Asymptotic theory of plane steady supersonic flows with separation zones

Neiland, V. Ya.

doi:10.1007/bf01019270

Cited by 18 publications

(19 citation statements)

References 5 publications

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“…Our calculations did not confirm the finite ramp angle singularity concept put forward by Smith & Khorrami (1991). The solution does show a sharpening of minimal skin friction prior to reattachment, but this behaviour proved to be well in line with Neiland's (1970) reattachment theory, which does not involve any restrictions on the ramp angle. In fact, it was intended by Neiland for finite values of θ (see figure 1), i.e.…”

Section: Discussionmentioning

confidence: 44%

“…Secondly, the solution follows Neiland's (1970) reattachment theory rather well. Readjusting his arguments for the compression ramp flow (see the Appendix) it may To study the effect of the outer boundary we performed calculations with different y M .…”

Section: Calculation Resultsmentioning

confidence: 99%

“…Here the processes taking place near the reattachment point will be discussed following Neiland's (1970) original work. His analysis was devoted to the reattachment of a shear layer which terminates a large-scale separation; correspondingly certain assumptions had been made on the velocity profile across the shear layer as it approaches the wall.…”

Section: Appendix Analysis Of the Reattachment Processmentioning

confidence: 99%

“…The velocity in the shear layer grows monotonically from the recirculating region towards the outer edge of the layer as shown in figure 14, and its value on the separation streamline may be estimated as u 0 ∼ 1/3 . (A 3) Neiland's (1970) reattachment theory is based on the following concept. As the shear layer impinges on the wall, the inviscid supersonic flow outside the boundary has to turn through angle β r to become parallel to the wall downstream of the reattachment point R. This causes the pressure to rise by the value ∆p = β r , and as α increases the pressure gradient induced in the reattachment region starts to dominate the viscous forces.…”

Section: Appendix Analysis Of the Reattachment Processmentioning

confidence: 99%

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Once again on the supersonic flow separation near a corner

2002

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Laminar boundary-layer separation in the supersonic flow past a corner point on a rigid body contour, also termed the compression ramp, is considered based on the viscous-inviscid interaction concept. The 'triple-deck model' is used to describe the interaction process. The governing equations of the interaction may be formally derived from the Navier-Stokes equations if the ramp angle θ is represented as θ = θ 0 Re −1/4 , where θ 0 is an order-one quantity and Re is the Reynolds number, assumed large. To solve the interaction problem two numerical methods have been used. The first method employs a finite-difference approximation of the governing equations with respect to both the streamwise and wall-normal coordinates. The resulting algebraic equations are linearized using a Newton-Raphson strategy and then solved with the Thomas-matrix technique. The second method uses finite differences in the streamwise direction in combination with Chebychev collocation in the normal direction and Newton-Raphson linearization.Our main concern is with the flow behaviour at large values of θ 0 . The calculations show that as the ramp angle θ 0 increases, additional eddies form near the corner point inside the separation region. The behaviour of the solution does not give any indication that there exists a critical value θ * 0 of the ramp angle θ 0 , as suggested by Smith & Khorrami (1991) who claimed that as θ 0 approaches θ * 0 , a singularity develops near the reattachment point, preventing the continuation of the solution beyond θ * 0 . Instead we find that the numerical solution agrees with Neiland's (1970) theory of reattachment, which does not involve any restriction upon the ramp angle.

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Section: Discussionmentioning

confidence: 44%

Section: Calculation Resultsmentioning

confidence: 99%

Section: Appendix Analysis Of the Reattachment Processmentioning

confidence: 99%

Section: Appendix Analysis Of the Reattachment Processmentioning

confidence: 99%

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Once again on the supersonic flow separation near a corner

2002

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“…[ Neyland (1970a)] totic expansion matching principle is used. At the outer edge, the conditions of compatibility with the outer supersonic flow and the zero normal velocity at the body surface are to be satisfied.…”

Section: Reattachmentmentioning

confidence: 99%