A global relaxation Navier Stokes algorithm for finite rate chemistry calculations in scramjets.

摘要

Global relaxation solution procedures for finite-rate chemistry calculations using the steady-state compressible Reduced Navier Stokes (RNS) or full Navier Stokes (NS) equations have been developed. The current work represents the first application of a finite rate chemistry model within the RNS relaxation framework. A hydrogen/air chemistry model is incorporated, allowing for calculations of combustion and non- reacting mixing. The procedure is quite general, however, and can be extended to other chemical reaction systems.; A computational fluid dynamic (CFD) code is developed to implement a hierarchy of flow solution tools. The code can solve the Parabolized Navier Stokes (PNS) equations using a single-sweep procedure, or the RNS or NS equations using a multiple-pass, global relaxation procedure. Based on analysis of the flow physics, desired level of accuracy, and CPU time constraints, an appropriate technique can be chosen.; An operator splitting of the NS equations is performed such that the RNS equations, which may be efficiently solved by relaxation procedures, are used as the implicit operator. The terms which represent the difference between the NS and RNS equations, namely the streamwise and higher order cross-flow diffusion terms, are included in the form of a Deferred Corrector (DC). The boundary conditions and discretization are not affected by the retention of the DC terms. At the outflow, only a boundary condition on pressure must be imposed, the same as for RNS solutions.; A pressure-based flux vector splitting, combined with a global relaxation procedure, is applied to the RNS implicit operator to allow for a stable, multiple sweep solution procedure. The pressure in subsonic regions and the velocities in reversed flow regions are relaxed from the previous sweep. This algorithm provides a solution technique which has advantages over traditional space-marching PNS and time-marching NS algorithms. Unlike PNS codes, the current relaxation method is able to solve fully subsonic flows and flows with recirculation. Compared to time-marching NS codes, the current method is more computationally efficient.; Numerical results are presented for a backward facing step and scramjet combustor models with parallel injection and transverse injection. These numerical results are compared with appropriate experimental and computational results.