servum vivum lavari oporteat. Nihil mihi and of enforcing cleanliness and a videtur iam interesse, ardeat balineum an temperature that is both is suitable for the caleat. Quantae nunc aliqui rusticitatis task and healthy—not the temperature damnant Scipionem quod non in caldarium which recently is found to be similar to suum latis specularibus diem admiserat, fire, to such an extent that a slave convicted quod non in multa luce decoquebatur et of some crime ought to be bathed alive. It expectabat ut in balneo concoqueret. seems to me that these days that there is no

difference between ‘the bath is blazing hot’

and ‘the bath is warm’. Nowadays, some

people condemn Scipio for being a great

boor because he did not admit daylight into

his caldarium through wide specularia,

because he did not stew himself in intense

daylight and he did not wait around to be

cooked in his bath water.

Commentary:

This passage reveals many details about the baths. In the last sentence, Seneca explicitly states that the current caldaria (1st century CE) have specularia in the windows, which allow daylight in. The question of what specularia are still remains.

When looked at in conjunction with the passage from Epistle 90.25 (presented later), it appears that this material is mica and not glass. Furthermore, as shown by the next passage, the Romans, including Seneca, had another word for glass: vitrum. According to

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the OLD (Glare, 1982), specularia are a transparent stone (usually a form of mica or gypsum) used for making windows, etc. It gives nine references to the word in the ancient texts. Modern authors translate the phrase differently. Examples include

“muscovite” Plin. HN. 3.30 (Rackham, 1938, 2:25); “transparent stone” Plin. HN. 19.64

(Rackham, 1938, 5:463); “spéculaire” or “mica” Plin. HN. 19.64 (André, 1964, 19:49,

19:122); “glass” Plin, Ep. 2.17.21 (Radice, 1969, 1:141); “glass” Mart. Ep. 7.14 (Ker,

1914, 2:13); “transparent panes” Mart. Ep. 7.14 (Shackleton Bailey, 1993, 2:171); “glass”

Columella 11.3.52 (Forster and Heffner, 1941, 3:161); “glass/windows” Juv. 4.21

(Nuttall, 1836, 67); “spéculaires” Juv. 4.21 (De Labroille and Villeneuve, 1974, 41);

“window panes” Sen. Q.Nat. 4b.13.7 (Corcoran, 1971, 67); “spéculaires or ‘lamelles de mica’” Sen. Q.Nat. 4b.13.7 (Oltramare, 1961, 206); “talc” Petron. 68.2 (Sedgewick,

1959, 124); “mica” Petron. 68.2 (Smith, 1975, 189). If it is mica, the optical properties are different from those of glass. Mica is cloudier than glass, which means that its transmittance is lower than that of glass. Also, unlike glass, the thicker mica is the more opaque it is. All these factors affect how much sunlight is able to enter and heat the room, which is of utmost importance with the Baths of Caracalla.

The remainder of the above passage paints a picture of the conditions inside a bath; however, it is key to remember that Seneca is a moralist. In his case, this means that he frowns upon the extravagances of the modern time and thinks that the past was ideal.

In this context, the comparisons make a little more sense in that they are most likely exaggerations, if not hyperbole. This does not mean that they are without merit, though.

While it is doubtful that water could cook a person or that there was enough sun to stew

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someone, it is not unreasonable that the water could have been near the upper limit of human comfort or that the caldarium could have been similar to a greenhouse.

Seneca the Younger — Epistulae 86.6

Pauper sibi videtur ac sordidu...nisi A man seems to himself to be poor uitro absconditur camera. and unkempt ... unless the vault is hidden

by glass [mosaic?]

Commentary:

To reiterate, this passage proves that Seneca used another word for glass, which suggests that specularia are something else.

A1.3 Passages about Heating

Seneca the Younger — Epistulae 90.25

Quaedam nostra demum prodisse We know certain things have come memoria scimus et speculariorum usum forth only within our memory, such as the perlucente testa clarum transmittentium use of mica sheets transmitting clear light lumen, et suspensuras balneorum et by means of a translucent testa [shell], the inpressos parietibus tubos, per quos hypocaust floors of the baths, and the tubes circumfunderetur calor, qui ima simul ac impressed into the walls, through which summa foveret aequaliter. the heat is distributed, which maintains the

same temperature at the bottom and at the

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top.

Commentary:

This passage contains three key aspects: one, the suggestion of the use of mica in windows to transmit light; the second, the first (and possibly only) reference to tubuli in the walls; and the third, the even temperature of the rooms in the vertical direction. The first, though better exemplified in Epistle 86.8-11 above, indicates that the Romans did employ a glazing material for their windows. The problem for us, though, is that the word balneorum does not appear until the second part of the sentence so, while Seneca heavily implies the connection to the baths, he does not explicitly say it. Furthermore, the glazing material is not glass or vitrum but rather mica, which has substantially different optical properties and thus would affect the amount of light entering the room. One thing to remember, however, is that Seneca wrote during the 1st century CE and perhaps by the time of Caracalla in the early 3rd century CE technology had progressed to glass as suggested by the archaeological record.

The second element is the use of the word tubos. Neither Vitruvius nor later architectural writers (Faventinus or Palladius; see Section A1.5) mention tubes. This suggests that tubuli were implemented after Vitruvius released his treatise. Given their apparent widespread use throughout the Empire, it is odd that they only appear twice in text. Interestingly though of his word choice. Why did he choose tubos instead of tubulus?

The third element of this passage is the more intriguing because it is the only mention of a temperature distribution in a bath. While it is virtually impossible for the

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temperature to be the same throughout the height, this tells us that (as far as Seneca was aware) the temperature gradient was very small from bottom to top. This is a qualitative marker for us, to ensure that the results are accurate. One potential problem, however, is the use of balneum instead of thermae. This means that this condition, which held for balnea, may not have been true for the larger thermae.

Seneca the Younger — Naturales Quaestiones 3.24.2-3

Facere solemus dracones et We usually make several forms of miliaria et complures formas in quibus vessels including snakes and cylindrical in aere tenui fistulas struimus per declive which we place small pipes of thin copper circumdatas, ut saepe eundem ignem arranged in descending spirals96 so that the ambiens aqua per tantum fluat spatii water passing around the same fire again quantum efficiendo calori sat est; frigida and again flows through a sufficient itaque intrat, effluit calida. Idem sub terra distance to heat it up. And thus, the water

Empedocles existamat fieri, quem non falli enters cold and leaves hot. Empedocles crede Baianis, quibus balnearia sine igne supposes that the same thing happens under calefiunt. Spiritus in illa fervens loco the earth. The people of Baiae, whose baths aestuanti infunditur; hic per tubos94 lapsus are heated without fire, agree with him. A non aliter quam igne subdito parietes et stream of hot air from a warm place is fed vasa balnei calefacit; omnis denique into those baths where it passes through frigida transitu mulatur in caldam nec tubes and heats the walls and water basins

94 In the original manuscript (MPZG), the word is pertusos (perforated). 301

trahit saporem e evaporario95 quia clausa of the bath as if a fire were underneath it. praelabitur. Essentially, all the cold water is

transformed into hot on route without

taking on the taste of the geothermal steam

because the water is always enclosed as it

flows along.

Commentary:

In this passage, Seneca is mainly describing water heating. While outside of the scope of this project, the first two sentences are fascinating—especially given the present emphasis on sustainability—because he describes a tankless or on-demand water heater.

These heat water without storing before extraction and, as such, use less overall energy.

Like the hypocaust, this is another example of a ‘modern’ technology that is not modern in origin.

The second portion of the passage describes a geothermal heat exchanger and room heater—both of which are common in modern society. Seneca realizes that, by keeping the bath water separated from the hot spring water, this prevents the bath water from obtaining the sulfurous odour while still gaining the heat. It would be interesting to see how effective this system was and how it compared with the regular bath setup.

96 It is important to note that a spiral tube is incredibly difficult to fabricate, especially given the ancient Roman pipe construction method of interlocking a flat piece of copper in on itself. 95 The more common word is vaporario (steam) but I feel the original word (in MSS) evaporario (effusion) is more appropriate given the context. 302

Finally, Seneca possibly uses the word tubos and again it is in reference to tubuli.

It is important to note, however, that this word is actually interpolated from the original manuscript so Seneca might not have been referring to tubuli at all.

Pliny the Younger — Epistulae 3.14

Larcius Macedo...lavabatur in Larcius Macedo…was taking a villa.... abiciunt in fervens pavimentum, ut bath in his villa.... [He is attacked by his experirentur an viveret. slaves.] They throw him onto an intensely

hot pavement, in order that they could see

whether he was alive.

Commentary:

This passage may have a useful statement about the floor temperature of baths.

The pavement here is so hot that Larcius Macedo, after being beaten, strangled, and thrown onto it, would have moved or screamed if was still alive. What is not clear, though, is whether the pavement was the hypocaust floor or a sun-baked patio. If it is the former, this gives an approximate temperature range for the floor, which is a key factor in the heating of the room.

A1.4 Passages about Bathing Time

Martial — Epistulae 10.48.3-4

Temperat haec thermas, nimios This hour [the eighth] tempers the

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prior hora vapores halat, et immodico sexta baths, the hour before exhales too many

Nerone calet. fumes, and at the sixth hour, the Baths of

Nero are excessively hot.

Commentary:

This passage gives a very important piece of information—when, according to

Martial, is the best time for bathing. Deciphering what is the modern equivalent of “the eighth hour,” however, is not as easy since the length of the 12 daylight Roman hours varied from season to season and latitude to latitude. For Rome, based on modern sunrise and sunset data, the eighth hour on the summer solstice is from 2:27 PM to 3:43 PM whereas on the winter solstice it is 1:01 PM to 1:47 PM. Sensibly, the summer prime bathing hour is longer but it is also later in the day, meaning that the bath would have had more time to heat up and have had more sunlight. This has implications on the running of the bath, most importantly, whether the fire was started anew every day or kept going throughout the night. In the summer, it might be possible to use solar heating to warm the baths initially and then fire up the furnaces closer to the eighth hour whereas, in the winter, this might not have been feasible. One must keep in mind, though, that this is the opinion of one man and may not have been the general consensus among the populace.

The comment about the seventh hour is intriguing as well, but very perplexing.

What does Martial mean by vapores? If it is “fumes” he seems to imply that the fires might have just got started but that it would have likely taken longer than a hour for the thermae to reach its operating temperature. If, however, it is “steam,” this would imply a dissipation of steam during the seventh hour, which leads to the questions of how and

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why, not only for the dispersion, but for the initial build-up.

Finally, it reminds us of a fact that is often ignored—every thermae is different and thus each has its own unique thermal environment. Martial states that the Baths of

Nero were especially hot. Therefore, it is important to be careful about making broad statements based on the results of the CFD analysis of the Baths of Caracalla. Perhaps the circular nature of the caldarium made it cooler or warmer than others. The only way to know for sure is to model other baths as well, which is beyond the scope of this project.

Scriptores Historiae Augustae — Severus Alexander 24.5-6

Bracariorum, linteonum, He instituted a really profitable tax vitrariorum, pellionum, claustrariorum, on pant makers, linen weavers, glass argentariorum, aurificum et ceterarum makers, tanners, locksmiths, silversmiths, artium vectigal pulcherrimum instituit ex goldsmiths, and other craftsmen and from eoque iussit thermas (et quas ipse this tax he ordered the baths, both those fundaverat et superiores) populi usibus which he founded and the earlier ones, to exhiberi; silvas thermis publicis deputavit. be maintained for the benefit of the

Addidit et oleum luminibus thermarum, cum populace; he even assigned forests to the antea et non ante auroram paterent et ante public baths. He added olive oil for the solis occasum clauderentur. lamps of the baths, since previously they

did not open before dawn and they were

closed before the setting of the sun.

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Commentary:

This seemingly innocuous passage reveals that after Severus Alexander implemented this tax the baths were able to have extended night hours because of the addition of oil for lamps. Interestingly, though, it does not mention any other necessary retrofits needed for nighttime bathing, implying that the baths were already equipped, with the exception of light, to handle cooler temperatures. Thermodynamically, this suggests that glazing was present because, without the sun, the bath would be relying entirely on the hypocaust for its heat and, without a window barrier, the night air could cool everything. Caution is necessary not to read too much into this passage. At any rate, it provides another testable scenario for the model.

A1.5 Passages about Bath Construction

Vitruvius — De Architectura 5.10.1-5

Primum eligendus locus est quam First of all, the place to be chosen calidissimus, id est aversus ab septemtrione must be as hot as possible, that is turned et aquilone. ipsa autem caldaria away from the north and west. The tepidariaque lumen habeant ab occidente tepidaria and caldaria should receive light hiberno, sin autem natura loci impedierit, from the setting winter sun, but if the utique a meridie, quod maxime tempus nature of the site is an impediment, at least lavandi a meridiano ad vesperum est from the south, because the best time for constitutum. Et item est animadvertendum bathing is from midday to evening. It also

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uti caldaria muliebria et virilia coniuncta et should be noted that the women’s and in isdem regionibus sint conlocata. Sic enim men’s caldaria are to be conjoined and efficietur ut vasaria et hypocausis communis with the same orientation; in this way they sit eorum utrisque. aenea supra hypocausim will be able to share the furnace and the tria sunt componenda, unum caldarium, heating vessels. Three bronze caldra are to alterum tepidarium, tertium frigidarium, et be placed together above the furnace—one ita conlocanda uti ex tepidario in caldarium for hot water, another for warm water, and quantum aquae caldae exierit, influat de the third for unheated water—so that as frigidario in tepidarium ad eundem modum, much hot water as flows from the warm testudinesque alveolorum ex communi caldron into the hot caldron also flows in hypocausi calfaciantur. the same way from the cold caldron into

Suspensurae caldariorum ita sunt the warm one. And the vaulted halls that faciendae ut primum sesquipedalibus tegulis contain the pools are to be heated by the solum sternatur inclinatum ad hypocausim, common furnace. uti pila cum mittatur non possit intro The suspensurae of the hot baths resistere sed rursus redeat ad praefurnium are to be made in such a way that first of ipsa per se; ita flamma facilius all the ground is paved with one-and-a- pervagabitur sub suspensione. supraque half-foot tiles and sloping down toward laterculis besalibus pilae struantur ita the furnace so that, when a ball is thrown dispositae uti bipedales tegulae possint in, it cannot stay within but it rolls back supra esse conlocatae; altitudinem autem again to the praefurnium all by itself; thus pilae habeant pedes duo, eaeque struantur the heat of the fire will spread more easily

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argilla cum capillo subacta, supraque under the upper floor. On the subfloor, the conlocentur tegulae bipedales quae pilae are to be built from bricks two-thirds sustineant pavimentum. of a foot on a side arranged in such a way

Concamarationes vero si ex that two-foot tiles can be laid on top of structura factae fuerint, erunt utiliores; sin them; and finally, the pilae have a height autem contignationes fuerint, figlinum opus of two feet. These pilae are to be made subiciatur. sed hoc ita erit faciendum. from potter’s clay kneaded with hair and

Regulae ferreae aut arcus fiant, eaeque above them two-foot tiles are to be laid uncinis ferreis ad contignationem together which sustain the upper suspendantur quam creberrimis; eaeque pavement. regulae sive arcus ita disponantur uti Now, the vaults will be more tegulae sine marginibus sedere in duabus functional if they are made of concrete and invehique possint, et ita totae brick, but if they are made of timber, the concamarationes in ferro nitentes sint undersurface should be tiled.97 This will perfectae. Earumque camararum superiora be done as follows: make iron rods, either coagmenta ex argilla cum capillo subacta straight or curved, and hang them on the liniantur, inferior autem pars, quae ad timber by iron building clamps spaced pavimentum spectat, primum testa cum very close together; and these straight or calce trullissetur, deinde opere albario sive curved bars are to be arranged in such a tectorio poliatur. eaeque camarae in way that rimless tiles can rest on and be caldariis si duplices factae fuerint, supported by a pair of them, and thus the

97 Rowland and Howe (1999) have sketches of their interpretation of these suspended ceilings on page 252. 308

meliorem habebunt usum. Non enim a entire vaults are completed resting on iron. vapore umor corrumpere poterit materiem The upper joints of these vaults are to be contignationis, sed inter duas camaras sealed with clay mixed with hair. The vagabitur. lower face, which looks down to the

Magnitudines autem balineorum pavement, is first of all to be plastered videntur fieri pro copia hominum; sint ita with pulverized tile and lime and then dispositae. quanta longitudo fuerit, tertia dressed with plaster or stucco work. Those dempta latitudo sit, praeter scholam labri et vaults in the caldaria will be more useful alvei. Labrum utique sub lumine faciundum if they are made double; for humidity videtur, ne stantes circum suis umbris cannot rot the system of joists but will be obscurent lucem. Scholas autem labrorum dispersed between the two vaults. ita fieri oportet spatiosas uti, cum priores Now, the size of the baths seems to occupaverint loca, circum spectantes reliqui be made in proportion to the number of recte stare possint. Alvei autem latitudo people. They are laid out thus. Apart from inter parietem et pluteum ne minus sit pedes the alcove containing the basin and senos, ut gradus inferior inde auferat et bathing pool, the width should be as much pulvinus duos pedes. as the length less a third. The basin should

Laconicum sudationesque sunt be placed beneath the natural light so that coniungendae tepidario, eaeque quam latae those standing around do not obscure the fuerint, tantam altitudinem habeant ad light with their shadows. The alcoves of imam curvaturam hemisphaerii. Mediumque the basins ought to be spacious enough so lumen in hemisphaerio relinquatur, ex that when the earlier bathers have taken

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eoque clupeum aeneum catenis pendeat, per their place around the inside of the basin cuius reductiones et demissiones perficietur the later ones can stand comfortably sudationis temperatura. Ipsumque ad watching for their turn. The breadth of the circinum fieri oportere videtur, ut bathing pool, between the back wall and aequaliter a medio flammae vaporisque vis the half-wall, should be no less than six per curvaturae rotundationes pervagetur. feet, from which the lower step (seat) and

the backrest should take away two feet.

The dry sauna and sweat rooms are

to be placed next to the tepidarium; these

rooms are to be as broad as they are high

to the springing of the dome. A window is

to be let into the middle of the dome and

from this a bronze disc should be hung by

chains; through the raising and lowering of

this disc the temperature of the sweat

room is moderated. This lens ought to be

made round, so that the force of the heat

and humidity may flow equally from the

middle to the rounded edge.98

98 That is, a square or rectangular “lens” would not allow an even flow rate over its edge due to the corners. A circular lens has a constant radius and therefore, no matter which direction the air leaves the centre of the lens, it has to travel the same distance. 310

Commentary:

Vitruvius’ On Architecture is considered the premier source when discussing

Roman architecture, but its time frame is important to remember. Vitruvius wrote this in the late 1st century BCE, contemporary with the Stabian Baths at Pompeii and before the age of the large Imperial thermae. As a result, much of what he outlines does not apply to the Baths of Caracalla and will be analyzed only briefly.

The first section describes the orientation and general bathing times, which appear to remain fairly consistent through the ages in Rome particularly. He specifies that the hot rooms should face south to southwest to ensure the best lighting. This is peculiar because he does not mention windows aside from an ocular in the roof and, when one considers Seneca’s passage describing the slits in the wall, it makes me wonder how important this orientation was at this time or if there was a hidden benefit to this.

An intriguing passage is about the water heating because it appears to suggest that the Romans were employing multistage boiling. In modern practice, multistage boiling is used in many industrial processes, most notably power generation, because it takes less energy to boil water in stages than in one go-through. Another point to consider is that this system had to be gravity fed; meaning that the three tanks would have to be on three different levels and probably sealed. Also, given that the flow in most baths was likely continuous, the traditional concept of a tall, slender boiler might not be accurate because of the limited heated surface area relative to its volume. When combined with Seneca’s passage on the intricacies of Roman heat transfer knowledge, the traditional image of a boiler seems more suspect. A more effective design for a continuous flow, externally-

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heated boiler is a squat but wide tank. Though this does not impact this project, it is an interesting fact.

Section 2 describes how to make the hypocaust. There are two points that are significant to point out. The first is the absence of any form of wall heating, whether it is tegulae mammatae or tubuli. This suggests that early baths were heated only from the floor, which would limit the temperature. The second is the slanted nature of the foundation floor. This angle would affect the flow dynamics of the exhaust gases in the plenum but doubling the angle would double (or even increase) the effect is not a certainty. This would be an interesting study both archaeologically (sample angles from sites) and using CFD. Unfortunately, due to the scope of this project, this cannot be considered here.

Section 3 outlines vaulting techniques and precaution. Vitruvius dedicates a fair amount of time to discussing timbered construction which, for the Baths of Caracalla, is not appropriate as masonry was used.

Section 4 reports the size of the baths but again the resemblance to the Imperial thermae is minimal. The bulk of the passage gives sizes for the area around basins and pools which were not present in the Baths of Caracalla in these sizes. The Baths of

Caracalla instead had much larger pools.

The final section covers the necessary equipment for the dry and wet saunas, both of which are beyond the scope of this project. However, the reference on the movable lens is important if the caldarium of the Baths of Caracalla had an oculus.

In summary, Vitruvius’ De Architectura Book 5, Chapter 10 provides the

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foundation for literary studies on baths but, given its temporal removal from the case study of the Baths of Caracalla and resulting lack of breadth, only fragments are relevant or applicable.

Cetus Faventinus — De Diversis Fabricis Architectonicae 16

Balneis locus eligendus est contra The place is to be chosen for the occasum hibernum aut partem meridianam baths facing the winter sunset [southwest] ut sole decendente vaporetur usque ad or facing the south, so that the place is vesperum quod tempus ad lavandum heated until evening, which is the time tributum est. Suspensurae calidarum assigned for bathing. The suspended floors cellarum ita sunt faciendae ut primum area of the hot rooms are to be made in such a sesquipedalibus tegulis consternatur, way that first of all the area is covered by inclinata ad fornacem ut pila missa intro one and a half foot bricks and also is resistere non possit sed redeat ad sloped down toward the furnace so that a praefurnium. Flamma enim sursum ball thrown into it cannot remain stationary adsrurgens calidiores efficit cellas. and rolls back to the praefurnium. The

Supraque laterculis bessalibus et rotundis flame, rising up, makes the rooms hotter. pilae instruantur ex capillo et argilla And on top of this [subfloor] are to be subacta, in privato pedibus binis semis, in placed the pilae, made from tiles 2/3 of a publico ternis. Tegulae bipedales super foot in diameter and rounded containing constituantur quae pavimentum dirigant. hair and potter’s clay, to a height of 2.5

Plumbeum vas quod patenam aeream feet in private baths and 3 feet in public

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habet, supra fornacem conlocetur, alterum ones. Two-foot-square tiles are to be set on simile frigidarium secus, ut quantum caldae top of the pilae, which will make a level ex eo in solio admittatur tantum frigidae [upper] pavement. A lead vessel, which has infundatur. Magnitudines autem balnearum a bronze platter, is to be placed above the pro hominum copia aut voluntatis gratia furnace, and another similar one next to the fieri debebunt, dummodo cellae sic cold bath room, so that as much cold water disponantur ut quanta longitudo fuerit is poured in as hot water is admitted into tertia dempta latitido disponatur. Melius the bath from it. The sizes of the baths will enim ignis per augustiora latitudinis need to be constructed in proportion to the cellarum operabitur. Lumen fenestris aut number of patrons or to your willingness to hibernis aut meridianis partibus tribuatur. meet their preferences, so long as the

Aestivis balneis hypocausteria pro loci rooms are laid out so that the width of the magnitudine cum piscinis in septentrione rooms is two-thirds of the length. For the vel aquilone constituantur, et ab eadem heat will work better along the shorter parte maxime lumen fenestris admittatur, ut sides of the rooms. Light should be salubriorem et corporibus iocundiorem admitted through the windows in the north gratiam praestet. In villa rustica balneum and south walls. In summer baths, the culinae coniungatur, ut facilius a rusticis hypocaust furnaces with the bathing pools, ministerium exhiberi possit. according to the size of the place, should

be placed on the north or the northeast side

and most of the light should be admitted

through windows on the same side, so as to

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furnish a healthier and more pleasant

atmosphere for the bodies. In a country

villa, the bath should be conjoined to the

kitchen so that your country slaves can

more easily attend to you.

Commentary:

Though written in the early 3rd century CE (after construction of the Baths of

Caracalla), Faventinus’ DDFA is little more than a condensed re-interpretation of

Vitruvius’ earlier work and as such does not provide much information on current practice. For instance, when describing the hypocaust, Faventinus omits wall heating, which the archaeological evidence shows was common at the time he was writing. It also seems that he had little personal experience with baths as some of the statements are unclear when compared to their counterparts in Vitruvius. And, like De Architectura,

DDFA provides few new clues that will help with this project.

Cetus Faventinus — De Diversis Fabricis Architectonicae 17

maior tamen et diligentiae et The balance between diligence and utilitatis ratio videtur, si duplices utility will appear better if the vaults of the balnearum cameae fiant, inferior bathing rooms are made double, the lower caementicia et superior suspensa. Inter one of cement and the upper one

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duas enim cameras umor retentus suspended.99 For the dampness trapped numquam vitiabit contignationes. between the two vaults will not harm the

Sudationes etiam praestabuntur meliores. wooden trusses. The saunas will be

particularly better off.

Commentary:

Unlike the previous passage by Faventinus, this one is not based on Vitruvius.

The concept of a double vault—particularly for the reason he states—is intriguing. It would seem like a waste of resources because cement is largely impervious to water.

Furthermore, if you have a cement vault, why would one need wooden trusses? This would seem to imply that the wooden trusses were used for something other than structural integrity. However, questions on structural integrity are beyond the scope of this project. How a double vault would affect the temperature distribution in the room could be a subject of future investigation.

Palladius — De Re Rustica 1.39.1-5

Non alienum est, si aquae copia If a supply of water is available it is patiatur, patrem familias de structura not inappropriate for the head of the balnei cogitare, quae res et voluptati household to think about the building of a plurimum conferat et saluti. Itaque balneum bath, which confers particular enjoyment

99 There is clearly some confusion here.

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constituemus in ea parte qua calor futurus as well as good health. And so we should est, loco ab umore suspenso, ne uligo eum build the bath in that part where the heat fornacibus vicina refrigeret. Lumina ei will be, in a place removed from humidity dabimus a parte meridiana et occidentis so that dampness near the furnace will not hiberni, ut tota die solis iuvetur et bring down the temperature. We will give inlustretur aspectu. the baths windows facing the noonday sun

Suspensuras uero cellarum sic and the winter sunset, so that for the whole facies: aream primo bipedis sternis; day they will enjoy the sun and its inclinata sit tamen stratura ad fornacem ut, illumination. si pilam miseris, intro stare non possit, sed You will make the suspensurae of ad fornacem recurrat: sic eveniet ut flamma the rooms as follows: first you pave the altum petendo cellas faciat plus calere. area with two-foot tiles, letting the

Supra hanc straturam pilae laterculis pavement be sloped down toward the argilla subacta et capillo constructae fiant, furnace so that if you throw out a ball it distantes a se spatio pedis unius et semissis, cannot stay in the middle but rolls back altae pedibus binis semis. Super has pilas toward the furnace; thus it will turn out bipedae constituantur binae in altum, atque that the heat, in rising up, will make the his superfundantur testacea pavimenta et rooms hotter. On this pavement pilae are to tunc, si copia est, marmora conlocentur. be placed, constructed from bricks and

Miliarium uero plumbeum, cui hair-laden mortar, separated by a space of aerea patina subest, inter soliorum spatia one and a half feet and standing two feet forinsecus statuamus fornace subiecta, ad high. On top of these pilae a pair of two-

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quod miliarium fistula frigidaria dirigatur, foot tiles are laid one on top of the other, et ab hoc ad solium similis magnitudinis and over these is poured a red paving fistula procedat, quae tantum calidae ducat cement and then pieces of marble are interius quantum fistula illi frigidi liquoris fitted, if you have the resources. intulerit. Cellae autem sic disponantur ut We should set up a tall cylindrical quadrae non sint, sed, verbi gratia, si lead boiler, under which is a copper platter, quindecim pedibus longae fuerint, decem in the space outside between the bathtubs latae sint: fortius enim uapor inter angusta and above the furnace. To this boiler, a luctabitur. pipe carrying cold water is fixed, and from

Soliorum forma pro uniuscuiusque this boiler to the bathtubs, a pipe of similar voluntate fundetur. Piscinales cellae in magnitude is attached, so that the amount aestivis balneis a septemtrione lumen of hot water that flows out is the same as accipiant, in hiemalibus a meridie. Si fieri the cold water that flows in. Now, the potest, ita constituantur balneae, ut omnis rooms should be laid out not as squares earum per hortos decurrat eluvies. but, for example, if they are fifteen feet

Camerae in balneis Signinae fortiores sunt; long, they will be ten feet wide; this way quae uero de tabulis fiunt, virgis ferreis the heat will be more evenly spread in the transversis et ferreis arcubus sustinentur. narrow spaces.

Sed si tabulas nolis inponere, super The design of the bathing tubs arcus ac virgas bipedas constitues ferreis should be based upon the desire of each ancoris conligatas capillo inter se atque individual. The rooms with swimming argilla subacta cohaerentes, et ita pools in the summer baths should receive

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inpensam testaceam subterinduces; deinde sunlight from the north side and those in albarii operis nitore decorabis. Possumus the winter baths, from the south side. If it etiam, si conpendio studemus, hiberna is possible, the baths should be arranged so aedificia balneis inponere: hinc et that their entire overflow is channeled habitationi teporem submittimus et through the gardens. The opus signinum fundamenta lucramur. vaults are stronger but those made from

terra cotta panels must be supported by

transverse iron rods and curved iron rods.

But if you do not want to use terra

cotta panels, above these curved and

straight rods you lay two-foot tiles bound

together by iron clamps and adhered to

each other with the assistance of hair-

laiden mortar between them, and you

should introduce heavy bricks below these.

Then you will decorate this with highly

polished stucco work. If we need to pay

attention to cost, we can also place winter

apartments above the baths. By doing this,

we both heat the living space from below

and economize on foundations.

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Commentary:

Like Faventinus before, the basic bath construction of Palladius does not go much beyond what Vitruvius had written nearly five hundred years earlier despite the advancement of buildings like the thermae. However, he may still have been writing for the Imperial engineers and architects because his descriptions seem to be for baths attached to apartments. He dedicates a substantial portion of the passage describing how to maximize the interplay between the bath byproducts and apartment. This is very much in keeping with modern ideals of sustainability and water conservation. It would be interesting to see how much heat is transferred if an apartment is placed on top of a bath and how that affects the temperature distribution in both rooms.

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