Numerical studies on behavior of Lorentz-force-applied boundary layer in supersonic flow

Behavior of boundary layer on a flat plate placed in Mach number 1.5 or 3.0 supersonic flow was studied under condition of applied Lorentz force. The Lorentz force was exerted by both an applied magnetic field and DC electrical current, which sustains the DC discharge near the wall. In this case, the Lorentz force is expected to selectively accelerate the boundary layer flow and to directly reduce the boundary layer momentum thickness. In order to confirm this expectation, two-dimensional numerical simulation was carried out, and results of numerical simulation were discussed with the integrated boundary layer equations including the Lorentz force. Results of numerical simulation indicated that the momentum thickness is remarkably reduced by the accelerating Lorentz force. At the same time, an analytical relation derived from the integrated boundary layer equation had explained well the numerically obtained relation between the MHD interaction parameter and the amount of reduction in the momentum thickness. The integrated boundary layer equation indicated that the reduction of displacement thickness by the Lorentz force is interfered with the Joule heating inside the boundary layer. As a result, the loading parameter to reduce the displacement thickness has the upper and the lower limits. Furthermore, it was shown that the reduction of displacement thickness becomes difficult with an increase of flow Mach number, though the Lorentz force is still effective for the reduction of momentum thickness. And also, the equations to estimate electrical current and electrical conductivity required to reduce both the momentum thickness and displacement thickness were derived.