A Survey of Unsteady Hypersonic Flow Problems

t
- 28 -
and r “” + u’ i + (1+K#)r ;+ v'~l+~Y) z + r\]+ (1+rgy) i’ = o(q’2),
ax
where u, + u' is velocity ccmponent in x-direction (see Fig. 7)
vo + v' is velocity component in y-direction
w' is velocity ccmpcnent in +djrecticn
is the steady flew density
. . . (2.53)
L
is the body surface curvature in the meridianal (x,y)-plane
9' is u', v', or w', whichever is the greater.
The terms in equations (2.50) - (2.53) are next subjected to an order
of magnitude analysis starting from the assumptmn that for hypersonic flow
PO
EC = - >> 1
and using the results of steady flow analyses to conclude that
PC.2
uo
PO
- = O(i), - = O(l),
U PO lJa
vo A
- e O($), and - = O(Gi 1,
U a,
. . . (2.54)
where A is the shock stand-cffdistance and & is the nose radius of curvature.
It is also established that if
u' V’ P' W’
-z O(K)