1. The calculation of aerodynamic heating on advanced entry vehicles is a challenging problem. Configurations of current interest are usually threedimensional geometries (Fig. 1) that can operate at large angles of attack during periods of peak heating. Since ground-based experimental facilitiescaiinot simulate the real gas environmentof flight, it is necessary to rely heavily on computationalfluid dynamic(CFD) flowfield codes to predict the flight environment.
2. Before the heating rate calculation can start, the grid from the inviscid flowfield solution is input a an ordered set of Cartesian coordinates (z,y,z) which is body fitted, i. e. one boundary of the physical grid is coincidentwith the bodysurface. TheCartesianvelocity components (u,u,w) and thermodynamicvariables (p and h) at these grid points are input in a similar manner, From the physical grid, a set of computational coordinates (, C,7,can be defined,such t,liat 7 = 0 on the surface (see Fig. 2). The calculation of both the streamlinesand metrics needed for the heating predictions are carried out in this computational space. The physical space is related to the computational space through the inverse transformation equations (4-6),and thus, the vehicle geometry can be obtained by setting 7 =0 in these equations. Similarly, the velocity components (u,v,tu) and thermodynamic variables (pand h)can beexpressed asfunctionsofthe computational coordinates by equationsof the gcncral form where T is the variableof integration, which is related to the distance along a streamline s by the equation where V is the total inviscid velocity 011the surface
3. 112 equations (4-6) and (17-21) at any general point III he = [(d +(Ye)2 +(zc)I
4. The streamline and metric equations (22-24, and 27) are singular at the stagnation point and the nose point (z = 0) and care must he exercised when integrating the equations in the region near these points. The use of r instead of s as the variable of integration helps control some of the problems associated with these singularities because it helps to automatically control the integration stepsizein physical space (0s) near these points. Since V i0at the stagnation point and hc +0 at the nose point, also +0 near these points (see Eq. (24)) and the integration of the differential equations proceeds more smoothly in these regions.
5. The solution for the nose region isobtained by selectingaseries ofstreamlines andsuccessively integrating the differential equations for the streamline path and metric (22-24 and 27) foreach ofthese streamlines from the stagnation point to a constant presclccted Estation downstream where <> e