University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Masters Theses Graduate School 12-2011 Quasi-One-Dimensional Flow for Use in Real-Time Facility Simulations Brett Matthew Boylston [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_gradthes Recommended Citation Boylston, Brett Matthew, "Quasi-One-Dimensional Flow for Use in Real-Time Facility Simulations. " Master's Thesis, University of Tennessee, 2011. https://trace.tennessee.edu/utk_gradthes/1058 This Thesis is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Masters Theses by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a thesis written by Brett Matthew Boylston entitled "Quasi-One- Dimensional Flow for Use in Real-Time Facility Simulations." I have examined the final electronic copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Master of Science, with a major in Aerospace Engineering. Trevor H. Moulden, Major Professor We have read this thesis and recommend its acceptance: Basil N. Antar, Ralph R. Jones Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Quasi-One-Dimensional Flow for Use in Real-Time Facility Simulations A Thesis Presented for the Master of Science Degree The University of Tennessee, Knoxville Brett Matthew Boylston December 2011 Acknowledgments I would like to thank the individuals and parties involved in helping me complete my thesis. None of this would have been possible without the work I perform at the Arnold Engineering Development Center. The opportunities I have had planted the seed for the work reported herein. A special thanks is in order for Dr. Greg Denny, who when the code became out of hand, suggested stepping back and taking a simpler approach. Lastly, I would like to thank my advisor, Dr. Trevor Moulden, for his patients and guidance throughout all of this. Thank you. ii Abstract Simulations have been, and continue to play, an important role at the Arnold Engineering Development Center as an aid in control system development and operator training. These models were just simple lumped-parameter methods. Since their initial inception, over ten years ago, little work has been done to increase the fidelity of the models. The processing power of the computer hardware used by the simulations has increased dramatically during this time and this left an opening for improvements to the models adopted in the simulation. To fill this void a quasi-one-dimensional control volume has been developed to run in real-time. The new control volume accounts for changes in area, transient effects, friction and other minor pressure losses, and localized heat transfer. All of which were previously unaccounted for. This new capability was compared against known analytical solutions and applied to an example flow system that demonstrates the new features. The result is a control volume that can be used in wind tunnel, or in other industrial process, simulations to provide a more realistic model. iii Table of Contents 1.0 Introduction ................................................................................................................................... 1 1.1 The Exiting Lumped-Parameter Method ................................................................................. 3 1.2 Improvements to the System .................................................................................................. 8 2.0 Current Needs and Development ................................................................................................ 10 3.0 Finite Volume Approach .............................................................................................................. 14 3.1 Conservation of Mass ............................................................................................................ 15 3.2 Conservation of Momentum ................................................................................................. 16 3.3 Conservation of Energy ......................................................................................................... 16 3.4 The Governing Equations for Quasi-One-Dimensional Flow ................................................ 18 3.4.1 Heat Transfer ........................................................................................................ 24 3.4.2 Friction and Other Minor Losses ........................................................................... 28 3.5 Discretization ........................................................................................................................ 32 3.6 Heun’s Method for Integration of the Time Derivatives ....................................................... 36 4.0 Implementation in Simulink® ....................................................................................................... 39 4.1 How to Use the New Control Volume in Simulink® .............................................................. 40 4.2 Interfacing with the Quasi-One-Dimensional Control Volume ............................................. 43 4.2.1 The Main Screen ................................................................................................... 45 4.2.2 The Geometry Screen ........................................................................................... 47 4.2.3 The Losses Screen ................................................................................................. 50 4.2.4 The Heat Transfer Screen ...................................................................................... 52 4.2.5 The Initial Conditions Screen ................................................................................ 54 iv 4.3 Organization of the Code ...................................................................................................... 54 4.3.1 Initialization ........................................................................................................... 56 4.3.2 Integration ............................................................................................................. 59 4.3.3 Time-rate of Change of Mass Flow ....................................................................... 59 4.3.4 Time-rate of Change of Mass and Energy ............................................................. 62 4.3.5 Time-rate of Change of Ducting Temperature ...................................................... 62 4.3.6 The Darcy Friction Factor ...................................................................................... 65 4.3.7 Heat Transfer Between the Fluid and Duct Wall .................................................. 65 5.0 Results and Comparison with Theory .......................................................................................... 67 5.1 Flow with Area Change ......................................................................................................... 68 5.2 Flow with Momentum Losses ............................................................................................... 81 5.3 Flow with Heat Transfer ........................................................................................................ 87 5.4 Transient Results ................................................................................................................... 94 5.5 Real-time Results ................................................................................................................... 99 6.0 Practical Example of a Flow Network ........................................................................................ 108 6.1 Tee Junction Block ............................................................................................................... 114 6.2 Analysis and Results of Example Network .......................................................................... 116 6.3 Real-time Results of Example Network ............................................................................... 125 6.4 Comparison Between the Quasi-One-Dimensional Code and the Lumped Parameter Method ...................................................................................................................................... 125 7.0 Conclusion .................................................................................................................................. 131 References .............................................................................................................................................. 133 v Vita .......................................................................................................................................................... 136 vi List of Tables Table 6.1 – Cold Leg Inputs ...................................................................................................................... 111 Table 6.2 – Hot Leg Inputs ........................................................................................................................ 111 Table 6.3 – Warm Leg Inputs ................................................................................................................... 112 Table 6.4 – Cold Leg Diameters