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# Large-eddy simulation of the flat-plate turbulent boundary layer at high Reynolds numbers

## Citation

Inoue, Michio (2012) Large-eddy simulation of the flat-plate turbulent boundary layer at high Reynolds numbers. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:05222012-183141047

## Abstract

The near-wall, subgrid-scale (SGS) model [Chung and Pullin, "Large-eddy simulation and wall-modeling of turbulent channel flow", J. Fluid Mech. 631, 281--309 (2009)] is used to perform large-eddy simulations (LES) of the incompressible developing, smooth-wall, flat-plate turbulent boundary layer. In this model, the stretched-vortex, SGS closure is utilized in conjunction with a tailored, near-wall model designed to incorporate anisotropic vorticity scales in the presence of the wall. The composite SGS-wall model is presently incorporated into a computer code suitable for the LES of developing flat-plate boundary layers. This is then used to study several aspects of zero- and adverse-pressure gradient turbulent boundary layers.

First, LES of the zero-pressure gradient turbulent boundary layer are performed at Reynolds numbers $Re_\theta$ based on the free-stream velocity and the momentum thickness in the range $Re_\theta = 10^3$--$10^{12}$. Results include the inverse skin friction coefficient, $\sqrt{2/C_f}$, velocity profiles, the shape factor $H$, the K\'arm\'an constant'', and the Coles wake factor as functions of $Re_\theta$. Comparisons with some direct numerical simulation (DNS) and experiment are made, including turbulent intensity data from atmospheric-layer measurements at $Re_\theta = \mathcal{O}(10^{6})$. At extremely large $Re_\theta$, the empirical Coles-Fernholz relation for skin-friction coefficient provides a reasonable representation of the LES predictions. While the present LES methodology cannot of itself probe the structure of the near-wall region, the present results show turbulence intensities that scale on the wall-friction velocity and on the Clauser length scale over almost all of the outer boundary layer. It is argued that the LES is suggestive of the asymptotic, infinite Reynolds-number limit for the smooth-wall turbulent boundary layer and different ways in which this limit can be approached are discussed. The maximum $Re_\theta$ of the present simulations appears to be limited by machine precision and it is speculated, but not demonstrated, that even larger $Re_\theta$ could be achieved with quad- or higher-precision arithmetic.

Second, the time series velocity signals obtained from LES within the logarithmic region of the zero-pressure gradient turbulent boundary layer are used in combination with an empirical, predictive inner--outer wall model [Marusic et al., Predictive model for wall-bounded turbulent flow'', Science 329, 193 (2010)] to calculate the statistics of the fluctuating streamwise velocity in the inner region of the zero-pressure gradient turbulent boundary layer. Results, including spectra and moments up to fourth order, are compared with equivalent predictions using experimental time series, as well as with direct experimental measurements at Reynolds numbers $Re_\tau$ based on the friction velocity and the boundary layer thickness, $Re_\tau =7,300$, $13,600$ and $19,000$. LES combined with the wall model are then used to extend the inner-layer predictions to Reynolds numbers $Re_\tau =62,000$, $100,000$ and $200,000$ that lie within a gap in $\log(Re_\tau)$ space between laboratory measurements and surface-layer, atmospheric experiments. The present results support a log-like increase in the near-wall peak of the streamwise turbulence intensities with $Re_\tau$ and also provide a means of extending LES results at large Reynolds numbers to the near-wall region of wall-bounded turbulent flows.

Finally, we apply the wall model to LES of a turbulent boundary layer subject to an adverse pressure gradient. Computed statistics are found to be consistent with recent experiments and some Reynolds number similarity is observed over a range of two orders of magnitude.

Item Type: Thesis (Dissertation (Ph.D.)) Turbulent boundary layers, subgrid scale modeling California Institute of Technology Engineering and Applied Science Aeronautics Applied And Computational Mathematics William F. Ballhaus Prize, 2012 Public (worldwide access) Pullin, Dale Ian McKeon, Beverley J. (chair)Colonius, Timothy E.Leonard, AnthonyPullin, Dale Ian 27 April 2012 CaltechTHESIS:05222012-183141047 http://resolver.caltech.edu/CaltechTHESIS:05222012-183141047 No commercial reproduction, distribution, display or performance rights in this work are provided. 7065 CaltechTHESIS Michio Inoue 30 May 2012 19:03 17 Jan 2013 18:28

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