Influence of Hall Effect on Electrodynamic Heat Shield System for Reentry Vehicles Hirotaka Otsu ∗ Shizuoka University, Shizuoka 432-8561, Japan Detlev Konigorski † EADS Astrium, Bremen 28199, Germany and Takashi Abe ‡ Japan Aerospace Exploration Agency (JAXA), Kanagawa 229-8510, Japan DOI: 10.2514/1.40372 The influence of the Hall effect on the magnetic flow control to a reentry vehicle with a hemispherical nose and the imposed dipole magnetic field was investigated. For this purpose, a parametric study for the Hall parameter was conducted. The present result shows that the Hall effect drastically affects the electric potential distribution and electric current pattern inside the shock layer, depending on the vehicle surface conductivity, but it does not affect the current strength in the circumferential direction in the case of the insulating wall. As a result, the shock-standoff distance does not change, even if the Hall effect is significant when the vehicle surface is regarded as an insulating wall. The present parametric study clarified that this conclusion is applicable in a wide variety of the Hall parameter and enables us to get an insight of the mechanism behind the phenomenon. This conclusion suggests that, if the vehicle surface is regarded as an insulating wall, the magnetic flow control for the reentry vehicle will prove to still be a useful technology, even when the Hall effect is taken into account. Nomenclature B = magnetic field vector B = magnetic field strength jBj b = unit vector defined by B=B C H = Hall parameter E = electric field vector E r ; 0;E z  e = elementary charge J = electric current density, A=m 2 J = electric current density vector J r ;J  ;J z  N e = number density of free electron, 1=m 3 V = velocity vector u r ;u  ;u z   = electric conductivity, S=m  = electric potential, V I. Introduction F OR typical thermal protection systems (TPS) applied to reentry vehicles, various materials that can withstand the severe aerodynamic heating are employed. A typical TPS is easily damaged, since it is exposed to a severe reentry heating; thus, it needs to be replaced or refurbished for the next flight. This indicates that a typical TPS is not suitable for a future reusable space transportation system. As one candidate of the alternatives of a typical TPS, a heat shield system that uses the electrodynamic force has attracted much attention recently. Such a system is called the electrodynamic heat shield system (EDH). In this system, the strong magnetic field is generated around the reentry vehicle, which produces the Lorentz force acting on the flow through an interaction with the ionized flow behind the strong bow shock. The Lorentz force thus produced is used to control the flow around the reentry vehicle, as illustrated in Fig. 1, so that, for instance, the heat flux is reduced. In this figure, J, B, and V are the electric current vector, magnetic field vector, and flow velocity vector, respectively. The dashed line shows the bow shock affected by the applied Lorentz force J  B. Also in this figure, the vehicle geometry is assumed to be a cylinder with a hemispherical nose, and the magnetic dipole is assumed at the center of the sphere. The situation represented in Fig. 1 is more or less realizable when the Hall effect can be assumed to be negligible. In fact, under this assumption, the analytical and numerical verification of the magnetic flow control for the reentry vehicle was clearly demonstrated [1]. In the case of typical orbital or suborbital reentry flight conditions, however, the Hall effect is expected to be strong [2]. When the Hall effect is strong, the Hall current may create the electric field, which does not appear under the condition that the Hall effect is negligible. Such an induced electric field may affect the electric current and, subsequently, modify the Lorentz force and the efficiency of EDH. Although most of the previous research does not take account of the Hall effect, the impact of the Hall effect was investigated analytically and numerically by some researchers [3–5]. Levy [3] analytically investigated the two-dimensional plasma flow around a cylinder with an imposed magnetic field, which is created by the current in the wire parallel to the axis of the cylinder. In this research, he concluded that the interaction between the magnetic field and the plasma flow was weakened because the current strength around the cylinder was reduced by the Hall effect. Porter and Cambel [4] investigated the plasma flow around a sphere with the imposed magnetic field. In this study, however, they simplified the governing equations to analytically calculate the flowfield around the stagnation region. As a result, they also showed that the Hall effect weakens the efficiency of this system. Recently, Fujino et al. [5,6] have performed computational fluid dynamics (CFD) analyses for a magnetic flow control for a reentry vehicle including the Hall effect. In their study, they investigated a three-dimensional flow around an axis-symmetry body and solved a full Navier–Stokes equation, including the non- equilibrium chemical reactions. In contrast to the previous studies, they showed that the Hall effect does not affect the efficiency of EDH when the vehicle surface is regarded as an insulating wall. In their Presented as Paper 2005-5049 at the 36th AIAA Plasmadynamics and Lasers Conference, Toronto, ON Canada, 6–9 June 2005; received 13 August 2008; revision received 17 May 2010; accepted for publication 17 May 2010. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0001-1452/10 and $10.00 in correspondence with the CCC. ∗ Associate Professor, Department of Mechanical Engineering, 3-5-1 Johoku, Naka-ku, Hamamatsu; currently Associate Professor, Department of Mechanical and Systems Engineering, Ryukoku University. Senior Member AIAA. † Technical Engineer, Huenefeldstrasse 1-5. Member AIAA. ‡ Professor, Institute of Space and Astronautical Science, 3-1-1 Yoshinodai, Sagamihara. Associate Fellow AIAA. AIAA JOURNAL Vol. 48, No. 10, October 2010 2177