Turbulent, compressible flows in rocket propulsion chambers are difficult to analyze using conventional turbulence modeling. The effects of wall injection and transition of the flow within the computational domain produce an especially complex environment. The present cooperative research effort is utilizing large-eddy and direct simulation techniques to analyze the flow. Of particular interest is the accuracy and stability of numerical methods for the compressible flows and their impact on subgrid modeling.

Most flow codes produce different flow solutions for the same flow problem when different grids are used, because truncation errors are functions of grid spacing and grid quality, and hence, different grids produce different errors in the flow solution. Sometimes, grid effects are beyond the level of tolerance, resulting in divergence of a solution process. The objective of this project is to develop grid-forgiving algorithms for fluid dynamics equations to reduce grid dependency of a flow solution. The method implements the concept of multidimensional upwinding on the physical domain. Conventional upwind schemes are based on one-dimensional analysis on the computational domain and hence strongly influenced by the grid.

The objective is to achieve a high rate of convergence in the solution procedure for the Euler and Navier-Stokes equations in high-speed flow calculations. Many existing acceleration schemes perform well for linear problems, but deteriorate as the degree of nonlinearity increases. Their performance depends on flow condition, grid size, and grid quality. The efficiency and robustness of convergence is improved through a combined use of generalized minimal residual (GMRES), implicit preconditioner, and multigrid in transonic flow calculations. Further study includes schemes such as vector-sequence extrapolation, incomplete LU factorization, and a multidimensional preconditioner.

The accuracy of a flow solution can be greatly enhanced by using a grid tailored to the specific geometry and flow solution. The objective is to investigate the need for quality grids and to develop a grid adaptation technique that improves grid quality in a systematic and automatic manner. A grid adaptation scheme is developed based on the potential theory and numerical mapping. In the approach, a distribution of grid control sources is defined from a flow solution and/or a grid quality measure of an initial grid, and grid points are redistributed through the influences of the grid control source. The use of adapted grids demonstrates a significant improvement in the quality of resulting flow solutions.

The objective is to develop a design technology that can produce a geometry yielding improved aerodynamic performance characteristics. An efficient aerodynamic design method is developed by combining advanced CFD capabilities with numerical optimization techniques. The flowfield is modeled with the Euler/boundary-layer or Navier-Stokes equations in order to improve the confidence level of design results. The method not only provides a reliable, automated design tool for design engineers, but also significantly reduces the cost and the engineering time for a design process.

This is a computational study that investigates stability of detonations with dust particles. Computational techniques include gradient sensitive adaptive grid generation and flux corrected transport-finite element method (FCT-FEM) schemes. Current focus is implementation of three-dimensional dusty gas effect in both a Lagrangian and Eulerian formulation to identify robustness and accuracy differences. Direct time-evolved comparisons with experimental shock attenuation show good agreement. Recent efforts have included incorporation of a two-step detonation reaction in the particle-laden flow.

A Monte Carlo simulation technique is applied to solve directly the Boltzmann equation for rarefied gas problems encountered in modern aerospace vehicle design. The solution procedure involves two explicit iterative steps. First, the collision integrals are evaluated at each computational node to define source terms in the Boltzmann equation. The source terms are then used to integrate the time-dependent multidimensional Boltzmann equation for the distribution function at the next time step. Steady-state solutions are achieved as a time asymptote. This integration scheme is well-suited to present-day supercomputers, which employ vectorization and parallel processing. The method is being validated for cases of simple geometry and solutions are to be compared with those from the continuum approach, e.g., Navier-Stokes solutions.