Shape optimization of a MHD generator based on pressure drop and power output constraints

The optimum shape and axial variation of electrical loading (power ratio) of a MHD generator are obtained for a prescribed fractional power output and pressure drop along the generator. These optimum solutions are obtained using the ADS (Automatic Design Synthesis) optimization code. The objective function (duct size) for the prescribed design conditions was obtained by Carter for a quasi 1-D flow with a simple power law model for electrical conductivity. In this work, a generalized numerical optimization scheme, capable of incorporating any arbitrary electrical conductivity model is presented. The numerical solutions obtained using this scheme is validated with analytical results obtained by Carter. We demonstrate the use of this scheme to minimize the volume of a duct with a hypothetical power law model incorporating the effect of residence time (function of inlet Mach number) on the electrical conductivity. We further demonstrate the use of this scheme for obtaining the optimum shape of a MHD generator using an E-beam generated ionized gas stream.