cases:case057

# 3-Dimensional Boundary Layer Generated by a Spinning Body

Experimental data are given for a three-dimensional, shear-driven, turbulent boundary layer subjected to sudden transverse strain. Measurements made with a three-component laser Doppler velocimeter include all components of mean flow, turbulent Reynolds stresses, and triple-product correlations.

The 3-dimensional boundary layer is generated over the cylinder shown in figure 1. A 2-D boundary layer develops over the upstream, stationary, section of the cylinder. The flow then passes over the rotating section of cylinder, which generates a large component of cross flow velocity near the surface. Away from the wall, where the effect of this new boundary condition is yet to be felt, the flow remains 2D. Further along the rotating cylinder the transverse flow reaches the edge of the boundary layer and the flow evolves into a collateral state (unidirectional when viewed from the rotating wall), again taking on the characteristics of a 2D boundary layer. As the flow passes on to the third, stationary, section of the cylinder the lateral flow near the surface of the cylinder is reduced, and a classic 3D boundary layer with a high degree of skewing develops. This is where most of the measurements have been taken. Far downstream, the boundary layer skewing diminishes, to the point where it is nearly 2D and flowing parallel to the cylinder axis again.

Fig. 1: Flow configuration and geometry

#### Test Configuration

The experiment was conducted using a $0.31 \times 0.31$ m low-speed wind tunnel with a 0.140 m diameter cylinder running the length of the tunnel along its centre-line. The walls around the test section were contoured from flexible plexiglas to create an adjustable diverging portion of tunnel wall, allowing both zero and adverse pressure gradient cases to be examined.

The middle section of the cylinder (0.914 m long) could be made to rotate, whilst the upstream and downstream sections remained stationary. The gap between the spinning and stationary sections was closed to within 0.254 mm. The spinning and stationary cylinders were equal in diameter (0.140 m) to within +/-0.04 mm. Measurements were taken primarily on the downstream stationary section, where the flow was relaxing back to a two-dimensional boundary layer.

The experiments were performed at nominal free-stream velocities, $U_e$, of 15 and 30 m/s, with corresponding free-stream turbulence intensities of 1% and 6% respectively. The spinning section of the cylinder was rotated at circumferential speeds, $W_s$, of 0, 15 and 30 m/s, depending on the test being conducted. The majority of cases for which data are given here correspond to $U_e = 30$ m/s and $W_s= 0$ or $30$ m/s. The boundary layer thicknesses at the end of the spinning section were 27 mm (for $W_s=U_e = 30$ m/s) and 18 mm ($U_e=30$ m/s, $W_s=0$), giving Reynolds numbers based on momentum thickness of 6000 and 4000 respectively.

Four cases with different streamwise pressure gradient distributions were created using different tunnel side wall configurations:

• Case A: the walls being parallel, and $\partial P/\partial x = 0$.
• Case B: the walls diverging with mild side wall boundary layer suction, starting at $x=-180$ mm, giving mild $\partial P/\partial x > 0$.
• Case C: the walls diverging with strong side wall boundary layer suction, starting at $x=-180$ mm, giving strong $\partial P/\partial x > 0$.
• Case C: the walls diverging with strong side wall boundary layer suction, starting at $x=-4$ mm, giving strong $\partial P/\partial x > 0$.

Four cases of spin rate were also considered, as given in the table below:

Case Name Spin Rate ($W_s/U_e$) $W_s$ [m/s] $U_e$ [m/s]
S0 0 0 30
S1/2 0.5 15 30
S1 1 30 30
S2 2 30 15

In the data files the cases are distinguished by the letter corresponding to the pressure gradient conditions, and the spin ratio case name (eg, A.S1, C.S0). The detailed LDV data provided here correspond to the spin ratio S0 and S1 cases.

Velocities were measured using 3-component, synchronous, 3-colour (LDV).

#### Measurements Errors

Surface skin friction was measured using fence gauge. uncertainties in the skin friction coefficient $C_f$ were estimated to be +/-10% of the measured value.

Uncertainties in $U$, $V$, and $W$ were estimated to be +/-2%.

Uncertainties in $U^2$, $\overline{u^2}$ and $\overline{w^2}$ were estimated to be +/-7%.

Uncertainties in $\overline{uv}$, $\overline{vw}$ and $\overline{uw}$ were estimated to fall in the range -7 to +20%.

The data available includes:

• Surface pressure measurements ($C_p$) for the adverse pressure gradient cases
• Wall shear stresses ($C_{fx}$ and $C_{fz}$)
• Surface skin friction direction angle (from oil-flow visualization)
• Profiles of mean velocity, Reynolds stresses and triple moments, at selected streamwise locations

Sample plots of selected quantities are available.

Surface pressure coefficients:

Spin Ratio Case B Case C Case D
0 cp_bs0.dat cp_cs0.dat cp_ds0.dat
1 cp_bs1.dat cp_cs1.dat cp_ds1.dat

Skin friction coefficients ($C_{fx}$ and $C_{fz}$):

Spin Ratio Case A Case B Case C Case D
0 cf_bs0.dat cf_bbs0.dat cf_cs0.dat cf_ds0.dat
0.5 cf_bbs05.dat cf_cs05.dat cf_ds05.dat
1 cf_as1.dat cf_bbs1.dat cf_cs1.dat cf_ds1.dat

Note: Read the text in the bbs0, bbs05 and bbs1 files before using data from them. They were obtained using not quite the tunnel design conditions, so may not be completely compatible with other data/cases.

Wall shear stress direction angles:

Spin Ratio Case A Case B Case C Case D
0.5 be_as05.dat be_bbs05.dat be_cs05.dat
1 be_as1.dat be_bbs1.dat be_cs1.dat be_ds1.dat
2 be_bbs2.dat

LDV profiles of mean velocity, Reynolds stresses and triple moments:

1. Driver, D.M., Hebbar, S.K. (1987). Experimental study of a three-dimensional, shear-driven, turbulent boundary layer. AIAA Journal, Vol. 25, p.35.
2. Driver, D.M., Johnston, J.P. (1990). Experimental stud of a three-dimensional shear-driven turbulent boundary layer with streamwise adverse pressure gradient. NASA Tech. Memo. 102211, Ames Research Center.

Indexed data:

case057 (dbcase, semi_confined_flow)
case057
title3-Dimensional Boundary Layer Generated by a Spinning body
authorDriver, Johnston
year1990
typeEXP
flow_tagaxisymmetric, 3dbl