The Effect of Pressure Pulsations and Vibrations on Fully Developed Pipe Flow

摘要

An analysis is presented of the effect of longitudinal pressure pulsations or vibrations on the velocity distribution in laminar or turbulent fully developed pipe flow. Specifically, the Reynolds equations are formulated in a noninertial reference frame so that the influence of pressure pulsations, vibrations, or a combined pressure and vibrational oscillation can be obtained from a single solution. For axisymmetric developed flow of a constant property (incompressible) fluid, the radial and circumferential momentum equations can be solved and the axial momentum equation is linearized so that the velocity field can be obtained as the sum of a steady and a time-dependent component. By obtaining a solution for the case where the pressure (or amplitude of vibration) varies sinusoidally, one obtains the solution for disturbances of arbitrary waveform through a Fourier series expansion of the disturbance. Results are presented that show that the velocity field is dependent upon the mean flow Reynolds number, a vibrational Reynolds number, and the amplitude of the forcing function. In general, the fluid response to differing waveforms is similar to that obtained for simple harmonic oscillations with respect to the various parameters explored.