Citation
Inoue, Michio (2012) Largeeddy simulation of the flatplate turbulent boundary layer at high Reynolds numbers. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:05222012183141047
Abstract
The nearwall, subgridscale (SGS) model [Chung and Pullin, "Largeeddy simulation and wallmodeling of turbulent channel flow", J. Fluid Mech. 631, 281309 (2009)] is used to perform largeeddy simulations (LES) of the incompressible developing, smoothwall, flatplate turbulent boundary layer. In this model, the stretchedvortex, SGS closure is utilized in conjunction with a tailored, nearwall model designed to incorporate anisotropic vorticity scales in the presence of the wall. The composite SGSwall model is presently incorporated into a computer code suitable for the LES of developing flatplate boundary layers. This is then used to study several aspects of zero and adversepressure gradient turbulent boundary layers.
First, LES of the zeropressure gradient turbulent boundary layer are performed at Reynolds numbers $Re_\theta$ based on the freestream 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 atmosphericlayer measurements at $Re_\theta = \mathcal{O}(10^{6})$. At extremely large $Re_\theta$, the empirical ColesFernholz relation for skinfriction coefficient provides a reasonable representation of the LES predictions. While the present LES methodology cannot of itself probe the structure of the nearwall region, the present results show turbulence intensities that scale on the wallfriction 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 Reynoldsnumber limit for the smoothwall 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 higherprecision arithmetic.
Second, the time series velocity signals obtained from LES within the logarithmic region of the zeropressure gradient turbulent boundary layer are used in combination with an empirical, predictive innerouter wall model [Marusic et al., ``Predictive model for wallbounded turbulent flow'', Science 329, 193 (2010)] to calculate the statistics of the fluctuating streamwise velocity in the inner region of the zeropressure 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 innerlayer 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 surfacelayer, atmospheric experiments. The present results support a loglike increase in the nearwall peak of the streamwise turbulence intensities with $Re_\tau$ and also provide a means of extending LES results at large Reynolds numbers to the nearwall region of wallbounded 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.)) 

Subject Keywords:  Turbulent boundary layers, subgrid scale modeling 
Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Aeronautics 
Minor Option:  Applied And Computational Mathematics 
Awards:  William F. Ballhaus Prize, 2012 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  27 April 2012 
Record Number:  CaltechTHESIS:05222012183141047 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:05222012183141047 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  7065 
Collection:  CaltechTHESIS 
Deposited By:  Michio Inoue 
Deposited On:  30 May 2012 19:03 
Last Modified:  17 Jan 2013 18:28 
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