Electric Power Generation By Steady Flow Liquid Metal MHD Generators

Equations were derived which specify parameters for maximum efficiency [(electric power out)/(fluid power in)] MHD electric generation by steady flow of liquid metal (LM) in a Hartmann geometry with Hartmann numbers M > 30. For any selected efficiency, fluid velocity, magnetic induction, and power out, the duct volume is least for LMs having a maximum value of (σ/pu), where σ is the electrical conductivity, p is the density, and u is the kinematic viscosity. Minimum values were calculated for duct volume, mass, power out, pressure head, current, voltage and current density corresponding to efficiencies ranging from 84% to 99.9% for Hg, Na, and NaK, for fluid velocities of 1, 10, 35 and 100 mis, and magnetic inductions of 1 and 4 T. Duct volume included an entry length required for the LM to attain laminar flow. Efficiencies of 99% and higher can be attained only by using very large ducts and high power. For example, the minimum size duct at 99% efficiency using liquid Na at 371 K and magnetic induction of 4 T, obtainable with superconducting electromagnets, has a gap spacing of 0.16 m, LM duct mass of 370 kg, and produces 370 MW with fluid velocity of 35 mis, pressure head of 42 MPa, and a power density of 920 MW/m
³
. In comparison, to obtain the same efficiency using Hg at 293 K, at the same magnetic induction and fluid velocity, the minimum size duct has a gap spacing of 0. 77 m, LM duct mass of 614,000 kg, power output of 4610 MW, pressure head of 23 MPa, and power density of 102 MW/m
³
. Minimum duct volume and corresponding minimum power output increase rapidly with small increases in efficiency above 99 %.