No abstract

Two new enhancements to the heat-balance integral (HBI) technique improve the rapid prediction of aerothermal response of heat shields of high-speed vehicles. The first enhancement uses a generalized cubic in-depth thermal profile to mitigate the well-known overreaction of classical HBI techniques to rapid changes in aerodynamic heat load. The second enhancement involves a direct method for solving in-depth charring problems in the context of an HBI solution. Together, these enhancements extend approximate HBI techniques to a broader range of aerothermal problems with improved accuracy at only a modest cost in computational speed.

Three dimensional generalized curvilinear grids are generated for cartesian, cylindrical, and spherical shaped bodies using parabolic partial differential equations. Elliptic grid equations are parabolized in an axial direction consistent with the Parabolized Navier Stokes (PNS) equations or the boundary layer equations. The parabolized grid equations are solved in a non-iterative fashion by marching in two directions. Any limitations of parabolic grid generation are investigated on convex and concave corners. Even though body surfaces are not smooth, the grid between axial stations is smoothed. Highly stretched and optimized grids for high Reynold's number are accurately and efficiently generated for the first time using parabolic grid equations with a difference approximation based on exponentials. The grid can also be adapted easily based on a flow solution at the previous axial station using this approach.

Three-dimensional generalized curvilinear grids are generated for Cartesian, cylindrical, and spherical shaped bodies using parabolic partial differential equations. Elliptic grid equations are parabolized in an axial direction consistent with the Parabolized Navier Stokes (PNS) equations or the boundary-layer equations. The parabolized grid equations are solved in a noniterative fashion by marching in two directions. Any limitations of parabolic grid generation are investigated on convex and concave corners. Even though body surfaces are not smooth, the grid between axial stations is smoothed. Highly stretched and optimized grids for high Reynold's number are accurately and efficiently generated for the first time using parabolic grid equations with a difference approximation based on exponentials. The grid can also be adapted easily based on a flow solution at the previous axial station using this approach.