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STUDY OF MHD INTERACTION IN HYPERSONIC FLOWS 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: bityurin@ihed.ras.ru J.Lineberry 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 399 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 400 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 flight. 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 in 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 , (11) ρu m e ρu τ ma (7) 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 401 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 2 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 402 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. u Bow Shock jxB jxB B j Fig.2. Schematic of MHD flow over the circular cylinder with axial electric current. 403 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 3 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 404 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 0 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 2 in the range of 101 ÷ 102. This explains why no visible interaction took place in the vicinity of 4 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 405 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 B=0 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 Interaction 406 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 407 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 408 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 angle. 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 409 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 Xe 4000 0 0 0.00E+0 0.00 0.02 0.04 0.06 0.08 Distance along stagnation line, m 0 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 8.0E+5 Heat flux density, W/m**2 B=0 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 4.0E+5 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 0.0E+0 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 410 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. 411 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 border. 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 412 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 413 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 50 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. 20 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 -10 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. 414 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- 3 ), and high Hall parameter (10 to 100). However, References the advantage compared to the MHD flow in the ground test facilities is low total Hall current. 1. Kantrowitz A.R. 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