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Ecole Polytechnique de Thi`es DIC2 Aerospace
Supersonic Aerodynamics Dr Birame SY
Tutorial 2: Normal Shock Waves
Exercise 1: Ramjet subsonic combustor inlet conditions
A ramjet engine is an air-breathing propulsion device with essentially no rotating
machinery as represented in Figure 1. The flow, moving from left to right, enters
the inlet, where it is compressed and slowed down. The compressed air then enters
the combustor at very low subsonic speed, where it is mixed and burned with a fuel.
The hot gas then expands through a nozzle. The net result is the production of
thrust toward the left in Figure 1.
In this figure the ramjet is shown in a supersonic free-stream with a detached shock
wave ahead of the inlet. The portion of the shock just to the left of point 1 is a
normal shock.
Figure 1: Schematic of a conventional subsonic-combustion ramjet engine.
After passing through the shock wave, the flow from point 1 to point 2, located at
the entrance to the combustor, is isentropic. The ramjet is flying at Mach 2 at a
standard altitude of 10 km, where the air pressure and temperature are 2.65 ×104
N/m2and 223.3 K, respectively.
Calculate the air temperature and pressure at point 2 when the Mach number at
that point is 0.2.
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Exercise 2: Different computations of a normal shock wave
Consider a normal shock with an upstream Mach number of 3.53.
1. Obtain the downstream Mach number by:
(a) Using the nearest entry in the tables.
(b) Interpolating the tabulated values.
(c) Exact analytical calculations.
2. Compare the accuracy of the results.
Exercise 3: Supersonic Pitot tube measurement
A Pitot tube is inserted into an airflow where the static pressure is 1 atm. Calculate
the flow Mach number when the Pitot tube measures (a) 1.276 atm, (b) 2.714 atm,
(c) 12.06 atm.
Figure 2: A Pitot tube in (a) subsonic flow and (b) supersonic flow.
Hints:
Isentropic flow: p0,1
p1
=1 + γ−1
2M2
1γ/(γ−1)
(1)
Rayleigh formula: p0,2
p1
=(γ+ 1)2M2
1
4γM2
1−2(γ−1)γ/(γ−1) 1−γ+ 2γM2
1
γ+ 1 (2)
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