02-14
Derivation and Analysis of Near Wall Models for Channel and Recirculating Flows
by Volker John; William J. Layton; Niyazi Sahin
Preprint series: 02-14, Preprints
- MSC:
- 76D10 Boundary-layer theory
Abstract: The problem of predicting features of turbulent flows occurs in many applications such as geophysical flows, turbulent mixing, pollution dispersal and even in the design of artificial hearts. One promising approach is large eddy simulation (LES), which seeks to predict local spacial averages $\ov{\bu}$ of the fluid\'s velocity $\bu$. There are several core difficulties in LES. Closure models are very important in applications in which the equations must be integrated over a long time interval. In engineering applications, however, often the equations are solved over moderate time intervals and the core difficulty is associated with modeling near wall turbulence in complex geometries. Thus, one important problem in LES is to find appropriate boundary conditions for the flow averages which depend on the behavior of the unknown flow near the wall. Inspired by early works of Navier and Maxwell, we develop such boundary conditions of the form $$ \ov{\bu} \cdot \bn = 0 \mbox{ and } \beta(\delta,Re,|\ov{\bu} \cdot \btau|) \ov{\bu}\cdot \btau +2Re^{-1}\bn \cdot \D(\ov\bu) \cdot \btau = 0 $$ on the wall. We derive effective friction coefficients $\beta$ appropriate for both channel flows and recirculating flows and study their asymptotic behavior as the averaging radius $\delta\to 0$ and as the Reynolds number $Re \to \infty$. In the first limit, no--slip conditions are recovered. In the second, free--slip conditions are recovered.
Keywords: large eddy simulation, near wall models, turbulence, boundary layer
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