12-les - Lecture 12 Large Eddy Simulation Applied...

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Lecture 12 - Large Eddy Simulation Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org © André Bakker (2002-2006) © Fluent Inc. (2002)
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Modeling turbulence Turbulence is a 3D transient phenomenon. Fluctuations cover a wide range of time and length scales. Turbulence models range from approximate to highly rigorous: Steady-state isotropic models. Transient 3D models of entire spectrum. Models are incorporated into the Navier-Stokes equations using a variety of methods.
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The turbulence spectrum Many scales of turbulent eddies exist: Large eddies contain most of the turbulent kinetic energy. Scale sizes are on the order of the flow passages. Energy cascades from large to small eddies. Small eddies dissipate the energy they receive from larger eddies in the spectrum. Difficulty in turbulence modeling is trying to accurately capture the contributions of all scales in the spectrum.
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Direct numerical simulation (DNS) Navier-Stokes equations are solved on a fine grid using a small time-step. Goal is to capture all eddy sizes, including the smallest turbulence scales. Result is accurate, 3D, transient behavior. Great for simple flows, but computationally intensive. The overall cost, including time step, of the computational effort is proportional to Re L 3 . Not suited to industrial applications with CPU resources available today.
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The number of grid points per dimension needed to resolve the small scales is: The number of grid points needed for a 3D DNS simulation is: The overall cost, including time step, of the computational effort is proportional to Re L 3. 3/ 4 1 L ~ Re , Re D L k N ρ μ = l 9/ 4 3 ~ Re D L N The cost of DNS
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-5/3 Large eddy simulation (LES) Small eddies are removed, and modeled using a subgrid-scale (SGS) model. Large eddies are retained, and solved for directly using a transient calculation. Requires 3-D transient modeling.
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