A THEORETICAL ANALYSIS OF THE FLOW DISTURBANCE INDUCED BY A SPHERE OSCILLATING IN INCOMPRESSIBLE FLUID

In order to improve the prediction method of the aerodynamic noise using the acoustic analogy theory based on incompressible flow fields, the characteristics of the disturbance propagation in the incompressible and compressible fluids should be studied firstly. In this paper, the analytical solution for the flow disturbance generated by a sphere oscillating in an incompressible fluid is obtained. The velocity and pressure fields are analyzed, and are compared to the results in a compressible fluid, namely, the acoustic field. It is shown that with respect to the velocity fields the disturbance has components with infinite and finite propagating speeds, while with respect to the pressure only disturbance with infinite propagating speed exists. When the fluid viscosity vanishes or the oscillating frequency becomes infinite, the velocity is identical to the near-field sound generated by the sphere oscillating in the compressible fluid; thus the acoustic near-field disturbance is incompressible, i.e., the pseudo-sound.