Семинар механике, 20. јул 2011.

• 06. Јул, 2011
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Наредни састанак семинара механике одржаће се у среду, 20 јула, у 16h у сали 307Ф Математичког института САНУ.

Предавачи: Prof. Peter Bradshaw (Professor of Experimental Aerodynamics, Department of Aeronautics, Imperial College, London University, England) i dr Srba Jović (NASA, Kalifornija)

Наслов предавања: A REVIEW OF TURBULENT FLOW

Садржај:

The enormous range of length scales makes it impossible to solve the exact Navier-Stokes* *(N-S) equations directly ("Direct Numerical Simulation" or DNS) for high-Reynolds-number turbulent flows.

The most gentle simplification is to solve N-S for large scales and to approximate ("model") the small eddies (Large Eddy Simulation, LES). Near a solid surface, unfortunately, there are NO large eddies! The approximate small-eddy model has to be used for the full range of length scales. This is the big obstacle to using LES in "wall-bounded" flows.

Today's engineers use Reynolds-Averaged N-S (RANS) equations. Usually, the complete range of eddy sizes is represented by just one length scale (plus the viscous length scale needed near solid surfaces). Nearly all the terms in the equations are modeled, i.e. replaced by dimensionally-correct and physically plausible combinations of the length and velocity scales and their spatial gradients. Each modeled term contains an empirical parameter, usually a constant.

The most obvious way to produce a RANS model is to derive Reynolds-averaged transport equations for all the mean-velocity components and all the Reynolds stresses, and model the unknown terms. This has been done quite successfully, but stress-transport models have the reputation of suffering numerical problems. This reputation dates from 20-30 years ago at least.

The ratio of a Reynolds stress to the rate of strain in the plane of that stress defines a so-called "eddy viscosity". It is different for different stresses, and varies greatly in space within the flow domain. It is a physically-meaningful quantity only if the scales of the turbulence are closely related to the scales of the mean flow. Most current engineering prediction methods are based on a scalar eddy viscosity (same for all stresses, a.k.a. isotropic") defined as   ( **) The dimensionless empirical parameter is (almost) always chosen to reproduce the logarithmic "law of the wall".

The review will end with a discussion of the capabilities of today's prediction methods.