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Motivated by the need for accurate determination of wall shear stress from profile measurements in turbulent boundary layer flows, the total shear stress balance is analysed and reformulated using several well-established semi-empirical relations. The analysis highlights the significant effect that small pressure gradients can have on parameters deduced from data even in nominally zero pressure gradient boundary layers. Using the comprehensive shear stress balance together with the log-law equation, it is shown that friction velocity, roughness length and zero-plane displacement can be determined with only velocity and turbulent shear stress profile measurements at a single streamwise location for nominally zero pressure gradient turbulent boundary layers. Application of the proposed analysis to turbulent smooth- and rough-wall experimental data shows that the friction velocity is determined with accuracy comparable to force balances (approximately 1 %–4 %). Additionally, application to boundary layer data from previous studies provides clear evidence that the often cited discrepancy between directly measured friction velocities (e.g. using force balances) and those derived from traditional total shear stress methods is likely due to the small favourable pressure gradient imposed by a fixed cross-section facility. The proposed comprehensive shear stress analysis can account for these small pressure gradients and allows more accurate boundary layer wall shear stress or friction velocity determination using commonly available mean velocity and shear stress profile data from a single streamwise location.
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DISPLACEMENT-THICKNESS BASED RECYCLING INFLOW GENERATION METHOD FOR SPATIALLY DEVELOPING TURBULENT BOUNDARY LAYER SIMULATIONS
A displacement thickness based inflow generation method, for simulation of a developing turbulent boundary layer, is proposed. Following existing rescaling/recycling methods, velocities from a plane sufficiently downstream of the inlet are recycled back and used as the inflow after re-scaling based on inner and outer length-scales. The inner length-scale is based on the viscous length-scale (for smooth walls) or surface specific scales (for rough walls). Prior recycling methods for smooth and rough boundary layers typically use d99 as the outer length-scale. Since d99 is a threshold based quantity, it is strongly dependent on the mean velocity profile and can have large undesired fluctuations, particularly if the profile shape is atypical or unsteady. Here, we propose the use of profile integrated quantities such as the displacement thickness (d1) to obtain a ‘surrogate’ for d99 in order to mitigate the adverse effects of having to determine the outer scale from a point-wise measurement of the mean velocity profile. The outer length- scale at the downstream plane is determined based on the local displacement thickness and higher-order moments of the integrated velocity profile. The inlet displacement thick- ness is fixed at a desired value and the outer length-scale at the inlet is determined through an iterative method. The use of high-order moments of the velocity profile is tested a- priori on DNS data for a developing boundary layer. Also, an initial application to LES over a surface with roughness elements is presented.
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- Award ID(s):
- 1738918
- PAR ID:
- 10174414
- Date Published:
- Journal Name:
- 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11)
- Volume:
- 11
- Issue:
- 2019
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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