Benchmark Study of Tornado Wind Loading on Low-Rise Buildings with Consideration of Internal Pressure

Liang Wu, B.S., M.S.

A Dissertation

National Wind Institute

Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of

DOCTOR OF PHILOSOPHY

Approved

Delong Zuo, Ph.D. Chair of Committee

Xinzhong Chen, Dr. Eng.

Christopher Weiss, Ph.D.

Mark Sheridan Dean of the Graduate School

August 2019

Texas Tech University, Liang Wu, August 2019

ACKNOWLEDGEMENTS

It has been a valuable experience for me to complete my doctoral research at Texas Tech University. Along this journey, I have received more than I ever thought possible. I would like to take this opportunity to express my sincere gratitude to the people who have helped and supported me in this journey.

First and foremost, I would like to express my appreciation to my advisor, Dr. Delong Zuo, who has provided continuous guidance and insightful advice for this research. His profound knowledge and enthusiastic pursuit of academic excellence has set up a great example of professionalism for me. The financial support from him throughout this study is also greatly acknowledged.

I would like to extend my appreciation to my committee members, Dr. Xinzhong Chen and Dr. Christopher Weiss, for their time and suggestions for this research and thesis.

I would also like to thank Dr. Zhuo Tang, Dr. Changda Feng, and Mr. Deyi Xu, who have helped me a lot in preparing and conducting experiments for this research. I am also grateful to the friends I met at Texas Tech University.

Last but not the least, special thanks are given to my parents and Ms. Shijin Ma. Their love and encouragement have helped me overcome many obstacles in this journey. My appreciation for them are beyond words.

Texas Tech University, Liang Wu, August 2019

TABLE OF CONTENTS

ACKNOWLEDGEMENTS ...... ii

ABSTRACT ...... v

LIST OF TABLES ...... vi

LIST OF FIGURES ...... vi

1. INTRODUCTION ...... 1

1.1. Background, Methodology and Research Objectives ...... 1 1.2. Organization of the Dissertation ...... 6 2. CHARACTERISTICS OF TORNADO-LIKE VORTICES SIMULATED IN THE VORTECH SIMULATOR ...... 7

2.1. Introduction ...... 7 2.2. Experimental Facility ...... 8 2.2.1. Tornado Simulator ...... 9 2.2.2. Velocity and Pressure Measurements ...... 10 2.3. Estimation of Controlling Parameters ...... 11 2.4. Experimental Configurations ...... 12 2.5. Characteristics of Simulated Flow and the Resultant Surface Pressure Deficit ...... 14 2.5.1. Effect of Swirl Ratio ...... 15 2.5.2. Effect of Radial Reynolds Number...... 28 2.6. Implications from Flow and Surface Pressure Measurements ...... 31 3. WIND TUNNEL TESTING OF A LOW-RISE BUILDING MODEL IN BOUNDARY-LAYER-TYPE FLOW ...... 32

3.1. Introduction ...... 32 3.2. Experimental Setup ...... 34 3.2.1. The Building Model ...... 35 3.2.2. Simulation of Boundary Layer Flows ...... 40 3.2.3. Test Configurations ...... 44 3.3. Data Processing ...... 46 3.4. Experimental Results ...... 48 3.4.1. Nominally Sealed Building ...... 48 3.4.2. Building with A Dominant Opening ...... 53

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3.4.3. Building with Multiple Dominant Openings ...... 67 3.5. Summary ...... 74 4. LABORATORY TESTING OF A LOW-RISE BUILING MODEL IN TORNADO-LIKE VORTICES ...... 76

4.1. Introduction ...... 76 4.2. The Tornado Simulator ...... 77 4.3. Experimental Setup ...... 78 4.3.1. The Building Model ...... 78 4.3.2. Tornadic Flow Field ...... 81 4.3.3. Experimental Configuration ...... 82 4.4. Data Processing ...... 84 4.5. Data Interpretation Technique ...... 85 4.5.1. Methods ...... 86 4.5.2. Illustrative Example ...... 88 4.6. Experimental Results ...... 91 4.6.1. Effect of Internal Volume Augmentation ...... 92 4.6.2. Effect of Translation Speed ...... 97 4.6.3. Comparison between Loading by Tornadic and Boundary-layer-type Wind ...... 111 4.7. Summary ...... 119 5. CONCLUSIONS AND FUTURE WORK ...... 121

5.1. Conclusions ...... 121 5.2. Future Work ...... 122 REFERENCES ...... 124

Texas Tech University, Liang Wu, August 2019

ABSTRACT

Tornadoes are historically among the most devastating natural hazards, and their impact on society has not subsided even with today’s rapid advancements in science and technology. In particular, tornadoes frequently cause failures of and severe damages to low-rise buildings, resulting in disastrous losses of life and property. The major reason for these failures and damages are that most buildings are not designed for tornadoes, primarily because the understanding of tornadic loading on buildings remains inadequate. This dissertation presents a comprehensive benchmark study of tornadic wind loading on low-rise buildings. In the study, a model of a full-scale building is tested in tornado-like vortices simulated in a large-scale tornado simulator. The factors that affect the tornadic loading, including the type of the tornado, the speed at which the tornado translates, and the orientation and location of the building relative to the path of the tornado, are investigated. Particular attention is placed on the internal pressure of the building during tornado passages, which can account for a large portion of the total loading on the structure, as well as the effects of the sizes and locations of large openings in the building envelope, which can be created by debris impact on the building, on the internal pressure. In consideration of the nonstationary nature of the loading by translating tornadoes, a technique based on adaptive Gaussian filtering and cross- validation is used to interpret the experimental data. In addition, to provide a context for the study of tornadic loading, a building model with the same configuration of the model tested in the tornado simulator is also tested in a boundary layer wind tunnel. A comparison between the loading by tornadic and boundary-layer-type winds is performed based on the data from the experiments.

Texas Tech University, Liang Wu, August 2019

LIST OF TABLES

2-1 Vertical resolution of the velocity measurements (Tang et al., 2018a) ...... 13 3-1 Dominant openings and leakages holes of the WERFL building model ...... 37 3-2 Configurations of openings for the WERFL building model ...... 45 4-1 Dominant openings and leakage holes of the 1:100 WERFL building model ...... 80 4-2 Key parameters of simulated vortices ...... 82 4-3 Model configurations ...... 83

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LIST OF FIGURES

2-1 A schematic illustration of VorTECH (Tang et al., 2018a) ...... 9 2-2 A picture of a simulated tornado-like vortex ...... 10 2-3 Example axial profiles of the mean tangential and radial velocity at the edge of the convergence zone (Tang et al., 2018a) ...... 12 2-4 An example flow velocity measurement grid (Tang et al., 2018a) ...... 14 2-5 Mean flow fields of vortices simulated at (a) S=0.17, a=1.0, (b) S=0.22, a=1.0, (c) S=0.36, a=1.0, and (d) S=0.84, a=1.0 (Tang et al., 2018a) ...... 16 2-6 Axial profiles of local core radius (a=1.0) (Tang et al., 2018a) ...... 17 2-7 Axial profiles of mean tangential velocity simulated at (a) S=0.17, a=1.0, (b) S=0.22, a=1.0, (c) S=0.36, a=1.0, and (d) S=0.84, a=1.0 (Tang et al., 2018a) ...... 18 2-8 Radial profiles of mean tangential velocity simulated at (a) S=0.17, a=1.0, (b) S=0.22, a=1.0, (c) S=0.36, a=1.0, and (d) S=0.84, a=1.0 (Tang et al., 2018a) ...... 19 2-9 Turbulence intensity of tangential velocity over various regions of the vortices simulated at of (a) S=0.17, a=1.0, (b) S=0.22, a=1.0, (c) S=0.36, a=1.0, and (d) S=0.84, a=1.0 (Tang et al., 2018a) ...... 21 2-10 Skewness of the tangential velocity component over various regions of the vortices simulated at of (a) S=0.17, a=1.0, (b) S=0.22, a=1.0, (c) S=0.36, a=1.0, and (d) S=0.84, a=1.0 (Tang et al., 2018a) ...... 22 2-11 Kurtosis of the tangential velocity component over various regions of the vortices simulated at of (a) S=0.17, a=1.0, (b) S=0.22, a=1.0, (c) S=0.36, a=1.0, and (d) S=0.84, a=1.0 (Tang et al., 2018a) ...... 23 2-12 (a) Profiles of mean surface pressure deficit and (b) the minimum mean pressure deficit against swirl ratio (Tang et al., 2018a) ...... 24 2-13 Comparison between radial profiles of mean surface pressure deficit of full- scale and simulated tornado vortices (Tang et al., 2018a) ...... 26 2-14 Dependence of (a) mean, (b) standard deviation, (c) skewness and (d) kurtosis of surface pressure deficit on swirl ratio (Tang et al., 2018a) ...... 27 5 2-15 Mean flow field of vortices simulated at (a) Rer=3.91×10 , S=0.44, and (b) 5 Rer=3.02×10 , S=0.44 (Tang et al., 2018a) ...... 28 2-16 Axial profiles of (a) local core radius and (b) maximum mean tangential velocity (Tang et al., 2018a)...... 29 2-17 Dependence of (a) mean, (b) standard deviation, (c) skewness, and (d) kurtosis of surface pressure deficit on radial Reynolds number (Tang et al., 2018a) ...... 30 3-1 The Boundary Layer Wind Tunnel at Texas Tech University...... 34 vii

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3-2 Plan view of the BLWT at Texas Tech University ...... 35 3-3 Geometries of (a) the grid system, and (b) spires ...... 35 3-4 The Wind Engineering Research Field Laboratory Building ...... 36 3-5 Dimensions of the WERFL building at Texas Tech University ...... 36 3-6 Exploded view of the WERFL building model showing basic dimensions, locations of openings (including leakage holes), and the layout of external pressure taps ...... 38 3-7 Layout of internal pressure taps (Unit: mm) ...... 39 3-8 Picture of (a) the model representing the WERFL building and (b) Scaled volume chamber ...... 40 3-9 Comparison between simulated flow and target flow: (a) Mean wind velocity profile; (b) Turbulent intensity profile ...... 43 3-10 Power spectral density of turbulence components at a full-scale equivalent height of z = 3.91 m ...... 44 3-11 Definition of the wind direction and the directions of the force components ...... 46 3-12 Amplitude and phase of the tubing frequency response function ...... 47 3-13 Distributions of the mean external pressure coefficient for (a) wind direction = 0° in Case 1, (b) wind direction = 0° in Case 3, (c) wind direction = 90° in Case 1, and (d) wind direction = 90° in Case 3 (Case 1: fully enclosed; Case 3: nominally sealed) ...... 49 3-14 Distributions of the standard deviation of the external pressure coefficient for (a) wind direction = 0° in Case 1, (b) wind direction = 0° in Case 3, (c) wind direction = 90° in Case 1, and (d) wind direction = 90° in Case 3 (Case 1: fully enclosed; Case 3: nominally sealed) ...... 50 3-15 Comparison between the internal pressure coefficient in Case 2 and Case 3 for wind direction = 0°: (a) mean value, and (b) standard deviation (Case 2: nominally sealed, porosity ratio of 2.2 104 ; Case 3: nominally sealed, porosity ratio of 6.5 104 ) ...... 51 3-16 Basic statistics of internal pressure coefficient for Case 3 (nominally sealed, porosity ratio of 6.5 104 ) ...... 51 3-17 (a) Mean value, (b) standard deviation, (c) maximum value, and (d) minimum value of the force coefficients for Case 3 (nominally sealed, porosity ratio of 6.5 104 ) ...... 52

3-18 (a) Mean value and (b) standard deviation of CFz for Case 2 and Case 3 (Case 2: nominally sealed, porosity ratio of 2.2 104 ; Case 3: nominally sealed, porosity ratio of 6.5 104 ) ...... 53

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3-19 (a) Mean pressure coefficients and (b) standard deviations of pressure coefficients of each internal tap at wind direction = 0° for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole) ...... 54 3-20 Distributions of the mean external pressure coefficient at wind direction = 0° for (a) Case 4: open front door, (b) Case 6: open front window, and (c) Case 7: open side hole ...... 55 3-21 Distributions of the standard deviation of the external pressure coefficient at wind direction = 0° for (a) Case 4: open front door, (b) Case 6: open front window, and (c) Case 7: open side hole ...... 56 3-22 Distributions of the mean external pressure coefficient at wind direction = 90° for (a) Case 4: open front door, (b) Case 6: open front window, and (c) Case 7: open side hole ...... 57 3-23 Distributions of the standard deviation of the external pressure coefficient at wind direction = 90° for (a) Case 4: open front door, (b) Case 6 : open front window, and (c) Case 7: open side hole ...... 58 3-24 (a) Mean value, (b) standard deviation, (c) maximum value, and (d) minimum value of the internal pressure coefficients for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole) ...... 60 3-25 (a) Mean value, and (b) standard deviation of the external pressure coefficients at the corresponding dominant opening for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole) ...... 61 3-26 PSD of internal and external pressure coefficients for (a) wind direction = 0° in Case 4 (open front door), (b) wind direction = 0° in Case 6 (open front window), and (c) wind direction = 90° in Case 7 (open side hole) ...... 63 3-27 (a) Mean value, (b) standard deviation, (c) maximum value, and (d)

minimum value of CFz for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole) ...... 64

3-28 (a) Maximum value, and (b) minimum value of CFx for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole) ...... 65

3-29 (a) Maximum value, and (b) minimum value of CFy for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole) ...... 65

3-30 (a) Skewness and (d) Kurtosis of CFz for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole) ...... 66

3-31 (a) Mean value of Cpi , (b) Standard deviation of Cpi , (c) Mean value of

CFz , and (d) Standard deviation of CFz for Case 4 (open front door, porosity ratio of 2.2 104 ) and Case 5 (open front door, porosity ratio of 6.5 104 ) ...... 67

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3-32 (a) Mean pressure coefficients and (b) Standard deviations of pressure coefficients of each internal tap at wind direction = 0° for Case 8 (open front door and open back window), Case 10 (open front door and open front window), Case 11 (open front door and open side hole), and Case 12 (open front window and open side hole) ...... 68 3-33 Distributions of the mean external pressure coefficient at wind direction = 0° for (a) Case 8: open front door and open back window, (b) Case 10: open front door and open front window, (c) Case 11: open front door and open side hole, and (d) Case 12: open front window and open side hole ...... 69 3-34 Distributions of the standard deviation of the external pressure coefficient at wind direction = 0° for (a) Case 8: open front door and open back window, (b) Case 10: open front door and open front window, (c) Case 11: open front door and open side hole, and (d) Case 12: open front window and open side hole ...... 70 3-35 (a) Mean value, (b) standard deviation, (c) maximum value, and (d) minimum value of the internal pressure coefficients for Case 8 (open front door and open back window), Case 10 (open front door and open front window), Case 11 (open front door and open side hole), and Case 12 (open front window and open side hole) ...... 71 3-36 PSD of internal pressure coefficients for (a) Case 8: open front door and open back window, (b) Case 10: open front door and open front window, (c) Case 11: open front door and open side hole, and (d) Case 12: open front window and open side hole ...... 72 3-37 (a) Mean value, (b) standard deviation, (c) maximum value, and (d)

minimum value of CFz for Case 8 (open front door and open back window), Case 10 (open front door and open front window), Case 11 (open front door and open side hole), and Case 12 (open front window and open side hole) ...... 73

3-38 (a) Maximum value, and (b) minimum value of CFx for Case 8 (open front door and open back window), Case 10 (open front door and open front window), Case 11 (open front door and open side hole), and Case 12 (open front window and open side hole) ...... 74

3-39 (a) Maximum value, and (b) minimum value of CFy for Case 8 (open front door and open back window), Case 10 (open front door and open front window), Case 11 (open front door and open side hole), and Case 12 (open front window and open side hole) ...... 74 4-1 A schematic illustration of upgraded VorTECH ...... 78 4-2 Exploded view of the 1:100 WERFL building model showing dimensions of the model, locations of openings (including leakage holes), and external pressure tap layout ...... 79 4-3 Layout of internal pressure taps of the 1:100 WERFL building model (Unit: mm) ...... 80

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4-4 Picture of (a) the building model and (b) the scaled volume chamber ...... 81 4-5 Mean flow fields of (a) single-celled vortex, and (b) two-celled vortex ...... 82 4-6 (a) Mean, and (b) Standard deviation of the surface pressure deficit for the single-celled and two-celled vortex ...... 82 4-7 Definition of the building orientation angle ( ) ...... 84 4-8 Amplitude and phase of the frequency response function of the tubing used in VorTECH ...... 85 4-9 Illustration of k-fold cross-validation (Xiao and Zuo, 2015) ...... 88 4-10 Example time history of the internal pressure coefficient for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at 1.0 m/s ...... 89 4-11 (a) MSE resulting from different scaling parameters, (b) Time-varying variance of a sample time history estimated using adaptive Gaussian filtering, and (c) Comparison between the time-varying variances estimated directly from an ensemble of 100 measurements and using adaptive Gaussian filtering based on 10 measurements for the building model of Case 3 (open front door) in the single-celled vortex translating at 1.0 m/s ...... 90 4-12 Comparison between the time-varying variances of the internal pressure coefficient estimated directly from an ensemble of 100 measurements and using adaptive Gaussian filtering based on 10 measurements for the building model of Case 3 (open front door) in the two-celled vortex translating at 1.0 m/s ...... 91 4-13 Histogram and estimated PDF of the minimum internal pressure coefficient for the building model of Case 3 (open front door) at   0 in (a) the single-celled vortex translating at 1.0 m/s and (b) the two-celled vortex translating at 1.0 m/s ...... 92 4-14 (a) Example time history of the external pressure coefficient, (b) Time history of the simulated internal pressure coefficient for the model with internal volume augmentation, and (c) Time history of the simulated internal pressure coefficient for the model without internal volume augmentation ...... 94 4-15 (a) Time history of the fluctuations of the internal pressure coefficient for the model with internal volume augmentation, (b) Time history of the fluctuations of the internal pressure coefficient for the model without internal volume augmentation ...... 94 4-16 (a) Comparison between the PSD of the external and the simulated internal pressure coefficients, and (b) Comparison between the PSD of the measured and the simulated internal pressure coefficients ...... 95

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4-17 Example Time history of the internal pressure coefficient for (a) Case 2 (the building model with the door opening but without volume augmentation) at   0 , and (b) Case 3 (the building model with the door opening and volume augmentation) at   0 ...... 97

 4-18 (a) Time-varying mean of Cpi for Case 2 and Case 3 at   0 , and (b)  Time-varying STD of Cpi for Case 2 and Case 3 at   0 (Case 2: the building model with the door opening but without volume augmentation; Case 3: the building model with the door opening and volume augmentation)` ...... 97 4-19 (a) Time-varying mean, and (b) Time-varying STD of the internal pressure coefficient for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at VS2 (0.5 m/) and VS3 (1.0 m/s) ...... 98 4-20 (a) Time-varying mean, and (b) Time-varying STD of the internal pressure coefficient for the building model of Case 3 (open front door) at   0 in the two-celled vortex translating at VD2 (0.5 m/s) and VD3 (0.5 m/s) ...... 99 4-21 Directions of the positive lateral and uplift force components when   0 .... 100

4-22 Time-varying mean of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the two-celled vortex translating at VD2 (0.5 m/s) and VD3 (1.0 m/s) ...... 100

4-23 Time-varying STD of (a) CFx , (b) CFy , and (c) .CFz . for the building model of Case 3 (open front door) at   0 in the two-celled vortex translating at VD2 (0.5 m/s) and VD3 (1.0 m/s) ...... 101

4-24 Time-varying mean of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at VS2 (0.5 m/s) and VS3 (1.0 m/s) ...... 103

4-25 Time-varying STD of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at VS2 (0.5 m/s) and VS3 (1.0 m/s) ...... 104 4-26 Maximum value of the force coefficients for the building model of Case 3 (open front door) at different building orientation angles in the single-celled vortex translating at VS2 and VS3, and in the two-celled vortex translating at VD2 and VD3 (VS2: 0.5 m/s; VS3: 1.0 m/s; VD2: 0.5 m/s; VD3: 1.0 m/s) ...... 105 4-27 Minimum value of the force coefficients for the building model of Case 3 (open front door) at different building orientation angles in the single-celled vortex translating at VS2 and VS3, and in the two-celled vortex translating at VD2 and VD3 (VS2: 0.5 m/s; VS3: 1.0 m/s; VD2: 0.5 m/s; VD3: 1.0 m/s) ...... 106

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4-28 (a) Time-varying STD of the internal pressure coefficient of the building model in the single-celled vortex translating at VS2 and VS3, and (b) Time- varying STD of the internal pressure coefficient of the building model in the two-celled vortex translating at VD2 and VD3 for Case 5 (open front door and open back window) at   0 (VS2: 0.5 m/s; VS3: 1.0 m/s; VD2: 0.5 m/s; VD3: 1.0 m/s) ...... 107

4-29 Time-varying STD of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 5 (open front door and open back window) at   0 in the single- celled vortex translating at VS2 (0.5 m/s) and VS3 (1.0 m/s) ...... 108

4-30 Time-varying STD of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 5 (open front door and open back window) at   0 in the two- celled vortex translating at VD2 (0.5 m/s) and VD3 (1.0 m/s) ...... 109 4-31 Maximum value of the force coefficients for the building model of Case 5 (open front door and open back window) at different building orientation angles in the single-celled vortex translating at VS2 and VS3, and in the two-celled vortex translating at VD2 and VD3 (VS2: 0.5 m/s; VS3: 1.0 m/s; VD2: 0.5 m/s; VD3: 1.0 m/s) ...... 110 4-32 Minimum value of the force coefficients for the building model of Case 5 (open front door and open back window) at different building orientation angles in the single-celled vortex translating at VS2 and VS3, and in the two-celled vortex translating at VD2 and VD3 (VS2: 0.5 m/s; VS3: 1.0 m/s; VD2: 0.5 m/s; VD3: 1.0 m/s) ...... 111 4-33 PSD functions of the external and internal pressure coefficients for the building model of Case 3 (open front door) mounted statically at the center of the single-celled vortex ...... 112 4-34 EPSD functions of (a) the external pressure coefficient, and (b) the internal pressure coefficient for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at 0.5 m/s ...... 113 4-35 Pseudo PSD functions of the external and internal pressure coefficients for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at 0.5 m/s ...... 113

4-36 Time-varying skewness of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at 0.5 m/s ...... 115

4-37 Time-varying kurtosis of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at 0.5 m/s ...... 116

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4-38 Time-varying skewness of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the two-celled vortex translating at 0.5 m/s ...... 117

4-39 Time-varying kurtosis of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the two-celled vortex translating at 0.5 m/s ...... 118 4-40 Kurtosis of the force coefficients for the building model of Case 3 (open front door) at   0 mounted statically in (a) the single-celled vortex, and (b) the two-celled vortex ...... 119

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CHAPTER 1

INTRODUCTION

1.1. Background, Methodology and Research Objectives

A tornado is a violently rotating column of air that extends from the base of a thunderstorm to the ground. This type of wind differs from boundary-layer-type winds in synoptic weather systems primarily in that tornadic winds have a rotational component of high speed that produces significant static pressure deficit inside the storm while boundary-layer-type winds can be assumed to travel along straight lines without causing substantial change to the static pressure. Due to the damages caused by the extreme wind speeds and in some cases the static pressure deficits, tornadoes have long been regarded as one of the most devastating natural hazards.

Though tornadoes occur in many parts of the world, they occur the most frequently in the United States (US). According to the Storm Events Database of the National Oceanic and Atmospheric Administration (NOAA), about 800 tornadoes are reported in the US annually, and tornado hazards are responsible for nearly 900 fatalities and more than $19B of property damage in the US in the past decade alone. The deadest tornado in the US history was the Tri-State Tornado on March 18, 1925 which inflicted 695 fatalities. The costliest tornado in recent history is the Joplin Tornado of May 22, 2011, which caused 158 fatalities and nearly $2.8 billion in damage. To reduce the loss of life and property, there is a need to advance the understanding of tornadic loading on structures.

The majority of tornado-caused damages are often to buildings. However, most buildings are not designed for tornadoes, because an adequate understanding of tornadic loading on structures is still lacking. The situation is mainly a result of the challenge in measuring the wind velocity and static pressure fields in tornadoes at adequate spatial and temporal resolutions, as well as the difficulty in directly measuring tornadic loading on full-scale structures. Indeed, to this date, the estimation of tornado wind speeds and tornado loading has primarily been based on forensic investigations and engineering

Texas Tech University, Liang Wu, August 2019 judgements. For instance, the Fujita Scale and the subsequent Enhanced Fujita Scale for the rating of tornado intensity are based on the damages caused by the wind storms (Edwards et al., 2013). However, with the progress of field-site measurements of full- scale tornadoes and laboratory as well as numerical simulations of tornado-like vortices, a more accurate quantification of tornadic loading on buildings has become more achievable.

It is not until in recent decades that measurements of wind speeds and ground pressures measured in full-scale tornados have become available (e.g., Lee and Wurman, 2005; Wurman and Alexander, 2005; Karstens et al., 2010; Tanamachi et al., 2013). Though the full-scale datasets do not contain any direct measurement of wind loading on structures, the measurements of wind speeds and surface pressures can serve as useful reference wind flow fields for laboratory and numerical simulations of tornado- like flows in which tornadic loading on structures can be evaluated. Recently, numerical simulations of tornadic winds based on computational fluid dynamics have made considerable progress (e.g., Lewellen et al., 1997; Ishihara et al., 2011; Natarajan and Hangan, 2012; Yuan et al., 2019). However, faithful simulation of the flow itself, especially the turbulence in tornadic winds, remains a challenge. In addition, in most circumstances, the characteristics of the resulting wind loading from numerical simulations need to be validated using either full-scale or laboratory data. As a result, physical laboratory simulation are chosen in this study as the main approach for researching tornadic loadings on low-rise buildings.

Laboratory investigation of tornadic loading on structures utilizes tornado simulators that are designed for the simulation of tornado-like flows. Ying and Chang (1970) developed the first tornado simulator at the Catholic University of America. They showed that this facility was able to generate vortices with the flow fields similar to those of full-scale tornadoes over a smooth flat plane. Since then, much progress has been made in the design of tornado simulators (e.g., Church et al., 1977; Haan et al., 2008; Mishra et al., 2008a; Refan and Hangan, 2018). The study of tornadic loading on low-rise buildings have benefitted from this progress, and made steady advancements in the past two decades (e.g., Haan et al., 2010; Sabareesh et al., 2011; Case et al., 2014;

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Wang et al., 2016; Razavi and Sarkar, 2018). For instance, Haan et al. (2008) developed a sophisticated laboratory tornado simulator at Iowa State University (ISU) in 2004 to facilitate the simulation of tornado-like vortices for the purpose of investigating tornado-induced loads on civil engineering structures. This facility was used to study the transient external pressures and the resultant wind loads on a fully-enclosed low-rise building model exposed to a number of tornado-like vortices with various translating speeds (Haan et al., 2010). The peak wind loads measured in this study were compared with those prescribed by ASCE 7-05 (2005) and it was suggested that tornado-like vortices can generate loads that are greater than those prescribed by the standard for boundary-layer-type winds over open terrain. The outcomes of this study also showed that the magnitude of the lateral force, i.e., the horizontal force component that is perpendicular to the tornado’s translation direction, decreases with increasing translation speed. Case et al. (2014) tested a number of fully-enclosed building models of various building geometries in the ISU simulator, and showed that the peak loads induced by tornadic winds vary as a function of eave height, roof pitch, aspect ratio, plan area, and other differences in geometry such as the addition of a garage, roof overhang and soffit. A more recent study by Razavi and Sarkar (2018) suggested that when subjected to a tornado of a lower swirl ratio, the peak uplift force acting on the roof of a fully-enclosed building increases with increasing tornado translation speed when the building is located on the tornado mean path, whereas the loading decreases with increasing translation speed at locations other than along the tornado mean path. It was also suggested that when subjected to a tornado of a higher swirl ratio, the effect of tornado translation speed on the peak uplift force is insignificant regardless of the location of the building relative to the tornado mean path.

In addition to the laboratory investigations of the loading on fully-enclosed buildings by tornadic winds, a number of studies have also investigated the internal pressure of buildings exposed to tornadic winds. Because the speed and direction of the wind as well as the static pressure drop in tornadoes change rapidly with the change of location inside the core of tornadoes, the patterns of loading on buildings exposed to tornadic winds are substantially different from those in regular boundary-layer-type winds (Letchford et al., 2015). With the presence of a dominant opening on a building

Texas Tech University, Liang Wu, August 2019 envelope, such as a broken window or door, the internal pressure will change rapidly in response to ambient pressure variations. This varying internal pressure can be a significant component of the total loading on the building, and must be adequately understood to enable an effective evaluation of tornadic loading on structures. Due to the constraint of research facilities, many previous studies on the internal pressure of buildings in tornadic flows were conducted in stationary vortices. For instance, Sabareesh et al. (2013a) studied the mean and peak internal pressures of a flat-roofed building model exposed to a stationary tornado-like vortex using the tornado simulator at Tokyo Polytechnic University. Subsequently, Sabareesh et al. (2013b) investigated the effect of ground roughness on the internal pressure in the same building model that was also exposed to stationary tornado-like flow. In addition to the limitation of the simulated vortices being stationary, the excessively small length scale (i.e., 1:1000) used in the experiment also limited the impact that these studies can generate. In a more recent study, Letchford et al. (2015) measured the external and internal pressures on a flat-roofed building model with various porosities and dominant openings in tornadic flow simulated in a tornado simulator at Texas Tech University. However, this series of experiments were also conducted in a stationary vortex, which cannot reveal the effect of tornado translation on the tornadic loading. In a study of tornadic loading by translating tornadoes, Thampi et al. (2011) investigated the interaction between a gable- roofed building model and a translating tornado-like vortex simulated using the ISU tornado simulator. A detailed finite element analysis in this study showed that the dynamically varying internal pressure can significantly change the sequence of failure and failure mode of the building.

Furthermore, previous studies (e.g., Haan et al., 2010; Thampi et al., 2011; Feng and Chen, 2018) have also shown that tornadic wind loading on low-rise buildings is highly nonstationary due to the translation of tornadoes. In addition, Tang et al. (2018a) revealed that the turbulence in tornadic winds and the corresponding fluctuation of the static pressure deficit can be highly non-Gaussian. This indicates that tornadic wind loading on building may also be highly non-Gaussian.

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While these previous studies have contributed to the understanding of tornadic loading on low-rise buildings, many gaps still exist in the knowledgebase of tornadic loading on buildings. The goal of the research presented in the dissertation is to fill two of the knowledge gaps:

1) The characteristics of internal pressure in low-rise buildings exposed to tornadic flows, and the effect of the internal pressure on the overall tornadic loading on this type of building. 2) The non-stationary fluctuation of loading on low-rise buildings by translating tornadoes.

To achieve this goal, experiments are conducted in a large-scale tornado simulator to evaluate the tornadic loading on a building model representing the full-scale Wind Engineering Research Field Laboratory (WERFL) low-rise building at Texas Tech University. The model is tested in two types of tornado-like vortex, one that is single- celled in structure and the other that is two-celled in structure, with and without strategically placed openings to enable a comprehensive investigation of the tornadic loading in various scenarios of building openings. During the experiments, the models are translated at two different speeds relative to the simulated vortices to enable an assessment of the effect of tornado translation on the tornadic loading. The location and orientation of the building model relative to the tornado mean path are also varied to investigate the effect of these factors on the loading. In addition, to investigate whether volume scaling is necessary for experimental study of internal pressure, models with and without additional sealed volume chamber are also tested.

To provide a context for the investigation of tornadic loading on low-rise buildings, a model of the WERFL building with the same opening configurations are also tested in a boundary layer wind tunnel. This enables a direct comparison between the major characteristics of the loading on low-rise buildings, such as the probabilistic characteristics of the force, and the relationship between the external and internal pressures, by tornadic and boundary-layer-type winds. Since tornadic wind loading on low-rise buildings is nonstationary due to the translation of tornadoes, conventional methods for characterization, modeling, and simulation of stationary wind loads on

Texas Tech University, Liang Wu, August 2019 buildings subjected to boundary-layer-type winds are no longer applicable to the study of tornadic wind loads. Therefore, a data interpretation technique developed on the basis of the framework developed by Xiao and Zuo (2015), which has been used to characterize, model, and simulate nonstationary processes, is utilized to process and interpret the data from the experiments conducted in the tornado simulator.

1.2. Organization of the Dissertation

The content of the dissertation is organized as follows:

Chapter 1 introduces the background and motivation for this research. The goal and methodologies of the research are also summarized.

Chapter 2 presents a study of tornado-like vortices simulated in the tornado simulator. The focus is placed on the key mean and fluctuating characteristics of the flow velocity and surface pressure deficit, as well as the dependence of these characteristics on the major parameters that control the structure of the simulated vortices.

Chapter 3 presents the experimental investigation of the loadings on the WERFL building model by boundary-layer-type wind. The experimental configurations and the procedures of the wind tunnel tests are described. Representative statistics such as the mean, standard deviation, and peak values of the pressure and force coefficients are estimated, and the spectra of the external and internal pressure coefficients are analyzed.

Chapter 4 presents the study of tornadic loadings on the WERFL building model. The configurations and the procedures of the experiments in the tornado simulator are also described. The effects of volume scaling on the internal pressure are first presented, and the effects of the other factors, including the location and orientation of the models and the translation speed of the model relative to the tornado-like vortices, are interpreted. Based on the experimental results in the tornado simulator and in the boundary layer wind tunnel, the characteristics of the wind loading induced by tornadic and boundary-layer-type winds are also compared.

Chapter 5 gives the conclusions of this study and the suggestions for future work.

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CHAPTER 2

CHARACTERISTICS OF TORNADO-LIKE VORTICES SIMULATED IN THE VORTECH SIMULATOR

2.1. Introduction

Tornadoes are considered one of the most violent types of windstorm in nature. Due to the difficulty in precisely predicting tornadoes and the challenges in measuring tornadoes in the field at high spatial and temporal resolutions, many numerical and physical simulations of tornadoes have been conducted to supplement the studies of full- scale tornadoes. Physical simulation of tornado-like flow in laboratories, in particular, has seen significant advancements since Ying and Chang (1970) built the first tornado simulator at the Catholic University of America. Since then, a variety of tornado simulators with different vortex generating mechanism have been built (e.g., Church et al., 1977; Haan et al., 2008; Mishra et al., 2008a; Sabareesh et al., 2013a; Wang et al., 2016; Refan and Hangan, 2018). Among them, the so-called Ward-type simulator, which is named after its conceptualizer (Ward, 1972), has enjoyed wide popularity (e.g., Mishra et al., 2008b; Sabareesh et al., 2013a). This type of simulator utilizes a fan or multiple fans at the top to generate an updraft, rotating screens or turning vanes at the periphery of the cylindrical testing chamber at the bottom to control the angular momentum of the inflow, and a baffle between the convection region above the updraft hole and the plenum below the exhaust to eliminate the influence of the vorticity created by the fan(s) on the flow below the baffle. It has been shown by a number of studies that the Ward-type simulator is capable of simulating vortices that resemble full-scale tornadoes in some major characteristics, such as the mean structure of the pressure deficit created by tornadic flows (Tang et al., 2018a).

The simulation of tornado-like vortices is governed by a number of parameters. Lewellen (1962) and Davies-Jones (1973) showed that the swirl ratio, the radial Reynolds number, and the aspect ratio are the three parameters that govern the dynamics and geometry of three-dimensional tornadic flows. Among the three, the swirl ratio, which is essentially a measure of the relative amount of angular to radial momentum in

Texas Tech University, Liang Wu, August 2019 the vortex, has been identified to be the most critical parameter that controls the structure of simulated vortices (e.g., Davies-Jones, 1973; Church et al., 1979). It has been observed that a single-celled vortex forms at a small swirl ratio and that with increasing swirl ratio, the core of the vortex transitions from a laminar state to a turbulent state. With a further increase of the swirl ratio, the flow transitions to a two- celled vortex with downflow in the region surrounding the axis of the simulator and ultimately to multiple vortices (Tang et al., 2018a). The aspect ratio, which is defined as the ratio of the vertical dimension of the inflow layer to the radial dimension of the convergence region (Church et al., 1979), was also found to have effects on the velocity and pressure fields of generated vortices. For example, the aspect ratio can affect the geometry of simulated vortices (Church et al., 1979; Tang et al., 2018b). The radial Reynolds number essentially represents the ratio of inertial forces to viscous forces within a vortex simulated in tornado simulators. Previous studies have shown that laboratory simulation of tornado-like vortices is independent of the radial Reynolds number, provided that it is sufficiently large (e.g., Church et al., 1979; Refan and Hangan, 2018; Tang et al., 2018b).

To enable an investigation of the tornadic wind loading on low-rise buildings by various types of tornadic flows, the tornado simulator is configured to achieve different controlling parameter values and the flow and pressure fields of each resulting vortex are measured. This chapter presents the experimental results of the simulations of tornado-like vortices in this tornado simulator and an interpretation of the measurements of the velocity and pressure fields of the simulated vortices. The focus is placed on the key mean and fluctuating characteristics of the flow and surface pressure deficit, as well as the dependence of these characteristics on the swirl ratio and the radial Reynolds number. Some of the findings presented in the paper by Tang et al. (2018a) are repeated here to provide a context for the subsequent study of tornadic loading on low-rise buildings. All the measurements presented in the chapter are for nominally stationary vortices. Experiments involving translating vortices will be conducted only when building models are tested in the simulator.

2.2. Experimental Facility

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2.2.1. Tornado Simulator

The experiments to investigate tornadic loading on low-rise buildings are conducted in VorTECH which is a large-scale Ward-type tornado simulator at Texas Tech University. As seen in the schematic drawing in Figure 2-1, VorTECH has a chamber of 10.2 m in diameter, an updraft hole of octagon cross-section that is 4 m in diameter, 64 turning vanes in the form of symmetric airfoils at the periphery of the chamber, 8 fans at the top, and a honeycomb that functions as the baffle in a Ward-type simulator. Compared with some other simulators around the world (e.g., Haan et al., 2010; Sabareesh et al., 2011; Wang et al., 2016), the simulator has two attractive features: the chamber of large diameter, which enables testing of building models at reasonable scales, and the capability of part of the floor to translate at a relatively high speed, which enables the simulator to accommodate tests with ratios of mean tangential velocity to mean tornado translation velocity that are close to those of some full-scale tornadoes. In addition, VorTECH is capable of simulating tornadic flows that are similar to full- scale tornadoes in some key characteristics. For example, it has been shown that this simulator can generate tornado-like vortices which produce mean surface pressure deficits that match those measured in a number of full-scale tornadoes (Tang et al., 2018a).

Figure 2-1 A schematic illustration of VorTECH (Tang et al., 2018a) Several components of the simulator can be adjusted to enable the generation of flows of desired structures. The orientations of the turning vanes can be varied to control the angular momentum of the inflow, the speed of the fans can be varied to control the

Texas Tech University, Liang Wu, August 2019 amount of updraft, and the heights of the chamber and the turning vanes can be adjusted between 1 m and 2 m to control the internal aspect ratio of the apparatus. Figure 2-2 shows a tornado-like vortex generated in VorTECH.

Figure 2-2 A picture of a simulated tornado-like vortex 2.2.2. Velocity and Pressure Measurements

The core of a tornado-like vortex is formed by flow with high amounts of swirl, where a predominant direction of the flow does not exist. This poses a challenge for the measurement of the flow field, as most sensors for wind velocity measurements are designed to measure non-swirling flows. To overcome this challenge, a Cobra probe (Turbulent Flow Instrumentation Pty Ltd) and an Omniprobe (Aeroprobe Corporation) are used in this study for wind velocity measurements. The Cobra probe has a response frequency up to 2000 Hz, but it can only accept flows within a ±45° cone. By contrast, the Omniprobe can accept wind angles as large as ±150°, but it cannot accurately measure high frequency turbulence in the flow. In the experiments, the Cobra probe was sampled by a dedicated data acquisition system, and the Omniprobe was sampled by a Scanivalve pressure measurement system. The Cobra probe was used whenever at least 98% percent of the flow was reported by the manufacturer-supplied software to be within the ±45° cone; otherwise the Omniprobe was used.

To measure the pressure on the floor of the simulator, a total of 195 pressure taps were evenly placed along a radial line on the simulator floor at an interval of 0.0191 m. The pressures at these taps (henceforth referred to simply as surface pressures) were measured by the same Scanivalve system that were used to sample the Omniprobe.

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The barometric pressure in a static bottle in the control room beneath the tornado simulator was chosen as the reference pressure for both the velocity and pressure measurements. The static bottle, in particular, was used to attenuate the fluctuations of the barometric pressure so that a stable reference pressure is ensured.

The Cobra probe was sampled at 625 Hz, and the Scanivalve pressure scanners for the Omniprobe and pressure taps sampled at 300 Hz. The duration of each individual velocity and pressure measurement was 2 minutes. For each experimental configuration, velocity measurements were conducted only once, but measurements of the surface pressure were repeated 10 times to provide ensembles for the estimation of the statistics. 2.3. Estimation of Controlling Parameters

The definitions of the three controlling parameters for tornado simulations (Church et al., 1979), in the order of the swirl ratio, the radial Reynolds number and the aspect ratio, are

Sr 0 /(2 Qh ) (2.1)

Rer  Q / (2 ) (2.2)

ahr / 0 (2.3) where h and r0 are the depth and radius of the convergence region of the flow, which for VorTECH are the height of the turning vanes and the radius of the updraft hole, respectively, Q is the volume flow rate per unit axial length, Γ is the circulation, and v is the kinematic viscosity of air.

Although the calculation of the aspect ratio is straightforward, the manner in which the swirl ratio and the Radial Reynolds number was estimated has varied in previous studies, depending on how the volume flow rate per unit axial length and the circulation were measured/estimated. This study adopts the approach used by Tang et al. (2018a), which estimated the volume flow rate and the circulation based on the velocities of the flow along an axial (i.e., vertical) line at the edge of the convergence region (i.e., a vertical line originated from the edge of the updraft hole). Figure 2-3 shows example profiles of the mean tangential and radial (i.e., along a radial line of the chamber)

Texas Tech University, Liang Wu, August 2019 velocity along a vertical line at the edge of the convergence region measured by the Cobra probe. h / z

Figure 2-3 Example axial profiles of the mean tangential and radial velocity at the edge of the convergence zone (Tang et al., 2018a) With these velocities and the assumption of axisymmetric flow, the volume flow rate per unit axial length and the circulation are then estimated as

N 2 rV0,rn h n Q  n1 (2.4) h

N 2 rVh0, nn  n1 (2.5) h

th in which Vrn, and V ,n are the mean radial and tangential velocities at the n point of measurement along the vertical line, hn is half the distance between the two measurement points surrounding this point, and N is the total number of measurement points.

2.4. Experimental Configurations

A number of vortices with different swirl ratios were generated in VorTECH by varying the angles of the turning vanes between 10° and 55° relative to the radial lines. The heights of the turning vanes were fixed at 2 m, which gives a unit aspect ratio. At a few selected turning vane angles, the speeds of the fans were varied to investigate the

Texas Tech University, Liang Wu, August 2019 effects of the radial Reynolds number on the simulated vortices. Because a major objective of the research is to provide a context for the following studies of tornadic loading on low-rise buildings, the velocity measurements focused on the flow over the lowest region of the chamber (i.e., up to 0.5 m above the simulator floor). In addition, it is assumed that the mean and turbulent characteristics of the vortices simulated in this study are axisymmetric, so the flow velocity was only measured within a vertical plane through the axis of the simulator. The vertical distribution of the velocity measurement grid was the same for all the experimental configurations, which varied from 0.005 m over the lower elevations to 0.05 m over the higher elevations, with finer resolution at bottom to capture the near-surface flow variations. The exact vertical resolutions of the velocity measurements are listed in Table 2-1. For the horizontal distribution of the velocity measurement grid, the number and locations of the measurement points along the radial direction were varied to ensure an adequate spatial range and resolution of measurements, so that the maximum mean tangential velocity component at each measurement height could be approximately captured, and the characteristics of the flow both inside and outside the radial positions of the maximum mean tangential velocity could be evaluated (Tang et al., 2018a). An example flow velocity measurement grid is shown in Figure 2-4, in which z is the height above the floor and r is the horizontal distance from the axis of the chamber.

Table 2-1 Vertical resolution of the velocity measurements (Tang et al., 2018a)

Elevation above floor (m) 0.01-0.05 0.05-0.1 0.1-0.2 0.2-0.26 0.26-0.3 0.3-0.5 Measurement resolution (m) 0.005 0.01 0.02 0.03 0.04 0.05

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Figure 2-4 An example flow velocity measurement grid (Tang et al., 2018a) 2.5. Characteristics of Simulated Flow and the Resultant Surface Pressure Deficit

In this section, the mean and turbulent characteristics of the flow velocity and the surface pressure deficit of a few representative vortices simulated in VorTECH are presented. Through the characterization of the flow and pressure field, a few implications on the tornadic loading on low-rise buildings are inferred, which provides guidance for the subsequent wind load experiments of low-rise buildings exposed to tornadic flows.

The definitions of velocity and position and the corresponding sign conventions used in the study follow those specified by Tang et al. (2018a). To facilitate the descriptions to follow, some of the definitions and sign conventions are introduced herein. The axial and radial components of the flow velocity are deemed positive if they point upward and toward the axis of the simulator, respectively. Assuming that the mean flow characteristics are axisymmetric, the local maximum mean tangential velocity,

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V z max , and the global maximum mean tangential velocity, V max , are defined as the maximum mean tangential velocity at a height of z above the floor and the maximum of the local maximum mean tangential velocity over the heights of measurement, respectively (i.e.,VVmax max(z max ) ). Correspondingly, the local core radius, rcz , and the representative core radius, rc , of the simulated vortex are defined as the radial distances between the axis of the simulator and the points of the local maximum mean tangential velocity at height z and the global maximum mean tangential velocity, respectively. The height at which the global maximum mean tangential velocity is achieved is designated zc .

2.5.1. Effect of Swirl Ratio

The effect of the swirl ratio on the simulated vortices is presented in the following. To separate the influence of the radial Reynolds number and the aspect ratio, the heights of turning vanes are fixed at 2 m (corresponding to a unit aspect ratio), and the fans are running at the full speed so that the radial Reynolds number of simulated vortices are between 3.11 105 and 410 5 , over which the mean characteristics of the simulated flow are essentially independent of the radial Reynolds number (Church et al., 1979).

2.5.1.1. Wind Flow Field

The mean flow fields of four representative vortices generated at swirl ratios of 0.17, 0.22, 0.36, and 0.84 are shown in Figure 2-5. The arrows in the graphs represent the resultants of the mean radial and axial components of the flow; the background colors represent the mean tangential velocities resulted from linear interpolations of the measured mean tangential velocities. It can be observed from Figure 2-5 that the swirl ratio critically affects the structure of the mean radial and axial components of the flow. Mostly notably, at swirl ratios of 0.17 and 0.22, the mean axial velocity component of the flow is positive at every point of measurement inside the cores of the vortices and, by contrast, apparent downdraft developed inside the cores of the two vortices simulated at swirl ratios of 0.36 and 0.84, respectively. As suggested by previous studies (e.g., Church et al., 1979; Davies-Jones et al., 2001), this reflects the evolvement of the flow from a single-celled vortex at lower swirl ratios to a two-celled vortex at higher swirl

Texas Tech University, Liang Wu, August 2019 ratios after the vortex breakdown stagnation point reaches the floor of the simulator at a critical swirl ratio. So it is deduced from Figure 2-5 that for the vortices simulated in VorTECH, the critical swirl ratio that separates the single-celled and two-celled vortex regimes is between 0.22 and 0.36.

Figure 2-5 Mean flow fields of vortices simulated at (a) S=0.17, a=1.0, (b) S=0.22, a=1.0, (c) S=0.36, a=1.0, and (d) S=0.84, a=1.0 (Tang et al., 2018a) Figure 2-6 plots the axial profiles of local core radius for the four vortices. As seen in Figure 2-6, at each height the vortex simulated at a larger swirl ratio has a larger local core radius than the vortices simulated at smaller swirl ratios. So it is shown that the size of the vortex core, which is defined as the volume enclosed by the points of local core radius at every elevation, increases with the swirl ratio.

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0.25 S = 0.17 0.2 S = 0.22 S = 0.36 0.15 S = 0.84

0.1

0.05

0 0 0.1 0.2 0.3 0.4 r /r cz 0

Figure 2-6 Axial profiles of local core radius (a=1.0) (Tang et al., 2018a) Figure 2-7 shows the axial profiles of the mean tangential velocity component for the four vortices at five representative locations: one at the position of the corresponding core radius rc , two at positions inside the core ( rr c ), and two outside the core ( rr c ). At all four swirl ratios, the axial profiles of the mean tangential velocity at the positions far outside the corresponding core radius (e.g., rr 2.6 c ) resemble the mean velocity profile of a straight-line boundary layer flow over a smooth terrain, while at the positions around or inside the core, the axial profiles of the mean tangential velocity become much more complex. For instance, inside the core the mean tangential velocity component increases with height from the floor until reaching a maximum value, which may partly arise from the shear in the boundary layer near the floor, and then decreases until reaching a near-constant value at greater heights. The effect of the swirl ratio is manifested in the rate at which the mean tangential velocity component changes from the edge of the core to the inner part of the core. As seen in Figure 2-7, at a given height, the differences between the mean tangential velocity component at approximately rrc  0.8 and rrc 1.0 are relatively small for the two single-celled vortices (S = 0.17 and S = 0.22), but for the two-celled vortices (S = 0.36 and S = 0.84) the differences between the mean tangential velocity component at similar relative locations are much larger. Figure 2-7 also shows that except at locations far away from the vortex center

(i.e.,rr 2.6 c ), the mean tangential velocity reaches its maximum value at very low height (below 0.1 h). This can be one of the reasons why low-rise buildings are particularly vulnerable to tornado hazards.

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h / z

Figure 2-7 Axial profiles of mean tangential velocity simulated at (a) S=0.17, a=1.0, (b) S=0.22, a=1.0, (c) S=0.36, a=1.0, and (d) S=0.84, a=1.0 (Tang et al., 2018a) To further investigate the influence of the swirl ratio on the mean structure of the simulated vortex, the profiles of the mean tangential velocity components at representative heights and radial positions are examined. Figure 2-8 shows the radial profiles of the normalized mean tangential velocity component at the height of the maximum mean tangential velocity, zc , and those at two heights below and two heights above zc for the above four vortices. Also plotted in the graphs are the radial profiles of the mean tangential velocity component prescribed by the modified Rankine combined-vortex model with a decay constant of 0.7, the Burgers-Rott model for single- celled vortices ( S  0.17 and S  0.22 ), and the Sullivan model for two-celled vortices ( S  0.36 and S  0.84 ). The equations of the mean tangential velocity component prescribed by these models, in the order of the modified Rankine combined-vortex model (Wurman et al., 2007), the Burgers-Rott model (Davies-Jones and Wood, 2006), and the Sullivan model (Wood and Brown, 2011), are

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()rrcz V zmax r r cz V   0.7 (2.6) ()rrcz V zmax rr cz

V1.4 V rr12 1 exp 1.2564 rr  (2.7) zczmax    cz

0.435 V V rr2.40.3 0.7 rr 7.89 (2.8) zczmax  cz

(a) (b) Rankine z/z = 2.00 Rankine z/z = 2.00 1 c 1 c Burgers-Rott z/z = 1.50 Burgers-Rott z/z = 1.56 c c 0.8 z/z = 1.00 0.8 z/z = 1.00 c c

z/z = 0.50 max z/z = 0.56 0.6 c z 0.6 c

z/z = 0.25 V c / z/z = 0.22 z c 0.4 0.4 V

0.2 0.2

0 0 012345678 012345678 r / r r / r cz cz (c) Rankine z/z = 2.00 1 c Sullivan z/z = 1.43 c 0.8 z/z = 1.00 c

max z/z = 0.57 max z 0.6 c z V V

/ z/z = 0.29 /

z c z 0.4 V V

0.2

0 012345678 r / r cz Figure 2-8 Radial profiles of mean tangential velocity simulated at (a) S=0.17, a=1.0, (b) S=0.22, a=1.0, (c) S=0.36, a=1.0, and (d) S=0.84, a=1.0 (Tang et al., 2018a) As seen in Figure 2-8, at all the heights considered, the radial profiles of the mean tangential velocity component of the single-celled vortices agree well with that prescribed by the Burgers–Rott model, and the corresponding profiles of the two-celled vortices agree well with that prescribed by the Sullivan model. However, the profiles of the mean tangential velocity component do not closely follow that prescribed by the Rankine combined-vortex model, regardless of single-celled or two-celled vortices. The different performances of the three models result from the inherent limitation of the

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Rankine combined-vortex model that neglects the radial and axial velocity components, while the Burgers–Rott and Sullivan models consider all three (i.e., tangential, radial and axial) velocity components, and thereby more closely represent the physically simulated vortices. In particular, the Rankine combined-vortex model treats the flow inside the core of the vortex as a rotating rigid body regardless of its fluid properties, so this model cannot represent the curved profile of the mean tangential velocity component of the flow inside the vortex core. Another observation from Figure 2-8 is that the mean tangential velocity changes very fast over a short distance in regions near the vortex center (i.e., rr 2 c ). Considering the translation of tornadoes, the wind loading on the buildings concerned should be a highly nonstationary process.

Figure 2-9 shows the contour plots of the turbulence intensity of the tangential velocity component ( I   V , where  is the standard deviation of the tangential Vv   v velocity component) over various regions of the four vortices based on measurements by the Cobra probe. As mentioned early, the Cobra probe cannot measure flow with directions beyond the ±45° cone around its head axis and the Omniprobe is incapable of capturing high-frequency flow fluctuations. Since the flow inside the core is very turbulent and unsteady, only the turbulence intensity in regions outside the core is plotted in Figure 2-9. It can be observed that the turbulence intensity of the tangential velocity component increases inversely with the radial distance in the region close to the core for all the four vortices. However, the turbulence intensity of the tangential velocity exhibits different trends along the height of measurement in this region between the single-celled (S = 0.17 and S = 0.22) and the two-celled vortices (S = 0.17 and S = 0.22). For the single-celled vortices, the change in turbulence intensity along the height in this region is insignificant, while for the two-celled vortices, the turbulence intensities at greater heights are much higher than those at lower heights.

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Figure 2-9 Turbulence intensity of tangential velocity over various regions of the vortices simulated at of (a) S=0.17, a=1.0, (b) S=0.22, a=1.0, (c) S=0.36, a=1.0, and (d) S=0.84, a=1.0 (Tang et al., 2018a) Figure 2-10 and Figure 2-11 show the contour plots of the skewness and kurtosis, respectively, of the tangential velocity component for the same four vortices. As seen in Figure 2-10 and Figure 2-11, in the most turbulent regions near the core of the vortices (see Figure 2-9), the skewness can be significantly non-zero and the kurtosis can be remarkably larger than 3, which implies a highly non-Gaussian wind flow in these regions. For tornadic loading on structures, such probabilistic characteristics of tornadic flow may significantly affect the probability distribution of the peak tornadic loading.

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Figure 2-10 Skewness of the tangential velocity component over various regions of the vortices simulated at of (a) S=0.17, a=1.0, (b) S=0.22, a=1.0, (c) S=0.36, a=1.0, and (d) S=0.84, a=1.0 (Tang et al., 2018a)

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Figure 2-11 Kurtosis of the tangential velocity component over various regions of the vortices simulated at of (a) S=0.17, a=1.0, (b) S=0.22, a=1.0, (c) S=0.36, a=1.0, and (d) S=0.84, a=1.0 (Tang et al., 2018a) 2.5.1.2. Surface Pressure Deficit

Unlike the straight-line wind, winds in tornadoes can cause significant changes to the static pressure of the air, which can contribute to the loading of buildings and other structures. For this reason, studying the characteristics of the surface pressure deficit can help understand the unique features of tornado loading on low-rise buildings. To characterize the effect of the swirl ratio on the surface pressure, additional tornado-like vortices were simulated in the VorTECH at different swirl ratios. The radial Reynolds numbers of these additional experiments are also between 3.11 105 and 410 5 .

Figure 2-12 (a) shows the radial profiles of the mean surface pressure deficit (P) at different swirl ratios tested, with each calculated by averaging the mean values of 10 surface pressure measurements of 2-min duration. The significant level of the mean surface pressure deficit near the center of the simulated vortices and the transition of the

Texas Tech University, Liang Wu, August 2019 mean surface pressure deficit profile due to the corresponding transition of the flow structure is clearly observed in Figure 2-12 (a). Specifically, the magnitude of the mean surface pressure deficit around the center of chamber floor initially increases with increasing swirl ratio, producing a single sharp pressure drop, and then with further increase of the swirl ratio, the profiles flatten and eventually develop into a shape with two valleys. A similar evolution of the mean surface pressure deficit profile with increasing swirl ratio has also been observed in previous studies (e.g., Snow et al., 1980; Refan and Hangan, 2016) and attributed to the transition of the flow from a single-celled vortex to a two-celled vortex with the increase of the swirl ratio. In particular, there is an obvious rise of the pressure deficit near the center of the profiles exhibiting two valleys, which according to Snow et al. (1980) results from the deceleration of the downflow from above the surface in a two-celled vortex. This is consistent with the velocity measurements in this study. As seen in Figure 2-5, at the swirl ratio of 0.84, the downdraft around the axis of the two-celled vortex clearly slows down as it approaches the floor from above.

(a) 0 (b) 0

-50 -50 -100 -100

-150 (Pa) (Pa) P S = 0.11, 0.17, min -150 -200 0.22, 0.28, 0.36, P 0.44, 0.57, 0.69, -250 0.84, 1.04, 1.34, -200 1.80 -300 -250 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 z/r 0 S

Figure 2-12 (a) Profiles of mean surface pressure deficit and (b) the minimum mean pressure deficit against swirl ratio (Tang et al., 2018a) Figure 2-12 (b) shows the minimum value of the mean surface pressure deficit

( Pmin ), which is actually the maximum pressure deficit in magnitude, for each profile plotted in Figure 2-12 (a). As seen in Figure 2-12 (b), Pmin first decreases and then increases with the swirl ratio, with the critical point separating the two trends corresponding to a swirl ratio of 0.22, which signifies the breakdown of the single-celled

Texas Tech University, Liang Wu, August 2019 vortex extending towards the surface. According to previous studies (Church et al., 1979; Refan and Hangan, 2016), the transition of the flow from a single-celled-vortex regime to that of a two-celled vortex soon follows with a further increase of the swirl ratio. This observation based on the surface pressure measurements also agrees with observations of the mean flow fields (Figure 2-5) that the critical transition from single-celled to two- celled occurs between the swirl ratios of 0.22 and 0.36.

Previously, comparisons between the flows of prototype tornadoes and tornado-like vortices simulated in laboratories were very difficult due to the lack of high-quality full- scale velocity measurements near the ground. It was not until recently that the near- ground surface pressure measurements became available, enabling the comparison between the surface pressure deficits of full-scale tornadoes and simulated vortices. Figure 2-13 shows the mean profiles of the surface pressure deficit estimated based on measurements in four real tornadoes (Karstens et al., 2010) and four corresponding profiles of simulated vortices in VorTECH. In Figure 2-13, the pressure and radial coordinate are normalized by using the absolute value of the minimum mean pressure deficit ( Pmin ), and the radius at which half of the maximum absolute mean pressure deficit is reached r , respectively. It can be observed that the resemblances between 0.5Pmin the normalized full-scale and laboratory profiles are remarkable. Especially, according to Karstens et al. (2010), the two Manchester tornadoes are single-celled in structure, the Tipton tornado has a two-celled structure, but it is unclear whether the Webb tornado is of a single-celled or two-celled structure, which is consistent with our observation that for the vortices simulated in VorTECH, the transition between single-celled and two-celled vortices occurs at a swirl ratio between 0.22 and 0.36. In addition, the swirl ratio (S = 0.28) that matches the Webb tornado is close to the critical transition, which is consistent with the ambiguous structure of the Webb tornado. For future wind load experiments in VorTECH, the above comparison has demonstrated that the VorTECH simulator is capable of generating vortices of similar mean pressure fields with the full- scale tornadoes.

Texas Tech University, Liang Wu, August 2019 | | min min P P /| /| P P

| | min min P P /| /| P P

Figure 2-13 Comparison between radial profiles of mean surface pressure deficit of full- scale and simulated tornado vortices (Tang et al., 2018a) The effects of the swirl ratio are reflected not only in the mean characteristics of surface pressure deficit but also in the features of its fluctuating component. Figure 2-14 shows the radial profiles of the first four moments of the surface pressure deficit for the four representative vortices analyzed above. The mean value of the surface pressure

2 deficit is represented by the mean pressure coefficient defined as CPP  (0.5 V max ), where  is the air density, and the second moment is represented by the standard deviation of surface pressure deficit normalized by the maximum value of the absolute pressure deficit. Each value shown in Figure 2-14 represents the ensemble average of the corresponding statistics based on the 10 individual test runs. The dependence of the pressure fluctuations on the swirl ratio is clearly seen in Figure 2-14. For instance, as seen in Figure 2-14 (b), when the vortex transitions from a single-celled structure at small swirl ratios to a two-celled structure at larger swirl ratios, the radial distribution of the variance of the surface pressure deficit transitions from a bell-shaped profile to symmetric bi-modal shaped. In addition, Figure 2-14 (c) and (d) show the profiles of

Texas Tech University, Liang Wu, August 2019 the skewness and kurtosis of the surface pressure fluctuations, which for the two single- celled vortices (i.e., S = 0.17 and S = 0.22) are essentially symmetric and bi-modal in shape, but for the two two-celled vortices (i.e., S = 0.36 and S = 0.84), though also essentially symmetric but are much more complex in shape. It is also observed that the pressure fluctuations over regions far outside the representative core radius of each vortex are approximately Gaussian (i.e., the skewness and the kurtosis are around zero and three, respectively), while the pressure fluctuations over the regions in and immediately surrounding the core radii of all four vortices are highly non-Gaussian. This has significant implications on the nature of tornado loading on low-rise buildings. It is reasonable to infer that for both single-celled and two-celled vortices, the external pressures on buildings located within the tornado damage paths can be highly non- Gaussian processes.

Figure 2-14 Dependence of (a) mean, (b) standard deviation, (c) skewness and (d) kurtosis of surface pressure deficit on swirl ratio (Tang et al., 2018a)

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2.5.2. Effect of Radial Reynolds Number

Previous studies have shown that the simulation of tornado-like vortices does not critically depend on the radial Reynolds number, provided this number is sufficiently large (e.g., Church et al., 1979; Refan and Hangan, 2016). However, these studies were primarily focused on the effects of the radial Reynolds number on the mean components of the flow velocity and surface pressure. In this study, the effects on both the mean and fluctuating characteristics of simulated flow and surface pressure deficit are studied for the radial Reynolds number. To separate the influence of the aspect ratio, the heights of turning vanes are still fixed at 2 m.

Figure 2-15 shows the mean flow fields of two vortices simulated at two different 5 5 radial Reynolds numbers (Rer = 3.91×10 and Rer = 3.02×10 ), but with practically identical swirl ratio of 0.44. It can be observed that the structures of the mean flow fields are very similar, with the only significant difference in the magnitudes of the respective velocity components. The axial profiles of the local core radius and the maximum mean tangential velocity of the two vortices are plotted in Figure 2-16, which shows the flow structures of the two vortices are practically identical. All these combined showed that the radial Reynolds number has negligible effect on the mean flow.

5 Figure 2-15 Mean flow field of vortices simulated at (a) Rer=3.91×10 , S=0.44, and (b) 5 Rer=3.02×10 , S=0.44 (Tang et al., 2018a)

Texas Tech University, Liang Wu, August 2019 h h / / z z

Figure 2-16 Axial profiles of (a) local core radius and (b) maximum mean tangential velocity (Tang et al., 2018a) Figure 2-17 shows the profiles of the normalized mean value and standard deviation, as well as the skewness and kurtosis of the surface pressure deficits at the swirl ratio of 0.44 for three different radial Reynolds numbers. As seen in Figure 2-17, generally the radial Reynolds number does not significantly affect the characteristics of the mean or the fluctuating component of the surface pressure deficit. However, it is indeed observed in Figure 2-17 (b) to (c) that there are some differences between the profiles of the three radial Reynolds numbers in regions far outside the cores. This is probably because in these regions the surface pressure deficit is very small as suggested by Figure 2-17 (a), and thereby the pressure signal from the transducer is very weak and unreliable.

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Figure 2-17 Dependence of (a) mean, (b) standard deviation, (c) skewness, and (d) kurtosis of surface pressure deficit on radial Reynolds number (Tang et al., 2018a) The above characterization has shown that both the mean and fluctuating characteristics of simulated vortices are not significantly affected by the radial Reynolds number, provided this number is sufficiently large. This means that the maximum mean tangential velocity can be adjusted without significantly changing the structure of simulated vortices. Therefore, by variation of the fan speed, a tornado simulator can simulate certain tornado-like vortices with similar maximum mean tangential velocity to translation velocity ratios as those of full-scale tornadoes. Considering that the maximum translation speeds of the tornado simulators are still very low, for instance, 0.61 m/s for the ISU simulator and 2.0 m/s for the bell mouth of the WindEEE dome (Refan and Hangan, 2018), this property is useful for laboratory simulations of tornado- like vortices.

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2.6. Implications from Flow and Surface Pressure Measurements

The observations of the characteristics of the vortices simulated in VorTECH has a number of implications on the study of tornadic loading on structures. The presentation above shows that the simulator can generate a broad range of vortices that resemble full- scale tornadoes in the static pressure deficit created by the tornadic flow. Also, since the major characteristics of the simulated vortex are independent of the Reynolds number over a broad range of this parameter, the simulator can be configured so that the ratio of maximum mean tangential velocity to the translation speed of the generated vortices can match those of many full-scale tornadoes. These makes VorTECH a viable facility for the study of tornadic loading on structures.

The velocity and pressure measurements conducted in the study show that single- celled and two-celled vortex have distinct flow structures and surface pressure fields, so it is expected that the loading induced by the two types of vortices are much different from each other. For this reason, the experiments to study the tornadic loading, which will be described in the following Chapter, are conducted in both single-celled and two- celled vortices. Also, because both the turbulence of the wind in the simulated vortices and the fluctuation of the surface pressure show significant non-Gaussian characteristics over significant regions of the measurements, it is likely that the tornadic loading on the low-rise buildings over those regions is also non-Gaussian. This will be a focus when the characteristics of the tornadic loading is interpreted in the following Chapter.

Another implication from the characterization of the simulated vortices is that both the mean and fluctuating characteristics of the flow velocity and surface pressure deficit vary at different locations relative to the vortex center, implying that the tornadic loading on low-rise buildings change with the locations of the buildings relative to the vortex center. Therefore, in subsequent wind load experiments in VorTECH, building models will be placed at different locations relative to the vortex center, and at each location, building models will be tested for various building orientations. In addition, because of the spatial variation of the velocity and pressure fields, it is expected that the tornadic loading on buildings are non-stationary when the vortex translates relative to the building.

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CHAPTER 3

WIND TUNNEL TESTING OF A LOW-RISE BUILDING MODEL IN BOUNDARY-LAYER-TYPE FLOW

3.1. Introduction

In the past few decades, many studies (e.g., Haan et al., 2010; Thampi et al., 2011; Sabareesh et al., 2013a; Case et al., 2014; Letchford et al., 2015) have been conducted to investigate the wind loading on buildings by tornadoes based on testing building models in tornado simulators. A number of these studies (e.g., Haan et al., 2010; Letchford et al., 2015) compared the net force coefficients resulted from the laboratory studies with those prescribed by design codes (e.g., ASCE 2010) to highlight the differences between the tornadic wind loading and the loading by boundary-layer-type winds. While these studies have contributed to the understanding of tornadic loading on structures, they have not revealed the differences between the two types of wind loading in terms of probabilistic characteristics of the pressures and those of the resultant forces as well as the correlations between the internal and external pressures. To address these knowledge gaps, this study directly compares the tornadic loading on a low-rise building model with the loading on an equivalent building model by winds simulated in a boundary layer wind tunnel instead of the loading prescribed by the design codes.

As is now well recognized, for buildings exposed to boundary-layer-type wind flow, the internal pressures can significantly contribute to the overall wind loading as a result of Helmholtz resonance (e.g., Holmes, 1979) when there is a dominant opening present in the building envelope. In addition, the resonant amplification effect of internal pressures becomes greater when the internal volume is small and the opening area is large (Holmes, 2015). This is particularly important for the design of low-rise buildings which usually have relatively small internal volumes but many large components (e.g., doors and windows) that could be breached during severe wind events (Kopp et al., 2008). For this reason, the internal pressure in low-rise buildings is a focus of this study.

Previous research has indicated that internal pressure depends on several factors (Holmes, 1979; Oh et al., 2007), including the external pressures at the openings, the

Texas Tech University, Liang Wu, August 2019 sizes and locations of the openings, vents or cracks (Liu and Rhee, 1986), the overall building leakage, the internal volume of the building, the fluid properties (density, viscosity), the wind direction, the turbulence in the upstream flow, the flexibility of building “skin” and structure (Vickery and Georgiou, 1991; Vickery, 1994; Sharma and Richards, 1997), and the compartmentalization within the building (Saathoff and Liu, 1983; Sharma and Richards, 2003; Kopp et al., 2008). Because the purpose of the experiments described in this chapter is to provide a context for the benchmark study of tornadic loading on low-rise buildings, the focus is placed on the effects of the opening geometries, the amount of building background leakages, and the wind direction relative to the building on the loading. The effects of compartmentalization are not studied, and neither is the effect of building envelope flexibility.

The WERFL building is chosen as the prototype for the study of tornadic loading and loading by boundary-layer-type wind because numerous studies on wind loading of this building have been published and the results from these publications can be used as a context for interpreting the results from the experiments in this study. For instance, Yeatts and Mehta (1993) studied the internal pressures of the WERFL building for static opening and sudden opening conditions. Ginger (2000) investigated the internal pressures of this building considering building envelope flexibility, and compared the net pressures on the cladding elements computed from measurements with the loading specified for this building by AS1170.2 (Standards Australia, 1989). In addition, National Institute of Standards and Technology (NIST) published a database with contribution from the University of Western Ontario for the purpose of providing time series of wind loading on low-rise buildings for public access (Ho et al., 2003). This database contains records of external and internal pressures from wind tunnel testing of a model of the WERFL building. However, this testing is only for a nominally sealed building. In this study, a WERFL building model is tested both with and without large openings in a series of systematically designed wind tunnel experiments. The effect of the amount of background leakage in the building envelope and that of the opening locations of the large openings are also investigated.

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3.2. Experimental Setup

The experiments were conducted in the Boundary Layer Wind Tunnel (BLWT) at Texas Tech University, which is a closed-circuit wind tunnel capable of generating wind speeds up to 50 m/s. A picture of this wind tunnel is shown in Figure 3-1. This wind tunnel has an aerodynamic section and a boundary layer section. The experiments were conducted in the boundary layer section, which has a cross-section of 1.8 m in width and 1.24 m in height. A plan view of the wind tunnel configured for the experiments for this study is shown in Figure 3-2. Measured from the center of the turntable on which the model is mounted, the boundary layer section has an upstream fetch of 14.6 m for the development of desired boundary layer flow. Devices used for simulating the desired upwind terrain conditions include a grid system at the end of settling chamber of the wind tunnel, followed by two spires, a fence of 28 cm in height, surface roughness elements and a carpet extended to the end of the boundary layer section. The geometries of the grid system and spires are shown in Figure 3-3. In the experiments, a Cobra probe (Turbulent Flow Instrumentation Pty Ltd) was used to measure the wind velocity along the height above the center of the turn table, and a Scanivalve system with ZOC33 scanners was used to measure the wind pressure acting on the building model.

Figure 3-1 The Boundary Layer Wind Tunnel at Texas Tech University

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Figure 3-2 Plan view of the BLWT at Texas Tech University

Figure 3-3 Geometries of (a) the grid system, and (b) spires 3.2.1. The Building Model

The WERFL building is a low-rise building located at a field testing site that is approximately 16 km west of Texas Tech University, in Lubbock, Texas. A picture of this building is shown in Figure 3-4 and a schematic drawing of this building is shown in Figure 3-5. As seen in Figure 3-5, the WERFL building is 13.82 m in length, 9.25 m in width, and 3.91 m in height. It has a nearly flat roof with a slope of 14:12, a door of 2.13 m × 0.91 m in the front wall, a square window of 0.86 m × 0.86 m in the back wall, and an estimated nominal internal volume of 470 m3 (Ginger, 2000). The porosity  , which is defined as the ratio of the leakage area to the corresponding external surface area, of the nominally sealed WERFL building was found to be in the range of 210 4 to 310 4 for an internal pressure range of 25-100 Pa (Yeatts and Mehta, 1993).

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Figure 3-4 The Wind Engineering Research Field Laboratory Building

Figure 3-5 Dimensions of the WERFL building at Texas Tech University The model of the WERFL building is constructed using Stereolithography (SLA) 3D printing technology at a scale of 1:50. Accordingly, the length, width, and height of the model are 276.4 mm, 185.0 mm, and 78.2 mm, respectively, and the dimensions of

Texas Tech University, Liang Wu, August 2019 the door in the front wall and the window in the back wall are 42.7 mm × 18.3 mm and 17.3 mm × 17.3 mm, respectively. In addition, a hole of 8.3 mm in diameter, and another square opening of 17.3 mm × 17.3 mm are placed in a side wall and the front wall, respectively. These additional dominant openings represent potential dominant openings that can be created in the building envelope by flying debris in wind storms. In addition to the dominant openings, 84 small holes of 1 mm in diameter are also built into the walls and roof of the model to represent the background leakage of the building envelope at full-scale. Table 3-1 lists the dimensions and opening ratios of the dominant openings. The opening ratio is the ratio of the area of the dominant opening to the area of the building wall in which the dominant opening is present.

Table 3-1 Dominant openings and leakages holes of the WERFL building model

Dominant Opening Building Components Openings Dimensions (mm) ratio* (%) Front wall Door 42.7 × 18.3 5.4 Front window 17.3 × 17.3 1.95 Leakage (12 holes) d = 1 / Side wall Side hole d = 8.3 0.25 Leakage (18 holes) d = 1 / Back wall Back window 17.3 × 17.3 1.95 Leakage (12 holes) d = 1 / Roof Leakage (42 holes) d = 1 /

* Opening ratio: the ratio of the opening area to the single wall area. Figure 3-6 shows the layout of the external pressure taps as wells as the sizes and locations of the openings. A total of 204 pressure taps, at locations nominally equivalent to those of the corresponding pressure taps on the full-scale WEFRL building that are used to measure the pressure acting on the structure, are placed on the external surfaces of the model, and 10 additional pressure taps are placed at selected locations on the internal surfaces of the model to measure the internal pressure. A few pressure taps are placed at locations near the dominant openings to enable an assessment of the potential localized effects of the dominant openings on the internal pressure in the vicinity. The locations of the internal pressure taps are shown in Figure 3-7.

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Figure 3-6 Exploded view of the WERFL building model showing basic dimensions, locations of openings (including leakage holes), and the layout of external pressure taps

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Figure 3-7 Layout of internal pressure taps (Unit: mm) When wind tunnel tests are used to study the internal pressure in buildings immersed in boundary-layer-type flows, proper scaling of the internal volume is critical (Holmes, 2015). Holmes (1979) suggested that in order to satisfy dynamic similarity (e.g., frequency and amplitude of internal pressure resonance) between the model and the prototype, the correct internal volume scaling for wind tunnel tests was not the nominal internal volume scale (i.e., the length scale cubed), but rather the ratio of the length scale cubed to the square of the velocity scale, i.e.,

3 V LLmf m  (3.1) V 2 f UUmf where V is the internal volume, L is the characteristic geometric length, U is the wind speed, and the subscripts m and f represent model and full scale, respectively. Typical velocity scales in wind tunnel studies are on the order of 1:4 or 1:5 (Kopp et al., 2008). For the experiments in the study, the velocity scale is chosen as 1:4. Because the length 39

Texas Tech University, Liang Wu, August 2019 scale used is 1:50, the correct internal volume scale is 1:7812.5. With the estimated nominal internal volume of the full-scale WERFL building being approximately 470 m3, the model used in the wind tunnel tests must have an internal volume of 60.16 1063 mm . Because the volume enclosed by the exposed walls and roof of the model is only 7.97 1063 mm , a sealed chamber of 52.19 1063 mm , which is made of acrylic glass, was attached to the bottom of the model to increase the overall internal volume, so that proper volume scaling is satisfied. A picture of the WERFL building model is shown in Figure 3-8 (a) and the chamber used as the augmented volume is shown in Figure 3-8 (b). A special feature of the model is that tunnels connected to the pressure taps are built into the walls and the roof of the model and that, as shown in Figure 3-8 (a), the connections between the pressure taps and the tubing system that are connected to the Scanivalve pressure scanners are through these tunnels. This eliminates the need for tubing and connectors inside the volume enclosed by the building model and the sealed chamber. As a result, it eliminates the need to quantify the internal volume occupied by the tubing system, which can cause unwanted uncertainties. In addition, it also eliminates the need to seal the opening through which the tubing system exits the sealed chamber, which can be practically challenging.

(a) (b)

Tubing Sealed chamber

Figure 3-8 Picture of (a) the model representing the WERFL building and (b) Scaled volume chamber 3.2.2. Simulation of Boundary Layer Flows

In the surface layer of a neural atmospheric boundary layer, i.e., the lowest 100 m to 200 m (Stull, 2012) above ground level, where most structures reside in, the variation

Texas Tech University, Liang Wu, August 2019 of the mean wind speed with height can be represented by the logarithmic law, which can be expressed as

u Uz() * ln zz (3.2) k 0

where, Uz() is the mean wind speed at height z, z0 is the roughness length of the terrain, u* is the shear velocity, and k is the von Karman’s constant which has been found experimentally to be approximately 0.4 (Holmes, 2015). Previous studies have indicated that the standard deviation of longitudinal wind speed near the earth’s surface,  u , is approximately equal to 2.5 u* (Holmes, 2015). Then in the surface layer, the longitudinal turbulence intensity Iuu  /()Uz can be approximated by the following equation

2.5u* Iu 1lnzz0 (3.3) uzz*00.4 ln 

Levitan and Mehta (1992) reported that the terrain surrounding the full-scale WERFL building can be categorized as an open country type with a roughness length of about 1.5 cm. The design 3-second gust wind speed at 10 m above ground for Risk Category II buildings in inland Texas is 51 m/s per ASCE 7-10 (2010). Based on the Durst curve (Durst, 1960), the corresponding 10-min mean wind speed at the 10 m height is 36.2 m/s. With these parameters, the target full-scale mean wind speed and longitudinal turbulent intensity profiles according to Eqs.(3.2) and (3.3) can be expressed as

Uz( ) 5.565ln z 0.015 (3.4)

Izu 1 ln 0.015 (3.5)

The simulated flow was measured at 625 Hz by a Cobra probe along a vertical line originated from the center of the turntable. The duration of the measurement at each vertical point is 2 minutes. Given the length scale of 1:50 and the velocity scale of 1:4, a comparison between the mean wind speed profile of the simulated flow and the target

Texas Tech University, Liang Wu, August 2019 profile (expressed by Eq.(3.4)) is shown in Figure 3-9 (a), and a comparison between the simulated and target (expressed by Eq.(3.5)) longitudinal turbulence intensity profiles is shown in Figure 3-9 (b). Below a full-scale height of 20 m, the profiles of the simulated flow match the corresponding target profiles well, while above the full-scale height of 20 m, the deviations between the turbulence intensity profiles become large. Considering that the eave height of the full-scale WERFL building is only 3.91 m, such deviations at higher levels are inconsequential as far as wind loading on the building model is concerned.

The power spectral density (PSD) functions of the three turbulence components (i.e., longitudinal, lateral, and vertical wind components represented by u, v, w) of the simulated flow are also computed and compared with those prescribed by the von Karman spectra (Von Karman, 1948), which are given by

nS4 n uu u (3.6)  2 2 56 u 1 70.8nu

2 nS 4nnvv 1 755.2  vv  (3.7)  2 2 11 6 v 1 283.2nv

2 nS 4nnww 1 755.2  ww  (3.8)  2 2 11 6 w 1 283.2nw

x f nLnUzii (), iuvw , , (3.9)

2 x f where Sii is the PSD of the respective turbulence component,  i and Li are the variance and the integral length scale in the x f direction for the respective turbulence component, ni is the non-dimensional frequency of the respective turbulence component, n is the frequency in Hertz. Figure 3-10 plots the PSD of the turbulence components at z = 7.8 cm above the wind tunnel floor, which corresponds to the eave height (z = 3.91 m) of the WERFL building, as well as the corresponding von Karman spectra (Von Karman, 1948) of the same turbulence components at the same height. The

Texas Tech University, Liang Wu, August 2019 spectra of the simulated turbulence reasonably match those specified by the corresponding von Karman spectra except that the simulated flow has slightly more energy at lower frequencies and less energy at higher frequencies than those specified by the von Karman spectra.

(a) 30 simulated open terrain 25 log fit (z =0.015 m) 0 20

15 (m) z 10

0 16 24 32 40 48

Figure 3-9 Comparison between simulated flow and target flow: (a) Mean wind velocity profile; (b) Turbulent intensity profile

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Figure 3-10 Power spectral density of turbulence components at a full-scale equivalent height of z = 3.91 m 3.2.3. Test Configurations

The WERFL building model with the 12 different configurations of openings specified in Table 3-2 were tested in the wind tunnel. For configurations with porosity type A, only 1/3 of the 84 background leakage holes were open; for configurations with porosity type B, all 84 background leakage holes were open. The porosity is the ratio of the leakage area to the area of the corresponding external surface. Generally, a dominant opening is defined as an opening with an opening area greater than about twice the total background leakage of the surface with the opening (Ginger, 2000). According to this definition, the door, front window, back window, and side hole can all be considered as

Texas Tech University, Liang Wu, August 2019 dominant openings. Therefore, testing of the cases listed in Table 3-2 enables an investigation of the wind loading on the building for the following scenarios: (1) the building being fully enclosed (2) the building with background leakage only, (3) the building with one dominant opening and background leakage, and (4) the building with multiple dominant openings at various locations and background leakage.

Table 3-2 Configurations of openings for the WERFL building model

Porosity* Case No. Factor Dominant opening of building envelope 1 Fully enclosed None 0 2 Background leakage None A 3 None B 4 Single dominant opening Door A 5 Door B 6 Front window A 7 Side hole A 8 Multiple dominant openings Door & Back window A 9 Door & Back window B 10 Door & Front window A 11 Door & Side hole A 12 Front window & side hole A

*Porosity type: A: 2.2 1044 ; B:  6.5 10

Because the WERFL building model is symmetric except for the dominant openings, each of the 12 configurations were tested for 19 wind directions relative to the building model ranging from 0 to 180° in 10° increments, as shown in Figure 3-11. For each wind direction, the Scanivalve system sampled the pressure taps at 400 Hz for 10 runs of 48 seconds. Because the length scale is 1:50 and the velocity scale is 1:4, the time scale for the wind tunnel tests is calculated as 1:12.5. Therefore, the duration of 48 seconds at model scale is equivalent to 10 minutes at full-scale.

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Figure 3-11 Definition of the wind direction and the directions of the force components 3.3. Data Processing

In wind tunnel tests, pressure measurements are commonly accomplished by connecting the pressure taps on the surfaces of building models to the pressure transducers via the tubing system. Typically, the diameters of these tubing are much smaller than their lengths. This creates distortion of the true dynamic pressure fluctuations, affecting both the amplitude and phase of the signal. Such distortion effects can be corrected by the inverse transfer function (ITF) method proposed by Irwin et al. (1979). The inner diameter and length of the tubing used in current wind tunnel tests are approximately 0.14 cm and 122 cm, respectively. The frequency response functions (provided by University of Florida) for the tubing system are shown in Figure 3-12.

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(a) 4 (b) 100

3 50

2 0

1 -50

0 -100 0 100 200 300 400 500 600 0 100 200 300 400 500 600 Frequency (Hz) Frequency (Hz)

Figure 3-12 Amplitude and phase of the tubing frequency response function The measured raw pressure data were corrected for tubing distortion using the ITF method based on the above frequency response functions. The corrected pressure data were then used to calculate the pressure coefficients defined as

p  p C  0 (3.10) p 1 U 2 2 h

where p is the corrected pressure at the tap of interest, p0 is the static pressure measured by a pitot tube installed at the same cross section of the wind tunnel with the center of the building model inside the wind tunnel,  is air density, Uh is the 48- second mean wind speed at the eave height of the building model which is 8.1 m/s. Based on the pressure coefficients, the coefficients of the forces acting on the model are estimated according to the following equation

Nx CApn, n Fxn1 CFx  AAFront wall Front wall

N y CApn, n Fy n1 CFy  AASide wall Side wall

Nz CApn, n Fz n1 CFz  (3.11) AARoof Roof

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where Fx , Fy and Fz are the components of the overall net force acting on the building model in the directions of x, y, and z axis (see Figure 3-11), respectively; Nx , N y , and

Nz are the number of the involved pressure taps for each corresponding force component; and C pn, and An are the pressure coefficient and the tributary area of the nth pressure tap, respectively. The areas of the front wall, side wall, and roof, i.e.,

AFront Wall , ASide Wall , and ARoof , are calculated based on the dimensions listed in Table 3-1.

The positive directions of Fx and Fy follow those defined in Figure 3-11, and Fz is deemed positive if pointing upwards.

3.4. Experimental Results

As stated earlier, 10 identical test runs are conducted for each experimental configuration. The measurement from each run gives a sample of the extreme value of the pressure coefficient. The extreme pressure coefficient at each pressure tap and the extreme force coefficients presented in this chapter are estimated using the Gringorten’s method (Gringorten, 1963) based on the corresponding 10 sample extreme values, assuming that the extreme value follows the type I extreme value distribution. The cumulative distribution function of the type I extreme value distribution for a random variable x is expressed as

Fx( ) exp{ exp[ ( x u ) / a ]} (3.12) where a is a scale factor, and u is a location parameter. In the application of the Gringorten’s method, the sample extreme values are first ranked in the order of smallest to largest, and then each sample extreme value is assigned a probability of non- exceedance. Subsequently, the parameters of the Type I extreme distribution (i.e., a and u) are estimated by applying linear regression to the reduced form of the Type I extreme distribution (Holmes, 2015) and yield a nearly unbiased estimate of the mean peak value. The mean value, standard deviation, skewness, and kurtosis of the wind loading presented in this chapter are calculated as the ensemble average of the corresponding statistics of each of the 10 repetitive measurements.

3.4.1. Nominally Sealed Building

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The pressure measurements conducted for configurations Case 1 and Case 3, in which the building model was fully enclosed and with background leakage only, respectively, show that the existence of background leakages doesn’t significantly influence the mean component or the fluctuations of the external pressure. As an illustration, Figure 3-13 depicts the distributions of the mean external pressure coefficient (C pe ) for wind directions of 0° and 90°, respectively, for testing Case 1 and Case 3. It can be observed in Figure 3-13 that for the same wind direction, the shape of distributions and the magnitude of the mean external pressure coefficient are very similar between Case 1 and Case 3. The standard deviations of the external pressure coefficient (Cpe ) for these configurations are shown in Figure 3-14. Again, for the same wind direction, no significant difference is observed between the Cpe for Case 1 and Case 3.

Figure 3-13 Distributions of the mean external pressure coefficient for (a) wind direction = 0° in Case 1, (b) wind direction = 0° in Case 3, (c) wind direction = 90° in Case 1, and (d) wind direction = 90° in Case 3 (Case 1: fully enclosed; Case 3: nominally sealed)

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Figure 3-14 Distributions of the standard deviation of the external pressure coefficient for (a) wind direction = 0° in Case 1, (b) wind direction = 0° in Case 3, (c) wind direction = 90° in Case 1, and (d) wind direction = 90° in Case 3 (Case 1: fully enclosed; Case 3: nominally sealed)

Figure 3-15 shows the mean values (Cpi ) and the standard deviations (Cpi ) of the pressure coefficients at the location of each internal tap for Case 2 and Case 3, which are the cases of nominally sealed building model with porosity ratios of 2.2 104 and 6.5 104 , respectively, for the wind direction of 0°. It can be observed that for the same statistic of the same configuration, the values at the ten internal taps are close to each other. Because the internal taps are placed at different locations inside the model, this means that the mean and fluctuating characteristics of internal pressures in nominally sealed buildings (i.e., buildings with only background leakage) are uniform throughout the internal space. In addition, as shown in Figure 3-15 (b), at each internal tap, the standard deviation of the internal pressure for Case 3 is larger than that for Case 2, indicating that for nominally sealed buildings increasing background leakage can increase the fluctuations of the internal pressure.

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(a) 0.75 (b) 0.1 Case 2 Case 2 0.5 Case 3 0.075 Case 3

0.25 0.05

0 0.025

-0.25 0 12345678910 12345678910 Internal Tap Number Internal Tap Number

Figure 3-15 Comparison between the internal pressure coefficient in Case 2 and Case 3 for wind direction = 0°: (a) mean value, and (b) standard deviation (Case 2: nominally sealed, porosity ratio of 2.2 104 ; Case 3: nominally sealed, porosity ratio of 6.5 104 )

Figure 3-16 shows the mean, maximum, minimum values, and the standard deviation (STD) of the internal pressure coefficients of the building model for different wind directions for Case 3 (i.e., the nominally sealed building model with porosity ratio of 6.5 104 ) The statistics presented are the averages of the corresponding statistics estimated based on measurements at the ten internal taps. As seen in this figure, there are no significant variations of these statistics with wind direction. This is in agreement with the findings by Oh et al. (2007) that internal pressures of buildings with only background leakage exhibit no significant variation with wind direction.

Figure 3-16 Basic statistics of internal pressure coefficient for Case 3 (nominally sealed, porosity ratio of 6.5 104 )

Based on the pressure coefficients, the coefficients of the force components are calculated based on Eq.(3.11). Figure 3-17 shows the mean, maximum and minimum values, as well as the standard deviation of the force coefficients for Case 3. Because

Texas Tech University, Liang Wu, August 2019 the envelope of the nominally sealed WERFL building is symmetric about the y-axis shown in Figure 3-11, it is expected that the statistics of CFy and CFz are symmetric about the wind direction of 90°. This is in agreement with the data presented in Figure 3-17.

Figure 3-17 (a) Mean value, (b) standard deviation, (c) maximum value, and (d) minimum value of the force coefficients for Case 3 (nominally sealed, porosity ratio of 6.5 104 )

Figure 3-18 shows the mean values and the standard deviations of the uplift force coefficient for Case 2 and Case 3, which are the cases of nominally sealed building model with porosity ratios of 2.2 104 and 6.5 104 , respectively. As seen in Figure 3-18 (a), the mean uplift force coefficient of the building model for Case 3 is much smaller than that for Case 2, indicating that for nominally sealed buildings, increasing background leakage can reduce the mean uplift force due to the change of internal pressure. In addition, Figure 3-18 (b) shows that increasing background leakage can lower the fluctuations of the uplift force, due to the attenuation of the internal pressure fluctuation with increasing background leakage as shown by Figure 3-15 (b).

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(a) 1 (b) 0.2 Case 2 Case 2 0.75 Case 3 0.15 Case 3

0.5 0.1

0.25 0.05

0 0 0 30 60 90 120 150 180 0 30 60 90 120 150 180 Wind Direction (°) Wind Direction (°)

Figure 3-18 (a) Mean value and (b) standard deviation of CFz for Case 2 and Case 3 (Case 2: nominally sealed, porosity ratio of 2.2 104 ; Case 3: nominally sealed, porosity ratio of 6.5 104 )

3.4.2. Building with A Dominant Opening

Figure 3-19 shows the mean values and standard deviations of the pressure coefficient at each internal tap for Cases 4, 6, and 7, which correspond to the configuration of the building model with a porosity of 2.2 104 and with the front door being open, the window in the front wall being open, and the circular hole in the side wall being open, respectively, when the wind is perpendicularly to the front wall (i.e., wind direction = 0°). As seen in this figure, for each case, there is no significant difference between the mean value or the standard deviations of the pressure coefficients at the ten internal taps, indicating that the mean and fluctuating characteristics of internal pressures in the model with one dominant opening are also essentially uniform throughout the internal space. Similar observations are also made for the mean values and the standard deviations of the internal pressure coefficient for the other wind directions. Therefore, unless otherwise specified, the statistics (e.g., the mean, maximum, minimum and standard deviation) and spectra of internal pressures presented in the following are the averages of the corresponding quantities at the ten internal taps.

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(a) 1.5 (b) 0.6 Case 4 Case 4 1.2 Case 6 0.5 Case 6 0.9 Case 7 0.4 Case 7 0.6 0.3 0.3 0.2 0 0.1 -0.3 0 12345678910 12345678910 Internal Tap Number Internal Tap Number

Figure 3-19 (a) Mean pressure coefficients and (b) standard deviations of pressure coefficients of each internal tap at wind direction = 0° for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole)

Figure 3-20 shows the distributions of the mean external pressure coefficient (C pe ) for Cases 4, 6, and 7 for wind direction of 0°. The configurations of openings for the three cases are also shown in Figure 3-20. It is observed that the distributions and the magnitudes of the mean external pressure coefficient are similar across the three cases. Figure 3-21 shows the distributions of the standard deviation of the external pressure coefficient (Cpe ) for the three cases for the same wind direction. It can be seen that the distributions of Cpe are also similar for the three cases. Similarly, Figure 3-22 and

Figure 3-23 show the distributions of C pe and Cpe for the three cases for the wind direction of 90°, respectively. Again, the distributions of the mean and standard deviation of the external pressure coefficient are similar across the three cases for the wind direction of 90°. Similar observations are also made for the mean value and the standard deviation of the external pressure coefficient for the other wind directions. Therefore, the presence of the dominant opening at various locations on the building envelope does not significantly affect the mean or the fluctuating characteristics of the external pressure.

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Figure 3-20 Distributions of the mean external pressure coefficient at wind direction = 0° for (a) Case 4: open front door, (b) Case 6: open front window, and (c) Case 7: open side hole

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Figure 3-21 Distributions of the standard deviation of the external pressure coefficient at wind direction = 0° for (a) Case 4: open front door, (b) Case 6: open front window, and (c) Case 7: open side hole

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Figure 3-22 Distributions of the mean external pressure coefficient at wind direction = 90° for (a) Case 4: open front door, (b) Case 6: open front window, and (c) Case 7: open side hole

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Figure 3-23 Distributions of the standard deviation of the external pressure coefficient at wind direction = 90° for (a) Case 4: open front door, (b) Case 6 : open front window, and (c) Case 7: open side hole Holmes (1979) found that the fluctuations of the internal pressure in a building with a dominant opening can be amplified compared to the fluctuations of the external pressure at the opening. Based on the concept of the Helmholtz resonator (e.g., Rayleigh, 1896; Malecki, 2013), which describes the movement of an air-slug driven by the external pressure based on the mass-conservation principle, Holmes (1979) modeled the internal pressures of a building with a dominant opening using the equation of motion of a nonlinear single-degree-of-freedom (SDOF) oscillator:

2  lVeh00 VU   CCCCCpi pi pi pi pe (3.13) pA002 k pA

where  is polytropic gas constant (taken as 1.4), p0 is the atmospheric pressure, A is the area of the opening,  is the air density, le is the effective length of the opening,

V0 is the internal volume, k is the orifice discharge coefficient (taken as 0.6 for large openings), and C p is the pressure coefficient with additional subscripts e and i

Texas Tech University, Liang Wu, August 2019 representing external and internal pressure, respectively. It is apparent that the damping

2 term in Eq.(3.13) (i.e., (2)VU00h k p A ) critically depends on the ratio of the internal volume to the opening area, i.e., VA0 . For a definite internal volume, a larger dominant opening area results in a smaller amount of damping (if all other parameters are held constant) and consequently induces greater resonant amplification. Figure 3-24 and Figure 3-25 depicts the mean value, the standard deviation, and the maximum and minimum values of the internal pressure coefficients and those of the external pressure coefficients at the locations of the dominant openings for Cases 4, 6, and 7, respectively. The external pressure coefficients are computed as the weighted average of the pressure coefficients of the nearest four external taps surrounding the dominant opening, assuming that the weight is inversely proportional to the distance between the pressure tap and the center of the dominant opening. According to Table 3-1, for the three cases, the size of the dominant opening in Case 4 is the largest, and that of the dominant opening in Case 7 is the smallest. According to Kopp et al. (2008), the Helmholtz resonance is the most significant when the wind is perpendicular to the wall with the dominant opening, but is minimal when the wind direction is parallel to the wall with the dominant opening. Figure 3-25 (b) shows that for the wind direction of 0° (i.e., when the wind is perpendicularly to the front wall), the standard deviations of external pressure coefficients of the building are very similar for Cases 4 and 6. However, according to Figure 3-24 (b), for the same wind direction of 0°, the standard deviation of the internal pressure coefficient of the building in Case 4 is clearly larger than that of the building in Case 6, which suggests that the amplification of the internal pressure is more significant in Case 4 than in Case 6. This agrees with the earlier observation that the smaller the VA0 , the stronger the internal pressure resonance. For the maximum and minimum pressure coefficients, Figure 3-24 and Figure 3-25 also show that for the same opening configuration, the variations of the extreme internal pressure coefficient and the extreme external pressure coefficient with wind direction follow similar trends.

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Figure 3-24 (a) Mean value, (b) standard deviation, (c) maximum value, and (d) minimum value of the internal pressure coefficients for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole)

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Figure 3-25 (a) Mean value, and (b) standard deviation of the external pressure coefficients at the corresponding dominant opening for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole) Holmes (1979) and Liu and Rhee (1986) studied buildings with a range of dominant openings and showed that internal pressure resonance occurs at a frequency close to the undamped Helmholtz frequency:

1  Ap0 fH  (3.14) 2lVe 0

Applying Eq.(3.14) and taking lle 0 0.89 A (Kopp et al., 2008), where l0 is the actual wall thickness of the model (l0 10.5mm ), the undamped Helmholtz frequencies of the internal pressure in the building model for Cases 4, 6, and 7 are 32.7 Hz, 23.6 Hz, and 12.4 Hz, respectively. Figure 3-26 shows the power spectral density (PSD) functions of the internal and external pressure coefficients for the three cases with the wind directions being normal to the corresponding dominant openings. In Figure 3-26

(a), the PSD of Cpi shows a clear peak near the frequency of 31 Hz, which is very close to the calculated Helmholtz frequency (32.7 Hz). At the same frequency, the PSD of

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C pe is much smaller than that of Cpi . This is evidence of significant resonance amplification occurring at this frequency for the internal pressure of the building model for Case 4. For Case 6, the undamped Helmholtz frequency of the internal pressure according to Eq.(3.14) is 23.6 Hz. Figure 3-26 (b) shows that at this frequency, the PSD of Cpi is only slightly larger than that of C pe , and there is no obvious peak near this frequency. This indicates that the internal pressure fluctuations for Case 6 are only marginally amplified. For Case 7, Figure 3-26 (c) shows that the PSD of Cpi is much smaller than that of C pe at all frequencies, meaning that the internal pressure fluctuations in Case 7 are substantially attenuated compared to the fluctuations of the external pressure. Such phenomena are in agreement with the predictions by the Helmholtz resonator model. As suggested earlier, the damping term in Eq.(3.13) critically depends on the ratio of the internal volume to the opening area. According to Table 3-1, the area of the dominant openings, from large to small, are 781 mm2 for Case 4, 299 mm2 for Case 6, and 54 mm2 for Case 7. Because the opening area in Case 4 is the largest, the damping provided by the internal volume in Case 4 is the smallest. Consequently, the fluctuation of the internal pressure in Case 4 is amplified the most. By contrast, the opening area in Case 7 is the smallest, the damping provided by the internal volume in Case 7 is the largest. This results in the fluctuation of the internal pressure being attenuated compared to that of the external pressure.

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Figure 3-26 PSD of internal and external pressure coefficients for (a) wind direction = 0° in Case 4 (open front door), (b) wind direction = 0° in Case 6 (open front window), and (c) wind direction = 90° in Case 7 (open side hole) In addition to the pressures at individual locations, the forces resulting from the pressures acting on the model are also investigated for Cases 4, 6, and 7. Figure 3-27 shows the mean value, the standard deviation as well as the maximum and minimum values of the uplift force coefficient for the three cases. Figure 3-27 (a) shows that for wind direction of 0°, the mean uplift force coefficients of the building model are almost the same for Case 4 and Case 6, while for the same wind direction of 0° the magnitude of the maximum uplift force coefficient of the building for Case 4 is larger than those of the building for Case 6. Because the minimum uplift force coefficients for Case 4 and Case 6 are also positive at the wind direction of 0°, there is no need to consider the minimum uplift force coefficient for the magnitude of the extreme uplift force coefficient for this wind direction. Since the distributions of the external pressure 63

Texas Tech University, Liang Wu, August 2019 coefficients are nearly identical for Case 4 and Case 6 (see Figure 3-20 and Figure 3-21), the difference between the maximum uplift force coefficients in the two cases shows that increasing the size of the dominant opening can result in larger extreme wind load due to the effect of Helmholtz resonance. This is in fact consistent with Figure 3-27 (b), which shows that for the wind direction of 90°, the standard deviation of CFz in Case 4 is larger than that in Case 6. For the other wind directions, especially when the wind direction is larger than 120°, the statistics of the uplift force coefficient in Case 4 and Case 6 become close to each other. For Case 7, the dominant opening (i.e., the circular hole), is located at the center of the side wall (see Figure 3-11). Therefore, as expected,

Figure 3-27 shows that all the statistics of CFz for Case 7 are approximately symmetric about the wind direction of 90°.

Figure 3-27 (a) Mean value, (b) standard deviation, (c) maximum value, and (d) minimum value of CFz for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole) Figure 3-28 and Figure 3-29 show the maximum and minimum values of the lateral force coefficients, C and C , of the building model for the three cases. As seen in Fx Fy these figures, the extreme values of the two lateral force coefficients are very similar for

Texas Tech University, Liang Wu, August 2019 all three cases. It is also observed that the size of the dominant opening does not significantly affect the magnitude of the extreme lateral force coefficients for buildings with a single dominant opening. The reasons for this phenomenon are two-fold. One is that the existence of the dominant opening does not significantly affect the distribution of the external pressure on the model, as shown by Figure 3-20 and Figure 3-21. The other is that for the lateral forces defined in this study, which are the force components of the overall net wind load on the model acting in the horizontal axes, the part of the lateral forces resulting from the internal pressure acting on the internal surfaces of the model almost cancels out.

(a) 2 (b) 0.5 Case 4 Case 4 1.5 Case 6 0 Case 6 Case 7 Case 7 1 -0.5 0.5 -1 0 -1.5 -0.5 -2 0 306090120150180 0 30 60 90 120 150 180 Wind Direction (°) Wind Direction (°)

Figure 3-28 (a) Maximum value, and (b) minimum value of CFx for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole)

(a) 1 (b) 0.5 Case 4 Case 4 Case 6 0 Case 6 0.5 Case 7 Case 7 -0.5

-1 0 -1.5 -0.5 -2 0 30 60 90 120 150 180 0 30 60 90 120 150 180 Wind Direction (°) Wind Direction (°)

Figure 3-29 (a) Maximum value, and (b) minimum value of CFy for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole) Davenport (1961) showed that the wind loads induced by boundary-layer-type flow are approximately Gaussian. This is in agreement with the experimental results in this study. As an illustration, Figure 3-30 shows the skewness ( SFz ) and kurtosis ( KFz ) of

Texas Tech University, Liang Wu, August 2019 the uplift force coefficient for Case 4, 6, and 7. The range of the skewness for the three cases is between -0.24 and 0.73, and the range of the kurtosis for the three cases is between 2.90 and 3.88. Therefore, the probabilistic characteristics of the uplift force coefficient are close to those of a Gaussian stochastic process.

(a) 1.5 (b) 4.5 Case 4 Case 4 Case 6 Case 6 1 4 Case 7 Case 7 0.5 3.5

0 3

-0.5 2.5 0 30 60 90 120 150 180 0 30 60 90 120 150 180 Wind Direction (°) Wind Direction (°)

Figure 3-30 (a) Skewness and (d) Kurtosis of CFz for Case 4 (open front door), Case 6 (open front window), and Case 7 (open side hole) To investigate the effects of background leakage on the wind loading on buildings with a single dominant opening, Figure 3-31 shows the mean value and standard deviation of the internal pressure coefficient and the uplift force coefficient for Case 4 and Case 5. Both cases correspond to the building model with the door in the front wall being open, but the porosity ratio of the building model for Case 4 is 2.2 104 and that of the building model for Case 5 is 6.5 104 . The two porosity ratios are both within the range of porosity of typical well-constructed wood frame houses in North America (Stathopoulos et al., 1979). As seen in Figure 3-31, the mean value and the standard deviation of Cpi and CFz in Case 4 are very close to the corresponding statistics of Cpi and CFz in Case 5. This suggests that for this range of porosity ratio, the wind loading of the building with a dominant opening does not depend significantly on the porosity of the building envelope.

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Figure 3-31 (a) Mean value of Cpi , (b) Standard deviation of Cpi , (c) Mean value of

CFz , and (d) Standard deviation of CFz for Case 4 (open front door, porosity ratio of 2.2 104 ) and Case 5 (open front door, porosity ratio of 6.5 104 )

3.4.3. Building with Multiple Dominant Openings

During severe windstorms, a building could have several dominant openings present in the building envelope. Figure 3-32 shows the mean and standard deviations of the pressures at each internal tap for Cases 8, 10, 11, and 12, which correspond to the door in the front wall and the window in the back wall being open, the door and the window in the front wall being open, the door in the front wall and the hole in the side wall being open, and the window in the front wall and the hole in the side wall being open, respectively, for wind direction of 0°. As seen in this figure, the mean values and the standard deviations of the pressure coefficients are consistent across the ten internal taps for Case 10, 11, and 12, while for Case 8 the two statistics for the pressure at the internal tap 5 are different from the corresponding statistics of the pressures at the locations of the other internal taps. A closer look at the internal pressure coefficient for Case 8 reveals that the mean internal pressure at tap 5 is 84.2% of the average of the mean pressures at the other internal taps, and the standard deviation of the internal

Texas Tech University, Liang Wu, August 2019 pressure at tap 5 is 93.6% of the average of the standard deviations of the pressures at the other internal taps. In Case 8, both the door in the front wall and the window in the back wall are open, and internal tap 5 is located near the lower edge of the back window inside the model as shown by Figure 3-7. The fact that the pressure at the location of the internal tap 5 is considerable different from the pressures at the other internal taps is a reflection of the effects of the local flow near the dominant opening. Therefore, unlike the nominally sealed building model and the building model with a dominant opening, the internal pressure in the building model with multiple dominant openings can be non-uniform in the internal space of the model. For this reason, for Cases 10, 11, and 12 the statistics and spectra of the internal pressure coefficients presented in the following are the averages of the corresponding quantities at the ten internal taps, while for Case 8 the statistics and spectra of the internal pressure coefficients are calculated only based on the 9 internal taps excluding tap 5.

(a) 1.2 (b) 0.6 Case 8 Case 8 1 Case 10 0.5 Case 10 Case 11 Case 11 0.8 Case 12 0.4 Case 12 0.6 0.3 0.4 0.2 0.2 0.1 12345678910 12345678910 Internal Tap Number Internal Tap Number

Figure 3-32 (a) Mean pressure coefficients and (b) Standard deviations of pressure coefficients of each internal tap at wind direction = 0° for Case 8 (open front door and open back window), Case 10 (open front door and open front window), Case 11 (open front door and open side hole), and Case 12 (open front window and open side hole)

Figure 3-33 depicts the distributions of the mean external pressure coefficient (C pe ) for Cases 8, 10, 11, and 12 for the wind direction of 0°. The configurations of the openings in the envelope of the building model for the four cases are also shown in this figure. It is observed that the shapes of distributions and the magnitudes of the mean external pressure coefficient are very similar for the four cases. This suggests that the presences of dominant openings at various locations do not significantly affect the mean characteristics of the external pressure. In addition, Figure 3-34 shows the distributions

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of the standard deviation of the external pressure coefficient (Cpe ) for the four cases at the same wind direction. It is seen that the distributions of Cpe are also similar for the four cases. This indicates that the fluctuating characteristics of the external pressure are not significantly affected by the dominant openings when there are multiple dominant openings in the building envelope.

Figure 3-33 Distributions of the mean external pressure coefficient at wind direction = 0° for (a) Case 8: open front door and open back window, (b) Case 10: open front door and open front window, (c) Case 11: open front door and open side hole, and (d) Case 12: open front window and open side hole

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Figure 3-34 Distributions of the standard deviation of the external pressure coefficient at wind direction = 0° for (a) Case 8: open front door and open back window, (b) Case 10: open front door and open front window, (c) Case 11: open front door and open side hole, and (d) Case 12: open front window and open side hole The mean value, standard deviation, and the maximum and minimum values of the internal pressure coefficient for Cases 8, 10, 11 and 12 are shown in Figure 3-35 for different wind directions. Apparently, each of the statistics varies with the wind direction. Since the larger dominant opening is always located in the front wall for the four cases, the mean value, standard deviation, and the maximum value reach their largest values when the wind direction is approximately normal to the front wall (i.e., between 0° and 20°), while the minimum reaches its largest value in magnitude when the wind direction is approximately parallel to the front wall (i.e., between 90° and 110°).

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Figure 3-35 (a) Mean value, (b) standard deviation, (c) maximum value, and (d) minimum value of the internal pressure coefficients for Case 8 (open front door and open back window), Case 10 (open front door and open front window), Case 11 (open front door and open side hole), and Case 12 (open front window and open side hole) Figure 3-36 shows the PSD of the internal pressure coefficients for the four cases for wind direction of 0°. For Case 10 and Case 11, the PSD of the internal pressure coefficient exhibits obvious peaks at frequencies around 33 Hz and 30 Hz, respectively, which indicates the occurrences of internal pressure resonance in the two cases. By contrast, for Case 8 and Case 12, the PSD of the internal pressure coefficient does not show any obvious peaks at higher frequencies. In Case 10, both the door and the window in the front wall are open. When the wind direction is normal to the front wall, the mean values and standard deviations of the external pressures at the two dominant openings are similar as shown by Figure 3-33 (b) and Figure 3-34 (b), and the external pressures at the two dominant openings are positively correlated (correlation coefficient is 0.54). Therefore, it is expected that internal pressure resonance occurs in this case. In Case 11, both the door in the front wall and the hole in the side wall are open. It was shown earlier in Figure 3-26 (a) that internal pressure resonance occurs in the building model with the door in the front wall being open (i.e., Case 4) when the wind direction is perpendicular

Texas Tech University, Liang Wu, August 2019 to the front wall. Therefore, Figure 3-36 (c) shows that the existence of the side hole does not eliminate the internal pressure resonance for Case 11, likely because the size of the side hole is so small that the effect of this opening on the internal pressure is insignificant. In Case 8, both the door in the front wall and the window in the back wall are open. Although the total opening area of the building model in Case 8 is the same as that in Case 10, internal pressure resonance does not occur in Case 8 as shown by Figure 3-36 (b). This shows that the location of the dominant opening can also affect the characteristics of the internal pressure. Finally, Case 12 is the configuration where the building has a window opening in the front wall and a circular opening in the side wall. As shown earlier in Figure 3-26 (b), the internal pressure in Case 6 where the model only have a window opening in the front wall is only slightly amplified. For this reason, it is expected that the PSD of the internal pressure in Case 12 shows no obvious peaks in Figure 3-36 (d).

Figure 3-36 PSD of internal pressure coefficients for (a) Case 8: open front door and open back window, (b) Case 10: open front door and open front window, (c) Case 11: open front door and open side hole, and (d) Case 12: open front window and open side hole

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The force coefficients of the building model for the four cases are also evaluated. Figure 3-37 shows the mean value, the standard deviation, and the maximum and minimum values of CFz for different wind directions for Case 8, 10, 11 and 12. Again, the mean value, the standard deviation, and the maximum value all reach their largest values when the wind direction is approximately perpendicular to the front wall, and the minimum reaches its largest value in magnitude when the wind direction is nearly parallel to the front wall. In particular, although the total area of the dominant openings are the same for Case 8 and Case 10, the statistics of the uplift force coefficient in the two cases are much different. This is also a reflection of the effect of the locations of the dominant openings on the internal pressure, which is part of the overall loading on the building.

Figure 3-37 (a) Mean value, (b) standard deviation, (c) maximum value, and (d) minimum value of CFz for Case 8 (open front door and open back window), Case 10 (open front door and open front window), Case 11 (open front door and open side hole), and Case 12 (open front window and open side hole) Figure 3-38 and Figure 3-39 show the maximum and minimum values of the lateral force coefficients, C and C , for the four cases. As seen in these figures, the extreme Fx Fy

Texas Tech University, Liang Wu, August 2019 values of the two lateral force coefficients are very similar for the four cases. The reason for this similarity is that the parts of the lateral forces induced by the internal pressures acting on the internal surfaces of the opposite walls are canceled out.

(a) 2 (b) 0.5 Case 8 Case 8 1.5 Case 10 0 Case 10 Case 11 Case 11 1 Case 12 -0.5 Case 12 0.5 -1 0 -1.5 -0.5 -2 0 30 60 90 120 150 180 0 30 60 90 120 150 180 Wind Direction (°) Wind Direction (°)

Figure 3-38 (a) Maximum value, and (b) minimum value of CFx for Case 8 (open front door and open back window), Case 10 (open front door and open front window), Case 11 (open front door and open side hole), and Case 12 (open front window and open side hole)

(a) 1 (b) 1 Case 8 Case 8 Case 10 Case 10 0.5 Case 11 0 Case 11 Case 12 Case 12

0 -1

-0.5 -2 0 30 60 90 120 150 180 0 30 60 90 120 150 180 Wind Direction (°) Wind Direction (°)

Figure 3-39 (a) Maximum value, and (b) minimum value of CFy for Case 8 (open front door and open back window), Case 10 (open front door and open front window), Case 11 (open front door and open side hole), and Case 12 (open front window and open side hole) 3.5. Summary

Wind tunnel testing of a model of the WERFL building was conducted in the Boundary Layer Wind Tunnel (BLWT) at Texas Tech University, and the corresponding experimental results are interpreted in this chapter. The building model was tested with various configurations of dominant openings and background leakages. It is found that the existence of dominant openings and background leakages does not significantly affect the mean or the fluctuating characteristics of the external pressure.

Texas Tech University, Liang Wu, August 2019

For internal pressures, it is shown that they are uniform throughout the internal space of nominally sealed buildings and buildings with a single dominant opening. However, in buildings with multiple dominant openings the internal pressure at locations close to a dominant opening can be different from the internal pressure at other locations far away from the dominant opening. In addition, in nominally sealed buildings the internal pressures do not significantly change with the wind direction, while in buildings with dominant opening(s) the internal pressures are distinct for different wind directions.

The Helmholtz resonance phenomenon is observed in the WERFL building model when the door in the front wall is open and meanwhile the wind direction is perpendicular to the front wall. It is found that for a given building with a single dominant opening, increasing the opening area results in stronger internal pressure resonance. It is also revealed that the locations of dominant openings influence the characteristics of internal pressures. This is reflected by the fact that when the wind direction is perpendicular to the front wall, internal pressure resonance occurred in the building model with a door and a window opening in the front wall, but not in the building model with a door in the front wall and a window opening in the back wall, although the total opening area of the two building models are the same.

Based on the pressure measurements, the force coefficients of the building model for each test configuration are evaluated. For nominally sealed buildings, increasing background leakage can reduce the mean and fluctuations of the uplift force. For buildings with a single dominant opening, the magnitude of the extreme uplift force is increased with the increase of the opening area, while the magnitudes of the extreme lateral forces are not significantly affected by the opening area. For buildings with multiple dominant openings, the magnitudes of the extreme uplift force can be affected by the locations of individual dominant opening, while the magnitudes of the extreme lateral forces are not significantly affected by the locations of the dominant openings.

Texas Tech University, Liang Wu, August 2019

CHAPTER 4

LABORATORY TESTING OF A LOW-RISE BUILING MODEL IN TORNADO-LIKE VORTICES

4.1. Introduction

As revealed by many previous studies, the loading on low-rise buildings by tornadic winds can be significantly different from that by boundary-layer-type winds. For instance, Haan et al. (2010) tested a fully enclosed building model in the ISU tornado simulator and observed that the peak lateral and uplift force coefficients of the building exposed to tornadoes can be as much as 1.5 and 3.2 times, respectively, as those specified by the ASCE 7-05 design provisions for boundary-layer-type winds over an open terrain. Recently, Feng and Chen (2018) did a further study to characterize the dynamic tornadic loading on the building tested in the study by Haan et al. (2010). Their results showed that the characteristics of dynamic pressure are strongly affected by the location of tornado relative to the building and that tornadic loading is very different from the loading by boundary-layer-type wind. In addition, this study also suggested that the pressure drop caused by tornadic wind plays a key role in defining the characteristics of the external pressure on the building.

A number of studies have also been conducted to investigate the internal pressure of buildings in tornado-like vortices. However, these studies mostly used the methods developed for boundary-layer-type winds to study the internal pressures of low-rise buildings exposed to stationary tornado-like vortices. For instance, Letchford et al. (2015) measured the external and internal pressures of a low-rise building model in a tornado-like vortex, and compared the frequency-domain characteristics of the measured internal pressures with those of the internal pressures simulated based on the Helmholtz resonator model. Although this model has been demonstrated by many studies (e.g., Holmes, 1979; Liu and Rhee, 1986; Kopp et al., 2008) to be effective in representing the dynamics of internal pressure for buildings subjected to boundary- layer-type winds, its effectiveness in modeling the internal pressure of buildings in translating tornadic winds is unclear. In particular, due to tornado translation and the

Texas Tech University, Liang Wu, August 2019 fact that both the static and dynamic pressures of the air vary spatially and temporally in a tornadic flow field, the external pressures on buildings exposed to tornadic flow are nonstationary in nature. For this reason, the internal pressure resonance occurring in the building with dominant opening(s) subjected to boundary-layer-type winds may not occur in tornadic winds. Also, it is unclear whether internal volume scaling is necessary in laboratory testing of buildings in simulated tornadic flows.

This research aims at developing a more comprehensive understanding of the loading on low-rise buildings by translating tornadoes with considerations of both the external and internal pressures. The emphasis is placed on the nonstationary fluctuations of the tornadic loading. To enable this investigation, a model of the WERFL building with the same configurations of openings as the model tested in the boundary layer wind tunnel is tested in VorTECH, with and without internal volume augmentation. The characteristics of the external and internal pressure in the WERFL building model are studied first. Based on the pressure measurements, the forces acting on the WERFL building model are estimated. The approach developed by Xiao and Zuo (2015) are utilized to characterize the non-stationary tornadic loading. Statistics such as the skewness and kurtosis of the tornadic loading on the building model are compared with those of the loading on the building model by boundary-layer-type wind. In addition, the relationship between the internal pressure and external pressure caused by the simulated tornado-like vortices is also compared with the corresponding relationship for the loading by boundary-layer-type wind.

4.2. The Tornado Simulator

The VorTECH at Texas Tech University (TTU) as a Ward-type tornado simulator was incapable of generating translating vortices. This has prohibited the study of loading on structures by translating tornado-like vortices. However, with a recent upgrade, a strip of the simulator floor spanning the diameter of the updraft hole can now translate for a distance of 4.0 m at a constant speed up to 1.06 m/s or less. A schematic drawing of the upgraded VorTECH simulator is shown in Figure 4-1. As seen in this figure, a total of 12 wheel blocks (6 in each row) driven by 3 electric motor are installed on two rails beneath the floor of the simulator. The other physical features of the simulator

Texas Tech University, Liang Wu, August 2019 remain unchanged except that now the height of the chamber can only be adjusted between 1.0 m and 1.7 m. During the experiments, the model of the WERFL building was securely mounted on the moving platform so that there is no relative movement between the model and the platform when the platform moves. The simulator floor is a smooth surface made of varnished plywood.

Figure 4-1 A schematic illustration of upgraded VorTECH 4.3. Experimental Setup

Laboratory testing of the model of the WERFL building was conducted in VorTECH. The flow velocity measurements were accomplished with a combination of a Cobra probe (Turbulent Flow Instrumentation Pty Ltd) and an Omniprobe (Aeroprobe Corporation) as described in Section 2.2.2, and the surface pressures and building model pressures were by with a Scanivalve ZOC33 system at the frequency of 625 Hz.

4.3.1. The Building Model

The WERFL building model tested in VorTECH is constructed at a length scale of 1:100 rather than the length scale of 1:50 for the model tested in the boundary layer wind tunnel. This model is also built with 3D printing technology. The dimension of the model is 92.5 mm by 39.1 mm by 138.2 mm (width by height by length). Figure 4-2 shows the dimensions of the model, the locations of dominant openings, as well as the layout of the external pressure taps. As seen in this figure, a total of 4 dominant openings are placed on the building model, i.e., a door and a square window in the front wall, a circular hole in the side wall, and a square window in the back wall. In addition to the dominant openings, 25 small holes of 1 mm in diameter are also built into the walls and

Texas Tech University, Liang Wu, August 2019 roof of the model to represent the background leakage of the building envelope at full- scale. The opening ratios of each dominant opening of each surface are listed in Table 4-1. A total of 204 pressure taps are placed on the external surfaces of the building model, mostly following the locations of the pressure taps on the full-scale WERFL building, and an additional 10 pressure taps are placed at selected locations on the internal surfaces of the model. In particular, a few pressure taps are placed at the locations near the dominant openings to enable an assessment of the potential localized effects of the dominant openings on the internal pressure. The locations of the internal pressure taps are shown in Figure 4-3.

Figure 4-2 Exploded view of the 1:100 WERFL building model showing dimensions of the model, locations of openings (including leakage holes), and external pressure tap layout

Texas Tech University, Liang Wu, August 2019

Table 4-1 Dominant openings and leakage holes of the 1:100 WERFL building model

Building Openings Dimensions (mm) Dominant Opening ratio* (%) Components Front wall Door 21.3 × 9.1 5.4 Front window 8.7 × 8.7 1.95 Leakage (3 holes) d = 1 / Side wall Side hole d = 4.2 0.25 Leakage (4 holes) d = 1 / Back wall Back window 8.7 × 8.7 1.95 Leakage (3 holes) d = 1 / Roof Leakage (11 holes) d = 1 /

* Opening ratio: the ratio of the opening area to the single wall area.

Figure 4-3 Layout of internal pressure taps of the 1:100 WERFL building model (Unit: mm) To investigate the effect of internal volume scaling on the internal pressure, the WERFL building model with two different internal volumes are tested. One is the building model without augmentation of the original internal volume enclosed by the

Texas Tech University, Liang Wu, August 2019 properly scaled walls and roof of the building, and the other is the building model with a sealed chamber added to the bottom of the building envelope to artificially increase the internal volume. The size of the sealed chamber is determined according to the relationship that is considered appropriate for scaling the internal volume of building models tested in boundary layer wind tunnels (i.e., Eq.(3.1)). A velocity scale of 1:4 is used. This, combined with the length scale of 1:100, results in an internal volume scale of 1:62500. Pictures of the building model and the scaled volume chamber located beneath the floor of VorTECH when the model is installed in the simulator for testing are shown in Figure 4-4.

(a) (b)

Sealed chamber

Figure 4-4 Picture of (a) the building model and (b) the scaled volume chamber 4.3.2. Tornadic Flow Field

The building model was tested in two types of tornado-like vortex. One type is a single-celled vortex generated at a swirl ratio of 0.24, and the other is two-celled vortex generated at a swirl ratio of 0.78. Both vortices are generated at the aspect ratio of 0.5, which corresponds to a uniform height of 1.0 m for the turning vanes. The mean flow fields of the two types of vortices are shown in Figure 4-5, and the mean and standard deviation of the surface pressure deficit of the two types of vortices are shown in Figure 4-6. For testing in each type of vortex, the building model is first tested when the platform is held stationary and then tested when the platform is translating at two different speeds of 0.5 m/s and 1 m/s, respectively. The translation speeds of 0 m/s, 0.5 m/s and 1.0 m/s for the single-celled vortex are referred to hereafter as VS1, VS2, and VS3, respectively. Similarly, the translation speeds of 0 m/s, 0.5 m/s and 1.0 m/s for the

Texas Tech University, Liang Wu, August 2019 two-celled vortex are referred to as VD1, VD2, and VD3, respectively. The key parameters of the two types of vortices are listed in Table 4-2.

Figure 4-5 Mean flow fields of (a) single-celled vortex, and (b) two-celled vortex

Figure 4-6 (a) Mean, and (b) Standard deviation of the surface pressure deficit for the single-celled and two-celled vortex Table 4-2 Key parameters of simulated vortices

Floor Translation Vortex Type S rc (m) UH (m/s) Re Aspect Ratio speed (m/s) Single-celled 0, 0.5, 1.0 0.24 0.12 15.29 7.21×105 0.5 Two-celled 0, 0.5, 1.0 0.78 0.32 14.29 6.50×105 0.5

Note: S = swirl ratio; rc = core radius; UH = the maximum mean horizontal velocity measured at the eave height (i.e., z = 3.9 cm in model scale) of the building; and Re = the radial Reynolds number. 4.3.3. Experimental Configuration

In the experiments in the boundary layer wind tunnel, the building model was tested with 12 opening configurations (Table 3-2). In the experiments in VorTECH, the

Texas Tech University, Liang Wu, August 2019 building model was tested with three of those opening configurations, with and without the chamber for volume augmentation. Table 4-3 lists the 5 building configuration cases tested in VorTECH. For each building configuration case, the WERFL building model is exposed to the two types of vortices with three different floor translation speeds, i.e., VS1~VS3, and VD1~VD3, and tested for 5 representative building orientations relative to the tornado mean path, i.e.,   0°, 45°, 90°, 135°, and 180°. The definition of the building orientation angle ( ) with respect to the tornado mean path is shown in Figure 4-7. For all the experiments, the center of the plan of the building model is always on the tornado mean path. The long axis and short axis of the model are represented by x and y, respectively, and the vertical axis of the model is represented by z. When the building orientation angle is   0 , the direction of the relative motion of the vortex is perpendicular to the front wall, and the model axis x is in line with the tornado mean path represented by X.

Table 4-3 Model configurations

Porosity* Augmented Case No. Factor Dominant opening of building envelope (%) Volume 1 Fully enclosed None 0 N

2 Single dominant Door 0.065 N opening 3 Door 0.065 Y

4 Multiple dominant Door & Back window 0.065 N openings 5 Door & Back window 0.065 Y

*Porosity: the ratio of leakage area to the corresponding external surface area

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Figure 4-7 Definition of the building orientation angle ( )

When the floor on which the building model is mounted does not translate relative to the vortices (i.e., VS1 and VD1), the model is placed at six different radial locations, defined according to the distance from the center of the building to the vortex center, i.e., r = 0, 0.5 rc , rc , 2 rc , 3 rc , and 4 rc . Each of the measurements in stationary vortices lasts 1 minute and is repeated 10 times.

When the simulator floor translates, the experiments are repeated 100 times for Case 3 (i.e., the building model with the door being open) for the building orientation angle of 0°. For the other test configurations, experiments are only repeated 10 times. The purpose of conducting many more repetitive tests at one experimental configuration is to validate the data interpretation technique used in this study, which will be presented in Section 4.5.

4.4. Data Processing

The external and internal pressures are measured by pressure taps connected to a Scanivalve system with a sampling frequency of 625 Hz. The inner diameter and length of the tubing used for the wind load experiments in VorTECH are approximately 0.14 cm and 45.7 cm, respectively. The frequency response functions (provided by University of Florida) for this tubing system are shown in Figure 4-8.

Texas Tech University, Liang Wu, August 2019

(a) 4 (b) 100

3 50

2 0

1 -50

0 -100 0 100 200 300 400 500 600 0 100 200 300 400 500 600 Frequency (Hz) Frequency (Hz)

Figure 4-8 Amplitude and phase of the frequency response function of the tubing used in VorTECH The measured raw pressure were corrected for tubing distortion using the inverse transfer function method (Irwin et al., 1979) based on the above frequency response functions. The corrected pressure data were then converted to pressure coefficients by the following equation

p  p C  0 (4.1) p 1 U 2 2 H

where p is the measured pressure, p0 is the barometric pressure of a static bottle in the control room beneath the tornado simulator,  is the air density, U H is the maximum mean horizontal wind speed of all the velocity measurements conducted at the eave height (i.e., z = 3.9 cm at model scale) of the building. The lateral and uplift force coefficients are estimated with the same equations used in boundary-layer wind tunnel tests (see Eq.(3.11)).

4.5. Data Interpretation Technique

Because the velocity and pressure fields of tornadoes vary both temporally and spatially, tornadic wind loading on low-rise buildings is nonstationary in nature. Therefore, the conventional methods for characterization, modeling, and simulation of stationary wind loads on buildings subjected to boundary-layer-type winds are no longer applicable to the study of tornadic wind loading. For this reason, a data interpretation technique based on the framework developed by Xiao and Zuo (2015), which has been

Texas Tech University, Liang Wu, August 2019 used to characterize, model, and simulate nonstationary winds, is used to process the tornadic loading data in this study.

4.5.1. Methods

The framework developed by Xiao and Zuo (2015) utilized a combination of discrete wavelet transform, Gaussian filtering, and cross validation to process the time histories of a non-stationary process. Consider a nonstationary process X, the discrete wavelet transform (DWT) of which can be expressed as

WTX W (4.2)

kk11 T where TW is the orthogonal DWT transform matrix, and WWW [,,,] W is the vector of DWT coefficients which consists of the approximation coefficient sub vector, W k1 , and the detail coefficient sub vectors of level 1, W 1 , to level k, W k . The time- varying mean component of the process X can be recovered from W k1 by inverse discrete wavelet transform (IDWT), and the fluctuating component is obtained by subtracting the time-varying mean from X, which is essentially a zero-mean nonstationary process denoted as X .

Statistics of a nonstationary stochastic process, such as the time-varying variance, skewness and kurtosis can be estimated based on a large ensemble of realizations of the process. However, this can be impractical in many situations because the ensemble may not be readily available. While the experiments in VorTECH can be repeated a large number of times to provide the necessary ensemble, this requires a prohibitive cost of time and labor. To reduce the workload in laboratories, a technique called adaptive Gaussian filtering (Blundell and Duncan, 1998) is used in the estimation of the statistics of the nonstationary loading acting on the building model by the simulated tornado-like vortices. Fundamentally, the adaptive Gaussian filtering makes inference about the population by smoothing the sample with a Gaussian kernel of varying variance adapted to the local variations of the sample. As an illustration example, the time-varying variance of a zero-mean nonstationary process X is estimated by convolving the square of the sample data points with an adaptive Gaussian smoothing kernel, expressed as

Texas Tech University, Liang Wu, August 2019

N  22()tXGt  ( ) ( ) (4.3) X   1

x2  1 2 Gx() e2 (4.4) 2 where N is the number of the sample data points, and  2 is the adaptive filter variance of the Gaussian kernel. Hodson et al. (1981) proposed a method to determine the adaptive filter variance using local curvature analysis, which is expressed as

2  2 ()x  (4.5) Fx() where Fx() is the second derivative of the noisy input signal Fx(), and  is the

amount of pre-defined error due to Gaussian filtering, i.e., Fxg () Fx ()  in which

Fxg () is the filtered signal. The magnitude of the allowed error  is determined by the noise level  N , which is estimated by a linear regression approach developed by Hodson et al. (1981), and the amount of smoothing required, expressed as

   N (4.6) h where h is a scaling parameter. Apparently, h has a strong influence on the results of estimations in that it decides how much smoothing will be allowed to the sample data. In this study, the technique of k-fold cross-validation (Refaeilzadeh et al., 2009) is used to determine the optimum scaling parameter from a number of candidate values. As schematically shown in Figure 4-9, the k-fold cross-validation randomly divides the original sample into k equal sized subsamples, of which a single subsample is retained as the validation dataset, and the remaining k-1 subsamples are used as training dataset. This process is repeated k times, with each of the k subsamples being used exactly once as the validation dataset. For each fold of data, quantitative measure of fit such as mean squared error (MSE) can be used to evaluate the level of fit of the trained model to the validation dataset. Then the k MSE from each fold of data are averaged to produce a

Texas Tech University, Liang Wu, August 2019 single evaluation for the candidate scaling parameter. The scaling parameter that has the best performance (i.e., the lowest MSE) is chosen as the optimal scaling parameter.

Sample 1 Sample 2 • • • Sample k-1 Sample k

Training Validation

k samples

3 -fold k • • •

Figure 4-9 Illustration of k-fold cross-validation (Xiao and Zuo, 2015) 4.5.2. Illustrative Example

As an illustrative example, the data interpretation techniques based on adaptive Gaussian filtering and k-fold cross validation are used to estimate the time-varying variance of the internal pressure coefficient, for Case 3 (i.e., the building model with the door being open). Figure 4-10 shows an example time history of the internal pressure coefficient for Case 3 when the building orientation angle is 0° and the building model translates at a velocity of 1.0 m/s relative to the single-celled vortex. First, the fluctuating components of Ctpi ( ) is obtained by subtracting the time-varying mean from the original time history. The time-varying mean of the internal pressure is estimated using the Sym5 wavelet and corresponds to the 7th level DWT (Percival and Walden, 2006) of the pressure coefficient. Then the 10-fold cross-validation technique is used to determine the optimal scaling parameter of the adaptive Gaussian kernel. With this scaling parameter, the adaptive filter variance of the Gaussian kernel is determined by Eqs.(4.5) and (4.6). Then the time-varying variances of each time history of the internal pressure coefficient are estimated by convolving the square of the sample data

Texas Tech University, Liang Wu, August 2019 points with the adaptive Gaussian kernel according to Eqs.(4.3) and (4.4). This procedure is repeated 10 times for an ensemble of 10 pressure measurements. Finally, the time-varying variance of the internal pressure coefficient is computed as the ensemble average of the time histories of the variance estimated based on the 10 individual records of internal pressure measured at the same location. Figure 4-11 (a) shows the MSE of the candidate scaling parameters ranging from 0.1 to 10 (with a spacing interval of 0.1) estimated via the 10-fold cross-validation. It is observed that the scaling parameter of 0.4 achieves the lowest MSE and is then selected as the optimal scaling parameter. With this scaling parameter, the time-varying variance of a sample time history is estimated by adaptive Gaussian filtering, which is shown in Figure 4-11 (b). By averaging the time-varying variances of each sample time history, the time- varying variance of the internal pressure coefficient is obtained, which is shown in Figure 4-11 (c). For comparison, the time-varying variance that is estimated directly (i.e., computed at each identical time instant across all the samples) from a much larger ensemble consisted of 100 pressure measurements taken at the same test configuration is also shown in Figure 4-11 (c). It is seen in Figure 4-11 (c) that the time varying variance of the internal pressure estimated using adaptive Gaussian filtering technique is close to the time-varying variance estimated based on the 100 measurements. Considering the number of measurements used by adaptive Gaussian filtering, the presented approach can greatly reduce the workload for laboratory simulations.

Figure 4-10 Example time history of the internal pressure coefficient for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at 1.0 m/s

Texas Tech University, Liang Wu, August 2019 MSE

Figure 4-11 (a) MSE resulting from different scaling parameters, (b) Time-varying variance of a sample time history estimated using adaptive Gaussian filtering, and (c) Comparison between the time-varying variances estimated directly from an ensemble of 100 measurements and using adaptive Gaussian filtering based on 10 measurements for the building model of Case 3 (open front door) in the single-celled vortex translating at 1.0 m/s Since two-celled vortices have distinct flow structures and pressure fields from single-celled vortices (Tang et al., 2018a), to further illustrate the effectiveness of the method for estimating the statistics of nonstationary process based on adaptive Gaussian filtering and cross-validation, Figure 4-12 shows the same kind of comparison for Case 3 when the building model translates at a speed of 1.0 m/s relative to the two-celled vortex. The sizes of the ensembles used for adaptive Gaussian filtering and direct measurement estimation are still 10 and 100, respectively. As seen in Figure 4-12, the

2 Ctp () estimated by adaptive Gaussian filtering can reasonably match that estimated directly from the ensemble of 100 measurements, showing that the described approach for estimating the statistics of nonstationary process is also applicable to two-celled vortices. Therefore, in this study whenever there are only 10 repetitive measurements

Texas Tech University, Liang Wu, August 2019 available for the experimental configuration, adaptive Gaussian filtering will be used to estimate the time-varying variance or the time-varying standard deviation at this configuration.

Figure 4-12 Comparison between the time-varying variances of the internal pressure coefficient estimated directly from an ensemble of 100 measurements and using adaptive Gaussian filtering based on 10 measurements for the building model of Case 3 (open front door) in the two-celled vortex translating at 1.0 m/s 4.6. Experimental Results

As mentioned earlier, for Case 3 (i.e., the building model with a door opening) at the building orientation angle of 0°, the experiments are repeated 100 times, while at the other test configurations, the experiments are only repeated 10 times. The probability distribution of the extreme values of tornadic loading can be inferred from the larger ensemble of measurements taken for Case 3. Because the internal pressure coefficient in tornadic flow is mostly negative according to the pressure measurements in this study, Figure 4-13 (a) and (b) show the histograms of the minimum internal pressure coefficient for Case 3 when the building model translates at speed of 1.0 m/s relative to the single-celled and two-celled vortices, respectively. Assuming that the peak values follow the Type I extreme value distribution and performing the Anderson-Darling test (Anderson and Darling, 1954) for goodness-of-fit, it is found that the p-values are 0.1092 for VS3, and 0.1027 for VD3. Since the p-values are both larger than 0.05, the Anderson-Darling tests fail to reject the null hypothesis that the samples come from a Type I extreme value distribution at the significance level of 0.05. Therefore, in the following, the extreme values of tornadic loading are estimated using the Gringorten’s method (Gringorten, 1963), which gives a nearly unbiased estimate for the parameters

Texas Tech University, Liang Wu, August 2019 of the Type I extreme value distribution. The probability density functions (PDF) of the estimated extreme value distributions are also plotted in Figure 4-13.

(b) 40 2

30 1.5

20 1 PDF PDF Frequency Frequency 10 0.5

0 0 -4 -3 -2 -1

Figure 4-13 Histogram and estimated PDF of the minimum internal pressure coefficient for the building model of Case 3 (open front door) at   0 in (a) the single-celled vortex translating at 1.0 m/s and (b) the two-celled vortex translating at 1.0 m/s 4.6.1. Effect of Internal Volume Augmentation

4.6.1.1. Preliminary Numerical Simulation Results

For experimental study of the internal pressure in building models in boundary layer wind tunnels, the internal volumes of building models must be artificially augmented to maintain dynamic similarity (e.g., natural frequency and amplitude of internal pressure fluctuations) to faithfully capture the effect of Helmholtz resonance. While this approach have also been applied by some researchers in the experimental studies of internal pressures in building models exposed to simulated tornadic flows (e.g., Thampi et al., 2011; Sabareesh et al., 2013a; Letchford et al., 2015), the necessity or validity of it for the wind load experiments in tornadic flows is still unclear. As a preliminary investigation, time histories of the internal pressure in the building model with the door in the front wall open, and both with and without internal volume augmentation are simulated based on the Helmholtz resonator equation (i.e., Eq.(3.13)). For each simulation, a time history of the external pressure measured in VorTECH is used as the input in Eq.(3.13), and the fourth-order Runge-Kutta method (Rao, 2001) is applied to numerically solve the Helmholtz resonator equation for the internal pressure.

Figure 4-14 (a) shows an example time history of the external pressure coefficient calculated based on the pressures measured in the vicinity of the door of the WERFL

Texas Tech University, Liang Wu, August 2019 building model when the model translates at a speed of 0.5 m/s relative to a two-celled vortex. Figure 4-14 (b) shows the time history of the simulated internal pressure coefficient for the case of the building model with an augmented internal volume. To investigate the effect of internal volume augmentation, the time history of the internal pressure coefficient for the same building configuration but without internal volume augmentation is also simulated, which is shown in Figure 4-14 (c). Comparing Figure 4-14 (b) and (c), it is clearly seen that the time histories of the internal pressure coefficient in the building models with and without volume augmentation are very  different. Figure 4-15 plots the fluctuating components (Ctpi ( ) ) of the two simulated internal pressure coefficients shown in Figure 4-14, which are obtained by subtracting the corresponding time-varying mean from the original time histories. The time-varying means are estimated using the Sym5 wavelet and is corresponding to the 6th level DWT (Percival and Walden, 2006) of the pressure coefficients. It is clearly seen that the fluctuations of the internal pressure is stronger in the building model without internal volume augmentation than in the model with internal volume augmentation. As indicated by Eq.(3.13), the damping of the system, which is the second term on the left side of the equation, critically depends on the ratio of the internal volume to the opening area, i.e., VA0 . As a result, the damping is reduced when the augmented volume does not exist, which leads to a less attenuated internal pressure. This indicates that for tornadic loadings, which are highly non-stationary, the effect of damping on the fluctuations of the internal pressure is still considerable, and the effect of internal volume augmentation on the simulations of tornadic loadings on low-rise buildings deserves further laboratory study.

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Figure 4-14 (a) Example time history of the external pressure coefficient, (b) Time history of the simulated internal pressure coefficient for the model with internal volume augmentation, and (c) Time history of the simulated internal pressure coefficient for the model without internal volume augmentation

(a) (b) With volume augmentation Without volume augmentation

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Figure 4-15 (a) Time history of the fluctuations of the internal pressure coefficient for the model with internal volume augmentation, (b) Time history of the fluctuations of the internal pressure coefficient for the model without internal volume augmentation

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To validate whether the numerical method used above can effectively predict the characteristics of the internal pressure based on the external pressure measurements, a time history of internal pressure coefficient for boundary-layer-type winds is also simulated. The external pressure measurement of Case 5 (see Table 3-2) presented in CHAPTER 3, which is also the configuration of the building with only the door opening, is used for the simulation of the internal pressure coefficient. Figure 4-16 (a) shows the power spectral density (PSD) functions of the external pressure coefficient at the door opening and the simulated internal pressure coefficient. An obvious peak is observed in the PSD of the simulated internal pressure coefficient, indicating the resonance of the internal pressure. Figure 4-16 (b) further compares the PSD of the measured and the simulated internal pressure coefficients. It is observed that the shapes of the two PSDs are very similar with the only difference that the PSD of the measured internal pressure coefficient is slightly smaller than that of the simulated internal pressure coefficient. The reason for this minor difference is that the influence of the background leakages, which is present in the experiment, on internal pressures is neglected in Eq.(3.13). As indicated by the study of Vickery and Bloxham (1992), the existence of background leakage can reduce the magnitude of internal pressure fluctuations in buildings with dominant opening(s).

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Figure 4-16 (a) Comparison between the PSD of the external and the simulated internal pressure coefficients, and (b) Comparison between the PSD of the measured and the simulated internal pressure coefficients 4.6.1.2. Physical Simulation Results

As suggested by the numerical simulations presented above, internal volume augmentation can attenuate the fluctuations of the internal pressure of a building in

Texas Tech University, Liang Wu, August 2019 tornadic flow. To further investigate the effect of internal volume augmentation on tornadic experiments, in the following the physical experiment results between the cases with and without scaled volume chamber are compared.

Figure 4-17 (a) and (b) show example internal pressure time histories for Case 2 and Case 3, respectively. For Case 2, the building model has a door opening but no internal volume augmentation, while for Case 3, the building model not only has a door opening but also internal volume augmentation. The pressure coefficients for the two cases shown in Figure 4-17 are measured when the building orientation angle is 0° and the building model translates at a speed of 1.0 m/s relative to the two-celled vortex. It is clearly seen in Figure 4-17 that the fluctuations of the internal pressure are much stronger in Case 2 than Case 3. To further study this phenomenon, Figure 4-18 (a) and (b) show the estimated time-varying mean and time-varying standard deviation (STD) of the internal pressure coefficient for Case 2 and Case 3, respectively. As seen in Figure

4-18 (a), in the time region between 2.8 and 3.2 seconds, the Ctpi () exhibit remarkable differences between the two cases, while outside this time region, the Ctpi () of the two cases are similar with each other. For the time-varying STD, Figure 4-18 (b) show that the Ctpi ( ) for Case 2 is much larger than that for Case 3 at almost all time points. The physical simulation results also show that internal volume augmentation can significantly attenuate the fluctuations of the internal pressures in building models exposed to translating vortices.

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(a) (b)

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Figure 4-17 Example Time history of the internal pressure coefficient for (a) Case 2 (the building model with the door opening but without volume augmentation) at   0 , and (b) Case 3 (the building model with the door opening and volume augmentation) at   0

(a) (b) Case 2 Case 3

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 Figure 4-18 (a) Time-varying mean of Cpi for Case 2 and Case 3 at   0 , and (b)  Time-varying STD of Cpi for Case 2 and Case 3 at   0 (Case 2: the building model with the door opening but without volume augmentation; Case 3: the building model with the door opening and volume augmentation) 4.6.2. Effect of Translation Speed

To investigate the effect of tornado translation speed on tornadic loading, the internal pressure coefficients in the building model exposed to vortices with different floor translation speeds are compared. Figure 4-19 (a) shows a comparison between the time-varying means of the internal pressure coefficient for the building model of configuration Case 3 (i.e., the building model with a door opening) translating at VS2 and VS3, i.e., 0.5 m/s and 1.0 m/s, relative to the single-celled vortex. At these test configurations, experiments are repeated 100 times. Because large datasets of repetitive test runs are available, the time-varying means shown in Figure 4-19 (a) are the

Texas Tech University, Liang Wu, August 2019 ensemble average of the internal pressure coefficients of each test run. Figure 4-19 shows that the magnitude of the mean internal pressure coefficient of the building model translating at VS2 is larger than that of the building model translating at VS3, indicating that in single-celled vortices an increase of translation speed can decrease the magnitude of the mean internal pressure coefficient. Figure 4-19 (b) shows a comparison between the time-varying standard deviations (STD) of the internal pressure coefficient for the building model translating at VS2 and VS3 relative to the single-celled vortex. The time- varying STD shown in Figure 4-19 (b) are also estimated directly from the ensemble of 100 measurements, i.e., computed at each identical time instant across all the sample measurements. Figure 4-19 (b) shows that the fluctuations of the internal pressure coefficient in single-celled vortices decrease with the increase of translation speed.

(a) (b) VS2 VS3

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Figure 4-19 (a) Time-varying mean, and (b) Time-varying STD of the internal pressure coefficient for the building model of Case 3 (open front door) at   0 in the single- celled vortex translating at VS2 (0.5 m/) and VS3 (1.0 m/s) Figure 4-20 shows a similar comparison between the statistics, i.e., the time-varying mean and time-varying STD, of the internal pressure coefficients for the building model of configuration Case 3 translating at VD2 and VD3, i.e., 0.5 m/s and 1.0 m/s, relative to the two-celled vortex. Unlike in single-celled vortices, the effect of translation speed on the mean internal pressure coefficient in two-celled vortices are much more complex. Figure 4-20 (a) shows that in the time region between 2.7 and 3.1 seconds, the magnitude of the mean internal pressure coefficient of the building model translating at VD3 is larger than that of the building model translating at VD2, while outside this region, the magnitude of the mean internal pressure coefficient of the building model translating at VD3 is smaller than that of the building model translating at VD2. In

Texas Tech University, Liang Wu, August 2019 addition, Figure 4-20 (b) shows that the time-varying STD of the internal pressure coefficient in two-celled vortices also decrease with the increase of the translation speed of the building model.

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Figure 4-20 (a) Time-varying mean, and (b) Time-varying STD of the internal pressure coefficient for the building model of Case 3 (open front door) at   0 in the two- celled vortex translating at VD2 (0.5 m/s) and VD3 (0.5 m/s) The effect of translation speed on the force coefficients in single-celled and two- celled vortices are also studied. Figure 4-22 shows the time-varying means of CFx , CFy , and CFz for the building model of configuration Case 3 (i.e., the building model with a door opening) at the building orientation angle of 0° translating at VD2 and VD3, i.e., 0.5 m/s and 1.0 m/s, relative to the two-celled vortex. The time-varying means shown in Figure 4-22 are the ensemble average of the force coefficients of the 100 repetitive test runs. As seen in Figure 4-22, the extreme values of the time-varying mean force coefficients of the building model translating at VD3 are all larger than the corresponding extreme values of the building model translating at VD2 in magnitude. Except for those differences in the magnitude of the mean force coefficients, the force coefficients in the two vortices also exhibit similar patterns with each other. Figure 4-21 shows a schematic drawing of the directions of the positive lateral and uplift force components when the building orientation angle is 0°. According to Figure 4-21 and the

CtFx () shown in Figure 4-22 (a), as the vortex translates relative to the building model, the model is first pulled in the negative x direction, and then in the positive x direction, regardless of the translation speed. Since the simulated vortices are rotating counterclockwise, the CtFy () shown in Figure 4-22 (b) indicates that the tangential

Texas Tech University, Liang Wu, August 2019 wind velocity component will first exert a force in the positive y direction when the vortex approaches the model, and then in the negative y direction when the vortex leaves the model. For the mean uplift force coefficients (CtFz ()) shown in Figure 4-22 (c), because there is a large static pressure drop in the vortex core, the CtFz () for both VD2 and VD3 are positive at all time points.

Figure 4-21 Directions of the positive lateral and uplift force components when   0

Figure 4-22 Time-varying mean of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the two-celled vortex translating at VD2 (0.5 m/s) and VD3 (1.0 m/s)

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Figure 4-23 shows the time-varying standard deviations (STD) of CFx , CFy , and

CFz for Case 3 at the same building orientation when the building model translates at VD2 and VD3, i.e., 0.5 m/s and 1.0 m/s, relative to the two-celled vortex. The time- varying STD are estimated directly based on an ensemble of 100 measurements. As seen in Figure 4-23, the time-varying STD of all the force coefficients are larger for the building model translating at VD2 than for the building model translating at VD3, indicating that for two-celled vortices the fluctuations of the wind loading decrease with the increase of the translation speed.

Figure 4-23 Time-varying STD of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the two-celled vortex translating at VD2 (0.5 m/s) and VD3 (1.0 m/s) Similarly, Figure 4-24 and Figure 4-25 show the time-varying means and time- varying STD of the force coefficients for Case 3 at the same building orientation when the building model translates at VS2 and VS3, i.e., 0.5 m/s and 1.0 m/s, relative to the single-celled vortex. Previously, Figure 4-22 shows that for two-celled vortices, an increase of translation speed can increase the magnitudes of the extreme values of the

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Texas Tech University, Liang Wu, August 2019 mean force coefficients. However, for single-celled vortices, the effect of translation speed on the mean force coefficients are much more complex. It can be seen in Figure

4-24 (a) that CtFx () has larger magnitude of extreme values for the building model translating at VS2 than for the building model translating at VS3. Figure 4-24 (b) shows that the maximum value of CtFy () for the building model translating at VS2 is slightly larger than that for the building model translating at VS3, while the minimum value of

CtFy () for the building model translating at VS2 is smaller than that for the building model translating at VS3 in magnitude. Figure 4-24 (c) shows the mean uplift force coefficients of the building model translating at VS2 and VS3 relative to the single- celled vortex. It can be seen that the maximum value of CtFz () for the building model translating at VS2 is larger than that for the building model translating at VS3, but the minimum value of CtFz () for the building model translating at VS2 is slightly smaller than that for the building model translating at VS3 in magnitude. In addition, unlike in two-celled vortices, the CtFz () can be negative during the passage of single-celled vortices. In addition, Figure 4-25 shows that the time-varying STD of the lateral and uplift force coefficients of the building model exposed to the single-celled vortex also decrease with the increase of translation speed.

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Figure 4-24 Time-varying mean of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at VS2 (0.5 m/s) and VS3 (1.0 m/s)

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Figure 4-25 Time-varying STD of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at VS2 (0.5 m/s) and VS3 (1.0 m/s) Figure 4-26 shows the maximum value of the force coefficients of the building model translating at different speeds (i.e., VS2, VS3, VD2, and VD3) in the two types of vortices for the configuration Case 3 at different building orientation angles, and Figure 4-27 shows the corresponding minimum value of the force coefficients at these test configurations. The extreme force coefficients shown in the two figures are estimated using the Gringorten’s method (Gringorten, 1963). As seen in Figure 4-26 and Figure 4-27, for the building model translating in the two-celled vortex, the magnitudes of the extreme force coefficients all decrease with an increase of translation speed, regardless of the building orientation angle. For the building model translating in the single-celled vortex, such relationship applies to the maximum and minimum lateral force coefficients as well as the maximum uplift force coefficient. The only exception is the minimum uplift force coefficient. As seen in Figure 4-26 (c), at   45 and   90 , the magnitude of the minimum uplift force coefficient of the building model

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Texas Tech University, Liang Wu, August 2019 in the single-celled vortex translating at VS2 is smaller than that of the building model in the single-celled vortex translating at VS3.

Figure 4-26 Maximum value of the force coefficients for the building model of Case 3 (open front door) at different building orientation angles in the single-celled vortex translating at VS2 and VS3, and in the two-celled vortex translating at VD2 and VD3 (VS2: 0.5 m/s; VS3: 1.0 m/s; VD2: 0.5 m/s; VD3: 1.0 m/s)

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Figure 4-27 Minimum value of the force coefficients for the building model of Case 3 (open front door) at different building orientation angles in the single-celled vortex translating at VS2 and VS3, and in the two-celled vortex translating at VD2 and VD3 (VS2: 0.5 m/s; VS3: 1.0 m/s; VD2: 0.5 m/s; VD3: 1.0 m/s) To investigate the effect of translation speed on the internal pressure in buildings with multiple dominant openings, Figure 4-28 (a) and (b) show the time-varying STD of the internal pressure coefficient for the building model of configuration Case 5 (i.e., the building model with a door in the front and a window opening in the back wall) translating in the single-celled and two-celled vortices, respectively. Because only 10 tests are repeated for this configuration, the time-varying STD shown in Figure 4-28 are estimated using the presented approach based on adaptive Gaussian filtering and k-fold cross validation. As seen in Figure 4-28, for the building model in both single-celled and two-celled vortices, the time-varying STD of the internal pressure coefficient decrease with the increase of translation speed.

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(a) (b) VS2 VD2 VS3 VD3

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Figure 4-28 (a) Time-varying STD of the internal pressure coefficient of the building model in the single-celled vortex translating at VS2 and VS3, and (b) Time-varying STD of the internal pressure coefficient of the building model in the two-celled vortex translating at VD2 and VD3 for Case 5 (open front door and open back window) at   0 (VS2: 0.5 m/s; VS3: 1.0 m/s; VD2: 0.5 m/s; VD3: 1.0 m/s)

Figure 4-29 and Figure 4-30 show the time-varying STD of the force coefficients for the building model of configuration Case 5 translating in the single-celled and two- celled vortices, respectively. As shown in the two figures, the time-varying STD of the force coefficients in buildings with multiple dominant openings also decrease with an increase of translation speed.

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Figure 4-29 Time-varying STD of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 5 (open front door and open back window) at   0 in the single-celled vortex translating at VS2 (0.5 m/s) and VS3 (1.0 m/s)

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Figure 4-30 Time-varying STD of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 5 (open front door and open back window) at   0 in the two-celled vortex translating at VD2 (0.5 m/s) and VD3 (1.0 m/s) Figure 4-31 and Figure 4-32 show the maximum and minimum values of the force coefficients for the building model of configuration Case 5 at different building orientation angles translating in the single-celled and two-celled vortices, respectively. Again, except for the minimum uplift force coefficient in single-celled vortices, the magnitudes of the extreme lateral and uplift force coefficients in buildings with multiple dominant openings decrease with increasing translation speed.

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(a) VS2 VD2 VS3 VD3

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Figure 4-31 Maximum value of the force coefficients for the building model of Case 5 (open front door and open back window) at different building orientation angles in the single-celled vortex translating at VS2 and VS3, and in the two-celled vortex translating at VD2 and VD3 (VS2: 0.5 m/s; VS3: 1.0 m/s; VD2: 0.5 m/s; VD3: 1.0 m/s)

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Figure 4-32 Minimum value of the force coefficients for the building model of Case 5 (open front door and open back window) at different building orientation angles in the single-celled vortex translating at VS2 and VS3, and in the two-celled vortex translating at VD2 and VD3 (VS2: 0.5 m/s; VS3: 1.0 m/s; VD2: 0.5 m/s; VD3: 1.0 m/s) 4.6.3. Comparison between Loading by Tornadic and Boundary-layer-type Wind

It has been shown in CHAPTER 3 that in boundary-layer-type flow, the fluctuations of the internal pressure in the WERFL building model with a door opening can be significantly amplified as a result of Helmholtz resonance (see Figure 3-26). To investigate whether internal pressure resonance also occurs in tornadic flow, the (evolutionary) power spectral density functions of the external and internal pressure coefficients for the building model of configuration Case 3 (i.e., the building model with a door opening) are studied. Figure 4-33 shows the power spectral density (PSD) functions of the external pressure coefficient at the door opening and the internal pressure coefficient for the building model of configuration Case 3 mounted statically at the center of the single-celled vortex. According to Eq. (3.14), the undamped Helmholtz frequency for the 1:100 WERFL building model is 58.5 Hz. As seen in

Figure 4-33, an obvious peak in the PSD of Cpi is present near this frequency. This

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Texas Tech University, Liang Wu, August 2019 suggests that internal pressure resonance can occur in building models exposed to stationary tornado-like vortices. ) -1 PSD (Hz

Figure 4-33 PSD functions of the external and internal pressure coefficients for the building model of Case 3 (open front door) mounted statically at the center of the single- celled vortex For translating vortices, it may be harder for internal pressure resonance to occur as the frequency characteristics of the external pressure changes with the time. Figure 4-34 shows the evolutionary power spectral density (EPSD) functions of the external and internal pressure coefficients for the building model of configuration Case 3 at the building orientation angle of 0° translating at 0.5 m/s relative to the single-celled vortex. The complex Morlet wavelet with a central frequency of 0.8 Hz is used for the estimation of the EPSD functions. As seen in Figure 4-34, most energy of Ctpe ( ) and

Ctpi () are concentrated within the same frequency band between 0.7 and 2.0 Hz, and the magnitude of the EPSD of the Ctpe () is larger than that of the Ctpi (). There is no evidence of occurrence of internal pressure resonance in Figure 4-34. Figure 4-35 shows the pseudo power spectral density (PSD) functions of Ctpe ( ) and Ctpi ( ) , obtained by integrating the corresponding EPSD functions over the time axis. As mentioned earlier, the undamped Helmholtz frequency for this model is 58.5 Hz. In Figure 4-35, there is no obvious peak near this frequency in the pseudo PSD of the Ctpi ( ) . Therefore, it is shown that internal pressure resonance cannot happen in building models exposed to translating vortices.

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Figure 4-34 EPSD functions of (a) the external pressure coefficient, and (b) the internal pressure coefficient for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at 0.5 m/s ) -1 PSD (Hz

Figure 4-35 Pseudo PSD functions of the external and internal pressure coefficients for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at 0.5 m/s Although the proposed study planned to compare the peak wind loads induced by tornadic and boundary-layer-type winds, it is later determined that such comparison is very challenging as many concepts that apply to boundary-layer-type wind do not exist in tornadic flow. For instance, in the previous wind tunnel tests the length of each measurement is 48 seconds which corresponds to 10 minutes at full scale. But for laboratory simulations, with the increase of translation speed, the time which the vortex takes to travel from one end to the other end of the building model will be less. Therefore, it is very hard to match the time scales between the experiments in the boundary-layer wind tunnel and in VorTECH. In addition, the pressure coefficients of the building model tested in VorTECH are obtained by normalizing the raw pressure with the dynamic pressure based on the mean horizontal wind speed measured in stationary

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Texas Tech University, Liang Wu, August 2019 vortices associated with a 2-minute model-scale averaging time, which does not have an appropriate physical counterpart at full scale. By contrast, the pressure coefficients in boundary-layer wind tunnel tests are obtained by normalizing the raw pressure with the dynamic pressure based on the mean wind speed associated with a 48-second model- scale averaging time, which corresponds to the 10-minute mean wind speed at full scale. Because of these reasons, instead of directly comparing the magnitudes of the peak force coefficients in the two types of wind, this study focuses on the differences between the probabilistic characteristics of the loadings induced by the two types of wind.

Figure 4-36 and Figure 4-37 show the time-varying skewness and kurtosis of the force coefficients for the building model of configuration Case 3 at the building orientation angle of 0° translating at 0.5 m/s relative to the single-celled vortex. Also plotted in the two figures are the statistics of the force coefficients for the building model of the same configuration of opening at the wind direction of 0° (i.e., the wind direction is perpendicular to the front wall) in the boundary-layer wind tunnel (BLWT). Figure 4-36 shows that the skewness of the force coefficients for the building model tested in BLWT are closed to 0, and Figure 4-37 shows that the kurtosis of the force coefficients for the building model tested in BLWT are closed to 3. Therefore, the wind loadings induced by boundary-layer-type flow can be approximately considered as Gaussian processes (Davenport, 1961). By contrast, it is observed that between the time instants of 2.0 and 4.0 seconds, the skewness and kurtosis of the force coefficients induced by the single-celled vortex are far away from those of a Gaussian process, indicating that these loadings are highly non-Gaussian. Similarly, Figure 4-38 and Figure 4-39 show the time-varying skewness and kurtosis of the force coefficients for the building model of configuration Case 3 at the same building orientation translating at 0.5 m/s relative to the two-celled vortex, respectively. It is shown by Figure 4-38 and Figure 4-39 that between 1.0 and 2.5 seconds, the skewness and kurtosis of the force coefficients for the building model exposed to the two-celled vortex are also much different from those of a Gaussian process. Therefore, it is concluded that during the passage of tornadoes, the loadings induced by tornadic winds can be highly non-Gaussian.

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Figure 4-36 Time-varying skewness of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at 0.5 m/s

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Figure 4-37 Time-varying kurtosis of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the single-celled vortex translating at 0.5 m/s

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Figure 4-38 Time-varying skewness of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the two-celled vortex translating at 0.5 m/s

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Figure 4-39 Time-varying kurtosis of (a) CFx , (b) CFy , and (c) CFz for the building model of Case 3 (open front door) at   0 in the two-celled vortex translating at 0.5 m/s Currently, the position sensor which is used to measure the location of the building model cannot synchronize with the pressure acquisition system. Therefore, the skewness and kurtosis shown in Figure 4-36 and Figure 4-37 cannot be correlated with the location of the building model during translation. Because the building model is also tested at a few radial locations relative to the vortex center when the simulator floor is held stationary, the loading data from the experiments at these configurations can be used to explore the relationship of the probabilistic characteristics of tornadic loading with the radial location of the building model. Figure 4-40 shows the kurtosis of the force coefficients of the building model of configuration Case 3 oriented at   0 measured at six different radial locations (i.e., 0, 0.5 rc , rc , 2 rc , 3 rc , and 4 rc ) relative to the centers of the single-celled and two-celled vortices, respectively. As seen in this figure, when the building model is in the single-celled vortex, the forces acting on the model are highly non-Gaussian at rr 2 c , and close to be Gaussian when the center of

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the model is far away from the center of the vortex (i.e., rr 3 c ) or close to the center of the vortex. By contrast, when the building model is in the two-celled vortex, the forces acting on the model are highly non-Gaussian when the center of the model is close to the center of the vortex, and close to be Gaussian when the center of the model is far away from the center of the vortex (i.e., rr 0.5 c ).

(a) 9 (b) 9

6 6

3 3

0 0 01234 01234 r/r r/r c c

Figure 4-40 Kurtosis of the force coefficients for the building model of Case 3 (open front door) at   0 mounted statically in (a) the single-celled vortex, and (b) the two- celled vortex 4.7. Summary

A model of the WERFL building with the same configurations of openings as those of the model tested in the boundary layer wind tunnel was tested in a large-scale tornado simulator, with and without internal volume augmentation. Since tornadic loadings are nonstationary in nature, a data interpretation technique based on adaptive Gaussian filtering and cross validation was used to characterize the non-stationary tornadic loading.

Preliminary numerical simulations suggests that internal volume augmentation can attenuate the fluctuations of internal pressures for tornadic loadings. This is confirmed by the physical experiments in the tornado simulator. The experimental results have shown that the time-varying standard deviation (STD) of the internal coefficient in the model with internal volume augmentation can be much smaller than that in the model without internal volume augmentation.

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The effect of translation speed of tornado-like vortex on tornadic loadings are also studied. It is shown that for both buildings with a single dominant opening and buildings with multiple dominant openings, an increase of translation speed can reduce the fluctuations of the internal pressures and the fluctuations of the lateral and uplift forces in the two types of buildings. In addition, except the minimum uplift force acting on the model by the single-celled vortices, an increase of translation speed can also reduce the magnitudes of the extreme lateral and uplift forces in the two types of buildings.

The characteristics of the loading induced by tornadic and boundary-layer-type winds are compared in this study. In the experiments in the boundary layer wind tunnel, internal pressure resonance was observed when there was a door opening present in the envelope of the WERFL building model. Such phenomenon is observed when the WERFL building model is exposed to stationary vortices, but not observed when the building model translates relative to the simulated vortices. In addition, unlike loadings induced by boundary-layer-type flow, tornadic loadings can be highly non-Gaussian, when the building model is at some locations relative to the center of the simulated vortices.

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CHAPTER 5

CONCLUSIONS AND FUTURE WORK

The goal of this study is to develop a comprehensive understanding of the loading on low-rise buildings exposed to translating tornadoes considering both the external and internal pressures. The main conclusions from this research and recommendations for future work are summarized below.

5.1. Conclusions

Tornado-like vortices with different swirl ratios and radial Reynolds numbers were simulated in the VorTECH simulator. It is revealed that the swirl ratio critically affects the simulation of the vortices. For instance, flow velocity measurements show that the flow transitions from a single-celled to a two-celled vortex with increasing swirl ratio, symbolled by the development of central downdraft extending to the surface. In addition, the surface pressure measurements show that with the increase of swirl ratio, the single sharp pressure drop appearing inside the core of single-celled vortices flattens and eventually develops into a shape with two valleys in two-celled vortices. For the radial Reynolds number, it is found that both the mean and fluctuating characteristics of simulated vortices are not significantly affected by this parameter, provided the radial Reynolds number is sufficiently large.

A model of the WERFL building with various configurations of openings and leakages was tested in the boundary layer wind tunnel at Texas Tech University. It is found that the presence of dominant openings and background leakages does not significantly affect the mean or fluctuating characteristics of the external pressure. It is also revealed that internal pressure resonance occurs in the WERFL building model when a large door opening is present in its front wall. Analysis of the force coefficients show that increasing background leakage can reduce the mean and fluctuations of the uplift force for nominally sealed buildings, and for buildings with a single dominant opening, the magnitude of the extreme uplift force increases with the increase of the opening area. In addition, for buildings with multiple dominant openings, the magnitude

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Texas Tech University, Liang Wu, August 2019 of the extreme uplift force is also affected by the locations of individual dominant opening.

Another model of the WERFL building with the same configurations of openings of the model tested in the boundary layer wind tunnel was tested in a large-scale tornado simulator, with and without internal volume augmentation. The experimental results show that the fluctuations of the internal pressure in the building model without internal volume augmentation are much stronger than those in the building model with internal volume augmentation. It is also shown that for both buildings with a single dominant opening and buildings with multiple dominant openings, an increase of translation speed of the tornado-like vortex can reduce the fluctuations of the internal pressure and the fluctuations of the lateral and uplift forces. In addition, except for the minimum uplift force acting on the model in single-celled vortices, an increase of translation speed can reduce the magnitudes of the peak lateral and uplift forces in the two types of buildings. While internal pressure resonance was observed in the building model in boundary- layer-type flow, this type of resonance is observed only when the tornado-like vortices are stationary relative to the building model. When the tornado-like vortices translate relative to the building model, internal pressure resonance is not observed because the external pressure acting on the model by translating vortices is nonstationary due to the spatial variations of both the wind velocity and the static pressure in the vortices. Lastly, an interpretation of the skewness and kurtosis of the force acting on the building model shows that the loading induced by boundary-layer-type wind are approximately Gaussian while tornadic loadings can be highly non-Gaussian when the building is at certain locations relative to the tornado-like vortices.

5.2. Future Work

Currently, the position sensor which is used to measure the location of the building model in the experiments in the tornado simulator cannot synchronize with the pressure acquisition system. As a result, the pressure measurements cannot be correlated with the location of the building model when the building translates relative to the simulated vortex. A future study can be conducted to investigate the characteristics of tornadic loadings at different locations relative to the center of vortices when the position and

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This study selected the WERFL building as the subject of study for the research of tornadic loadings. Because the WERFL building is a nearly-flat-roofed low-rise building, in the future models of buildings of other roof types with separate attic space will be tested in both a boundary-layer wind tunnel and the VorTECH simulator. With these experiments, the effect of compartmentalization on tornadic loadings can be investigated.

This study mainly focused on the loading on the WERFL building for the main wind force resisting system (MWFRS). The wind loading for components and cladding has not been systematically studied in the dissertation. Future work might consider comparing the characteristics of loading induced tornadic and boundary-layer-type wind for components and cladding.

One inherent limitation of laboratory simulations is that the size of the simulated vortices is relatively small. Refan et al. (2014) showed that the ratio of the core radius of full-scale tornadoes to generated vortices in tornado simulators are usually on the order of thousands. If building models are constructed using this length scale, it would be impossible to place enough external pressure taps to capture the local pressure fluctuations on building surfaces. However, such limitation does not exist in numerical simulations. In future work, the experimental results from the VorTECH simulator can be used to validate the numerical model created by the computational fluid dynamics (CFD) software. The validated model can be used subsequently to simulate the tornado flow fields around certain building geometries. From the numerical simulations, the tornadic loading on the building can be investigated.

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