1. For a particular liquid propellant thrust chamber the following data are given:
Chamber presure 68 MPa
Chamber shape cylindrical
Internal chamber diameter 0.270 m
Length of cylindrical section 0.500 m
Nozzle convergent section angle 45° Throat diameter and radius of wall curvature 0.050 m
Injector face Flat
Average chamber gas temperature 2800 K
Average chamber gas molecular weight 20 kg/kg-mol
Assume the gas composition and temperature to be uniform in the cylindrical chamber section. State any other assumptions that may be needed. Determine the approximate resonance frequencies in the first longitudinal mode, radial mode, and tangential mode.
2. In Problem 1, explain how these three frequencies will change with combustion temperature, chamber pressure, chamber length, chamber diameter, and throat diameter.
3. Why does heat transfer increase during combustion instability?
4. Prepare a list of steps for undertaking a series of tests to validate the stability of a new pressure-fed liquid bipropellant rocket engine.
5. Estimate the resonant frequency of a set of each of nine cavities similar to Fig. 9-7. Here the chamber diameter D = 0.200 m, the slot width is 1.0 mm, and the width and height of the cavity are each 20.0 mm. The walls separating the individual cavities are 10.0 mm thick. Assume L = 4.00 mm, AL = 3.00 mm, and a = 1050 m/sec. Answer, approximately 3138 cycles/sec.
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