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A new technology was developed in this study which provides a successful numerical simulation of the whole process of flow transition in 3-D boundary layers, including linear growth, secondary instability, breakdown, and transition at relatively low CPU cost. Most other spatial numerical simulations require high CPU cost and blow up at the stage of flow breakdown. A fourth-order finite difference scheme on stretched and staggered grids, a fully implicit time marching technique, a semi-coarsening multigrid based on the so-called approximate line-box relaxation, and a buffer domain for the outflow boundary conditions were all used for high-order accuracy, good stability, and fast convergence. A new fine-coarse-fine grid mapping technique was developed to keep the code running after the laminar flow breaks down. The computational results are in good agreement with linear stability theory, secondary instability theory, and some experiments. The cost for a typical case with 162 x 34 x 34 grid is around 2 CRAY-YMP CPU hours for 10 T-S periods. Liu, Chaoqun and Liu, Zhining Glenn Research Center NAS1-10312; NCC3-233; RTOP 505-90-5K...
Computational Fluid Dynamics, Second Edition, provides an introduction to CFD fundamentals that focuses on the use of commercial CFD software to solve engineering problems. This new edition provides expanded coverage of CFD techniques including discretisation via finite element and spectral element as well as finite difference and finite volume methods and multigrid method. There is additional coverage of high-pressure fluid dynamics and meshless approach to provide a broader overview of the application areas where CFD can be used. The book combines an appropriate level of mathematical background, worked examples, computer screen shots, and step-by-step processes, walking students through modeling and computing as well as interpretation of CFD results. It is ideal for senior level undergraduate and graduate students of mechanical, aerospace, civil, chemical, environmental and marine engineering. It can also help beginner users of commercial CFD software tools (including CFX and FLUENT). A more comprehensive coverage of CFD techniques including discretisation via finite element and spectral element as well as finite difference and finite volume methods and multigrid method Coverage of different approaches to CFD grid generation in order to closely match how CFD meshing is being used in industry Additional coverage of high-pressure fluid dynamics and meshless approach to provide a broader overview of the application areas where CFD can be used 20% new content
An oblique transition process of a flat-plate boundary layer at a free-stream Mach number of M (infinity) =4.5 and a Reynolds number of 10000 based on free-stream velocity and inflow displacement thickness is simulated as the validation of the code. Four transitional stages are observed: the linear and weakly nonlinear growth, the appearance of staggered A-vortex patterns, the evolution of A-vortex into hairpin vortex, the breakdown of hairpin vortical structures. The evolution of averaged quantities, such as the skin-friction coefficient, the mean velocity profile, the boundary layer thickness are all computed and found agreed very well with theoretic and experimental results. For complex geometry, 2D and 3D numerical grid generation method are used to generate high-quality meshes. Subsonic flow around 2D NACA 0012 airfoil and 3D Delta wing with a large angle of attack are investigated with large eddy simulation. Flow separations and large eddy structures are observed, the interactions between vortical structures will be studied.