Accuracy of Parabolized Navier-Stokes Schemes for Stability Analysis of Hypersonic Axisymmetric Flows

Abstract

The accuracy of the parabolized Navier ‐Stokes (PNS) and globally iterated PNS (IPNS) schemes for use as basic e ows is studied for stability analysis of hypersonic axisymmetric e ow over blunt and sharp slender cones at Mach 8. The numerical solution of the PNS and IPNS models is obtained by using the implicit e nite difference algorithm of Beam and Warming with a shock-e tting procedure. Both the PNS and IPNS solutions are thoroughly verie ed and compared with the thin-layer Navier ‐Stokes (TLNS) solution and experimental data. The stability analysis and transition prediction are performed using theparallel-e owlinearstability theory together with the eN method.Asystematicsensitivitystudyisperformedforbasicstatesolutions,includingproe lesandtheirderivatives, and spatial growth rates obtained from the PNS and IPNS models. The basic e ow and stability results and the predicted transition location based on the PNS model are qualitatively in good agreement with those of other theoretical investigations using various basic e ow models. Improved agreement with the TLNS model for both basic state solution and stability results is achieved when the IPNS model is applied. Attention is concentrated on those features of the numerical methods of the basic e ow computation that need particular care if adequate stability results are to be obtained. The study shows that the number of grid points, the grid distribution, and the amount of numerical dissipation have signie cant effects on the stability results. Moreover, indications are that carefulnumericalsolutionsofthePNSandIPNSschemesaslaminarbasice owcalculationsleadto amorepractical transition prediction tool in hypersonic e ows.