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Truncation of scales by relaxation
No full textThis paper is about a relaxation model for large-eddy simulation of turbulent flow that truncates the too small scales of motion by making sure that they do not get energy from the larger eddies. To verify that a box filter is introduced and the relaxation parameter is determined in such a way that the production of small, box-fitting scales is counteracted by the modeled dissipation. This dissipation-production balance is worked out with the help of Poincar\'{e}'s inequality, which results in a relaxation model that depends on the invariants of the velocity gradient. This model is discretized and equipped with a Schumann filter. It is successfully tested for isotropic turbulence as well as for turbulent channel flow
Parameter-Free Symmetry-Preserving Regularization Modelling of Turbulent Natural Convection Flows
Full text linkNumerical Simulation of a Turbulent Flow in a Channel with Surface Mounted Cubes
Full text linkIn this paper we report on a fourth-order, spectro-consistent simulation of a complex turbulent flow. A spatial discretization of a convection-diffusion equation is termed spectro-consistent if the spectral properties of the convective and diffusive operators are preserved, i.e. convection ↔ skew-symmetric; diffusion ↔ symmetric positive definite. We consider a fully developed flow in a channel, where a matrix of cubes is placed at a wall of the channel. The Reynolds number (based on the channel width and the mean bulk velocity) is equal to Re = 13,000. The three-dimensional flow around the surface mounted cubes has served at a test case at the 6th ERCOFTAC/IAHR/COST workshop on refined flow modeling (Delft, June 1997). Here, mean velocity profiles as well as Reynolds stresses at various locations in the channel have been computed without using any turbulence models. The results agree well with the available experimental data.
Merging Filtering, Modeling and Discretization to Simulate Large Eddies in Burgers' Turbulence
No full textWe see large eddy simulation (LES) as a synthesis of filter, model and discretization. The merger of these three components is elaborated to simulate Burgers' turbulence. Too small scales of motion are filtered out by applying the conservation law to volumes of a (user-chosen) minimum size that fixes the grid. The flux through the faces of these volumes is to be approximated by an interpolation rule. Hence, there are two spatial filters at play: the volume average defines the first filter, the volume-to-face interpolation introduces the second filter. The large eddies are defined by the interpolation filter and a model is added to account for the aggregate effect of smaller scales. This model can be interpreted both physically and numerically. The difference between these interpretations disappears when filtering, modeling and discretization merge into a unified whole. As all scales are interconnected by nonlinear convection, the LES model must break this to separate the large eddies. The two filters divide the kinetic energy into three: a subgrid piece, the energy of the large eddies and that of the remaining supergrid scales (that are filtered out by interpolation). The latter scales are subordinate to the large eddies and the subgrid scales are cutoff by the grid. This simplifies modeling considerably. The model is determined such that the large eddies do not produce any other scales of motion. Its consistency is further improved by Richardson extrapolation. The discretization of time gives rise to a third, temporal, filter.The methodology is successfully tested on decaying Burgers' turbulence in 1D. It needs to be further developed in follow-up research to eventually use it for LES of 3D turbulent flows
Numerical simulation of a turbulent flow in a channel with surface mounted cubes
Full text linkIn this paper we report on a fourth-order, spectre-consistent simulation of a complex turbulent flow. A spatial discretization of a convection-diffusion equation is termed spectro-consistent if the spectral properties of the convective and diffusive operators are preserved, i.e. convection skew-symmetric; diffusion symmetric positive definite. We consider a fully developed Bow in a channel, where a matrix of cubes is placed at a wall of the channel. The Reynolds number (based on the channel width and the mean bulk velocity) is equal to Re = 13,000. The three-dimensional flow around the surface mounted cubes has served at a test case at the 6th ERCOFTAC/IAHR/COST workshop on refined flow modeling (Delft, June 1997). Here, mean velocity profiles as well as Reynolds stresses at various locations in the channel have been computed without using any turbulence models. The results agree well with the available experimental data.</p
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