Page 196 - 48Fundamentals of Compressible Fluid Mechanics

158 CHAPTER 9. FANNO FLOW
Fanno Flow

M as a function of M for the subsonic brench
1 2
5
4fL
4.5 ¾¾ = 0.1
D
= 0.2
4
= 0.4
= 0.1 shock
3.5
= 0.4
3

M 1 2.5

2

1.5
1

0.5

0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
M
2
Tue Jan 4 11:26:19 2005

Fig. 9.10: % as a function for different for supersonic entrance velocity

9.7.2 The Pressure Ratio, , effects

In this section the studied parameter is the variation of the back pressure and thus,
%
the pressure ratio variations. For very low pressure ratio the flow can be as-
. As the
pressure ratio increases (smaller back pressure, ), the exit and entrance Mach
sumed as incompressible while exit Mach number are smaller than QS
is constant (friction
factor, , is independent of the parameters such as, Mach number, Reynolds num-
numbers increase. According to Fanno model the value of WYXaZ [
ber etc) thus the flow remains on the same Fanno line. For case where the supply
come from a reservoir with a constant pressure, the entrance pressure decreases
as well because the increase in the entrance Mach number (velocity).
Again a differentiation of the feeding is important to point out. If the feed-
ing nozzle is converging than the flow will be only subsonic. If the nozzle is
“converging–diverging” than in some part supersonic flow is possible. At first the
converging nozzle is presented and later the converging-diverging nozzle is ex-