[PDF] Weighted Essentially Non Oscillatory Simulations And Modeling Of Complex Hydrodynamic Flows Part 2 Single Mode Richtmyer Meshkov Instability With Reshock eBook
Weighted Essentially Non Oscillatory Simulations And Modeling Of Complex Hydrodynamic Flows Part 2 Single Mode Richtmyer Meshkov Instability With Reshock Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Weighted Essentially Non Oscillatory Simulations And Modeling Of Complex Hydrodynamic Flows Part 2 Single Mode Richtmyer Meshkov Instability With Reshock book. This book definitely worth reading, it is an incredibly well-written.
The Richtmyer-Meshkov instability is a fundamental fluid instability that occurs when perturbations on an interface separating gases with different properties grow following the passage of a shock. This instability is typically studied in shock tube experiments, and constitutes a fundamental example of a complex hydrodynamic flow. Numerical simulations and models for the instability growth and evolution have also been used to further elucidate the physics of the Richtmyer-Meshkov instability. In the present work, the formally high-order accurate weighted essentially non-oscillatory (WENO) shock-capturing method using a third-order total-variation diminishing (TVD) Runge-Kutta time-evolution scheme (as implemented in the HOPE code [68]) is applied to simulate the single-mode Richtmyer-Meshkov instability with reshock in two spatial dimensions. The initial conditions and computational domain for the simulations are modeled after the Collins and Jacobs [29] single-mode, Mach 1.21 air(acetone)/SF6 shock tube experiment. The following boundary conditions are used: (1) periodic in the spanwise direction corresponding to the cross section of the test section; (2) outflow at the entrance of the test section in the streamwise direction, and; (3) reflecting at the end wall of the test section in the streamwise direction. The present investigation has three principal motivations: (1) to provide additional validation of the HOPE code against available experimental data; (2) to provide numerical simulation data for detailed analysis of mixing induced by the Richtmyer-Meshkov instability with reshock, and; (3) to systematically investigate the dependence of mixing properties on both the order of WENO reconstruction and on the spatial resolution. The present study constitutes the first comprehensive application of the high-resolution WENO method to the Richtmyer-Meshkov instability with reshock, as well as analysis of the resulting mixing.
The Richtmyer-Meshkov instability is a fundamental fluid instability that occurs when perturbations on an interface separating gases with different properties grow following the passage of a shock. This instability is typically studied in shock tube experiments, and constitutes a fundamental example of a complex hydrodynamic flow. Numerical simulations and models for the instability growth and evolution have also been used to further understand the physics of the Richtmyer-Meshkov instability. In the present work, the formally high-order accurate weighted essentially non-oscillatory (WENO) shock-capturing method using a third-order total-variation diminishing (TVD) Runge-Kutta time-evolution scheme (as implemented in the HOPE code [57]) is applied to simulate the single-mode Richtmyer-Meshkov instability with reshock in two spatial dimensions. The initial conditions and computational domain for the simulations are modeled after the Collins and Jacobs [23] single-mode, Mach 1.21 air(acetone)/SF6 shock tube experiment. The following boundary conditions are used: (1) periodic in the spanwise direction corresponding to the cross-section of the test section; (2) outflow at the entrance of the test section in the streamwise direction, and; (3) reflecting at the end wall of the test section in the streamwise direction. The present investigation has three principal motivations: (1) to provide additional validation of the HOPE code against available experimental data; (2) to provide numerical simulation data for detailed analysis of mixing induced by the Richtmyer-Meshkov instability with reshock, and; (3) to systematically investigate the dependence of mixing properties on both the order of WENO reconstruction and spatial resolution. The present study constitutes the first comprehensive application of the high-resolution WENO method to the Richtmyer-Meshkov instability with reshock, as well as analysis of the resulting mixing. First, analytical, semi-analytical, and phenomenological models for the growth of a single- and multi-mode perturbation are reviewed (impulsive, vortex, perturbation, potential flow, and asymptotic power-law growth models), including models for diffuse and reshocked interfaces. A model for baroclinic circulation deposition is also reviewed. Numerical simulations are performed using the third-, fifth-, and ninth-order WENO method with spatial resolutions corresponding to a uniform grid with 128, 256, and 512 points per initial perturbation wavelength. The density from the fifth- and ninth-order simulation is compared to the corrected experimental PLIF images of Collins and Jacobs at selected times. The amplitude obtained from the fifth-order simulation at a resolution of 256 points per initial perturbation wavelength is compared to the experimental data of Collins and Jacobs and to the predictions of linear and nonlinear amplitude growth models before and after reshock. The prediction of the Zhang-Sohn nonlinear amplitude growth model is in best agreement with the simulation data prior to reshock. The simulation data is also in excellent agreement with the experimentally-measured amplitude prior to reshock. The absence of the initial rarefaction wave (resulting from the rupture of the membrane that generates the first shock in the experiment) in the numerical simulations results in a time lag between the numerical and experimental interface evolution following reshock. The results of this component of the present investigation also serve as an additional validation of the HOPE code as applied to a shock-induced hydrodynamic instability. Second, local and global properties of the mixing during the linear, nonlinear, pre- and post-reshock, and late-time phases are investigated and discussed, including a quantitative investigation of the time-dependence and structure of various related mixing parameters defined in terms of the mole fraction and one-dimensional energy spectra. Spatial averaging of quantities along the spanwise (periodic) flow direction yields streamwise profiles, and is used to define instantaneous Reynolds and Favre averages and fluctuations. The fluctuations are Fourier-transformed along the spanwise direction to define time-dependent energy (abstract truncated).
Shock refraction is a fundamental shock phenomenon observed when shocks interact with a material interface separating gases with different properties. Following refraction, a transmitted shock enters the second gas and a reflected wave returns back into the first gas. In the case of regular shock refraction all waves meet at a single point called the triple-point, creating five different states for the two gases. Analytical methods based on shock polar analysis [9, 16] have been developed to determine the state of two ideal gases in each of the five refraction regions. Furthermore, shock refraction constitutes a basic example of complex hydrodynamic flows. For this reason, shock refraction is used in this report as one validation of the high-order accurate weighted essentially non-oscillatory (WENO) shock-capturing method, as implemented in the HOPE code. The following two-step validation process is adopted. First, analytical results are obtained for the normal and oblique shock refraction (with shock-interface angle {beta}{sub int} = 75) observed for a Ma = 1.2 shock. To validate the single-fluid and the two-fluid implementations of the WENO method, two pairs of gases, argon/xenon, having equal adiabatic exponents {gamma} and air(acetone)/sulfur hexafluoride, having different adiabatic exponents {gamma}, are considered. Both the light-to-heavy and heavy-to-light configurations are considered. Second, numerical simulations are performed using the fifth-order WENO method and values of the density, pressure, temperature, speed of sound, and flow velocity in each of the five refraction regions are compared with the analytical predictions from shock polar analysis. In all cases considered, excellent agreement between the simulation results and the analytical predictions was found. The results from this investigation suggest that the WENO method is a very useful numerical method for the simulation and modeling of complex hydrodynamic flows.
This book provides state-of-the-art results and theories in homogeneous turbulence, including anisotropy and compressibility effects with extension to quantum turbulence, magneto-hydodynamic turbulence and turbulence in non-newtonian fluids. Each chapter is devoted to a given type of interaction (strain, rotation, shear, etc.), and presents and compares experimental data, numerical results, analysis of the Reynolds stress budget equations and advanced multipoint spectral theories. The role of both linear and non-linear mechanisms is emphasized. The link between the statistical properties and the dynamics of coherent structures is also addressed. Despite its restriction to homogeneous turbulence, the book is of interest to all people working in turbulence, since the basic physical mechanisms which are present in all turbulent flows are explained. The reader will find a unified presentation of the results and a clear presentation of existing controversies. Special attention is given to bridge the results obtained in different research communities. Mathematical tools and advanced physical models are detailed in dedicated chapters.
The numerical simulation of turbulent flows is a subject of great practical importance to scientists and engineers. The difficulty in achieving predictive simulations is perhaps best illustrated by the wide range of approaches that have been developed and are still being used by the turbulence modeling community. In this book the authors describe one of these approaches, Implicit Large Eddy Simulation (ILES). ILES is a relatively new approach that combines generality and computational efficiency with documented success in many areas of complex fluid flow. This book synthesizes the theoretical basis of the ILES methodology and reviews its accomplishments. ILES pioneers and lead researchers combine here their experience to present a comprehensive description of the methodology. This book should be of fundamental interest to graduate students, basic research scientists, as well as professionals involved in the design and analysis of complex turbulent flows.
The field of Large Eddy Simulations is reaching a level of maturity that brings this approach to the mainstream of engineering computations, while it opens opportunities and challenges. The main objective of this volume is to bring together leading experts in presenting the state-of-the-art and emerging approaches for treating complex effects in LES. A common theme throughout is the role of LES in the context of multiscale modeling and simulation.
The phenomenon of shock wave reflection was first reported by the distinguished philosopher Ernst Mach in 1878. Its study was then abandoned for a period of about 60 years until its investigation was initiated in the early 1940s by Professor John von Neumann and Professor Bleakney. Under their supervision, 15 years of intensive research related to various aspects of the reflection of shock waves in pseudo-steady flows were carried out. It was during this period that the four basic shock wave reflection configurations were discovered. Then, for a period of about 10 years from the mid 1950s until the mid 1960s, investigation of the reflection phenomenon of shock waves was kept on a low flame all over the world (e. g. Australia, Japan, Canada, U. S. A. , U. S. S. R. , etc. ) until Professor Bazhenova from the U. S. S. R. , Professor Irvine Glass from Canada, and Professor Roy Henderson from Australia re initiated the study of this and related phenomena. Under their scientific supervision and leadership, numerous findings related to this phenomenon were reported. Probably the most productive research group in the mid 1970s was that led by Professor Irvine Glass in the Institute of Aerospace Studies of the University of Toronto. In 1978, exactly 100 years after Ernst Mach first reported his discovery of the reflection phenomenon, I published my Ph. D. thesis in which, for the first time, analytical transition criteria between the various shock wave reflection configurations were established.
The book is devoted to using of parallel multiprocessor computer systems for numerical simulation of the problems which can be described by the equations of continuum mechanics. Parallel algorithms and software, the problems of meta-computing are discussed in details, some results of high performance simulation of modern gas dynamic problems, combustion phenomena, plasma physics etc are presented. · Parallel Algorithms for Multidisciplinary Studies