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Summary Turbulence Models - Foundations of Fluid Mechanics II - Lecture Notes, Summaries of Fluid Mechanics

This is the second course of a two-semester fluid mechanics sequence for graduate students in the thermal sciences. This course includes topics like fully turbulent flows, turbulent boundary layers and free shear flows, turbulence modeling, laminar boundary layers including axisymmetric and 3-D boundary layers. Key points in this lecture are: Summary Turbulence Models, Chart of Incompressible Flow, Algebraic Models, Algebraic Reynolds Stress Models, Boussinesq Eddy Viscosity Model, Viscosity Mod

Typology: Summaries

2012/2013

Uploaded on 10/03/2013

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Summary Chart of Incompressible Flow Turbulence Models
Introduction
Here is a chart showing some of the major characteristics of turbulence models.
The order is from least complex to most complex.
For simplicity, consider incompressible flow without buoyancy, but the flow is three-dimensional.
Direct numerical simulation is included for completeness, even though it is not a turbulence model.
Model Number of additional
transport equations Assumptions/Approximations
Algebraic models
(zero-equation models)
0
One-equation models
1
Two-equation models
2
Algebraic Reynolds
stress models (ASM)
2
Reynolds stress models
(RSM)
7
Large Eddy Simulation
(LES)
either 0 (algebraic
equations) or 1
(transport equation) for
the smallest scales
Direct Numerical
Simulation (DNS)
0
Mixing length
Boussinesq eddy viscosity model,
turbulent
2
32
ij i j ij e ij
uu K E
τρ ρδμ
=− ≈− +
Nonlinear extension of Boussinesq eddy
viscosity model,
turbulent
2
32
ij i j ij e ij
uu K E
τρ ρδμ
=− ≈− + +
additional higher order terms
Solve for ensemble-averaged quantities only (no
details about time-dependent turbulence quantities)
Model small-scale
turbulence only
Exact time-dependent
solution of large scales
Exact - model all scales of
turbulence (small to large)
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Summary Chart of Incompressible Flow Turbulence Models

Introduction

  • Here is a chart showing some of the major characteristics of turbulence models.
  • The order is from least complex to most complex.
  • For simplicity, consider incompressible flow without buoyancy, but the flow is three-dimensional.
  • Direct numerical simulation is included for completeness, even though it is not a turbulence model.

Model Number of additional transport equations

Assumptions/Approximations

Algebraic models (zero-equation models) 0

One-equation models 1

Two-equation models 2

Algebraic Reynolds stress models (ASM) 2

Reynolds stress models (RSM) 7

Large Eddy Simulation (LES)

either 0 (algebraic equations) or 1 (transport equation) for the smallest scales

Direct Numerical Simulation (DNS) 0

Mixing length

Boussinesq eddy viscosity model,

turbulent

2

τ ij = − ρ u ui j ≈ − 3 ρ K δ ij + 2 μ e Eij

Nonlinear extension of Boussinesq eddy viscosity model,

turbulent

2

τ ij = − ρ u ui j ≈ − 3 ρ K δ ij + 2 μ e Eij +

additional higher order terms

Solve for ensemble-averaged quantities only (no details about time-dependent turbulence quantities)

Model small-scale turbulence only

Exact time-dependent solution of large scales

Exact - model all scales of turbulence (small to large)

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