Tech. Center at MRTI, PhD. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. 4 - 7 January 2010, Orlando, ...
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition 4 - 7 January 2010, Orlando, Florida
AIAA 2010-1006
Electrodynamic Problems of Boundary-Layer Control Method Based on Array of Microwave-Heated Elements Igor I. Esakov1, Kirill V. Khodataev2, Pavel B. Lavrov3, Alexander A. Ravaev4 Moscow Radiotechnical Institute RAS, Moscow 117519, Russia
First results of theoretical and experimental investigations being an integral part of the works on development of new boundary-layer control method using regular spanwise array of MW-heated elements on a dielectric surface of airfoil model are considered in this paper. Attention is paid to three basic electrodynamic problems of the project. The first one is to develop and design new electrodynamic system consisting of tens of closely located electromagnetically coupled and, what is very important, homogeneously heated elements. The second problem is to provide high responsivity of such system, i.e. high efficiency of its heating under action of microwave radiation from remotely located irradiating system of the MW generator with limited output power. And the last problem is to create required spanwise temperature profile (contrast) on a model surface during tests in a wind-tunnel. Various types and versions of MW-heated elements, including high and low-Q resistive vibrators based on ceramic resistors and composite materials, principally new systems of high-Q metallic and graphite vibrators located on a thin foil-laminated substrate, “usual” quarter-wave plate-type MW absorbers and some others have been studied. The results of their numerical simulation and experimental investigations, comparative analysis, advantages and disadvantages are considered in detail. By the moment almost all the specified problems were successfully solved. Physical grounds of creation of regular multisystem of MW-heated vibrators on a dielectric surface were developed. This allowed to design airfoil model and to start joint aerodynamic windtunnel tests together with specialists from Institute of Hydromechanics and National Aviation University in Kiev.
Nomenclature MW EM E and E0 H and H0 ,
Q T texp z
РMW Ploss tanδ R
µ µ
= = = = = = = = = = = = = = = =
microwave electromagnetic amplitude of electric field of EM radiation amplitude of magnetic field of EM radiation MW radiation circular frequency and wave length quality factor temperature exposure time spanwise period of MW-discharge system MW generator power MW power losses loss-tangent electric conductivity ohmic resistance magnetic permeability magnetic permeability
1
Deputy director of MRTI on science, PhD Head of Plasma Physics Department, Professor, Dr. of phys.-math. sci., AIAA Member 3 Post-graduate student 4 Deputy director of Plasma Physics Sci.-Tech. Center at MRTI, PhD 2
1 American Institute of Aeronautics and Astronautics Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
I.
Introduction
T
HE paper is devoted to the analysis and search for ways of solution of the most important electrodynamic problems accruing at the development of a new boundary-layer control method based on a turbulent scale modification in a vicinity of an airfoil surface. In contrast to the “plasma” modification of this method using multivibrator system of initiators of MW discharges [1,2,3], this one is based on application of spanwise array of MW-heated vibrators. The main aerodynamic idea lying in the basis of both methods is well described in Ref. [4,5]. Attention is paid to three basic electrodynamic problems of the project. The first one is to develop principally new electrodynamic system consisting of tens of closely located electromagnetically coupled and homogeneously heated elements. Scrupulous analysis of available science press has indicated that nobody studied and solved the problem of uniform excitation of such array of multiple passive electromagnetic vibrators in a quasioptical EM beam till now. The second problem is to provide high responsivity of such system, i.e. high efficiency of its heating under action of microwave radiation from remotely located irradiating system of a MW generator with strictly limited output power. And the last problem is to create required spanwise temperature profile (contrast) on a model surface during tests in a wind-tunnel. First one should consider two classes of multi-vibrator systems, namely: high and low Q-factor vibrators.
II.
System of high-Q thin metallic vibrators
Choice of material and a cross section of a metal-strip vibrator It is well known that at interaction of microwaves with a metallic body EM energy is dissipated only in its thin surface layer – in so called “skin-layer”. Therefore from the viewpoint of absorption of MW radiation (and consequently heating efficiency), a metallic vibrator has optimal parameters if its typical span-wise size a (halfwidth of a strip or a radius of a wire segment) is commensurable with a skin-layer depth: 1/ 2
2 2a 0
,
(2.1)
Fig.1. Radial distribution of MW power losses where ω is circle frequency, µ0 = 4π·10-7 H/m – in the cross-section of infinite Ni-Cr wire. Results magnetic constant, µ – material permeability, and σ – its of numerical simulation ( = 12.24 cm, a = 100 μm) conductivity. For example, in case of Ni-Cr alloy with a conductivity σ = 1·106 S/m the skin-layer depth is δ ~ 10 µm at MW frequency of 2.45 GHz. A temperature of a MW-heated conductor is proportional to the absorbed energy and an exposure time, T ~ Q·t. Arising conducting currents (Foucault currents) in the metallic vibrator result in the dissipation of EM energy Q, which is released in a form of Joule heat. A value of Q can be determined by different ways: (i) through the current density and the conductor’s conductivity in the field E:
Q jEdV E 2 dV , (ii) from the solution of the diffraction problem and using concepts of scattering (radiation) and absorption crosssections, (iii) calculating the magnetic moment and complex magnetic polarizability (susceptibility) of the conducting body α = α' + iα", and finally, (iv) applying modern numerical simulation methods by using such powerful program products as CST Studio Suite or AnSoft HFSS. Authors of [6] considered the skin-effect in quasi-stationary EM field (at a > a,
(2.2)
at δ
