LIQUID-METAL MHD FLOW IN RECTANGULAR DUCTS WITH THIN CONDUCTING OR INSULATING WALLS - LAMINAR AND TURBULENT SOLUTIONS

This paper treats the steady, fully-developed flow of a liquid metal i n a rectangular duct of constant cross-section with a uniform, transve rse magnetic field. Thin conducting wall boundary conditions at the to p/bottom walls (perpendicular to the magnetic field) are extended to a llow electrical currents to return through either the wall or the Hart mann layers. Hence, a unified analysis of flows in ducts with wall con ductance ratios in the range of interest of fusion blanket application s, namely, from thin conducting to insulating wall ducts, is conducted . The flow in laminar and turbulent regimes is investigated through a composite core-side-layer spectral collocation solution which explicit ly resolves the flow in the side layers (parallel to the magnetic fiel d) even for very large Hartmann numbers. Turbulent profiles are obtain ed through an iterative scheme in which turbulence is introduced throu gh an eddy viscosity model from the renormalization group theory of tu rbulence [Yakhot, V. and Orsag, S. A., J. Sci. Comput., 1986, 1(1), 3] . The transition from a flow in a duct with thin conducting walls to o ne with insulating walls is clearly displayed by varying the wall cond uctance ratio from 0.05 to 0 for Hartmann numbers in the range 10(3)-1 0(5). In turbulent regime, Reynolds numbers vary in the range 5 x 10(4 )-5 x 10(5). For thin conducting wall duct flows, turbulence is concen trated in the increased side layers while the core remains unperturbed . In insulating wall ducts, the flow remains in the laminar regime wit hin the considered range of Reynolds numbers. (C) 1997 Elsevier Scienc e Ltd.