Daniela Tordella, POLITECNICO DI TORINO

DNS and LES In the past years, DNS and LES become viable tools to treat transitioning and turbulent flows --- Improvements in numerical methods --- Improvements in computers – speed, memory, cost today is not unusual to have capabilities equivalent of Cray 1 in a small group Successful application to a number of problems Tremendous potential in the future for: Understanding transition and turbulence Prediction in applications

DNS Numerical calculation that solves for the time development of the detailed, unsteady structures in a transitioning or a turbulent flow field NOT a numerical solution of Reynolds- or Favre- averaged equations It is a numerical experiment analogous to a laboratory experiment statistical scatter researcher must think like an experimentalist and ask proper questions, etc.

Strengths of Approach Compared to laboratory experiments * know all the variables at each point in space and time can follow large-scale structures can in theory comoute any statistic of interest, e.g. pressure-velocity correlation can readily compare with theory * Easy to control parameters to respect experimental conditions Compared to theory * Circumvent the closure problem

Weaknesses of Approach Limited spatial and temporal resolution Limits Reynolds number (and other key paramenters) without resorting to modeling Considers physics depending mainly on the large-scale motions, difficult to treat Kolmogorov-scale processes Opinion – complementary to laboratory experiment, theory in any particular problem (whether fundamental or applied) use methods (laboratory, theory, etc.) best suited for the problem.

Full Turbulence Simulation FTS Calculation in which all of the dynamically significant lenghth and time scales are included L_e -- energy-containing scale (e.g., integral scale) L_ k -- Kolmogorov scale (viscous dissipation scale) L_k = ( ³/  )¼ L_e / L_ k = Re ¾ N -- number of grid poits in one direction ~ Re ¾ Ntot ~ N³ ~ ( Re ¾)³ Number of time steps increases with Re as well

Large Eddy Simulation LES Motivated by the desire to remove Reynolds number limitations Prior to numerical integration are spatially filtered to eliminate the scales of motion smaller than those resolvable on the computational mesh. The effect of the subgrid-scale (SGS) motion is modeled u = ū + u’ ū – grid-scale (computed) motions u’ – subgrid-scale (modeled) motions Several approaches – model using analogies with Reynolds- averaged models

LES compared to FTS Advantages: potential to treat very high Reynolds number flows; fast reaction, etc. possibility of use in applied problems Disadvantages: ad hoc models are necessary to close euqations introduces some uncertainty into validity of results

LES compared to Reynolds-averaging approach Advantages: Large-scale motions treated directly; Can follow large-scale structures Only small scales are modeled Less energy in modeled scale; more universality Expected to provide more realistic results Disadvantages: 3D, time-dependent, high resolution

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