A computer study of hypersonic laminar boundary-layer/shock-wave interaction using the time-dependent compressible Navier-Stokes equations /

This report presents the results of an investigation of hypersonic laminar boundary-layer/shock-wave interactions using the method of MacCormack to solve the time-dependent compressible Navier-Stokes equations. Comparisons of the numerical solutions with experimental data were made to ascertain the validity of the numerical method and to identify regions of anomalous behavior. The algorithm gave good results when applied to hypersonic laminar interactions that caused either small or no separated regions and marginal performance when applied to hypersonic laminar interactions having large regions of separated flow. The extents of the separated regions in interactions having large regions of separated flow were underpredicted when compared with experimental data. The predicted wall heat-transfer rates exhibited the correct qualitative trend but not the experimentally measured quantitative values. Consideration of the effects of needed stabilizing terms as well as grid resolution suggests inadequate mesh spacing in the longitudinal direction as the cause of the aforementioned anomalies. If inadequate mesh spacing (and the corresponding lack of support for every term of the Navier-Stokes equations) is a prime cause of the cited discrepancies between the numerical results and the experimental data, then the needed reduction of several orders of magnitude in delta x, would increase CPU time and core storage requirements to untenable levels. (Author)."September 1976.""Final Report: July 1974 -- April 1976."Includes bibliographical references (pages 38-41).This report presents the results of an investigation of hypersonic laminar boundary-layer/shock-wave interactions using the method of MacCormack to solve the time-dependent compressible Navier-Stokes equations. Comparisons of the numerical solutions with experimental data were made to ascertain the validity of the numerical method and to identify regions of anomalous behavior. The algorithm gave good results when applied to hypersonic laminar interactions that caused either small or no separated regions and marginal performance when applied to hypersonic laminar interactions having large regions of separated flow. The extents of the separated regions in interactions having large regions of separated flow were underpredicted when compared with experimental data. The predicted wall heat-transfer rates exhibited the correct qualitative trend but not the experimentally measured quantitative values. Consideration of the effects of needed stabilizing terms as well as grid resolution suggests inadequate mesh spacing in the longitudinal direction as the cause of the aforementioned anomalies. If inadequate mesh spacing (and the corresponding lack of support for every term of the Navier-Stokes equations) is a prime cause of the cited discrepancies between the numerical results and the experimental data, then the needed reduction of several orders of magnitude in delta x, would increase CPU time and core storage requirements to untenable levels. (Author).Report supported by the Air Force Systems Command and prepared by ARO, Inc, under Program Element,Mode of access: Internet