Abstract
The time-averaged velocity profile of a turbulent boundary layer can be predicted by combining its different trends in the inner and outer regions in a single law of the wake. A new non-dimensional coordinate system that projects the time-averaged velocity profiles of the inner and the outer regions on the same non-dimensional plane is introduced, leading to a unified treatment for the mixing region. In this coordinate system, various laws of the wake are shown to be the same but a constant. The non-dimensionalization is tested on a specific law of the wake, in which the closure coefficients are regressed from wind tunnel measurements and direct numerical simulations of turbulent boundary layers under zero-pressure gradient, over a good range of boundary layer thickness based Reynolds numbers. This data fit produced profiles within 2% of the reference values. This is of practical use to numerical modellers for generating boundary layer inflow profiles.
Highlights
The zero-pressure gradient boundary layer is an established test case for improved near-wall velocity profile formulations for turbulent wall-bounded flows. Buschmann and Gad-el-Hak (2007) review the use of scaling laws for turbulent boundary layers, demonstrating that a universally applicable functional is lacking, with neither power law nor logarithmic behaviours being ruled out
Its outer region is described by a defect velocity approach
Using the method by Krogstad et al (1992), a similar linear regression was performed for the fitted von Kármán constant k versus the free-stream Reynolds number, indicating a positive correlation between k and the freestream Reynolds number
Summary
The zero-pressure gradient boundary layer is an established test case for improved near-wall velocity profile formulations for turbulent wall-bounded flows. Buschmann and Gad-el-Hak (2007) review the use of scaling laws for turbulent boundary layers, demonstrating that a universally applicable functional is lacking, with neither power law nor logarithmic behaviours being ruled out. Krogstad et al (1992) determined k and B empirically by regressing measured velocity profiles Following their approach, this work presents regressed values of k, B, and of the wake parameter Π over the boundary layer thickness-based Reynolds number range of 145 ≤ R ≤ 13030, where R = δuτ/ν. This work presents regressed values of k, B, and of the wake parameter Π over the boundary layer thickness-based Reynolds number range of 145 ≤ R ≤ 13030, where R = δuτ/ν These give velocity profiles by the law of the wake of Finley et al (1966) within ±2% of the measurements.
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