On Dynamic Modeling For Multiscale Turbulence Problems

S. Chester
PhD Thesis, The Johns Hopkins University
July 2006
Baltimore MD

ABSTRACT: Simulating multiscale flows is a challenge because of the vast computational resources required to follow the large number of degrees of freedom in such flows. The dynamic procedure (Germano et al., 1991) is a powerful modeling tool in the simulation of inherently multiscale turbulent flows, and is the basis for the two main parts of this work. In the first part, high-Reynolds-number flow over tree-like fractals is considered, with emphasis on the drag forces produced. Using large-eddy simulation (LES) of flow over prefractals with multiple branch generations, the dependence of the tree drag on the inner cutoff scale of the fractal is studied. It is found that the convergence of the drag coefficient towards a value that is independent of inner cutoff-scale is slow enough that directly resolving the geometry of all the relevant small-scale branches is highly impractical. To address this fundamental difficulty, a new numerical modeling technique called Renormalized Numerical Simulation (RNS) is introduced. RNS models the drag of the unresolved branches using drag coefficients measured from both resolved branches and unresolved branches as modeled in previous iterations of the procedure. The RNS technique and its convergence properties are tested by means of a series of simulations using different levels of resolution. Then, RNS is used to investigate the influence of the tree fractal dimension on the tree drag coefficient. Results illustrate that RNS enables numerical modeling of physical processes associated with fractal geometries using affordable computational resolution. The second part of this work is an analysis of the errors incurred by replacing the test-filtering operator by its truncated Taylor series expansion, in an effort to simplify implementation of the dynamic procedure in simulations of complex-geometry flows. Errors are quantified using a priori and a posteriori tests of forced isotropic turbulence. Results indicate that truncation of the Taylor series at second order provides a reasonable approximation to the true dynamic coefficient, but inclusion of higher-order terms does not necessarily improve the results due to limitations in accurately evaluating high-orderderivatives in LES.

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