Natural Ventilation in Building Design: Dynamic Performance Metrics and Interactive Modeling
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Citation Yoon, Nari. 2019. Natural Ventilation in Building Design: Dynamic Performance Metrics and Interactive Modeling. Doctoral dissertation, Harvard Graduate School of Design.
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Natural Ventilation in Building Design: dynamic performance metrics and interactive modeling
A dissertation presented by Nari Yoon
MDesS, Harvard University, 2012 B.Arch, Hongik University, 2010
to The Harvard Graduate School of Design
in partial fulfillment of the requirements for the degree of Doctor of Design
Harvard University Cambridge,Massachusetts
January 2019 Copyright c 2019 by Nari Yoon. All rights reserved. Advisors: Author: Nari Yoon Professor Ali Malkawi Professor Holly W. Samuelson Professor Leslie K. Norford
Natural Ventilation in Building Design: dynamic performance metrics and interactive modeling
Abstract
This study proposes a new method to evaluate natural ventilation performance in the early design phase by introducing dynamic performance metrics of natural ventilation and devel- oping an interactive tool that applies the metrics. The tool will help understand how a given design utilizes natural ventilation and which spatial variances could improve the effectiveness of natural ventilation. It also looks into important design aspects, including materials, thermal mass, aperture configurations, occupancy etc. These factors influence whether or not natural ventilation might be effective for the given design.
There are four sub-topics: natural ventilation metrics, thermal mass and window con- trols, validation, and tool implementation. These sub-topics, in this order, structure the thesis.
First, it introduces dynamic metrics that gauge the degree of cooling power that is achieved through natural ventilation. The metrics will be first developed under steady-state conditions, and be demonstrated in a feasibility study using an interactive design platform.
Second, once metrics for steady-state are established, the effect of thermal mass and window controls are considered. Thermal mass interacts with its environment through time in a dynamic way which must be explored to refine the natural ventilation metrics. Therefore, this part will analyze the temperature change through time, examine the impact of different window operations, and further suggest efficient ventilation routines.
Third, the process of calculating the dynamic metrics is validated with experiments.
This ensures that the proposed method works as intended. Lastly, an interactive design procedure that utilizes the dynamic performance metrics is demonstrated in the 3D modeling environment.
This study contributes to early-staged building design in three ways. First, quick simu- lation time and interactivity will provide users with rapid feedback on different design possi- bilities. Second, natural ventilation performance is estimated for a customized building design, albeit with some limitations, as opposed to a general box model. The tool may yield different results for buildings with different sizes, features, and construction conditions. By yielding metrics for a specific design, it will help users to alter the design to enhance performance.
Third, the tool helps designers understand that the thermal environment is influenced by im- portant factors including window operation, thermal mass, and internal heat gains. Users will be able to learn the sensitivity of the thermal environment to various construction materials and thermal masses, which is pedagogically important.
ii Acknowledgements
Thank you, Prof. Malkawi, Prof. Samuelson, and Prof. Norford, for sharing your invaluable insights, guidance, and care. I am forever indebted to you.
Thank you, Christoph Reinhart, Joyce Rosenthal, Alejandra Menchaca, and Yuya Ando, for showing confidence in me and supporting my doctoral journey.
Thank you, my colleagues at the GSD and the CGBC, for inspiring me with your talents and encouraging me with your sympathy. Special thanks to Bin for your kindness and support that goes beyond colleagueship.
Thank you, my friends in Korea, USA and anywhere on the globe, for laughing, grumbling, and singing with me. A special shout-out to Jung Min and Jung Hyun for our countless coffee breaks.
Thank you, Min Ju, for taking the seat next to me on this roller coaster of life. I am thrilled for more to come.
한국에 계신 가족들,
감사하고 사랑합니다.
Contents
Abstract i
Acknowledgements iii
List of Tables xi
List of Figures xiii
1 Introduction 1 1.1 Research statement...... 1 1.2 Research objectives...... 2 1.3 Research methodology...... 4 1.3.1 Natural ventilation performance metrics...... 4 1.3.2 Natural ventilation performance assisted by additional passive design strategies...... 4 1.3.3 Software selection for tool implementation...... 5 1.3.4 Validation with the HouseZero project...... 6 1.4 Structure of dissertation...... 6
2 Literature Review7 2.1 Natural ventilation in Architecture...... 7 2.1.1 Natural ventilation and energy savings...... 7 2.1.2 Natural ventilation and thermal mass...... 9 2.1.3 Controls for natural ventilation and energy savings...... 11 2.2 Evaluation of natural ventilation...... 12 2.2.1 Common metrics used in natural ventilation evaluation...... 12 Contents
2.2.2 Customized indices used in natural ventilation evaluation...... 14 2.3 Natural ventilation modeling in design processes...... 18 2.3.1 Site evaluation and conceptual design phase...... 19 2.3.2 Design development phase...... 23
3 Dynamic metrics for interactive modeling 29 3.1 Metrics of natural ventilation performance...... 30 3.1.1 Static and dynamic metrics of natural ventilation...... 30 3.1.2 Terminology...... 31 3.2 Dynamic performance metrics for natural ventilation...... 35 3.2.1 Design natural ventilation cooling effectiveness (dNVCE)...... 35 3.2.2 Climate Potential Utilization Rate (CPUR)...... 39 3.2.3 Understanding dNVCE and CPUR together...... 39 3.2.4 Framework for dNVCE and CPUR...... 40 3.3 Feasibility study for interactive modeling...... 42 3.3.1 Study description...... 42 3.3.2 Geometry...... 42 3.3.3 Climate natural ventilation effectiveness (cNVCE)...... 43
3.3.4 Pressure coefficient (cp) and available cooling power...... 44 3.3.5 Ideal cooling capacity...... 45 3.3.6 Initial results and testing more design alternatives...... 46 3.3.7 Results...... 47 3.3.8 Discussions...... 47
4 Thermal mass, dynamic window controls, and natural ventilation 51 4.1 Multi-zone thermal mass solution...... 52 4.1.1 Single-zone model...... 52 4.1.2 Multi-zone model: two-zone problem...... 56 4.1.3 Multi-zone: more than two zones...... 60 4.1.4 Implications of the multi-zone solution...... 62 4.2 Model verification: with windows closed...... 63 4.2.1 Objective of verification...... 63 vi Contents
4.2.2 Verification methods...... 64 4.2.3 Single-zone model setting: with windows closed...... 65 4.2.4 Single-zone model verification results: with windows closed...... 66 4.2.5 Multi-zone model setting: with windows closed...... 67 4.2.6 Multi-zone model verification results: with windows closed...... 69 4.3 Model verification: with windows open...... 70 4.3.1 Model assumptions with natural ventilation...... 70 4.3.2 Model settings for natural ventilation...... 70 4.3.3 Single-zone verification results: with windows open...... 72 4.3.4 Multi-zone verification results: with windows open...... 74 4.3.5 Conclusion from the verification...... 75 4.4 Thermal mass and dynamic window operation...... 75 4.5 Calculation of dNVCE in a transient state...... 77
4.5.1 Available cooling power (qavail) in a transient state...... 77
4.5.2 Ideal cooling power (qideal) in a transient state...... 78 4.5.3 Design natural ventilation cooling effectiveness (dNVCE) in a transient state...... 78 4.6 Discussion...... 80 4.6.1 Impact of thermal mass and window controls on dNVCE...... 80 4.6.2 Impact of thermal mass and window controls on CPUR...... 81 4.7 Limitations...... 81 4.7.1 Geometry...... 81 4.7.2 Zoning for natural ventilation...... 82 4.7.3 Thickness of thermal mass...... 83 4.8 Conclusions...... 83
5 Validation with HouseZero 85 5.1 Field Measurements...... 86 5.1.1 Data collection...... 86 5.1.2 Test room description...... 89 5.1.3 Processed input data...... 92 5.2 Model calibration...... 93
vii Contents
5.2.1 Calibration: building envelope...... 95 5.2.2 Calibration: slab...... 96 5.2.3 Calibrated model for validation...... 97 5.3 Validation: without natural ventilation...... 100 5.3.1 Thermal zones...... 100 5.3.2 Test 1: Steady state...... 101 5.3.3 Test 2: Unsteady-state with simplified thermal mass...... 102 5.3.4 Test 3: Unsteady-state with at least one thermal mass specified in a zone 104 5.3.5 Test 4 final model...... 108 5.4 Validation with natural ventilation...... 112 5.4.1 Experiment setting...... 112 5.4.2 Division of thermal zones for simulation...... 112 5.4.3 Prediction of ventilation rate...... 113 5.4.4 Results...... 114 5.5 Summary and discussions...... 117
6 Implementation for parametric study 119 6.1 Overview...... 120 6.1.1 Objectives...... 120 6.1.2 Methodology...... 120 6.2 3D Implementation...... 121 6.2.1 Inputs...... 121 6.2.2 The solver...... 123 6.2.3 Outputs...... 126 6.3 Parametric study...... 127 6.3.1 3D parametric study and visualization...... 127 6.3.2 Improving natural ventilation performance...... 127 6.4 Discussions...... 131 6.4.1 Multi-zone implementation...... 131
7 Conclusion 135 7.1 Contribution...... 135 viii Contents
7.2 Findings...... 137 7.2.1 Cooling effect assisted by other passive design strategies...... 137 7.2.2 Zoning of thermal mass and indoor spaces...... 137 7.2.3 Expandability of the implemented tool...... 137 7.3 Applications...... 138 7.3.1 Prediction of window schedules in existing buildings...... 138 7.3.2 Optimization of thermal mass...... 138 7.3.3 Urban wind environment for indoor optimization...... 139 7.3.4 Thermally activated building systems and model predictive control... 139
Bibliography 141
Appendices
A Results of Section 4.2 155 A.1 Results of verification: RMSE of single-zone verification...... 155 A.2 Results of verification: RMSE of multi-zone verification...... 156
B Settings and results of a single-zone test 157 B.1 Settings used in Sections 4.4 and 4.5 and chapter 6...... 157 B.2 Hourly outdoor temperature and indoor results for Sections 4.4 and 4.5 and chap- ter 6...... 159 B.3 Hourly dNVCE results for Sections 4.4 and 4.5 and chapter 6...... 160
C Validation results of Dataset 2 161 C.1 Dataset 2 temperature graphs...... 161 C.2 Dataset 2 correlation and RMSE results...... 161
ix
List of Tables
2.1 Design phases for natural ventilation...... 19
3.1 Natural ventilation performance metrics...... 31 3.2 Settings of test cases...... 46
3.3 dNVCE(may−oct) and CPUR results of design alternatives...... 47
4.1 Specification of single-zone model, without natural ventilation...... 65 4.2 Specification of single-zone model, without natural ventilation...... 68 4.3 Thermal resistance of multi-zone model, with natural ventilation...... 72
5.1 Data collection: items and location...... 86 5.2 Data collection time...... 89 5.3 Thermal heat capacity of roof, external wall, and slab calculated from building construction materials...... 91 5.4 Test 3A simulation inputs: heat storage and thermal resistance...... 105 5.5 Test 3B simulation inputs: heat storage and thermal resistance...... 106 5.6 Test 1: correlation and RMSE...... 110 5.7 Test 2: correlation and RMSE...... 110 5.8 Test 3A: correlation and RMSE...... 110 5.9 Test 3B: correlation and RMSE...... 111 5.10 Test 4: correlation and RMSE...... 111 5.11 Pressure coefficient differentials between north-facing wall and skylight roof of HouseZero with eight (8) different wind directions according to Orme et al. (1998)114 5.12 RMSE and correlation coefficients of simulation results with different flowrates 116
6.1 Indoor temperature results with different initial conditions...... 125 List of Tables
A.1 RMSE of single-zone verification result...... 155 A.2 RMSE of multi-zone verification result...... 156
B.1 Building settings and boundary conditions...... 157 B.2 Input outdoor temperature and output indoor temperatures under different conditions...... 159
B.3 Hourly qavail, qideal, and dNVCE under different conditions...... 160
C.1 Dataset 2: correlation and RMSE...... 162
xii List of Figures
1.1 Projected visualization of the dNVCE and CPUR...... 3
3.1 Relationships among cNVCE, NVAQ and NVE in two different virtual cases.. 34 3.2 Understanding dNVCE and CPUR...... 40 3.3 Procedure to Evaluate Natural Ventilation Effectiveness in Building Design. Im- age from Yoon and Malkawi (2017)...... 42 3.4 Test room geometry created in Grasshopper, Rhino. Image from Yoon and Malkawi (2017)...... 43 3.5 A cNVCE map of Boston from May 15th to October 15th...... 43 3.6 Connections among components in Grasshopper and Rhino. Image from Yoon and Malkawi (2017)...... 45 3.7 The dNVCE map (May 15- Oct 15) of base case. Windows on the South and West facades with operable window area of 0.25 m2...... 48 3.8 The dNVCE map (May 15- Oct 15) of Alt 2. Windows on the North and South facades with operable window area of 0.25 m2...... 48 3.9 The dNVCE map (May 15- Oct 15) of Alt 5. Windows on the South and East facades with operable window area of 0.50 m2...... 48 3.10 Annual dNVCE map of the test building in Santa Monica, CA...... 49 3.11 Annual dNVCE map of the test building in Boston, MA...... 49 3.12 Annual dNVCE map of the test building in Dallas, TX...... 49
4.1 Single-zone geometry description and circuit analogy diagram...... 52 4.2 Multi-zone geometry description and circuit analogy diagram...... 56 4.3 A three-zone model description and circuit analogy diagram...... 60 4.4 Transformation of multi-zone problems into single-zone problems...... 62 4.5 Description of analytical model and numerical model...... 65 List of Figures
4.6 Single-zone modeling in Modelica. Windows are closed. Calculation without heat gain (left) and with heat gain (right) are displayed...... 66 4.7 RMSE of cases using different time steps and heat gains. Windows are closed.. 66 4.8 Single-zone temperature graphs of indoor and outdoor using Eq. (4.22) and Modelica. Windows are closed...... 67 4.9 Multi-zone modeling in Modelica. Windows are closed...... 68 4.10 Multi-zone graphs of indoor and outdoor temperatures using Eq. (4.31) and Modelica. Windows are closed, and no heat gain is applied to either room.... 69 4.11 Multi-zone graphs of indoor and outdoor temperatures using Eq. (4.31) and Modelica. Windows are closed. Room 1 has 325 W of internal heat gain, while Room 2 does not...... 69 4.12 Single-zone modeling in Modelica. Windows are open...... 71 4.13 Multi-zone modeling in Modelica. Windows are open...... 71 4.14 Temperature of indoor and outdoor using Eq. (4.22) and Modelica. Windows are open...... 73 4.15 RMSE of cases using different time steps and heat gains. Windows are open... 73 4.16 Multi-zone temperature graphs of indoor and outdoor using Eq. (4.31) and Modelica. Windows are open, and no heat gain is applied to both rooms..... 74 4.17 Multi-zone temperature graphs of indoor and outdoor using Eq. (4.31) and Modelica. Windows are open. Room 1 has 325 W internal heat gain, while Room 2 does not...... 74 4.18 Graph of temperatures using different design strategies...... 76
4.19 Graph of qideal with different design strategies based on Figure 4.18...... 79 4.20 cNVCE and dNVCE of different design strategies based on Figure 4.18..... 79 4.21 Percentage of NVhs in a day using different design strategies, based on Figure 4.18 80 4.22 Geometries that can be used by the suggested analytical models...... 82
5.1 Orientation of HouseZero and surroundings...... 87 5.2 Photographs of the entrance (left) and the panoramic view of test room (right).. 87 5.3 Rendered image of the test room. There are north-facing windows, skylight, two glazing walls, and interior door...... 88 5.4 Location of the test room in HouseZero. The room is located on the third floor of the house...... 88 5.5 Side view of the test room...... 88 5.6 Top view of the test room...... 88 xiv List of Figures
5.7 Solar radiation calculation...... 92 5.8 Thermal connection of the test room and other thermal zones...... 94 5.9 Measurement during 07/27 - 7/30...... 94 5.10 Calibration of the heat capacity of the building envelope...... 96 5.11 Calibration of the absorptance of the building envelope...... 96 5.12 Calibration of the heat capacity of the concrete slab...... 97 5.13 Calibrated thermal resistance (K/W), thermal storage (J/K), and absorptance.. 98 5.14 Simulation results with calibrated parameters compared to the field measure- ments with Dataset 1...... 99 5.15 Simulation results with calibrated parameters compared to the field measure- ments with Dataset 2...... 99 5.16 Simulation results with calibrated parameters compared to the field measure- ments with Dataset 3...... 99 5.17 Steady-state simulation setup and result...... 101 5.18 Diagram of simplified model (Test 2)...... 102 5.19 Result of simplified model...... 103 5.20 Test 3 models (3A and 3B) diagrams...... 104 5.21 Result of test 3A: a simplified model simulation with an additional zone of the envelope...... 107 5.22 Result of test 3B: a simplified model simulation with an additional zone of the slab...... 107 5.23 Diagram of a final model...... 108 5.24 Result of test 4: a final model with two discrete thermal mass zones...... 109 5.25 Pictures of the hopper type windows (left) and skylight (right)...... 112 5.26 Diagram of a model with natural ventilation...... 113 5.27 Measurement during 09/07 (FRI) 6PM - 09/10 (MON) 0AM...... 115 5.28 Simulation result of Dataset 4: natural ventilation...... 115
6.1 Screenshot of geometry and structure of simulation controls in Rhino and Grasshop- per. Closer views are available in Figures 6.2 and 6.3...... 120 6.2 Closer view of the geometry and boundary setting components...... 122 6.3 Closer view of the solver component. Left-side items of the solution component are inputs and right-side items are outputs...... 123 6.4 Parametric study for natural ventilation performance...... 128
xv List of Figures
6.5 Graph of dNVCE of a day under different thermal heat storages Cm (J/K).... 129 6.6 Graph of dNVCE of a day under different flow rates v˙ (m3/s)...... 129 6.7 Graph of dNVCE of a day under different heat gain q (J/s)...... 130 6.8 Graph of dNVCE of a day under different U-values U (W/K)...... 130 6.9 A diagram using EnergyPlus, Honeybee and Ladybug...... 132 6.10 A diagram using EnergyPlus, CONTAM, and FMU...... 132 6.11 A diagram using EnergyPlus and Modelica...... 132
7.1 Prediction of indoor temperature using window controls...... 139
A.1 Graphs of RMSE of single-zone verification results...... 155 A.2 Graphs of RMSE of multi-zone verification results...... 156
C.1 Dataset 2: graphs of measured and calculated temperature...... 161
xvi Chapter 1
Introduction
1.1 Research statement
This dissertation investigates building simulations for sustainable design with a focus on nat- ural ventilation. Many sustainable design strategies incorporating daylight and solar radiation have been studied to support sustainable design processes. For example, daylight has served as a key inspiration for creative designs that are energy-conscious, aesthetically pleasing, or dynamically responsive buildings. Daylight studies are supported by a well-established dy- namic metric system that includes Daylight Autonomy, Useful Daylight Illuminance, Spatial
Daylight Autonomy, and Annual Sunlight Exposure. These metrics have been suggested by various researchers and institutions including Nabil and Mardaljevic (2005); Reinhart et al.
(2006); and the Illuminating Engineering Society of North America (2012). Daylight simula- tion processes are well well-integrated in architectural design phases. Daylight-dedicated tools include Radiance, Daysim, and DIVA for Rhino, and energy simulation tools that support day- light analysis include IESVE and OpenStudio.
Natural ventilation, on the other hand, has not been studied as effectively as daylight in design for the exact opposite reasons. There is a lack of dynamic performance metrics that are commonly used for natural ventilation analysis in building design, and computational Chapter 1. Introduction methods are challenging to be integrated in design processes. Common natural ventilation metrics are either point-in-time metrics, such as volume flow rate and air change rate per hour (ACH), or static metrics that do not respond to specific designs, such as climate natural ventilation potential. Energy simulation tools, for example, EnergyPlus, offer natural venti- lation options, but they are considered user inputs rather than the analysis target that will influence architectural design. The motivation behind this thesis is to overcome these weak- nesses by creating possibilities for designers and students to explore the relationship between natural ventilation performance and building design, ultimately in conjunction with daylight and energy simulation.
1.2 Research objectives
This research tries to help designers answer the following questions:
• How effective is it to use natural ventilation to cool a given room?
• How does performance change when there is thermal mass with different window
configurations, different building materials, and different layouts?
• What can designers do to improve natural ventilation performance?
In answering these questions, this study contributes to early-stage building design in the following ways:
1. A quick simulation time and interactive analysis will provide users with rapid feed-
back on different design possibilities.
2. Natural ventilation performance is estimated for a customized building design, as
opposed to a general box model.
• This method will be able to yield different results for buildings with differ-
ent sizes, features, and thermal conditions. By yielding dynamic metrics for a
specific design, it will help users to alter the design to improve performance.
2 1.2. Research objectives
3. This study provides intuitive and applicable knowledge in addition to point-in-time
information. Example results may include:
• “natural ventilation works for 50% of the time during summer,” and
• "natural ventilation does not work at 3pm on July 15th."
4. The proposed method helps designers understand that the thermal environment is in-
fluenced by important factors including window operation, thermal mass, and internal
heat gains.
• Users will be able to understand the sensitivity of the thermal environment of
various building materials and thermal masses, which is pedagogically impor-
tant.
Figure 1.1 illustrates the objective of this project. It shows five rooms with differ- ent window configurations. Colors indicate the effectiveness of the natural ventilation of the rooms. Toggles with design options on the top left enable the user to explore different scenar- ios, results of which will show in the metrics on the right side of the figure.
Figure 1.1: Projected visualization of the dNVCE and CPUR
3 Chapter 1. Introduction
1.3 Research methodology
1.3.1 Natural ventilation performance metrics
In evaluating natural ventilation, conventional airflow simulation tools yield the quantity of airflow, including air speed, flow rate and air-change rate per hour (ACH). These are im- portant data, but they do not explain the adequacy of natural ventilation for customized architectural design, thus lacking the capacity of explaining how those analyses should affect design. For example, although a simulation may confirm that a room is expected to have 3.0 m3/s or 10 ACH, it is hard to evaluate whether this is sufficient to cool a room until contex- tual information is given about room sizes, heat storage of building materials, internal heat gains, cooling criteria, and so on. To overcome this shortcoming of the conventional metrics, this dissertation suggests design-applicable natural ventilation metrics that can directly give informative feedback on the effectiveness of natural ventilation to designs.
One metric measures the cooling power that natural ventilation alone can offer com- pared to the cooling power that the building requires throughout the period of interest. This measures how effective natural ventilation is for cooling a designed room, hence the name
"design Natural Ventilation Cooling Effectiveness" (dNVCE). The other metric evaluates how much the current design utilizes the climate, and is called the Climate Potential Utilization
Rate (CPUR).
1.3.2 Natural ventilation performance assisted by additional passive design strate- gies
Natural ventilation uses outdoor temperature as a major resource to cool the indoors. The capacity of cooling may be assisted by additional passive strategies including thermal mass and smart window operation. For example, thermal mass influences indoor temperature by delaying the time it takes for outdoor conditions to affect indoor temperature, compared to materials that have less specific heat capacity. This impact also depends on whether windows
4 1.3. Research methodology are open or closed, which is highly related to natural ventilation performance. When thermal mass is considered, the heat transfer is no longer at a steady state. The metrics will be influ- enced by this transient behavior. Including these dynamics in a natural ventilation study is essential.
1.3.3 Software selection for tool implementation
1.3.3.1 Rhino and Grasshopper
Rhinoceros (or Rhino) is a non-uniform rational basis spline (NURBS)-based 3D modeling tool that is widely used for architectural design. The generation of the geometries can be visual- ized and parametrized in an algorithm editor called Grasshopper. In addition to the ability to parametrize the geometry, Grasshopper allows computational simulations to be implemented with coding. For example, Ladybug, a climate analysis Grasshopper plug-in, decomposes the weather file and visualizes the climate information of a user’s choice. Another example of a
Grasshopper plug-in is Honeybee. Honeybee enables the creation of a building geometry in the Rhino environment and conducts an energy simulation by running EnergyPlus as well as
Radiance and Daysim.
For the implementation purposes in this study, Rhino is used as a 3D modeling plat- form and Grasshopper is used for interactive simulation. This study codes the analytic solu- tion in the computer language Python.
1.3.3.2 Modelica
In this dissertation, an object-oriented modeling language called Modelica is used to verify analytical solutions and calibrate building settings. As an equation-based computational lan- guage, Modelica allows physics to be modeled in various engineering problems (Fritzson,
2010). Modelica-supportive tools, such as Dymola and OpenModelica, graphically visualize the modeling. To crosscheck the calculations for transient analysis, test cases are set up with analytical solutions and written using Modelica language in Dymola for comparison.
5 Chapter 1. Introduction
1.3.4 Validation with the HouseZero project
To validate the proposed evaluation method, several sets of experiments were conducted in a room of HouseZero, a building located at 20 Sumner Rd., Cambridge, MA. The HouseZero room was equipped with many sensors that measure indoor air temperature as well as floor temperature.
Two cases were tested. First, indoor temperature was measured with the windows kept closed for several days. After that, the windows were opened and indoor temperature was measured. The outdoor conditions, including temperature, solar radiation intensity, wind direction and wind velocity, were measured on the roof of the Harvard Graduate School of Design building. The simulation results based on the proposed analysis were compared against the measurement.
1.4 Structure of dissertation
This dissertation contains seven chapters. Chapter 1 outlines the focus of research and method- ology. Chapter 2 reviews literature in related fields, and Chapter 3 proposes two important metrics to be used in an interactive design procedure. As natural ventilation performance can be assisted by other passive strategies, Chapter 4 tries to integrate thermal mass and window controls into the dynamic performance metrics. In Chapter 5, the analytic solutions with the thermal mass effect considered are validated by an existing room equipped with tempera- ture sensors. Finally, Chapter 6 implements the solutions in a 3D modeling environment to demonstrate their use. This is followed by conclusions in Chapter 7.
6 Chapter 2
Literature Review
2.1 Natural ventilation in Architecture
Natural ventilation, which can be driven by both thermal buoyancy and wind, is free, con- tributes to high work productivity (Allen et al., 2016; Datz, 2015), and provides the natural quality of breeze that some people prefer over a HVAC system (Carrilho da Graça and Lin- den, 2016). Aside from the many benefits of natural ventilation, the following sections will emphasize one of the most important aspects of natural ventilation: energy savings. This sec- tion reviews the studies that analyze how much energy could be saved by natural ventilation across many regions. The section also introduces different strategies to enhance the perfor- mance of natural ventilation including thermal mass and innovative controls.
2.1.1 Natural ventilation and energy savings
Potential energy savings from natural ventilation have been studied in various climate regions.
A study in Bangkok, Thailand, suggested that ensuring a certain level of air velocity was important to satisfy thermal comfort criteria (Tantasavasdi et al., 2001). This study used a typical residential house in Thailand with both a mechanical system for the hot and rainy seasons and a natural ventilation system for the cooler months. This study found that during Chapter 2. Literature Review
1,825 hours a year, which is approximately 20% of a year, thermal comfort could be achieved by natural ventilation if air velocity of 0.4 m/s was secured. Since the climate was characterized as hot and humid, the comfortable hours were mostly during winter. This low utilization of natural ventilation is understandable given the hot summer and rainy season that span from
March to October in Thailand. Although the prospective annual energy savings was less than
20%, the authors claimed that natural ventilation would still be worth considering due to its significant contribution to indoor air quality.
A 23-story building in Tokyo, Japan, The Liberty Tower of Meiji University, was in- vestigated for natural ventilation performance (Chikamoto et al., 1999; Kato and Chikamoto,
2002; Wood and Salib, 2013). The building used both buoyancy and wind for ventilation, and the window-wall sections were designed to allow air to flow in but to prevent outdoor noise at the same time (Wood and Salib, 2013). In this building, a special floor, called a “wind floor,” was built on the 18th level that would act as a large outlet of the building to facilitate better air intake in other floors (Chikamoto et al., 1999). The performance of the building was studied using a computational fluid dynamics software and compared with that of a building without the wind floor. This case study reported an air change rate 30% higher in a building with a wind floor, estimating a 35% reduction in annual cooling energy consumption. The energy savings were estimated to increase by 50% if a hybrid ventilation system was used (Kato and
Chikamoto, 2002).
Additionally, a traditional Italian building was investigated to evaluate the energy savings using natural ventilation (Cardinale et al., 2003). The study considered three locations
(Bologna, Ancona, and Alghero), three summer months (July to September), and three build- ing orientations (SW, SE, and S). These cases were compared with and without using natural ventilation by conducting simulations. The results showed that natural ventilation saved as much as 53%, 43%, and 48% in Bologna, Ancona, and Alghero, respectively. This study found that natural ventilation would reduce energy consumption without sacrificing indoor thermal comfort and addressed that additional passive controls including a solar shield would further enhance the performance of natural ventilation.
8 2.1. Natural ventilation in Architecture
In another study, natural ventilation’s energy savings potential in various regions in
Mexico was evaluated by utilizing a coupled thermal airflow simulation program (Oropeza-
Perez et al., 2012). For natural ventilation in a hot-and-dry climate, high heat capacity building materials led to higher energy savings potential, whereas in a hot-and-humid climate, lower heat capacity materials worked better to meet the thermal comfort. The study pointed out that natural ventilation would not be efficient for an extremely humid climate. If the effect of natural ventilation was converted into U.S. dollars, the estimated energy savings for Mexico in the year of 2008 was $ 801 - $ 1,035 million, which would be equivalent to 54.4% of the total cooling energy consumption by the residential sector in Mexico (Oropeza-Perez and
Østergaard, 2014).
The energy savings potential was also investigated for 35 cities in China (Tong et al.,
2016b). Of the five climate zones in China (cold, hot-summer-cold-winter, hot-summer-warm- winter, severe cold, and mild), the hot-summer-cold-winter zone was found to be least advan- tageous for using natural ventilation. Additionally, the hours favorable to natural ventilation significantly dropped when air pollution was considered. For example, the city of Zhengzhou, most severely impacted by pollution, lost 1,655 hours. The study concluded that China could have saved 112 GWh based on the data in the year of 2015 if buildings had used natural ventilation.
The Carnegie Mellon University research team collected and analyzed more than 150 case studies regarding high performance buildings and life-cycle value (Loftness et al., 2004).
From their analysis, the team found that using natural ventilation either solely or together with mechanical system could lead to a 47-79% energy reduction in HVAC. In addition to the energy savings, natural ventilation reduced health cost by 0.8-1.3% and increased productivity and return on investment by 3-18% and 120%, respectively.
2.1.2 Natural ventilation and thermal mass
The cooling capacity of natural ventilation can be assisted by thermal mass. Many studies were conducted to identify the effect of thermal mass used with natural ventilation. A study about
9 Chapter 2. Literature Review night-time ventilation found that incorporating thermal mass in a night-time natural ventila- tion system in Israel could reduce indoor temperatures by 3-6 degrees Celsius, although the performance of the strategy varied by thermal mass, ventilation rate, and diurnal temperature
fluctuation (Shaviv et al., 2001).
A dimensionless metric for characterizing the effectiveness of thermal mass in build- ings was proposed by Taylor and Miner (2014). The authors defined the metric as:
P I b = (ρ · c · thk) e ∆T · ( w ) Pm Is where:
ρ : density (kg/m3)
c : specific heat capacity (kJ/kgK)
thk : thickness of material (m)
−1 Pe : price of peak electricity (kJ )
−2 Pm : price of unit area of materials (m )
∆T : outdoor temperature range (K)
2 Is : daily average insolation in summer (kJ/m )
2 Iw : daily average insolation in winter (kJ/m )
This metric (b) considered two aspects: thermal mass property (ρ · c · thk) and economic con- cerns including energy and material costs ( Pe ∆T · ( Iw )). The authors demonstrated the vari- Pm Is ance in the effectiveness of thermal mass depending on materials including hardwood floors, granite, clay tiles, and concrete; and climate zones in Australia, USA, and other places.
In addition, a theoretical study about the relationship between airflow rate, indoor temperature and thermal mass was conducted using a sinusoidal function of outdoor tem- perature (Yam et al., 2003). In this study, an asymptotic behavior in thermal lag varying by thermal mass amount was observed. The thermal lag due to thermal mass was proved not to exceed six hours, which suggested that thermal mass amount should be set at the point in
10 2.1. Natural ventilation in Architecture which adding more mass would not effectively increase the thermal lag.
An experimentation with the effect of controlling windows on thermal comfort with thermal mass was also conducted (La Roche and Milne, 2004). In this study, one test room was an experimental group which had variable air change rate per hour (ACH) from 0.7 to
3.9 with a smart operable venting system, and the other was a control group which had a
fixed ACH of 0.7. In addition to the ACH, various settings included the existence of windows and the amount of thermal mass. This experimentation found that the room with the smart venting system achieved more thermal comfort throughout the experimental periods.
2.1.3 Controls for natural ventilation and energy savings
Research reveals that energy savings from natural ventilation can be influenced by controls.
For example, the San Francisco Federal Building, which is a naturally ventilated office build- ing, allows users to control windows. The natural ventilation performance with various con- trols of the building was tested in a study on control strategies (Carrilho da Graça et al., 2004).
To maximize indoor thermal comfort, the study controlled the indoor airflow velocities, uti- lized the thermal mass and heating energy, and controlled the indoor environment during harsh weather including storms and gusts. With the optimal control, the study emphasized that the success of the natural ventilation strategy significantly depended on user behavior.
Given well-informed occupants, it was estimated that the indoor temperature of the building would be less than 28 degrees Celsius except during 20 hours per year.
In regards to user-controls, an automatic control system can overcome the adverse ef- fect from the uninformed occupants. A study conducted in two adjacent classrooms compared two systems—automatic control system and manual control system (Stazi et al., 2017). In the case of users’ direct control, the main trigger for occupants operating the windows was indoor and outdoor temperature, but CO2 concentration was often neglected. The indoor temperature could oscillate substantially because students tended to operate windows during the breaks, and the internal heat gain dropped when they all left. According to the study, the discom- fort level under users’ control was roughly five times higher than the one under automatic
11 Chapter 2. Literature Review control. On the other hand, indoor temperature did not fluctuate by adopting an automatic control system, and that the automation was expected to lower energy consumption.
Controls for energy savings were not limited to natural ventilation. A study on an integrated control system investigated the relationship between energy savings, human com- forts, and collective controls of lights, natural ventilation, and HVAC systems (Sun et al., 2010).
The "dynamic programing-derived rules" jointly controlled shading blinds, lights, a window, and a fan coil unit. Test cases included a humid hot summer day with a large cooling load, a summer day with a big temperature difference between day and night, and a day in May with a low cooling load. Then these cases were compared with traditional control systems in which operation was controlled individually. In all cases, the integrated control system out- performed other systems. Particularly, their control system was designed not to use natural ventilation even if the temperature was favorable. This was because when humidity became higher than the threshold by using natural ventilation, the system determined that the need for dehumidification would be beyond the capacity of the HVAC system.
2.2 Evaluation of natural ventilation
Many researchers have developed different methodologies to evaluate natural ventilation. The most commonly used metrics include volume flow rates and air-change rate per hour (ACH).
This section reviews these and other metrics customized by researchers to measure natural ventilation performance.
2.2.1 Common metrics used in natural ventilation evaluation
2.2.1.1 Volume flow rates
Volume flow rates (m3/s, L/s · m2, or c f m) are one of the the most commonly used metrics for natural ventilation evaluation. There are various ways to measure volume flow rates. Ex- periments can be conducted using the tracer gas method (Gough et al., 2018) and wind tunnel tests. Numerical modeling using Airflow Network (AFN) and Computational Fluid Dynamics
12 2.2. Evaluation of natural ventilation
(CFD) is also used to calculate natural ventilation volume flow rates (Bangalee et al., 2012; Ray et al., 2014; Wu et al., 2012). Some analytical methods use pressure difference and temperature difference to calculate volume flow rates.
ASHRAE (2013a) requires that a certain ventilation rate (Vbz) be met in a breathing zone depending on the zone population (Pz), zone floor area (Zz), and occupancy categories (e.g., bedroom, lobby, or office room). The calculation is given by:
Vbz = Rp · Pz + Ra · Az
where :
Rp : outdoor airflow rate required per person
Pz : zone population
Ra : outdoor airflow rate required per unit area
Az : zone floor area
Rp and Ra for different occupancy categories are listed in ASHRAE (2013a), p.12-15.
2.2.1.2 Air-change rate per hour
An air-change rate per hour (ACH) is another popular metric for evaluating ventilation perfor- mance. It measures the ratio of volume of incoming airflow for an hour to the room volume.
For example, an ACH of 2 means that the air volume amount that is equivalent to twice the room volume is replaced by the outside air (or air from another zone) during an hour. An
ACH can be written as:
3, 600(s) · V˙ ACH = Vol where :
V˙ : airflow rate (m3/s)
Vol : room volume (m3)
13 Chapter 2. Literature Review
ACHs were used to validate a multizone network airflow model against tracer gas decay tests (Musser et al., 2001), to evaluate natural ventilation efficiency in a bedroom with different window settings (Chou et al., 2008), and to study the relationship between outdoor wind and indoor ACH in a two-story atrium (Horan and Finn, 2008).
ACHs were also used as a target criterion to create natural ventilation potential maps
(Hiyama and Glicksman, 2015), and to evaluate the the influence of surroundings on indoor ventilation by computing ACHs using CFD simulations (Tong et al., 2016a).
An ACH was calculated by a different formula to understand single-sided ventilation in a relation to the outdoor wind environment (Jin et al., 2016). The customized ACH was computed as:
C 1 ACH = 3600 · ln 0 · Cr τ where :
C0 : initial CO2 concentration
Cr : CO2 concentration at the time τ
In addition to the usage of ACH in indoor ventilation studies, ACHs were also adopted in urban wind studies (Hang et al., 2010; M. Lin et al., 2014), and in transit stations (Gao et al.,
2011).
2.2.2 Customized indices used in natural ventilation evaluation
2.2.2.1 Natural ventilation evaluation by the site and climate conditions
Natural ventilation potential (NVP) has been defined and quantified in a various ways. Roulet et al. (2002) defined NVP as “the possibility to ensure an acceptable indoor air quality by natural ventilation only” and passive cooling potential (PCP) as “the possibility to ensure an acceptable indoor thermal comfort using natural ventilation.” The authors described NVP levels of districts in Geneva, Switzerland, with good, medium, and poor NVP and visualized
14 2.2. Evaluation of natural ventilation them on a map using GIS. No building information was considered since the purpose was to evaluate the NVP of a site rather than of a building. Criteria of NVP included but are not limited to wind speed, direction, and air temperature, mean height of buildings, mean orientation of the streets, and distance to neighboring buildings.
Similarly, but with different criteria, Germano and Roulet (2006) evaluated the NVP of five sites. In addition to wind speed and direction, the criteria discussed in this study also included stack effect, noise levels, and pollutant levels as well as urban fabric and experts’ ratings. NVPs were rated as very high, high, medium, and poor. In another study, the NVPs of Basel, Switzerland, were evaluated and categorized as highest, intermediate, and lower
NVPs (Germano, 2007). The study created maps for pollution hours, noise hours, stack hours, and wind hours and analyzed them to yield NVP.
A metric named climate potential for natural ventilation (CPNV) quantified a climate’s suitability for natural ventilation. Suggested by Causone (2016), the CPNV is calculated by the sum of the hours available for natural ventilation in a year divided by the total number of hours in a year, and is given as:
∑n h CPNV = i=1 NV,i htot where :
th hNV,i : 1 if natural ventilation is available during the i hour of a year. 0 otherwise.
htot : total number of hours in a year
2.2.2.2 Natural ventilation evaluation by pressure difference
A natural ventilation performance indicator using pressure differences was proposed by Yang et al. (2005). The authors suggested the pressure difference Pascal hours (PDPH) as a means to predict NVP. The equation for the ‘effective pressure difference’ was calculated by the building’s ventilation rate due to stack and wind effects, using the orifice flow equation.
Also, the ‘required effective pressure difference’ was considered per the ASHRAE Standard
15 Chapter 2. Literature Review
62.2P—Ventilation and Acceptable Indoor. The PDPH is an index analogous to degree-days, which can be expressed as:
∆ ∆ ∆ ∆ p = ( Pe f f − PR) if Pe f f ≥ PR PDHD = 1h ∗ ∑ p hours ∆ ∆ p = 0 if Pe f f < PR
where :
∆ Pe f f : effective pressure difference
∆PR : required effective pressure difference
∆ ∆ The PDHD counted the positive values of ( Pe f f − PR) as noted in the equation. In this study, the PDPHs of four cities in China were calculated with several assumptions: south- facing buildings, identical openings on the south and the north facades, and uniform indoor air temperature at 22 degrees Celsius. The required effective pressure difference (∆PR) was determined by the minimum requirements from the ASHRAE Std. 62.2P neglecting possible internal loads. The approach using the pressure difference gave useful information about NVP at a city scale.
2.2.2.3 Natural ventilation evaluation by temperature difference
A metric named climate cooling potential (CCP) was suggested to explain degree-hours for the difference between indoor and outdoor air temperature (Artmann et al., 2007). Defined as “a summation of products between building/external air temperature-difference and time interval,” the CCP represented the cooling potential of a climate and its impact on a building.
The value of CCP was 1 if the temperature difference was the same or larget than the critical temperature difference for night-time ventilation, and the value was 0 otherwise. The metric
16 2.2. Evaluation of natural ventilation is written as:
h f ∆ 1 N m = 1h if Tb − Te ≥ Tcrit CCP = ∑ ∑ m (T − T ) N n,h b,n,h e,n,h n=1 h=hi ∆ m = 0 if Tb − Te < Tcrit
where :
h : the time of a day (h = 0, . . . , 24)
hi : initial hour of the night-time ventilation
h f : final hour of the night-time ventilation
Tb : building temperature
Te : external temperature ∆ Tcrit : critical temperature difference for night-time ventilation
2.2.2.4 Natural ventilation evaluation by buoyancy effect
An indicator for stack ventilation in multi-story buildings, the ventilation performance indi- cator (VPI), was suggested by Acred and Hunt (2014). The authors attempted to provide a dimensionless design approach that informs how users could meet the ventilation rate and indoor temperature requirements. This indicator, λ, is defined as:
Q2 1 λ = 2 g0 H5
where :
Q : flow rate through the room (m3/s)
g0 : reduced gravity (m/s2)
H : height of a story (m)
17 Chapter 2. Literature Review
2.2.2.5 Natural ventilation evaluation of building design
To evaluate the natural ventilation potential of a customized building design, a metric called natural ventilation effectiveness (NVE) was suggested (Yoon and Malkawi, 2017). The metric compared the hourly airflow rates of a customized building’s to the airflow rates that was required to offset the cooling load. The ratio of these two airflow rates was added for the total hours of the test period and then divided by the total hours. The NVE was calculated as:
∑ ACHavailable ACH NVE = required Total hours of season of interest
2.3 Natural ventilation modeling in design processes
From site evaluation to the conceptual design phase, it is often the case that only limited in- formation about the building design is available. Therefore, detailed data about the natural ventilation performance, such as zonal cooling effects and airflow movements, cannot be prop- erly assessed. Instead, the potential of natural ventilation with the given site under the given climate is investigated during this early design phase. Also, massing, programing, orienting, and goal setting are discussed. Requirements for acceptable thermal comfort and air quality should be studied while developing strategies for natural ventilation. Abundant research has been conducted on this topic and will be discussed in later sections (Causone, 2016; S.-H. Lin,
2014; Preiser and Vischer, 2005; Zhao, 2007).
During the design development phase, specific floor plans, sections, and elevations are delivered. It is an important phase in which multidisciplinary issues, including energy- conscious design, acoustic design, lighting design, envelope design, and indoor environmental design are addressed. For this reason, partnerships among various disciplines are critical, and iterative efforts are made during this phase (AIA, 2007; Emerging Professional’s Companion,
2013).
When a design is finalized and a building is constructed, it is finally possible to as- sess the detailed performance of natural ventilation. Once the building is constructed and
18 2.3. Natural ventilation modeling in design processes occupied, the evaluation can be even more robust with the actual measurements.
As mentioned above, there is no single answer yet to predict natural ventilation. One method can perform better than another depending on the problem that should be solved. This constantly evolving problem of natural ventilation can be of a great challenge for practitioners throughout the design process, because different design phases require different kinds of information, as outlined in Table 2.1.
Table 2.1: Design phases for natural ventilation
Design Phase Tasks Methodology
Climate and site evaluation - Suitability test for natural Analytical and empirical ventilation: temperature, humidity, approach noise, pollution
Conceptual design - Massing, programing, orienting, Analytical and empirical goal setting for natural ventilation approach - Checking requirements - Developing strategy
Design development - Prediction of performance: Experimental and cooling effect during cooling computational approach seasons, and fresh air supply
Design evaluation - Detailed evaluation of airflow, air On-site measurements and quality, and health aspects computational approach
2.3.1 Site evaluation and conceptual design phase
The outdoor environment is one of the most influential factors in assessing natural ventilation.
Understanding the local climate and environmental conditions should thus be the first step to investigate. For site analysis, building design may not have been initiated, and there may be limited information about the building. Therefore, the possibility of having natural ventilation is often discussed using the term, natural ventilation potential, or NVP.
Although the evaluation in this section does not consider specific building design, this could be done during the schematic design phase, the first design step outlined by AIA, in which the sustainable design strategies are discussed (AIA, 2007).
19 Chapter 2. Literature Review
2.3.1.1 Popular tools to evaluate natural ventilation potential in early design phases
Several computational tools have been developed and updated during the past ten years to support the natural ventilation evaluation in early design phases. The tools include Climate
Consultant, ASHRAE Thermal Comfort Tool, Ecotect Weather Tool, CBE’s Thermal Comfort
Tool, and Climate Suitability Tool, which are publicly available for download or purchase, or accessible free on-line.
The software Climate Consultant imports weather files, reads local annual climate data, and visualizes the data (Milne et al., 2009, 2007). Based on climate, the tool suggests possible design strategies to reach various comfort levels depending on a comfort model of choice. The tool also offers design guidelines and corresponding visual explanations for the site, demon- strating that energy-efficient design may require different types of buildings in each climate.
There are four options of comfort models available in the tool, among which the Adaptive
Comfort Model of ASHRAE Standard 55-2010 provides the percentage of comfortable hours in a year when natural ventilation is used.
The ASHRAE Thermal Comfort Tool is useful for the thermal comfort calculation com- plying with ANSI/ASHRAE Standard 55, Thermal Environmental Conditions for Human
Occupancy, as well as the U.S. Green Building Council (USGBC)’s Leadership in Energy and
Environmental Design (LEED). With four models including predicted mean vote (PMV) with elevated air speed, PMV Only, elevated air speed only, and adaptive models described in the
Standard, users input an activity level in the unit of metabolic rate, and clothing level. Then the result shows whether it complies with the Standard. Features also include mean radiant temperature calculator and clothing level calculator (Huizenga, 2011).
The Ecotect Weather Tool is another tool with which weather data are visualized. It provides passive design strategies, solar position, psychrometric chart, and wind data analysis
(Autodesk, n.d.).
The Center for the Built Environment (CBE)’s Thermal Comfort Tool is a web applica- tion that gives thermal comfort information in psychrometric charts, and informs users of
20 2.3. Natural ventilation modeling in design processes compliance with ASHRAE Standard 55. The web-based application incorporates the up-to- date Standard as opposed to the static ASHRAE Thermal Comfort Tool (Schiavon et al., 2014).
Of the two models the CBE tool provides, the adaptive model can be used for natural ven- tilation potential. The application lets users view the compliance documentation for thermal comfort for the USGBC’s LEED.
Climate Suitability Tool was developed specifically for thermal comfort via natural ven- tilation. The National Institute of Standards and Technology (NIST) developed a climate suit- ability analysis method (Axley, 2001; Axley and Emmerich, 2002), that the tool applies. The tool is available online (Emmerich et al., 2011). This is a single-zone model tool, and it calcu- lates the required ventilation rate in a way that the level of thermal comfort can be met by natural ventilation during the cooling seasons for commercial buildings.
2.3.1.2 Research methods to evaluate natural ventilation potential in early design phases
Researchers have developed evaluation methods and tools for early design phases that em- phasize certain functions to fit customized purposes. These methods and tools utilize urban fabric analysis, a geographic information system (GIS) software, analytical investigations, pro- totypical models, and parametric models.
In the project URBVENT which investigated natural ventilation potential in European cities, the urban fabric was a critical component of the analysis (Germano and Roulet, 2005).
The project was conducted by many researchers covering extensive topics in urban natural ventilation (Georgakis and Santamouris, 2008; Niachou et al., 2008a,b; Santamouris et al.,
2008). While the cooling effect of natural ventilation constrained by wind velocity, tempera- ture, noise, and pollution was considered (Ghiaus et al., 2005), an algorithm to calculate the wind speed in urban canyons for natural ventilation was proposed, which was validated with
field measurements (Georgakis and Santamouris, 2008). This study of an urban street canyon for natural ventilation evaluation was continued by measuring the air and surface temperature in Athens, Greece (Niachou et al., 2008a).
The natural ventilation potential of various cities was also presented on maps. Sheffield,
21 Chapter 2. Literature Review a city in England, was investigated by using GIS software (Hsie and Ward, 2006). In this inves- tigation, a geography-processing tool was developed using GIS and climate maps considering urban morphology, microclimate, and energy density were created. This GIS-extended pro- gram first created three layers in GIS: rugosity, porosity, and sinuosity of an urban structure.
CFD simulations were then run to get air distribution, and the ‘absolute indicators of urban morphology’ as a metric was next created as a GIS layer. The authors did not explain the simulation settings for CFD and how the urban morphology indicator was derived.
Additionally, the U.S. cities were also examined for NVP (Hiyama and Glicksman,
2015). In this study, target air change rates per hour (ACHs) were calculated from energy simulation to generate a map showing the NVP that varied based on the internal heat load.
The study suggested that the higher the internal heat gain, the higher the ACH required and the more cooling potential through natural ventilation of a site.
A tool for a building performance-based climate analysis was devised by Arsano and
Reinhart (2017). First, a single-zone “climate box” was created as a base-case model, in which users chose different options for the building and occupant preferences. The model was then tested for residential and office type programs. After simulations were run in EnergyPlus, the authors calculated the hours of thermal comfort and discomfort based on the ASHRAE 55
Adaptive Comfort Model and Elevated Air Speed standard. The tool was tested with 20 cities’ climate data, including Vancouver, Los Angeles, Lisbon, Mumbai, and Kuwait.
An interactive tool was proposed to calculate the effectiveness of natural ventilation for a given design (Yoon and Malkawi, 2017). While prior studies tested a prototypical geom- etry to evaluate the natural ventilation potential in an early design stage, this interactive tool utilized 3D modeling and parametrization tools to take the customized design into account from the early design stage.
In addition to the research mentioned earlier, natural ventilation potential has been researched in various climates. Turkey’s NVP was investigated by utilizing CFD simulations, which were conducted to test the impact of different blockages of buildings in urban settings and different interior partitions (Ayata and Yıldız, 2006). The NVP of Hong Kong’s warm and
22 2.3. Natural ventilation modeling in design processes humid climates was measured based on solar radiation, temperature, degree-days, degree- hours, building orientation, and thermal comfort improvement (Haase and Amato, 2009).
NVP studies looking at the temperature difference between day and night were conducted to evaluate NVPs of other Mediterranean coastal regions as well (Faggianelli et al., 2013).
2.3.2 Design development phase
The next step in the design process is the design development phase. This phase involves fast- paced design alterations and dynamic feedback among many practitioners, in which compu- tational tools can be used to support decision making. The tools and methods reviewed in the previous section do not require a specific building design. Instead, the NVP of a site is used to check the feasibility and suitability of adopting natural ventilation during the initial design stage. This means that the NVP of a site itself is not sufficient to provide informative feedback during the design development phase. Therefore, different approaches need to be employed as a design is developed. Computationally, there are two major approaches: the airflow network
(AFN) model for macroscopic airflow of buildings, and the computational fluid dynamics
(CFD) model for microscopic airflow (Axley, 2007). This section will cover both models as well as a coupled model of AFN and CFD.
2.3.2.1 Airflow Network Model (AFN)
The AFN model can be a useful tool to predict natural ventilation in design development phase. In AFN models, air flow rates of a zone are calculated within a network that con- nects to the adjacent zones based on pressure difference. The assumption that distinguishes an AFN model from a CFD model is that the uniformity of temperature and contaminant con- centration that an AFM model use (L. Wang and Q. Chen, 2008). This assumption can cause significant errors by neglecting the inflow momentum effect and temperature variance in a zone. Therefore, it is important to identify the simulation cases for which running an AFN model is adequate (Clarke, 2001; Megri and Haghighat, 2007; L. Wang and Q. Chen, 2008).
Input parameters of AFN were explored to find ways to lower uncertainty caused by
23 Chapter 2. Literature Review the assumptions. A sensitivity analysis conducted by Monari and Strachan (2015) character- ized the AFN model by sequential processes including factor screening, prioritizing, fixing, and mapping. This study elucidated the influence of uncertainty on the model’s performance and identify the critical parameters in the modeling. This analysis also revealed that the ratio of convection to radiation of heaters, mechanical ventilation inflow rate, and wind direction influenced the airflow result the most.
Knowing that the pressure difference is critical to AFN models, Cóstola et al. (2009) focused on pressure coefficient data in building energy simulation and AFN models. They reviewed the various sources to obtain pressure coefficients (Cp) admitting that a very pre- cise Cp is hard to obtain in practice. The study categorized the sources of Cp into two. The primary Cp sources refer to those that can be obtained by full-scale measurements, reduced- scale wind tunnel tests, and CFD. The secondary sources include the Cp databases from AIVC (Liddament, 1986; Orme et al., 1998), ASHRAE (ASHRAE, 2013b), empirical models (Swami and Chandra, 1988), CpCalc+ (Grosso, 1992), and Cp Generator (Knoll et al., 1995). This study addressed that the primary sources tended to be more accurate than the secondary sources, but the primary sources often cost more and the secondary sources were used more frequently in the BES and AFN models. In this study, a large discrepancy in Cp values was found among different sources, even with a simple box-shape building. This indicates that more studies are required to identify the appropriate method to measure Cp values.
Researchers have also proposed several nodal models to be implemented in AFN mod- els. These models used one, two, or three nodes in a single zone to consider the temperature gradient of a room, which a basic AFN alone would not consider. Mateus and Carrilho da
Graça (2015) proposed a simplified three-node model, estimated the neutral height for the displacement ventilation using the plume flow, and validated this approach by experimental data. This study also examined the cases in which multiple buoyancy sources occurred by con- sidering the thermal plume coalescence and identifying the relative strength of the sources.
The results were validated by using experimental data, as well as by comparing earlier nodal models developed by Carrilho da Graça and Linden (2004), Li et al. (1992), and Mundt (1996).
24 2.3. Natural ventilation modeling in design processes
Further research was conducted to enhance the three-node model in EnergyPlus (Ma- teus and Carrilho da Graça, 2017), in which both the measured and simulated performance of displacement ventilation were compared. The authors concluded that the displacement model of EnergyPlus could satisfactorily model the thermal comfort and CO2 concentration.
2.3.2.2 Computational Fluid Dynamics (CFD)
One critical drawback of the AFN models is that they do not provide the microscopic airflow, while CFD models allow investigation of the detailed airflow within a zone. Popular com- mercial CFD packages include ANSYS’ Fluent and CFX, and CHAM’s PHOENICS. They are general purpose CFD tools, meaning that these tools are used for various purposes from small electronic parts to urban scale analysis.
Less robust but more simplified CFD software for building simulation include IES VE’s
Microflo, and DesignBuilder’s CFD module. These tools are embedded within the commonly used building energy simulation (BES) software, thus providing better connection between
CFD and BES.
Not integrated into BES but offering other advantages to building simulation are
CHAM’s RhinoCFD and Ladybug Tool’s Butterfly. The former uses Rhinoceros as its GUI, offer- ing an opportunity for designers to explore CFD within their 3D modeling environment. The engine uses the essential features of PHOENICS (CHAM, 2016). The latter is a plug-in tool for
Grasshopper, which allows a user to run a CFD simulation in Rhinoceros (or Rhino). The engine of Butterfly is an open source CFD software, OpenFOAM, which was initially published by
OpenCFD Ltd. in 2004 (Ladybug Tools, 2019; OpenFOAM, 2016).
Within one CFD software, there exist various turbulence models including Reynolds- averaged Navier-Stokes (RANS) models, and Large Eddy Simulation (LES) models (Reiter,
2008). Each model has advantages and limitations to be adopted for natural ventilation study.
Tominaga et al. (2002) reported that the standard k-epsilon model, which is one of the RANS models, showed weakness in predicting reverse flow on roofs, and the revised k-epsilon mod- els could fix the problem. Jiang et al. (2003) investigated the LES model to test three types
25 Chapter 2. Literature Review of ventilation: single-sided ventilation with an opening in a windward wall, single-sided ven- tilation with an opening in a leeward wall, and cross ventilation. They concluded that the
LES model is appropriate for natural ventilation study. However, Reiter (2008) addressed that choosing the right boundary conditions for LES models are challenging, and the significant computational loads and fine mesh led to a long computational time. Reiter thus chose to validate the RANS models offered in Fluent with a single building, a group of buildings, and a dense urban environment, and concluded that RANS models can be used to study wind en- vironments for natural ventilation when the input settings follow a set of guidelines. Meroney
(2009) also confirmed that CFD can be used for natural ventilation prediction by compar- ing with wind-tunnel experiments and further demonstrated the benefit of decomposing the external and the internal airflow simulation, which saved computational time.
2.3.2.3 Coupling AFN and CFD
The previous sections, 2.3.2.1- 2.3.2.2, reviewed the AFN and CFD tools and their usages. The
AFN modeling was often used to understand the overall airflow, with the node of each zone represented by either pressure values or airflow rates. This fast simulation enables annual analysis. On the other hand, CFD allows detailed airflow analysis, and is often used to exam- ine phenomena that cannot be identified by AFN, such as the relationships between buoyancy and wind effects when they occur simultaneously. However, the intensive computational load discourages its usage in overall long-term behavior. Therefore, researchers have tried to make the most out of the advantages of each model by coupling AFN and CFD. Coupling AFN and
CFD may also be considered as coupling BES and CFD since commonly used BES tools (e.g.,
EnergyPlus) implement the AFN model to account for natural ventilation. This section will discuss the methods suggested by recent studies.
To improve accuracy of airflow modeling, L. Wang and Q. Chen (2007) coupled CON-
TAM, an AFN model developed by Dols and Walton (2002); and CFD0, a CFD code developed by Srebric et al. (1999). The authors found that coupling through pressure values from one simulation to another was the best way to couple, since the convergence of the solution was
26 2.3. Natural ventilation modeling in design processes stable. While the method improved the accuracy of simulation, this was an internal coupling that used specific computing for one turbulence model. Therefore, L. Wang and Wong (2009) proposed an external coupling for better flexibility in selecting turbulence models. The cou- pling was done for ESP-r and Fluent, and the boundary conditions, including pressure and velocity, were exchanged through the interface they developed. They once again validated the
findings of L. Wang and Q. Chen (2007) that using pressure boundary of the openings led to more reliable results.
To demonstrate the improved accuracy by the coupling methods, several studies com- pared heat transfer coefficients between the results from a coupling method and a single BES model (Yi and Feng, 2013; Zhang et al., 2013). In these coupling studies, heat transfer co- efficients were first obtained from CFD, which were then transported to BES. These studies observed that the coupling method could improve the accuracy of prediction.
Many studies tried to determine the appropriate tool and method for a given purpose, identify the most critical parameters in simulation results, and combine different methods to improve the accuracy of the simulation. To apply various tools and methods in building de- sign, more discussions on design procedures are required. It is not clear how designers should determine the suitability of using AFN over CFD, or vice versa. Moreover, it is important that the simulation results are reflected in design decisions in a timely and appropriate manner.
In this regard, a new way of performance evaluation and visualization in the 3D modeling environment may help enhance the natural ventilation performance of the building design.
27
Chapter 3
Dynamic metrics for interactive modeling
This chapter first discusses the natural ventilation performance metrics. It categorizes static and dynamic natural ventilation performance metrics and addresses the importance of dy- namic metrics. The chapter then proposes two important metrics — Design Natural Ventila- tion Cooling Effectiveness and Climate Potential Utilization Rate — that work in an interactive design procedure. The design procedure is then demonstrated in a feasibility study. The chap- ter describes these metrics for a steady-state condition. Calculations for transient conditions are described in the Chapter 4. Chapter 3. Dynamic metrics for interactive modeling
3.1 Metrics of natural ventilation performance
3.1.1 Static and dynamic metrics of natural ventilation
As Chapter 2 revealed, natural ventilation performance is evaluated in various ways. Com- monly used static metrics include flow rates, speeds, and ACH. One of the customized static metrics is defined as the number of hours when the meteorological data show favorable for natural ventilation. This metric has been referred to by different names: Natural Ventilation
Potential (Buckley, 2014); Climate Potential for Natural Ventilation (CPNV) (Causone, 2016); and natural ventilation hours (Y. Chen et al., 2017; Luo et al., 2007; Tan and Deng, 2017). These met- rics provide information about the characteristics of the given climate only or of a fixed indoor condition, and thus are considered static metrics. On the other hand, metrics such as Pressure
Difference Pascal hours (PDPH) (Luo et al., 2007; Yang et al., 2005), Climate Cooling Potential
(CCP) (Artmann et al., 2007), Satisfied Natural Ventilation Hour (SNVH) (Tan and Deng, 2017), and Natural Ventilation Effectiveness (NVE) (Yoon and Malkawi, 2017) depend on the indoor environment, and are considered dynamic metrics.
This section suggests two revised metrics based on NVE to improve the usability of the metrics for interactive modeling. Metrics for interactive modeling should provide designers with design-applicable information to help improve their designs. Conventional ventilation metrics including velocity and volume flow rates may be used to evaluate the ventilation quality, but these values cannot be directly applied to design without additional information.
For example, even though a user knows that a zone will have a volume flow rate of 3 m3/s, she or he will not be able to tell whether this value indicates sufficient cooling effect from natural ventilation. To overcome this shortcoming of the conventional metrics, this section introduces two metrics that can give informative feedback on designs. One measures the ratio of cooling capacity that natural ventilation alone offers compared to the ideal cooling capacity that will keep the building meeting certain comfort criteria throughout the period of interest. This metric measures how effective natural ventilation is for cooling, and is called
Design Natural Ventilation Cooling Effectiveness, or dNVCE. The other metric evaluates how well
30 3.1. Metrics of natural ventilation performance a building design has utilized the natural ventilation potential of the climate. This metric is named Climate Potential Utilization Rate, or CPUR.
3.1.2 Terminology
As mentioned earlier, there is no single term that describes the potential of natural ventila- tion. In fact, natural ventilation potential has many aspects, and researchers have used the term “potential” in different ways. Therefore, it is important to illustrate these various aspects and use terms consistently. Prior to further discussion, this section organizes and defines sev- eral terms that will be used in this dissertation. The metrics, including two newly proposed metrics, are summarized in Table 3.1.
Table 3.1: Natural ventilation performance metrics
Metrics Climate (static) Design (dynamic)
Natural ventilation hour (NVh) NVh: 0 or 1 NVh: 0 or 1 Natural ventilation air quality (NVAQ) NVAQ: 0 or 1 NVAQ: 0 or 1
Natural ventilation cooling effectiveness (NVCE) cNVCE: 0 or 1 dNVCE: in range [0, 1]
Natural ventilation effectiveness (NVE) cNVE: 0 or 1 dNVE: in range [0, 1]
dNVCE Climate potential utilization rate (CPUR) - CPUR = cNVCE
3.1.2.1 Natural ventilation hour (NVh)
A natural ventilation hour (NVh) of 1 is an hour when the air—either outdoor or indoor depending on analysis types—meets the thermal criteria. A NVh of 0 is an hour when the air is not usable due to either thermal or quality concerns. Each hour can earn either 1 NVh or 0
NVh. Therefore, a day may get 24 NVh at most, and a year may get 8760 NVh at most. Natural ventilation hours assume that the time step for a simulation is an hour. When a shorter time step is used, however, such a duration may be referred to in a partial NVh. The term “NVh” has been used in several studies (Y. Chen et al., 2017; Luo et al., 2007; Tan and Deng, 2017),
31 Chapter 3. Dynamic metrics for interactive modeling although there may exist subtle differences in usage across these references. The following sentences show the usage examples of NVh in this dissertation:
• Under Boston’s climate conditions, 12 pm on July 1st has 1 NVh.
• This room gets only 3 NVhs, while outdoor air has a potential of 6 NVhs for a day.
The second example statement implies that the total number of NVh that a room can earn may be different than what climate conditions could offer. The next few terms identify this difference.
3.1.2.2 Natural ventilation cooling effectiveness (NVCE) and climate potential utilization
rate (CPUR)
Natural ventilation cooling effectiveness (NVCE) is the most essential term that this disser- tation is focused on. This metric considers how effective natural ventilation is for cooling a space. To calculate this term, there must be a customized thermal criteria. This means that the cooling effectiveness that natural ventilation will bring can vary depending on one’s thermal criteria. For example, a narrower target indoor temperature range, such as a range between 20 to 25 degrees Celsius, may compute a lower NVCE than a more generous target range, such as 10 to 30 degrees Celsius. Humidity can be another thermal criterion.
This dissertation proposes to differentiate an NVCE computed based on climate con- ditions only from that computed based on the indoor environment, hence the climate NVCE
(cNVCE) and design NVCE (dNVCE). While cNVCE explains the existing concepts of natural ventilation potential, dNVCE is newly proposed as a dynamic metric.
• Climate NVCE (cNVCE): Climate NVCE is determined by the local climate, and thus
is a static condition. Its value is the mean NVhs of climate conditions during the
period of interest. For example, if the site has 80 NVh during the 100 hours of analysis
period, the cNVCE of the site becomes 0.8. The cNVCE of Boston, MA in summer may
be greater than that of Dallas, TX.
32 3.1. Metrics of natural ventilation performance
• Design NVCE (dNVCE): Design NVCE is the mean NVhs of a period of interest during
which a targeted room can benefit from the outdoor air. Unlike climate NVCE, design
NVCE is a dynamic metric that depends on a particular building design. Its value
ranges from 0 to 1. Under a steady-state condition, dNVCE is always less than, or at
most equal to the cNVCE of the site due to internal heat gain. The comprehensive
process to calculate this metric is explained in Section 3.2.1.
• Climate Potential Utilization Rate (CPUR): A CPUR is a ratio of dNVCE to cNVCE.
Section 3.2.2 elaborates further on this metric.
3.1.2.3 Natural ventilation air quality (NVAQ)
Natural ventilation air quality (NVAQ) brings aspects of air quality, including noise, pollen, pollution, and so on, into consideration. Thermal conditions are not considered, as they are considered by NVCE. The reason that the effectiveness of cooling and air quality are consid- ered separately is because there is no consistent correlation between outdoor temperature and air quality. For example, high temperature does not necessarily imply high or low air qual- ity. Rather, air quality depends on pollen seasons and nearby construction and/or industry.
Figure 3.1 illustrates two cases in which the general effectiveness of natural ventilation varied despite the same cNVCEs (0.79) and NVAQs (0.83) in both cases. When cooling effectiveness and air quality are considered simultaneously, each hour can earn 1 NVh only if cNVCE and
NVAQ are both 1. In this regards, Case 1 received less NVh than Case 2 due to the timing of
NVhs in cNVCE and NVAQ.
Poor air quality is not desirable either indoors or outdoors. In absence of indoor pol- lutants, climate NVAQ and design NVAQ will be the same values. An NVh of an NVAQ is 1 when air quality is considered acceptable, and 0 otherwise. Although indoor pollutants from photocopying machines, cooking, and human metabolism affect the natural ventilation anal- ysis, this dissertation assumes that the NVAQ is always 1 in order to focus on the thermal aspect of natural ventilation in buildings.
33 Chapter 3. Dynamic metrics for interactive modeling
Figure 3.1: Relationships among cNVCE, NVAQ and NVE in two different virtual cases
3.1.2.4 Natural ventilation effectiveness (NVE)
Natural ventilation effectiveness (NVE) is a generic and comprehensive term that considers both the cooling and air quality aspects of natural ventilation. If either of the aspects does not meet the comfort criteria, natural ventilation is not effective. Therefore, NVE is always less than or equal to NVCE (Figure 3.1). If NVAQ is always 1, NVE is equal to NVCE, thus they can be used interchangeably.
• Climate NVE (cNVE): Climate NVE is the mean of the NVhs when both cNVCE and
NVAQ are 1. The cNVE can be less than the cNVCE if the NVhs for cooling are
compromised by the NVhs for air quality (Figure 3.1– Case 1).
• Design NVE (dNVE): Design NVE is similar to cNVE but is determined by dNVCE
instead of cNVCE.
Design natural ventilation effectiveness (dNVE) is also a new dynamic term. However, since this dissertation does not consider NVAQ, the rest of the dissertation concentrates more on dNVCE rather than dNVE.
34 3.2. Dynamic performance metrics for natural ventilation
3.2 Dynamic performance metrics for natural ventilation
This section examines the detailed calculation processes of dNVCE and CPUR, which are key performance metrics proposed in this study. This section also discusses the interpretation of these metrics and suggests a design framework to demonstrate how feedback from these metrics could be useful.
3.2.1 Design natural ventilation cooling effectiveness (dNVCE)
The dNVCE of a space explains how effective natural ventilation is for cooling the space for a certain period of time. It looks at the ideal cooling power of natural ventilation (qideal) and the actual cooling potential obtainable from natural ventilation (qavail). If natural ventilation’s cooling potential is ideal, then it is enough to cool the indoor space to the desired temperature
(Ttarget) for an hour, and the dNVCE is 1. If the resultant indoor temperature is higher than
Ttarget for another hour, a dNVCE is then calculated as the ratio of qavail to qideal as in Eq. (3.1). This ratio indicates how far or close it is from achieving 1 dNVCE under the current situation.
If the dNVCE is 0.9, it may be easy to achieve a value of 1 by adjusting some design options.
If the dNVCE is 0.1—meaning that natural ventilation cooling can provide only 10% of what is needed—it may be a challenge to increase the value to 1.
1 if qavail ≥ qideal dNVCE(hour) = (3.1) qavail otherwise qideal
Design natural ventilation cooling effectiveness considers thermal characteristics de- termined by design aspects of a building. For example, qavail depends on outdoor conditions and the flow rate, which varies by window configuration and type of ventilation. The ideal cooling capacity, qideal, is related to many more conditions including building materials, win- dow configurations, room sizes, and internal heat gain of the space, in addition to climate conditions. As architects revise the design, qavail and qideal change accordingly, while dNVCE
35 Chapter 3. Dynamic metrics for interactive modeling provides information during the design phase on the effectiveness of natural ventilation in cooling. A dNVCE can be calculated for any duration, from a small time step like an hour to a large one like a year. The dNVCE of a year is the mean dNVCE of each time step. The rest of the section elaborates on the calculation of each of the two key cooling powers—qavail and qideal—with a 1 hour time step for a 1 hour duration, calculated in a steady state for simplicity.
3.2.1.1 Heat balance between outdoor and indoor
In a steady state, the heat balance between outdoor and indoor can be written as
UA(Tin − Tout) + ρcV˙ (Tin − Tout) = qsolar + qinternal. (3.2)
The left-hand side terms are heat loss through the building envelope, infiltration, and venti- lation when Tout ≤ Tin. The two terms on the right-hand side are the heat gains from solar radiation, occupants, appliances, and so on, referred to as qgain for convenience. With every- thing else but the indoor temperature (Tin) known, Tin is the function of these various building settings. To calculate a dNVCE, a part of this heat transfer is defined as the cooling potential of natural ventilation, and the other part as the cooling load.
3.2.1.2 Available cooling power of natural ventilation, qavail
The numerator of the dNVCE is the cooling potential (qavail) that natural ventilation can pro- vide under certain design settings. As a building is designed to have a flow rate, V˙avail, the available cooling capacity by which the outdoor air (Tout) helps the indoor air achieve the target temperature (Ttarget) is defined as Eq. (3.3):
qavail = −ρcV˙avail(Ttarget − Tout), (3.3)
where the negative sign denotes that qavail is heat loss and Ttarget is a user-defined criterion.
The flow rate (V˙avail) is determined by various design aspects: the type of natural ventila- tion (single-sided ventilation, cross-ventilation, or displacement ventilation), window loca-
36 3.2. Dynamic performance metrics for natural ventilation tions, window sizes, and outdoor wind direction and speed. As Chapter 2 revealed, there are many methods to determine V˙avail, so users should adopt an appropriate method that fits their purpose and design process.
3.2.1.3 Ideal cooling power of natural ventilation, qideal
Consider a case where Tout is below the upper limit temperature of the comfort zone (Ttarget).
In an ideal case where natural ventilation rate (V˙ ) provides sufficient cooling power, Tin is less than or equal to Ttarget, the cooling load is zero, and Tin is
qgain Tin ≤ Ttarget = + Tout. (3.4) UA + ρcV˙
On the other hand, if V˙ is not enough to cool the space, Tin may become greater than Ttarget.
In this case, additional cooling (qreq) is necessary to achieve Ttarget. The qreq can be written as,
qgain + qreq Ttarget = + Tout UA + ρcV˙
qreq = (Ttarget − Tout)(UA + ρcV˙ ) − qgain. (3.5)
Note that qreq is a negative value. Now we define the ideal cooling power as qavail + qreq.
qideal = qavail + qreq
= −ρcV˙ (Ttarget − Tout) + (Ttarget − Tout)(UA + ρcV˙ ) − qgain
= −(qgain − UA(Ttarget − Tout)) (3.6)
Eq. (3.6) is the denominator of the dNVCE. With qavail and qideal, the dNVCE from Eq. (3.1) becomes
qavail dNVCE(hour) = (3.7) qavail + qreq
ρcV˙ (Ttarget − Tout) = . (3.8) qgain − UA(Ttarget − Tout)
37 Chapter 3. Dynamic metrics for interactive modeling
A close examination of Eq. (3.8) reveals that the denominator is the cooling capacity that the ideal natural ventilation could have offered, as in
ρcV˙ideal(Ttarget − Tout) = qgain − UA(Ttarget − Tout), (3.9)
where V˙ideal is the flow rate that would have been ideal to achieve Ttarget. Therefore, a dNVCE can also be written as
qavail V˙avail ACHavail dNVCE(hour) = = = . (3.10) qideal V˙ideal ACHideal
3.2.1.4 Interpretation of dNVCE
As Eq. (3.7) indicates, if qavail = 0, then the dNVCE is also 0. If qreq = 0, meaning that there is no need for additional cooling, then the dNVCE is 1. If the dNVCE is between 0 and 1, it is the fractional cooling capacity that natural ventilation can provide compared to the ideal cooling capacity.
The above calculation was based on a time period of 1 hour, which only had one time step. If the simulation period is extended to n hours, the dNVCE becomes the average of all hourly dNVCEs, as in
Σn qavail,i i=1 q dNVCE = ideal,i , (3.11) (duration) n
th where qavail,i and qideal,i denote the values of i hour. It is practical and recommended to indicate the time period of the metric, such as dNVCE(May−Oct) or dNVCE(July8).
The calculation was also based on a steady state. In an unsteady state, where the current temperature affects the next time step, qideal needs to be modified. This is required especially when a building has thermal mass, which will be discussed in Chapter 4. In the current chapter, we limit the description of dNVCE to steady-state conditions.
38 3.2. Dynamic performance metrics for natural ventilation
3.2.2 Climate Potential Utilization Rate (CPUR)
The dNVCE indicated the status quo of the current design in terms of natural ventilation’s cooling performance. To help understand how much room for improvement there is under the given climate, this dissertation also introduces the climate potential utilization rate (CPUR).
A CPUR is defined as the ratio of dNVCE to cNVCE. A CPUR of 1 indicates that the current building achieves the same number of comfortable hours as the climate does without a build- ing, and a CPUR of 0.5 means the design achieves 50% of the thermally comfortable hours that the climate alone can achieve. In a steady-state simulation, dNVCE would be generally less than or at most equal to cNVCE due to internal and solar heat gains. This may change with thermal mass and window controls allowing dNVCE to exceed cNVCE, which will be discussed in Chapter 4.
While dNVCE can be calculated for any duration, the duration for which cNVCE is calculated must be carefully determined, especially when thermal mass is considered. For a given time step, for example, an hour, dNVCE may be a positive number due to a thermal lag, while climate potential is 0. This may happen when the outdoor temperature is not within the comfort zone but the indoor temperature is still comfortable due to the high heat capacity of thermal mass. In this case, the CPUR becomes infinite, so it is not meaningful to calculate this metric for only an hour. The CPUR is more useful for an extended period of simulation time.
3.2.3 Understanding dNVCE and CPUR together
The combination of the two metrics of dNVCE and CPUR can then be used in interactive en- ergy modeling. Figure 3.2 explains the interpretation of the combination. A high dNVCE and a high CPUR imply that natural ventilation has high potential for cooling the building, and the design has achieved sufficient natural ventilation performance by effectively utilizing the climate. A low dNVCE and a low CPUR indicate that natural ventilation cannot offer as much cooling power as the specific building needs, but there is rooms to improve the dNVCE since it does not utilize the climate potential very well. A low dNVCE and a high CPUR may not
39 Chapter 3. Dynamic metrics for interactive modeling
Figure 3.2: Understanding dNVCE and CPUR be encouraging, as this combination implies that the building has low performance despite a high utilization ratio of its climate resources. Having this information while developing a building design would allow architects to revise their design to better utilize natural ventila- tion. The following subsections explain the detailed processes of calculating the metrics and discuss their usage in interactive performance modeling.
3.2.4 Framework for dNVCE and CPUR
The following procedure is a suggested design framework that utilizes the dynamic perfor- mance metrics explained above.
1. Set up an initial design.
• Design a room. Determine room size, volume, and wall areas.
• Choose building materials. This will determine the U-value of walls.
• Design windows. The location and size will determine the type of ventilation
and available flow rate.
40 3.2. Dynamic performance metrics for natural ventilation
• Set a thermal criterion, for example, an upper temperature limit of 23 degrees
Celsius.
• Set a time period of interest, for example, May to October.
2. Run a simulation that yields the two metrics.
• Look into dNVCE: how effective is natural ventilation in cooling your space?
• Look into CPUR: is the design well utilizing the climate potential well?
3. Interpret the result.
• A low dNVCE and a low CPUR indicate that natural ventilation is not effective
but there is room for improvement.
• A low dNVCE and a high CPUR indicate that natural ventilation is not effec-
tive, and likely will not be easy to improve at this point.
4. Try some modifications that affect cooling loads and see how the metrics change.
• Reduce heat gain: install shading device, revise occupant density if possible,
and so on.
• Change the window configurations: make larger openings, change the loca-
tions, and so on.
• Apply some passive strategies: install thermal mass and control window sched-
ules.
5. Finalize the design from the analysis.
41 Chapter 3. Dynamic metrics for interactive modeling
3.3 Feasibility study for interactive modeling
This section tests the framework suggested in the previous section and demonstrates the feasi- bility of using the dynamic metrics in an interactive design environment. This section contains descriptions, images, and implementation methods that were introduced in the author’s pre- vious study (Yoon and Malkawi, 2017).
3.3.1 Study description
This study develops a parametric design system for wind-driven natural ventilation for demon- stration purposes. It uses a 3D parametric design platform, 3D Rhino and Grasshopper. The cal- culations of dynamic metrics are performed in combination with the energy modeling tools including Honeybee and Ladybug, customized scripts in Python, and cp resources as described in Figure 3.3.
Figure 3.3: Procedure to Evaluate Natural Ventilation Effectiveness in Building Design. Image from Yoon and Malkawi (2017)
3.3.2 Geometry
A one-story office building of 5 x 5 x 4 (m3) was modeled and examined for this case study.
The geometry was created using Grasshopper components for parameterization. Figure 3.4 de- scribes the parameterization of the room and window sizes. The base case had two windows
42 3.3. Feasibility study for interactive modeling on the east and south-sides of the building envelope with the dimensions of 0.5 · 0.5(m2), and the centers of the windows were at 1.5 m from the ground. For the simulation engine to recog- nize the different building surfaces, including slab, ceiling, and walls, Honeybee components were connected with the geometry components.
Figure 3.4: Test room geometry created in Grasshopper, Rhino. Image from Yoon and Malkawi (2017)
3.3.3 Climate natural ventilation effectiveness (cNVCE)
The Ttarget was set to 23 degrees Celsius. This is an arbitrary criterion, and users may change it. As climate NVCE (cNVCE) does not require any building settings, the cNVCE(may−oct) can be calculated using weather data only. With an upper limit of 23 degrees Celsius and a lower limit of 13 degrees Celsius, Boston’s cNVCE(may−oct) was 0.67, and each NVh is mapped in Figure 3.5. The way that the map was created indicates once again that this climate metric is static and does not respond to any building design.
Figure 3.5: A cNVCE map of Boston from May 15th to October 15th
43 Chapter 3. Dynamic metrics for interactive modeling
3.3.4 Pressure coefficient (cp) and available cooling power
When wind-driven ventilation is considered, pressure coefficients (cp) at windows plays a key role in creating airflow, as written in Eq. (3.12):
1 ∆P = ρv2(c − c ) (3.12) 2 p,1 p,2 where :
v : undisturbed wind speed at building height
cp,1 − cp,2 : pressure coefficient difference between two windows.
For implementation purposes, the study used the cp calculation model suggested by Swami and Chandra (1987), which provided two cp equations for both low-rise and high-rise build- ings. In their study, the cp equation for a rectangular low-rise building was given as a function of the angle between the orientation of a wall and wind direction, and the ratio of the hori- zontal widths of the wall of interest and the adjacent wall. Their empirical equation was then coded within Grasshopper for this study (Figure 3.6). Wind directions and speeds, which were required to calculation cp values, were obtained using Ladybug.
Now that the pressure coefficient differential is known, V˙avail, ACHavail, and qavail can be obtained as in:
q ∆ V˙avail = ACdv cp
ACHavail = 3600V˙avail/vol
qavail = −ρcV˙avail(Ttarget − Tout) by definition from Eq. (3.3). (3.13)
In lieu of using the empirical cp values from Swami and Chandra (1987), other sources includ- ing wind tunnel tests and CFD simulations can also be used to calculate cp values (Cóstola et al., 2009).
44 3.3. Feasibility study for interactive modeling
Figure 3.6: Connections among components in Grasshopper and Rhino. Image from Yoon and Malkawi (2017)
3.3.5 Ideal cooling capacity
To obtain the ideal cooling capacity (qideal), the cooling load qreq was first calculated. An energy simulation was run by Honeybee, and a list of the hourly cooling loads (qreq in Eq. (3.5)) during the designated timeframe was obtained by selecting the Ideal Loads Air System setting. This ensures that the indoor temperature was kept at Ttarget and the cooling power used to meet this criterion was recorded for further calculation. This simulation was performed based on the following assumptions: 15 W/m2 of equipment load, 10 W/m2 of lighting load, 0.0004 m3/s · person · m2 of infiltration rate, and 0.1 ppl/m2 of occupant density. The site was located in Boston, MA, and May 15th - Oct 15th was chosen for the simulation period.
Next, qideal, V˙ideal, and ACHideal were calculated as in Eq. (3.14).
qideal = qavail + qreq
qideal V˙ideal = − ρc(Ttarget − Tout)
ACHideal = 3, 600V˙ideal/vol (3.14)
Lastly, the ACHreq was compared with the minimum airflow rate suggested by ASHRAE
(2013a): if ACHreq 45 Chapter 3. Dynamic metrics for interactive modeling 3.3.6 Initial results and testing more design alternatives The ratio of ACHavail to ACHideal was calculated to yield hourly dNVCEs. To represent the performance throughout the analysis period which was May 15th to October 15th, the 3,696 individual dNVCE values were averaged as in Eq. (3.15). An hourly dNVCE value larger than 1 was regarded as 1. Σ ACHavail dNVCE = ACHideal = 0.45 (3.15) (may−oct) 3, 969 The dNVCE of the initial design was 0.45. This was 68% of the cNVCE, leading to a CPUR of 0.68. Although the initial dNVCE was only 0.45, the low CPUR suggested that there could be some other options to improve the dNVCE. To explore how various design options would influence these metrics, five more design settings were tested. Design modification included the location of the openings, the size of the openings, and the volume of the zone as listed in Table 3.2. Three sets of window locations were tested: south and west, north and south, and south and east sides. Two different window areas were 0.50 m2 or 0.25 m2. Window sizes in the first alternative case (Alt 1) were double the base case. Alt 2 and 3 had north and south-facing windows with window sizes of 0.25 m2 and 0.50 m2 respectively, and Alt 4 and 5 had south and east-facing windows with window sizes of 0.25 m2 and 0.50 m2 respectively. Table 3.2: Settings of test cases Windows location Operable window area (m2) Base case S, W 0.25 Alt 1 S, W 0.50 Alt 2 N, S 0.25 Alt 3 N, S 0.50 Alt 4 S, E 0.25 Alt 5 S, E 0.50 46 3.3. Feasibility study for interactive modeling 3.3.7 Results The dNVCE and CPUR of all six cases are shown in Table 3.3. Of the six cases, Figures 3.7 to 3.9 show three dNVCE maps of the base case, Alt 2, and Alt 5, which demonstrated the worst to the best performances. These results support the hypothesis that the performance of natural ventilation may vary based on different design options and that investigating a cNVCE only would not be sufficient to understand the building’s performance. Table 3.3: dNVCE(may−oct) and CPUR results of design alternatives Base case Alt 1 Alt 2 Alt 3 Alt 4 Alt 5 dNVCE(may−oct) 0.45 0.56 0.51 0.57 0.46 0.57 CPUR 0.68 0.85 0.76 0.86 0.70 0.86 As a reference, the base case was run with a new target temperature of 26 degrees Celsius for the entire year, from January to December, based on Boston’s weather data. Two additional climate zones were tested for comparison: Santa Monica, CA, and Dallas, TX. The results of these three cities are shown in Figures 3.10 to 3.12. This comparison showed that Santa Monica had the greatest potential for this design. The low performances of natural ventilation in the other cities were mainly attributed to Boston’s cold winter and Dallas’ hot summer. 3.3.8 Discussions This interactive parametric study was conducted to check the feasibility of the dynamic met- rics’ usage during an early design phase. The result demonstrated that cNVCE shown in Figure 3.5 was substantially different than the dNVCE of the base case, which was reduced by 68 % from the cNVCE. This reduction in effectiveness demonstrated that natural venti- lation performance depends on design options, thus dNVCE should be studied in addition to climate analysis. The benefits of the interactive modeling with dynamic metrics are the following: 47 Chapter 3. Dynamic metrics for interactive modeling Figure 3.7: The dNVCE map (May 15- Oct 15) of base case. Windows on the South and West facades with operable window area of 0.25 m2. Figure 3.8: The dNVCE map (May 15- Oct 15) of Alt 2. Windows on the North and South facades with operable window area of 0.25 m2. Figure 3.9: The dNVCE map (May 15- Oct 15) of Alt 5. Windows on the South and East facades with operable window area of 0.50 m2. 48 3.3. Feasibility study for interactive modeling Figure 3.10: Annual dNVCE map of the test building in Santa Monica, CA. Figure 3.11: Annual dNVCE map of the test building in Boston, MA. Figure 3.12: Annual dNVCE map of the test building in Dallas, TX. Note. Figures 3.10 to 3.12 were reproduced from (Yoon and Malkawi, 2017) with permission. 49 Chapter 3. Dynamic metrics for interactive modeling • Intuitive and quick evaluation of natural ventilation performance is accessible to de- signers. • The dynamic metrics of dNVCE and CPUR offer instant insight into how well users’ goals are being achieved. • The relationship between design options and building performance is revealed during design processes. • The analysis uses one node per zone, so the calculation is faster than CFD simulations. • The energy simulation engine used in this study was EnergyPlus, but the same analy- sis procedure can be pursued in any simulation engine or a customized model as long as it can be properly implemented into the interactive modeling environment. In this test, the calculation of dNVCE and CPUR was performed for a single-zone room. Also, this section mainly discussed steady-state cases, where thermal mass cannot be properly considered. Therefore, the following items will be discussed in the next chapter: • refinement of metrics to consider transient simulations; • the impact of other passive strategies on natural ventilation performance; • expansion to multi-zone buildings; • validation with experiments; and • links to the emerging simulation tools. 50 Chapter 4 Thermal mass, dynamic window controls, and natural ventilation The NVE and NVUR calculations introduced in the previous section are based on steady- state conditions. Thermal mass, as one of the passive design strategies, is thus not considered. However, since installing thermal mass may significantly influence indoor thermal comfort, the transient behavior of this setting and its impact on NVE are worth investigating. In this chapter, the analytical model for the thermal mass effect is first examined, because the model can be easily integrated into the NVE and NVUR calculation. The first sec- tion reviews the single-zone solution and develops it to a multi-zone solution. The analytical multi-zone solution is verified in the next few sections with and without natural ventilation, confirming the correctness of the solution. Later sections suggest a dynamic window opera- tion responsive to the thermal mass and natural ventilation, revealing a few limitations of this approach. Chapter 4. Thermal mass, dynamic window controls, and natural ventilation 4.1 Multi-zone thermal mass solution In this section, heat transfer of a multi-zone building with thermal mass is derived to obtain the ideal cooling power (qideal). This qideal is then used to calculate dNVCE. This section first reviews the thermal behavior of a single-zone room, and derives equations for a multi-zone room. 4.1.1 Single-zone model In steady state, the heat transfer between Zone 0 (outdoor) and Zone 1 described in Figure 4.1 (a) depends on the outdoor air temperature (T0), the air temperature of Zone 1 (T1), and the thermal resistance between the zones (R01). It can be written as the following equation: T0 − T1 q01 = . R01 R01 is the sum of thermal resistance from conduction through n numbers of walls and convec- tion due to infiltration as in Eq. (4.1): 1 R = , (4.1) 01 Σi ˙ n=1Ui Ai + ρCpV01 th th where Ui is the U-value of the i wall, Ai is the area of the i wall, ρ is air density, Cp is air specific heat, and V˙01 is the infiltration rate. Considering a thermal mass with the thermal capacitance of C1 placed in Zone 1 and internal heat gain of qint (Figure 4.1 (b)), and allowing (a) Single-zone model (b) Circuit analogy with thermal mass Figure 4.1: Single-zone geometry description and circuit analogy diagram 52 4.1. Multi-zone thermal mass solution T1 to change, the following equation holds: dT1 T0 − T1 C1 = + qint. (4.2) dt R01 4.1.1.1 Case 1: T0 is a non-zero constant and qint is zero. To begin with, a simple case in which T0 is a non-zero constant and qint is 0 is considered. ∆ T01 is the temperature difference between the outdoor and Zone 1 (T0 − T1). Because T0 is a dT0 constant, dt = 0, and d∆T d(T − T ) dT 01 = 0 1 = − 1 . (4.3) dt dt dt Multiplying R01 by both terms of Eq. (4.2) leads to: dT R C 1 = T − T + R q (4.4) 01 mass dt 0 1 01 int ∆ = T01 + R01qint ∆ = T01. With a thermal time constance defined as τ = R01Cmass, Eq. (4.4) becomes: dT τ 1 = ∆T . (4.5) dt 01 ∆ dT1 d T01 Replacing dt with a term of dt causes Eq. (4.5) to change to: d∆T τ(− 01 ) = ∆T dt 01 ∆ d T01 1 ∆ = − dt T01 τ ∆ ln T01 = −t/τ + A ∆ −t/τ+A −t/τ T01 = e = β e , (4.6) ∆ where A is a constant of integration and β is the initial T01 where t = 0. 53 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation 4.1.1.2 Case 2: T0 and qint are non-zero constants Next, a case in which both T0 and qint non-zero constants is considered. For this case, a ∆ modified form of T01 from Eq. (4.6) is taken and then differentiated as in: ∆ −t/τ T01 = β(t) e (4.7) d∆T d(T − T ) dT 01 = 0 1 = − 1 dt dt dt 1 dβ(t) = − β(t) e−t/τ + e−t/τ . (4.8) τ dt Re-writing Eq. (4.4) with non-zero qint, and plugging Eq. (4.7) and Eq. (4.8) into it, Eq. (4.9) can be derived as: dT τ 1 = ∆T + R q dt 01 01 int 1 dβ(t) τ[ β(t)e−t/τ − e−t/τ ] = β(t)e−t/τ + R q τ dt 01 int dβ(t) R q = −τe−t/τ . (4.9) 01 int dt Next, solving for β(t): dβ(t) R q = − 01 int et/τ dt τ t/τ β(t) = −R01qint e + D, (4.10) where D is a constant of integration. Plugging Eq. (4.10) into Eq. (4.7), ∆ t/τ −t/τ T01 = (−R01qint e + D)e . (4.11) ∆ ∆ Let the initial T01 be T01,initial = T0 − T1,initial. When t = 0, ∆ 0 0 T01,initial = (−R01qinte + D)e ∆ D = T01,initial + R01qint. (4.12) 54 4.1. Multi-zone thermal mass solution Eq. (4.11) becomes, ∆ t/τ ∆ −t/τ T01 = (−R01qint e + T01,initial + R01qint)e ∆ −t/τ −t/τ = −R01qint + T01,initial e + R01qint e −t/τ ∆ −t/τ = R01qint(e − 1) + T01,initial e = T0 − T1. (4.13) Finally, −t/τ ∆ −t/τ T1 = T0 + R01qint(1 − e ) − T01,initial e −t/τ −t/τ = T0 + R01qint(1 − e ) − (T0 + T1,initial) e −t/τ −t/τ = T1,initial e + (T0 + R01qint)(1 − e ). (4.14) 4.1.1.3 Case 3: T0 and qint vary but only by a discretized time step. Finally, a case in which T0 and qint change by time is considered. However, T0 and qint are assumed to remain constant within a time step. Within the first time step, Hour 0, T0 and qint remain constant. From Eq. (4.14), T1 at the time t from the beginning of Hour 0, −t/τ −t/τ T1,t = T1,0 e + (T0,0 + R01qint,0)(1 − e ). (4.15) At the end of the Hour 0 (t = 1), −1/τ −1/τ T1,1 = T1,0 e + (T0,0 + R01qint,0)(1 − e ). (4.16) In the next time step, Hour 1, T0 and qint remain constant, but their values at t = 0 start with T0,1, T1,1, and qint,1 from the previous time step, Hour 0. Therefore, T1 at the time t from the beginning of Hour 1 is: −t/τ −t/τ T1,t = T1,1 e + (T0,1 + R01qint,1)(1 − e ). (4.17) 55 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation At the end of the Hour 1 (t = 1), −1/τ −1/τ T1,2 = T1,1 e + (T0,1 + R01qint,1)(1 − e ). (4.18) Eq. (4.18) can then be generalized for any Hour n: −t/τ −t/τ T1,n+1 = T1,n e + (T0,n + R01qint,n)(1 − e ). (4.19) Since R01 is the thermal resistance between Zone 0 and Zone 1, it may include the conduction through the wall and the infiltration between the zones, as defined in Eq. (4.1). Therefore, Eq. (4.19) is equivalent to: 1 = −t/τ + ( + )( − −t/τ) T1,n+1 T1,n e T0,n Σ qint,n 1 e . (4.20) Ui Ai + ρcpV˙ 4.1.2 Multi-zone model: two-zone problem The thermal mass effect in a single zone was discussed in the previous section. Eq. (4.20) works when the inflow temperature of the infiltration is identical to T0 and when the only temperature that influences the Zone 1 temperature is T0. This does not apply when Zone 1 is adjacent to another zone. For example, Zone 1 in Figure 4.2 is adjacent to the outdoors (Zone 0) and Zone 2, and the temperature of each of these zones may be different. The temperature of Zone 1 will not only depend on T0 and T2, but it is also influenced by the infiltration rates from the outdoors to Zone 1 (V˙01), and from Zone 2 to Zone 1 (V˙21). (a) Multi-zone model (b) Circuit analogy with thermal mass Figure 4.2: Multi-zone geometry description and circuit analogy diagram 56 4.1. Multi-zone thermal mass solution In steady state, the heat transfer between Zone 0 and Zone 1 and between Zone 2 and Zone 1 can be written as the following equations: T0 − T1 T2 − T1 q = q01 + q21 + qint = + + qint R01 R21 ∆ ∆ T01 T21 = + + qint. (4.21) R01 R21 Considering a thermal mass with the thermal capacitance of C1 placed in Zone 1, and allowing T1 to change by time t, ∆ ∆ dT1 T01 T21 C1 = + + qint. (4.22) dt R01 R21 The rest of the derivation follows the exact same procedure explained in the previous section. Three cases are examined: first, when T0 and T2 are non-zero constants and qint is zero; second, when T0, T2, and qint are all non-zero constants; and lastly, when they vary at discrete time steps. 4.1.2.1 Case 1: T0 and T2 are non-zero constants and qint is zero. dT0 dT2 Because T0 and T2 are constants, dt = dt = 0, and d∆T d∆T dT 01 = 21 = − 1 . (4.23) dt dt dt Multiplying both terms of Eq. (4.22) by R01R21 and further dividing by R01 + R21, the following equations can be derived: dT R R C 1 = R (T − T ) + R (T − T ) + R R q (4.24) 01 21 1 dt 21 0 1 01 2 1 01 21 int R01R21C1 dT1 R21T0 + R01T2 R01R21 = − T1 + qint. (4.25) R01 + R21 dt R01 + R21 R01 + R21 57 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation Since there is more than one thermal resistance and zone, the following parameters are defined in lieu of a single R and T0, such that: 1 R∗ = 1/R01 + 1/R21 ∗ τ = R C1 T0/R01 + T2/R21 Tcomb = 1/R01 + 1/R21 ∗ = (T0/R01 + T2/R21) ∗ R ∆ Tcomb1 = Tcomb − T1. Then, Eq. (4.25) simplifies to: dT τ 1 = T − T + R∗q . (4.26) dt comb 1 int With zero internal heat, dT τ 1 = ∆T . (4.27) dt comb1 ∆ Differentiating Tcomb1 as in: d(∆T ) dT dT comb1 = comb − 1 dt dt dt dT = − 1 , (4.28) dt ∆ dT1 d( Tcomb1) Eq. (4.27) can then be re-written by replacing dt with a term of dt using Eq. (4.28), d(∆T ) τ(− comb1 ) = ∆T dt comb ∆ d( Tcomb1) 1 ∆ = − dt Tcomb1 τ 1 ln (∆T ) = − t + A comb1 τ 1 1 ∆ τ t+A − τ t Tcomb1 = e = βe , (4.29) 58 4.1. Multi-zone thermal mass solution ∆ where A is a constant of integration and β is the initial Tcomb1 where t = 0. Recall that ∆ Tcomb1 = Tcomb − T1, then: − 1 t T1 = Tcomb − βe τ . (4.30) The same procedures discussed for Case 2 and Case 3 of the single zone could have been continued for the multi-zone analysis. However, it is not necessary because Eq. (4.29) is ∆ in the same form of Eq. (4.6) except for the fact that the multi-zone model uses Tcomb instead ∆ as T01. In fact, in further considerations using non-zero internal heat gain (Case 2) and incrementally varying T0, T2, and qint (Case 3), the equations will be in the same forms with ∗ those of single-zone models, except using Tcomb and R instead of T0 and R01. Furthermore, applying the same idea to the temperature of Zone 2 with respect to the outdoors and Zone 1, following equations for Case 2 and Case 3 can be derived. 4.1.2.2 Case 2: T0, T2, and qint are non-zero constants The indoor temperature of Zone 1 and Zone 2 when T0, T2, and qint are non-zero constants can be written as: −t/τ ∗ −t/τ T1 = T1,initial e + (Tcomb1 + R1qint1 )(1 − e ) −t/τ ∗ −t/τ T2 = T2,initial e + (Tcomb2 + R2qint2 )(1 − e ). 4.1.2.3 Case 3: T0, T2, and qint vary, but only by a discretized time step. The indoor temperature of Zone 1 and Zone 2 of the next time step when T0, T2, and qint vary yet only by a discretized time step can be written as: −t/τ ∗ −t/τ T1,n+1 = T1,n e + (Tcomb1,n + R1 qint1,n)(1 − e ) (4.31) −t/τ ∗ −t/τ T2,n+1 = T2,n e + (Tcomb2,n + R2 qint2,n)(1 − e ), 59 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation or, more explicitly, −(R +R )t −(R +R )t 01 21 R21T0,n + R01T2,n R01R21 01 21 R01R21C1 R01R21C1 T1,n+1 = T1,n e + ( + qint1,n)(1 − e ) (4.32) R01 + R21 R01 + R21 −(R +R )t −(R +R )t 02 12 R12T0,n + R02T1,n R02R12 02 12 R02R12C2 R02R12C2 T2,n+1 = T2,n e + ( + qint2,n)(1 − e ) R02 + R12 R02 + R12 When the infiltration rate from Zone 1 to Zone 2 is equal to the infiltration rate from Zone 2 to Zone 1, then R12 is equal to R21. However, they may be different if the infiltration rates are different. 4.1.3 Multi-zone: more than two zones This section investigates whether it is possible to expand the previous methodology to more than two zones. To examine the possibility, a zone placed in between two other zones was considered, as illustrated in Figure 4.3. In this case, Zone 1 interacts with the temperatures of the outdoors, Zone 2, and Zone 3, and the infiltration rates from these zones into Zone 1. Similar to the previous models, allowing T1 to vary through time t and assuming that the adjacent zones have constant temperatures, the following equation holds: ∆ ∆ ∆ ∆ d T1 T01 T21 T31 = + + + qint1 . (4.33) dt R01 R21 R31 (a) A three-zone model (b) Circuit analogy with thermal mass Figure 4.3: A three-zone model description and circuit analogy diagram 60 4.1. Multi-zone thermal mass solution To simplify, R, τ, and Tcomb were re-defined as follows: 1 R∗ = 1/R01 + 1/R21 + 1/R31 ∗ τ = R C1 T0/R01 + T2/R21 + T3/R31 Tcomb = 1/R01 + 1/R21 + 1/R31 ∗ = (T0/R01 + T2/R21 + T3/R31) ∗ R . Multiplying Eq. (4.33) by R∗ will yield dT τ 1 = T − T + R∗q . (4.34) dt comb 1 int1 ∗ Eq. (4.34) is in the same form as Eq. (4.26). The new parameters, R , τ, and Tcomb, are modified in a way that they consider the thermal aspects of the added zones. This indicates that Eq. (4.31) is applicable to this three-zone model. More importantly, the modification of the parameters (R, τ, and Tcomb) suggests that this analysis can be generalized to a room that is adjacent to n − 1 numbers of zones. Totaling n numbers of zones including Zone 1, the parameters can be modified as below: 1 R∗ = ∑n (4.35) n=1 1/Rn n ∗ Tcomb = R ( ∑ Tn/Rn). (4.36) n=1 61 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation 4.1.4 Implications of the multi-zone solution In a single-zone problem, there is one thermal resistance value, one thermal mass storage value, and one neighboring zone temperature to consider, as represented in Figure 4.4 (a) and Eq. (4.19). When more than one adjacent zone exists, the problem may require additional equa- tions to solve for the target zone’s temperature given relationships between multiple zones. However, the solution shown in Eq. (4.31) suggests that a multi-zone problem can be trans- formed into a single-zone problem when parameters are properly modified, as in Eqs. (4.35) and (4.36). The concept of this transformation is illustrated in Figure 4.4. For example, in ∗ Figure 4.4 (c1)-(c2), R is the comprehensive term representing both R1 and R2, and Tcomb is inclusive of both Tadj1 and Tadj2. Figure 4.4: Transformation of multi-zone problems into single-zone problems 62 4.2. Model verification: with windows closed 4.2 Model verification: with windows closed 4.2.1 Objective of verification In this section, the analytical models for a single zone (Eq. (4.22)) and multiple zones (Eq. (4.31)) are verified by the numerical model coded in Modelica. The major objective of the verification is to ensure that the solution is correctly derived. For example, the equations are based on the assumption that T1 , T0, and q are discretized (i.e., not continuous) during a time step. This means that when the time step of the simulation is an hour (t = 1), it assumes that the temperature and heat gains of the previous time step remain the same for an hour. This may cause a problem if the temperature changes significantly during that 1-hour time step, which in turn may cause a critical discrepancy between the estimation and reality. For this reason, the proposed model needs to be verified to determine whether the derivation is free of error and whether the assumptions are reasonable. Another significant benefit of verifying these models using Modelica is that once they are verified to be compatible, either model can be adopted depending on the simulation pur- pose. For example, a multi-zone solution can be implemented in 3D software, for example, Rhino, for a parametric design study. The simple form of the solutions allows users to write codes in computer languages such as Python for their customized usage. Also, the Modelica models, once appropriately coded, can be later used in validation. Since there are numerous parameters and settings, it would be challenging to set up complicated building settings using spreadsheets. In sum, the goals of this section are: • to confirm the correctness of the equations, • to determine the reasonable time step when a discretized time step is used, and • to utilize the Modelica model in validation. 63 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation 4.2.2 Verification methods The solutions suggested in Section 4.1 can be considered analytical models as they derive exact solutions from the inputs. On the other hand, a numerical model as illustrated in Fig- ure 4.5 (b) examines the relationship between each component that is passed into another component. For example, this model will receive the outdoor temperature, yield the external surface temperature, calculate the internal surface temperature, and then finally output the indoor temperature. Unlike the analytical model, this numerical model does not identify a di- rect relationship between outdoor and indoor temperatures, but can be useful to understand the process of simulation. In this section, the numerical model is built to verify the analytical model. For the analytical model, several test room models were set up in MS Excel spread- sheets, and indoor temperatures were calculated using Eqs. (4.22) and (4.31). Both single-zone and multi-zone models were tested, and each model was tested with and without heat gains. Time steps used in the spreadsheet calculation were 60 min, 30 min, 15 min, 9 min, and 3 min. For the numerical model, the same test room settings were applied in Dymola, which provided a simulation interface using Modelica, a computer language. In Dymola, the outdoor temperature of each hour was linearized. A differential/algebraic system solver (DASSL) was used in the Dymola model where time step was variable and determined by the algorithm. These two sets of data—one calculated in a spreadsheet and the other in Modelica— were then compared. To quantify the agreement between the models, a root-mean-square error (RMSE) was calculated. An RMSE informs about the average deviation of the two datasets, and the range could vary. Calculated as in Eq. (4.37), an RMSE of 2, for example, indicates that the values of a dataset X deviate by two units on average from a dataset Y. r ∑n (x − y )2 RMSE = i=1 i i (4.37) n 64 4.2. Model verification: with windows closed Figure 4.5: Description of analytical model and numerical model 4.2.3 Single-zone model setting: with windows closed A single-zone room of 5*5*4 m3 with a thermal heat storage of 2.4 MJ/K was tested. The windows were closed, yet there was 0.005 m3/s of infiltration. With the U-value of the en- velope being 0.15 W/m2/K, Eq. (4.1) yielded a thermal resistance of 0.053 K/W. The model was tested first without internal heat gain and then with a constant heat gain of 325 W. The values used in this simulation are listed in Table 4.1. Detailed data used in this simulation and additional result graphs are available in Appendix A. The calculation for both cases was performed for the 24 hour period, and the initial indoor temperature was set to 20.6 degrees Celsius. Figure 4.6 shows the single-zone Modelica models with and without internal heat gain set in Dymola’s interface. Table 4.1: Specification of single-zone model, without natural ventilation Room dimension 5*5*4 (m3) Heat gain 0 W, 325 W Window area 0.25 (m2) Thermal mass storage 2.4 MJ/K Infiltration rate 0.005 (m3/s) Thermal Resistances 0.053 (K/W) U-value of envelope 0.15 (W/m2/K) Time steps 60, 30, 15, 9, 3 min 65 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation Figure 4.6: Single-zone modeling in Modelica. Windows are closed. Calculation without heat gain (left) and with heat gain (right) are displayed. 4.2.4 Single-zone model verification results: with windows closed The comparison between the two simulation methods—MS Excel and Dymola—showed great agreement when windows were closed, regardless of internal heat gain and time step (Fig- ures 4.7 and 4.8). When internal heat of 325 W was applied, the indoor temperature of Fig- ure 4.8 (b) appeared to keep increasing because the case did not reach the steady periodic condition. Albeit minimal, the tests found that a smaller the time step led to a smaller the RMSE. However, even with the biggest time step, which was 60 min, the RMSE was only 0.06 K. This RMSE can be regarded as small, given that the range of outdoor temperature used in the simulation was 11.7 degrees with a minimum of 15.0 degrees Celsius and a maximum of 26.7 degrees Celsius. The correlation of all cases were above 0.99, therefore, comparing correlation coefficients across the cases was not meaningful. Figure 4.7 shows the decreasing trend of RMSE as time steps become smaller. Figure 4.7: RMSE of cases using different time steps and heat gains. Windows are closed. 66 4.2. Model verification: with windows closed (a) Internal heat gain 0 W (b) Internal heat gain 325 W Figure 4.8: Single-zone temperature graphs of indoor and outdoor using Eq. (4.22) and Modelica. Windows are closed. 4.2.5 Multi-zone model setting: with windows closed Two rooms were created to test the multi-zone model. Room 1 was the room of interest, and Room 2 and the outdoors were the two adjacent zones. Each room was 5*5*4 (m3) with a thermal storage of 2.4 MK/K. The infiltration rate was 0.010 m3/s and the windows were still closed. Two internal heat gain settings (0 W and 325 W) were tested for Room 1, while no heat gain was given to Room 2 in both cases. Several time steps (60 min, 30 min, 15 min, 9 min, and 3 min) were tested. Table 4.2 lists the simulation settings, and Figure 4.9 shows the diagram of simulation in Dymola’s interface. 67 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation Table 4.2: Specification of single-zone model, without natural ventilation Room dimension 5*5*4 (m3) Heat gain, Room 1 0 W, 325 W Window area 0.25 (m2) Heat gain, Room 2 0 w Infiltration rate 0.010 (m3/s) Thermal mass storage 2.4 MK/K U-value of envelope 0.15 (W/m2/K) Thermal resistance (envelope) 0.040 (K/W) U-value of interior wall 0.30 (W/m2/K) Thermal resistance (interior) 0.004 (K/W) Time steps 60, 15, 3 min Figure 4.9: Multi-zone modeling in Modelica. Windows are closed. 68 4.2. Model verification: with windows closed 4.2.6 Multi-zone model verification results: with windows closed Figure 4.10 shows the graphs of the two rooms when no internal heat gain was applied. Since the settings of the rooms were identical, so were the indoor temperatures. However, in Figure 4.11, Room 1’s temperature increased because of the internal heat gain of 325 W. The temperature of Room 2 was also slightly increasing due to heat gain through interior wall conduction from Room 1. In both cases, with heat and without heat, the analytical and numerical models demonstrated great agreement, with the largest RMSE being 0.10 K and the smallest being 0.01 K. Figure 4.10: Multi-zone graphs of indoor and outdoor temperatures using Eq. (4.31) and Modelica. Windows are closed, and no heat gain is applied to either room. Figure 4.11: Multi-zone graphs of indoor and outdoor temperatures using Eq. (4.31) and Modelica. Windows are closed. Room 1 has 325 W of internal heat gain, while Room 2 does not. 69 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation 4.3 Model verification: with windows open 4.3.1 Model assumptions with natural ventilation The analytical model was developed with an assumption that the thermal mass and indoor air would always be in equilibrium, tolerating negligible temperature differences. It may be a reasonable assumption that when a room is enclosed by a single-material thermal mass, then the mass temperature is almost the same as the indoor air temperature. However, when a large amount of outdoor air enters a room, for example, if two walls were entirely open (as an extreme case), the outdoor temperature would affect the indoor temperature instantaneously even if there were large thermal masses on the floor and the ceiling of the room. In the following verification with airflow, the infiltration rate is increased to represent a ventilation effect; therefore, this section does not fix this issue of the assumption addressed above. The purpose of this verification is to check the correctness of the equation using a higher airflow rate and to check the compatibility with a numerical model. The process of fixing assumptions will be discussed in a later chapter. 4.3.2 Model settings for natural ventilation The settings for single-zone and multi-zone cases for natural ventilation were identical to Tables 4.1 and 4.2 except that there was an added ventilation rate of 0.20 m3/s because the windows were open. This added flow rate led to a thermal resistance between the outdoors and the indoors of 0.004 K/W. Figures 4.12 and 4.13 show both the single-zone and multi-zone cases set up in the Dymola interface. In this numerical simulation setting, the ventilation rate is set by the pressure differ- ence between two openings. To reproduce the same ventilation rate as in the analytical model, the pressure difference is calculated by Eq. (4.38), ˙ 2 ∆ ρ V P = ( ∗ ) = 1.818(Pa), (4.38) 2 Cd A 70 4.3. Model verification: with windows open Figure 4.12: Single-zone modeling in Modelica. Windows are open. Figure 4.13: Multi-zone modeling in Modelica. Windows are open. 71 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation where the discharge coefficient (Cd) is 0.61. Assuming that all windows types were the same, and thus had the same discharge coefficient, the effective window area (A∗) was calculated by the following equation: ∗ A1 A2 2 2 A = = 0.177(m ) when A = A2 = 0.25(m ). p 2 2 1 A1 + A2 In the multi-zone cases, the outdoor air passed through Room 1 and then Room 2. This means that the temperature of the inflow was T1 rather than Toutdoor. Even though only Room 1 received internal heat gain, Room 2 was expected to have the effect of having a small amount of heat gain due to the airflow coming from Room 1. Each value of thermal resistance across zones is listed in Table 4.3. Table 4.3: Thermal resistance of multi-zone model, with natural ventilation Thermal resistance (out→Room1) 0.004 (K/W) Thermal resistance (out→Room2) 0.078 (K/W) Thermal resistance (Room1→Room2) 0.004 (K/W) Thermal resistance (Room2→Room1) 0.167 (K/W) 4.3.3 Single-zone verification results: with windows open Figure 4.14 shows the temperature graphs when the windows were open, allowing 0.20 m3/s of airflow to enter the room. Indoor temperature (T1) responded to the outdoor temperature (gray line) with a delay due to the heat storage of thermal mass. While all cases agreed reasonably well with the numerical simulation results, the time step settings of 1 hour (red dots) showed a visible discrepancy in both graphs. The RMSEs of the cases with 1-hour time steps were 0.41 K without internal heat gain and 0.36 K with internal heat gain. These are still small numbers, but these RMSEs are about eight times larger than those tested in Section 4.2, suggesting a larger time step may lead to noticeable error in a more complicated simulation. 72 4.3. Model verification: with windows open Figure 4.14: Temperature of indoor and outdoor using Eq. (4.22) and Modelica. Windows are open Figure 4.15: RMSE of cases using different time steps and heat gains. Windows are open. 73 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation 4.3.4 Multi-zone verification results: with windows open Two cases were tested: a case where both rooms were without heat gain, and another case where only Room 1 received internal heat gain. In both cases, the flow came in from the outdoors, passed through Room 1, and exited through Room 2. The RMSE ranges of both cases were similar to the single-zone cases, ranging from 0.10 K to 0.47 K. Figure 4.16: Multi-zone temperature graphs of indoor and outdoor using Eq. (4.31) and Modelica. Windows are open, and no heat gain is applied to both rooms. Figure 4.17: Multi-zone temperature graphs of indoor and outdoor using Eq. (4.31) and Modelica. Windows are open. Room 1 has 325 W internal heat gain, while Room 2 does not. 74 4.4. Thermal mass and dynamic window operation 4.3.5 Conclusion from the verification Sections 4.2 and 4.3 explained the verification of the analytical models with numerical models. Single-zone cases were tested first, followed by multi-zone cases with different heat gains. All analytical models, regardless of the multiplicity of zones, internal heat gain, or time steps, showed acceptable agreements with the numerical models, confirming that the analytical models and numerical models were compatible. However, there was a systematic delay in the 1 hour time step when windows were open. This delay was significantly improved by having smaller time step, such as 30 min or 15 min. There were no noticeable differences between 15 min, 5 min, and 3 min time steps. Therefore, the 1 hour time step should be avoided. This verification study becomes useful in the next chapter, Chapter 5, which validates the analytical model against experiments. Prior to validation, the model first needs the right inputs to reflect the real building settings, for example, the walls’ thermal properties, internal heat gain, and thermal heat storage. Since several uncertainties exist in the real environment, the determination of the right inputs can benefit from sensitivity analyses. Through sensitivity analyses, the numerical model offers an easier means of tuning the detailed settings than the analytical model would thanks to the customizability of the numerical model. 4.4 Thermal mass and dynamic window operation 4.4.0.1 Window controls in response to thermal mass Under a steady-state assumption, a window operation schedule for natural ventilation is straightforward: windows can be open when the outdoor temperature is favorable, and closed when it is too warm or too cold. However, studies in this chapter have revealed that this is not always the case when thermal mass exists. The temperature of a room depends on the previous thermal status of the room and the surrounding environments. Nighttime ventilation is one of several passive-cooling strategies that utilize this char- acteristic of thermal mass in natural ventilation. This strategy lets the mass cool down during 75 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation the night, and benefits from its heat storage such that the room maintains a relatively lower temperature during the day. Identifying the time to open windows is important in this case as the duration of the windows being open and the outdoor temperature determine the potential cooling power that the mass may provide. This principal may be applicable with daytime ven- tilation as well. In daytime ventilation, determining the time to close the windows is crucial to preventing an excessive warming effect. That is, the windows are open when the outdoor temperature is favorable, but the closing time should be determined according to the thermal lag caused by the thermal mass. The graph in Figure 4.18 compares different possible indoor temperatures given the same outdoor temperature, demonstrating the advantage of adopting this window operation strategy for natural ventilation. The band ranging from 16 degrees Celsius to 26 degrees Cel- sius is a customized thermal comfort zone that can be defined by the user. The green dotted line is the indoor temperature without presenting any thermal mass effects, while the solid green line is the indoor temperature with natural ventilation. When windows are open, the indoor temperature follows the outdoor temperature (gray line) rela- tively evenly, but at a higher degree is raised by the internal heat gain. The brown dotted line in the range of 31 degrees Celsius to 35 degrees Celsius is the Figure 4.18: Graph of temperatures using different design strategies 76 4.5. Calculation of dNVCE in a transient state result of having a thermal mass with the windows closed. Its initial temperature is higher because this graph is a result of iterative simulation. This means that the temperature of this brown dotted line would be the indoor temperature if the outdoor temperature of the 24 hours in question is repeated for many days. It reveals that if no natural ventilation were available, the room would need cooling throughout the entire simulation period even if the outdoor temperature were much lower. The solid brown line represents the same thermal mass settings, but with the windows open. The range is similar as with the steady-state ventilation, but the warmest hour of the day has been delayed by two hours, and the hottest temperature of the day is slightly lower than that on the green line due to thermal mass. Lastly, the orange dashed line is the indoor temperature when the windows are oper- ated to maximize the cooling effect. From midnight to 7 AM, the windows are open, thus the orange dashed line is identical to the brown line. From 7 AM to 3 PM, even though the out- door conditions are within the comfort zone, the windows are shut to prevent a stiffer increase in indoor temperature. From 3 PM to 6 PM, the outdoors is warmer than the comfort criteria, so the windows remain closed. From 6 PM, the outdoors falls back into the comfort zone, so the windows are opened to take advantage of the cooling effects of natural ventilation. 4.5 Calculation of dNVCE in a transient state As discussed, a dNVCE is calculated by: qavail qavail dNVCEhour = = . qideal qavail + qreq 4.5.1 Available cooling power (qavail) in a transient state The cooling power that can be provided by a certain design condition, qavail, relies on both window size and location and outdoor wind speed and direction. However, it is not influenced 77 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation by the heat storage of building materials. Therefore, Eq. (3.3) still holds, as in: qavail = −ρcV˙avail(Ttarget − Tout). 4.5.2 Ideal cooling power (qideal) in a transient state The calculation procedure of qideal resembles what was discussed in Section 3.2.1.3. In a tran- sient state, when T1,n+1 is going to be greater than Ttarget, additional cooling power (qreq) is needed to achieve Ttarget. Eq. (4.19) can be modified to ensure that the temperature of the next step is Ttarget as in Eq. (4.40), and obtain qideal as in Eq. (4.41). −t/τ −t/τ Ttarget,n+1 = T1,n e + (T0,n + R(qgain,n + qreq,n))(1 − e ) (4.39) −t/τ Ttarget,n+1 − T1,ne 1 qreq,n = ( − T n) · − q (4.40) 1 − e−t/τ 0, R gain,n qideal = qavail + qreq −t/τ Ttarget,n+1 − T1,ne 1 = −ρcV˙ (Ttarget − Tout) + ( − T n) · − q (4.41) avail 1 − e−t/τ 0, R gain,n When additional cooling is necessary, qideal is a negative value. If qideal is positive or zero, cooling is not necessary, and the current cooling capacity of natural ventilation is sufficient to keep the temperature of a room below Ttarget. 4.5.3 Design natural ventilation cooling effectiveness (dNVCE) in a transient state Finally, a dNVCE of thermal mass can be written as in Eq. (4.42): ρcV˙avail(Ttarget − Tout) dNVCE = . (4.42) T −T e−t/τ cV˙ (T − T ) − ( target,n+1 1,n − T ) · 1 + q ρ avail target out 1−e−t/τ 0,n R gain,n Figure 4.19 shows the qideal of different cases overlaid with the qavail. The vertical values are negative, but the order is reversed to represent the magnitude of cooling capacity. Narrow bars of green, brown, and light brown show the ideal cooling capacities of a room without thermal mass, with thermal mass, and with window controls with thermal mass. The wide 78 4.5. Calculation of dNVCE in a transient state gray bar is the available cooling capacity. Figure 4.19: Graph of qideal with different design strategies based on Figure 4.18 When (−)qavail is greater than (−)qideal during an hour, it earns 1 NVh, which is re- flected in Figure 4.20. When there is a lower (−)qavail than (−)qideal, Figure 4.20 shows the ratio of these two cooling rates. For example, when thermal mass is used, the dNVCE of an hour 19 is 0.8, while the dNVCE of the entire day is 0.74. The fractional value of each time step indicates that a small design adjustment could earn hour 19 a full credit of 1 NVh. Figure 4.20: cNVCE and dNVCE of different design strategies based on Figure 4.18 79 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation 4.6 Discussion 4.6.1 Impact of thermal mass and window controls on dNVCE Dynamic window schedules along with the thermal mass effect influence the effectiveness of natural ventilation. For example, a day illustrated in Figure 4.18 can be considered. The green and brown dotted lines show that the test room needs cooling all the time both with and without thermal mass. The climate is not favorable between 1 PM and 6 PM for using natural ventilation for cooling, which means that natural ventilation is available for cooling during 79% of the day. With some added heat gain from occupants, the availability decreases to 71% of the day in a steady state. Using thermal mass, the room earns two additional NVhs, putting the effectiveness back to 79% hours of a day. However, when strategic window operation is used with thermal mass and natural ventilation, only three hours exceed the upper limit of the comfort criteria, increasing the comfortable time of the day to 88%. Figure 4.21: Percentage of NVhs in a day using different design strategies, based on Figure 4.18 These numbers first imply that natural ventilation with thermal mass can keep the indoors at a more favorable temperature than natural ventilation without thermal mass. In addition, a strategic window operation demonstrates that a combination of thermal mass, window operation, and natural ventilation may provide cooling that is greater than the cli- mate’s cooling potential. The timing of closing and opening windows needs to be determined by predicting 80 4.7. Limitations the temperature of the next hours. In Figure 4.18, the windows were closed at 7 AM (orange dashed line) to maximize the dNVCE. However, if windows were not closed by 7 AM but left open until 1 PM, it would have been too late to close them at 2 PM. Closing windows at the wrong time may not only reduce thermal comfort, but also increase cooling loads due to the heat stored in the thermal mass. The algorithm used to determine the optimal operation schedule will be explained in Chapter 6, Section 6.2.2.3. 4.6.2 Impact of thermal mass and window controls on CPUR In a steady-state study, a dNVCE is always less than or equal to its counterpart, cNVCE, so the CPUR is less than or equal to 1. However, previous sections demonstrated that thermal lags occurred due to high heat storage. Optimal window operation taking advantage of thermal mass may assist a dNVCE in outperforming its cNVCE. In Figure 4.21, the CPURs of the steady state, thermal mass, and thermal mass with window controls are 0.90, 1.00, and 1.05. 4.7 Limitations 4.7.1 Geometry Geometries used in the analytical model are simplified: they are one-dimensional. Ceilings, walls, and floors are transformed into one material, as illustrated in Figure 4.4. However, this does not mean that three-dimensional characteristics cannot be considered. When calculating U-values, air films near the surface are determined depending on whether they are vertical, such as walls, or horizontal, such as floors or ceilings. ASHRAE (2013b) provides these values varying by the positions of surfaces, which may then be added to material properties before transforming multiple walls into one. Figure 4.22 describes the geometries that can be represented in the proposed model. Single zone settings can easily be set up. In multi-zone settings, the proposed model can consider various surrounding zones—for example, the outdoors contacted through a ceiling, 81 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation a lower level contacted through a floor, or next rooms contacted through walls. However, the biggest challenge for a multi-zone natural ventilation analysis is to find the correct airflow rates for each zone. To calculate flow rates, an analytical model, an AFN simulation, or a CFD simulation may be conducted, but connecting the airflow results with the proposed model requires coupling techniques. Since this dissertation does not develop a dedicated model to calculate cross-zonal airflow rates, it limits the geometric boundaries to multi-zone buildings where a known air path is unidirectional. Figure 4.22: Geometries that can be used by the suggested analytical models 4.7.2 Zoning for natural ventilation The proposed model considered infiltration by adding the air movement term (ρcpV˙ ) to the thermal resistance (R). The assumption behind the R calculation was that the thermal mass would be in equilibrium with the air, ignoring the temperature difference between the thermal mass and the air. The resultant indoor temperatures in the previous tests (T1) were, therefore, technically the thermal mass temperatures rather than air temperatures. This assumption be- comes problematic when the infiltration rate is large enough to be considered natural ventila- tion. When a large amount of airflow enters the room from the outdoors, the indoor tempera- ture will be instantly changed, whereas the thermal mass temperature will slowly respond to the outdoor air. Therefore, the more airflow V˙ , the more error the result will show. A separate zone solely for thermal mass can be created to avoid this zoning issue. This solves the problem of the air-mass temperature assumption because there is no air in the 82 4.8. Conclusions zone. Creating a dedicated zone for thermal mass is further discussed in the next chapter on validation. 4.7.3 Thickness of thermal mass The thickness of thermal mass needs to be considered when creating the “thermal mass zone.” Having one node for a thermal mass, Eq. (4.31) used the lumped capacitance assumption, which was analogous to the ”well-mixed air assumption”. If a thermal mass of a wall or floor is too thick, however, the temperature difference from a surface to the center becomes larger. To ensure that the lumped capacitance assumption is valid, the Biot number (Bi) can be examined, which is defined as: internal conduction resistance L h L Bi = = kA = c , external convection resistance 1 k hc A where : L : thickness from the center of the thermal mass to one surface if exposed on both sides or the thickness from two surfaces if exposed on one side k : thermal conductivity of the mass A : surface area hc : surface heat transfer coefficient. When Bi < 0.1, the external convection resistance is relatively large compared to the internal conduction resistance. The result is that the temperature difference within the material is less than the difference between the mass surface and the external material (air). For example, for a concrete slab, L < 0.04m ensures that the Biot number is less than 0.1. 4.8 Conclusions Chapter 4 examined the thermal mass effect in a single-zone model and developed an ana- lytical model that worked for multi-zone buildings by transforming a multi-zone model into 83 Chapter 4. Thermal mass, dynamic window controls, and natural ventilation a single-zone equivalent model. The model was verified by a compatible numerical model created in Modelica. A dynamic window schedule method was introduced and demonstrated to increase natural ventilation performance. The next chapter will validate the model with measurements. The simulated results will be compared to real-life experiments to see how closely the model can predict indoor temperature. 84 Chapter 5 Validation with HouseZero In this chapter, the analytic solution for a building with thermal mass discussed in Chapter 4 is validated with field measurements from a test bed (HouseZero). For easier control of various time-steps and time-related inputs, a Modelica model was created for calibration prior to validation. The Modelica model was built in a way that it is comparable to the analytic model. After the thermal properties of HouseZero were calibrated, the analytic model was validated using the calibrated input setting. For field measurements, the windows of the test room were kept closed during the first three weekends, and then opened for another two weekends. The indoor temperatures in these cases were compared with analytic solutions. Chapter 5. Validation with HouseZero 5.1 Field Measurements 5.1.1 Data collection Field measurement tests were conducted to validate the method discussed in Chapter 4. The measurements were collected from two resources. Outdoor conditions were collected from a weather station of the Harvard Graduate School of Design (GSD), and the indoor data were collected from a test bed called HouseZero of the Harvard Center for Green Buildings and Cities (CGBC). Table 5.1: Data collection: items and location GSD weather station CGBC HouseZero Outdoor temperature Indoor temperature Wind speed Data measured Slab temperature Wind direction Window operation status Solar radiation 5.1.1.1 GSD weather station The GSD weather station was installed on the roof of Gund Hall, and measures outdoor temperature, wind speed, wind direction, and solar radiation every five minutes. It uses the HOBO U30 Station model (firmware Version: 2.006), and is located about 20 meters above the ground. 5.1.1.2 HouseZero thermal sensors The CGBC laboratory where the thermal sensor measurements were taken is on the third floor of HouseZero and located a block away from Gund Hall. The lab is equipped with thermal sensors that measure indoor temperature, slab temperature, and relative humidity. Images of the test room are shown in Figures 5.1 to 5.6. 86 5.1. Field Measurements Figure 5.1: Orientation of HouseZero and surroundings Figure 5.2: Photographs of the entrance (left) and the panoramic view of test room (right). 87 Chapter 5. Validation with HouseZero Figure 5.3: Rendered image of the test room. Figure 5.4: Location of the test room in House- There are north-facing windows, skylight, two Zero. The room is located on the third floor of glazing walls, and interior door. the house. Figure 5.5: Side view of the test room Figure 5.6: Top view of the test room 88 5.1. Field Measurements 5.1.1.3 Time of datasets and test cases Four datasets were collected during the weekends of the study. This is to prevent occupant interference by people entering the room, and to be independent of occupants’ controlling the indoor temperature during weekdays. The first set of data was collected from the afternoon of Friday, July 27, when the weekday occupants left the lab, to the morning of Monday, July 30, when the weekday occupants came to work. During this time, all the windows were kept closed to rule out ventilation effects. This first set of data was used to calibrate the model, as discussed in Section 5.2. The same conditions were used for the other two weekends (Aug 3 through Aug 5 and Aug 10 through Aug 14). Three sets of data, including that from the first weekend, were used to validate a model with the windows closed. For the last dataset (Sep 7 through Sep 10), the manual windows of the north wall were kept open to validate a model using natural ventilation. The datasets and their corresponding times are shown in Table 5.2. Table 5.2: Data collection time Collection time Natural ventilation status Dataset 1 Jul 27 - Jul 30 Closed Dataset 2 Aug 3 - Aug 5 Closed Dataset 3 Aug 10 - Aug14 Closed Dataset 4 Sep 7 - Sep 10 Cross ventilation 5.1.2 Test room description 5.1.2.1 Geometry As shown in Figures 5.1 to 5.6, the test room is in an irregular shape with a floor area of 5.9 m2 and a highest floor-to-ceiling height of 3.2 m. The pentagonal section area is 7.5 m2, and the air volume of the room is 18.5 m3. 89 Chapter 5. Validation with HouseZero 5.1.2.2 Thermal zones The test room is located on the third floor of HouseZero. The north wall of the room and the roof are exposed to the outdoors. The two glazing walls are adjacent to the second floor, which has high ceilings spanning to the roof. The slab of the room is controlled by a heat pump that uses a geothermal system, so it may be considered a fixed temperature condition. However, the heat pump can be disabled when the room is not in use, rendering the floor thermally connected to the second floor. The interior side wall and door face the corridor on the same floor. This wall can be considered adiabatic, as the temperature difference between the corridor and the room is negligible. 5.1.2.3 Materials and thermal properties Important thermal properties for this exercise include U-value, infiltration rate, ventilation rate, and thermal heat capacity of each material. There are three major thermal masses in the room, which are roof, external wall, and concrete slab. The heat capacities of these thermal masses were calculated as shown in Table 5.3. Although this initial calculation is a useful start, the thermal properties must be calibrated to better estimate indoor temperature. This is mainly because parts like the roof and floor connect to another zone that may influence the effective U-values and heat capacities, and the actual construction of the room may have been done in a different way than indicated in the original drawings. The calibration of the model is discussed in Section 5.2. 5.1.2.4 Ventilation The room has five operative windows. Four are on the northern wall, and the last is a sky- light on the west-facing pitched roof. The upper two windows of the wall are mechanically operated, while the lower two are manually operated. When the skylight is closed, it only has single-sided ventilation, but cross-ventilation is possible when the skylight is open. 90 5.1. Field Measurements Table 5.3: Thermal heat capacity of roof, external wall, and slab calculated from building construction materials ρ Cp LAVCm (density) (specific heat) (thickness) (area) (volume) (heat capacity) Roof Gypsum 600.00 1,090.00 0.01 11.65 0.15 99,048.30 2"x7" rafters 455.00 1,500.00 0.18 11.65 2.04 1,391,446.88 Gutex 80.00 840.00 0.10 11.65 1.17 78,288.00 Total heat capacity 1,568,783.18 External wall Clay plaster 1,514.00 1,000.00 0.02 9.42 0.19 285,237.60 Existing Gypsum Board 165.00 1,700.00 0.02 9.42 0.14 39,634.65 Insulation 80.00 840.00 0.10 9.42 0.89 60,137.28 Pavatex Pavatherm 80.00 840.00 0.10 9.42 0.94 63,302.40 Board 455.00 1,500.00 0.02 9.42 0.14 96,437.25 Total heat capacity 544,749.18 Slab Concrete 2,400.00 1,000.00 0.20 9.80 1.96 4,703,328.00 Total heat capacity 4,703,328.00 91 Chapter 5. Validation with HouseZero 5.1.3 Processed input data 5.1.3.1 Solar radiation 2 Global horizontal irradiance (GHI) (Qsolar, W/m ) was measured from the GSD’s weather sta- tion. Since the amount of solar radiation that each wall and roof of HouseZero received varies according to their relative angles to the sun, they must be separately calculated. The calcula- tion was performed by extracting solar ray vectors at each time step and determining their relative angles (θ) to the surface’s normal vector. The total amount of solar radiation that a surface will receive at a given time (qsolar,sur f , W) is then calculated by the following formula: Qsolar,sur f = Qsolar ∗ cosθ Asur f ∗ Qsolar,sur f if θ ≤ π/2 qsolar,sur f = 0 if θ > π/2 (Sun is behind the surface.) Figure 5.7: Solar radiation calculation This calculation did not distinguish direct normal irradiation (DNI) and diffuse hori- zontal irradiation (DHI), which were included in GHI. Instead, the next section will calibrate the reflectance, absorptance, and transmittance of the building materials to estimate the solar heat gain. 92 5.2. Model calibration 5.1.3.2 Internal heat gain The internal heat gain that this room receives is mostly from solar radiation through the skylight when it is not shaded. There are no occupants or appliances that emit heat in the room. The solar heat gain through the skylight is calculated in the same way that is described in the sub-section above, using the area of the skylight and assuming transmittance. 5.2 Model calibration Prior to validation, the simulation model of the test room must be calibrated in order to re- duce uncertainties. As the room temperature is the result of multi-zonal heat transfer, thermal resistance (R) from the room to each adjacent zone is important. Materials with high heat ca- pacitance (C), including concrete slabs, exterior walls, and the ceiling should be investigated. Figure 5.8 illustrates both measured thermal properties and unknown thermal properties that needed to be investigated. Known factors included the outdoor temperatures (Toutdoor), the temperature of the room (Tin), temperature of the second floor (TF2), and temperature of the concrete slab (Tslab). The temperature of the glazing walls, which contact the second floor, was not known, but this was less of an issue because the thermal resistance of the glazing wall (Rglazingwall) is easy to assume under steady-state conditions. Using the single-glazing property for the internal walls, the thermal resistance of the internal walls was set to 0.02 K/W. Although TF2, Tslab, and Tin were all known, the thermal resistance of the concrete slab (Rslab) had to be carefully investigated due to the heat capacity of concrete (Cslab), for which a steady-state assumption is no longer appropriate. The building envelope, including the ceil- ing and the north-side wall, had the most uncertainty: neither its thermal mass heat capacity (Cenvelope), temperature (Tenvelope), nor thermal resistance (Renvelope) were known. In addition, the solar radiation absorptance (αenvelope) of the envelope plays an important role, and this was also unknown. Therefore, it was important to first find reasonable thermal configurations of the building envelope. 93 Chapter 5. Validation with HouseZero The measurements of the room’s thermal condition are described in Figure 5.9. The slab temperature increases as soon as the heat pump is turned off around 7 PM, and notably decreases when the pump is turned back on the following week. Figure 5.8: Thermal connection of the test room and other thermal zones Figure 5.9: Measurement during 07/27 - 7/30 94 5.2. Model calibration 5.2.1 Calibration: building envelope For simplification, the roof and the north-side exterior wall were considered one material because both are assembled parts and both transfer heat with the outdoor conditions. The pitched roof is an assembly of various layers of materials including gypsum board, rafters, insulation, a vented air space, photovoltaic panels, and shingle roofing. The exterior north-side wall is also built with layers of clay plaster, gypsum board, studs, insulation, air, board, shingle siding, and so on. As such, this exercise tried to find reasonable properties including the thermal mass heat capacity (Cenvelope), the thermal resistance (Renvelope), and the absorptance (αenvelope) of the envelope. To test the sensitivity of the envelope properties, other parts of the building materials are fixed. Therefore, instead of referring to the thermal heat capacity and thermal resistance of the concrete slab, which are unknown, the slab temperature was used. First, different heat capacities of the envelope were tested. As shown in Figure 5.10, the peak indoor temperature of the day varies depended on the heat capacity. Assuming that the indoor air heat capacity and glazing wall heat capacity are relatively negligible versus that of the envelope, the peak hour is then only influenced by the heat storage of the envelope. In this case, the floor heat storage did not influence the peak hour because the model used the slab temperature as a fixed input. Based on this, the model selected 2,000,000 J/K of heat storage for the envelope. The peak hour with 2,000,000 J/K of heat storage agreed well with the measured room temperature. However, the magnitude of fluctuation of the simulated temperature was much larger than the measurements. This is because it overestimated the solar radiation the envelope receives. Therefore, Figure 5.11 tested different absorptances from 1 to 0.25. The absorptance is defined as the ratio of the radiant flux that a surface absorbs to the radiant flux that the surface receives. As a result, 0.50 was selected. 95 Chapter 5. Validation with HouseZero Figure 5.10: Calibration of the heat capacity of the building envelope Figure 5.11: Calibration of the absorptance of the building envelope 5.2.2 Calibration: slab The floor is an exposed concrete slab, the specific heat capacity of which is well known. How- ever, because the concrete slab spans through to the corridor next to the room, the effective thermal heat storage of the room might be different than the calculation. The floor receives solar radiation that is transmitted through the skylight. Therefore, the radiant flux that floor absorbs is the solar radiation that the skylight receives minus the flux reflected at the skylight, minus the flux absorbed by the skylight, minus the flux reflected 96 5.2. Model calibration at the floor surface. The absorptance sensitivity analysis was conducted in the same way that building envelope’s absorptance was found, and resulted in a value of 0.25. Water pipes pass through the slab for the geothermal heat system, above which a temperature sensor is installed. Therefore, there is thermal resistance between the indoor tem- perature and the slab temperature that is measured by the sensor. For a sensitivity analysis of the thermal resistance, 0.10 K/W was used. Finally, thermal heat storage was calibrated. Figure 5.12 shows the sensitivity of in- door temperature and slab temperature depending on the slab’s heat storage. It reveals that 5,000,000 J/K of heat storage acceptably represents the test room’s slab. Figure 5.12: Calibration of the heat capacity of the concrete slab 5.2.3 Calibrated model for validation From the calibration of the model settings, the final model to be used for validation was determined. Section 5.2.3 shows thermal resistances from one zone to another, heat storages of thermal mass, and absorptances of the materials. The calibrated model should work with other datasets obtained under the same set- tings, for example, the datasets collected with the windows closed. The simulation settings 97 Chapter 5. Validation with HouseZero were applied to Dataset 2 and Dataset 3. Figures 5.14 to 5.16 demonstrate that the Modelica setting with the calibrated thermal properties of the house may reasonably replicate the field measurements. Figure 5.13: Calibrated thermal resistance (K/W), thermal storage (J/K), and absorptance 98 5.2. Model calibration Figure 5.14: Simulation results with calibrated parameters compared to the field measurements with Dataset 1. Figure 5.15: Simulation results with calibrated parameters compared to the field measurements with Dataset 2. Figure 5.16: Simulation results with calibrated parameters compared to the field measurements with Dataset 3. 99 Chapter 5. Validation with HouseZero 5.3 Validation: without natural ventilation The model developed in Chapter 4 is validated with field measurements using the thermal properties that were calibrated in the previous section. To quantify the differences between the measurements and analytical calculations, each dataset was used to find a correlation coefficient (or correlation) and a root-mean-square error (RMSE). A correlation coefficient, ranging -1 to 1, is a useful indicator of the variance in different datasets. If two datasets co- vary in a direct way, that is, one dataset increases or decreases proportionally with the other’s increases or decreases, their correlation is 1. If one dataset varies in an opposite way, for example, one dataset increases with the other’s decrease, their correlation is -1. This indicator is calculated using the following equation. ∑n i=1(xi − x¯)(yi − y¯) rxy = (5.1) p∑n 2 ∑n 2 i=1(xi − x¯) i=1(yi − y¯) This section particularly validates the numerical solution for a case when the windows are closed, and thus no natural ventilation is used. A case where the windows are open will be discussed in Section 5.4. The dataset used in the calibration serves as an observed sample, which the numerical solution aims to match. 5.3.1 Thermal zones The room of interest is a single-zone space with no interior thermal divisions. However, the room contacts two different zones, the outdoors and the second floor (F2). Therefore, the estimation of the test room becomes a multi-zone problem with at least two thermal resis- tances: one facing the outdoors (Renvelope) and the other facing the second floor (RF2). Since F2 has contact with the glazing walls and the concrete slab, RF2 can be divided into Rwall and Rslab. It is noteworthy that Renvelope and Rslab involve thermal storage while Rwall does not, and therefore, one must carefully identify how thermal zones are divided and which thermal properties are used in their simulations. In this validation, several cases with different thermal 100 5.3. Validation: without natural ventilation zone divisions are tested, and the result of each division type is discussed. As demonstrated in Section 4.1.4, thermal resistances can be re-defined for multi-zone analysis. This means that, depending on the way thermal zones are arranged, Eq. (4.31) would use different thermal resistances. 5.3.2 Test 1: Steady state Before testing transient simulations with thermal mass effect, this section tests the validity of the proposed model when used in a steady state. This will prevent calculation errors from occurring due to the thermal lag. While the real building behaves as a transient phenomenon, it can be converted into a steady-state case by using fixed temperatures of materials. That is, instead of Toutdoor and Renvelope for heat transfer between the outdoor and the indoor en- vironments, Tenvelope and Renvelope:sur f ace can be used. Likewise, TF2 and Rslab for heat transfer between F2 and the indoor environment can be substituted by Tslab and Rslab:sur f ace. The case then becomes a steady-state problem. Consequently, the zones consist of a room, an envelope, a slab, and F2, while the zones except the room do not thermally interact with each other. This modified thermal zone setting is illustrated in Figure 5.17a. As shown in Table 5.6 and Figure 5.17b, the measurement and simulation results show a correlation of 0.98, with a RMSE of only 0.32 K. This means that the simulation results have a 0.32 degree (a) Diagram of steady-state model (b) Result of steady-state model Figure 5.17: Steady-state simulation setup and result 101 Chapter 5. Validation with HouseZero Celsius discrepancy on average from the measurement, and are highly correlated. The result confirms that the model calculates the basic heat balance correctly. 5.3.3 Test 2: Unsteady-state with simplified thermal mass 5.3.3.1 Setting Test 1 proved that the analytical model is reliable for multi-zone analysis when all boundary temperatures with associated thermal resistances are known. It used the envelope tempera- ture calculated from the Modelica calibration in Section 5.2 and the slab temperature measured from HouseZero. If these temperatures were unknown, and only the air temperatures of adja- cent zones were available, the approach of Test 1 would not be appropriate. Moreover, Tenvelope and Tslab are dependent on the characteristics of thermal masses, thus requiring a transient analysis. In Test 2, a simplified transient model is tested using two known air temperatures: the outdoor temperature and the temperature of F2 (Figure 5.18). Figure 5.18: Diagram of simplified model (Test 2) The thermal masses of the envelope and slab were assumed to be equally distributed in the test room for simplification, so the total thermal storage of the room became the sum of Cenvelope, Cslab, and Croom, which are listed in Section 5.2.3. For the thermal resistances between the outdoors and the room (Renvelope) and between F2 and the room (RF2), the following values 102 5.3. Validation: without natural ventilation were calculated, also based on Section 5.2.3: Renvelope = Renvelope:sur f aceOut + Renvelope:sur f aceIn = 0.02 + 0.085 = 0.105 (5.2) 1 1 RF2 = 1/( + ) Rslab:sur f In + Rslab:sur f Out Rwall 1 1 = 1/( + ) = 0.018 (5.3) 0.01 + 0.20 0.02 5.3.3.2 Test 2 results and discussion Figure 5.19 shows the simulated room temperature (solid red line) overlaid on the measure- ments (dotted lines). The RMSE of 9.11 K demonstrates that this model overestimates the room temperature by 9.11 degrees Celsius on average, although the thermal lag matches well with the measured room temperature, showing a correlation of 0.97. This overestimation is due to the simplification of thermal mass, which suggests that the model has to be modified to properly represent the thermal masses and room air. Figure 5.19: Result of simplified model 5.3.3.3 Assumptions revisited To understand the huge discrepancy between the measurements and the simulation result, two major assumptions used in the analytical model need to be addressed: thermal mass and 103 Chapter 5. Validation with HouseZero solar radiation. In the test room, in reality, the thermal storage of the room air is marginal compared to those of the envelope and the slab. The envelope receives solar radiation, and a portion of the solar radiation is transmitted to the indoor environment and heats up the concrete slab. On the other hand, in the Test 2 set up, the proposed model assumes that one large thermal mass, equivalent to the sum of the envelope, slab and air, is allocated in the air. Moreover, the exterior solar radiation is considered as internal heat gains, which explains the overestimation of the temperature shown in Figure 5.19. To improve the simulation results, the room has to be subdivided to represent the different thermal masses with different heat gains. The next few sections will explore options for doing this. 5.3.4 Test 3: Unsteady-state with at least one thermal mass specified in a zone This section tests two models that have an additional zone assigned for thermal mass. One model adds a zone that represents the thermal mass of the envelope (Figure 5.20a), so that the room’s thermal mass storage is now the sum of only Croom and CSlab. The other model adds a zone representing the slab’s thermal mass (Figure 5.20b), and the room’s thermal mass storage becomes the sum of Croom and Cenvelope. The advantages of testing these models are twofold. First, they are expected to mitigate the over-simplification issue observed in Sec- tion 5.3.3, while still being simpler than a model specifying all mass zones separately. Second, by comparing these two models, the effect of each thermal mass as a separate zone can be understood. (a) Test 3A: Additional zone of envelope. The thermal (b) Test 3B: Additional zone of slab. The thermal mass mass of room represents the slab mass. of room represents the envelope mass Figure 5.20: Test 3 models (3A and 3B) diagrams 104 5.3. Validation: without natural ventilation 5.3.4.1 Test 3A: A zone added to represent the envelope’s thermal mass This model (Figure 5.20a) was tested in order to understand the effect of separating the build- ing envelope from the room zone. It defines three adjacent zones as the outdoors, F2, and the envelope. In this model, the room is not directly contacting the outdoors since the envelope zone is placed between the room and the outdoors. The envelope receives solar radiation, and the room receives a part of the solar radiation that is transmitted through the skylight. The room’s thermal storage still includes the slab’s thermal storage. Table 5.4 lists the rest of the inputs for the model. Table 5.4: Test 3A simulation inputs: heat storage and thermal resistance Heat storage of room 5,534,000 (J/K) Routdoor−envelope 0.020 (K/W) Heat storage of envelope 2,113,532 (J/K) Renvelope−room 0.085 (K/W) Rroom−F2 0.018 (K/W) Figure 5.21 shows the calculated temperatures of the room and the envelope as solid lines compared to the measured temperatures. The additional envelope zone was effective in that the overestimated indoor temperature in Test 2 was significantly reduced represented by a RMSE of 1.95 K. By separating the envelope from the room, the envelope was heated by receiving solar radiation (blue line in Figure 5.21) and the room was heated by the convection from the slab surface, which was warmed by solar radiation (red line in Figure 5.21). This reconfirms that the high temperature shown in Test 2 was attributed to those zones being modeled together as one room. However, the room temperature still did not agree with the measurement. There was a 0.70 decrease in correlation. For example, during nighttime, the ac- tual room temperature went down, while the calculated temperature increased. This suggests a critical drawback of this model. The trend of the temperature fluctuations of the simulated room temperature resem- bles that of the measured slab’s temperature (green dotted line). In fact, their correlation was 0.84, which was higher than what was found in Test 1. On the other hand, the correlation between the simulation room temperature and the envelope plummeted. The increased corre- 105 Chapter 5. Validation with HouseZero lation between the simulated room temperature and the measured slab temperature indicates that this may be due to the fact that the room zone accounts for the slab’s thermal mass. The next model will use a setting to verify this. 5.3.4.2 Test 3B: A zone added to represent the slab’s thermal mass This model (Figure 5.20b) also has three adjacent zones, but instead of the envelope zone, it creates a slab zone. Since there is no specific zone assigned for the envelope, the envelope’s thermal mass property is included in the room zone, including external solar radiation. The slab receives internal heat gains from solar radiation. Table 5.5 describes the simulation inputs of the model. Table 5.5: Test 3B simulation inputs: heat storage and thermal resistance Heat storage of room 2,147,532 (J/K) Routdoor−room 0.105 (K/W) Heat storage of slab 5,500,000 (J/K) Rroom−F2 0.020 (K/W) Rroom−slab 0.010 (K/W) Rslab−F2 0.200 (K/W) Figure 5.22 shows the results of this model: the calculated temperatures of the room and slab as solid lines, and the measurements as dotted lines. The correlation between the calculation and the measurement of the room was better than that from Test 3A. That is, the calculated temperature increased when the measured temperature increased. However, the magnitude of error became significantly larger, leading to a larger RMSE. Consequently, the higher room temperature influenced the calculated slab temperature to be higher than the measurement. 5.3.4.3 Test 3A and 3B discussions In this section, two models were tested to see the effects of separating the envelope and the slab from the rest of the room in calculations. The models first revealed that the assumption of having an aggregated thermal mass within the air is not appropriate, because thermal 106 5.3. Validation: without natural ventilation Figure 5.21: Result of test 3A: a simplified model simulation with an additional zone of the envelope Figure 5.22: Result of test 3B: a simplified model simulation with an additional zone of the slab 107 Chapter 5. Validation with HouseZero masses behave very differently than the air itself. In transient simulations like the models tested above, thermal lag is a function of thermal storage, thus the thermal lag of the room should only be directly calculated from the room’s thermal storage, not from the thermal storage of the envelope or the slab. Secondly, solar radiation needs to be carefully applied since its impact on thermal masses is significant. The resultant temperatures of the envelope and the slab were greatly different not only because one is facing the outdoors and the other is facing F2, but also because one receives the external solar radiation and the other receives only a part of the solar radiation. This exercise concludes that the proper model for this room in HouseZero is to separate both thermal masses into separate zones. 5.3.5 Test 4 final model 5.3.5.1 Test 4 setting The models tested in the previous sections reveal that each thermal mass should be modeled in a dedicated zone, since two major thermal masses contact different thermal zones and receive different amount of solar radiation. Figure 5.23 illustrates the locations of the thermal masses and thermal resistances needed in the calculation. This model used the thermal properties listed in Section 5.2.3. Figure 5.23: Diagram of a final model 108 5.3. Validation: without natural ventilation 5.3.5.2 Test 4 results and discussions The RMSE of the calculated and simulated envelope temperatures was 0.47 K with a corre- lation of 1.00. The RMSE of measured and simulated slab temperatures was 0.26 K with a correlation of 0.99. The RMSE of the measured and simulated room temperature was 0.47 K with a correlation of 0.96. The tests above used Dataset 1. In another study using Dataset 2 where the windows were also kept closed, the findings of Tests 1 through 4 remained valid. The results of the study with Dataset 2 are available in Appendix C. Figure 5.24: Result of test 4: a final model with two discrete thermal mass zones 109 Chapter 5. Validation with HouseZero Table 5.6: Test 1: correlation and RMSE Outdoor F2 Envelope Envelope, sim Slab Slab, sim Rm Rm, sim RMSE Outdoor 1.00 F2 0.44 1.00 Envelope 0.82 0.79 1.00 Envelope, sim - - - - Slab -0.21 0.64 0.10 - 1.00 Slab, sim ------Rm 0.50 0.98 0.83 - 0.61 - 1.00 Rm, sim 0.36 0.98 0.73 - 0.74 - 0.98 1.00 0.32 Table 5.7: Test 2: correlation and RMSE Outdoor F2 Envelope Envelope, sim Slab Slab, sim Rm Rm, sim RMSE Outdoor 1.00 F2 0.44 1.00 Envelope 0.82 0.79 1.00 Envelope, sim - - - - Slab -0.21 0.64 0.10 - 1.00 Slab, sim ------Rm 0.50 0.98 0.83 - 0.61 - 1.00 Rm, sim 0.34 0.96 0.70 - 0.77 - 0.97 1.00 9.11 Table 5.8: Test 3A: correlation and RMSE Outdoor F2 Envelope Envelope, sim Slab Slab, sim Rm Rm, sim RMSE Outdoor 1.00 F2 0.44 1.00 Envelope 0.82 0.79 1.00 Envelope, sim 0.79 0.80 1.00 1.00 0.54 Slab -0.21 0.64 0.10 0.11 1.00 Slab, sim ------Rm 0.50 0.98 0.83 0.84 0.61 - 1.00 Rm, sim -0.23 0.75 0.26 0.31 0.84 - 0.70 1.00 1.95 110 5.3. Validation: without natural ventilation Table 5.9: Test 3B: correlation and RMSE Outdoor F2 Envelope Envelope, sim Slab Slab, sim Rm Rm, sim RMSE Outdoor 1.00 F2 0.44 1.00 Envelope 0.82 0.79 1.00 Envelope, sim - - - - Slab -0.21 0.64 0.10 - 1.00 Slab, sim -0.14 0.79 0.28 - 0.95 1.00 5.85 Rm 0.50 0.98 0.83 - 0.61 0.75 1.00 Rm, sim 0.82 0.78 0.92 - 0.27 0.34 0.84 1.00 7.41 Table 5.10: Test 4: correlation and RMSE Outdoor F2 Envelope Envelope, sim Slab Slab, sim Rm Rm, sim RMSE Outdoor 1.00 F2 0.44 1.00 Envelope 0.82 0.79 1.00 Envelope, sim 0.79 0.81 1.00 1.00 0.47 Slab -0.21 0.64 0.10 0.12 1.00 Slab, sim -0.27 0.62 0.06 0.08 0.99 1.00 0.26 Rm 0.50 0.98 0.83 0.85 0.61 0.58 1.00 Rm, sim 0.27 0.96 0.66 0.69 0.79 0.77 0.96 1.00 0.47 111 Chapter 5. Validation with HouseZero 5.4 Validation with natural ventilation 5.4.1 Experiment setting There are three types of windows: skylight, automatic windows, and manual windows. The lower manual windows were left open during the entire test period. The mechanical con- trol for the upper windows was disabled during the test, and the skylight was kept closed. The manual windows are of the hopper type, and the opening angle was around 15 degrees (1/12π). Figure 5.25: Pictures of the hopper type windows (left) and skylight (right). 5.4.2 Division of thermal zones for simulation Section 5.3.5 demonstrated that dividing thermal zones in the way described by Figure 5.23 was reasonable. This validation case with natural ventilation will modify zone configuration and add several parameters to consider airflows. First, since the outdoor zone is now an adjacent zone, a thermal resistance (RNV) between the outdoors and the room should be calculated (Figure 5.26). This RNV is solely due to natural ventilation, and thus is equal to 1/ρCpV˙ . Note the omitted term Ui Ai from Eq. (4.1). Second, since RNV influences the room temperature, Tcomb is modified as in Eq. (5.4) to consider natural ventilation when available. The heat transfer between the outdoor air and the envelope is neglected. 112 5.4. Validation with natural ventilation Tout Tenvelope T T /R + /R + slab/R + F2/R NV envelope:sur f ace slab:sur f ace wall with wind 1 + 1 + 1 + 1 /RNV /Renvelope:sur f ace /Rslab:sur f ace /Rwall Tcomb = (5.4) Tenvelope T T /R + slab/R + F2/R envelope:sur f ace slab:sur f ace wall with no wind 1 1 1 /Renvelope:sur f ace + /Rslab:sur f ace + /Rwall Figure 5.26: Diagram of a model with natural ventilation 5.4.3 Prediction of ventilation rate In the test room, cross ventilation is available when the skylight is open. HouseZero was in automatic operation mode, meaning that the windows opened automatically when fresh air was needed or when outdoor temperature could be used for cooling. To estimate the airflow rate (m3/s) due to cross ventilation, this section uses the pres- sure coefficient data published by Orme et al. (1998). Table 5.11 shows the differentials of the pressure coefficients of the north-side wall and the skylight roof depending on incident wind directions. Flow rates (V˙ ) were then calculated by the orifice equation, which is given as: q ∆ V˙ = (ACd)e f f v | cp|, (5.5) ∆ where v is wind speed and cp is the pressure coefficient differential of two openings. (ACd)e f f is the effective opening area with a consideration of an associated discharge coefficient (Cd). 113 Chapter 5. Validation with HouseZero Table 5.11: Pressure coefficient differentials between north-facing wall and skylight roof of HouseZero with eight (8) different wind directions according to Orme et al. (1998) Table valid only with figures Wind Direction N NE E SE S SW W NW North-facing wall (cp,(Wall)) 0.2 0.05 -0.25 -0.3 -0.25 -0.3 -0.25 0.05 Skylight roof (cp,(Roo f )) -0.08 -0.3 -0.5 -0.3 -0.08 -0.3 -0.5 -0.3 ∆ cp(cp,(Wall) − cp,(Roo f )) 0.28 0.35 0.25 0 0.17 0 0.25 0.35 Note.Wind pressure coefficient (cp) data for the north wall and skylight roof based on ‘’Numerical Data for Air Infiltration and Natural Ventilation Calculations” by Malcolm Orme, Martin W. Liddament, and Andrew Wilson, 1998. With n number of openings, the effective opening area is given as: 1 (ACd)e f f = . (5.6) qΣn 1 i=1 2 (ACd)i 5.4.4 Results Figure 5.27 shows the graphs of the measured temperatures. The red dotted line is the room temperature measurement that the analytical model aims to reproduce. Besides the flow rates estimated from the previous section, three more sets of simulations were run for comparison. These three additional settings were a zero flow rate, single-sided natural ventilation, and an overestimated flow rate from the local wind without adjustment. The solid red line in Figure 5.28 shows the simulated indoor temperature when the flow rates were calculated based on Eq. (5.5). The RMSE was 0.52 K and the correlation was 0.96 (Table 5.12). The discrepancy between the calculated and measured datasets is reasonable 114 5.4. Validation with natural ventilation Figure 5.27: Measurement during 09/07 (FRI) 6PM - 09/10 (MON) 0AM Figure 5.28: Simulation result of Dataset 4: natural ventilation considering the results of Datasets 1 through 3 discussed in Section 5.3. 5.4.4.1 Assumption of no flow rate This test with no flow rate tried to understand hypothetical case where natural ventilation was unavailable, either because v = 0 or |∆cp| = 0. The case assumes that other zone temperatures, such as those of the second floor and mass zones, were not affected by the closed room assumption, or that the influence of the assumption was negligible. The black solid line in 115 Chapter 5. Validation with HouseZero Table 5.12: RMSE and correlation coefficients of simulation results with different flowrates RMSE Correlation coefficient No flowrate 2.61 0.62 Single-sided natural ventilation 2.06 0.89 Cross ventilation 0.52 0.96 Over-optimistic flowrates 1.59 0.93 Figure 5.28 shows the simulated temperature graph of this case. As the graph shows, the room temperature would have been significantly higher if there was no natural ventilation at all times. The case showed a RMSE of 2.61 K and a correlation with the measurements of 0.62. 5.4.4.2 Assumption of single-sided natural ventilation Although the experiment had cross-ventilation, single-sided ventilation is also possible when the skylight is closed. For calculation, the flow rate is determined by: V˙ = 0.05A · v, (5.7) where v is wind speed at the building height as suggested by Warren and Parkins (1984). As the solid gray line of Figure 5.27 shows, the hypothetical flow rate from single-sided natural ventilation resulted in much higher indoor temperatures, showing a RMSE of 2.06 K . 5.4.4.3 Applying local wind speeds as inflow wind speeds This test used wind data from the GSD weather station as the inflow speed at the openings. The wind speeds were multiplied by the effective opening area to obtain over-optimistic flow rates. The flow rates are unrealistic because the calculation does not consider pressure coeffi- cients discussed in Eq. (5.5), but the test was still run for reference. The solid bright red line in Figure 5.28 shows the resultant indoor temperature of this case, which was generally lower than measurements. The RMSE of this case was 1.59 K and correlation with the measurements was 0.93. 116 5.5. Summary and discussions 5.5 Summary and discussions In this chapter, the analytical solution for a room with thermal masses with and without nat- ural ventilation was validated by comparing the calculated temperatures with the measure- ments. Four datasets were collected from a three-story building. Three datasets were collected when windows in the test room were all closed, and one dataset was collected when the windows were open. The validation started with the calibration of the simulation settings. Based on the HouseZero’s construction materials, thermal resistances and thermal mass properties were determined. The calibration was conducted using Datasets 1 through 3 to cross-check, and modeled in Modelica. Once the settings for the simulation were finalized, Datasets 1 and 2 and Dataset 4 were validated using an analytical solution set up in MS Excel. The study found that the analytical model is valid, with RMSEs of 0.47, 0.24, and 0.52 K found for the datasets respectively. Zoning was found to be critical when thermal mass is considered. As Sections 5.3.3 to 5.3.5 revealed, the ways that zones and boundaries were defined significantly influenced the results. The underlying assumption of the original model was that the difference in thermal mass and indoor temperatures would be negligible. However, the validation demonstrated that some buildings, like this test room, may not follow that assumption. To solve this issue, thermal masses in the ceiling and the floor were separated from the room zone, calculated as adjacent zones. This method made this seemingly single-zone problem into a multi-zone problem. 117 Chapter 6 Implementation for parametric study This chapter demonstrates the feasibility of interactive building design with natural ventila- tion simulation. With the dynamic metrics introduced in Chapter 3, Section 3.3 has shown that a natural-ventilation-inspired parametric design for steady-state simulations can be con- ducted in Rhino and Grasshopper by utilizing the existing simulation engine and the tools including EnergyPlus, Honeybee, and Ladybug. This chapter replaces the existing tools with the analytical model explained in Chapter 4 and tests a single zone as described in Section 4.4. Chapter 6. Implementation for parametric study 6.1 Overview 6.1.1 Objectives The objective of this chapter is to demonstrate the usage of the dynamic natural ventilation metrics in design process while passive design strategies discussed in the previous chapters are considered. Section 3.3 has shown the feasibility of using these dynamic metrics for build- ing design, albeit with some limitations. The feasibility study uses EnergyPlus (EP) as an engine that is implemented in Honeybee. Therefore, the feasibility study can handle most of the EP settings as long as Honeybee has made them possible. This chapter implements the analytical solution derived in Chapter 4 in lieu of EP and Honeybee to enable users to explore passive strategies such as window controls with thermal mass and understand their impacts on dNVCE. The parametric study was conducted for a single-zone case only. Once a single-zone case is successfully demonstrated, it would be possible to expand the method to multi-zone cases, since both single-zone and multi-zone scenarios have been discussed in the previous chapters. 6.1.2 Methodology As in the earlier feasibility study, the implementation of this section was conducted using the 3D parametric modeling platforms, Rhino and Grasshopper. The analytical solution was coded into a Grasshopper component and connected to the geometry in Rhino (Figure 6.1). Figure 6.1: Screenshot of geometry and structure of simulation controls in Rhino and Grasshopper. Closer views are available in Figures 6.2 and 6.3. 120 6.2. 3D Implementation 6.2 3D Implementation 6.2.1 Inputs 6.2.1.1 Weather data This study used 24-hour data that was used in previous chapters. The hourly outdoor tem- peratures, ventilation rates, and internal heat gains are described in Appendix B. This study used the same weather data to allow crosschecking with previous calculations and to confirm the correctness of the implementation. In general, weather data available at the EnergyPlus website (https://energyplus.net/weather) can be used and connected to the simulation com- ponent. 6.2.1.2 Ventilation types For the implementation purpose, this chapter used wind-driven cross ventilation. The same pressure coefficients that were used in Appendix B were applied, and the orifice equation (Eq. (5.5)) was coded into the ventilation rate component to calculate wind flow rates through openings. If single-sided ventilation is used, empirical models (H. Wang and Q. Chen, 2012; H. Wang and Q. ( Chen, 2015; Warren and Parkins, 1984) can be used. This tool can also consider buoyancy-driven natural ventilation by calculating flow rates caused by thermal buoyancy, which can be expressed as Eq. (6.1). " s #2/3 2g V˙ = Cd Ae f f qh (6.1) ρCpTre f where : 2 Ae f f : effective opening area (m ) g : gravitational acceleration (m/s2) q : internal heat gain (J/s) h : height between the lower and the upper openings (m) 121 Chapter 6. Implementation for parametric study 6.2.1.3 Parameterized inputs Several geometry-related inputs were modeled within Rhino, which were then connected to thermal components in Grasshopper (Figure 6.2). The room surface area was connected to a component that calculates thermal resistance as explained in Eq. (4.1), while U-value and infiltration rates were user-inputs. The floor area was connected to the internal heat gain, as- suming that the number of occupants, lighting load, and the use of appliances would increase in proportion to the floor area. Two windows are connected to the flow rate component in the tool, calculating the effective window area and flow rates per the orifice equation explained in Eq. (5.5). Figure 6.2: Closer view of the geometry and boundary setting components 122 6.2. 3D Implementation 6.2.2 The solver The solver of this tool calculates hourly indoor temperatures to eventually calculate dNVCE and CPUR based on the analytical solutions discussed in Section 3.2. The solutions were coded in Python. The solver needs inputs which include hourly outdoor temperature, thermal resis- tance, internal heat gain, thermal mass’ heat storage, flow rates, target indoor temperature, and time step resolution. In addition to these inputs, there are several other options to choose. Thermal mass and smart window operation are two design options, which can be enabled and disabled in the solver. Initialization of the indoor temperature is another optional function. Figure 6.3: Closer view of the solver component. Left-side items of the solution component are inputs and right-side items are outputs. 123 Chapter 6. Implementation for parametric study 6.2.2.1 Initialization of indoor temperature If thermal mass is not considered, the calculation does not require an initial indoor tempera- ture because only the current status counts in the heat balance equation. This is not the case in transient simulations when the heat storage of a material influences the outputs of successive time steps. The indoor temperature of the entire simulation period may vary due to the initial indoor temperature that is given by users. Therefore, it is important to determine the initial temperature. In previous chapters where calculations were computed in spreadsheets, the cal- culations were iterated until the last timestep temperature came close to the first timestep’s temperature. The initialization option was also implemented in this parametric study. When this option is enabled, the solver checks the difference between the initial temperature and the last hour’s temperature. Depending on the convergence tolerance set by users, for example, 0.5 degrees Celsius, the calculation will be iterated until the difference becomes less than the tolerance. If the difference is larger than the tolerance, the solver uses the last timestep’s temperature as a new initial temperature for each iteration. The last two items of the solver component shown in Figure 6.3, named “initialize” and “convergenceCrit,” are the controls for the initialization: one is to turn on/off this option and the other is to set the convergence criterion. Table 6.1 shows the indoor temperature results both when the starting temperature is initialized and when it is not initialized in transient states. It demonstrates that the different initial temperatures (35 degrees Celsius and 15 degrees Celsius, for instance) have made a difference as great as 15.04 degrees Celsius in one hour. With initialization, on the other hand, the solver finds a new initial temperature that is independent of the user’s input. 6.2.2.2 Calculation of thermal mass The thermal mass solutions derived in Section 4.1 were implemented in the solver (Figure 6.3). When this option is enabled, the solver uses the transient solution for dNVCE (Eq. (4.42)) instead of the steady-state solution (Eq. (3.8)). 124 6.2. 3D Implementation Table 6.1: Indoor temperature results with different initial conditions Thermal mass with Thermal mass with Unit natural ventilation natural ventilation & smart controls ◦C No initialization∗ Initialized∗∗ No initialization∗ Initialized∗∗ ∗∗∗ ∗∗∗ Tinitial 35.00 15.00 23.08 35.00 15.00 22.98 1 30.80 16.37 22.20 30.80 [15.76] 22.13 2 27.63 17.22 21.43 27.63 [16.45] 21.37 3 25.04 17.52 20.56 25.04 16.97 20.52 4 23.05 17.63 19.82 23.05 17.23 19.79 5 21.62 17.71 19.29 21.62 17.42 19.27 6 20.67 17.85 18.99 20.67 17.64 18.98 7 20.54 18.51 19.33 20.54 [18.28] 19.32 8 21.09 19.62 20.22 21.09 [19.01] [19.99] 9 21.93 20.87 21.30 [21.76] [19.77] [20.71] 10 22.85 22.08 22.39 [22.44] [20.56] [21.45] 11 23.67 23.12 23.34 [23.12] [21.33] [22.18] 12 24.57 24.18 24.34 [23.82] [22.12] [22.93] 13 25.53 25.24 25.36 [24.54] [22.93] [23.69] 14 26.31 26.10 26.18 [25.25] [23.71] [24.43] 15 27.03 26.88 26.94 [25.94] [24.48] [25.17] 16 27.44 27.34 27.38 [26.58] [25.19] [25.85] 17 27.69 27.61 27.64 27.06 [25.86] [26.48] 18 27.64 27.58 27.60 27.19 26.32 26.77 19 26.82 26.78 26.80 26.50 25.87 26.20 20 26.07 26.04 26.05 25.84 25.38 25.62 21 25.22 25.20 25.21 25.05 24.72 24.89 22 24.44 24.42 24.43 24.32 24.08 24.20 23 23.73 23.72 23.73 23.65 23.48 23.56 24 23.09 23.08 23.08 23.02 22.90 22.97 dNVCE 0.72 0.74 0.74 0.82 0.92 0.88 CPUR 0.91 0.94 0.94 1.03 1.16 1.11 Values in [ ] mark denotes the closed status of windows. ∗ Calculations are computed only once without iterations. ∗∗ Calculations are iterated until the hour 24 of the last iteration has less than 0.1◦C difference with the temperature of the current hour 24. ∗∗∗ New initial temperature determined by solver. The solver finds this value regardless of user inputs. 125 Chapter 6. Implementation for parametric study 6.2.2.3 Algorithm for smart window controls The smart window control option discussed in Section 4.4 was also implemented in the solver. For this option, an algorithm that searched for the optimum operation—open or close—was developed. To maximize dNVCE, the algorithm first creates two hourly lists of thermal resistances that vary by ventilation rates: Rclosed and Ropen. It calculates the indoor temperature of the next time step with both thermal resistances, and determines whether windows should be open or closed based on the resultant indoor temperature. For example, at the nth time step, the solver calculates the indoor temperatures of the (n + 1)th time step for both open and closed cases. If the indoor temperature of the open case is lower then that of the closed case, the algorithm chooses to open the window, and vice versa. The current algorithm seeks to achieve the lowest temperature as possible, since it aims to maximize the cooling capacity of natural ventilation. If it is important to ensure that the indoor temperature does not go below the comfort level, a lower boundary of the temperature can be added to the algorithm as an additional criterion. 6.2.3 Outputs The solver outputs a list of indoor temperatures, a list of available cooling power (qavail), a list of additional cooling power required (qreq), a list of hourly cNVCE and the mean of the hourly values (cNVCE), a list of hourly dNVCE and the mean of the hourly values (dNVCE), and the CPUR (Figure 6.3). 126 6.3. Parametric study 6.3 Parametric study 6.3.1 3D parametric study and visualization A solver that calculates dNVCE and CPUR for single-zone buildings was successfully imple- mented in the 3D modeling environment. This section explores alterations of design options by discussing how each modification affects the dynamic metrics and which parameters would improve the metrics. In steady-state simulation, design parameters that influence natural ventilation per- formance include the U-values of materials, building dimensions, window sizes, internal heat gain, ventilation rates, and the target temperature. When thermal mass is adopted, additional parameters such as previous indoor temperature and the heat storage of masses need to be considered. Figure 6.4 applies various settings and visualizes the dNVCE results in Rhino. Fig- ure 6.4 (1-2) shows the difference that passive strategies like thermal mass and window con- trols make. In Figure 6.4 (3), a more forgiving target temperature is applied. Raising the target temperature by 1 degree Celsius instantly increased the dNVCE to 0.99. Figure 6.4 (4-6) shows the impact of having different internal heat gains. This model calculates a heat gain rate rel- ative to the floor area. Having twice the floor area implies twice the internal heat load, while maintaining constant flow rates. In Figure 6.4 (4), the available cooling power is 66% of the ideal cooling power with an increased heat load, while in Figure 6.4 (6), the dNVCE is 1. The impact of having different flow rates is shown in Figure 6.4 (7-9). 6.3.2 Improving natural ventilation performance This section draws graphs that present the relationship between each parameter and dNVCE. Figures 6.5 to 6.8 plot dNVCE graphs as functions of Cm, V˙ , qgain, and Uvalue during a day based on the data in Table B.3. The graphs were obtained by running the simulation using the tool developed in this chapter. 127 Chapter 6. Implementation for parametric study (1) (2) (3) (4) (5) (6) (7) (8) (9) Figure 6.4: Parametric study for natural ventilation performance 128 6.3. Parametric study Figure 6.5: Graph of dNVCE of a day under different thermal heat storages Cm (J/K) Figure 6.6: Graph of dNVCE of a day under different flow rates v˙ (m3/s) 129 Chapter 6. Implementation for parametric study Figure 6.7: Graph of dNVCE of a day under different heat gain q (J/s) Figure 6.8: Graph of dNVCE of a day under different U-values U (W/K) 130 6.4. Discussions The graphs of this parametric study offer an insight into the natural ventilation perfor- mance based on a particular design component. For example, Figure 6.5 shows that reducing the heat capacity of thermal mass did not affect dNVCE while increasing the heat storage significantly improved dNVCE. Also Figure 6.6 demonstrates that higher volume flow rates yielded higher dNVCEs and window contols substantially contributed to increasing dNVCE. Expectedly, a greater internal heat gain led to a lower dNVCE as shown in Figure 6.7. Com- pared to the other parameters, dNVCE showed the least sensitivity to U-values (Figure 6.8). 6.4 Discussions 6.4.1 Multi-zone implementation Analytical multi-zone solutions have been derived and explained in Chapter 4. This chapter, however, implemented the proposed method for a single-zone room only. This was because it is convenient to check the feasibility and identify the challenges with a single-zone model first, which may prove to be useful for further steps in multi-zone implementation. Due to the complexity that multi-zone problems bring about, searching for the optimal way to consider multi-zone modeling in a 3D environment would be another topic to explore. There are several ways to approach the implementation of multi-zone problems. One option utilizes Honeybee, a parametric energy simulation plug-in for Grasshopper. A multi- zone analysis for dNVCE and CPUR can benefit from some of the components that Honeybee already offers (Figure 6.9), for example, Honeybee is able to recognize boxes attached to each other and turn them into adjacent zones for energy simulation. Another approach to implement multi-zone analysis is functional mock-up unit (FMU) and functional mock-up interface (FMI) (Figure 6.10), which standardize a simulation inter- face for easier model exchange and co-simulation between various simulation tools (Modelica Association, 2018). As a software library, an FMU can be created by an FMI-implemented sim- ulation tool. In the building industry, FMUs can be incorporated with EnergyPlus (Nouidui et al., 2014). A new modeling language called Modelica can be also used to create a FMU to be 131 Chapter 6. Implementation for parametric study Figure 6.9: A diagram using EnergyPlus, Honeybee and Ladybug Figure 6.10: A diagram using EnergyPlus, CONTAM, and FMU Figure 6.11: A diagram using EnergyPlus and Modelica 132 6.4. Discussions imported to EnergyPlus. EnergyPlus and CONTAM both can export FMUs. Third method for multi-zone implementation translates 3D geometry to Modelica components and brings the simulation data back into a 3D environment (Figure 6.11). Lastly, a hard-coded component, as demonstrated in the single-zone in Chapter 6 may work as well. Since each approach presents its own strengths and weaknesses, thorough examina- tion of all methods will be required to determine the optimal way of multi-zone implementa- tion. 133 Chapter 7 Conclusion 7.1 Contribution The methods of evaluating natural ventilation performance vary by design phases as every stage of design brings its own challenges. Recognizing the importance of quick and intuitive feedback that reflects various design options in the early design phase, this dissertation pro- posed an interactive simulation method for natural ventilation evaluation by incorporating dynamic performance metrics. 3D Rhino, a 3D modeling platform that enables parametric design, was used to realize this interactive simulation. The dynamic performance metrics of natural ventilation reflected the result of design decisions explored within the interactive modeling. Additionally, parametric studies offered an insight into crucial design parameters, providing various ways to improve the performance. Chapter 7. Conclusion The new dynamic performance metrics of natural ventilation—design natural venti- lation cooling effectiveness (dNVCE) and climate potential utilization rate (CPUR)—played pivotal roles in the interactive modeling. Compared to conventional metrics, these new met- rics conveyed intuitive information, offering three distinguished aspects in natural ventilation performance: cooling needs, time spans of analysis, and potential for performance improve- ment. First, dNVCE and CPUR compute values that designers can easily interpret concern- ing the cooling capacity obtained by natural ventilation. For example, a dNVCE of 0.5 repre- sents that half of the cooling needs of the design is met by the natural ventilation’s cooling capacity, instructing that modifications of room size, window size, or orientation would im- prove the performance. This feedback on cooling capacity would have been challenging with conventional metrics because volume flow rates and airflow rates do not present as readily applicable calculations. Second, these new metrics can consider the performance within various time periods as opposed to point-in-time metrics. Depending on users’ interests, dNVCE and CPUR can be calculated for an hour, a day, a season, or a year. Lastly, CPUR, defined as the ratio of dNVCE to climate potential, elucidates the poten- tial to improve the performance. A CPUR of 1 means that a building utilized cooling potential from a given climate, while a lower CPUR shows the room for improvement of performance. Moreover, a CPUR greater than 1 can be achieved when assisted by passive design strategies, such as thermal mass and window operations. In conclusion, this dissertation contributed to making natural ventilation evaluation accessible to designers by incorporating dynamic performance metrics of natural ventilation into interactive modeling. Easier simulation procedures and design-applicable metrics offer a new methodology and inspiration for environmentally-conscious building design. 136 7.2. Findings 7.2 Findings 7.2.1 Cooling effect assisted by other passive design strategies This study demonstrated substantial impact of adopting various passive design strategies on natural ventilation’s cooling effectiveness. While natural ventilation may alone be investigated during the design phase, the study found that having thermal mass with appropriate window controls remarkably improved the performance metrics. The influence of thermal mass and window controls on natural ventilation perfor- mance suggests that additional passive strategies, including shading device and insulation, may also need to be investigated when considering natural ventilation performance. 7.2.2 Zoning of thermal mass and indoor spaces The validation of this study through the HouseZero measurements revealed an important finding: a proper thermal zoning is crucial to predict a building’s indoor temperature. The calculation showed entirely different results based on how the thermal zones were assigned. To properly calculate the dynamic metrics, thermal mases should be assigned as discrete zones, separated from an indoor zone. 7.2.3 Expandability of the implemented tool The flexibility of the parametric 3D environment reveals a connection between the natural ventilation analysis discussed in this study and other simulations such as daylight model- ing and CFD modeling. For example, some parametric simulation plug-ins for Grasshopper within Rhino, including DIVA for Grasshopper and Butterfly, may calculate solar radiation and flow rates, respectively, which can then be transported into this natural ventilation tool that this dissertation proposed. This connection between different tools, when properly coupled, will initiate the integrative simulations of natural ventilation, daylight, and energy simulation. 137 Chapter 7. Conclusion 7.3 Applications 7.3.1 Prediction of window schedules in existing buildings The algorithm for smart window controls adopted in Chapter 6 can be utilized in existing buildings to predict daily window operations. The challenge is knowing the exact building properties, including the thermal resistance of the building envelope and internal boundaries, the solar radiation, and internal heat loads. The HouseZero model used in Chapter 5 has configured settings for the test room achieved through calibration, so this model can be used to predict the window schedules. As an example, the data from August 5th in Dataset 2 can be investigated. Assuming that ventilation rates can be estimated from the weather forecast of the day, and assuming that the rate is constant, a graph for window operation prediction can be drawn as shown in Figure 7.1. In addition to the outdoor temperature and the indoor temperature when windows are closed, this figure shows two more predicted indoor temperatures: one with the windows always open, and the other with windows operated by the algorithm. The algorithm suggests that windows should be closed at 9:30 AM and be open at 6:30 PM to maintain the lowest indoor temperature. 7.3.2 Optimization of thermal mass This study provides insight into the desirable heat storage of thermal mass. In some cases, more mass may help improve dNVCE by storing heat during the day and releasing it during the night. In other cases, however, an excessive thermal mass could store more heat than desired and can make the indoors undesirably warm even when the weather is favorable outside. The parametric graphs (Figure 6.5) that showed dNVCE as a function of thermal heat storage help determine the optimal thermal mass for a given design. 138 7.3. Applications Figure 7.1: Prediction of indoor temperature using window controls 7.3.3 Urban wind environment for indoor optimization This dissertation used constant ventilation rates, variable yet hypothetical ventilation rates, and ventilation rates calculated by the pressure coefficient table using meteorological data. These ventilation rates can also be obtained from CFD simulations, in which case the tool developed in this chapter can be coupled with the urban wind environment analysis for in- door optimization. For example, if pressure coefficient (cp) values on building surfaces are obtained from CFD simulations, the pressure values can be translated into Grasshopper. By finding optimal window locations that offer desirable flow rates, an optimized dNVCE can be obtained. 7.3.4 Thermally activated building systems and model predictive control The study about window operation with thermal mass used in Chapter 4 demonstrated a potential to be applied in thermally activated building systems (TABS) while being a part of model predictive control (MPC). The optimal operation of windows together with HVAC systems and natural ventilation strategy could be predicted by MPC, and the TABS performs 139 Chapter 7. Conclusion the actual operations. A potential example is HouseZero, for which natural ventilation is one of the major strategies used to achieve net-zero and is equipped with TABS. 140 Bibliography Acred, A. and Hunt, G. R. (2014). “Stack ventilation in multi-storey atrium buildings: A di- mensionless design approach”. 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Blacksburg, VA: Virginia Polytechnic Institute and State University. 153 Appendix A Results of Section 4.2 A.1 Results of verification: RMSE of single-zone verification Table A.1: RMSE of single-zone verification result Single-zone verification results Conditions Timestep Natural ventilation Internal heat 60 min 30 min 15 min 9 min 3 min N/A N/A 0.06 0.03 0.01 0.01 0.00 N/A 325 W 0.06 0.03 0.01 0.01 0.00 0.2 m3/s N/A 0.41 0.22 0.12 0.07 0.03 0.2 m3/s 325 W 0.36 0.17 0.08 0.06 0.05 Figure A.1: Graphs of RMSE of single-zone verification results. Appendix A. Results of Section 4.2 A.2 Results of verification: RMSE of multi-zone verification Table A.2: RMSE of multi-zone verification result Multi-zone verification results Conditions Timestep Natural ventilation Internal heat 60 min 15 min 3 min Zone 1 N/A N/A 0.07 0.02 0.00 Zone 2 N/A N/A 0.07 0.02 0.00 Zone 1 N/A 325 W 0.41 0.12 0.03 Zone 2 N/A N/A 0.36 0.08 0.05 Zone 1 0.2 m3/s N/A 0.42 0.15 0.10 Zone 2 0.2 m3/s N/A 0.48 0.10 0.10 Zone 1 0.2 m3/s 325 W 0.38 0.15 0.12 Zone 2 0.2 m3/s N/A 0.19 0.17 0.18 Figure A.2: Graphs of RMSE of multi-zone verification results. 156 Appendix B Settings and results of a single-zone test B.1 Settings used in Sections 4.4 and 4.5 and chapter 6 Table B.1: Building settings and boundary conditions Symbol Description Value Unit Universal constants ρair Density of air 1.20 (kg/m3) Cp,air Specific heat capacity of air 1000.00 (J/kgK) Buildling Dimension w Width 6 (m) l Length 12 (m) h Height 5 (m) Σ Abldg Surface area of building 252 (m2) Window Dimension w Width 1.36 (m) l Length 2 (m) Awindow) Area of window 2.72 (m) Ae f f Area of effective window 1.173232 (m2) Building Envelope Construction k Thermal conductivity 0.029 (W/m-K) th Thickness 0.1 (m) Uvalue U-Value 0.29 (W/m2-K) Cmass Heat storage 5190005 (J/K) Continued on next page Appendix B. Settings and results of a single-zone test Table B.1 – Continued from previous page Symbol Description Value Unit Internal heat gain qint Total internal heat gain 900.00 (W) Ventilation requirements V˙in f Infiltration rate 0.01 (m3/s) V˙NV Natural ventilation rate 0.33 (m3/s) Time Constant when windows are shut Σ Uvalue · Abldg Conduction through building envelope 73.08 (W/K) ρairCp,airV˙in f Infiltration through building envelope 6 (W/K) Rclose Thermal resistance of building enclosure 0.012645 (K/W) τclose Time constant (sec), Rclose · τclose 65629.8 (s) τclose Time constant (hour) 18.2305 (hr) e−1/(τclose 0.946624 Time Constant when windows are open Σ Uvalue · Abldg Conduction through building envelope 73.08 (W/K) ρairCp,airV˙NV Ventilation through building envelope 398.208 (W/K) Ropen Thermal resistance of building enclosure 0.002122 (K/W) τopen Time constant (sec) 11012.38 (s) τopen Time constant (hour) 3.058996 (hr) e−1/(τopen 0.721152 158 B.2. Hourly outdoor temperature and indoor results for Sections 4.4 and 4.5 and chapter 6 B.2 Hourly outdoor temperature and indoor results for Sections 4.4 and 4.5 and chapter 6 Table B.2: Input outdoor temperature and output indoor temperatures under different conditions Hour Outdoor Steady-state, Steady-state, NV with NV with Thermal closed NV thermal mass thermal mass mass, closed & window controls 1 18.00 29.38 19.91 22.19 22.16 33.26 2 17.50 28.88 19.41 21.42 21.39 33.02 3 16.40 27.78 18.31 20.55 20.53 32.74 4 16.00 27.38 17.91 19.81 19.80 32.46 5 16.00 27.38 17.91 19.28 19.27 32.19 6 16.30 27.68 18.21 18.98 18.98 31.95 7 18.30 29.68 20.21 19.33 19.32 31.83 8 20.60 31.98 22.51 20.21 20.21 31.83 9 22.20 33.58 24.11 21.30 20.92 31.93 10 23.30 34.68 25.21 22.39 21.66 32.07 11 23.90 35.28 25.81 23.34 22.38 32.25 12 25.00 36.38 26.91 24.34 23.13 32.47 13 26.10 37.48 28.01 25.36 23.90 32.73 14 26.40 37.78 28.31 26.18 24.64 33.00 15 27.00 38.38 28.91 26.94 25.37 33.29 16 26.60 37.98 28.51 27.38 26.05 33.54 17 26.40 37.78 28.31 27.64 26.67 33.77 18 25.60 36.98 27.51 27.60 26.91 33.94 19 22.80 34.18 24.71 26.80 26.29 33.95 20 22.20 33.58 24.11 26.05 25.68 33.93 21 21.10 32.48 23.01 25.20 24.94 33.85 22 20.50 31.88 22.41 24.42 24.23 33.75 23 20.00 31.38 21.91 23.72 23.59 33.62 24 19.50 30.88 21.41 23.08 22.98 33.48 159 Appendix B. Settings and results of a single-zone test B.3 Hourly dNVCE results for Sections 4.4 and 4.5 and chapter 6 Table B.3: Hourly qavail, qideal, and dNVCE under different conditions Climate Steady-state Thermal mass Mass+control Hour qavail cNVCE qideal dNVCE qideal dNVCE qideal dNVCE 1 -3185.66 1 -315.36 1 4323.92 1 4371.09 1 2 -3384.77 1 -278.82 1 5306.67 1 5340.69 1 3 -3822.80 1 -198.43 1 6443.28 1 6467.81 1 4 -3982.08 1 -169.20 1 7370.16 1 7387.84 1 5 -3982.08 1 -169.20 1 8017.49 1 8030.25 1 6 -3862.62 1 -191.12 1 8360.44 1 8369.64 1 7 -3066.20 1 -337.28 1 7797.66 1 7804.30 1 8 -2150.32 1 -505.37 1 6547.43 1 6812.55 1 9 -1513.19 1 -622.30 1 5106.32 1 5811.84 1 10 -1075.16 1 -702.68 1 3697.13 1 4823.27 1 11 -836.24 1 -746.53 1 2491.10 1 3880.69 1 12 -398.21 1 -826.92 0.5 1198.74 1 2877.98 1 13 0.00 0 -947.13 0 -169.34 0 1813.11 1 14 0.00 0 -1088.52 0 -1312.60 0 757.97 1 15 0.00 0 -1371.29 0 -2521.79 0 -428.82 0 16 0.00 0 -1182.77 0 -2865.42 0 -1070.05 0 17 0.00 0 -1088.52 0 -3086.95 0 -1748.23 0 18 -159.28 1 -870.77 0.2 -2825.03 0.1 -1859.61 0.1 19 -1274.27 1 -666.14 1 -1636.92 0.8 -940.70 1 20 -1513.19 1 -622.30 1 -679.90 1 -177.82 1 21 -1951.22 1 -541.91 1 432.88 1 794.95 1 22 -2190.14 1 -498.06 1 1425.16 1 1686.27 1 23 -2389.25 1 -461.52 1 2315.60 1 2503.90 1 24 -2588.35 1 -424.98 1 3137.87 1 3273.66 1 Note. Negative heat rates indicate cooling loads and positive heat rates indicate heating loads. A dNVCE is one (1) when a qideal is greater than zero. 160 Appendix C Validation results of Dataset 2 C.1 Dataset 2 temperature graphs Figure C.1: Dataset 2: graphs of measured and calculated temperature C.2 Dataset 2 correlation and RMSE results Appendix C. Validation results of Dataset 2 Table C.1: Dataset 2: correlation and RMSE Outdoor F2 Envelope Envelope, sim Slab Slab, sim Rm Rm, sim RMSE Outdoor 1.00 F2 0.74 1.00 Envelope 0.87 0.97 1.00 Envelope, sim 0.84 0.98 1.00 1.00 0.72 Slab 0.56 0.93 0.84 0.86 1.00 Slab, sim 0.52 0.92 0.81 0.84 0.98 1.00 0.38 Rm 0.70 0.99 0.95 0.97 0.96 0.94 1.00 Rm, sim 0.69 0.99 0.95 0.96 0.94 0.95 1.00 1.00 0.24 162