9.5 Home-made supersonic tunnel
CC-???
A PhD student is thinking about constructing his/her own supersonic wind tunnel.
To this purpose, s/he designs a converging-diverging tube with variable square cross-
section. The throat T is 0,1 x 0,1 m; the tunnel expands progressively to an outlet nozzle
of 0,13 x 0,13 m cross-section. The outlet exits directly in the ambient atmosphere. On
the inlet side of the tunnel, the student hopes to install a very large concrete reservoir
(fig. 9.12).
1. What is the maximum reservoir pressure for which the flow in the tunnel is
subsonic everywhere?
2. What reservoir pressure would be required to generate a shock-less expansion to
supersonic flow in the tunnel?
3. If the outlet temperature was to be ambient (11,3 °C), what would the outlet velocity
be?
4. Which mass flow rate would then be passing in the tunnel?
5. Describe qualitatively (ie. without numerical data) the pressure distribution
throughout the nozzle for both flow cases above.
$P_0$
$T_0$
$A_T$
$P_b$
Figure 9.12-A nozzle in which compressed air in a reservoir (left) is expanded as it accelerates
towards the right. The back (outlet) pressure $p_b$ is always atmospheric.
In order to impress his/her friends, the PhD student wishes to generate a perpendicular
shock wave inside the tunnel at exactly one desired position (labeled 1 in fig. 9.12 above).
At this position, the cross-section area is 0,01439 m².
6. Describe qualitatively (ie. without numerical data) the pressure distribution
throughout the nozzle for this case, along the two other pressure distributions.
7. (difficult question] What reservoir pressure would be required to generate the shock
wave at exactly the desired position?
8. What would the outlet velocity approximately be?
