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Stability of highly cooled hypervelocity boundary layers

Published online by Cambridge University Press:  05 August 2015

N. P. Bitter*
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
J. E. Shepherd
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
*
Email address for correspondence: [email protected]

Abstract

The influence of high levels of wall cooling on the stability of hypervelocity boundary layers is investigated. Such conditions are relevant to experiments in high-enthalpy impulse facilities, where the wall temperature is much smaller than the free-stream temperature, as well as to some real flight scenarios. Some effects of wall cooling are well known, for instance, the stabilization of the first mode and destabilization of the second mode. In this paper, several new instability phenomena are investigated that arise only for high Mach numbers and high levels of wall cooling. In particular, certain unstable modes can travel supersonically with respect to the free stream, which changes the nature of the dispersion curve and leads to instability over a much wider band of frequencies. The cause of this phenomenon, the range of parameters for which it occurs and its implications for boundary layer stability are examined. Additionally, growth rates are systematically reported for a wide range of conditions relevant to high-enthalpy impulse facilities, and the stability trends in terms of Mach number and wall temperature are mapped out. Thermal non-equilibrium is included in the analysis and its influence on the stability characteristics of flows in impulse facilities is assessed.

Type
Papers
Copyright
© 2015 Cambridge University Press 

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References

Adam, P. H. & Hornung, H. G. 1997 Enthalpy effects on hypervelocity boundary-layer transition: ground test and flight data. J. Spacecr. Rockets 34 (5), 614619.Google Scholar
Balakumar, P. & Malik, M. R. 1992 Discrete modes and continuous spectra in supersonic boundary layers. J. Fluid Mech. 239, 631656.Google Scholar
Bertolotti, F. P. 1998 The influence of rotational and vibrational energy relaxation on boundary-layer stability. J. Fluid Mech. 372, 93118.CrossRefGoogle Scholar
Bitter, N. P. & Shepherd, J. E.2014 Transient growth in hypersonic boundary layers. In Proceedings of the 7th AIAA Theoretical Fluid Mechanics Conference. Atlanta, GA AIAA-2014-2497.Google Scholar
Bres, G. A., Inkman, M. I., Colonius, T. & Fedorov, A. V. 2013 Second-mode attenuation and cancellation by porous coatings in a high-speed boundary layer. J. Fluid Mech. 726, 312337.Google Scholar
Chang, C. L., Malik, M. R. & Hussaini, M. Y.1990 Effects of shock on the stability of hypersonic boundary layers. In Proceedings of the 21st AIAA Fluid Dynamics, Plasma Dynamics, and Lasers Conference, Seattle, WA, AIAA-90-1448.Google Scholar
Chang, C. L., Vinh, H. & Malik, M. R.1997 Hypersonic boundary-layer stability with chemical reactions using PSE. In Proceedings of the 28th AIAA Fluid Dynamics Conference, Snowmass Village, CO, AIAA-97-2012.Google Scholar
Clarke, J. F. & McChesney, M. 1964 The Dynamics of Real Gases. Butterworth.CrossRefGoogle Scholar
Cole, W. A. & Wakeham, W. A. 1985 The viscosity of nitrogen, oxygen, and their binary mixtures in the limit of zero density. J. Phys. Chem. Ref. Data 14 (1), 209226.Google Scholar
Conte, S. D. 1966 The numerical solution of linear boundary value problems. SIAM Rev. 8 (3), 309321.Google Scholar
Davey, A. 1983 An automatic orthonormalization method for solving stiff boundary-value problems. J. Comput. Phys. 51 (2), 343356.Google Scholar
Demetriades, A.1977 Laminar boundary layer stability measurements at Mach 7 including wall temperature effects. Tech. Rep. AFOSR-TR-77-1311. US Air Force Office of Scientific Research.Google Scholar
Estorf, M., Wolf, T. & Radespiel, R. 2004 Experimental and numerical investigations on the operation of the Hypersonic Ludwieg Tube Braunschweig. In 5th European Symposium on Aerothermodynamics for Space Vehicles.Google Scholar
Fedorov, A. V., Bres, G. A., Inkman, M. & Colonius, T.2011 Instability of hypersonic boundary layer on a wall with resonating micro-cavities. In Proceedings of the 49th AIAA Aerospace Sciences Meeting, Orlando, FL, AIAA-2011-373.Google Scholar
Fedorov, A. & Khokhlov, A. 2001 Prehistory of instability in a hypersonic boundary layer. Theor. Comput. Fluid Dyn. 14 (6), 359375.CrossRefGoogle Scholar
Fedorov, A. V., Malmuth, N. D., Rasheed, A. & Hornung, H. G. 2001 Stabilization of hypersonic boundary layers by porous coatings. AIAA J. 39 (4), 605610.Google Scholar
Fedorov, A. V., Ryzhov, A. A., Soudakov, V. G. & Utyuzhnikov, S. V. 2013 Receptivity of a high-speed boundary layer to temperature spottiness. J. Fluid Mech. 722, 533553.Google Scholar
Fedorov, A., Shiplyuk, A., Maslov, A., Burov, E. & Malmuth, N. 2003 Stabilization of a hypersonic boundary layer using an ultrasonically absorptive coating. J. Fluid Mech. 479, 99124.Google Scholar
Fedorov, A. V., Soudakov, V. G. & Leyva, I. A.2014 Stability analysis of high-speed boundary-layer flow with gas injection. In Proceedings of the 7th AIAA Theoretical Fluid Mechanics Conference, Atlanta, GA, AIAA-2014-2498.Google Scholar
Fedorov, A. & Tumin, A. 2003 Initial-value problem for hypersonic boundary-layer flows. AIAA J. 41 (3), 379389.CrossRefGoogle Scholar
Fedorov, A. & Tumin, A. 2011 High-speed boundary-layer instability: old terminology and a new framework. AIAA J. 49 (8), 16471657.CrossRefGoogle Scholar
Fujii, K. & Hornung, H. G. 2003 Experimental investigation of high-enthalpy effects on attachment-line boundary-layer transition. AIAA J. 41 (7), 12821291.Google Scholar
Garg, V. K. 1980 Improved shooting techniques for linear boundary value problems. Comput. Meth. Appl. Mech. Engng 22 (1), 8799.Google Scholar
Germain, P. D. & Hornung, H. G. 1997 Transition on a slender cone in hypervelocity flow. Exp. Fluids 22, 183190.Google Scholar
Heitmann, D., Radespiel, R. & Knauss, H. 2011 Experimental study of Mach 6 boundary layer response to laser generated disturbances. In Proceedings of the 41st AIAA Fluid Dynamics Conference, Honolulu HI. AIAA.Google Scholar
Hollis, B. R. 2012 Blunt-body entry vehicle aerothermodynamics: transition and turbulent heating. J. Spacecr. Rockets 49 (3), 435449.Google Scholar
Hudson, M. L., Chokani, N. & Candler, G. V. 1997 Linear stability of hypersonic flow in thermochemical nonequilibrium. AIAA J. 35 (6), 958964.CrossRefGoogle Scholar
Johnson, H. B.2000 Thermochemical interactions in hypersonic boundary layer stability. PhD thesis, University of Minnesota.Google Scholar
Johnson, H. B., Alba, C. R. & Candler, G. V. 2008 Boundary-layer stability analysis of the hypersonic international flight research transition experiments. J. Spacecr. Rockets 45 (2), 228236.CrossRefGoogle Scholar
Johnson, H. B., Seipp, T. G. & Candler, G. V. 1998 Numerical study of hypersonic reacting boundary layer transition on cones. Phys. Fluids 10 (10), 26762685.Google Scholar
Kadoya, K., Matsunaga, N. & Nagashima, A. 1985 Viscosity and thermal conductivity of dry air in the gaseous phase. J. Phys. Chem. Ref. Data 14 (4), 947970.Google Scholar
Klentzman, J. & Tumin, A.2013 Stability and receptivity of high speed boundary layers in oxygen. In Proceedings of the 43rd AIAA Fluid Dynamics Conference, San Diego, CA, AIAA2013-2882.Google Scholar
Klunker, E. B. & McLean, F. E.1953 Effect of thermal properties on laminar-boundary-layer characteristics. Tech. Rep. NACA TN-2916. National Advisory Committee for Aeronautics.Google Scholar
Lau, K. Y. 2008 Hypersonic boundary-layer transition: application to high-speed vehicle design. J. Spacecr. Rockets 45 (2), 176183.Google Scholar
Laurence, S. J., Wagner, A., Ozawa, H., Schramm, J. M. & Hannemann, K.2014 Visualization of a hypersonic boundary-layer transition on a slender cone. In Proceedings of the 19th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Atlanta, GA, AIAA-2014-3110.Google Scholar
Lees, L.1947 The stability of the laminar boundary layer in a compressible fluid. Tech. Rep. 876. National Advisory Committee for Aeronautics.Google Scholar
Lees, L. & Lin, C. C.1946 Investigation of the stability of the laminar boundary layer in a compressible fluid. Tech. Rep. TN-1115. National Advisory Committee for Aeronautics.Google Scholar
Lees, L. & Reshotko, E. 1962 Stability of the compressible laminar boundary layer. J. Fluid Mech. 12, 555590.CrossRefGoogle Scholar
Lighthill, M. J. 1956 Viscosity effects in sound waves of finite amplitude. In Surveys in Mechanics (ed. Batchelor, G. K. & Davies, R. M.), pp. 250351. Cambridge University Press.Google Scholar
Lin, C. C. 1944 On the stability of two-dimensional parallel flows. Proc. Natl Acad. Sci. USA 30 (10), 316324.Google Scholar
Lin, T. C. 2008 Influence of laminar boundary-layer transition on entry vehicle designs. J. Spacecr. Rockets 45 (2), 165175.Google Scholar
Ma, Y. & Zhong, X. 2003 Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions. J. Fluid Mech. 488, 3178.Google Scholar
Mack, L. M. 1965 Computations of the stability of the laminar compressible boundary layer. In Methods in Computational Physics (ed. Alder, B., Fernback, S. & Rotenberg, M.), vol. 4, pp. 247299. Academic.Google Scholar
Mack, L. M.1969 Boundary layer stability theory. Tech. Rep. JPL Report 900-277. Jet Propulsion Lab, California Institute of Technology.Google Scholar
Mack, L. M. 1975 Linear stability theory and the problem of supersonic boundary-layer transition. AIAA J. 13 (3), 278289.Google Scholar
Mack, L. M.1984 Boundary-layer linear stability theory. In AGARD Report No. 709. North Atlantic Treaty Organization.Google Scholar
Mack, L. M. 1987 Review of Linear Compressible Stability Theory. pp. 164187. Springer.Google Scholar
Mack, L. M. 1993 Effect of cooling on boundary-layer stability at Mach number 3. In Instabilities and Turbulence in Engineering Flows (ed. Ashpis, D. E., Gatski, T. B. & Hirsch, R.), Springer.Google Scholar
Malik, M. R. 1989a Prediction and control of transition in supersonic and hypersonic boundary layers. AIAA J. 27 (11), 14871493.Google Scholar
Malik, M. R. 1989b Stability theory for chemically reacting flows. In Laminar-Turbulent Transition (ed. Arnal, D. & Michel, R.), pp. 251260. IUTAM Symposium Toulouse/France.Google Scholar
Malik, M. R. 1990 Numerical methods for hypersonic boundary layers. J. Comput. Phys. 86, 376413.Google Scholar
Malik, M. R. 2003 Hypersonic flight transition data analysis using parabolized stability equations with chemistry effects. J. Spacecr. Rockets 40 (3), 332344.Google Scholar
Malik, M. R. & Anderson, E. C. 1991 Real gas effects on hypersonic boundary-layer stability. Phys. Fluids 3 (5), 803821.Google Scholar
Malik, M. R. & Spall, R. E. 1991 On the stability of compressible flow past axisymmetric bodies. J. Fluid Mech. 228, 443463.Google Scholar
Marineau, E. C., Moraru, G., Lewis, D. R., Norris, J. D., Lafferty, J. F., Wagnild, R. M. & Smith, J. A.2014 Mach 10 boundary-layer transition experiments on sharp and blunted cones. In Proceedings of the 19th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Atlanta, GA, AIAA-2014-3108.Google Scholar
Masad, J. A., Nayfeh, A. H. & Al-Maaitah, A. A. 1992 Effect of heat transfer on the stability of compressible boundary layers. Comput. Fluids 21 (1), 4361.Google Scholar
Millikan, R. C. & White, D. R. 1963 Systematics of vibrational relaxation. J. Chem. Phys. 139 (12), 32093213.Google Scholar
Morkovin, M. V.1969 Critical evaluation of transition from laminar to turbulent shear layers with emphasis on hypersonically traveling bodies. Tech. Rep. AFFDL-TR-68-149. Air Force Flight Dynamics Laboratory.Google Scholar
Park, C. 1990 Nonequilibrium Hypersonic Aerothermodynamics. John Wiley & Sons.Google Scholar
Parziale, N.2013 Slender-body hypervelocity boundary-layer instability. PhD thesis, California Institute of Technology.Google Scholar
Parziale, N. J., Shepherd, J. E. & Hornung, H. G. 2013 Differential interferometric measurement of instability in a hypervelocity boundary layer. AIAA J. 51 (3), 750753.Google Scholar
Rasheed, A., Hornung, H. G., Fedorov, A. V. & Malmuth, N. D. 2002 Experiments on passive hypervelocity boundary-layer control using an ultrasonically absorptive surface. AIAA J. 40 (3), 481489.Google Scholar
Rayleigh, L. 1880 On the stability, or instability, of certain fluid motions. Proc. Lond. Math. Soc. 11, 5770.Google Scholar
Schlichting, H. & Gersten, K. 2000 Boundary Layer Theory, 8th edn. Springer.Google Scholar
Schneider, S. P. 2001 Effects of high-speed tunnel noise on laminar–turbulent transition. J. Spacecr. Rockets 38 (3), 323333.Google Scholar
Schneider, S. P. 2004 Hypersonic laminar–turbulent transition on circular cones and scramjet forebodies. Prog. Aerosp. Sci. 40, 150.Google Scholar
Schneider, S. P.2006 Hypersonic laminar instability on round cones near zero angle of attack. Tech. Rep. NATO Research and Technology Organization, RTO-AVT-007-V3, pp. 1-1-24.Google Scholar
Sherman, M. M. & Nakamura, T. 1970 Flight test measurements of boundary-layer transition on a nonablating 22 deg cone. J. Spacecr. Rockets 7 (2), 137142.Google Scholar
Stetson, K. F.1980 Hypersonic boundary layer transition experiments. Tech. Rep. AFWAL-TR-80-3062. Air Force Wright Aeronautical Laboratories.Google Scholar
Stetson, K. F., Thompson, E. R., Donaldson, J. C. & Siler, L. G.1983 Laminar boundary layer stability experiments on a cone at Mach 8, part 1: sharp cone. In Proceedings of the 16th AIAA Fluid and Plasma Dynamics Conference, Danvers, MA, AIAA-83-1761.Google Scholar
Stetson, K. F., Thompson, E. R., Donaldson, J. C. & Siler, L. G.1984 Laminar boundary layer stability experiments on a cone at Mach 8, part 2: blunt cone. In Proceedings of the 22nd AIAA Aerospace Sciences Meeting, Reno, NV, AIAA-84-0006.Google Scholar
Stuckert, G. H. & Reed, H. L. 1994 Linear stability of hypersonic flow in thermochemical nonequilibrium. AIAA J. 32 (7), 13841393.Google Scholar
Taylor, R. L. & Bitterman, S. 1969 Survey of vibrational relaxation data for processes important in the $\text{CO}_{2}{-}\text{N}_{2}$ laser system. Rev. Mod. Phys. 41 (1), 2647.Google Scholar
Van Driest, E. R. 1952 Calculation of the stability of the laminar boundary layer in a compressible fluid on a flat plate with heat transfer. J. Aeronaut. Sci. 19 (12), 801812.Google Scholar
Vincenti, W. G. & Kruger, C. H. 1967 Introduction to Physical Gas Dynamics. John Wiley and Sons.Google Scholar
Wilke, C. R. 1950 A viscosity equation for gas mixtures. J. Chem. Phys. 18 (4), 517519.Google Scholar
Wright, M. J., Candler, G. V. & Bose, D. 1998 Data-parallel line relaxation method for the Navier–Stokes equations. AIAA J. 36 (9), 16031609.Google Scholar