Turbulent Shear Layer Re-Attachment with Special Emphasis on the Base Pressure Problem

SummaryAn analysis is presented which enables the boundary-layer thickness parameters of a re-attaching shear layer to be determined when the free-stream flow upstream of the base is supersonic, the base pressure is known, and die initial boundary layer is turbulent. The application of this analysis to some experimental results, on the flow behind blunt-trailing-edge wings and over a back-step where both the base pressure and the initial boundary layer are known, would appear to indicate that the re-attached profile could be specified by one parameter, namely the transformed shape parameter, the transformation used being a turbulent analogue of the well-known Stewartson-Illingworth transformation of the laminar boundary layer and where the shape parameter is defined as the ratio of boundary-layer displacement to momentum thickness. By adopting a value of the shape parameter in advance, it is possible to use the analysis to determine the base pressure by an iterative process and so, on this basis, it is suggested that this analysis is used to replace the existing recompression criterion of the Chapman-Korst model of separated flow which aims to predict base pressures and is known to be capable of improvement.As part of this investigation, an improvement had to be made to the existing compressible turbulent shear layer velocity profiles of Korst and others and this was achieved by means of the compressibility transformation.

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The reattachment and relaxation of a turbulent shear layer

Journal of Fluid Mechanics ◽

10.1017/s002211207200299x ◽

1972 ◽

Vol 52 (1) ◽

pp. 113-135 ◽

Cited By ~ 304

Author(s):

P. Bradshaw ◽

F. Y. F. Wong

Keyword(s):

Boundary Layer ◽

Shear Layer ◽

Flow Region ◽

Turbulent Shear ◽

Length Scale ◽

Low Speed ◽

Turbulent Shear Layer ◽

Recirculating Flow ◽

Speed Flow ◽

Complicated Nature

Existing experiments on the low-speed flow downstream of steps and fences, and some new measurements downstream of a backward-facing step, are used to demonstrate the complicated nature of the flow in the reattachment region and its effect on the slow non-monotonic return of the shear layer to the ordinary boundary-layer state. A key feature of the flow is found to be the splitting of the shear layer at reattachment, where part of the flow is deflected upstream into the recirculating flow region to supply the entrainment; the part of the flow that continues downstream suffers a pronounced decrease in eddy length scale, evidently because the larger eddies are torn in two. This phenomenon will occur in all cases where a shear layer reattaches after a prolonged region of separation, either at low speed or in supersonic flow. For simplicity, the discussion in the present paper is confined to low-speed flows.

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Investigation of a Reattaching Turbulent Shear Layer: Flow Over a Backward-Facing Step

Journal of Fluids Engineering ◽

10.1115/1.3240686 ◽

1980 ◽

Vol 102 (3) ◽

pp. 302-308 ◽

Cited By ~ 181

Author(s):

J. Kim ◽

S. J. Kline ◽

J. P. Johnston

Keyword(s):

Boundary Layer ◽

Shear Layer ◽

Eddy Viscosity ◽

Flow Characteristics ◽

Turbulent Shear ◽

Turbulence Structure ◽

Backward Facing Step ◽

Turbulent Shear Layer ◽

Separated Shear Layer ◽

Layer Flow

Incompressible flow over a backward-facing step is studied in order to investigate the flow characteristics in the separated shear-layer, the reattachment zone, and the redeveloping boundary layer after reattachment. Two different step-heights are used: h/δs = 2.2 and h/δs = 3.3. The boundary layer at separation is turbulent for both cases. Turbulent intensities and shear stress reach maxima in the reattachment zone, followed by rapid decay near the surface after reattachment. Downstream of reattachnent, the flow returns very slowly to the structure of an ordinary turbulent boundary layer. In the reattached layer the conventional normalization of outerlayer eddy viscosity by U∞ δ* does not collapse the data. However, it was found that normalization by U∞ (δ − δ*) does collapse the data to within ± 10% of a single curve as far downstream as x/xR ≈ 2, the last data station. This result illustrates the strong downstream persistence of the energetic turbulence structure created in the separated shear layer.

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A study of the turbulent separated-flow region occurring at a compression corner in supersonic flow

Journal of Fluid Mechanics ◽

10.1017/s0022112065000927 ◽

1965 ◽

Vol 22 (3) ◽

pp. 481-505 ◽

Cited By ~ 11

Author(s):

H. McDonald

Keyword(s):

Boundary Layer ◽

Single Layer ◽

Separated Flow ◽

Flow Region ◽

Initial Boundary ◽

Base Pressure ◽

Layer Model ◽

Compression Corner ◽

Shock Configuration ◽

Turbulent Separated Flow

The turbulent separated-flow region occurring at a compression corner under certain circumstances at supersonic speed has been examined in the light of recent improvements to base pressure theory (McDonald 1964). This base pressure theory is further extended from what could be termed a single-layer model of the re-attaching boundary layer to a two-layer model, thus enabling the inviscid shock configuration which occurs at the corner to be determined. Application of this analysis to some experimental results indicates a substantial measure of agreement.While this analysis has been framed for estimating the scale of the corner interaction, the extension can of course be applied to increase the range of initial boundary-layer thicknesses to which McDonald's analysis is applicable. An example of such an application is shown to be in good agreement with experiment.

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