Page 211 - 48Fundamentals of Compressible Fluid Mechanics
P. 211
10.2. GOVERNING EQUATION 173
can noticed that equations ray:eq:momentum;ray:eq:mass;ray:eq:state are similar
to the equations that was solved for the shock wave.
(10.5)
The equation of state (10.4) can further assist in obtaining the temperature ratio
as !
(10.6)
!
The density ratio can be expressed in term of mass conservation as
!
(10.7)
!
"
Substituting equations (10.5) and (10.7) into equation (10.6) yields
"
!
"
"$
(10.8)
Transferring the temperature ratio to left hand side and squaring results in
!
(10.9)
and
The second
%
law is used to find the expression for derivative.
*
The Rayleigh line exhibits two possible maximums one for
(10.10)
. The second maximum can be expressed as
for
E
I
(10.11)
E ) E
"
Let the initial condition , and are constant then the variable parameters are
, and . A derivative of equation (10.11) results in
E
I
E
" !"
!"
(10.12)
"
#
Take the derivative of the equation (10.9) when letting the variable parameters be
E
, and results in
I
(10.13)
E
%$'&)( (
/.
+*-, * !"
