Compressible Flow Propulsion and Digital Approaches in Fluid Mechanics by Ledoux Michel; El Hami Abdelkhalak; & Abdelkhalak El Hami

Author:Ledoux, Michel; El Hami, Abdelkhalak; & Abdelkhalak El Hami [Ledoux, Michel & El Hami, Abdelkhalak]
Language: eng
Format: epub
Publisher: John Wiley & Sons, Incorporated
Published: 2017-01-30T21:00:00+00:00

Figure 3.5. Thermocouple testing device

A tube consists of two chambers A and B separated by a membrane. The chamber B is at atmospheric pressure Pa = 1bar and ambient temperature Ta = 20°C.

The pressure in chamber A increases and the membrane breaks very abruptly when the pressure in A reaches p2 = 10bar.

The thermocouple to be tested is set in chamber B. Upon the passage of the shock wave generated by the membrane breaking, the temperature of the air surrounding the thermocouple sharply increases. We shall attempt to evaluate this increase in temperature and the time needed for this increase, as registered by the thermocouple.

1) Calculate:

The Mach number, M1

The celerity of the shock wave, c1

The temperature T2 that is consequently reached by the gas in the chamber.

2) The thermocouple to be tested has the shape of a sphere of diameter d = 50 µm. We shall evaluate the time of the temperature scale imposed on the thermocouple, which will be assimilated to the time of contact between the surface of the discontinuity represented by the shock wave, and the thermocouple.

Find the value τ of this time duration.

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