Travis W. Drayna

A parallel unstructured implicit solver for hypersonic reacting flow simulation

Publisher Summary The chapter focuses on two aspects of the solver, as well as the parallel performance of the hybrid implicit method. A new parallel implicit solver for the solution of the compressible Navier–Stokes equations with finite rate chemistry on unstructured finite volume meshes is presented in the chapter. The solver employs the data-parallel line relaxation (DPLR) method for implicit time integration along the lines of cells that are normal to the wall. A point-implicit method is used in the regions where surface-normal lines are not constructed. The new method combines the robustness and efficiency of the implicit DPLR method with the flexibility of using unstructured discretizations. The solver employs a low-dissipation pure-upwind numerical scheme based on the Steger-Warming split flux method, as well as a MUSCL-type scheme designed for unstructured discretizations. The DPLR method is superior to other parallel methods, such as matrix-based point-implicit methods designed for chemically reacting hypersonic flow simulations.

Unstructured grid approaches for accurate aeroheating simulations

The use of tetrahedral, prismatic, and hybrid hexahedral-prismatic-tetrahedral grids for the accurate prediction of aerodynamic heating at hypersonic conditions is investigated. We find that tetrahedral grids introduce significant error in the vicinity of strong shock waves, which results in unacceptable aeroheating predictions. The source of this error is studied with an idealized model, and it is found that a large spurious component of post-shock velocity is generated by triangular and tetrahedral elements. This type error is much smaller and easier to control on quadrilateral or hexahedral grids. Thus, we are very skeptical about the utility of tetrahedral grids for accurate hypersonic aeroheating predictions. Several comparisons of heating predictions for a three-dimensional sphere are made, and it is found that the stagnation region results are very sensitive to the grid design. Based on this work and our experience, we advocate the use of unstructured hexahedral grids which increase the grid design space, reduce the element count for many geometries, and result in accurate aeroheating predictions.

Development of the US3D Code for Advanced Compressible and Reacting Flow Simulations

Aerothermodynamics and hypersonic flows involve complex multi-disciplinary physics, including finite-rate gas-phase kinetics, finite-rate internal energy relaxation, gas-surface interactions with finite-rate oxidation and sublimation, transition to turbulence, large-scale unsteadiness, shock-boundary layer interactions, fluid-structure interactions, and thermal protection system ablation and thermal response. Many of the flows have a large range of length and time scales, requiring large computational grids, implicit time integration, and large solution run times. The University of Minnesota / NASA US3D code was designed for the simulation of these complex, highly-coupled flows. It has many of the features of the well-established DPLR code, but uses unstructured grids and has many advanced numerical capabilities and physical models for multi-physics problems. The main capabilities of the code are described, the physical modeling approaches are discussed, the different types of numerical flux functions and time integration approaches are outlined, and the parallelization strategy is overviewed. Comparisons between US3D and the NASA DPLR code are presented, and several advanced simulations are presented to illustrate some of novel features of the code.

Detached Eddy Simulation of a Generic Scramjet Inlet and Combustor

Results are presented which detail progress toward building the capability of simulating full scramjet powered vehicles. Important issues involved in the design of hypersonic, inward-turning inlets are disscussed and a process by which the performance of the inlets can be optimized is outlined. The geometry of the inlet is defined in terms of cubic rational Bezier curves. This allows for automated generation of high quality grids, as well as providing parameters which drive the optimizaiton process. The simulations used in the optimization of the inlets use a steady-state Reynolds-averaged Navier-Stokes model for turbulence closure. Simulations of the combustor section of a scramjet engine require a different modeling approach. A hybrid Reynolds-averaged Navier-Stokes and large eddy simulation methodology based on the detached-eddy simulation formulation is used. This allows for the large-scale unsteadiness of the flow to be resolved, which is key in simulating this type of flow accurately. The RANS portion of the method provides wall-modeling for large eddy simulation regions as well as fully modeling the turbulence in regions away from where mixing and combustion occur. This reduces the cost over a full LES. Preliminary results from simulations of two combustor configurations are presented. The first configuration involves the combustion of hydrogen injected through a normal, circular injector downstream of a small step. The second configuration involves a hydrogen-fluorine reaction in an expansion-ramp combustor. Finite-rate chemistry is used in the simulations; however, the current simulations do not include the effects of a subgrid model for the chemical source term. The simulations demonstrate the large range of time scales involved in combustor flows, which make an efficient solver with implicit time integration necessary. A low-dissipation, kinetic energy conserving numerical scheme is used in the simulation of the second configuration. This scheme resolves a larger range of turbulent scales on the same grid at minimal additional cost over standard upwind-biased schemes.

Numerical Simulation of the AEDC Waverider at Mach 8

A waverider designed for Mach 14 flight is numerically simulated using the University of Minnesota US3D computational fluid dynamics code. Numerical results are compared with experimental data provided by the Arnold Engineering Development Center Hypervelocity Wind Tunnel Number 9. Two sets of nominal Mach 8 flight conditions are examined, with a low Reynolds number of 14 million/m and a high Reynolds number of 54 million/m. Pitch angle sweeps in the range of -10° to 5° are presented for both cases. Very good agreement between numerical simulation and experimental measurement is shown in plots of lift-todrag ratio vs. alpha, lift and drag coefficients vs. alpha, and pitch moment coefficient vs. alpha. In addition, direct comparisons are made for the complete set of discrete pressure taps and heat transfer probes.