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Aerothermodynamic correlations for high-speed flow

Published online by Cambridge University Press:  25 May 2017

Narendra Singh Open the ORCID record for Narendra Singh [Opens in a new window]  and
Thomas E. Schwartzentruber
Narendra Singh*
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
Thomas E. Schwartzentruber
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: singh455@umn.edu
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Abstract

Heat flux and drag correlations are developed for high-speed flow over spherical geometries that are accurate for any Knudsen number ranging from continuum to free-molecular conditions. A stagnation point heat flux correlation is derived as a correction to the continuum (Fourier model) heat flux and also reproduces the correct heat flux in the free-molecular limit by use of a bridging function. In this manner, the correlation can be combined with existing continuum correlations based on computational fluid dynamics simulations, yet it can now be used accurately in the transitional and free-molecular regimes. The functional form of the stagnation point heat flux correlation is physics based, and was derived via the Burnett and super-Burnett equations in a recent article, Singh & Schwartzentruber (J. Fluid Mech., vol. 792, 2016, pp. 981–996). In addition, correlation parameters from the literature are used to construct simple expressions for the local heat flux around the sphere as well as the integrated drag coefficient. A large number of direct simulation Monte Carlo calculations are performed over a wide range of conditions. The computed heat flux and drag data are used to validate the correlations and also to fit the correlation parameters. Compared to existing continuum-based correlations, the new correlations will enable engineering analysis of flight conditions at higher altitudes and/or smaller geometry radii, useful for a variety of applications including blunt body planetary entry, sharp leading edges, low orbiting satellites, meteorites and space debris.

JFM classification

Aerodynamics: Aerodynamics Aerodynamics: High-speed flow Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 821 , 25 June 2017 , pp. 421 - 439
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Copyright
© 2017 Cambridge University Press 

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References

Agarwal, R. K., Yun, K.-Y. & Balakrishnan, R. 2001 Beyond Navier–Stokes: Burnett equations for flows in the continuum–transition regime. Phys. Fluids 13 (10), 3061–3085.CrossRefGoogle Scholar
Anderson, J. D. 2000 Hypersonic and High Temperature Gas Dynamics. AIAA.Google Scholar
Bergemann, F. & Boyd, I. D. 1994 New discrete vibrational energy model for the direct simulation Monte Carlo method. Prog. Astronaut. Aeronaut. 158, 174–174.Google Scholar
Bird, G. A. 1970 Breakdown of translational and rotational equilibrium in gaseous expansions. AIAA J. 8 (11), 1998–2003.CrossRefGoogle Scholar
Bird, G. A. 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon.Google Scholar
Boyd, I. D., Chen, G. & Candler, G. V. 1995 Predicting failure of the continuum fluid equations in transitional hypersonic flows. Phys. Fluids 7 (1), 210–219.Google Scholar
Boylan, D. E. 1971 Laminar convective heat-transfer rates on a hemisphere cylinder in rarefied hypersonic flow. AIAA J. 9 (8), 1661–1663.Google Scholar
Brandis, A. M. & Johnston, C. O. 2014 Characterization of stagnation-point heat flux for earth entry. AIAA J. 2374 (2014), 20.Google Scholar
Cheng, H. K. 1961 Hypersonic shock-layer theory of the stagnation region at low Reynolds number. In Proceedings of the 1961 Heat Transfer and Fluid Mechanics Institute, pp. 161–175. Stanford University Press.Google Scholar
Dogra, V. K., Wilmoth, R. G. & Moss, J. N. 1992 Aerothermodynamics of a 1.6-meter-diameter sphere in hypersonic rarefied flow. AIAA J. 30 (7), 1789–1794.CrossRefGoogle Scholar
Fay, J. A. & Riddell, F. R. 1958 Theory of stagnation point in dissociated air. J. Aero. Sci. 25, 73–85.Google Scholar
Gao, D., Zhang, C. & Schwartzentruber, T. E. 2011 Particle simulations of planetary probe flows employing automated mesh refinement. J. Spacecr. Rockets 48 (3), 397–405.Google Scholar
Glass, C. E. & Moss, J. N. 2001 Aerothermodynamic characteristics in the hypersonic continuum-rarefied transitional regime. In 35th AIAA Thermophysics Conference, p. 2962. AIAA.Google Scholar
Gökçen, T. & MacCormack, R. W.1989 Nonequilibrium effects for hypersonic transitional flows using continuum approach. AIAA Paper 461.Google Scholar
Gökçen, T., MacCormack, R. W. & Chapman, D. R.1987 Computational fluid dynamics near the continuum limit. AIAA Paper 1115.Google Scholar
Holman, T. D. & Boyd, I. D. 2009 Effects of continuum breakdown on the surface properties of a hypersonic sphere. J. Thermophys. Heat Transfer 23 (4), 660–673.Google Scholar
Johnston, C. O., Hollis, B. R. & Sutton, K. 2008a Non-Boltzmann modeling for air shock-layer radiation at lunar-return conditions. J. Spacecr. Rockets 45 (5), 879–890.CrossRefGoogle Scholar
Johnston, C. O., Hollis, B. R. & Sutton, K. 2008b Spectrum modeling for air shock-layer radiation at lunar-return conditions. J. Spacecr. Rockets 45 (5), 865–878.Google Scholar
Lofthouse, A. J., Scalabrin, L. C. & Boyd, I. D. 2008 Velocity slip and temperature jump in hypersonic aerothermodynamics. J. Thermophys. Heat Transfer 22 (1), 38–49.CrossRefGoogle Scholar
Macrossan, M. N. 2007 Scaling parameters for hypersonic flow: correlation of sphere drag data. In 25th International Symposium on Rarefied Gas Dynamics, vol. 1, pp. 759–764. Siberian Branch of the Russian Academy of Sciences.Google Scholar
Matting, F. W.1964 General solution of the laminar compressible boundary layer in the stagnation region of blunt bodies in axisymmetric flow. NASA Tech. Rep. D-2234.Google Scholar
Mazaheri, A., Gnoffo, P., Johnston, C. & Kleb, B.2010 LAURA Users Manual. NASA Tech. Rep. TM, 2010-216836.Google Scholar
Murzinov, I. N. 1966 Laminar boundary layer on a sphere in hypersonic flow of equilibrium dissociating air. Fluid Dyn. 1 (2), 131–133.Google Scholar
Nompelis, I. & Schwartzentruber, T. E. 2013 Strategies for Parallelization of the DSMC Method. vol. 2000, p. 55455. University of Minnesota.Google Scholar
Patterson, G. N. 1971 Introduction to the Kinetic Theory of Gas Flows. University of Toronto Press.Google Scholar
Phillips, W. M. & Kuhlthau, A. R. 1971 Transition regime sphere drag near the free molecule limit. AIAA J. 9 (7), 1434–1435.Google Scholar
Singh, N. & Agrawal, A. 2016 Onsager’s-principle-consistent 13-moment transport equations. Phys. Rev. E 93 (6), 063111.Google Scholar
Singh, N. & Schwartzentruber, T. E. 2016 Heat flux correlation for high-speed flow in the transitional regime. J. Fluid Mech. 792, 981–996.CrossRefGoogle Scholar
Sutton, K. & Graves, R. Jr. 1971 A general stagnation-point convective heating equation for arbitrary gas mixtures. NASA Tech. Rep. R-376, 12-10.Google Scholar
Tsien, H.-S. 1946 Superaerodynamics, mechanics of rarefied gases. J. Aero. Sci. 13, 342.Google Scholar
Wang, Z., Bao, L. & Tong, B. 2010 Rarefaction criterion and non-fourier heat transfer in hypersonic rarefied flows. Phys. Fluids 22 (12), 126103.Google Scholar
Wen, C.-Y. & Hornung, H. G. 1995 Non-equilibrium dissociating flow over spheres. J. Fluid Mech. 299, 389–405.Google Scholar
Whiting, E. E., Park, C., Liu, Y., Arnold, J. O. & Paterson, J. A1996 NEQAIR96, nonequilibrium and equilibrium radiative transport and spectra program: user’s manual. NASA Reference Publication 1389.Google Scholar
Zhang, C. & Schwartzentruber, T. 2012a Numerical assessment of vibration and dissociation models in DSMC for hypersonic stagnation line flows. In 43rd AIAA Thermophysics Conference, p. 2992. AIAA.Google Scholar
Zhang, C. & Schwartzentruber, T. E. 2012b Robust cut-cell algorithms for DSMC implementations employing multi-level cartesian grids. Comput. Fluids 69, 122–135.CrossRefGoogle Scholar