Development of a Dynamic Model of a Counterflow Compact Heat Exchanger for Simulation of the Gt-Mhr Recuperator Using Matlab and Simulink
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DEVELOPMENT OF A DYNAMIC MODEL OF A COUNTERFLOW COMPACT HEAT EXCHANGER FOR SIMULATION OF THE GT-MHR RECUPERATOR USING MATLAB AND SIMULINK A THESIS Presented in Partial Fulfillment of the Requirements for the Degree of Master of Science in the Graduate School of The Ohio State University By David P. Hawn, B.S. ***** The Ohio State University 2009 Thesis Committee: Dr. Thomas Blue, Adviser Dr. Richard Christensen Approved by ___________________________________ Adviser Nuclear Engineering Graduate Program ABSTRACT A computational model was developed to determine the dynamic behavior of counter flow compact heat exchangers. This code was written with the intention of becoming a component of a larger system dynamics model of a Brayton cycle nuclear power plant. Several configurations for the GT-MHR recuperator were analyzed, but the code can easily be modified to analyze many types of compact heat exchangers with a variety of applications. Helium was the working fluid used in this project, but the code can be modified to use other gases. This code was written in Matlab and Simulink but the methods outlined in this report could be easily reapplied in other programming languages. This code is also useful for designing counter flow compact heat exchangers in general. In this model the heat exchanger is discretized in time and in space. The resolution of the discretization is defined by the user. Helium properties are reevaluated for each volume before each time step. The dynamic inputs to the model are the inlet temperature, mass flow rate and pressure for each side of the heat exchanger. This model assumes low Mach number flows and treats the propagation of pressure and mass flow rate changes as instantaneous. The outlet temperature and pressure drop for each side is determined. The results of the simulation were successfully validated against results available in the literature. Contact the author for a copy of this code. ii DEDICATION Dedicated to my family and friends iii ACKNOWLEDGEMENTS First I would like to thank my friends and family who were always supportive and patient throughout this process. I am especially grateful for my fiancée who spent countless late nights and weekends working with me in the computer labs of Scott Laboratories. I am also in debt to my adviser, Dr. Blue, for his support and patience throughout this project and my time in graduate school. Of course I also owe Dr. Blue thanks for reviewing my thesis. I would also like to thank Dr. Christensen for providing encouragement, answering many questions, sitting on my committee, and reviewing my thesis. I would also like to thank Dr. Freuler and everyone I had the pleasure to work with in the FEH program. The FEH program is top-notch and I hope I can give back to it as much as it has given to me. Finally, and most importantly, is thanks due to God for the amazing world in which we live and the relentless curiosity given to me to explore it. iv VITA.. February 27, 1982………………………..........……………Born – Columbus, Ohio, USA 2005……………………………B.S. Mechanical Engineering, The Ohio State University 2005-2006………………….………………University Fellow, The Ohio State University 2006-2008……………………...Graduate Teaching Assistant, The Ohio State University 2008-Present……………………………..………NRC Fellow, The Ohio State University PUBLICATIONS 1. “Theoretical and Experimental Analysis of Response of SiC in Thermal Neutron Environment”, V. Krishnan, B. Khorsandi, J. Kulisek, D. Hawn, T. E. Blue, and D.W., Transactions of the American Nuclear Society, v. 96, 2007, p. 705. FIELDS OF STUDY Major Field: Nuclear Engineering v TABLE OF CONTENTS Abstract ............................................................................................................................... ii Dedication .......................................................................................................................... iii Acknowledgements ............................................................................................................ iv Vita.. .................................................................................................................................... v List of Figures .................................................................................................................... ix List of Tables ..................................................................................................................... xi 1. Introduction ................................................................................................................. 1 1.1. Objectives ............................................................................................................. 4 1.2. Summary .............................................................................................................. 5 2. Literature Review........................................................................................................ 8 2.1. Introduction .......................................................................................................... 8 2.2. Evolution of the Design and Analysis of the GT-MHR Recuperator ................ 10 2.2.1. Introduction ................................................................................................. 10 2.2.2. 1994 General Atomics Recuperator Design ............................................... 11 2.2.3. 2003 General Atomics and OKBM Recuperator Design ............................ 14 2.3. Kays and London Compact Heat Exchanger Design Data ................................ 18 2.3.1. Selected Heat Exchange Surfaces and Geometric Relationships ............... 19 2.3.2. Empirical Data for Selected Heat Exchanger Cores ................................... 24 2.4. Compact Heat Exchanger Analysis .................................................................... 26 2.4.1. Static Analysis ............................................................................................ 27 2.4.1.1. Estimation of Average Gas Properties .................................................... 28 2.4.1.2. Determination of Outlet Temperatures ................................................... 30 2.4.1.3. Determination of Pressure Drop .............................................................. 35 2.4.2. Transient Analysis ...................................................................................... 38 2.5. Summary of Literature Review .......................................................................... 40 3. Recuperator modeling in Matlab & Simulink ........................................................... 42 3.1. Introduction ........................................................................................................ 42 3.2. Introduction to Matlab and Simulink ................................................................. 44 3.2.1. Differences between Matlab and Simulink ................................................. 44 3.2.2. Parallel Processing in Matlab and Simulink ............................................... 48 vi 3.3. Dynamic Model .................................................................................................. 49 3.3.1. Introduction ................................................................................................. 49 3.3.2. Assumptions ................................................................................................ 52 3.3.3. Model Revisions and Development ............................................................ 53 3.3.4. Heat Exchanger Discretization ................................................................... 55 3.3.5. User Definable Parameters and Initial Conditions ...................................... 60 3.3.5.1. Initial Conditions ..................................................................................... 61 3.3.5.2. Inlet Conditions ....................................................................................... 62 3.3.6. Property Lookup ......................................................................................... 63 3.3.7. Heat Transfer Model ................................................................................... 65 3.3.8. Pressure Drop Model .................................................................................. 70 3.3.8.1. Entrance and Exit Effects ........................................................................ 74 3.3.8.2. Flow Acceleration ................................................................................... 76 3.3.8.3. Core Friction ........................................................................................... 77 3.3.9. Determination of Values at End of Time Step ............................................ 78 3.3.10. Error Reporting ....................................................................................... 81 3.4. Data Output ........................................................................................................ 83 4. Validation .................................................................................................................. 86 4.1. Introduction ........................................................................................................ 86 4.2. Steady State Temperature Response .................................................................. 88 4.3. Steady State Pressure Drop ................................................................................ 92 4.4. Transient Temperature Response ....................................................................... 95 4.4.1.