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High-speed unsteady flows around spiked-blunt bodies
- ARGYRIS G. PANARAS, DIMITRIS DRIKAKIS
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- Journal:
- Journal of Fluid Mechanics / Volume 632 / 10 August 2009
- Published online by Cambridge University Press:
- 27 July 2009, pp. 69-96
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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.
Numerical investigation of the high-speed conical flow past a sharp fin
- Argyris G. Panaras
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- Journal:
- Journal of Fluid Mechanics / Volume 236 / March 1992
- Published online by Cambridge University Press:
- 26 April 2006, pp. 607-633
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The supersonic flow past a fin mounted on a flat plate is simulated numerically by solving the Reynolds averaged Navier—Stokes equations. The results agree well with the experimental data. Post-processing of the numerical solution provides the missing flow-field evidence for confirming the currently accepted flow model, whose conception was based mainly on surface data. It is found that the flow is dominated by a large vortical structure, which lies on the plate and whose core has a remarkably conical shape with flattened elliptical cross-section. Along the fin and close to the corner, a slowly growing smaller vortex develops. On top of the conical vortex and along it a λ-shock is formed. Quantitative data are presented, which show that the flow is not actually purely conical but a small deviation exists, especially at the part between the separation shock and the plate. This deviation is detected when the stream wise extent of the flow is more than 20–30 initial boundary-layer thicknesses. Owing to the rather quasi-conical nature of the flow, the various flow variables do not remain constant along rays that start at the origin of the conical flow field, but they vary slowly. Data are presented which support the view that this deviation from conical behaviour is mainly due to the effect of the smaller rate of development of the boundary later of the plate, compared to the conical vortex.
Pressure pulses generated by the interaction of a discrete vortex with an edge
- Argyris G. Panaras
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- Journal:
- Journal of Fluid Mechanics / Volume 154 / May 1985
- Published online by Cambridge University Press:
- 20 April 2006, pp. 445-461
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A central role in the mechanism of the self-sustained oscillations of the flow about cavity-type bodies is played by the reattachment edge. Experimentally it has been found that periodic pressure pulses generated on this edge are fed back to the origin of the shear layer and cause the production of discrete vortices. The oscillations have been found to be suppressed or attenuated when the edge has the shape of a ramp of small angle, or when it is properly rounded. To clarify the role of the shape of the reattachment edge in the mechanism of the oscillations, a mathematical model is developed for the vortex–edge interaction. In this model the interaction of one discrete vortex, imbedded within a constant-speed parallel flow, with the reattachment edge is studied. Two typical shapes of the reattachment edge are examined; a ramp of variable angle and an ellipse. The main conclusion of the present analysis is the strong dependence of the pressure pulses, that are induced on the surface of the edge, on the specific shape of the edge. The pressure pulses on reattachment edges with shapes that give rise to steady flows have been found to be of insignificant amplitude. On the other hand, when the reattachment edge has a shape that is known to result in oscillating flow, the induced pressure pulses are of very large amplitude. Intermediate values of the pressure are found for configurations known to stabilize partially the flow. The present results indicate that, for the establishment of the oscillation, the feedback force generated by the vortex–edge interaction must have an appropriate value. The feedback force may be eliminated if the shape of the lip of the edge is properly designed.
The effect of the structure of swept-shock-wave/turbulent-boundary-layer interactions on turbulence modelling
- ARGYRIS G. PANARAS
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- Journal:
- Journal of Fluid Mechanics / Volume 338 / 10 May 1997
- Published online by Cambridge University Press:
- 10 May 1997, pp. 203-230
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The physical reasons for the diffculty in predicting accurately strong swept-shock-wave/turbulent-boundary-layer interactions are investigated. A well-documented sharp-fin/plate flow has been selected as the main test case for analysis. The selected flow is calculated by applying a version of the Baldwin–Lomax turbulence model, which is known to provide reliable results in flows characterized by the appearance of crossflow vortices. After the validation of the results, by comparison with appropriate experimental data, the test case flow is studied by means of stream surfaces which start at the inflow plane, within the undisturbed boundary layer, and which are initially parallel to the plate. Each of these surfaces has been represented by a number of streamlines. Calculation of the spatial evolution of some selected stream surfaces revealed that the inner layers of the undisturbed boundary layer, which are composed of turbulent air, wind around the core of the vortex. However, the outer layers, which are composed of low-turbulence air, fold over the vortex and at the reattachment region penetrate into the separation bubble forming a low-turbulence tongue, which lies along the plate, underneath the vortex. The conical vortex at its initial stage of development is completely composed of turbulent air, but gradually, as it grows linearly in the flow direction, the low-turbulence tongue is formed. Also the tongue grows in the flow direction and penetrates further into the separation region. When it reaches the expansion region inboard of the primary vortex, the secondary vortex starts to be formed at its tip. Examination of additional test cases indicated that the turbulence level of the elongated tongue decreases if the interaction strength increases. The existence of the low-turbulence tongue in strong swept-shock-wave/turbulent-boundary-layer interactions creates a mixed-type separation bubble: turbulent in the region of the separation line and almost laminar between the secondary vortex and the reattachment line. This type of separation cannot be simulated accurately with the currently used algebraic turbulence models, because the basic relations of these models are based on the physics of two-dimensional flows, whereas in a separation bubble the whole recirculation region is turbulent. For improving the accuracy of the existing algebraic turbulence models in predicting swept-shock-wave/turbulent-boundary-layer interactions, it is necessary to develop new equations for the calculation of the eddy viscosity in the separation region, which will consider the mixed-flow character of the conical vortex.