Browsing by Author "D. S. McRae, Committee Member"

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Large-Eddy Simulation/ Reynolds-Averaged Navier-Stokes Hybrid Schemes for High Speed Flows
(2003-02-05) Xiao, Xudong; F. R. DeJarnette, Committee Member; J. R. Edwards, Committee Member; R. E. Funderlic, Committee Member; D. S. McRae, Committee Member; H. A. Hassan, Committee Chair
Three LES/RANS hybrid schemes have been proposed for the prediction of high speed separated flows. Each method couples the k—ζ(Enstrophy) RANS model with an LES subgrid scale one-equation model by using a blending function that is coordinate system independent. Two of these functions are based on turbulence dissipation length scale and grid size, while the third one has no explicit dependence on the grid. To implement the LES/RANS hybrid schemes, a new rescaling-reintroducing method is used to generate time-dependent turbulent inflow conditions. The hybrid schemes have been tested on a Mach 2.88 flow over 25 degree compression-expansion ramp and a Mach 2.79 flow over 20 degree compression ramp. A special computation procedure has been designed to prevent the separation zone from expanding upstream to the recycle-plane. The code is parallelized using Message Passing Interface (MPI) and is optimized for running on IBM-SP3 parallel machine. The scheme was validated first for a flat plate. It was shown that the blending function has to be monotonic to prevent the RANS region from appearing in the LES region. In the 25 deg ramp case, the hybrid schemes provided better agreement with experiment in the recovery region. Grid refinement studies demonstrated the importance of using a grid independent blend function and further improvement with experiment in the recovery region. In the 20 deg ramp case, with a relatively finer grid, the hybrid scheme characterized by grid independent blending function well predicted the flow field in both the separation region and the recovery region. Therefore, with 'appropriately' fine grid, current hybrid schemes are promising for the simulation of shock wave/boundary layer interaction problems.
Numerical Simulation of Scramjet Combustion in a Shock Tunnel
(2005-12-09) Star, Jason Blue; Jack R. Edwards Jr., Committee Chair; Hassan A. Hassan, Committee Member; D. S. McRae, Committee Member; William L. Roberts, Committee Member
Three-dimensional computational simulations of reactive flowfields within a hydrogen-fueled scramjet-like geometry experimentally tested in a free piston shock tunnel are presented. The experimental configuration (Odam and Paull, AIAA Paper 2003-5244) involves injection of hydrogen fuel into the scramjet inlet, followed by mixing, shock-induced ignition, and combustion. The predictions for both fuel-off and fuel-on conditions were observed to be sensitive to the choice of the wall temperature boundary conditions. The best comparison with experimental data were achieved through the implementation of an approach that involves a simplified conjugate heat transfer model that couples the heat conduction through the wall with the heat conduction of the fluid within the boundary layer. This approach is able to predict thermal loads on the walls of the scramjet model due to shock wave interactions and due to heat release. As such, it is able to more accurately represent the physical temperature response of the engine model. Also shown to produce very good agreement with the statistically-steady experimental data was the isothermal ghost-cell boundary condition, which is based on a simplification of the time-dependent conjugate heat transfer boundary condition. This simplified boundary condition assumes a linear temperature distribution within the wall based on the effective depth that an applied heat load would penetrate, thus, it also allows the actual wall temperature to vary in response to the applied heat load. Results for fuel-off simulations showed that the solution generated by a steady-state simulation implementing the isothermal ghost-cell wall boundary condition was very comparable with the statistically-steady solution obtained from a fully transient simulation with coupled heat conduction within the walls. When integrated in a fully time-accurate manner, the fuel-on simulations showed a striking sensitivity to the modeled rate of air ingestion into the engine. For experimental data that showed steady combustion, the transient simulations resulted in either a steady combusting solution or a progression toward engine unstart, depending on the modeled rate of air ingestion. Also, for experimental data that showed an unsteady thermal choking event leading to eventual unstart, the transient simulations were able to predict both unstart and steady combustion, once again depending on the air ingestion rate. In all cases, the modeled air ingestion process is an approximation of the actual experimental process, in that uniform conditions are imposed as linear functions of time over the inlet plane. The computational results also provide some support for a 'radical-farming' hypothesis, proposed to explain the ability of the hydrogen-air mixture to auto-ignite at relatively low inlet contraction ratios.
Temporal and Pseudo-Temporal Numerical Integration Methods
(2002-10-28) Coffey, Todd Stirling; C. T. Kelley, Committee Member; C. S. Woodward, Committee Member; D. S. McRae, Committee Member; M. Shearer, Committee Member; P. A. Gremaud, Committee Member
Numerical methods for integrating partial differential equations are used in nearly every scientific field. In this dissertation we study two types of numerical integration methods, transient methods and pseudo-transient methods. Transient methods for partial differential equations look for time-accurate solutions that explain the evolution of the equation (although a steady state solution may evolve). Pseudo-transient methods look for steady-state solutions of partial differential equations while paying attention to the transient behavior to aid in stability. In contrast, root-finding methods, e.g. line-search methods, look only for a steady-state solution often not paying attention at all to the transient behavior of the problem. Pseudo-transient continuation is a method for solving steady state solutions of partial differential equations, and is used when traditional line-search methods fail to converge or converge to non-physical solutions. The method is a hybrid between implicit Euler and Newton's method where variable step-sizes are used to transfer from one method to the other. We demonstrate the performance of pseudo-transient continuation both numerically and theoretically on a variety of problems. We extend the global convergence theory, which currently covers a class of ordinary differential equations, to include a class of semi-explicit index-1 differential-algebraic equations. We also studied CVode, a transient code for solving nonlinear partial differential equations. In this work, we explain how CVode was extended to allow for a two-grid nonlinear solver. The two-grid solver coarsens a given mesh and solves the nonlinear problem on the coarse mesh, which is then moved back to the fine mesh for refining. This approach can be less expensive than computing the full nonlinear solution on the fine mesh. We explore some of the theoretical and computational issues involved in implementing this method for a radiative transfer problem as might be seen in stellar fusion.