Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T10:34:33.756Z Has data issue: false hasContentIssue false
  • English
  • Français

Unsteadiness boundaries in supersonic flow over double cones

Published online by Cambridge University Press:  06 April 2021

H.G. Hornung Open the ORCID record for H.G. Hornung [Opens in a new window] ,
R.J. Gollan Open the ORCID record for R.J. Gollan [Opens in a new window]  and
P.A. Jacobs
H.G. Hornung*
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA91125, USA
R.J. Gollan
Affiliation:
Centre for Hypersonics, School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, Australia
P.A. Jacobs
Affiliation:
Centre for Hypersonics, School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, Australia
*
†Email address for correspondence: hans@caltech.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A computational parameter study of the viscous axisymmetric supersonic flow over a double cone is made with a view to determining the boundary of the region in which such flows are unsteady. The study is restricted to the case when the boundary layer is laminar. The features of both the steady and unsteady flows in different characteristic regions of the parameter space are described. In particular, the phenomenon of pulsating flow typical of spiked blunt bodies (small first-cone angle, $\theta _1$, and large second-cone angle, $\theta _2$), is shown to be inviscid in nature. In $\theta _1$–$\theta _2$ space, the region of unsteady flow is enclosed in a loop with a lower and an upper $\theta _2$ branch with a maximum $\theta _1$ between. The location of the lower $\theta _2$ branch is determined by the second-cone detachment angle $\theta _{2d}$. For this reason, the gas model in one of the conditions is chosen to be thermally perfect carbon dioxide (at Mach number 8) for which $\theta _{2d}$ is quite large. In the other cases, the gas model is perfect-gas nitrogen at Mach numbers 2, 4 and 7.7. In the hypersonic range, within the uncertainties, and in the parameter range covered, the unsteadiness boundary is shown to depend on only three dimensionless parameters.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Hypersonic Flow Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A5
Check for updates
Copyright
© The Author(s), 2021. 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

Ahmed, M.Y.M. & Qin, N. 2011 Aerothermodynamics of spiked bodies, Part I. In Proceedings of the 14th International Conference on Aerospace Sciences and Aviation Technology. Egyptian Ministry of Defence.CrossRefGoogle Scholar
van Albada, G.D., van Leer, B. & Roberts, W.W. 1981 A comparative study of computational methods in cosmic gas dynamics. ICASE Rep. 81-24. NASA Langley Research Center.Google Scholar
Bogdonoff, S.M. & Vas, I.E. 1959 Preliminary investigations of spiked bodies at hypersonic speeds. J. Aerosp. Sci. 26, 65–74.CrossRefGoogle Scholar
Feszty, D., Badcock, K.J. & Richards, B.E. 2004 Driving mechanisms of high-speed unsteady spiked body flows. Part 1. Pulsation mode. AIAA J. 42, 95–106.CrossRefGoogle Scholar
Gollan, R.J. & Jacobs, P.A. 2013 About the formulation, verification and validation of the hypersonic flow solver Eilmer. Intl J. Numer. Meth. Fluids 73, 19–57.CrossRefGoogle Scholar
Gordon, S. & McBride, B.J. 1994 Computer program for calculation of complex chemical equilibrium compositions and applications. Part 1: Analysis. NASA Reference Publication 1311. NASA Lewis Research Center.Google Scholar
Hayes, W.D. & Probstein, R.F. 1959 Hypersonic Flow Theory. Academic Press.Google Scholar
Holden, M.S. 1966 Experimental studies of separated flows at hypersonic speeds. Part 1. Separated flows over axisymmetric spiked bodies. AIAA J. 4, 591–599.CrossRefGoogle Scholar
Holden, M.S., Wadhams, T.P., Harvey, J.K. & Candler, G.V. 2007 Comparison between measurements in regions of laminar shock wave boundary layer interaction in hypersonic flows with Navier–Stokes and DSMC solutions. Tech. Rep. RTO-AVT-007-V3. RTO.Google Scholar
Hornung, H.G., Martinez Schramm, J. & Hannemann, K. 2019 Hypersonic flow over spherically blunted cones for atmospheric entry. Part 1. The sharp cone and the sphere. J. Fluid Mech. 871, 1097–1116.CrossRefGoogle Scholar
Jacobs, P.A. 1991 Single-block Navier–Stokes integrator. ICASE Interim Rep. 18. NASA Langley Research Center.Google Scholar
Kenworthy, M.A. 1978 A study of unsteady axisymmetric separation in high-speed flows. PhD thesis, Virginia Polytechnic Institute and State University.Google Scholar
Knisely, A.M. 2016 Experimental investigation of non-equilibrium and separation scaling in double-cone and double-wedge geometries. PhD thesis, University of Illinois at Urbana-Champaign.Google Scholar
Kokkinakis, I.W., Drikakis, D., Ritos, K. & Spottswood, S.M. 2020 Direct numerical simulation of supersonic flow and acoustics over a compression ramp. Phys. Fluids 32, 066107.CrossRefGoogle Scholar
Macrossan, M.N. 1989 The equilibrium flux method for the calculation of flows with non-equilibrium chemical reactions. J. Comput. Phys. 80 (1), 204–231.CrossRefGoogle Scholar
Mair, W. 1952 Experiments on separation of boundary layer on probes in front of blunt nosed bodies in a supersonic stream. Phil. Mag. 43, 596–601.CrossRefGoogle Scholar
Maull, D.J. 1960 Hypersonic flow over axisymmetric spiked bodies. J. Fluid Mech. 8, 584–592.CrossRefGoogle Scholar
Olejniczak, J., Candler, G.V. & Hornung, H.G. 1997 Computation of double-cone experiments in high enthalpy nitrogen. In Proceedings of the 32nd AIAA Thermophysics Conference. American Institute of Aeronautics and Astrronautics.CrossRefGoogle Scholar
Panaras, A.G. & Drikakis, D. 2009 High-speed unsteady flows around spiked blunt bodies. J. Fluid Mech. 632, 69–96.CrossRefGoogle Scholar
Ritos, K., Kokkinakis, I.W. & Drikakis, D. 2018 Performance of high-order implicit large-eddy simulations. Comput. Fluids 173, 307–312.CrossRefGoogle Scholar
Stollery, J.L., Maull, D.J. & Belcher, B.J. 1960 The Imperial College gun tunnel. J. R. Aero. Soc. 64, 24–33.CrossRefGoogle Scholar
Tumuklu, O., Theofilis, V. & Levin, D.A. 2018 On the unsteadiness of shock laminar boundary layer interactions of hypersonic flows over a double cone. Phys. Fluids 30, 106111–1–106111–12.Google Scholar
Wada, Y. & Liou, M.S. 1994 A flux splitting scheme with high-resolution and robustness for discontinuities. AIAA Paper 94-0083.CrossRefGoogle Scholar
Wood, C.J. 1961 Hypersonic flow over spiked cones. J. Fluid Mech. 12, 614–624.CrossRefGoogle Scholar