Page 125 - 48Fundamentals of Compressible Fluid Mechanics

5.3. THE MOVING SHOCKS 87

(the coefficient is only approximated as 0.5) as it shown in Figure (5.7). From Fig-

Mach number,
ure also it can be noted that high velocity can results in much larger velocity of
and

equation (5.58) provides that

the reflective shock. For example, for Much number close to one, which easily can

be obtained in Fanno flow, result in about double sonic velocity of reflective shock.
Some times this phenomenon can have tremendous significance in industrial ap-
plications.
Note, that to achieve super-
Shock in A Suddenly Close Valve
sonic velocity (in stationary coordi- k = 1 4
nate) requires diverging–converging 3
M
nozzle. Here no such device is M sx
sy
needed! Luckily and hopefully, engi-
neers who are dealing supersonic flow 2
when installing the nozzle and pipe
systems for gaseous medium under-
stand the importance of the reflective 1
shock wave.
Two numerical methods and
the algorithm employed to solve this 0
0.1 1
problem is provided herein: M x
Thu Aug 3 18:54:21 2006
,
Fig. 5.7: The moving shock Mach numbers as
(a) Guess
(b) Using shock table or Potto GDC to results of sudden and complete stop

,
calculate temperature ratio and

(c) Calculate the

. and adjust the new guess
accordingly. to the given
(d) Compare to the calculated

The second method is successive substitution which has better convergence to the

solution initial in most ranges but less effective to higher accuracy.
,

(a) Guess
,

(b) Using shock table or Potto GDC to calculate temperature ratio and

(c) Calculate the

to
return to part (b). if not satisfactory is the new
(d) Check if new
approach the old

calculate