CADFamily.com: Introduction to CFX-Turbulence

What is Turbulence?

Unsteady, irregular (non-periodic) motion in which transported quantities (mass, momentum, scalar species) fluctuate in time and space

-Identifiable swirling patterns characterize turbulent eddies

-Enhanced mixing (matter, momentum, energy, etc.) results

Fluid properties and velocity exhibit random variations

-Statistical averaging results in accountable, turbulence related transport mechanisms

-This characteristic allows for turbulence modeling

Contains a wide range of turbulent eddy sizes (scales spectrum)

-The size/velocity of large eddies is on the order of the mean flow

Large eddies derive energy from the mean flow

-Energy is transferred from larger eddies to smaller eddies

In the smallest eddies, turbulent energy is converted to internal energy by viscous dissipation

Is the Flow Turbulent?

Flows can be characterized by the Reynolds Number, Re

Observation by O. Reynolds

Turbulent Flow Structures

Governing Equations

Conservation Equations

Note that there is no turbulence equation in the governing Navier-Stokes equations!

Overview of Computational Approaches

Direct Numerical Simulation (DNS)

-Theoretically, all turbulent (and laminar / transition) flows can be simulated by numerically solving the full Navier-Stokes equations

-Resolves the whole spectrum of scales. No modeling is required

-But the cost is too prohibitive! Not practical for industrial flows

Large Eddy Simulation (LES) type models

-Solves the spatially averaged N-S equations

-Large eddies are directly resolved, but eddies smaller than the mesh are modeled

-Less expensive than DNS, but the amount of computational resources and efforts are still too large for most practical applications

Reynolds-Averaged Navier-Stokes (RANS) models

-Solve time-averaged Navier-Stokes equations

-All turbulent length scales are modeled in RANS

Various different models are available

-This is the most widely used approach for calculating industrial flows

There is not yet a single, practical turbulence model that can reliably predict all turbulent flows with sufficient accuracy

RANS Modeling – Time Averaging

Ensemble (time) averaging may be used to extract the mean flow properties from the instantaneous ones

-The instantaneous velocity, ui, is split into average and fluctuating components

The Reynolds-averaged momentum equations are as follows

-The Reynolds stresses are additional unknowns introduced by the averaging procedure, hence they must be modeled (related to the averaged flow quantities) in order to close the system of governing equations

RANS Modeling – The Closure Problem

Closure problem: Relate the unknown Reynolds Stresses to the known mean flow variables through new equations

-The new equations are the turbulence model

Equations can be:

-Algebraic

-Transport equations

All turbulence models contain empiricism

-Equations cannot be derived from fundamental principles

-Some calibrating to observed solutions and “intelligent guessing” is contained in the models

The RANS models can be closed in one of the following ways

(1) Eddy Viscosity Models (via the Boussinesq hypothesis)

Boussinesq hypothesis – Reynolds stresses are modeled using an eddy (or turbulent) viscosity, μT. The hypothesis is reasonable for simple turbulent shear flows: boundary layers, round jets, mixing layers, channel flows, etc.

(2) Reynolds-Stress Models (via transport equations for Reynolds stresses)

Modeling is still required for many terms in the transport equations

RSM is more advantageous in complex 3D turbulent flows with large streamline curvature and swirl, but the model is more complex, computationally intensive, more difficult to converge than eddy viscosity models

Available Turbulence Models

A large number of turbulence models are available in CFX, some have very specific applications while others can be applied to a wider class of flows with a reasonable degree of confidence