Acoustic and Entropy Waves in a Nonideal Combustion MHD Generator

Abstract

Experimental measurements and a linearized theory using integral transforms examine the growth and attenuation of acoustic and entropy waves in MHD generators of weak interaction. A generalized quasi-onedimensional model for the electrical parameters which includes implicitly some two-and three-dimensional nonideal effects such as boundary layers, heat-transfer, and near electrode phenomena has been included. The wave growth rates are obtained by perturbing the normal acoustic wave solutions with the effects of magnetic interaction. The model predicts that these nonideal phenomena have a mitigating effect on the level of magnetic interaction and may reduce wave growth rates significantly when the boundary-layer resistance is larger than the plasma core resistance. The experimental results suggest the presence of secondary flows which affect the nearelectrode boundary layers and would exist in MHD generators of any scale.= equilibrium sonic velocity = coefficients for nondimensional linearized equations of motion = channel cross-sectional area = poles of determinant of Eq. (11) = magnetic field strength = coefficients for nondimensional linearized equations of motion = specific heat at constant volume = hydraulic diameter = electric field strength --channel height = average heat-transfer coefficient = current density = active MHD channel length = ratio of current, J y /J x --Mach number = molecular weight = pressure = heat loss rate per unit volume = heat-transfer perturbation variable = plasma gas constant = effective boundary-layer resistance = external load resistance = Fourier transform variable = time = normalized time, ta 0 /L = temperature = plasma velocity = normalized augmentation voltage, V/a 0 B 0 h -channel width = axial, transverse, and span wise spatial components = normalized axial spatial component, x/L = constant coefficients of perturbation expansion, Eq. (23) = Hall parameter respectively 7 = ratio of specific heats 6,6* = first-order perturbation coefficients for wave growth e,e* = first-order perturbation coefficients for the wave speeds ju 0 = nondimensional coefficient, Eq. (17) p = mass density a = electrical conductivity O P ,O T = (P 0 /a 0 )(da/dP) T and (T 0 /a 0 )(do/dT) P , respectively 7 = Laplace transform variable <j > = diagonalization angle Subscripts and Superscripts A =anode B= augmentation c = plasma core / = initial condition K = cathode w = wall location 0 = mean, equilibrium value ( )' = fluctuation, normalized on mean value ( ) = vector quantity