Flow Control of Hypersonic Separated Flows by Applied Magnetic Fields

Abstract

*† Flow control of a laminar hypersonic flow over a compression corner is numerically investigated. A magnetic field is applied locally to modify the surface pressure, skin friction, and heat transfer rate. The magnetohydrodynamic governing equations are simplified under the low magnetic Reynolds number approximation. Experimental results are used to compare the numerical solution, in the absence of a magnetic field. Several configurations are studied to conclude on the effect of the location and magnitude of the applied magnetic field. I. Introduction HE design of hypersonic vehicles is a challenging task, due to the high level of energy associated with highspeed flows. Efficient flow control is one key element of the design process. An innovative means of flow control through the application of an electromagnetic field has been the subject of many investigations over the past decades. The suitable application of magnetohydrodynamics (MHD) principles to the design of hypersonic vehicles has led to the promising AJAX concept 1-4 , for which the magnetic field is beneficially utilized both for flow control and energy extraction. Due to the complexity of high-speed flows subject to electromagnetic fields, and limited computational resources, mathematical and numerical investigations have been performed on simple, but fundamental types of flow fields. Many useful conclusions could be drawn and have promoted the interest in magnetohydrodynamics. The investigations of flows over blunt bodies or flat plates have demonstrated the beneficial effect of the electromagnetic field 5-7 , when combined with high-speed flows. It has been observed that a substantial reduction in the heat transfer and skin friction could be achieved by an appropriate combination of magnetic and electric fields. Furthermore, The interaction between the electromagnetic field and velocity field generates a body force, called Lorentz force, which can be used to control boundary layers. The Lorentz force is generated by a suitable arrangement of magnets, coils, and electrodes. The possibility of delaying the boundary layer separation has been demonstrated both experimentally and numerically 8-11 . With the advent of Computational Fluid Dynamics (CFD), numerical simulations have become practical tools to analyze and understand MHD flows. Both qualitative and quantitative results can be obtained by numerically solving the equations that describe MHD flows. Improvement of computational resources and the development of high performance computing software and hardware will make numerical analysis even more prominent in the future. However, appropriate physical models and numerical methods are needed to obtain meaningful results. The equations governing MHD flows are obtained by combining the Navier-Stokes equations and the Maxwell’s equations. The resulting system of equations is composed of eight equations (full MHD equations). Since flows associated with aerospace engineering applications are generally characterized by a low electrical conductivity, the governing equations can be simplified. The resulting formulation is known as the low magnetic Reynolds number formulation. It has been shown that this formulation is not only simpler but also alleviates some numerical problems associated with the full MHD equations. For example, it is difficult to maintain a divergence-free magnetic field when solving the full MHD equations. Different techniques have been proposed