Response of a burning fuel plate to sound vibrations.

Abstract

Combustion instability is considered from the viewpoint of the time-dependent response of a flat-plate boundary layer with mass transfer to standing or traveling acoustic vibrations in the gas. The acoustic admittance is denned in terms of the response of the boundary layer at i] = co and is employed to obtain necessary conditions for wave amplification. Results for the gasification rate at the wall, the wall shear stress, and the acoustic admittance are obtained as expansions in the parameter ux/U; co = oscillation frequency, x = distance from the upstream edge of the plate, and 17 = velocity of gas relative to the plate. It is shown that the zero-order (quasisteady) response rarely leads to amplification of a standing wave. Effects of pressure oscillations alone seldom produce wave amplification. The velocity oscillations lead to the greatest acoustical energy emission and absorption, and the presence of a flame in the boundary layer greatly enhances the influence of velocity oscillations. Results to first and second orders in the parameter ux/U are presented. The opposite limiting case, in which (i)X/Ui& large compared with unity, is also considered.