An Investigation of Three-dimensional Turbulent Shear Flow Experiments and New Modeling Parameters

INTRODUCTION Simple turbulence models extended from two-dimensional (2D) methods and applied to 3D turbulent boundary layers (TBL) generally give poor results. The Reynolds stresses are complicated to model for 3D flows due to the fact that they depend strongly on history effects, flow skewing, pressure gradients, strain-rate, and other flow parameters (Simpson, 1995). A common assumption in these extensions is that the resultant Reynolds shear stress direction is the same as the local mean velocity gradient angle, which implies an isotropic eddy viscosity. Experimental results show that this is not true, (Pompeo, 1992; Schwarz and Bradshaw, 1992; Ölçmen and Simpson, 1995a; Driver and Johnston, 1990). Recent comparisons of the performance of such models with experimental data illustrate the following points: (1) eddy viscosity and existing mixing length models do not adequately reflect the physics of the flow (Ölçmen and Simpson, 1993, 1995a); (2) available secondorder models also make some physically weak assumptions (Hytopoulos and Simpson, 1993); (3) no strong general "law-ofthe-wall" mean velocity profile correlation exists (Ölçmen and Simpson, 1992). These points were also confirmed by Bettelini and Fanneløp (1993) with experimental data and algebraic models that were not employed by Ölçmen and Simpson (1993). Based on these conclusions more effort must be applied to modeling the physics of 3D turbulent boundary layers which must rely heavily on experimental results. Turbulence models should reflect the behavior observed in 3D experiments. It is known that the mean flow is the first to respond to a spanwise pressure gradient or surface stress. The turbulence structure, with its length and velocity scales, lags the mean flow behavior. The direct numerical simulation (DNS) performed by Sendstad and Moin (1992) of a low Reynolds number pressure driven flow presents a good overview of the typical turbulence structure that must be accounted for in a turbulent 3D boundary layer. Townsend's a1 parameter, the ratio of the turbulent shear stresses ( |τ/ρ| = (−uv ) + (−vw ) ) to twice the turbulent kinetic energy (TKE), maintains a constant value of approximately 0.15 over a large range of y/δ (δ, TBL thickness) for 2D flows. However, in 3D flows reductions in a1 from the 2D value are observed. This reduction is thought to result from changes in the turbulence structure in the presence of crossflow. New turbulence models should account for these experimental observations and apply to various real flow geometries. The momentum equations for the x and z directions, the continuity equation, and the transport equations for the −uv ,−vw ,