Page 201 - 48Fundamentals of Compressible Fluid Mechanics

9.7. WORKING CONDITIONS "!$#&% ')( *+$,-/. 0 3 12 163

456

shock 7 8 8 8 8 8 8 89;:=<>9;:@?;<

Fig. 9.15: schematic of a “long” tube in supersonic branch

.

analysis deals with the case where W`XaZ [
is shorter than total WYXaZ [
as result to entrance Mach number. is equal to W`XaZ [
Obviously, in this situation, the critical point is where W`XaZ [
The process of decreasing the diverging-converging nozzle’s throat, in-
creases the entrance 17 Mach number. If the tube contains no supersonic flow then
reducing the nozzle throat area wouldn’t increase the entrance Mach number. why? make a question, is in-
crease can increase the pos-
This part is for the case where some part of the tube under supersonic sibility to supersonic flow?
regime and there is shock as transition to subsonic branch. Decreasing the nozzle
throat area moves the shock location downstream. The “payment” for increase in
the supersonic length is by reducing the mass flow. Further, decrease of of the
throat area results in flashing the shock out the tube. By doing so, the throat area
decreases. The mass flow rate is proportional linear to throat area and therefore
the mass flow rate reduces. The process of decreases the throat area also results
18 19
in increasing the pressure drop of the nozzle (larger resistance in the nozzle ) . Admittedly, this author have
and can explain it mathe-
the exit Mach number increases matically. The author did
found any physical explana-
with the decrease of the throat area. Once the exit Mach number reaches one no tion developed one. Perhaps

it is challenge to public as
WYX(Z [
In the case of large tube WYX(Z [
further increases is possible. However, the location of the shock wave approaches an open question of how to
explain it. This similar to
. surface tension phenomenon
that can be explained only
heavy mathematics.
b
to the theoretical location if entrance Mach, N
H
9.7.3.0.1 The maximum location of the shock The main point in this discus-
sion however, to find the furtherest shock location downstream. Figure 9.16 shows
WYXaZ [
as function of retreat of the location of the shock wave from
, if the
the possible A

b
the maximum location. When the entrance Mach number is infinity, N
and possible HTI results in N HTI
H
shock location is at the Maximum length, than shock at N
17 The word referred to the tube and not to the nozzle. The reference to the tube because it is the
focus of the study.
18 Strange? frictionless nozzle has a larger resistance when the throat area decreases
19
It is one of the strange phenomenon that in one way increasing the resistance (changing the throat
area) decreases the flow rate while in a different way (increasing the ) does not affect the flow rate.