Propulsive Effect of Wall Vibrations

Abstract

Propulsion generated by wall vibrations in the form of traveling waves was investigated. A model problem consisting of two parallel plates free to move with respect to each other was used. Vibration of one of these plates generated movement of the other plate, whose velocity was used to assess the effectiveness of such propulsion. Three types of responses were identified: a “sloshing” response for long waves, a “moving wall” response for short waves, and an “intermediate” response for in-between waves. Long and transitional waves produced propulsion of marginal interest. Short waves produced effective propulsion with the velocity of the plate increasing proportionally to the second power of the wave number and the second power of the amplitude, and approximately proportionally to the wave velocity. The vibrating wall appeared in this limit to the bulk of the fluid as a moving wall. The effectiveness of vibrations significantly increased by tilting waves. The best response for short fast waves was achieved using adjacent discrete elements spaced by about three-fourths of the wavelength. An analysis of waves of arbitrary shapes demonstrated that concentrating the vibration energy in the largest available and dominant wave number (monochromatic waves) resulted in the best system performance.