Abstract
A numerical procedure based on a five-wave model associated with non-ideal, low magnetic Reynolds number magnetohydrodynamic (MHD) flows was developed. It is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations, in conjunction with an SOR method for solving the elliptic equation governing the electrical potential of flow field. To validate the developed procedure, two different test cases were used which included MHD Rayleigh problem and MHD Hartmann problem. The simulations were performed under the assumption of low magnetic Reynolds number. The simulated results were found to be in good agreement with the closed form analytical solutions deduced in the present study, showing that the present algorithm could simulate engineering MHD flow at low magnetic Reynolds number effectively. In the end, a flow field between a pair of segmented electrodes in a three dimensional MHD channel was simulated using the present algorithm with and without including Hall effects. Without the introduction of Hall effects, no distortion was observed in the current and potential lines. By taking the Hall effects into account, the potential lines distorted and clustered at the upstream and downstream edges of the cathode and anode, respectively.
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Gurijanov E P, Harsha P T. AJAX: New directions in hypersonic technology. In: 7th International Space Planes and Hypersonic Systems and Technologies Conference, Norfolk, Virginia, 1996. AIAA 96-4609
Macheret S O, Shneider M N, Miles R B. Electron beam generated plasmas in hypersonic MHD channels. AIAA J, 2001, 39(6): 1127–1138
Macheret S O, Shneider M N, Miles R B. Magnetohydrodynamic control of hypersonic flows and scramjet inlets using electron beam ionization. AIAA J, 2002, 40(1): 74–81
Macheret S O, Shneider M N, Miles R B. Optimum performance of electron beam driven magnetohydrodynamic generators for scramjet inlet control. AIAA J, 2007, 45(9): 2157–2163
Macheret S O, Shneider M N, Miles R B. Potential performance of supersonic MHD power generators. In: 39th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2001. AIAA 2001-0795
Fay J A. Hall Effects in a Laminar Boundary Layer of the Hartmann Type. Avco-Everelt Research Report. 1959
Tani I. Steady flow of conducting fluids in channels under transverse magnetic field with consideration of Hall effect. J Aerospace Sci, 1962, 29: 297–305
Vanka S P, Ahluwalia R K. Three-dimensional flow and thermal development in magnetohydrodynamic channels. J Energ, 1982, 6(3): 218–224
Ahluwalia R K, Vanka S P. Secondary flow effects in diagonal MHD channels. J Energ, 1983, 7(5): 387–388
Girshick S L, Kruger C H. Experimental study of secondary flow in a magnetohydrodynamic channel. J Fluid Mech, 1986, 170: 233–252
Moreau R. Magnetohydrodynamics. Netherlands: Kluwer Academic Publishers, 1990
Sutton G.W, Sherman A. Engineering Magnetohydrodynamics. New York: Mcgraw-Hill Book Company, 1965
Dong H T, Zhang L D, Lee C H. Domain decomposition method utilizing chimera grids in conjunction with a second order difference scheme based on an entropy condition (in Chinese). Chinese J Comput Phys, 2003, 20(3): 102–106
Dong H T, Zhang L D, Lee C H. High order discontinuity decomposition entropy condition schemes for Euler equations. CFD J, 2002, 10(4): 563–568
Oliver D A, Mitchner M. Nonuniform electrical conduction in MHD channels. AIAA J, 1967, 5(8): 1424–1432
Ishikawa M, Tamai K, Tateishi K, et al. Three-dimensional behavior of MHD plasma near electrode of MHD generator. In: 28th Plasmadynamics and Lasers Conference, Atlanta, Georgia, 1997. AIAA 97-2373
Gaitonde D V, Poggie J. Elements of a numerical procedure for 3-D MGD flow control analysis. In: 40th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2002. AIAA 2002-0198
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Lu, H., Lee, C. Simulation of three-dimensional nonideal MHD flow at low magnetic Reynolds number. Sci. China Ser. E-Technol. Sci. 52, 3690–3697 (2009). https://doi.org/10.1007/s11431-009-0263-5
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DOI: https://doi.org/10.1007/s11431-009-0263-5