A Survey of Unsteady Hypersonic Flow Problems

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u cot cl
ucota = . . . (2.35)
u co3 a
and, on the windward side of the body, the disturbances are confined between the
body and the shock wave, which lies close to the body, and consequently u is
of order 6v or 6w, and ucota is of order 6
( cot a is of order u co3 a
The right-hand sdes of equations (2.30) to (2.34) are, then, of order 6' a!d can
be neglected if 6 is small. If the equations are now transformed to axes parallel
to the original axes and moving in the +ve F; direction with velocity V, cos a,
and the substltutlons:
are made, equations (2.30) to
JF
6 cot a -+
at'
6 cot a - +
at*
JY
Scota- +
at'
ai
6 cot a - +
aT1
as
6 cot a - +
aP
a a
-=-
G a?51
a a a
- = --ax
at* a~;'
(2-S) transform to
a(i;s) J(F)
-+- = 0 ,
a? JE
JG JG 6
Y--++-++t.tana- = 0,
JY aE aP
_ ai;, a7 ap
v-+w-+- = 0,
aiy JZ JYj
a: aii ap
;--+;---+- = 0,
a? JZ aZ
as as
v-+w- = 0,
aij aZ
. . . (2.36)
. . . (2.37)
. . . (2.38)
. . . (2.39)
. . . (2.40)
. . . (2.41)
and the problem reduces to that of an expanding, contracting and translating piston
in two dunensions.
In the original derivation by Sychev, he states that the equations are
valid only for a body wxth all transverse dunensions small In comparison with its
length. In fact, there seems no reason why the results should not apply in
two-dimensional flow and for swept wings on a strip basu, provded the flow
remains attached at the leading edge. But, clearly, there 1s a range of bodzes
which have significant lateral dimensions on which the flow detaches at the
leading edge at moderate angles of attack, or IS never attached, and in these
cases the theory will not apply.
>*