Laterally strained turbulent boundary layers near a plane of symmetry

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Abstract
Experiments are presented for three turbulent boundary layers generated by laterally converging, laterally diverging and parallel flow on a flat plate. A converging potential flow field outside the boundary layer was generated by superposing a parallel flow in the x-direction, a row of equally spaced line sources in the wall-normal (y) direction and an analogous row of sinks in the transversal (z) direction. This arrangement resulted in a velocity that was constant far upstream, far downstream and along the x-axis. The convergence – ∂W/∂z has its maximum in the plane of the source and sink rows. This flow field was realized with the test section shown in figure 1, based on streamlines intersecting a rectangular cross-section far upstream. The diverging flow was generated by reversing the flow direction through the test section.The tests were conducted at about 42 m/s leading to a unit Reynolds number of 2.5 × 106/m and to a Reynolds number based on the momentum thickness of 4000 to 4700 at the inlet of the test sections, increasing up to 25000 at the outlet. In all three cases the velocity distribution near the wall agreed very well with the logarithmic law of the wall. The wake contribution in the outer layer was considerably increased by convergence and decreased by divergence. The Reynolds stresses, measured with crossed hot-wire probes, and the wall shear stress, measured with a floating-element balance, were generally increased by divergence and decreased by convergence and the same holds true for the mixing length and the turbulent viscosity.A finite-difference boundary-layer code using a simple turbulence model was used to predict the experimental results. The comparison showed good agreement for the two-dimensional flow, reasonable agreement for the diverging flow and poor agreement for the converging one. Use of the experimentally determined turbulent viscosity as input into the computation did not systematically improve the agreement but excellent agreement was found if it was combined with anisotropy of the turbulent viscosity. It was much more difficult to predict the converging flow as small errors in the crossflow had a large effect on the flow in the plane of symmetry (z = 0).