The hypersonic wind tunnel at the University of Southern Queensland relies en free piston
compression to increase the temperature of the test gas. The arrangement is illustrated in Figure 1.
When the valve is opened, compressed aur from the high pressure aur reservour accelerates the piston
The motion of the piston compresses the gas ahead of it until the time of diaphragm rupture. The
diaphragm is located at the inlet of the Mach 6 nozzle, at the downstream end of the barrel The
barrel is 16 m long and its diameter is 130 mm The piston is initially located at the far upstream end
of the barrel (closest to the valve), and it accelerates from rest. From the time the piston starts
move to the time of diaphragm rupture is approximately 1 second
(a) Arrangement of the facility
high pressure air
Pressure is measured using transducers located close to the nozzle end of the barrel and pressure
measurements from one particular run of the facility are presented in Figure 2. The discrete data
presented in this figure are also included in Table 1.
Treat the aur which is compressed by the piston as an ideal gas with constant specific heats and
relevant constants as defined in Table A-2 of the text. Assume that there is no leakage of aur past the
In its present form. the facility generates hypersonic flows suitable for aerodynamic testing, but higher
temperatures are required for testing supersonic combustion systems. A possible approach for
generating higher temperatures in the wind tunnel facility is adding heat after the piston compression
process is completed Heat can be added via the combustion of a small amount of fuel in the
(a)If the initial temperature of the air in the barrel prior to compression was 27°C, determine the
temperature of the compressed air between the piston and the diaphragm at the time of diaphragm
rupture (1.5373 seconds), assuming the compression process is isentropic.
(h) (Determine the work dome by the pistom en the air ahead of it during the accumed isentropir
(c)Heat transfer from the air during the compression process of 4.0 kJ means the actual compression
process is not isentropic and the final temperature of the compressed sir at the time of diaphragm
rupture is actually 550K Determine the work done on the air by the piston in this case.
(d) Determine the volume of the air between the piston and the diaphragm at the time of diaphragm
rupture (1.5373 seconds) for the measured temperature at diaphragm rupture of 550K
(e) Suppose heat is added to the compressed air between the piston and the diaphragm in a constant
pressure heat addition process just prior to diaphragn rupture. Determine the amount of heat that
must be added toraise the temperature of the air from 550 K to 1000 K
(f) Instead of the constant pressure heat addition process of part (e), suppose heat is added to the
compressed aur betweem the pistom and the diaphragm in a constant volume heat addition process
just prior to diaphragm rupture. Determine the amount of heat that must be added to raise the
temperature of the air from 550 K to 1000 K
(g) With reference to the physical processes involved, explain why less heat needs to be added to the
air to reach the necessary tempenture in the constant volume process relative to the constant
Figure 2. Pressure measured at the end
Table 1. Pressure measured at the end of the barrel
pistom motion starts
pistom speed is
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In the present test case – the air chamber is compressed by the free movement of the piston to heat the trapped air. The movement of the piston compresses the test air and subsequently increases the temperature of the trapped air.
The barrel length is 16m and the diameter of the barrel is 130mm.
Hence the actual air trapped in the barrel volume is given by,
V1 = (3.14/4 * 130² * 16 * 1000 )mm³ = 0.212264 m³
The time it takes for the diaphragm to rupture from the start...