Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-25T21:15:05.564Z Has data issue: false hasContentIssue false
  • English
  • Français

Theoretical and numerical study of the binary scaling law for electron distribution in thermochemical non-equilibrium flows under extremely high Mach number

Published online by Cambridge University Press:  05 April 2022

You Wu ,
Xu Xu Open the ORCID record for Xu Xu [Opens in a new window] ,
Bing Chen  and
Qingchun Yang
You Wu
Affiliation:
School of Astronautics, Beihang University, Beijing102206, PR China
Xu Xu*
Affiliation:
School of Astronautics, Beihang University, Beijing102206, PR China
Bing Chen
Affiliation:
School of Astronautics, Beihang University, Beijing102206, PR China
Qingchun Yang
Affiliation:
School of Astronautics, Beihang University, Beijing102206, PR China
*
†Email address for correspondence: xuxu_1521@126.com
Get access Rights & Permissions [Opens in a new window]

Abstract

The binary scaling law is a classical similarity law used in analysing hypersonic flow fields. The objective of this study is to investigate the applicability of the binary scaling law in thermochemical non-equilibrium airflow. Dimensional analysis of vibrational and electron–electronic energy conservation equations was employed to explore the theoretical reasons for the failure of the binary scaling law. Numerical simulation based on a multi-temperature model (translational–rotational temperature T, electron–electronic excitation temperature ${T_e}$ and the vibrational temperatures of ${\textrm{O}_2}$ and ${\textrm{N}_2}$, $\; {T_{{v_{{\textrm{O}_2}}}}}$and ${T_{{v_{{\textrm{N}_2}}}}}$) with two chemical models (the Gupta model and the Park model) was adopted to study the accuracy of the binary scaling law for electron distribution at high altitude with extremely high Mach number. The results of theoretical analysis indicate that the three-body collision reactions and the translation–electron energy exchange from collisions between electrons and ions, ${Q_{t - e\_ions}}$, can cause the failure of the binary scaling law. The results of numerical simulation show that the electron-impact ionization reactions are the main reasons for the invalidation of the binary scaling law for electron distribution at high altitude with high Mach number. With an increase of free-stream Mach number, the negative effect on the binary scaling law caused by ${Q_{t - e\_ions}}$ cannot be ignored.

JFM classification

Compressible Flows: Hypersonic Flow Reacting Flows: Laminar reacting flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 940 , 10 June 2022 , A3
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Anderson, J.D.J.R. 2006 Hypersonic and High-Temperature Gas Dynamics, 2nd edn. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Appleton, J.P. & Bray, K.N.C. 1964 The conservation equations for a non-equilibrium plasma. J. Fluid Mech. 20 (4), 659–672.CrossRefGoogle Scholar
Birkhoff, G. 1960 Hydrodynamics: A Study in Logic, Fact and Similitude, 2nd edn. Princeton University Press.Google Scholar
Birkhoff, G. & Eckerman, J. 1963 Binary collision modeling. J. Math. Mech. 12 (4), 543–556.Google Scholar
Blazek, J. 2015 Computational Fluid Dynamics: Principles and Applications. Butterworth-Heinemann.Google Scholar
Camm, J.C., Kivel, B., Taylor, R.L. & Teare, J.D. 1961 Absolute intensity of non-equilibrium radiation in air and stagnation heating at high altitudes. J. Quant. Spectrosc. Radiat. Transfer 1 (1), 53–75.CrossRefGoogle Scholar
Candler, G.V. 1988 The computation of weakly ionized hypersonic flows in thermo-chemical nonequilibrium. PhD dissertation, Stanford University.Google Scholar
Candler, G.V. 2019 Rate effects in hypersonic flows. Annu. Rev. Fluid Mech. 51, 379–402.CrossRefGoogle Scholar
Candler, G.V. & Maccormack, R.W. 1991 Computation of weakly ionized hypersonic flows in thermochemical nonequilibrium. J. Thermophys. Heat Transfer 5 (3), 266–273.CrossRefGoogle Scholar
Dunn, M.G. 1971 Measurement of C+ + e− + e− and CO+ + e− recombination in carbon monoxide flows. AIAA J. 9 (11), 2184–2191.CrossRefGoogle Scholar
Dunn, M.G. & Kang, S.W. 1973 Theoretical and Experimental Studies of Reentry Plasmas, vol. 2232. National Aeronautics and Space Administration.Google Scholar
Ellington, D. 1967 Binary scaling limits for hypersonic flight. AIAA J. 5 (9), 1705–1706.CrossRefGoogle Scholar
Farbar, E., Boyd, I.D. & Martin, A. 2013 Numerical prediction of hypersonic flowfields including effects of electron translational nonequilibrium. J. Thermophys. Heat Transfer 27 (4), 593–606.CrossRefGoogle Scholar
Garicano-Mena, J., Lani, A. & Degrez, G. 2018 An entropy-variables-based formulation of residual distribution schemes for non-equilibrium flows. J. Comput. Phys. 362, 163–189.CrossRefGoogle Scholar
Ghezali, Y., Haoui, R. & Chpoun, A. 2019 Study of physico-chemical phenomena in a non-equilibrium hypersonic air flow behind a strong shock wave. Thermophys. Aeromech. 26 (5), 693–710.CrossRefGoogle Scholar
Gibson, W.E. & Marrone, P.V. 1964 A similitude for non-equilibrium phenomena in hypersonic flight. In AGARDograph, vol. 68, pp. 105–131. Elsevier.CrossRefGoogle Scholar
Gnoffo, P.A., Gupta, R.N. & Shinn, J.L. 1989 Conservation equations and physical models for hypersonic air flows in thermal and chemical nonequilibrium. NASA Tech. Paper 2867.Google Scholar
Gupta, R.N., Yos, J.M., Thompson, R.A. & Lee, K.P. 1990 A review of reaction and thermodynamic and transport properties for an 11-species air model for chemical and thermal nonequilibrium calculations to 30000K. NASA Tech. Rep. 1232.Google Scholar
Hall, J.G., Eschenroeder, A.Q. & Marrone, P.V. 1962 Blunt-nose inviscid airflows with coupled nonequilibrium processes. J. Aerosp. Sci. 29 (9), 1038–1051.CrossRefGoogle Scholar
Hao, J., Wang, J. & Lee, C. 2016 Numerical study of hypersonic flows over reentry configurations with different chemical nonequilibrium models. Acta Astronaut. 126, 1–10.CrossRefGoogle Scholar
Hornung, H.G. 1972 Non-equilibrium dissociating nitrogen flow over spheres and circular cylinders. J. Fluid Mech. 53 (1), 149–176.CrossRefGoogle Scholar
Hornung, H.G. 1988 28th Lanchester memorial lecture—experimental real-gas hypersonics. Aeronaut. J. 92 (920), 379–389.CrossRefGoogle Scholar
Houwing, A.F.P., Nonaka, S., Mizuno, H. & Takayama, K. 2000 Effects of vibrational relaxation on bow shock standoff distance for nonequilibrium flows. AIAA J. 38 (9), 1760–1763.CrossRefGoogle Scholar
Jones, W.L. & Cross, A.E. 1972 Electrostatic-probe measurements of plasma parameters for two reentry flight experiments at 25000 feet per second. Rep. no. 6617. National Aeronautics and Space Administration.Google Scholar
Kim, S.D., Lee, B.J., Lee, H.J. & Jeung, I.S. 2009 Robust HLLC Riemann solver with weighted average flux scheme for strong shock. J. Comput. Phys. 228 (20), 7634–7642.CrossRefGoogle Scholar
Landau, L. & Teller, E. 1936 Theory of sound dispersion. Phys. Z. Sowjetunion 10, 34–43.Google Scholar
Lee, J.H. 1984 Basic governing equations for the flight regimes of aeroassisted orbital transfer vehicles. In 19th Thermophysics Conference, Snowmass, Colorado, AIAA Paper 84-1729.Google Scholar
Lee, J.H. 1993 Electron-impact vibrational relaxation in high-temperature nitrogen. J. Thermophys. Heat Transfer 7 (3), 399–405.CrossRefGoogle Scholar
Lee, R.H. & Baker, R.L. 1969 Binary scaling of air ionization on slender cones at small yaw. AIAA J. 7 (2), 355–358.CrossRefGoogle Scholar
Marschall, J. & Maclean, M. 2011 Finite-rate surface chemistry model, I: formulation and reaction system examples. In 42nd AIAA Thermophysics Conference, Honolulu, Hawaii, San Diego, CA, AIAA Paper 2011-3783.Google Scholar
Matsuzaki, R. 1988 Quasi-one-dimensional aerodynamics with chemical, vibrational and thermal nonequilibrium. Trans. Japan Soc. Aeronaut. Space Sci. 30, 243–258.Google Scholar
Men'shov, I.S. & Nakamura, Y. 2000 Numerical simulations and experimental comparisons for high-speed nonequilibrium air flows. Fluid Dyn. Res. 27 (5), 305–334.CrossRefGoogle Scholar
Miller, J., Tannehill, J., Lawrence, S. & Edwards, T. 1995 Development of an upwind pns code for thermo-chemical nonequilibrium flows. In 30th AIAA Thermophysics Conference, AIAA Paper 95-2009.Google Scholar
Millikan, R.C. & White, D.R. 1963 Systematics of vibrational relaxation. J. Chem. Phys. 39 (12), 3209–3213.CrossRefGoogle Scholar
Muylaert, J., Walpot, L., Häuser, J., Sagnier, P., Devezeaux, D., Papirnyk, O. & Lourme, D. 1992 Standard model testing in the European high enthalpy facility F4 and extrapolation to flight. In 17th Aerospace Ground Testing Conference, Nashville, TN, AIAA Paper 92-3905.Google Scholar
Niu, Q., Yuan, Z., Dong, S. & Tan, H. 2018 Assessment of nonequilibrium air-chemistry models on species formation in hypersonic shock layer. Intl J. Heat Mass Transfer 127, 703–716.CrossRefGoogle Scholar
Ozawa, T., Zhong, J. & Levin, D.A. 2008 Development of kinetic-based energy exchange models for noncontinuum, ionized hypersonic flows. Phys. Fluids 20 (4), 442–165.CrossRefGoogle Scholar
Park, C. 1968 Measurement of ionic recombination rate of nitrogen. AIAA J. 6 (11), 2090–2094.CrossRefGoogle Scholar
Park, C. 1973 Comparison of electron and electronic temperatures in recombining nozzle flow of ionized nitrogen—hydrogen mixture. Part 1. Theory. J. Plasma Phys. 9 (2), 187–215.CrossRefGoogle Scholar
Park, C. 1985 Convergence of computations of chemical reacting flows. Prog. Astronaut. Aeronaut. 103, 478–513.Google Scholar
Park, C. 1990 Nonequilibrium Hypersonic Aerothermodynamics. Wiley.Google Scholar
Park, C. 1993 Review of chemical-kinetic problems of future NASA missions. I-earth entries. J. Thermophys. Heat transfer 7 (3), 385–398.CrossRefGoogle Scholar
Park, C. & Lee, S.H. 1995 Validation of multitemperature nozzle flow code. J. Thermophys. Heat Transfer 9 (1), 9–16.CrossRefGoogle Scholar
Park, J.S., Yoon, S.H. & Kim, C. 2010 Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids. J. Comput. Phys. 229 (3), 788–812.CrossRefGoogle Scholar
Petschek, H. & Byron, S. 1957 Approach to equilibrium ionization behind strong shock waves in argon. Ann. Phys. 1, 270–315.CrossRefGoogle Scholar
Ramjatan, S., Lani, A., Boccelli, S., Hove, B.V., Karatekin, Ö, Magin, T. & Thoemel, J. 2020 Blackout analysis of Mars entry missions. J. Fluid Mech. 904, A26.CrossRefGoogle Scholar
Roberts, T. 1994 The development of a multi-vibrational model and incorporation into a chemical reacting Navier-Stokes solver. In 6th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, Colorado Springs, CO AIAA Paper 94-1988.Google Scholar
Roberts, T. 1996 Implementation into TINA modelling for electron/electronic energy equation. In 31st AIAA Thermophysics Conference, New Orleans, LA, AIAA Paper 96-1851.Google Scholar
Scalabrin, L.C. 2007 Numerical simulation of weakly ionized hypersonic flow over reentry capsules. PhD dissertation, University of Michigan.CrossRefGoogle Scholar
Shen, C. 2005 Rarefied Gas Dynamics: Fundamentals, Simulations and Micro Flows. Springer Science & Business Media.CrossRefGoogle Scholar
Sivolella, D. 2014 To Orbit and Back Again: How the Space Shuttle Flew in Space. Springer.CrossRefGoogle Scholar
Teare, J.D., Georgiev, S. & Allen, R.A. 1962 Radiation from the non-equilibrium shock front. In Hypersonic Flow Research, pp. 281–317. Elsevier.CrossRefGoogle Scholar
Thoenes, J. 1969 Inviscid hypersonic flow of chemically relaxing air about pointed circular cones. UARI Res. Rep. 66, Alabama Univ, Huntsville, AL.Google Scholar
Wilke, C.R. 1950 A viscosity equation for gas mixtures. J. Chem. Phys. 18 (4), 517–519.CrossRefGoogle Scholar
Zeng, M. 2007 Numerical rebuilding of free-stream measurement and analysis of nonequilibrium effects in high-enthalpy tunnel. PhD dissertation, Institute of Mechanics, CAS (in Chinese).Google Scholar
Zeng, M., Lin, Z., Liu, J. & Qu, Z. 2009 Numerical analysis of the validity of binary scaling parameter ρ∞L in nonequilibrium flow. Chin. J. Theor. Appl. Mech. 41 (2), 177–184 (in Chinese).Google Scholar
Zhang, H.X. 1990 The similarity law for real gas flow. Acta Aerodyn. Sin. 8 (1), 1–8 (in Chinese).Google Scholar
Zhang, F., Liu, J. & Chen, B. 2018 Modified multi-dimensional limiting process with enhanced shock stability on unstructured grids. Comput. Fluids 161, 171–188.CrossRefGoogle Scholar
Zhu, Y., Lee, C., Chen, X., Wu, J., Chen, S. & Gad-el-Hak, M. 2018 Newly identified principle for aerodynamic heating in hypersonic flows. J. Fluid Mech. 855, 152–180.CrossRefGoogle Scholar