cases:case050

# Boundary Layer on the Verge of Separation

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.

Fig. 1: Flow geometry and configuration

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.

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)
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]
1. 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.
2. 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)
case050
titleBoundary layer on the verge of separation
authorDengel, Fernholz
year1989
typeEXP
flow_tagaxisymmetric, 2dbl