Analysis of Pulsating Flows in Infinite and Finite Conical Nozzles

The pulsating flows in both infinite and finite conical nozzles were analyzed theoretically. Sinusoidal pressure disturbances were impressed at the nozzle exit for the infinite nozzle and at either the inlet or at the exit for the case of a finite nozzle. The results have been calculated in terms of mass-flux response. The parameters involved are the Mach number and the modified Strouhal number; the inlet and exit radii ratio enters as an additional parameter for a finite nozzle. The results for an infinite conical nozzle indicate that, when the frequency is low, the quasistatic relationship between the pressure and mass-flux fluctuations holds; the same was reported in reference [1]. But, as the frequency increases, the dynamic characteristics of the pulsating flow become important. And, at high frequencies, the mass-flux response is less than the quasistatic value by an amount depending on the Mach number. For a finite conical nozzle the quasistatic condition is still valid if the frequency is low. However, at higher frequencies, the dynamic behavior becomes critically dependent on the frequency expressed in terms of w, for a given nozzle geometry and exit Mach number.