Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-08T05:32:23.277Z Has data issue: false hasContentIssue false

High-speed unsteady flows around spiked-blunt bodies

Published online by Cambridge University Press:  27 July 2009

ARGYRIS G. PANARAS*
Affiliation:
Department of Aerospace Sciences, Cranfield University, Cranfield MK43 0AL, UK
DIMITRIS DRIKAKIS
Affiliation:
Department of Aerospace Sciences, Cranfield University, Cranfield MK43 0AL, UK
*
E-mail address for correspondence: [email protected]

Abstract

This paper presents a detailed investigation of unsteady supersonic and hypersonic flows around spiked-blunt bodies, including the investigation of the effects of the flow field initialization on the flow results. Past experimental research has shown that if the geometry of a spiked-blunt body is such that a shock formation consisting of an oblique foreshock and a bow aftershock appears, then the flow may be unsteady. The unsteady flow is characterized by periodic radial inflation and collapse of the conical separation bubble formed around the spike (pulsation). Beyond a certain spike length the flow is ‘stable’, i.e. steady or mildly oscillating in the radial direction. Both unsteady and ‘stable’ conditions have been reported when increasing or decreasing the spike length during an experimental test and, additionally, hysteresis effects have been observed. The present study reveals that for certain geometries the numerically simulated flow depends strongly on the assumed initial flow field, including the occurrence of bifurcations due to inherent hysteresis effects and the appearance of unsteady flow modes. Computations using several different configurations reveal that the transient (initial) flow development corresponds to a nearly inviscid flow field characterized by a foreshock–aftershock interaction. When the flow is pulsating, the further flow development is not sensitive to initial conditions, whereas for an oscillating or almost ‘steady’ flow, the flow development depends strongly on the assumed initial flow field.

Type
Papers
Copyright
Copyright © Cambridge University Press 2009

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

Batchelor, G. K. 2000 An Introduction to Fluid Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Calarese, W. & Hankey, W. L. 1985 Modes of shock-wave oscillations on spike-tipped bodies. AIAA J. 23, 185192.CrossRefGoogle Scholar
Crawford, D. H. 1959 Investigation of the flow over a spiked-nose hemisphere-cylinder at a Mach number of 6.8. NASA D-118.Google Scholar
Drikakis, D. & Rider, W. 2005 High-Resolution Methods for Incompressible and Low-Speed Flows. Springer.Google Scholar
Drikakis, D. & Smolarkiewicz, P. K. 2001 On spurious vortical structures. J. Comput. Phys. 172, 309325.CrossRefGoogle Scholar
Edney, D. 1968 Anomalous heat transfer and pressure distributions on blunt bodies at hypersonic speeds in the presence of an impinging shock. FFA Rep. 115.CrossRefGoogle Scholar
Feszty, D., Badcock, K. J. & Richards, B. E. 2004 a Driving mechanisms of high-speed unsteady spiked body flows. Part 1. Pulsation mode. AIAA J. 42, 95106.CrossRefGoogle Scholar
Feszty, D., Badcock, K. J. & Richards, B. E. 2004 bDriving mechanisms of high-speed unsteady spiked body flows. Part 2. Oscillation mode. AIAA J. 42, 107113.CrossRefGoogle Scholar
Holden, M. S., Wandhams, T. P., Harvey, J. K. & Candler, G. V. 2002 Comparisons between DSMC and Navier–Stokes solutions and measurements in regions of laminar shock wave boundary layer interaction in hypersonic flows. AIAA Paper 2002–0435.CrossRefGoogle Scholar
Kabelitz, H. 1971 Zur Stabilitaet geschlossener Grenzschichtabloese-gebiete an konischen Drenkoerpern bei Hyperschallaus-stroemung. DLR FB 71–77.Google Scholar
Kenworthy, M. 1978 A study of unstable axisymmetric separation in high speed flows. Ph.D. Dissertation, Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute And State University, Blacksburg, VA, USA.Google Scholar
Mair, W. 1952 Experiments on separated boundary layers on probes in front of blunt nosed bodies in a supersonic air stream. Phil. Mag. 43, 695716.CrossRefGoogle Scholar
Maull, D. 1962 Hypersonic flow over axially symmetric spiked bodies. J. Fluid Mech. 12, 614624.Google Scholar
Mehta, R. C. 2002 Numerical analysis of pressure oscillations over axisymmetric spiked blunt bodies at Mach 6.80. Shock Waves 11, 431440.CrossRefGoogle Scholar
Morrison, J. H. 1992 A compressible Navier–Stokes solver with two-equation and Reynolds stress turbulence closure models. NASA CR-4440.Google Scholar
Panaras, A. G. 1976 The high speed unsteady separation around concave bodies can be explained by an inviscid flow mechanism. These Annexe, VKI-Free University of Brussels.Google Scholar
Panaras, A. G. 1977 High speed unsteady separation about concave bodies – A physical explanation, von Karman Institute, Tech. Note 123.Google Scholar
Panaras, A. G. 1981 Pulsating flows about axisymmetric concave bodies. AIAA J. 9, 804806.CrossRefGoogle Scholar
Panaras, A. G. 1985 Pressure pulses generated by the interaction of discrete vortices with an edge. J. Fluid Mech. 154, 445462.CrossRefGoogle Scholar
Roe, P. L. 1981 Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comp. Phys. 43, 357372.CrossRefGoogle Scholar
Rumsey, C. L., Sanetrik, M. D., Biedron, R. T., Melson, N. D. & Parlette, E. B. 1996 Efficiency and accuracy of time-accurate turbulent Navier–Stokes computations. Comput. Fluids. 25 (2), 217236.CrossRefGoogle Scholar
Schramm, J. M. & Eitelberg, G 1999 Shock boundary layer interaction in hypersonic high enthalpy flow on a double wedge, Paper 5150, 22nd International Symposium on Shock Waves, Imperial College, London, UK, July 1823.Google Scholar
Shang, J. S., Hankey, W. L. & Smith, R. E. 1980 Flow oscillations of spike-tipped bodies. AIAA Paper 80-0062.CrossRefGoogle Scholar
Van Leer, B. 1979 Towards the ultimate conservative difference scheme V. A second order Sequel to Godunov's method. J. Comp. Phys. 32, 101136.CrossRefGoogle Scholar
Wood, C. 1960 Experimental flow over spiked flows. J. Fluid Mech. 8 584594.Google Scholar
Yee, H. C. 2001 Building block for reliable non-linear numerical simulations. In Turbulent Flow Computation (Ed. Drikakis, D. & Geurts, B.). Kluwer Academic Publisher.Google Scholar