CFX-Intro 14.5 L10 Turbulence

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© 2012 ANSYS, Inc. December 17, 2012 1 Release 14.5

14.5 Release

Lecture 10Turbulence

Introduction to ANSYS CFX




Introduction

• Lecture Theme:The majority of engineering flows are turbulent.Successfully simulating such flows requires understanding a few basicconcepts of turbulence theory and modeling.This allows one to make the best choice from the available turbulence

models and near-wall options for any given problem.• Learning Aims – you will learn:

Basic turbulent flow and turbulence modeling theoryTurbulence models and near wall optionsHow to choose an appropriate turbulence model for a given problem

How to specify turbulence boundary conditions at inlets• Learning Objectives:

You will understand the challenges inherent in turbulent flowsimulation and be able to identify the most suitable model and near-wall treatment for a given problem.

Introduction Theory Models Near-Wall Treatments Inlet BCs Summary




Observation by O. Reynolds

• Flows can be classified as either :Laminar:• Low Reynolds number

Transition:• Increasing Reynolds number

Turbulent:• Higher Reynolds number





Observation by O. Reynolds

• The Reynolds number is the criterion used to determinewhether the flow is laminar or turbulent

• The Reynolds number is based on the characteristic length scale L, theflow velocity u and the fluid properties r and m

• Transition to Turbulence varies depending on the type of flow:• External flow

along a surface : Re X > 5·10 5 around on obstacle : Re L > 2·10 4

• Internal flow : Re D > 2.300

m

r LuRe





Turbulent Flow Structures

• A Turbulent Flow contains a wide range of turbulent eddysizes Characteristics

Unsteady, tridimensional, irregular, stochasticTransported quantities fluctuate in time and space

Unpredictability in detailLarge-scale coherent structures are different in each flow, whereassmall eddies are more universal

Smallstructures

Largestructures





Turbulent Flow Structures

• Energy is transferred from larger eddies to smaller eddies(Kolmogorov Cascade)

Large scale contains most of the energyIn the smallest eddies, turbulent energy is converted to internal energyby viscous dissipation

Energy Cascade Richardson(1922), Kolmogorov (1941)



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Turbulent Flow Structures (1)

• Characteristics of the Turbulent Structures:Length Scale:• Describing size of large energy-containing eddies in a turbulent flow• In many cases defined by a relation

Turbulent kinetic energy:

Velocity Scale:

Time Scale:

smk /

ml

sk

l

²/²2

1 222 smwvuk


2/3

~ k

l



Turbulent Flow Structures (2)

• Characteristics of the Turbulent Structures:Turbulent dissipation:

Turbulent frequency:

Turbulent Reynolds number:

Turbulent Intensity:

³/²/~ 2/3 sml k

²~Re

k l k t

3

21' k

uu

u I


sk

/11



Overview of Computational Approaches

• Different approaches to simulateturbulenceDNS: direct numerical simulation• Full resolution• No modeling required

Too expensive for practical flows

LES: large eddy simulation• Large eddies directly resolved,

smaller ones modeled Less expensive than DNS, but veryoften still too expensive forpractical applications

RANS: Reynolds averaged Navier-Stokes simulation• Solution of time-averaged

equations Most widely used approach forindustrial flows




RANS Modeling : Justification

• For most engineering applications it is unnecessary to resolvethe details of the turbulent fluctuations

• We only need to know how turbulence affects the mean flow• A useful turbulence model has to be:

– applicable in wide ranges, – accurate, – simple, – and economical to run.

URANSLES




RANS Modeling : Averaging

• Fluid properties and velocityexhibit random variations

Statistical averaging results inaccountable, turbulencerelated transport mechanisms.

• Ensemble (time) averagingmay be used to extract themean flow properties fromthe instantaneous ones

The instantaneous velocity, u i ,is split into average andfluctuating components

N

n

n

i N

i t u N

t u1

,1lim, xx

Example: Fully-Developed Turbulent PipeFlowVelocity Profile

t ui ,

x

t ui ,

x

t ui ,

x

t ut ut uiii ,,,

xxx





RANS Modeling : Averaging

• Applying the averaging procedure to the Navier-Stokesmomentum we get:

The Reynolds stresses R ij are additional unknowns introduced by theaveraging procedure,they must be modeled in order to close the system of governingequations,Rij represents a symmetric tensor, so there are 6 additional unknowns.

jiij uu R r

j

ij

j

i

jik

ik

i

x

R

xu

x x p

xu

ut u

m

r





RANS Modeling : The Closure Problem

• The components of the Reynolds-stress tensor, R ij , have tobe determined

• the RANS models can be closed in two ways:Reynolds-Stress Models (RSM)• The components of R ij are directly solved via transport equations• Advantageous in complex 3D flows with streamline curvature / swirl• Models are complex, computational intensiveEddy Viscosity Models• The components of Rij are modeled using an eddy (turbulent)

viscosity µ t• Reasonable approach for simple turbulent shear flows: boundary

layers, round jets, mixing layers, channel flows, etc.





RANS Modeling : The Closure Problem

• The key concept of the Eddy Viscosity models is theBoussinesq hypothesis

• This hypothesis assumes that the Reynolds Stresses can beexpressed analogously to the normal stresses, but applying

a turbulent viscosity mt

• In turbulent flows usually mt >> m• The effective viscosity in the flow is given by meff m t m

ijijk

k

i

j

j

i jiij k

xu

x

u

xu

uu R r m m r 3

2

3

2tt





Turbulence Models in CFX

• A large number of turbulence models are available, some forvery specific applications, others can be applied to a widerclass of flows with a reasonable degree of confidence

RANSEddy-viscosity Models

RANSReynolds-Stress Models

Eddy Simulation Models(Scale Resolving Models SRS)

Zero Equation model SSG model Large Eddy Simulation (LES)

Standard k- ԑ, k-ω model LRR model Detached Eddy Simulation (DES)

SST model BSL EARSM model Scale Adaptive Simulation SST (SAS)





k- Models

• Good compromise between numerical effort andcomputational accuracy

Two transport equations for the solution of TKI and dissipationTurbulent viscosity is modeled as product of turbulent velocity andturbulent length scale

• Good predictions for many flows of engineering interest• k- models not suitable for modeling

flows with boundary layer separation,flows with sudden changes in the mean strain rate,flows in rotating fluids,flows over curved surfaces.





k- Models

• Good compromise between numerical effort andcomputational accuracy

Two transport equations for the solution of TKI and frequencyTurbulent viscosity is modeled as product of turbulent velocity andturbulent length scale

• Good predictions for many flows of engineering interest• k- models better than k- models for boundary layer flows

separation,transition,low Re effects,impingement.





Shear Stress Transport (SST) Model (1)• SST model was developed to overcome shortcomings in the k-ԑ

and k-ω models• The relative performances of the k-ԑ and k-ω models depend on

the region of flow:k-ω model performs much better for boundary layer flowsoriginal k- ω model is sensitive to the free-stream conditions but k- ԑ is not

•

To take advantage of the strengths of each we blend between thetwo models according to the distance from the wall

This blending gives us the Baseline (BSL) k- model, which isdeveloped further to produce the SST model

k-

k-Wall





j

t

j j jk

j

ji

x x x xk

F P k x

U

t

m

m

r r

r r

)~(2

)1(~~)()(

12

SST Model: Blending k- and k- Models (2)

• Two transport equationsturbulent kinetic energy

turbulent frequency

• Blending function F1 switchesfrom k- ԑ to k-w

1 near the wall

0 towards edge of boundary layer

j

t

jk

j

j

xk

xk P

x

k U

t k

)~()()(

m

m r r r





SST Model: Turbulent shear stress (3)

• k-ω modeldoes not predict properly the onset and degree of separation fromsmooth surfacesmain reason is that it does not account for the transport of turbulentshear stress and so over-predicts eddy viscosity

• SST modelaccounts for this transport by means of a limiter in the formulation ofeddy viscosity.

• Where shear stress, S , dominatesBSL k-ω + limiter = SST


y

uuu t ji

12

1

,max aSF

k at

k auu ji 1

and




SST Model: Validation Example (4)

SST result and experiment

Standard k- fails to predict separation

Experiment Gersten et al.


The SST model predicts well the onset and the amount of flowseparation




Turbulence Near the Wall






• Walls are main source of vorticityand turbulence

• The velocity profile near the wall isimportant:

Pressure dropSeparationShear effectsRecirculationHeat transfer

• Accurate near-wall modeling isimportant for most engineeringapplications

Turbulence models are generally suitedto model the flow outside theboundary layer but need special treatments near the walls The above graph shows non-dimensional velocity

versus non-dimensional distance from the wall.






• The graph shows• non-dimensional velocity

•

versus non-dimensionaldistance from the wall

• Log scale axes are used• Near to a wall, the velocity

changes rapidly

r /Wall

uu

r /Wall y

y

LinearLogarithmic






• Since near-wall conditions are often predictable, wall functions can beused to determine the near-wall profiles rather than using a fine meshto actually resolve the profile

• In ANSYS CFX the variable Yplus reports the location of the first vertexadjacent to the wall

Boundary layer





Location of The First Vertex

• Logarithmic-based wall functions each wall-adjacent vertex should be located within the log-law layer:y+ ≈ 20 -200

• Resolved wall treatment each wall-adjacent vertex should be within the viscous sublayer :

y+

≈ 1 with a minimum of 10 nodes in boundary layerPossible only with the automatic wall treatment available with -based turbulence models, e.g. SST, which switches between wallfunction and low-Re wall treatment as the mesh is refined

• Scalable wall functions (k- models)the mesh is shifted virtually to y + = 11.067, the point of transition fromlinear to logarithmic behaviorFurther refinement of the mesh near the wall has no effect





Limitations of Wall Function

• In some situations, such as boundary layer separation,logarithmic-based wall functions do not correctly predict theboundary layer profile

logarithmic-based wall functions should not be usedresolving the boundary layer can provide accurate results





Wall Function and Heat Transfer

• Heat flux at the wall, q w , is given by:

• T w is the wall temperature and T f is the near-walltemperature in the fluid

• The equations for u * and the non-dimensionaltemperature, T + , depend on the type of wall function

For scalable wall functions T + follows a log-law relationship

For automatic wall functions the correlation between T + and walldistance blends between the viscous sublayer and the log law


f wc f w p

w T T hT T T

ucq

*

r




Inlet Turbulence Conditions

• When turbulent flow enters a domain, turbulent boundaryconditions must be specified, depending on whichturbulence model has been selected

• Several options exist for the specification of turbulencequantities

Explicitly input k and either ε or ω Turbulence intensity and length scaleTurbulence intensity and turbulent viscosity ratio

Turbulent Intensity:

Turbulent viscosity ratio:3

21 k

uu

u I

m m /t






• If you have absolutely no idea of the turbulence levels in yoursimulation, you could use following values of turbulence intensities andlength scales:

Usual turbulence intensities range from 1% to 5%The default turbulence intensity value of 0.037 (that is, 3.7%) is

sufficient for normal turbulence through a circular inlet, and is a goodestimate in the absence of experimental data

Some more details for the specification of the inlet turbulenceconditions can be found in the appendix

Low Medium High

I 1% 5% 10%

μ/μ t 1 10 100





Summary - Turbulence ModelingGuidelines

• Calculate Re to determine whether the flow is turbulent• Estimate y + before generating the mesh• The SST model is good choice for most flows• Use the RSM or the SST model with Curvature Correction

for highly-swirling flows• Consider using SRS models , such as LES, DES and SAS, if

you need to resolve the turbulence structure, e.g. foracoustics/vibration applications

• Use the default model parameters unless you areconfident that you have better values!





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Appendices




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Appendix: Pipe Expansion withHeat Transfer




Example: Pipe Expansion with Heat Transfer

• Reynolds Number Re D= 40750• Fully Developed Turbulent Flow at Inlet• Experiments by Baughn et al. (1984)

q=const

Outlet

axis

H

H 40 x H

Inlet

q=0.

d

D





Example: Pipe Expansion with HeatTransfer

• Plot shows dimensionlessdistance versus NusseltNumber

• Best agreement is with SST

and k- models• Better in capturing flow

recirculation zonesaccurately





Pipe Expansion With Heat Transfer

• Heat transfer predictionsWall function approach (k- Model)

Standard Scalable




Pipe Expansion With Heat Transfer

• Heat transfer predictionsAutomatic Wall treatment (SST-Model)

Low Re Automatic




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Appendix: Summary of RANSModels




Appendix: RANS Turbulence Model

Model Description

Standard k –ε The baseline two-transport-equation model solving for k and ε. This is the default k –ε model. Coefficientsare empirically derived; valid for fully turbulent flows only. Options to account for viscous heating,buoyancy, and compressibility are shared with other k –ε models.

RNG k –ε A variant of the standard k –ε model. Equations and coefficients are analytically derived. Significant changesin the ε equation improves the ability to model highly strained flows. Additional options aid in predictingswirling and low Reynolds number flows.

Standard k –ω A two-transport-equation model solving for k and ω, the specific dissipation rate ( ε / k) based on Wilcox(1998). This is the default k –ω model. Demonstrates superior performance for wall-bounded and lowReynolds number flows. Shows potential for predicting transition. Options account for transitional, freeshear, and compressible flows.

SST k –ω A variant of the standard k –ω model. Combines the original Wilcox model for use near walls and thestandard k –ε model away from walls using a blending function. Also limits turbulent viscosity to guaranteethat τT ~ k. The transition and shearing options are borrowed from standard k –ω . No option to includecompressibility.

RSM Reynolds stresses are solved directly using transport equations, avoiding isotropic viscosity assumption ofother models. Use for highly swirling flows. Quadratic pressure-strain option improves performance formany basic shear flows.




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Appendix: Prediction of FirstCell Height




Example in predicting near-wall cell size

•

During the pre-processing stage, you will need to know a suitable size forthe first layer of grid cells (inflation layer) so that y+ is in the desired range.• The actual flow-field will not be known until you have computed the

solution (and indeed it is sometimes unavoidable to have to go back andremesh your model on account of the computed y+ values).

• To reduce the risk of needing to remesh, you may want to try and predictthe cell size by performing a hand calculation at the start. For example:

• For a flat plate, Reynolds number gives Re = 1.4x10 6 • (Recall from earlier slide, flow over a surface is turbulent when Re > 5x10 5)

Flat plate, 1m longAir at 20 m/sr = 1.225 kg/m 3

m = 1.8x10 -5 kg/ms

y

The question is what height(y) should the first row ofgrid cells be. We will useSWF, and are aiming for Y +

50




Example in predicting near-wall cell size [2]

•

A literature search suggests a formula forthe skin friction on a plate:

• Use this value to predict the wall shearstress w:

• From tw compute the velocity u :

• Rearranging the equation shownpreviously for y + gives a formula for the

first cell height, y, in terms of u • In this example we are aiming for y+ of

50, hence our first cell height y should beapproximately 1 mm.

2.0Re058.0

l f C

2

21 U C f w r

r

wU




Example in predicting near-wall cell size [3]

• For Conjugate Heat Transfer Simulations one would need ay+ value of 1. Let‘s estimate the first grid node for y+= 1:

V= 20 m/s , ρ = 1.225 kg/m3 , μ = 1.8x10-5 kg/ms

Cf =0.0034 tw = 0.83 kg/ms 2

Uτ = 0.82 m/s

y = 0.02 mm

m

r VLl Re Rel = 1.4x10 6

2.0Re058.0

l f C

r

wU

mU

y y

5

5

108.1

10469.1

r

m

aiming for y+ of 1:our first cell height yshould be ≈ 0.02 mm




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Appendix: Inlet TurbulenceConditions





• Default Intensity and Autocompute Length ScaleThe default turbulence intensity of 0.037 (3.7%) is used together with acomputed length scale to approximate inlet values of k and . The lengthscale is calculated to take into account varying levels of turbulence.In general, the autocomputed length scale is not suitable for external flows

• Intensity and Autocompute Length ScaleThis option allows you to specify a value of turbulence intensity but thelength scale is still automatically computed. The allowable range ofturbulence intensities is restricted to 0.1%-10.0% to correspond to verylow and very high levels of turbulence accordingly.

In general, the autocomputed length scale is not suitable for external flows• Intensity and Length Scale

You can specify the turbulence intensity and length scale directly, fromwhich values of k and ε are calculated




Inlet Turbulence Conditions [2]

•

Low Intensity = 1%This defines a 1% intensity and a viscosity ratio equal to 1• Medium Intensity = 5%

This defines a 5% intensity and a viscosity ratio equal to 10This is the recommended option if you do not have any informationabout the inlet turbulence

• High Intensity = 10%This defines a 10% intensity and a viscosity ratio equal to 100

• Specified Intensity and Eddy Viscosity RatioThis defines a 10% intensity and a viscosity ratio equal to 100Use this feature if you wish to enter your own values for intensity andviscosity ratio

• k andSpecify the values of k and ε directly

• Zero GradientUse this setting for fully developed turbulence conditions


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