Minimum-Dissipation Model for Large Eddy Simulation using OpenFOAM

  • Sun, Jing (University of Groningen)
  • Verstappen, Roel (University of Groningen)

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Large eddy simulation (LES) represents the large turbulent motions directly and models the effect of the small-scale motions with a sub-grid model. The minimum-dissipation model \cite{Rozema} is based on the invariants of the rate of strain tensor. By confining the sub-grid kinetic energy with Poincaré's inequality, the minimum amount of eddy viscosity damping needed to counteract the nonlinear production is given by $\nu_e = C_\Delta \overline{|r(v)|} / \overline {q(v)}$, where $q$ and $r$ are the second and third invariant of the rate of strain tensor (the first invariant is $\nabla\cdot v = 0$); $C_\Delta$ depends on the filter length. Note that the Smagorinsky model only depends on $q(v)$, i.e., not on r(v). The resulting eddy viscosity vanishes in any laminar (part of the) flow since $r=0$ in laminar flow. At a no-slip wall $r=0$ as well; hence $\nu_e=0$ at the wall. To assess the applicability of the minimum-dissipation model to bluff body flow and for computing separated flows, simulations of channel flow up to $Re_b = 42971$, flow past a circular cylinder at $Re=3900$ and flow over periodic hills at $Re=10595$ have been investigated. Numerical simulations were performed in OpenFOAM which is based on finite volume methods for discretising partial differential equations. We used second order accurate discretisation methods on structured meshes. The results are compared to the DNS and experimental data. The results of channel flow mainly demonstrate the mesh convergence and the accuracy of predicting mean and invariance of turbulence up to $Re_b = 42971$ without a wall damping function. The results for the flow over a cylinder show that mean velocity, drag coefficient, and lift coefficient are in good agreement with the experimental data. The various comparisons carried out for flows over periodic hills demonstrate the need to use central difference schemes in OpenFOAM in combination with the minimum dissipation model. The rotational channel flow will be simulated in order to investigate the rotating flows.