Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T03:18:16.499Z Has data issue: false hasContentIssue false
  • English
  • Français

Mechanisms in the hypersonic laminar near wake of a blunt body

Published online by Cambridge University Press:  25 January 2018

W. Schuyler Hinman Open the ORCID record for W. Schuyler Hinman [Opens in a new window]  and
Craig T. Johansen
W. Schuyler Hinman
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB T2N1N4, Canada
Craig T. Johansen*
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB T2N1N4, Canada
*
†Email address for correspondence: johansen@ucalgary.ca
Get access Rights & Permissions [Opens in a new window]

Abstract

A new theoretical framework, based on the analysis of Navier–Stokes solutions for the hypersonic laminar near wake of two-dimensional and axisymmetric blunt bodies, is presented. A semi-empirical relationship is derived between the free-stream Mach and Reynolds numbers and a characteristic wake Reynolds number. A control volume analysis was performed to assess the validity of some common assumptions used in the literature. Analysis of the momentum and vorticity equations is used to assess the dominant mechanisms of momentum transfer along and across the dividing streamline and centreline which enclose the near wake. An observed stagnation pressure gain along the dividing streamline is explained using the entropy transport equation, demonstrating an unbalance between entropy generation due to viscous dissipation and entropy diffusion. The rear-stagnation point flow is analysed using an analogy to a reversed flow jet which allows for the centreline Mach number to be solved. A new viscous–inviscid interaction theory is presented for the reattachment shock formation process for both planar and axisymmetric wakes. Finally, all of the sub-mechanisms are combined into an overall wake mechanism. The resulting equations constitute the first overall theoretical framework of the laminar near-wake mechanism including separation, reattachment, rear-stagnation point flow and dividing streamline stagnation pressure gain for both planar and axisymmetric near wakes. Scaling arguments are presented throughout the work for each of the key sub-mechanisms. Recommendations are made for how experimental and numerical results for the near wake should be presented. The equations and recommendations presented here are then used to perform a detailed disambiguation of laminar capsule studies in the literature.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Shock waves Wakes/Jets: Wakes/Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 839 , 25 March 2018 , pp. 33 - 75
Copyright
© 2018 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

Arisman, C. & Johansen, C. T. 2015 Nitric oxide chemistry effects in hypersonic boundary layers. AIAA J. 53 (12), 3652–3660.Google Scholar
Arisman, C., Johansen, C. T., Bathel, B. & Danehy, P. 2015 Investigation of gas seeding for planar laser-induced fluorescence in hypersonic boundary layers. AIAA J. 53 (12), 3637–3651.Google Scholar
Balla, R. J.2013 Iodine tagging velocimetry and mechanism in the hypersonic near wake of a multipurpose crew vehicle. NASA Tech. Rep. TM-20130218027 (July).Google Scholar
Barnhardt, M. & Candler, G. V. 2012 Detached-Eddy simulation of the Reentry-F flight experiment. J. Spacecr. Rockets 49 (4), 691–699.Google Scholar
Bashkin, V. A., Egorov, I. V., Egorova, M. V. & Ivanov, D. V. 1998 Initiation and development of separated flow behind a circular cylinder in a supersonic stream. Fluid Dyn. 33 (6), 833–841.Google Scholar
Bashkin, V. A., Vaganov, A. V., Egorov, I. V., Ivanov, D. V. & Ignatova, G. A. 2002 Comparison of calculated and experimental data on supersonic flow past a circular cylinder. Fluid Dyn. 37 (3), 473–483.CrossRefGoogle Scholar
Batchelor, G. K. 1956 On steady laminar flow with closed streamlines at large Reynolds number. J. Fluid Mech. 1 (02), 177–190.Google Scholar
Baum, E. 1967 Interacting supersonic laminar wake calculations by a finite difference method. AIAA J. 5 (7), 1224–1230.Google Scholar
Baum, E. 1968 An interaction model of a supersonic laminar boundary layer on sharpand rounded backward facing steps. AIAA J. 6 (3), 440–447.CrossRefGoogle Scholar
Baum, E., King, H. H. & Denison, M. R. 1964 Recent studies of the laminar base-flow region. AIAA J. 2 (9), 1527–1534.Google Scholar
Berger, K. T. 2009 Aerothermodynamic testing of the crew exploration vehicle at Mach 6 and Mach 10. J. Spacecr. Rockets 46 (4), 758–765.Google Scholar
Brock, J. M., Subbareddy, P. K. & Candler, G. V. 2015 Detached-eddy simulations of hypersonic capsule wake flow. AIAA J. 53 (1), 70–80.Google Scholar
Chapman, D. R.1950 Laminar mixing of a compressible fluid. Tech. Rep. 958. National Advisory Committee for Aeronautics.Google Scholar
Chapman, D. R., Kuehn, D. M. & Larson, H. K.1958 Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition. Tech. Rep. 1356. National Advisory Committee for Aeronautics.Google Scholar
Combs, C. S., Clemens, N. T., Danehy, P. M., Bathel, B., Parker, R., Wadhams, T., Holden, M. & Kirk, B. 2013 NO PLIF visualization of the Orion Capsule in LENS-I. In 51st AIAA Aerospace Sciences Meeting, Grapevine, Texas. American Institute of Aeronautics and Astronautics.Google Scholar
Crocco, L. & Lees, L. 1952 A mixing theory for the interaction between dissipative flows and nearly isentropic streams. J. Aeronaut. Sci. 19 (10), 649–676.Google Scholar
Deck, S. & Thorigny, P. 2007 Unsteadiness of an axisymmetric separating-reattaching flow: numerical investigation. Phys. Fluids 19 (6), 65103.CrossRefGoogle Scholar
Delery, J. 2011 Physical introduction. In Shock Wave-Boundary Layer Interactions, 1st edn. (ed. Babinsky, H. & Harvey, J. K.), chap. 2, pp. 5–86. Cambridge University Press.CrossRefGoogle Scholar
Delery, J. & Lacau, R. G.1988 Prediction of base-flows. Tech. Rep. AGARD - NATO.Google Scholar
Denison, M. R. & Baum, E. 1963 Compressible free shear layer with finite initial thickness. AIAA J. 1 (2), 342–349.Google Scholar
Desikan, S. L. N., Patil, M. M. & Subramanian, S. Sarabhai, Vikram & Centre, Space 2015 understanding of flow features over a typical crew module at Mach 4. Aeronaut. J. 119 (1216), 727–746.Google Scholar
Dewey, C. F.1963 Measurements in highly dissipative regions of hypersonic flows. Part II. The near wake of a blunt body at hypersonic speeds. PhD thesis, California Institute of Technology.CrossRefGoogle Scholar
Dewey, C. F. 1965 Near wake of a blunt body at hypersonic speeds. AIAA J. 3 (6), 1001–1010.CrossRefGoogle Scholar
Dogra, V. K., Moss, J. N. & Price, J. M. 1994 Near-wake structure for a generic configuration of aeroassisted space transfer vehicles. J. Spacecr. Rockets 31 (6), 953–959.CrossRefGoogle Scholar
Dutton, J. C., Herrin, J. L., Molezzi, M. J., Mathur, T. & Smith, K.M.1995 Recent progress on high-speed separated base flows. In 33rd Aerospace Sciences Meeting and Exhibit. Reno, NV. AIAA Paper 95-0472.Google Scholar
Forsythe, J. R., Hoffmann, K. A., Cummings, R. M. & Squires, K. D. 2002 Detached-eddy simulation with compressibility corrections applied to a supersonic axisymmetric base flow. J. Fluids Engng 124 (December), 911.Google Scholar
Fureby, C., Nilsson, Y. & Andersson, K.1999 Large eddy simulation of supersonic base flow. In 37th Aerospace Sciences Meeting and Exhibit. AIAA Paper 1999-426.Google Scholar
Grange, J.-M., Klineberg, J. M. & Lees, L. 1967 Laminar boundary-layer separation and near-wake flow for a smooth blunt body at supersonic and hypersonic speeds. AIAA J. 5 (6), 1089–1096.Google Scholar
Grasso, F. & Pettinelli, C. 1995 Analysis of laminar near-wake hypersonic flows. J. Spacecr. Rockets 32 (6), 970–980.Google Scholar
Herrin, J. L. & Dutton, J. C. 1994 Supersonic base flow experiments in the near wake of a cylindrical afterbody. AIAA J. 32 (1), 77–83.Google Scholar
Herrin, J. L. & Dutton, J. C. 1995 Effect of a rapid expansion on the development of compressible free shear layers. Phys. Fluids 7 (1), 159.Google Scholar
Hideyuki, T., Tomoyuki, K., Kazuo, S., Masathoshi, K. & Katsuhiro, I.2013 Free-flight aerodynamic test with projectile-onboard data recorder in a ballistic range. AIAA Paper 2013-0475 (January), 1–8.Google Scholar
Hinman, W. S. & Johansen, C. T. 2016a Interaction theory of hypersonic laminar near-wake flow behind an adiabatic circular cylinder. Shock Waves 26 (6), 717–727.CrossRefGoogle Scholar
Hinman, W. S. & Johansen, C. T. 2016b Rapid prediction of hypersonic blunt body flows for parametric design studies. Aerosp. Sci. Technol. 58, 48–59.Google Scholar
Hinman, W. S. & Johansen, C. T. 2016c Reynolds and mach number dependence of hypersonic blunt body laminar near wakes. AIAA J. 55 (2), 1–9.Google Scholar
Hollis, B. R., Berger, K. T., Horvath, T. J., Coblish, J. J., Norris, J. D., Lillard, R. P. & Kirk, B. S. 2009 Aeroheating testing and predictions for project Orion CEV at turbulent conditions. J. Spacecr. Rockets 46 (4), 1–15.Google Scholar
Hollis, B. R. & Collier, A. S. 2008 Turbulent aeroheating testing of mars science laboratory entry vehicle. J. Spacecr. Rockets 45 (3), 417–427.CrossRefGoogle Scholar
Hrubecky, H. F. 1963 An approximate analysis for the turbulent boundary layer thickness on a cone in supersonic flow. Appl. Sci. Res. A 11 (4), 441–450.Google Scholar
Hruschka, R., O’Byrne, S. & Kleine, H. 2008 Diode-laser-based near-resonantly enhanced flow visualization in shock tunnels. Appl. Opt. 47 (24), 4352–4360.CrossRefGoogle ScholarPubMed
Hruschka, R., O’Byrne, S. & Kleine, H. 2010 Two-component Doppler-shift fluorescence velocimetry applied to a generic planetary entry probe model. Exp. Fluids 48 (6), 1109–1120.CrossRefGoogle Scholar
Hruschka, R., O’Byrne, S. & Kleine, H. 2011 Comparison of velocity and temperature measurements with simulations in a hypersonic wake flow. Exp. Fluids 51 (2), 407–421.CrossRefGoogle Scholar
Humble, R. A., Scarano, F. & van Oudheusden, B. W. 2007 Unsteady flow organization of compressible planar base flows. Phys. Fluids 19 (7), 1–18.Google Scholar
Johansen, C. T., Danehy, P. M., Ashcraft, S. W., Bathel, B. F., Inman, J. a. & Jones, S. B. 2013a Planar laser-induced fluorescence of mars science laboratory reaction control system jets. J. Spacecr. Rockets 50 (4), 781–792.Google Scholar
Johansen, C. T., Novak, L., Bathel, B. F., Ashcraft, S. W. & Danehy, P. M. 2013b Mars science laboratory reaction control system jet computations with visualization and velocimetry. J. Spacecr. Rockets 50 (6), 1183–1195.Google Scholar
Johnston, C. O. & Brandis, A. M. 2015 Features of afterbody radiative heating for earth entry. J. Spacecr. Rockets 52 (1), 105–119.Google Scholar
Kastengren, A. L. & Dutton, J. C. 2005 Large-structure topology in a three-dimensional supersonic base flow. AIAA J. 43 (5), 1053–1063.CrossRefGoogle Scholar
Kawai, S. & Fujii, K. 2005 Computational study of a supersonic base flow using hybrid turbulence methodology. AIAA J. 43 (6), 1265–1275.Google Scholar
Lachney, E. R. & Clemens, N. T. 1998 PLIF imaging of mean temperature and pressure in a supersonic bluff wake. Exp. Fluids 24 (4), 354–363.Google Scholar
Lamb, J. P. & Oberkampf, W. L. 1995 Review and development of base pressure and base heating correlations in supersonic flow. J. Spacecr. Rockets 32 (1), 8–23.Google Scholar
Lees, L. 1964 Hypersonic wakes and trails. AIAA J. 2 (3), 417–428.Google Scholar
Lees, L. & Reeves, B. L. 1964 Supersonic separated and reattaching laminar flows: I. General theory and application to adiabatic boundary-layer/shock-wave interactions. AIAA J. 2 (11), 1907–1920.Google Scholar
Liever, P. A., Habchi, S. D., Burnell, S. I. & Lingard, J. S. 2003 Computational fluid dynamics prediction of the Beagle 2 aerodynamic database. J. Spacecr. Rockets 40 (5), 632–638.Google Scholar
McCarthy, J. F. & Kubota, T. 1964 A study of wakes behind a circular cylinder at M equal 5.7. AIAA J. 2 (4), 629–636.Google Scholar
McDaniel, R. D., Wright, M. J. & Songer, J. T. 2011 Aeroheating predictions for phoenix entry vehicle. J. Spacecr. Rockets 48 (5), 727–745.CrossRefGoogle Scholar
Mehta, R. C. 2006 Numerical simulation of supersonic flow past reentry capsules. Shock Waves 15 (1), 31–41.CrossRefGoogle Scholar
Mehta, R. C. 2008 Computations of flow field over Apollo and OREX reentry modules at high speed. Indian J. Engng Mater. Sci. 15 (6), 459–466.Google Scholar
Mitcheltree, R. A. & Gnoffo, P. A. 1995 Wake flow about the mars pathfinder entry vehicle. J. Spacecr. Rockets 32 (5), 758–764.CrossRefGoogle Scholar
Mitcheltree, R. A., Moss, J. N., Cheatwood, F. M., Greene, F. A. & Braun, R. D. 1999 Aerodynamics of the mars microprobe entry vehicles. J. Spacecr. Rockets 36 (3), 392–398.Google Scholar
Mitcheltree, R. A., Wilmoth, R. G., Cheatwood, F. M., Brauckmann, G. J. & Greene, F. A.1997 Aerodynamics of stardust sample return capsule. In 15th Applied Aerodynamics Conference. AIAA Paper 1997-2304.Google Scholar
Moss, J. N., Gupta, R. N. & Price, J. M.1996 DSMC Simulations of OREX entry conditions. NASA Tech. Rep. Google Scholar
Mudford, N. R., O’Byrne, S., Neely, A., Buttsworth, D. & Balage, S. 2015 Hypersonic wind-tunnel free-flying experiments with onboard instrumentation. J. Spacecr. Rockets 52 (1), 231–242.Google Scholar
Nakamura, H., Manabe, K. & Nishio, M. 2006 Flow patterns around the MESUR capsule traveling at supersonic/hypersonic speeds. JSME Intl J. B 49 (2), 384–392.Google Scholar
NIST-JANAF2013 NIST-JANAF Thermochemical Tables. Obtained from http://kinetics.nist.gov/janaf/.Google Scholar
Olynick, D., Chen, Y. & Tauber, M. 1999 Aerodynamics of the stardust sample return capsule. J. Spacecr. Rockets 36 (3), 436–441.CrossRefGoogle Scholar
Otsu, H., Abe, T., Ohnishi, Y., Sasoh, A. & Takayama, K. 2002 Numerical investigation of high-enthalpy flows generated by expansion tube. AIAA J. 40 (12), 2423–2430.Google Scholar
Ottens, H. B. A. 2002 Preliminary computational investigation on aerodynamic phenomena on delft aerospace re-entry test vehicle. In 4th Europ. Symp. Aerothermodynamics for Space Applications, Capua. European Space Agency.Google Scholar
Park, G., Gai, S. L. & Neely, A. J. 2010a Aerothermodynamics behind a blunt body at superorbital speeds. AIAA J. 48 (8), 1804–1816.CrossRefGoogle Scholar
Park, G., Gai, S. L. & Neely, A. J. 2010b Laminar near wake of a circular cylinder at hypersonic speeds. AIAA J. 48 (1), 236–248.Google Scholar
Park, G., Gai, S. L. & Neely, A. J. 2016 Base flow of circular cylinder at hypersonic speeds. AIAA J. 54 (2), 1–11.Google Scholar
Poling, B. E., Prausnitz, J. M. & O’Connell, J. P. 2001 Thermal conductivity. In The Properties of Gases and Liquids, 5th edn, chap. 10, 10.1–10.70, McGraw-Hill.Google Scholar
Reddy, D. S. K. & Sinha, K. 2009 Hypersonic turbulent flow simulation of fire II reentry vehicle afterbody. J. Spacecr. Rockets 46 (4), 745–757.Google Scholar
Reeves, B. L. & Lees, L. 1965 Theory of laminar near wake of blunt bodies in hypersonic flow. AIAA J. 3 (11), 2061–2074.Google Scholar
Salazar, G. & Edwards, J. R. 2014 Mach 6 wake flow simulations using a large-eddy simulation/Reynolds-averaged Navier–Stokes model. J. Spacecr. Rockets 51 (4), 1329–1348.Google Scholar
Scarano, F. & Van Oudheusden, B. W. 2003 Planar velocity measurements of a two-dimensional compressible wake. Exp. Fluids 34 (3), 430–441.Google Scholar
Schlichting, H. 1979 Exact solutions of the Navier–Stokes equations. In Boundary-Layer Theory, 3rd edn. pp. 83–110. McGraw-Hill.Google Scholar
Schmidt, B. E. & Shepherd, J. E. 2015 Oscillations in cylinder wakes at Mach 4. J. Fluid Mech. 785 (R3), 1–8.CrossRefGoogle Scholar
Schneider, S. P. 2008 Summary of hypersonic boundary-layer transition experiments on blunt bodies with roughness. J. Spacecr. Rockets 45 (6), 1090–1105.Google Scholar
Schrijer, F. F. J. & Walpot, L.2010 Experimental investigation of re-entry aerodynamic phenomena In 48th AIAA Aerospace Sciences Meeting. AIAA Paper 2010-1251.Google Scholar
Schwing, A. M. & Candler, G. V. 2015 Detached-eddy simulation of capsule wake flows and comparison to wind-tunnel test data. J. Spacecr. Rockets 52 (2), 439–449.Google Scholar
Settles, G. S. & Williams, D. R. 1982 Reattachment of a compressible turbulent free shear layer. AIAA J. 20 (1), 60–67.CrossRefGoogle Scholar
Shang, J. S. & Surzhikov, S. T. 2011 Simulating stardust earth reentry with radiation heat transfer. J. Spacecr. Rockets 48 (3), 385–396.Google Scholar
Simon, F., Deck, S., Guillen, P. & Sagaut, P. 2006 Reynolds-averaged Navier–Stokes/large-eddy simulations of supersonic base flow. AIAA J. 44 (11), 2578–2590.Google Scholar
Simon, F., Deck, S., Merlen, A., Guillen, P. & Sagaut, P. 2007 Numerical simulation of the compressible mixing layer past an axisymmetric trailing edge. J. Fluid Mech. 591 (2007), 215–253.Google Scholar
Sinha, K. & Dey, A.2010 Simulation of flow separation and reattachment on a re-entry capsule afterbody frustum. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. pp. 1–17. AIAA Paper 2010-1561.Google Scholar
Smith, J. H. & Lamb, J. P. 1974 Eclectic merger of crocco-lees and Chapman-Korst approach to near wake. Intl J. Heat Mass Transfer 17 (12), 1571–1589.Google Scholar
Suzuki, K. & Abe, T.1994 Wind tunnel experiments on wake flow field behind a reentry capsule from a viewpoint of parachute deployment at supersonic speeds. Rep. no. 655. JAXA Institute of Space and Astronautical Science.Google Scholar
Tewfik, O. K. & Giedt, W. H. 1960 Heat transfer, recovery factor and pressure distributions around a circular cylinder normal to a supersonic rarefied-air stream. J. Aeronaut. Sci. 27 (10), 721–729.Google Scholar
Tu, C. V. V. & Wood, D. H. H. 1996 Wall pressure and shear stress measurements beneath an impinging jet. Exp. Therm. Fluid Sci. 13 (4), 364–373.Google Scholar
Walpot, L. 2002 Numerical analysis of the ARD Capulse in S4 wind tunnel. In 4th Europ. Symp. Aerothermodynamics for Space Applications. European Space Agency.Google Scholar
Walpot, L. M. G., Wright, M. J., Noeding, P. & Schrijer, F. 2012 Base flow investigation of the Apollo AS-202 command module. Prog. Aerosp. Sci. 48–49, 57–74.Google Scholar
Weinbaum, S. 1966 Rapid expansion of a supersonic boundary layer and its application to the near wake. AIAA J. 4 (2), 217–226.Google Scholar
Weiss, R. F. 1966 Base pressure of slender bodies in laminar, hypersonic flow. AIAA J. 4 (9), 1557–1559.Google Scholar
Weiss, R. F. 1967 A new theoretical solution of the laminar, hypersonic near wake. AIAA J. 5 (12), 2142–2149.Google Scholar
Weiss, R. F. & Weinbaum, S. 1966 Hypersonic boundary-layer separation and the base flow problem. AIAA J. 4 (8), 1321–1330.Google Scholar
Wood, W. A., Gnoffo, P. A. & Rault, D. F. G. 1996 Aerodynamic analysis of commercial experiment transporter re-entry capsule. J. Spacecr. Rockets 33 (5), 632–646.Google Scholar
Zhong, J., Ozawa, T. & Levin, D. A. 2008a Modeling of stardust reentry ablation flows in the near-continuum flight regime. AIAA J. 46 (10), 2568–2581.CrossRefGoogle Scholar
Zhong, J., Ozawa, T. & Levin, D. A. 2008b Comparison of high-altitude hypersonic wake flows of slender and blunt bodies. AIAA J. 46 (1), 251–262.Google Scholar