This work presents a multidisciplinary mathematical model, as a set of coupled governing equations and auxiliary relations describing the fluid-flow, thermal, and electric fields of partially-ionized plasma with low magnetic Reynolds numbers. The model is generic enough to handle three-dimensionality, Hall effect, compressibility, and variability of fluid, thermal, and electric properties of the plasma. The model can be of interest to computational modelers aiming to build a solver that quantitatively assesses direct extraction of electric energy from a plasma flow. Three different approaches are proposed to solve numerically for the electric fields with different levels of tolerance toward possible numerical instability encountered at a large Hall parameter, where the effective conductivity tensor loses diagonal dominance and becomes close to singular. A submodel for calculating the local electric properties of the plasma is presented in detail and is applied to demonstrate the effect of different factors on the electric conductivity, including the fuel’s carbon/hydrogen ratio and the alkaline seed element that acts as the ionizing species. An analytical expression for the collision cross-section for argon is developed, such that this noble gas can be included as one of the gaseous species comprising the plasma.
Osama Ahmed Marzouk,
Multi-Physics Mathematical Model of Weakly-Ionized Plasma Flows, American Journal of Modern Physics.
Vol. 7, No. 2,
2018, pp. 87-102.
E. de Hoffmann and V. Stroobant, Mass Spectrometry: Principles and Applications (3rd Edition), John Wiley & Sons, 2007.
K.-L. D. Gottfried and G. Penn, "Chapter: 2 Clinical Applications of Ionizing Radiation," in Radiation in Medicine: A Need for Regulatory Reform, The National Academies Press, 1996.
S. W. Angrist, Direct Energy Conversion (4th Edition), USA: Allyn and Bacon, 1982.
D. V. Freck, "On the electrical conductivity of seeded air combustion products," British Journal of Applied Physics, vol. 15, no. 3, pp. 301-310, 1964.
N. Kayukawa, "Open-cycle magnetohydrodynamic electrical power generation: a review and future perspectives," Progress in Energy and Combustion Science, vol. 30, no. 1, pp. 33-60, 2004.
J. Swithenbank, "Magnetohydrodynamics and Electrodynamics of Combustion Systems," in Combustion Technology: Some Modern Developments, Academic Press, 1974.
L. Chen, S. Z. Yong and A. F. Ghoniem, "Oxy-fuel combustion of pulverized coal: Characterization, fundamentals, stabilization and CFD modeling," Progress in Energy and Combustion Science, vol. 38, no. 2, p. 156–214, 2012.
E. P. Velikhov and Y. M. Volkov, "Prospects of pulsed MHD power development and application for geology and geophysic," Preprint of I. V. Kurchatov Institute of Atomic Energy, Moscow, 1981.
J. Babakov, V. Eremenko, N. Krivosheev and R. Kuzmin, "Powerful self-contained solid propellant fueled MHD Generator "Sojuz" for area and deep geoelectrical prospecting," in 12th International Conference on MHD Electrical Power Generation, Yokohama, Japan, 1996, October 15-18.
The U. D. Department of Energy's Magnetohydrodynamics Development Program, "GAO/RCED-93-174 DOE's MHD Development Program: Report to the Chairman, Subcommittee on Energy, Committee on Science, Space, and Technology, House of Representatives," United States General Accounting Office (GAO), Washington, DC, USA, July 1993.
J. X. Bouillard and G. F. Berry, "Performance of a multigrid three-dimensional magnetohydrodynamic generator calculation procedure," International Journal of Heat and Mass Transfer, vol. 35, no. 9, pp. 2219-2232, 1992.
I. Inoue, Y. Inui, N. Hayanose and M. Ishikawa, "Analysis of transiently stable control of commercial-scale MHD generator connected to power network," in 33rd Plasmadynamics and Lasers Conference, Hawaii, May 20-23, 2002.
V. H. Blackman, J. M. S. Jones and A. Demetriades, "MHD power generation studies in rectangular channels," in 2nd Symposium on the Engineering Aspects of Magnetohydrodynamics, Philadelphia, Pennsylvania, March 9-10, 1961.
E. D. Doss, G. S. Argyropoulos and S. T. Demetr, "Two-dimensional flow inside MHD ducts with transverse asymmetries," AIAA Journal, vol. 13, no. 5, pp. 545-546, 1975.
M. Ishikawa and J. Umoto, "A new approach to calculation of three-dimensional flow in MHD generators," Journal of Propulsion and Power, vol. 2, no. 1, pp. 11-17, 1986.
K. A. Hoffmann and S. T. Chiang, Computational Fluid Dynamics for Engineers - Volume II, Texas: Engineering Education System, 1993.
C. R. Woodside, K. H. Casleton, E. D. Huckaby, T. Ochs, D. Oryshchyn, G. Richards, P. A. Strakey, J. Pepper, I. B. Celik, J. Escobar-Vargas, D. C. Haworth, O. A. Marzouk and X. Zhao, "Direct Power Extraction with Oxy-Combustion: An Overview of Magnetohydrodynamic Research Activities at the NETL-Regional University Alliance (RUA)," in 29th Annual International Pittsburgh Coal Conference, Pittsburgh, PA, October 15 - 18, 2012.
P. A. Davidson, An Introduction to Magnetohydrodynamics, USA: Cambridge University Press, 2001.
SymPy Development Team, "SymPy," [Online]. Available: www.sympy.org/en/index.html. [Accessed 21 November 2015].
Python Software Foundation, [Online]. Available: www.python.org.
M. N. Saha, "Ionization in the solar chromosphere," Philosophical Magazine, vol. 40, pp. 472-488, 1920.
M. N. Saha, "On a physical theory of stellar spectra," Proceedings of the Royal Society of London. Series A, vol. 99, no. 697, pp. 135-153, 1921.
Israel Science and Technology Directory, "List of Periodic Table Elements Sorted by Ionization energy," [Online]. Available: http://www.science.co.il/ptelements.asp?s=ionization. [Accessed 22 November 2015].
R. Serway, J. Faughn and C. Vuille, College Physics (Volume 10), USA: Cengage Learning, 2008.
R. J. Rosa, C. H. Krueger and S. Shioda, "Plasmas in MHD power generation," IEEE Transactions on Plasma Science, vol. 19, no. 6, pp. 1180-1190, 1991.
L. S. Frost, "Conductivity of seeded atmospheric pressure plasmas," Journal of Applied Physics, vol. 32, no. 10, pp. 2029-2036, 1961.
A. G. Engelhardt and A. V. Phelps, "Transport Coefficients and Cross Sections in Argon and Hydrogen-Argon Mixtures," Physical Review, vol. 133, no. 2A, pp. A375-A380, 1964.
M. S. Tillack and N. B. Morley, "Magnetohydrodynamics," in Standard Handbook for Electrical Engineers (14th edition), McGraw Hill, 2000, pp. 11-109 – 11-144.
T. R. Brogan and J. S. Forrest, Gas Discharges and the Electricity Supply Industry, London: Butterworths, 1962.
R. Bryce, Power Hungry: The Myths of "Green" Energy and the Real Fuels of the Future, New York: PublicAffairs, 2011.
J. A. Moulijn, M. Makkee and A. E. van Diepen, Chemical Process Technology (2nd Edition), UK: John Wiley & Sons, 2013.
J. H. Ferziger and M. Perić, Computational Methods for Fluid Dynamics (3rd Edition), Germany: Springer-Verlag, 2002.
D. Veynante and L. Vervisch, "Turbulent Combustion Modeling," Progress in Energy and Combustion Science, vol. 28, pp. 193-266, 2002.
B. J. McBride, S. Gordon and M. A. Reno, "Coefficients for Calculating Thermodynamic and Transport Properties of Individual Species (NASA Technical Momorandum TM-4513)," NASA, 1993.
J. Warnatz, U. Maas and R. W. Dibble, Combustion, Physical and Chemical Fundamentals, Modelling and Simulation, Experiments, Poluutant Formation, Germany: Springer, 1996.
K. K. Kuo, Principles of Combustion (2nd Edition), USA: John Wiley & Sons, 2005.
ANSYS, Inc., "ANSYS FLUENT Magnetohydrodynamics (MHD) Module Manual," ANSYS, Inc., Canonsburg, Pennsylvania, 2010.
H. Carl-W, D. L. Coleman and T. Mikus, "Technology Overview for Integration of an MHD Topping Cycle with the CES Oxyfuel Combustor," CO2-Global, LLC, Houston, USA, 2009.
J. K. Wright, "Physical principles of MHD generation," Proceedings of the Institution of Mechanical Engineers Conference, vol. 178, no. 3H, pp. 39-47, 1963.
A. Fridman, Plasma Chemistry, Cambridge University Press, 2012.
National Institute of Standards and Technology (NIST), "Elementary Charge: The NIST Reference on Constants, Units, and Uncertainty," Physical Measurement Laboratory of NIST, [Online]. Available: http://physics.nist.gov/cgi-bin/cuu/Value?e. [Accessed 18 November 2015].
National Institute of Standards and Technology (NIST), "Conversion factors for energy equivalents: NIST Reference on Constants, Units, and Uncertainty," Physical Measurement Laboratory of NIST, [Online]. Available: http://physics.nist.gov/cuu/Constants/factors.html. [Accessed 24 November 2015].
J. P. Freidberg, Plasma Physics and Fusion Energy, Cambridge University Press, 2008.
A. Sitenko and A. Malnev, Plasma Physics Theory, UK: Chapman & Hall, 1995.
National Institute of Standards and Technology (NIST), "Boltzmann Constant: NIST Reference on Constants, Units, and Uncertainty," Physical Measurement Laboratory of NIST, [Online]. Available: http://physics.nist.gov/cgi-bin/cuu/Value?k. [Accessed 18 November 2015].
National Institute of Standards and Technology (NIST), "Conversion from J to eV: The NIST Reference on Constants, Units, and Uncertainty," [Online]. Available: http://physics.nist.gov/cgi-bin/cuu/Convert?exp=-23&num=1.38064852&From=j&To=ev&Action=Convert+value+and+show+factor. [Accessed 22 November 2015].
National Institute of Standards and Technology (NIST), "Planck constant: The NIST Reference on Constants, Units, and Uncertainty," [Online]. Available: http://physics.nist.gov/cgi-bin/cuu/Value?h. [Accessed 22 November 2015].
National Institute of Standards and Technology (NIST), "Electron Mass: The NIST Reference on Constants, Units, and Uncertainty," Physical Measurement Laboratory of NIST, [Online]. Available: http://physics.nist.gov/cgi-bin/cuu/Value?me. [Accessed 18 November 2015].
R. C. Hibbeler, Engineering Mechanics: Dynamics (13th ed), New Jersey: Pearson Prentice Hall, 2013.
H. K. Messerle, Magnetohydrodynamic Electrical Power Generation, England: John Wiley & Sons, 1995.
National Institute of Standards and Technology (NIST), "Magnetic Constant: NIST Reference on Constants, Units, and Uncertainty," Physical Measurement Laboratory of NIST, [Online]. Available: http://physics.nist.gov/cgi-bin/cuu/Value?mu0. [Accessed 18 November 2015].
E. H. John, Introduction to Plasma Technology: Science, Engineering, and Applications, Germany: John Wiley & Sons, 2013.
National Institute of Standards and Technology (NIST), "Electric Constant: NIST Reference on Constants, Units, and Uncertainty," Physical Measurement Laboratory of NIST, [Online]. Available: http://physics.nist.gov/cgi-bin/cuu/Value?ep0. [Accessed 18 November 2015].
M. Urban, F. Couchot, X. Sarazin and A. Djannati-Atai, "The quantum vacuum as the origin of the speed of light," The European Physical Journal D, pp. 67-58, 2013.
S. Smolentsev, S. Cuevas and A. Beltrán, "Induced electric current-based formulation in computations of low magnetic Reynolds number magnetohydrodynamic flows," Journal of Computational Physics, vol. 229, pp. 1558-1572, 2010.
Y. A. Çengel and J. M. Cimbala, Fluid Mechanics Fundamentals and Applications (3rd Edition), McGraw-Hill Education, 2013.
S. M. Aitha, "Characteristics of optimum power extraction in a MHD generator with subsonic and supersonic inlets," Energy Conversion and Management, vol. 50, pp. 765-771, 2009.
M. Goossens, An Introduction to Plasma Astrophysics and Magnetohydrodynamics, Netherlands: Kluwer Academic Publishers, 2003.
G. McCracken and P. Stott, Fusion: The Energy of the Universe (2nd Edition), China: Academic Press, 2012.
T. J. Boyd and J. J. Sanderson, The Physics of Plasmas, Cambridge, UK: Cambridge University Press, 2003.