Gas Flows in Rocket Motors. Volume 2. Appendix C. Time Iterative Solution of Viscous Supersonic Flow

Numerical solutions of supersonic viscous flows are studied by applying an implicit time-dependent scheme to the thin-layer Navier-Stokes (TLNS) equations. The alternating direction implicit (ADI) scheme is first formulated to solve transonic viscous axisymmetric flows in two dimensions. The results indicate that the ADI scheme is not efficient enough for supersonic viscous calculations. A spatial discretization scheme using upwind flux-vector split differencing in the streamwise direction and central differencing in the cross-stream direction is chosen. Three approximate factorization schemes and one fully implicit direct solver are considered. Of them, the diagonally dominant ADI(DDADI) and the parabolized ADI are found to be much faster than the standard ADI procedure. These numerical algorithms are applied to solve supersonic flows through conical and high expansion ratio contoured nozzles for different Reynolds numbers, wall temperatures, and back pressures. Proper downstream boundary conditions for the subsonic portion of the outflow are shown to allow variations of the boundary layer thickness at the exit plane and recirculating separated flows for sufficiently high back pressure. Parabolized Navier-Stokes (PNS) procedures are also studied. Swirling viscous flows in transonic and supersonic propulsive nozzles have been investigated numerically. The algorithms developed for axisymmetric two-dimensional flows are extended to solve the three-dimensional TLNS equations.
Prepared in cooperation with Pennsylvania State Univ., Mechanical Engineering Dept., University Park, PA. See also Volume 3, AD-A213 350.