Page 190 - 48Fundamentals of Compressible Fluid Mechanics

152 CHAPTER 9. FANNO FLOW

work by Frossel 10 since has shown that the error is not significant. Nevertheless,
the comparison with shows that heat transfer cause changes to the flow and they
needed to be expected. This changes includes the choking point at lower Mach
To insert example on the number.
change in the flow rate
between isothermal flow
to Fanno Flow. Insert also
example on percentage of 9.6 Maximum length for the supersonic flow
heat transfer.
on the comparison of the
maximum length of isother- It has to be noted and recognized that as oppose to subsonic branch the su-
mal model and Fanno Model.
personic branch has a limited length. It also must be recognized that there is a
11
maximum length for which only supersonic flow can exist . These results were
obtained from the mathematical derivations but were verified by numerous experi-
12
as follow: V " H b % % % b H
ments . The maximum length of the supersonic can be evaluated when N H

b

b

WYXaZ [ N

%

b

b

b

H
% %

b

b
% %
The maximum length of the supersonic flow is limited by the above number. From

% % b

the above analysis, it can be observed that no matter how high the entrance Mach
%
% %
H WYX(Z [ N F H I
S V H\QS % I
as shown in figure 9.5.
number will be the tube length is limited and depends only on specific heat ratio, F
9.7 Working Conditions
It has to be recognized that there are two regimes that can occurs in Fanno flow
model one of subsonic flow and supersonic flow. Even the flow in the tube starts
as a supersonic parts of the tube can be transformed into the subsonic branch.
A shock wave can occur and some portion of the tube will be in a subsonic flow
pattern.
The discussion has to differentiate between two ways of feeding the tube:
converging nozzle or a converging-diverging nozzle. Three parameters, the di-
, and the pressure ratio,
are controlling the flow. Only combination of two these parameters are truly
b
mensionless friction, W`XaZ [
, the entrance Mach number, N
independent. However, all the three parameters can be varied and there are dis-
b
cussed separately here.

10
11 Many in the industry have difficulties to understand this concept. This author seeking nice explana-
tion of this concept for the non–fluid mechanics engineers. This solicitation is about how to explain this
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issue to non-engineers or engineer without proper background.
12 If you have experiments demonstrating this point, please provide to the undersign so they can be
added to this book. Many of the pictures in the literature carry copyright problems.