A New Parabolized Navier-Stokes Algorithm and its Applications in Some Hypersonic Propulsion Aerodynamic Problems

Abstract

A new implicit finite-volume Single-Sweep Parabolized Navier-Stokes (SSPNS) algorithm is developed. Theoretical analysis is focused on the mathematic properties about the parabolized Navier-Stokes (PNS) Equations, especially on the treatment of streamwise pressure gradient. Then the original implicit time iterative Lower-Upper Symmetric GaussSeidel (LU-SGS) method is successfully extended to integrate the PNS Equations in the streamwise direction. The hybrid upwind schemes, including Advection Upstream Splitting Method (AUSM) family schemes and Low-Diffusion Flux-Splitting (LDFSS) schemes, are used to compute the crossflow inviscid fluxes, while central schemes for the viscous fluxes. Three typical flows, i.e., supersonic flat plate flow, 15° ramp hypersonic flow, and cone flows with different angles of attack, are calculated with the SSPNS codes. Numerical results agree well with those obtained from NASA’s UPS PNS codes and experimental results by Tracy or Holden et al. Furthermore, several scramjet component flowfields, including 3 hypersonic inlet flows and 2 Single-Expansion Ramp Nozzle (SERN) flows, are also obtained with the SSPNS codes. Results of inlets, such as flow structures, wall pressure distributions, and heat transfer coefficients, show good agreement with those of NASA UPS codes, IMPNS codes, SCRAMIN NS codes, and experimental data by Holland et al. SSPNS results of the 2D and 3D SERN flowfields also agree well with those of NASA’s experiments. By comparison with the traditional time-iterative Full Navier-Stokes (FNS) flow solvers, the SSPNS codes show 1~2 order of magnitude of computational speed faster and at least 1 order of magnitude of storage saving in the 3D hypersonic inlet flow field simulation. All the numerical results indicate that SSPNS is a highly efficient, highly accurate, and also highly robust algorithm for steady supersonic/hypersonic flows without any large streamwise separation, and it is appropriate to be used in the aerodynamic optimization design of scramjet inlet and nozzle.