Composite reduced Navier Stokes procedures for flow problems with strong pressure interactions
Abstract
The Reduced Navier Stokes (RNS) formulation for viscousinviscid interacting flows with significant upstream or elliptic effects was applied for transient flow over airfoils at incidence, and steady 2D and 3D flows over cavity, wing and afterbody configurations. The solution technique applies uniformly over the entire Mach number range and allows for shock boundary layer interaction, and for moderate regions of axial and secondary flow recirculation. For 2D problems with recirculation, it was demonstrated that for laminar flows there exists a critical Reynolds number, that is geometry dependent, above which the solution exhibits a breakdown. This occurs in the region of recirculation and very close to the reattachment point. This phenomena is grid dependent and can be missed with insufficiently refined grids or when artificial viscosity is introduced. It was shown that the pressuresplit RNS procedure is in fact a special form of flux vector splitting that has very favorable properties for sharp shock capturing. A sparse matrix direct solver procedure has been applied for both twodimensional transient flows, and for threedimensional steady flows with the RNS fluxsplit strategy. A unidirectional or semicoarsening multigrid procedure has been further developed for viscous interacting flows, where significant grid stretching is required in order to adequately evaluate both thin viscous layers and large inviscid regions, with and without shock interaction.
 Publication:

Final Report
 Pub Date:
 January 1990
 Bibcode:
 1990cinu.rept.....R
 Keywords:

 Aircraft Configurations;
 Computational Grids;
 Flow Distribution;
 Laminar Flow Airfoils;
 NavierStokes Equation;
 Recirculative Fluid Flow;
 Three Dimensional Flow;
 Transient Pressures;
 Afterbodies;
 Boundary Layer Separation;
 Computational Fluid Dynamics;
 Flux Vector Splitting;
 Inviscid Flow;
 Mach Number;
 Matrices (Mathematics);
 Reattached Flow;
 Reynolds Number;
 Secondary Flow;
 Shock Layers;
 Steady Flow;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer