Electron-beam-generated plasmas in hypersonic magnetohydrodynamic channels

Macheret, Sergey; Shneider, Mikhail N.; Miles, Richard B.; Lipinski, Ronald J.

doi:10.2514/3.14848

Cited by 15 publications

(21 citation statements)

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“…Recent experimental and computational results suggest that such values of electrical conductivity in low-temperature supersonic flows can be achieved using efficient nonequilibrium ionization methods, such as high-energy electron beams or pulsed electric discharges. 6,7 The preceding estimate also suggests that noticeable MHD effects in cold supersonic flows can be produced only using powerful, large-scale superconducting magnets. Indeed, Eq.…”

Section: Introductionmentioning

confidence: 93%

Measurement of Flow Conductivity and Density Fluctuations in Supersonic Nonequilibrium Magnetohydrodynamic Flows

et al. 2005

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A new blowdown nonequilibrium plasma magnetohydrodynamic (MHD) supersonic wind tunnel operated at complete steady state has been developed and tested at Ohio State. The wind tunnel can be operated at Mach numbers up to M = 3-4 and mass flow rates of up to 45 g/s at a stagnation pressure of 1 atm. Pitot tube and schlieren measurements in a M = 3 test section showed reasonably good flow quality, up to 80% inviscid core across the larger dimension and up to 50% inviscid core across the smaller dimension of the flow. Stable and diffuse transverse rf discharges (rf power up to 1 kW) have been sustained in M = 3 nitrogen flows, at magnetic fields of up to B = 1.5 T. Operation at higher magnetic fields produced a more uniform rf plasma in the MHD test section. Hall parameter and electric conductivity of the flow have been inferred from the dc (MHD) current and voltage measurements at different values of the magnetic field. At B = 1.5 T and rf power of 500 W, the Hall parameter is β ∼ = 3 and the conductivity is σ ∼ = 0.05 mho/m. At the rf power of 1 kW, the extrapolated conductivity is ∼0.1 mho/m. The results of the present work demonstrate the Lorentz force effect on the supersonic boundary layer in M = 3 flows of nitrogen ionized by a high-power transverse rf discharge in the presence of the magnetic field. Boundary-layer density fluctuation spectra are measured using the laser-differential-interferometry diagnostics. In particular, decelerating Lorentz force applied to the flow produces a well-reproduced increase of the density fluctuation intensity by up to 10-20% (1-2 dB), compared to the accelerating force of the same magnitude applied to the same flow. The effect is produced for two possible combinations of the magnetic field and MHD current directions producing the same Lorentz force direction (both for accelerating and decelerating force). The effect is observed to increase with the flow conductivity. On the other hand, the effect of Joule heating on the density fluctuation spectra appears insignificant.

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Section: Introductionmentioning

confidence: 93%

Measurement of Flow Conductivity and Density Fluctuations in Supersonic Nonequilibrium Magnetohydrodynamic Flows

et al. 2005

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“…8 This is particularly the case in external situations where arti cial ionization techniques are dif cult to implement. The pertinent nondimensional parameter determining the relative magnitude of ¾ is the magneticReynolds number introducedearlier.…”

Section: Source-term Formulationmentioning

confidence: 99%

“…8 These constraints may be speci ed in terms of nondimensional parameters, magnetic Reynolds number Re ¾ and the magnetic pressure number…”

Section: Introductionmentioning

confidence: 99%

Implicit Technique for Three-Dimensional Turbulent Magnetoaerodynamics

Gaitonde

Poggie

2003

AIAA Journal

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A high-resolution numerical procedure designed to simulate three-dimensional nonideal magnetogasdynamic (MGD) phenomena on complex con gurations is extended to enhance computational ef ciency and physicaldelity. A loosely coupled approximatelyfactored implicit method is developed to overcome time-step size limitations of explicit methods. A sub-iteration strategy is included to recover up to second-order time accuracy. Veri cation exercises, covering wave propagation and diffusion phenomena, are presented to demonstrate accuracy and characterize the ef ciency of the numerical procedure. Because the aerodynamic environment will exhibit relatively small electrical conductivities and large compensatory magnetic elds, a low magnetic Reynolds number Re¾ formulation and its solution procedure are described and veri ed by considering MGD-control of a compressible, laminar at-plate boundary layer at different interaction parameters. A two-equation k-² turbulence model with low-Reynolds-number near-wall terms is incorporated with additional expressions to reproduce the damping effect of the magnetic eld. The effect of a magnetic dipole on a supersonic turbulent at-plate boundary layer is examined. An exploratory study of MGD control of ow past a classic reentry vehicle con guration demonstrates the capabilities of the numerical scheme. NomenclatureA; B; C = inviscid ux Jacobians a; b = coef cient in compact differencing B = magnetic eld vector C p = speci c heat at constant pressure C ¹ ; C ² 1; C M 1 = closure coef cients in turbulence model E = electric eld vector e = total energy without magnetic eld component F; G; H = ux vectors J = mesh Jacobian j = current vector k = thermal conductivity; turbulent kinetic energy M = Mach number P = static plus magnetic pressure P k = production term in k equation Pr = Prandtl number Pr t = turbulent Prandtl number p = static pressure Q = viscous ux Jacobians Q = magnetic interaction parameter Q ht = heat ux term R = residual R b = magnetic pressure number Re = Reynolds number Re ¾ = magnetic Reynolds number S = source term vector T = temperature t = time U = velocity vector u; v; w = Cartesian velocity components X = conserved vector x; y; z = Cartesian coordinates Z = total conserved energy 0 = coef cient in compact differencing°= ratio of speci c heats 1 = difference operator ± = boundary-layer thickness ² = turbulence energy dissipation rate ¹ m = magnetic permeability ¹ t = eddy viscosity coef cient »;´; = curvilinear coordinates ½ = density ¾ = electrical conductivity ¾ k ; ¾ ² = closure coef cients in turbulence model N N ¿ = shear stress tensor Á = electrical potential; time-integration parameter Subscripts f = uid dynamic components m = magnetic eld components ref = reference Superscript p = subiteration counter

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“…t , where is determined from Wilke's mixing rule with polynomials for each species found in [12]. The turbulence transport equation is derived from the laminar form (outlined in [13,14]) using a similar approach used to derive the Favre-averaged Navier-Stokes equations outlined in [15]: (4) where Pr t the turbulent Prandtl number, which is set to the same value as that used in the total-energy transport equation (i.e., 0.9). The fraction of the Joule heating consumed in the excitation of the vibration levels of the nitrogen molecule, v , is obtained from the effective electric field in the electron frame of reference, as tabulated in Table 2.…”

Section: Fluid Dynamicsmentioning

confidence: 99%

“…The nitrogen characteristic vibration temperature is set to 3353 K [19] and R N 2 is set to 296:8 J=kg K. The vibration-translation relaxation time (in seconds) can be obtained from [13,14]: …”

Section: Fluid Dynamicsmentioning

confidence: 99%

Numerical Study of an Electron-Beam-Confined Faraday Accelerator

Parent

Macheret

Shneider

et al. 2007

Journal of Propulsion and Power

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The numerical solution of a magnetoplasmadynamics accelerator intended for supersonic airbreathing propulsion systems is presented. The numerical method solves the Favre-averaged Navier-Stokes equations closed by the Wilcox k! model, including the nitrogen vibrational energy and a finite rate chemical solver accounting for electron-beam ionization, electron attachment, and dissociative recombination. The fluid-flow equations are solved in conjunction with the electric-field-potential equation. Because of the recombination time of the electrons with the charged particles being in the order of microseconds, the interaction region is more or less confined to the area when e-beam ionization is applied. In this manner, a Faraday-type configuration can be obtained by using only one electrode pair. The impact of the length of the interaction region and the strength of the magnetic field on the efficiency are assessed. It is observed that the efficiency obtained numerically is as much as 40% less than the theoretical predictions for the highest magnetic field considered of 4 T. This is attributed to 1) the current concentration near the electrodes' edges causing a significant voltage drop and 2) unsteady behavior in the center of the channel due to the interaction between finite rate chemistry and electromagnetism. Nonetheless, an efficiency within 25% of the theoretical predictions can be obtained at high magnetic field by decreasing the width of the interaction region to one-tenth of its height. NomenclatureA = Avogadro's number, 6:02257 10 23 B = magnetic field vector b = constant function of and K C = charge, C C P = specific heat at constant pressure c = mass fraction E = electric field vector E = total energy e = charge of one electron, 1:60207 10 19 C e = internal energy e v = nitrogen vibrational energy e 0 v = nitrogen vibrational energy at equilibrium h = enthalpy j = current vector K = work interaction parameter, E y =v x B z k = turbulence kinetic energy L = length of the interaction region M = Mach number M = molecular weight m = atom or molecule mass N = number density P = pressure P k = turbulence kinetic energy production term Pr = Prandtl number q = flow speed q b = energy deposited to the flow from the electron beams R = gas constant Sc = Schmidt number St = Stuart number, eff B 2 L=q s = sign of a species ( 1 for negative ions and electrons and 1 for positive ions) T = temperature v = velocity vector W = chemical source term X = matrix needed to compute the effective conductivity = ratio of the specific heats ij = Kronecker delta = efficiency v = nitrogen characteristic vibration temperature = thermal conductivity e = electron thermal diffusion = viscosity, mobility = mass diffusion coefficient = ratio between the Joule heating and the work = density = electrical conductivitỹ = tensor conductivity eff = effective electrical conductivity taking into account ion slip k = user-defined constant for the Wilcox k! model ! = user-defined constant for the Wilcox k! model vt = vibration-translation relaxation t...

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Electron-beam-generated plasmas in hypersonic magnetohydrodynamic channels

Cited by 15 publications

References 0 publications

Measurement of Flow Conductivity and Density Fluctuations in Supersonic Nonequilibrium Magnetohydrodynamic Flows

Measurement of Flow Conductivity and Density Fluctuations in Supersonic Nonequilibrium Magnetohydrodynamic Flows

Implicit Technique for Three-Dimensional Turbulent Magnetoaerodynamics

Numerical Study of an Electron-Beam-Confined Faraday Accelerator

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