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                                           V.A.Bityurin, A.N.Bocharov
                Institute for High Temperatures of Russian Academy of Sciences, Moscow, Russia
                                Tel. 7 (095) 484 28 44, E-mail:
                                           LyTec LLC, Tullahoma, TN, USA

Abstract. Experimental and theoretical studies of the MHD flow interaction around aerobodies [9,10,16-24,26,30,31] in a
hypersonic ionized air stream are presented with comments on potential application for flow and flight control for advanced
aerospace vehicles. The current work is a continuation of past efforts by the authors’ directed at characterization of MHD
flow field interaction over/around several different basic geometric configurations with mutually orthogonal magnetic field
and velocity vectors. Experimental results from tests conducted with wedge models in a hypervelocity MHD accelerator
driven wind tunnel facility with ionized air flow at an MHD interaction parameter, Su, of 0.1.are presented. Distinctive MHD
influence on the flow structure around the wedge was confirmed in experiments. Experimental and numerical simulations
with a wedge configuration that is representative of a hypersonic inlet are reported. The potential for use of MHD interaction
to adjust the oblique shock system to achieve an on-cowl lip condition when flight operation is off-design was demonstrated.
Supporting analysis work has achieved correlation with experimental observations and provides a means to project MHD
interaction effects to full-scale hypersonic vehicles subject to real atmospheric flight.

Introduction                                                      investigated in more details. The incompressible
                                                                  MHD flows around bodies including cylindrical that
          A new MHD role for aerospace                            were vastly studied in 60th (see, for example, [3]).
applications was formulated at fiftieth [1] when the              Many exact and approximate analytical methods
re-entry problem became real and critically                       were developed for solving problems on the MHD
important. Several proposals have been developed to               flow over bodies of different shape. The
reduce heat flux strength at critical point by means              bibliography of earlier studies on the finite
of magnetic field created by an on-board system. At               conductivity MHD flows can be found in [4]. In one
the same time two new areas were formed where the                 of the first work on the supersonic MHD flow
MHD effects are the primary importance – MHD                      around a body [4] it was shown that increasing
electrical power generation as a direct heat energy               MHD interaction factor leads to increasing of the
conversion into electricity and thermonuclear                     bow-shock stand-off distance. Many fundamental
reactors with magnetic sustain of active matter – hot             features of MHD flows have been revealed in works
high temperature plasma.                                          of Bush [6,7] and Bleviss [8]. From recent studies
          A number of successful demonstration of                 on MHD flows around bodies note the works [9-13].
MHD interaction stimulated research and                           In papers [9-12] the Hall effect was neglected. In
development a numerous applications and                           [10] the effects of chemistry on the MHD flow
particularly for space. One of the practically                    around a blunt body were evaluated. In [13] the two-
developed branches is the development of so called                dimensional analysis of the Scramjet inlet has been
MHD low thrust accelerators for long term                         carried out.
interplanetary journey. Another example of the                              Later a number of papers are published at
successful development of a large-scale MHD                       AIAA Aerospace Science meetings (USA), Weakly
system is pulse MHD generator in power output                     Ionized Gas Workshop (AF,USA) , Moscow
range from 1MWe till 100MWe for special                           Workshop        on    Magneto-Aerodynamics        for
applications in defense systems.                                  Aerospace Applications (RAS/EOARD) and at
          Since 50th considerable attention has been              others forums.
paid to the flows around blunt body in the presence                         In hypersonic low-pressure air flows
of external magnetic field. At high magnetic                      (M>10) the electrical conductivity behind the bow-
Reynolds number the fluid deforms the magnetic                    shock may become sufficient for the strong MHD
field, rather than passes through it. As a result liquid          interaction to appear in the presence of magnetic
free cavities are produced near the body, which                   field of order of one Tesla.
prevents to appearing of large heat flux into the                           The     primary    conditions    for   the
body surface [2]. The application problems of                     implementation of any on-board MHD technology
author’s interest are those in which magnetic                     are the first - to provide a sufficient level of
Reynolds number values are of order of unit or even               electrical conductivity of airflow and, the second –
much less. In this case the feasibility of MHD flow               to make proper design of the magnetic system,
control relies on another principles and should be                which is known to be a weight critical component.
                                                                  In this respect, the physical background of flow

parameters modification and the magnetic system          In the case under consideration when one of the
assessments are discussed further in this Section.       main peculiarities of the process is the ionization
The magnet size and weight must be gauged against        phenomena in shock layer on the vehicle surface the
the gain that can be obtained in terms of flow           magnetohydrodynamic (MHD) interaction can be
optimization. Some general relationships are             used to extend the optimizing flow control.
obtained in this Section, which should be useful for              Generally speaking the MHD interaction is
the development of a systematic approach to this         characterized by the local momentum and energy
problem.                                                 conversion and their redistribution over the flow
          The MHD flow/flight control is one of the      field. The ponderomotive force
clearest options of MHD technology applications in
this field. However in literature there are not so       F = ∫ j × BdV                                   (1)
many good examples of such a suggestion.
Typically the MHD flow control is the natural
component of another suggestion including MHD            integrated over whole external flow has provided the
interaction such as, for example, MHD scramjet in-       reaction R = − F and, probably, the moment
take optimization.
          The latter is included in one of the most      K = ∫ r × ( j × B)dV .                          (2)
intrigue cases of MHD application in aerospace so-
called AJAX concept proposed more than ten years                These two body force integral values in
ago in Russia. The basic idea is to use MHD energy       combination with conventional gasdynamics force
conversion cycle to provide more desirable flow          and moment
conditions inside of scramjet flow train from in-take
up to the nozzle exit. The results of estimation for
                                                         Fgd = − ∫ p n dS , K = − ∫ r × p n dS           (3)
this type of system, based on a simplified analysis,
are discussed herein.
          One of the most promising fields for MHD       define the motion of the aircraft in atmosphere. It is
applications is MHD control of the bow shock             important     to    note     that     electrodynamics
characteristics. In particular, optimization of the      ponderomotive force f-j×B and energy source jE
drag to thrust ratio and/or a significant reduction in   modifies the flow field and, consequently indirectly
vehicle heat stress can be expected. Theoretical         change the gasdynamics values Fgd and Kgd.
estimations and numerical simulation have shown                    Thus,     the       magnetohydrodynamics
that the bow shock configuration changes                 interaction between the external flow and electrical
significantly when in the presence of an externally      and magnetic fields can be used as an additional
applied magnetic field. On the other hand, the           flight control system influencing on the external
reliable flow parameters prediction is still             flow in some vicinity of the vehicle. The flow region
problematic due to very complicated phenomena            affected by such a control system is independent
that occur in the vicinity of a hypersonic vehicle       directly upon Mach number distribution.
nose.                                                              The MHD interaction intensity is
                                                         characterized by the value of so-called MHD
Background                                               interaction parameters (or Steward Number) equal to
                                                         the ratio of the electromagnetic body force j×B
         The motion of spacecraft in the upper           times characteristics length l to the dynamics
atmosphere occurs with hypersonic velocity and for       pressure gradient
these reason results in a strong shock wave creation.
The strong shock waves form highly non-uniform           S = j × B l ρu 2 ≈ σB 2 l ρu ,                  (4)
flow field. The velocity of spacecraft between 7 and
11km/s corresponds to temperature elevation just
                                                         where j is the electrical current density, B is the
behind the shock up to 10000-20000K. Due to
                                                         magnetic induction, and l represents a characteristics
relaxation phenomena the air temperature decreases
                                                         length (a deceleration distance). It should be noted
to the level of 5000-10000K at the vehicle surface.
                                                         that the second definition of the Steward number is
High heat fluxes in the vicinity of critical points of
                                                         based on an implicit assumption that the electrical
spacecraft limit the acceptable trajectories of
                                                         current is self-generated. The current is produce by
different kinds of spacecraft and need to optimize
                                                         the mechanical work done by the flow against body
the flow around the hypervelocity vehicle.
                                                         force j×B. In an on-board MHD flow/flight control
Traditional gas dynamics approach is based on the
                                                         system, the electrical current can be defined by
vehicle shape and trajectory optimization. The
                                                         externally applied electrical field, which could be
potential of the condition optimization can be
                                                         much higher as compared with the characteristic
increased significantly by involving additional
                                                         value of induced field u×B. In such cases the actual
physical phenomena influencing on the flow field.
                                                         MHD interaction could be correspondingly much

higher than the classical MHD estimation. One of                     In the case of externally applied electric
the examples is a MHD accelerator providing                field the similar estimation gives
significant increase of the jet impulse.                          σEBl ne e 2τ EBl                 eV
         Electrical current density j is defined by the     Sp ≈        =                = K = αωτ     . (8)
                                                                    p       me na kTa              kTa
generalized Ohm's law, one of the it’s simplest form
including so-called Hall effect is
                                                                    In this expression V represents an external
j + ωτ Bj × B = σ (E + u × B ) ,                 (5)       voltage applied over the whole interaction area.
                                                                    In high Mach number supersonic flow it is
                                                           important to note that two different definition of
where σ is electrical conductivity and ωτ Hall             MHD interaction parameter – by momentum Su and
parameter. The electrical conductivity can be              by pressure Sp are connected as following:
estimated by formula σ = ne e 2 τ me , where ne is         S p ≈ S uγ M 2 .
electron number density and τ is a free path time.
                                                                     One of the most important meaning of the
Consequently in the same approximation the Hall
                                                           Hall parameter is to indicate when the scalar
parameter is
                                                           (‘conventional’)      character      of    the     plasma
                                                           conductivity in external magnetic field (ωτ<<1)
ωτ = eB m eτ or ωτ = σB ne e .
                                                           changes to the tensor character of the conductivity
                                                           (ωτ≥1). The tensor character of the conductivity
          It is clear that there are two key values        results, in particular, in the fact that the directions of
needed for actual MHD interaction: electrical              electrical field and current density vectors are
conductivity and magnetic field. The magnetic field        significant different. Furthermore the effective
can be in principle created with a proper on-board         plasma impedance becomes higher along with the
magnetic system. The electrical conductivity needs         value of (1+ωτ2). It is known however that the
the presence of free charges in the gas flow – in          effective conductivity of plasma in magnetic field
practice it should be electrons. Taking as an example      can be recovered in principle with special
the conditions of upper atmospheric hypersonic             configuration of electric field. Unfortunately under
flight: velocity 3000m/s, temperature 250K, pressure       realistic conditions of more or less significant non-
1kPa, gas density 0.01kg/m3 one can find the current       uniformity of electrical conductivity in flow such an
density required for effective MHD interaction (S ~        electrical field re-configuration becomes not
1) j ~ ρu2/Bl ~ 104 - 105A/m2 for B=1T and l~1m.           effective – the effective plasma impedance is
          Thus, the required level of the electrical
                                                           estimated as r = G σ , where so-called G-factor
conductivity is from several Siemens till several tens
of Siemens. In the pure air such a level of electrical     firstly introduced by R. Rosa [14] is defined as
conductivity corresponds under thermal equilibrium
conditions to the temperature above 6000-7000K.            G = (κ − 1)(ωτ ) 2 + κ ,
This level is reached in the hypersonic viscous                                                                (9)
                                                           κ = 〈σ 〉〈1 σ 〉 where κ ≥ 1
shock layer formed behind bow shock in hypersonic
          Another possibility to provide the                        Furthermore, under conditions when the
conductivity is an artificially created a rather high      Hall current leakage is allowed the G-factor should
ionization degree. The latter can be estimated as          be modified as

       meQea     3kTe                                      G x = (κ − k x )(ωτ ) 2 + κ , where   kx ≤ 1 .      (10)
α ≈σ                  ≈ 10-3-10-2 .              (6)
         e2       me
                                                                    Substitution of (10) into (7) and (8) results
         From the other hand the MHD interaction
parameter based on an induced current density as a
characteristic value can be presented in the                      σB 2l ne e2τ B 2l
                                                           Su ≈         =           =
following form:                                                   ρuG x   me ρuG x
                                                                  t me ωτ 2    t me    1
                                                           K=α              →α                         when ρu→∞
     σB 2 l n e e 2τ B 2 l      t me                              τ ma Gx      τ ma (κ − k x )
Su ≈       =               =K=α      (ωτ )2            ,
      ρu      m e ρu            τ ma
                                                                    Thus, MHD interaction parameter for non-
where t is a residence time in working volume.             uniform non-perfectly insulated plasma formation
                                                           saturates at some level with ωτ2→∞ (magnetic field

strength!). For this reason the operation under high     (µ0 is the magnetic permeability of vacuum). Variety
Hall parameter condition (ωτ>1) is rather                of flow regimes is determined by first six
undesirable because results in much more                 gasdynamics         parameters     and      by     four
complexity of on-board MHD system. Then the              electrodynamics ones.
relationships presented above can be used to                        It is notable that under hypersonic flight
estimate the value of governing parameters when the      conditions the non-equilibrium and finite rate
Hall parameter is limited.                               kinetics effects play an important role. Thus, for the
          As it will be shown later the typical values   full characterization of the hypersonic flow over a
of the parameters in MHD interaction parameter           body the Damkoeler number Da=τchu∞ /L is to be
formula for the conditions of hypervelocity flight in    introduced into the expression (13). Moreover,
upper atmosphere are as follows: σ∼200S/m, ρu∼1,         taking into account the low pressure at high altitude
and for the characteristics length the shock wave        and rather limited size of the bodies considered the
distant can be used l∼0.1m. So for effective MHD         Knudsen number Kn = lf /L is to be added into the
interaction the magnetic induction needed is about       right hand side of the symbolic expression (13). It
B≥0.2T that is the routine electromechanical level.      can be shown that the Knudsen number is naturally
However, the discussed above Hall effect limits the      appeared in expressions (7), (8), and (11) in place of
effectiveness significantly.                             τ/t ratio. This fact seems to be very important saying
          In calculating the hypersonic flow over        that the fundamental linear scale for MHD aerospace
blunt body one should take into account the              applications is the free path length of electron.
radiation transfer from the high temperature region.                Three main aspects are considered as a
Also note that factor M2/Re (M is the Mach number        potential for MHD interaction applications to
and Re is the Reynolds number) becomes of order of       hypersonic, and in particularly to re-entry flights:
one, which leads to smearing of the shock wave.          − Heat flux management to reduce the peak heat
          Under conditions mentioned above the               flux values;
MHD flow is described by the following set of the        − On-board MHD electrical power generation;
governing parameters:                                    − MHD hypersonic/reentry flight control.
                                                                    The local MHD flow control such as
ρ∞, p∞, v∞, r, cp, µ, λ, γ, Tw, qR, T, B*, Ez   (12)     boundary layer separation/attachment, laminar-to –
                                                         turbulent transition control are to be considered as
          In (12) cp is the heat capacity at constant    well.
pressure, γ is the ratio of heat capacities, qR is the
characteristic radiation power, or the value of          MHD Flow Around Circular Cylinder
divergence of radiative heat flux, µ=ωeτe/B, ωeτe is
the Hall parameter.                                                The first numerical and experimental
          According to the theory of similarity and      studies of MHD interaction in hypersonic flow were
dimensionality (see, for example [15]), any              conducted with the circular cylinder. Experimental
dimensionless flow characteristics is the function of    studies were carried out on the TsAGI MHD WT
the set of the following parameters                      Facility [20-25]. Bottom part of the facility and the
                                                         test section are schematically shown in Fig.1. The
Γ= {M, Re, γ, Pr, Tw , qR ; S, K, β, Rem},      (13)     feature of the TsAGI Facility is use of MHD
                                                         accelerator to increase the speed of flow up to
          Here M is the Mach number, Re is the           hypersonic values, M ~ 10-15. MHD flow around
Reynolds number, Pr is the Prandtl number, Tw is         cylinder is schematically shown in Fig.2. Magnetic
                                                         field is generated by the current flowing within the
the temperature factor, the ratio of surface             cylinder along the cylinder axis. In such
temperature and the free-stream stagnation               configuration the plasma current providing MHD
temperature. qR is the characteristic radiation          interaction (faraday current) should also flow along
power. S and K are MHD interaction factor and            the cylinder axis, see Fig.2. Plasma is due to the
electric load coefficient, respectively. β is the Hall   presence of atoms of Na or K, which could be
parameter, Rem is the magnetic Reynolds number.          ionized at high temperatures. Seeding is used in
These magnitudes are defined as follows:                 MHD accelerator, and we were assuming that seed
        u2 ρ           ρ u r           cpµ               atoms and/or ions are available in the flow coming
 M 2 = ∞ ∞ , Re = ∞ ∞ , Pr =                ,            into test section. In numerical studies two models of
        γ p∞              µ              λ
                                                         electrical conductivity of flow were considered. In
    σB∗ r        Ez         eτB∗                         first model it was assumed that seed atoms could be
S=         , K=       , β =      ,
    ρ ∞ u∞      u∞ B∗        m                           ionized at high temperatures behind the bow shock.
                                                         In second model we assumed that fully ionized seed
Re m = u∞ rσµ0                                  (14)
                                                         is present in the oncoming flow. Such a
                                                         consideration relies on the supposition that electrons

              Fig.1. General Test Bed Arrangement for Wedge Model MHD Flow Interaction Experiments

available in the MHD accelerator are “frozen”                   source terms are added to the Navier-Stokes
during fast expansion in the nozzle at temperature of           equations. The MHD force and the work of
order of 5500K close to the vibrational temperature             electromagnetic field are found from the solution to
of diatomic molecules. For brevity, the first model is          equation for electric potential. The latter is obtained
referred to as the equilibrium ionization model, and            from the electric charge conservation along with the
the second is referred to as the frozen ionization              generalized Ohm’s low. The solution to the coupled
model. It should be noticed that the first model is             set of gasdynamic and electrodynamic equations is
closer to the re-entry conditions, while the second             sought in the plane of flow and magnetic field. Third
model has appeared to be typical of the given                   (faraday) component of electric current density can
facility. The following flow conditions were                    be derived algebraically from the solution. Details
considered in the numerical simulations, which are              can be found in Refs. [21,30]. The computational
typical for the facility under consideration:                   domain was spread 10 cm upstream the model, 30
                                                                cm downstream, and 20 cm in height. Due to
ρ0 = 1.725·10-4 kg/m3, p0 = 33 Pa, V0 = 5000 m/s,               symmetry, only half of the whole domain can be
T0 = 550 K, M = 9.44.                                           considered. To model ground conditions in the test
                                                                section zero potential was set at the outer boundary.
16 mm cylinder was tested both in experiments and               At the upstream part of the outer boundary the
computations. For these conditions, Reynolds                    oncoming flow conditions were applied as boundary
number based on cylinder diameter is ~800. The 2%               conditions. At the downstream part of the boundary
seed mole fraction was taken. Azimuthal magnetic                two types of boundary conditions were applied. For
field is generated by the pulse of electric current,            supersonic outflow simple extrapolation of flow
such that at-surface magnetic induction varies from             variables from the interior was used. For subsonic
0 to 2 tesla and back for 2 ms. However, steady-state           outflow typical for strong MHD interaction the static
solutions with constant magnetic field were sought              pressure was set to prevent the backward flow
in computations.                                                entering into the domain. At the cylinder surface no-
          As seen from Fig.2 the designed                       slip conditions along with the constant temperature
configuration allows one to apply the two-                      condition were specified. Insulating boundary
dimensional numerical models to analyze the MHD                 conditions were set in the electrodynamics problem.
flow around the cylinder. Low magnetic Reynolds                 Symmetry conditions were applied at the symmetry
number approach was used, in which the MHD                      lines.

                       Bow Shock


                      jxB                                                   B

                  Fig.2. Schematic of MHD flow over the circular cylinder with axial electric current.

                                  a)                                                      b)
          Fig.3. Distribution of pressure for B0=1.25T. a) equilibrium ionization model; b) frozen ionization model.

                                 a)                                                      b)
        Fig.4. Distribution of temperature for B=1.25T. a) equilibrium ionization model; b) frozen ionization model.

          Fig.3 and Fig.4 demonstrate the flow fields             flux on the surface. This well known result has been
obtained for two ionization models and at-surface                 predicted by many authors, but with one exception.
magnetic field 1.25 tesla. In Fig.3a the static                   In most of publications the Hall effect (direction of
pressure distribution at the vicinity of cylinder is              electric current density doesn’t coincide with the
shown for the case of equilibrium ionization model                direction of electric field) was neglected. Our
(model 1). In Fig.3b the same field is shown for the              analysis (see, for example, Refs. [20-22]) has shown
frozen ionization model (model 2). Fig.4a and 4b                  that in low-density flows Hall effect is a key factor
demonstrate the temperature distributions for the                 and cannot be omitted. For comparison, the Curves
conditions corresponding to Figs.3. Several features              4 on both graphs correspond to the case of no Hall
are clearly seen from the pictures. The bow shock                 effect and should be compared with Curves 1. In
stand-off distance is essentially larger in the case of           spite the significant differences in characteristics
equilibrium ionization model. Both position and                   obtained with taking Hall effect into account and
shape of the shock in the case of equilibrium                     with neglecting it, the attractive features related with
ionization model differ significantly from the                    MHD flow control could remain even in the case of
original, MHD-off case values. For the frozen                     very strong Hall effect (it is characterized by the so
ionization model, the bow shock slightly changes                  called Hall parameter, βe = ωe·τe, production of
from its original shape. Also, perturbation of the                electron gyro-magnetic frequency and mean electron
flow field behind the shock differs dramatically for              collision time). As far as the frozen ionization model
these two ionization models. From these one could
conclude that effect of magnetic field on the flow is                             5
much stronger for the case of equilibrium ionization
model than for the case of frozen ionization one. At
the same time, in the case of frozen ionization                                   4
remarkable perturbation of temperature is observed                                                          3
                                                                  Pressure, kPa

in a large region upstream the bow shock, compare
Fig.4a and 4b. This means that MHD interaction
takes place in this cold, low conductivity region.                                                          4
Before giving several comments on the influence of                                2
external magnetic field on the hypersonic flow
around circular cylinder, some local characteristics
will be presented for the case of equilibrium                                     1
                                                                                          0    1        2
ionization model. In Fig.5 the position of bow shock
on the stagnation line is shown for the different                                 0
values of the at-surface magnetic induction. For the
same magnetic induction values, Fig.6 represents the                                  0.00      0.01       0.02         0.03
distributions of the heat flux density on the cylinder                                  Distance along stagnation line, m
surface. It is seen that both stand-off distance and             Fig.5. Effect of magnetic field on distribution of pressure
the heat flux distribution correlate well with the                  along stagnation line. Curve 0–B=0; 1–B=1T; 2-
magnetic field amplitude: the higher magnetic field,                  B=1.25T; 3-B=1.50T; 4-B=1T, no Hall effect.
the larger stand-off distance and the lower the heat

                                                                                    field), is low. In this case one could say that the
                               4                                                    operation mode is close to the short-circuit
                                                                                    conditions for the Hall electric field. From analysis
  Heat flux density, MW/m**2
                                                                                    Ref. [21] it follows that Hall current should be large,
                               3   1
                                                                                    and overall efficiency of MHD effect is reduced by
                                                                                    factor 1/(1+ βe2) from its nominal value achievable
                                   2                                                in the case of no Hall effect case. Experimental
                                   3                                                conditions were such that Hall parameter βe can vary
                                                                                    in the range of 101 ÷ 102. This explains why no
                                                                                    visible interaction took place in the vicinity of
                                                                                    cylinder where magnetic field is maximal. In the
                               1                                                    large regions upstream the bow shock and in region
                                                                                    of wake the treatment given above is valid. The
                                                                                    difference from the near-body region is that the
                               0                                                    amplitude of magnetic field is essentially smaller;
                                0.00         0.01     0.02       0.03               therefore efficiency of MHD interaction is
                                       Distance along surface, m                    essentially higher in those regions.
                                                                                              The case of equilibrium ionization model
  Fig.6. Effect of magnetic field on the surface heat flux.                         rather corresponds to the so called open-circuit
 Curve 0-B=0; 1-B=1T; 2-B=1.25T; 3-B=1.50T; 4-B=1T,                                 conditions for the Hall current (zero total Hall
                      no Hall effect.                                               current). In this case large longitudinal voltage drop
                                                                                    should take place, and overall efficiency of MHD
                                                                                    interaction becomes comparable with the case when
is concerned, no remarkable effect of magnetic field                                the Hall effect is neglected. Note, that such the case
on the near cylinder flow field has been observed.                                  is more suitable for the flight conditions because the
          Intensive experimental studies on MHD                                     bow shock represents a natural boundary for the
flow around a circular cylinder confirmed                                           ionization domain, within which the overall Hall
hypothesis that the flow in test section is much                                    current is expected to be small.
closer to the frozen ionization model than to
equilibrium one. No visible shock displacement has                                  MHD Interaction Over Wedge
been revealed. However, noticeable changes in flow
structure were detected in a large region upstream                                           In the more recent experimental work [24],
cylinder and in the wake. Details on experimental                                   wedge shaped models were used. Again, the wedge
setup and results can be found in Refs. [20,21,30].                                 models were designed with an embedded
          Here we shortly summarize the main                                        electromagnet and surface electrodes to view
features of MHD flow around a cylinder with                                         perturbation of the flow structure around the wedge
current. As the flow in the test section of TsAGI                                   by MHD interaction and measurement of induced
MHD WT Facility is ionized everywhere, MHD                                          electrodynamics. A simplistic sketch of the wedge
interaction could take place in a whole flow region,                                model and general test configuration is provided in
not only in the vicinity of cylinder behind the bow                                 Fig.7.
shock. Under such conditions two principal factors                                           The wedge simulates a geometric
determine the character of MHD flow: Hall effect                                    configuration that is representative of a hypersonic
and electrical circuit including plasma bulk, facility                              vehicle forebody and inlet. Active control for
elements and external circuit. Due to grounding of                                  positioning the bow to cowl oblique shock structure
all elements of the facility the voltage drop along the                             is considered to be an application for the MHD inlet
flow direction, or longitudinal electric field (Hall                                to advance hypersonic technology. This concept was

                                        Fig.7. General Test Bed Arrangement for Wedge Model MHD Flow Interaction Experiments

posed at the onset of this research project.                           Ionized Gases workshop. Parameters of the
         Experiments conducted in the MHD                              incoming ionized air stream to the test section are as
accelerator tunnel under this project during 2003-                     follows:
2004 utilized various wedge models with embedded
electromagnets and surface electrodes. One model                       ρ0 = 2.835·10-4 kg/m3, p0 = 33 Pa,
was configured to simulate a hypersonic inlet ramp                     V0 = 4,760 m/s, T0 = 350 K.
and opposing cowl lip.
                                                                                The magnet is configured by a set of
                800                                                    conductors embedded in the ramp plate and aligned
                                                                       normal to the plate surface. Therefore, magnetic
                                                                       field is in the same plane as the incoming flow
                600                                                    direction. It should be noticed that this type of
                                                                       magnet configuration differs from more traditional
Pressure, Pa

                        model 2                   model 1              ideas in which the magnetic field is perpendicular to
                                                                       the plane of flow. This choice was due to design
                400                                                    constraints.
                                                  B = 2T
                                                                                 Along with the latest experimental effort
                200                               B = 1T               has been extensive analysis of past results through
                                                                       use of project developed 2-D CFD/MHD
                                                                       simulations methodologies. This analysis work has
                   0                                                   been directed at using the experimental results to
                                                                       validate the computational codes and then utilizing
                    0.00              0.04           0.08
                                                                       the code as a means to extrapolate results towards
                           Distance from the wall, m                   true hypersonic flight conditions and flight scale
                                                                       hardware. Reporting on these latest activities is
               Fig.8. Outlet Boundary Pressure Distribution for        provided in the following.
                    Computational Cases Shown in Fig.9.                          First impressions on the MHD flow over
                                                                       the wedge can be obtained view of Figs.8 and 9.
                                                                       These figures map the pressure fields for the two
          One of the most significant results obtained                 electrical conductivity models and for two distinct
in this project was a demonstration of MHD                             values of magnetic field intensity.
interaction flow field manipulation with the inlet                               he first model assumes that seeding atoms
model. This result was reported in our previous                        can be ionized only at high temperatures behind the
AIAA publication9 at the 5th Air Force Weakly                          oblique shock. The second conductivity model
                                                                       assumes that gas is ionized everywhere with relative

               Electrical Conductivity Model 2 – B = 1.0 Tesla Case   Electrical Conductivity Model 1 – B = 1.0 Tesla Case

               Electrical Conductivity Model 2 – B = 2.0 Tesla Case   Electrical Conductivity Model 1 – B = 2.0 Tesla Case

       Fig.9. Representative Numerical Simulations of Ionized Air Flow Over a Wedge Surface With Varying Level of MHD

    Experimental Photographs of Wedge Model Test (Right Side Photo Images – Left Side Spectral Enhanced Images)

                MHD - Off Flow                                 Conductivity Model 2 – B = 2.0 Tesla

                             Representative Numerical Simulations of Temperature Field

                 Fig.10. Hypersonic Flow Over a Single Wedge – Experimental and Numerical Results

electron concentration as high as 0.01. As a measure         considered as the most prominent effect of MHD
of magnetic field intensity, the value of magnetic           interaction on the flow. It is seen from Fig.9 that
induction at the plate surface is used.                      shock deviation increases with increasing the
          The top pictures in Fig.9 correspond to a          magnetic field level.
magnetic induction value of 1 Tesla and the bottom                     In Fig.8, the pressure distributions along
pictures correspond to 2 Tesla. (It should be                the outlet (right) boundary are shown for the cases
mentioned that magnetic field in the domain is               presented in Fig.9. Both the influence of magnetic
inversely proportional to the distance from the              field and the difference between the two
magnetic system. Therefore, the domain-averaged              conductivity models are distinctively seen.
magnetic induction value is approximately one order                    Experimental photographs with evidence of
of magnitude less than characteristic one.) The left         the presence of MHD interaction on the flow over
row of pictures corresponds to the second                    the wedge can be seen in Fig. 10. The left photos
conductivity model while the right rows correspond           represent the flow visualization made by 2000 fps
to the first one. The black-colored lines on the             camera. The right images of the same flow were
pictures show the location of shock for undisturbed          obtained with spectral filtering. A filter with the
flow field (no MHD). The main feature of these               wavelength 779 nm and the width 15nm was used.
distributions is that MHD interaction takes place for        The top photos correspond to the non-MHD case
both conductivity models. The oblique shock                  and bottom pictures correspond to the MHD-On
deviates from the wedge surface, which is                    case. The influence of MHD interaction can be

           Electromagnetic Force (J×B) Distribution                                 Energy Deposition (J.E)

           Electromagnetic Force (J×B) Distribution                                 Energy Deposition (J.E)

                          Fig.11. Numerical Simulations of MHD Interacting Flow Over a Wedge

detected both by increasing the luminosity and by            conductivity model, the situation is closer to open-
increasing the angle of deviation of oblique shock           circuit conditions, i.e. non-zero electric field along
from the wedge surface. The right bottom image               with the small Hall current. As a consequence, non-
shows that there is a disturbance of intensity in the        zero Faraday current prevails. It was also noted that
region upstream the body leading edge. This is               there are several MHD operation modes within the
caused by the presence of MHD interaction in the             flow field. For the shorted Hall lectric field
oncoming flow specific for the second conductivity           (experimental conditions), the region just upstream
model.                                                       the cylinder is the MHD-acceleration zone, i.e., the
          The qualitative agreement of the                   electromagnetic force acts toward the body surface.
experimental and computational flow fields can be            At the same time the large region behind the
seen by comparing photographs to calculations in             cylinder was the MHD power generation zone. The
Fig.10. The temperature field is shown                       energy from MHD generation zone is transferred to
corresponding to the calculations made with the two          the MHD acceleration and flow braking zones. The
conductivity models and with characteristic                  latter zone is located between the nozzle and the
magnetic induction value 2 Tesla.                            bow shock.
          The effect of conductivity model on the                     All these effects as derived from analysis of
flow field is well seen. In general, stronger MHD            the cylinder studies also take place in the flow over
interaction takes place in the case of first model.          the wedge. Fig.11 shows the distribution of flow
This displays in a higher level of pressure and a            directed component of electromagnetic force [J×B]x
larger deviation of shock from the wedge surface.            (upper picture) and the distribution of energy
The reasons for these distinctions were recognized           source-term (J@E). (On all pictures the blue color
in References [20-23] where experimental and                 corresponds to negative values of the force and
theoretical study of flow around a circular cylinder         power rate, yellow-red color corresponds to positive
was reported.                                                values, and green denotes close-to-zero values.)
          It was determined in the previous works            These distributions were obtained for the
with the cylinder geometry, that the Hall effect is the      characteristic magnetic field value 2 Tesla with the
primary influence on the flow structure. In the case         upper pair being for the second conductivity model
of the second conductivity model, the fluid is               (or Hall field shorted condition) and the lower pair
conductive in the entire domain and since all the test       being for the first conductivity model (open-circuit
cell elements are grounded, near zero electric field         Hall field).
in the direction of main flow exists (i.e., short-circuit             Most of the oncoming flow experiences as
conditions). This results in a large current leakage in      the MHD brake force since energy is released and
the flow direction (Hall current) and the force-             the flow decelerates. Two regions left and right of
generating Faraday current (perpendicular to the             magnetic system operate as the MHD generator:
flow plane) is small. Whereas, in the case of the first      energy is extracted and flow decelerates. The region

just above the magnetic system operates as the MHD         cylinder case, provide a positive effect on the flow
accelerator both power and force are positive. This        structure over a wedge. Namely, a significant
structure is almost the same as was observed in the        change in the oblique shock angle is confirmed by
circular cylinder studies of previous works. In the        both the experimental studies and computations.
wedge case both generation zones are placed near                    Second, much stronger MHD interaction
the surface. Unlike the cylinder, MHD-induced flow         has been observed in the numerical simulations for
deformations occur in the region of flow to be             the open-circuit conditions, i.e. for conditions close
modified. As a result noticeable changes in the flow       to those of real flight. In spite of the large values of
field take place even in non-ideal, short-circuit case.    Hall parameter inherent to the low-density flows, the
          Two MHD generation zones left and right          configuration of electric fields is such that the
of the magnetic system are present in both cases           undesirable Hall currents have a bounded influence
calculated, as well as, the MHD acceleration zone          on the MHD interaction intensity. This gives an
between them. However, the intensities of                  opportunity for the MHD flow control under real
interaction in the cases differ essentially as can be      flight conditions and some predictions will be
seen from reference values shown in Figures.               discussed later.
          According to the analysis made in [21-23],
the absence of total Hall current may restore the          Prediction of MHD control of at Flight
MHD interaction characterized to the ideal factor,         Scale
which is realized in non-magnetized fluid. In the
case of first conductivity model, the total Hall                     Analysis work has extended to consider
current is close to zero because of the closed loop        MHD interaction for flight scale hypersonic bodies.
character of the current pattern. This circumstance        Emphasis has been in study of a blunt nose body and
reduces the nominal MHD interaction by a factor of         is made on two aspects: the effect of MHD
two at higher characteristic values of magnetic field,     interaction on the bow shock position and the
but not by an order of magnitude as seen in the case       decrease or redistribution of the heat flux on the
of the first model. From one viewpoint, this is due to     surface of the body. It is assumed that the magnetic
applied boundary conditions (zero electric                 field is created by the coil producing dipole-like
potential). From another, these boundary conditions        magnetic field near the critical point of the body.
simulate the grounded conditions of bottom ends of         The coil (one turn with current) of radius of 0.2 m
the test bed. In the case of short-circuit conditions, a   was used to generate the dipole-like magnetic field
large Hall current (consequence of small amplitude         near the stagnation point of the spherical part of the
of Hall electric field) results in a situation, when the   body. The magnetic strength value at the stagnation
intensity of MHD interaction is significantly              point is characterizes the magnetic field amplitude.
affected by a factor of 1/(1+ βe 2).                       The body itself is a spherical-conical configuration
          This study revealed two important features
                                                           with spherical nose radius of 0.72m and a 15° cone
of hypersonic MHD flow. First, even under not the
best conditions realized in experimental facility the
                                                                     Flight conditions selected for analysis
MHD interaction can significantly impact the flow
                                                           corresponding to the altitude of 60 km with
structure, such that desirable flow properties can be
achieved. This has been demonstrated both by
                                                           P∞ = 11 Pa, ρ∞ = 1.64·10-4 kg/m3,
experiments and numerical analyses. The
                                                           V∞ = 6500 m/s, M∞ = 21.15.
unanticipated results obtained in the experimental
study of flow around the cylinder were due to the
                                                                    The flow behind the bow shock is known to
fact that short-circuit conditions specific for the
                                                           be in thermo-chemical non-equilibrium. To
MHD WT facility were realized. This resulted in
                                                           determine the flow characteristics the computational
little interaction in the region near the cylinder
                                                           model described in Refs. [26,27] is applied. This
stagnation point, which was considered as the region
                                                           model includes the Navier-Stokes equations coupled
of primary interest. At the same time, significant
                                                           with the equations for mass conservation of
MHD interaction was detected in the region far
                                                           individual species. In addition, the vibrational
downstream the cylinder.
                                                           excitation and vibrational energy transport is taken
          As far as the flow over a wedge is
                                                           into account for each diatomic species. The
concerned the structure of electric fields is
                                                           vibrational-translational relaxation is estimated on
qualitatively same as in the case of the cylinder.
                                                           the base of the Landau-Teller model for the
However, the small interaction region located just
                                                           vibrational-translational characteristic relaxation
above the magnetic system (which is similar to the
                                                           times. The species production rates due to chemical
region just in front of the cylinder) is in general
                                                           conversions are evaluated from the chemical kinetics
surrounded by two regions where strong MHD
                                                           model described in Ref. [27] that includes 11 species
interaction is observed. These strong interaction
                                                           with 80 reactions. (The original 11 species – 98
regions, similar to the downstream regions for the
                                                           reactions model was reduced since addition of

molecular oxygen ion to the scheme has negligible                                         Xe = ε + X0 ⋅ th((T-T0)/D),
effect.) The reaction rate constants for dissociation
reactions are modified in accordance with the                                             where ε = 10-9, T0 = 3000 K, D = 3000 K, X0 = 0.002
Marrone-Treanor model (Ref. [28]) to take into                                                     The steady-state solution was sought for
account the influence of vibrational excitation of                                        each characteristic value of the magnetic field
diatomic molecules on the dissociation. The                                               induction.
transport coefficients are calculated according to the                                             Fig.13a gives the distributions of
work of Ref. [29] (also Ref. [27]).                                                       temperature along the stagnation line with
         The      two-dimensional        axisymmetric                                     dependence on magnetic field amplitude. It is seen
formulation is used. The free-stream data along with                                      that position of the bow shock changes with
79% N2 + 21% O2 (mole fractions) air composition                                          increasing of the magnetic field amplitude. Within
are applied as inlet boundary conditions. At the                                          the shock layer the electromagnetic force acts
body surface, the no-slip conditions are specified,                                       mainly against the flow. This leads to shifting the
the wall temperature Tw = 1,650 K is set, and zero-                                       bow shock position toward the free stream flow and
gradient condition is applied for species                                                 a re-distribution of temperature within the shock
concentrations and vibrational temperatures.                                              layer. The temperature re-distribution is such that
Symmetry conditions are applied at the symmetry                                           the temperature gradient drops, and, hence,
axis. Numerical solution is obtained with same                                            conductive heat flux into the surface decreases.
technique described in Ref.[30].                                                          However, the structure of the flow field within the
                                                                                          shock layer depends on both the magnetic field
                                                                                          configuration and magnetic induction level.

Pressure, Pa                     Temperature, K                                                                        12000
8000                                           15000   1.50E-3

                   P             T                                                                                                                     B=0
                                                                 Electron mole fraction

                                                                                                                                                       B = 0.042 T
                                                                                          Temperature, K

                                               10000   1.00E-3
                                                                                                                        8000                            B = 0.084 T
4000                                                                                                                                                    B = 0.126 T
                                               5000    5.00E-4

   0                                           0       0.00E+0
       0.00        0.02   0.04   0.06   0.08
       Distance along stagnation line, m
Fig.12. Simulation of Flow and Electrophysical Properties                                                                   0.00           0.04         0.08      0.12
alongStagnation Streamline for Blunt Body at Hypersonic                                                                        Distance along stagnation line, m
                    Flight Conditions                                                                                           (a) Temperature Distribution

                                                                                           Heat flux density, W/m**2

                                                                                                                                                        B = 0.042 T
          Some results characterizing the flow behind
the bow shock are shown in Fig.12 where the                                                                                                             B = 0.084 T
distributions of static pressure, translational                                                                                                         B = 0.126 T
temperature and electron concentration along the
stagnation line are given. Also, vibrational
temperatures of N2 and O2 are shown.
          Such calculations are still very costly,
therefore a simplified formulation of MHD
hypersonic flow was considered. It is nearly same as
those considered in previous Section, but the ratio of
specific heats, γ, is approximated as function of                                                                            0.00          0.40         0.80      1.20
                                                                                                                                  Distance along the surface, m
density and pressure. To take into account non-
                                                                                                                                 (b) Heat Flux Distribution
uniformity of electron concentration across the
shock layer the following approximation for electron                                      Fig.13. Simulation of of Hypersonic Blunt Nose Body for
mole fraction is applied.                                                                                Varying MHD Interaction

                      Fig. 14. A concept of On-Board surface MHD Generator on a Re-Entry vehicle.

 Red lines represent (left) the magnetic field lines, and blue – the induced current lines. The electrically conducting flow is
 assumed behind the bow shock, the surface electrodes are located just above the magnetic system leads and imbedded into
                                                      the flow face surface.

         Fig.13b demonstrates the dependence of the                 On Board MHD Electrical Power
surface heat flux on the magnetic field intensity.                  generation
Two features of these distributions can be noticed.
First, changes in heat flux take place only on a                              A concept of the on-board surface MHD
spatial scale of order of the magnetic system size.                 electrical power generator converting some part of
Second, a significant decrease of the heat flux is                  the kinetic energy of a (re-entry) vehicle into the
observed even at moderate magnetic field intensity.                 electricity for on-board use was first proposed in our
This sample shows that MHD indeed has a potential                   papers [17,9]. Some rough estimation made at that
to control a hypersonic flow, at least from the                     time [9] has shown rather promising performance of
viewpoint of protecting the surface from extreme                    such a device. The Faraday type MHD generator
thermal loads.

                         (a)                            (b)                                      (c)

                                   (d)                                                  (e)
                               Fig. 15. The experimental Model of the surface MHD generator.

(a) – concept design; (b) during the assemblage; (c) on a holder; (d) – in a test section; (e) – after power extraction run,
                                           200W power extraction estimated.

                     Fig.16. The arrangement of experiments on surface MHD generator at HFP WT

with multi pole electromagnet as qualitatively shown         resulted in flow separation induced by the body
in Fig.14 was considered. The complicated                    force are recorded through flow visualization. Some
mechanism of the electrical charge transfer in low-          information on this series is presented from Fig. 16
pressure air and in rather strong magnetic filed             to Fig.19. The numerical simulation has qualitatively
forced us later to consider as the first candidate a so-     (2D center plane flow is considered instead of full
called Hall configured MHD generator. Thus, in our           3D approach) confirmed the explanation of the
recent experiments we tested both Hall and Faraday           phenomena observed. For more details of the
configurations compromised in the same model.                experiment and data analysis the Ref.[31] could be
         The example of the surface MHD generator            helpful.
model tested at Hypervelocity Wind Tunnel Facility
with MHD accelerator [25] is presented in Fig 15. In
series of five tests the very stable results are
obtained with power extraction of about 200-250
Watts estimated from current and voltage
measurements at three of 12 electrodes. The model
was designed for a single test run and was destroyed
by heat load in hypersonic flow especially at the jet
         Another experimental series was recently
conducted [31] at the HFP driven subsonic Wind
Tunnel of TsNIImash. The similar but larger size
model was tested. The airflow parameters
correspond to those of hypersonic flight behind the
bow shock. The airflow is closed to thermal                          Fig.17. Two frames of flow visualization .
equilibrium conditions, and electrical conductivity in         Upper – just before the magnetic field pulse; lower – at
core flow is estimated as high as 200-300 mOh/m.              the moment of ~ maximal magnetic field. Main stream is
The problem revealed during the experiments is very             separated from plate surface, the back wall windows
poor conductivity near “cold” wall, and probably for                              becomes visible.
this reason no measurable power output was
recorded. Nevertheless, the strong MHD interaction

 Fig.18. The 2D numerical simulation of the flow filed    Fig.19. The 2D numerical simulation of the flow filed
 (Mach number and velocity) at B = 0, B=0.2, B=0.4,        (temperature and magnetic force) at B = 0, B=0.2,
                  and B=0.6 tesla.                                      B=0.4, and B=0.6 tesla.

MHD Hypersonic (Re-Entry) Flight                         reason in comparison with classical gasdynamic
Control                                                  drag. Because the cylinder is far from any practical
                                                         application it was decided to check this result for
          The analysis of the large amount of            more «practical» configuration shaped as an airfoil
experimental and simulations results on MHD flow         with magnet dipole inside. The several of angle-of-
control partly discussed in this paper has clearly       attack are considered. The drag and lift forces are
shown the potential of MHD interaction in                found as functions of magnetic filed intensity. The
hypersonic flights, and in particularly in re-entry      expectation was even exceeded.
flights is much wider than just the local flow field               In Fig.20 the flow filed is presented for
modification. MHD interaction being significantly        reference case (no MHD) and regular MHD
distributed practically over whole area where the        interaction case with magnetic induction 2.0 Tesla
magnetic filed is presented even at low level            and seed mole fraction 0.01. The magnetic system is
intensity can efficiently influence on the integrated    a dipole type located at centres of upstream-and
forces and moments applied to the vehicle. This          downstream-blunted edges shaped as a circular half
could be used as a strong mechanism of flight            cylinder. The case of 10 deg of angle-of-attack is
control, providing additional tool of the trajectory     shown. It is interesting to see that MHD interaction
optimisation, manoeuvring, stability control etc.        reveals a trend to «recover» the symmetry of the
MHD interaction flight control tool has advanced         flow filed. Absolute values of forces acting on the
with very fast of response time typical of               airfoil from plasma weakly depend on angle-of-
electrodynamics rather than mechanical device.           attack. Normalized drag and lift are plotted in Fig.21
          The MHD interaction phenomena are rather       as function of magnetic filed strength for several
complicated and realized in various form. In our         angle-of-attack values. Both drag and lift are
paper [19] we discussed at first a so-called «MHD        normalized to dynamic pressure times the middle
parachute effect» characterized by an extended           cross-section of airfoil; the latter increases as sine of
subsonic flow region formed behind the body (the         angle-of-attack. The gasdynamic drag is not shown,
cylinder was considered there). It was found that        as it is less than unit. MHD cases are characterized
integral drag has increased several times for this       by the drag one-two order of magnitude higher as
                                                         compared to classical gasdynamic one. It is clearly

      Fig.20. The flow filed (temperature – filled, and flow stream lines) for no MHD case (left) and MHD On case (right). Flow
      conditions: velocity 5000m/s, seed=0.01. Angle-of-attack is 10 deg. Magnetic induction is 2.0 Tesla at the airfoil surface.

seen that lift modification is relatively weak with                      Concluding Remarks
configuration considered here. The negative lift
values can be attributed to the secondary effect of                                The study of MHD interaction influence on
the static pressure redistribution over the body                         hypersonic flow structure has been carried out in the
surface due to MHD interaction in the bulk.                              paper and proceeding works by the authors. Under
                                                                         experimental conditions of the MHD wind tunnel
                                                                         facility, investigated and detailed analysis of the
                                                                         MHD interaction performed. Differences in MHD
                                                                         flow structure for the flow around a cylinder and
Nornalized Drag and Lift

                           40                                            over the wedge have been recognized. The
                                                        Drag, 0 deg
                                                                         prediction to the MHD flow over a blunt body under
                           30                           Drag, 10 deg     real flight conditions have been simulated and effect
                                                                         of external magnetic field on the surface thermal
                                                                         loads has been investigated.
                                                        Drag, 30 deg               As in our previous works, in this paper it
                                                                         was shown that the real MHD operation mode is
                           10                                            between two limiting cases: fully shorted Hall
                                                                         electric field (short-circuit conditions) and zero Hall
                            0                                            current density (open-circuit conditions). Under
                                                        Lift             short-circuit conditions, the potential level of MHD
                                                                         interaction intensity is approximately reduced by
                                                                         factor of 1/(1+ βe 2). In the second case, or even in
                                 0.0              1.0              2.0
                                                                         the case of low total Hall current, MHD interaction
                                       Magnetic induction, tesla         patterns look similar to the case where Hall effect is
           Fig.21. The integral characteristics of MHD parachute         missing.
                                   effects                                         Three features characterized the flow in the
                                                                         experiments: large values of Hall parameter,
                                                                         presence of charged particles in the entire flow and
         It should be also mentioned here that the                       low voltage drops between facility units due to
peak heat flux density near upstream stagnation                          ground. Under such conditions the MHD interaction
point has usually decreased. However, the heat flux                      is closer to the short-circuit conditions for the Hall
density integrated over the whole surface is slightly                    field. Therefore, MHD interaction factor
higher and changes irregularly with magnetic filed                       characterizing intensity of MHD interaction may
strength. This effect needs probably more accurate                       achieve just several percents of its nominal value
analysis as well.                                                        corresponding to the ideal open-circuit conditions.

          The spatial structure of MHD interaction in      Acknowledgements
the flow over a wedge is such that there are two
zones of MHD generation located left and right of                   This work has been made possible by
the magnetic system and MHD acceleration zone in           resources provided under an AFRL SBIR Phase II
between. In generation zones the flow decelerates,         out of WPAFB (DoD F33615-00-C-3006), through
the pressure rises and the angle between the oblique       the ISTC/EOARD projects 1892p, 2196p, DOE
shock and the wedge surface increases. This primary        SBIR Phase II, and the Russian Academy of
effect of MHD interaction over a wedge has been            Sciences through Fundamental Research Program
obtained numerically and confirmed by experiments          #20. Authors thank colleagues from IVTAN
even under bad conditions of low Hall voltage and          (D.Baranov, S.Bychkov, S.Leonov, D.Yarantsev),
high Hall current. If one could diminish the Hall          TsAGI (V.Alferov, A. Podmazov, V.Tikhonov,
currents in the test section, significantly higher         A.Tikhonchuk) and TsNIImash (A.Krasilnikov,
MHD interaction intensity could be achieved.               V.Knotko) for conducting experiments, and CIAM
          Hypersonic flow around a blunt body under        (A. Vatazhin, V.Kopchenov, O.Gusev) for fruitful
real flight conditions is characterized by low             discussions on numerical simulations problem.
density, low electron concentration (of order of 10-
  ), and high Hall parameter (10 to 100). However,         References
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                                                               Perspective of MHD Technology in Aerospace
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                                                               Applications. // AIAA Paper 96-2355, 27th AIAA
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                                                               0452, Jan, 2000.

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16.   V.A.Bityurin and J.T. Lineberry, “Aerospace                   Temperature, 2000, Vol. 38, No. 2, pp. 300-313.
      Applications of MHD,” Invited Lecture, 13th             26.   A.N.Bocharov, V.A. Bityurin, I. B. Klement’eva, S.
      International Conference on MHD, IEE AC, Beijing,             B.Leonov, “A Study of MHD Assisted Mixing and
      China, Oct 1999.                                              Combustion,” AIAA Paper 2002-5878, Reno, NV,
17.   Bityurin V.A., Ivanov V.A. An Alternative Energy              2002.
      Source Utilization with an MHD Generator //             27.   Zubkov A.I., Tirskiy G.A.,Levin V.A., Sakharov
      Proceedings of the 33rd Symposium on Engineering              V.I. “Motion of bodies in Earth’s and Planet’s
      Aspects of Magnetohydrodynamics, Tennessee,                   Atmospheres with Supersonic and Hypersonic
      USA, June 13-15, 1995, pp.X.2-                                Velocities    under     Conditions     of  Chemical
18.   Lineberry J.T., et al., “Prospects of MHD Flow                Conversions, Heat Transfer and Radiation,” Rep.
      Control for Hypersonics,” AIAA 2000-3057, July                No.4507, Inst. Of Mech of Moscow State University,
      2000, Las Vegas, NV.                                          1998.
19.   Bityurin, V.A. and Lineberry, J.T. “Assessments of      28.   G.G.Chernyi, S.A.Losev, S.O.Macheret, B. V.
      MHD Interaction for Aerospace Applicaations”, 5th             Potapkin, “Physical and Chemical Processes in Gas
      International Workshop on Magneto-Aerodynamics                Dynamics: Cross Sections and Rate Constants,”
      for Aerospace Applications, April 12-16, 2003,                Progress in Astronautics and Aeronautics, Vol. 196,
      IVTAN, Moscow, Russia.                                        Published by AIAA, 2002.
20.   Bityurin, V.A., et al., “Theoretical and Experimental   29.   Andriatis A.V., Zhluktov S.A., Sokolova I.A.
      Study of an MHD Interaction Effects at Circular               “Transport       Coefficients      for     Chemical
      Cylinder in a Transversal Hypersonic Flow”, 40th              Nonequilibrium Components of Air Mixtures," J.
      AIAA Aerospace Sciences Meeting, Jan, 2002,                   Mathematical Modeling, v.4, No.1, 1992.
      AIAA 2002-0491, Reno, NV.                               30.   V.A.Bityurin, A.N.Bocharov, J.T.Lineberry, Results
21.   Lineberry, J.T., Bityurin, V.A., and Bocharov, A.N.,          of Experiments on MHD Hypersonic Flow
      “MHD Flow Control Studies - Analytical Study of               Control//Paper AIAA-2004-2263, 35th AIAA
      MHD Flow Interaction Around a Right Circular                  Plamadynamics and Lasers Conference, 28 June - 1
      Cylinder in Transverse Hypersonic Flow,” 14th                 July, Portland, Oregon.
      International Conference on MHD, Maui, Hawaii,          31.   V.A. Вityuriп, A.N. Bocharov, D.S. Baraпov, А.V.
      May, 2002.                                                    Krasilпikov, V.B. Knotko, Yu.А. Plastinin Study of
22.   Bityurin V.A., et al., “Experimental Studies of MHD           Experimental MНD Generator Models at High
      Interaction at Circular Cylinder in Hypersonic                Frequency Plasmatron // Paper AIAA-2005-0982,
      Airflow,” 4th Moscow Workshop on Magneto-                     43rd AIAA Aerospace Sciences Meeting aпd
      Plasma Aerodynamics in Aerospace Applications,                Exhibit, 10-13 Jan, Reno Hilton, Reno, Nevada.
      IVTAN, Moscow, April, 2002
23.   Bityurin V.A., Bocharov A.N., Lineberry J.T.,
      Suckomel C., “Studies on MHD Interaction in
      Hypervelocity Ionized Air Flow over Aero-Surfaces”
      43rd AIAA Aerospace Sciences Meeting & Exhibit,


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