Introduction to Turbulence Modeling
-Characterization of Turbulent Flows
-From Navier-Stokes Equations to Reynolds-Averaged Navier-Stokes (RANS) Models
-Reynolds Stress Tensor and the Closure Problem
-Turbulence Kinetic Energy (k) Equation
-Eddy Viscosity Models (EVM)
-Reynolds Stress Model
-Near-wall Treatments Options and Mesh Requirement
-Inlet Boundary Conditions
-Summary: Turbulence Modeling Guidelines
-Appendix
Characteristics of Turbulence
-Inherently unsteady, three dimensional and aperiodic swirling motions (fluctuations) resulting in enhancement of mixing, heat transfer and shear.
-Instantaneous fluctuations are random (unpredictable) both in space and in time. But statistical averaging of turbulence fluctuations results in accountable transport mechanisms
-Wide range of length scales (vortices or eddies) exist in all turbulent flows (from very small to very large).
-Very sensitive to (or dependent on) initial conditions.
Turbulent Flow Structures
Is the Flow Turbulent?
Reynolds Number Effects
Backward Facing Step
Plume in Cross Flow
On the left is an instantaneous snap shot of a plume, on the right is a time-lapse picture which smoothes out the detailed structures (vortices) and shows only the averaged, diffused state of the same flow
RANS Equations and the Closure Problem
The time-averaging is defined as
The instantaneous field is defined as the sum of the mean and the fluctuating component, such as
By averaging the Navier-Stokes equations, we obtain the Reynolds averaged Navier-Stokes (RANS) equations:
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