Characterization of Transition to Turbulence for Blood In
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CHARACTERIZATION OF TRANSITION TO TURBULENCE FOR BLOOD IN AN ECCENTRIC STENOSIS UNDER STEADY FLOW CONDITIONS Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Engineering David Casey December, 2014 CHARACTERIZATION OF TRANSITION TO TURBULENCE FOR BLOOD IN AN ECCENTRIC STENOSIS UNDER STEADY FLOW CONDITIONS David Casey Thesis Approved: Accepted: ____________________________ _____________________________ Advisor Department Chair Dr. Francis Loth Dr. Sergio D. Felicelli ____________________________ _____________________________ Committee Member Dean of the College Dr. Yang H. Yun Dr. George K. Haritos ____________________________ _____________________________ Committee Member Interim Dean of the Graduate School Dr. Abhilash Chandy Dr. Rex Ramsier _____________________________ Date ii ABSTRACT Blood is a complex fluid that consists of approximately 45% solid particulates by volume. These solid particulates, erythrocytes, cause the fluid to exhibit a non-Newtonian, shear thinning rheology under low shear rates (<200s-1) and Newtonian rheology otherwise. Many researchers employ Newtonian blood analogs to study the relationship between hemodynamics and morphogenesis when the predominant shear rates in the vessel are high. Non-biological, shear thinning fluids have been observed to transition from laminar to turbulent flow differently than Newtonian fluids. A discrepancy between the critical Reynolds number of blood and a Newtonian analog could result in erroneous predictions of hemodynamic forces. The goal of the present study was to compare velocity profiles near transition to turbulence of whole blood and a Newtonian blood analog downstream of a stenosis under steady flow conditions. Doppler ultrasound was used to measure velocity profiles of whole porcine blood and a Newtonian fluid in an in vitro experiment at 13 different Reynolds numbers ranging from 150 to 1200. Three samples of each fluid were examined and fluid rheology was measured before and after each experiment. Results show parabolic like velocity profiles for both whole blood and the Newtonian fluid at Reynolds numbers less than 250 (based on the viscosity at 400s-1). The Newtonian fluid had blunt velocity profiles with large velocity fluctuations (root iii mean square as high as 25%) starting at Reynolds numbers ~250 which indicated transition to turbulence. In contrast, whole blood did not transition to turbulence until a Reynolds number of ~300-600. All three blood samples were delayed compared to that of the Newtonian fluid, although there were variabilities between the critical Reynolds numbers. For Reynolds numbers larger than 700, the delay in transition resulted in differences in velocity profiles between the two fluids as high as 35%. A Newtonian assumption for blood at flow conditions near transition can lead to large errors in velocity prediction for steady flow in a post- stenotic flow field. Since this study was limited to a single velocity profile, further studies are required to fully understand the post-stenotic flow field. Further research is necessary to understand the importance of pulsatile flow and compliance. iv ACKNOWLEDGEMENTS I would like to start by acknowledging Nickolas Shaffer. Without the patience and teaching of Nick, I would not have lasted a single semester in undergraduate Engineering. Nick literally saved me from a life of Accountancy. I would also like to acknowledge Dale Eartly who graciously gave much of his time to help us design the experimental setup. I would like to thank my thesis committee members, Dr. Abhilash Chandy and Dr. Yang Yun, whose guidance and critiques have greatly improved the quality of thesis. This work builds upon the work of Dipankar Biswas, and I am deeply grateful that he allowed me to join him on his research project. His years of hard work and analysis made this study possible. I would like to thank my advisor, Dr. Francis Loth, who is the single handedly the most influential teacher I have ever had. He has taught me as much about life as he has about fluid mechanics. Finally, I would like acknowledge my loving wife Allison, whose encouragement and understanding kept me going even during the tough times. I love you more than I can express in words. -Dave v TABLE OF CONTENTS Page LIST OF TABLES ............................................................................................... viii LIST OF FIGURES ............................................................................................... ix CHAPTER I. INTRODUCTION ............................................................................................... 1 Introduction and Background .......................................................................... 1 Literature Review ............................................................................................ 2 Blood rheology ........................................................................................... 2 In Vivo Turbulence Studies ........................................................................ 3 Effects of Turbulence on the Cardiovascular System ................................ 5 In Vitro Transition to Turbulence Experiments ........................................... 6 Numerical Simulations ............................................................................. 14 Aim of Current Work ...................................................................................... 16 II. EXPERIMENTAL SETUP ............................................................................... 17 Eccentric Stenosis Geometry ........................................................................ 17 Experimental Flow Circuit.............................................................................. 19 Composition of Test Fluids ............................................................................ 24 Instrument Calibration ................................................................................... 25 Blood Rheology ............................................................................................. 25 Red Blood Cell Evaluation............................................................................. 26 vi Doppler Ultrasound Signal Processing .......................................................... 27 III. RESULTS ...................................................................................................... 29 IV. DISCUSSION ................................................................................................ 39 Limitations ..................................................................................................... 46 V. CONCLUSION ............................................................................................... 51 REFERENCES ................................................................................................... 52 APPENDICES .................................................................................................... 56 APPENDIX A. SUPPLIMENTARY FIGURES ................................................ 57 APPENDIX B. RHEOLGY PROCEDURES ................................................... 60 APPENDIX C. RHEOLOGY VALIDATION ................................................... 87 APPENDIX D. CURRICULUM VITAE ......................................................... 106 vii LIST OF TABLES Figure Page 1 Critical Re using different TT detection methods. .................................. 43 2 Viscosity standards reported viscosities [cP] ......................................... 103 viii LIST OF FIGURES Figure Page 1 Straight Pipe Velocity Time Traces ............................................................ 9 2 Straight Pipe Normalized Average Velocity Profiles. ............................... 10 3 Straight Pipe RMS as a Function of Re and Radial Position .................... 11 4 Straight Pipe Mean Percent Difference between BL and WG .................. 12 5 Eccentric Stenosis Model Rendering ....................................................... 18 6 Eccentric Stenosis Experimental Geometry ............................................. 19 7 Photo of Experimental Flow Circuit .......................................................... 22 8 Centrifugal Blood Pump ........................................................................... 23 9 Heat Exchanger Coil ................................................................................ 24 10 Average Rheology ................................................................................... 30 11 Representative Blood Micrographs .......................................................... 31 12 Velocity Time Trace for BL and WG Sample 1. ....................................... 32 13 Velocity Time Trace for BL and WG Sample 2. ....................................... 33 14 Velocity Time Trace for BL and WG Sample 3. ....................................... 34 15 Velocity Profiles for BL and WG Sample 1. .............................................. 35 16 Velocity Profiles for BL and WG Sample 2. .............................................. 36 17 Velocity Profiles for BL and WG sample 3 ............................................... 36 18 Mean velocity profiles .............................................................................. 37 19 RMS Velocity as a Function of Re and Radial Position. .......................... 38 ix 20 Percent Standard Error of Normalized Mean Velocity. ............................ 42 21 Mean Velocity Percent