Effect of upstream conditions on the outer flow of turbulent boundary layers

摘要

It will he shown that the boundary layer develops differently depending on the upstream conditions (e.g., the wind-tunnel speed, size of tripping wire, or recent history). Also, it will be demonstrated that almost all of the Reynolds-number dependence observed in the outer velocity deficit profiles is caused primarily by changes in the upstream conditions and not to the local Reynolds number. The empirical velocity scale of Zagarola and Smits (Zagarola,M. V.,and Smits, A. J., "Mean-Flow Scaling of Turbulent Pipe Flow," Journal of Fluid Mechanics, Vol. 373, 1998, pp. 33-79) is derived here for boundary layers with and without pressure gradient using similarity principles. This scaling is successful in removing the effect of upstream conditions and the residual dependence on the local Reynolds number from the mean velocity deficit. Even more interesting, it produces only three profiles in turbulent boundary layers, regardless of the strength of the pressure gradient: one for adverse pressure gradient, one for favorable pressure gradient, and one for zero pressure gradient. These results are consistent with results of Castillo and George (Castillo, L., and George, W. K., "Boundary Layers with Pressure Gradient: Similarity of the Velocity Deficit Region," AlAA Paper 2000-0913, Jan. 2000) obtained by means of similarity analysis of the Reynolds-averaged Navier-Stokes equations for equilibrium flows. References: 25