Boundary Layer on the Verge of Separation
Experiments by Dengel and Fernholz
Description
The data characterises the behaviour of boundary layers in the vicinity of separation. Three similar flows are studied, each with slightly different pressure distributions resulting in finite regions of small, constant, but different skin frictions: case 1, approximately zero; case 2, slightly positive (\(C_f \approx 0.0001\)); and case 3, slightly negative (\(C_f \approx -0.0001\)).
This study uses pulsed-wire anemometry and examines the sensitivity of a boundary layer near separation to small perturbations in the stream-wise pressure gradient. In addition, case 3 includes a long, shallow separation bubble. The bubble is small (compared to the boundary-layer thickness) and minimises viscid/inviscid interaction and normal pressure gradients. It is steady (no flapping) and grows on an axisymmetric cylinder to prevent three-dimensional effects.
The flows are at a Reynolds number of \(Re = 10^6\) m^{-1}, based on the velocity \(u_d\) at the inlet of the test section.
Experimental Details
The wind tunnel used in this investigation (Dengel & Fernholz 1990) was a low-speed blower tunnel with a 12kW motor and a centrifugal fan, an air-filter intake, and 2 m long settling chamber of circular cross-section containing, at its upstream end, a precisely manufactured, perforated metal screen (64% open area ratio), and a non-woven filter mat. The nozzle leading to the axisymmetric test section had a contraction ratio of 11:1. The core velocity distribution was uniform at the nozzle exit to within +/-0.30%. with a turbulence intensity of 0.2%. The test section, shown in figure 1, consisted of a sting-mounted, horizontal, inner circular cylinder (0.25 m diameter, 1.85 m long. and made of Ultramid S) with an elliptical nose cone (0.30 m long) extending upstream into the nozzle and thus increasing the contraction ratio to 13.4:1. The inner cylinder could be rotated through a circumferential angle of 160 degrees. The outer cylindrical wall was concentric with the inner surface and both the outer wall and the back plate were constructed of perforated metal sheet (38% open area ratio). Non-uniformities in the skin-friction distribution around the circumference of the inner were around +/-1%.
The pressure distributions which generated the three boundary layers were set up by partially closing the open areas of the back plate and the outer cylinder. Sufficiently accurate measurements of pressure distributions can only be made if the pressure is measured with a single pressure tapping (movable in the \(x\)-direction) and not with a series of tappings along a generator of the cylinder. Because this technique measures relative pressure levels so accurately, the pressure gradients, calculated without smoothing, can be clearly distinguished between the three cases.
In the upstream part of the flow, the skin friction was measured by Preston tubes. Downstream, where instantaneous reverse flow occurred, the skin friction was measured by a wall pulsed-wire probe.
Available measurements
Data available includes:
- Development of \(C_p\), \(C_f\), boundary layer thicknesses and shape factors along the streamwise direction
- Profiles of mean \(U\) velocity Reynolds stress components at selected streamwise locations
- Kurtosis and skewness of streamwise mean velocity at selected streamwise locations
- Profiles of reverse flow percentage parameter at selected streamwise locations
Sample plots of selected quantities are available.
The data can be downloaded as compressed archives from the links below, or as individual files from the tables.
Boundary Layer Development Quantities (for all three cases) | |
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File | Description |
cf.dat | Skin friction coefficient |
cp-dcp.dat | Pressure coefficient (and its streamwise gradient) |
delta123.dat | Displacement, Momentum and energy thicknesses |
delta995.dat | 99.5% Boundary layer thickness |
h12_h32.dat | Boundary layer shape factors |
re_del12.dat | Reynolds numbers based on displacement and momentum thicknesses |
chi.dat | Reverse flow percentage parameter at wall |
udel.dat | Outer velocity scale |
us.dat | Schofield velocity scale |
Profiles at Selected Streamwise Locations | ||||
---|---|---|---|---|
Quantity | Case 1 | Case 2 | Case 3 | Notes |
Mean \(U\) velocity | umean_1.dat | umean_2.dat | umean_3.dat | Profiles at \(x=\) 0.435, 0.531, 0.631, 0.731, 0.831, 0.931, 1.031, 1.131, 1.231, 1.331, 1.431, 1.531 [m] |
\(\overline{u^2}\) Reynolds stress | ufluct_1.dat | ufluct_2.dat | ufluct_3.dat | Profiles at \(x=\) 0.435, 0.531, 0.631, 0.731, 0.831, 0.931, 1.031, 1.131, 1.231, 1.331, 1.431, 1.531 [m] |
\(\overline{v^2}\) Reynolds stress | vfluct_1.dat | vfluct_2.dat | vfluct_3.dat | Profiles at \(x=\) 0.435, 0.531, 0.631, 0.731, 0.831, 0.931 [m] |
\(\overline{w^2}\) Reynolds stress | wfluct_1.dat | wfluct_2.dat | wfluct_3.dat | Profiles at \(x=\) 0.435, 0.531, 0.631, 0.731, 0.831, 0.931 [m] |
\(\overline{uv}\) Reynolds stress | uvfluct_1.dat | uvfluct_2.dat | uvfluct_3.dat | Profiles at \(x=\) 0.435, 0.531, 0.631, 0.731, 0.831, 0.931, 1.031, 1.131, 1.231, 1.331, 1.431 [m] |
\(u\) Kurtosis | kurtos_1.dat | kurtos_2.dat | kurtos_3.dat | Profiles at \(x=\) 0.931, 1.031, 1.131, 1.231, 1.331, 1.431, 1.531 [m] |
\(u\) Skewness | schiefe_1.dat | schiefe_2.dat | schiefe_3.dat | Profiles at \(x=\) 0.931, 1.031, 1.131, 1.231, 1.331, 1.431, 1.531 [m] |
Reverse flow parameter \(\chi\) | ruecks_1.dat | ruecks_2.dat | ruecks_3.dat | Profiles at \(x=\) 0.931, 1.031, 1.131, 1.231, 1.331, 1.431, 1.531 [m] |
References
- Dengel, P., Fernholz, H.H. (1990). An experimental investigation of an incompressible turbulent boundary layer in the vicinity of separation. J. Fluid Mech., Vol. 212, pp. 615-636.
- Dengel, P., Fernholz, H.H. (1989). A study of the sensitivity of an incompressible turbulent boundary layer on the verge of separation. Proc. Seventh Int. Symp. on Turbulent Shear Flows, Stanford University.
Indexed data:
case050 (dbcase, semi_confined_flow) | |
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case | 050 |
title | Boundary layer on the verge of separation |
author | Dengel, Fernholz |
year | 1989 |
type | EXP |
flow_tag | axisymmetric, 2dbl |