**4.3 Newtonian impact theory**

366 Computational Simulations and Applications

Figure 10 shows the Mach contour plots over the OREX and Apollo modules. For the sake of brevity we are presenting windward and leeward sides flow field over OREX with smooth and without smooth shoulder, ARD, Apollo II and spherical-cone configurations are shown at M = 10.0 and at angle of attack 10.0 degree in Fig. 10. The Mach contour plots display the flow field in the windward and the leeward side of the capsules. A shock wave stands in front of the reentry blunt body and forms a region of subsonic flow around the stagnation region. Characteristic features of the flow field around the blunt body at high speed, such as bow shock wave ahead of the capsule and the expansion waves on the shoulder of the capsules. The bow shock wave follows the body contour and the fore body is entirely subsonic up to the corner tangency point of the ARD, the Apollo and the OREX where the sonic line is located. In the case of the spherically blunted cone-flare module, the sonic line is located at the junction of the sphere cone as seen in the Mach contour plots. The flow expands at the base corner. The flow field over the reentry modules became complicated due to the presence of corner at the shoulder and the base shell of the capsule as delineated in the Mach contour plots. Detailed flow field analysis is presented in (Mehta 2007). It is found at the transonic flow cases that a steady state solution could not be achieved due to unsteady nature of the base flow. Table 5 shows the aerodynamic drag numerically

Fig. 10. Mach contour plots over reentry capsules at M = 6.0 and angle of attack 5 deg.

ARD Apollo II

OREX sharp shoulder OREX smooth houlder

**4.2 Flow field over vehicle at angle of attack** 

computed for COMET and Beagle-2 reentry modules.

In the Newtonian flow concept the shock wave is assumed to coincide with the body surface. It is also assumed that the freestream maintain its speed and direction unchanged until it strike the surface exposed to the flow. The impact theory does not specify the pressure on surface that do not "visualize" the flow, that is, the surfaces on which gas dynamics would predict Prandtl-Mayer flow. When the flow is curved in the direction of freestream, the difference in pressure from the shock wave to the body surface equals the centrifugal force, due to the curvature of the flow.

A computer program is written to compute the aerodynamic coefficients using the modified Newtonian sine-squared law Cp = Cp,max sin2, where is the angle between the freestream velocity vector, and Cp, max maximum pressure coefficient, which is calculated at a stagnation point behind a normal shock using the Rayleigh pitot tube formula for frozen gas chemistry (constant specific ratio of heats). (Lees, 1955) proposed a modified Newtonian theory, which consists in scaling down so as to be exact at stagnation point, where the correct value is known. The forebody aerodynamic drag is also computed using Newtonian flow assumptions. The numerical simulation can be validated with the post flight data of the Gemini, Apollo and Star dust flights data (Griffith, 1967; Griffith & Boylan, 1968; Lockman, 1970; & Wood, 1997).
