Page 188 - 48Fundamentals of Compressible Fluid Mechanics

150 CHAPTER 9. FANNO FLOW

The exit pressure determines the location of the shock, if a shock exists, by
. Two possibilities needed to be checked; one,
the shock at the entrance of the tube, and two, shock at the exit and comparing
the pressure ratios. First, possibility of the shock wave occurs immediately at

comparing “possible” to
are (shock wave table)
the entrance for which the ratio for N

Q^S V(' I
I(Q^S
Q^S
%'
V

SQUQ
QUQ

After shock wave the flow is subsonic with “N (' I . (fanno flow table)

b
S3!( Q
S%( I
'

'
”H QS V

]

IUS
I
S
I V
Q=V 3 V Q Q I( I
S_I-V % I
Q^S V(* I
S
are I=S QS ]

The stagnation values for N H Q0S V(* I

QS
I=S
Q0S
Q^S
I

The ratio of exit pressure to the chamber total pressure is b I=S_I
Q^S V(* I '3( % V
Q
V %'3(/3
b

b

H

b

I
QS
Q0S
I %*3'%
%
V
H
I

S V
is smaller than the case in which
Q0S I V

#
# # #
shock occurs at the entrance. Thus, the shock is somewhere downstream.

The actual pressure ratio I
Q
One possible way to find the exit temperature, L is by finding the location of the
H (*3

is needed.
shock. To find the location of the shock ratio of the pressure ratio,
With the location of shock, “claiming” up stream from the exit through shock to
S3 HTQS

'%
the entrance. For example, calculating the parameters for shock location with
in the “y” side. Then either utilizing shock table or the program to
obtained the upstream Mach number.
known W`XaZ [
The procedure of the calculations:
1) Calculated the entrance Mach number assuming the shock occurs at the
exit: