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(b)
12.3 The Newtonian pressure coefficient is independent of Mach number. Cp = 2 sin2 c
12.4 There are various ways of approaching this problem, using either a shock-capturing or a
shock-fitting philosophy (see Section 11.15). Since the time-dependent blunt body discussion in
Section 12.5 uses a shock-fitting approach, we will consider the same here.
(1) Geometry.
133
Continuity:
t
u
r r
v w
z
u
r
= − − − −
( ) ( ) ( )
1
tus
r
r
z
5. The independent variables can be transformed in order to map the shock layer in a
right parallelpiped (analogous to the rectangular domain in Section 12.5). Define a local shock
(6) The flowfield at the internal grid points can be calculated by using MacCormack’s
predictor-corrector approach. The shock and body points can be treated by a method-of-
(7) For detailed information concerning this solution, as well as some numerical results,
see the following reference:
12.5
First, consider the drag on the hemispherical portion. At a given angular location , the pressure
p acts on a circumferential elemental area (shaded above) of (2R sin ) R d . The elemental
drag on this area is
q
Hence, the contribution of the hemispherical portion to the total drag is
2
2p
2
