THERMALLY DRIVEN NONLINEAR OSCILLATION IN A PIPE WITH TRAVELLING SHOCK WAVES

Abstract : Lin's method of characteristics perturbation was successfully applied to the calculation of a case of periodic nonlinear vibration of a column of gas in a pipe. The system consists of a heater located at the mid-section of a pipe closed at both ends. When the frequency of change in the heat-release rate is nearly equal to the natural frequency of the column of gas to one side of the heater, the fluctuation in pressure at the heater becomes almost in phase with the fluctuating change in heat-release rate. As a result, the amplitude of fluctuation in the pipe increases linearly with time until shock waves are formed in the system. Ultimately the level of fluctuation in the pipe attains a limiting value and the changes in the pipe become periodic. The results of this calculation of periodic nonlinear vibration agree with those of Betchov. (Phys. Fluid, I 205-212, 1958) The method used here opens the way toward solving many similar problems of nonlinear vibration by a straight-forward and systematic procedure. (Author)