Complex fluid flows are encountered widely in nature, in living beings and in engineering practice. These flows often involve both geometric and dynamic complexity and present problems that are difficult to analyse because of their wide range of length and time scales, as well as their geometric configuration. This book describes some newly developed computational techniques and modelling strategies for analysing and predicting complex transport phenomena. It summarizes advances in the context of a pressure-based algorithm. Among methods discussed are discretization schemes for treating convection and pressure, parallel computing, multigrid methods, and composite, multiblock techniques. With respect to physical modelling, the book addresses issues of turbulence closure and multiscale, multiphase transport from an engineering viewpoint. Both fundamental and practical issues are considered, along with the relative merits of competing approaches. The final chapter is devoted to practical applications that illustrate the advantages of various numerical and physical tools. Numerous examples are given throughout the text. Mechanical, aerospace, chemical and materials engineers can use the techniques presented in this book to tackle important, practical problems more effectively.
Cryogenic cavitation experiences phase change in an environment where the vapor pressure is temperature dependent. The cavitation dynamics have critical implications on the performance and safety of liquid rocket engines, but there is no established method to estimate the actual loads due to cavitation on the inducer blades. To help develop such a computational capability, we conduct a systematic investigation of a transport-based, homogeneous cryogenic cavitation model for code validation and model improvement exercises. We assess the role of model parameters in the cavitation model and uncertainties in material properties via global sensitivity analysis coupled with multiple surrogate models including polynomial response surface, radial basis neural network, Kriging and a weighted average composite model. The results indicate that while the predictions are more sensitive to changes in cavitation model parameters than uncertainties in material properties, the impact of uncertainty in temperature dependent vapor pressure on the performance is significant. We calibrate the cryogenic cavitation model parameters using a multiple surrogates-based optimization strategy. The optimal parameters increase the importance of condensation terms and show improved prediction performance on a number of benchmark problems.
The implementation and verification of real-fluid effects towards the high-fidelity large eddy simulation of rocket combustors is reported. The non-ideal fluid behavior is modeled using a cubic Peng-Robinson equation of state; a thermodynamically consistent approach is used to convert conserved into primitive variables. The viscosity is estimated by Chung et al.'s method 1, 2 in the supercritical gas phase. In the transcritical liquid phase, a simple, accurate and efficient method to estimate the viscosity as a function of temperature and pressure is proposed. The highly non-linear coupling of the primitive thermodynamic variables requires special consideration in regions of high-density gradients to avoid spurious numerical oscillations. The characterization of the non-linearity of the equation of state identifies the regions of high sensitivity. In these regions, small relative changes in the pressure lead to significant changes in density and/or temperature, therefore, numerical instabilities tend to be amplified in these regions. To avoid non-physical oscillations, a first-order and second-order essentially non-oscillatory (ENO) schemes are locally applied to the flux computation on the faces identified with a dual-threshold relative density sensor. The evaluation of the sensor and capabilities of the non-oscillatory schemes on canonical test cases are presented. Finally, these schemes are used to model two canonical cases.
Two-dimensional driven cavity flows with the Reynolds number ranging from 10 2 to 3.2 x 10 3 are used to assess the performance of second-order upwind and central difference schemes for the convection terms. Three different implementations of the second-order upwind scheme are designed and tested in the context of the SIMPLE algorithm, with the grid size varying from 21 x 21 to 161 x 161 uniformly spaced nodes. Converged solutions are obtained for all Reynolds numbers. Although these different implementations of the second-order upwind scheme have the same formal order of accuracy, significant differences in numerical accuracy are observed. It is demonstrated that better performance can be obtained for the second-order upwind scheme if the discretization is cast in accordance with the finite volume formulation. Although both the second-order upwind and central difference schemes exhibit no oscillations in the solution, the upwind scheme is more accurate. In assessing and comparing the performance of these schemes, the distribution of cell Reynolds number is discussed and its impact on numerical accuracy illustrated.
I am grateful to several individuals for their support in my dissertation work. The greater part of this work was made possible by the instruction of my teachers, and the love and support of my family and friends. It is with my heartfelt gratitude that I acknowledge each of them. Firstly, I would like to express sincere thanks and appreciation to my advisor, Dr. Wei Shyy, for his excellent guidance, support, trust, and patience throughout my doctoral studies. I am very grateful for his remarkable wisdom, thought-provoking ideas, and critical questions during the course of my research work. I thank him for encouraging, motivating, and always prodding me to perform beyond my own limits. Secondly, I would like to express sincere gratitude towards my co-advisor, Dr. Nagaraj Arakere, for his firm support and caring attitude during some difficult times in my graduate studies. I also would like to express my appreciation to the members of my dissertation committee Dr. Louis Cattafesta, Dr. James Klausner, and Dr. Don Slinn, for their valuable comments and expertise to better my work. I deeply thank Dr. Siddharth Thakur (ST) for providing me substantial assistance with the STREAM code and for his cordial suggestions on research work and career planning. My thanks go to all the members of our lab, with whom I have had the privilege to work. Due to the presence of all these wonderful people, work is more enjoyable. In particular, it was a delightful experience to collaborate with Jiongyang Wu, Tushar Goel, and Baoning Zhang on various research topics. v I would like to express my deepest gratitude towards my family members. My parents have always provided me unconditional love. They have always given top priority to my education, which made it possible for me to pursue graduate studies in the United States. I would like to thank my grandparents for their selfless affection and loving attitude during my early years. My wife's parents and her sister's family have been extremely supportive throughout my graduate education. I greatly appreciate their trust in my abilities. Last but never least, I am thankful beyond words to my wife, Neeti Pathare. Together, we have walked through this memorable, cherishable, and joyful journey of graduate education. Her honest and unfaltering love has been my most precious possession all these times. I thank her for standing besides me every time and every where. To Neeti and my parents, I dedicate this thesis! vi
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