Simulation of Starting Transients in the UTSIMHD Generator

Abstract

A numerical procedure for solving the unsteady, two-dimensional, compressible Navier-Stokes equations has been extended for magnetohydrodynamic (MHD) flows by the inclusion of the appropriate Lorentz force and Joule heating terms in the governing equations. With appropriate initial and boundary conditions, the procedure can be used for the investigation of transient phenomena as well as the asymptotic steady-state characteristics of internal MHD flows. Results obtained for the simulation of starting processes in the UTSI coal-fired MHD flow train are presented and found to be in good agreement with experimental observations. NomenclatureA = cross-sectional area of the channel, m 2 a = local speed of sound, m/s B = magnetic field, T E = electrical field, V/m h = height of the channel (in y direction), m I L = load current, A I s = local short circuit current, A ij = lead-out current in they th frame, A / = current density, A/m 2 L = channel length, m / = mixing length, m P = electrical power, W Pr = Prandtl number p = static pressure, N/m 2 RJ = resistance of theyth ballast resistor, 0 R L = load resistance, Q Rf = resistance per unit length of the channel, 0/m r = internal resistance of the plasma, 12 S = one electrode pitch, m T = static temperature, K u = velocity in x direction, m/s u r = wall friction velocity, m/s V d = voltage drop, V v = velocity in y direction, m/s x,y, t = physical space coordinates j3 = Hall parameter 7 = specific heat ratio <5 = boundary-layer thickness, m £ y. r = computational space coordinates 0 = diagonalization angle K = thermal conductivity, W/m • K X = second coefficient of viscosity, N • s/m 2 fji = molecular viscosity, N • s/m 2 v = kinematic viscosity, m 2 /s p = density, kg/m 3 a = electrical conductivity, S/m T = shear stress, N/m 2 $ = electrical potential function, V ty = current stream function, A/m