**3.1.4 Time marching scheme**

The spatial discretization described above reduces the governing flow equations to semidiscrete ordinary differential equations. The integration is performed employing an efficient multistage scheme (Jameson et al., 1981). The following three-stage, timestepping method is adopted. A conservative choice of the Courant-Friedritchs-Lewy number (1.4) was made to achieve a stable numerical solution. The numerical algorithm is second-order accurate in space and time discretization. A global time step was used rather than the grid-varying time step to simulate time-accurate solution and is calculated as mentioned (Mehta, 2001).

Computations of Flowfield over Reentry Modules at High Speed 357

The dimensional detail of the Apollo is shown in Fig. 2 are of axisymmetric designs. The Apollo capsule has a spherical blunt nose diameter of D = 3.95 m, spherical nose radius of N = 4.595 m and a shoulder radius of RC = 0.186 m. The back shell has an inclination angle, B = 32.5 deg relative to the vehicle's axis of symmetry. The overall length of the module is L

The spherically blunted-cone/flare configuration is illustrated in Fig. 2. The conical forebody has RN = 0.51 m, D = 2.03 m, L = 1.67 m and N = 20 deg. The flare has a half-angle cone of 25 deg and is terminated with a right circular cylinder and a geometrically similar to the REV of the DART demonstrator. Table 1(b) gives the semi-cone angle of various reentry

One of the controlling factors for the numerical simulation is the proper grid arrangement. The following procedure is used to generate grid in the computational region of the bluntedbody. The computational domain is divided into number of non-overlapping zone. The mesh points are generated in each zone using finite element method (Mehta, 2011) in conjunction with the homotopy scheme (Shang, 1984). The spiked blunt nosed body is defined by a number of grid points in the cylindrical coordinate system. Using these surface points as the reference nodes, the normal coordinate is then described by the exponentially

Grid independence tests (Mehta, 2006; and Mehta 2008) were carried out, taking into consideration the effect of the computational domain, the stretching factor to control the grid intensity near the wall, and the number of grid points in the axial and normal directions. The outer boundary of the computational domain is varied from 2.5 to 3.0 times the maximum diameter D and the grid-stretching factor in the radial direction is varied from

stretched grid points extending outwards up to an outer computational boundary.

1.5 to 5. These stretched grids are generated in an orderly manner.

Fig. 4. Comparison between density contour and schlieren picture.

**3.2.4 Apollo capsule** 

**3.2.5 Spherically blunted-cone/flare capsule** 

= 3.522 m.

vehicles.

**3.3 Computational grid** 
