04 turbulence

8/11/2019 04 Turbulence

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Turbulence and Fluenturbulence and Fluent


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Turbulence Modeling


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What is Turbulence?

We do not really know

3D, unsteady, irregular motion in which transported quantitiesfluctuate in time and space. Turbulent eddies (spatial structures). Diffusive (mixing).

Self-sustaining if a mean shear exist. Entrainment.

Energy cascade. Energy is added at the large eddies. Energy is dissipated at the small eddies.


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Turbulent Flows

LargerStructures

SmallerStructures


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Computational Approaches

DNS (Direct Numerical Simulation) Solves the Navier-Stokes (N-S) equations. No turbulence modeling required. Not practical for industrial flows (requires Low Re and simple geometries).

LES (Large Eddy Simulation) Solves a filtered version of the N-S equations. Less expensive than DNS, but still too expensive for most applications.

RANS (Reynolds-Averaged N-S) Solve the ensemble-averaged N-S equations. All turbulence is modeled. The most widely used approach for calculating industrial flows.

There is not yet a single turbulence model that can reliably predict allturbulent flows found in industrial applications with sufficient accuracy.


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Computational Approaches 2)

LES, DNS

RANS


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RANS Modeling

Reynolds decomposition:

The Reynolds-averaged momentum equations are as follows:

where is called the Reynolds stresses . The Reynolds stressesmust be modeled to close the equations.

j

ij

j

i

jik

ik

i

x

R

x

U

x x

p

x

U U

t

U

+

+

=

+

jiij uu R =

( ) ( ) ( )t xut xU t xu iii ,,, rrr +=

Turbulentfluctuation

Mean

u' i

U i ui

time

u


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The Closure ProblemReynolds equations does not contain enough equations to solve for all the

uknown variables. Thus, the Reynolds stresses must be modeled.

Modeling approaches Eddy-Viscosity Models (EVM):

Boussinesq hypothesis: Reynolds stresses are modeled using an eddy (orturbulent) viscosity t . Assumes Isotropic turbulence.

Reynolds-Stress Models (RSM): solves transport equations for all individual Reynolds stresses. Require modeling for many terms in the Reynolds stress equations. Does NOT assume isotropic turbulence.

ijijk

k

i

j

j

i jiij k x

U xU

xU uu R

32

32 tt

+==


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Modeling the Eddy Viscosity

Basic approach made through dimensional arguments Units of t = t/ are [m 2/s] Typically one needs 2 out of the 3 scales:

velocity - length - time

Commonly used scales is the turbulent kinetic energy [L2/T2]

is the turbulence dissipation rate [L2/T3] is the specific dissipation rate [1/T]

Models classified in terms of number of transport equations solved,

zero-equation models one-equation models two-equation models


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Spalart-Allmaras A one-equation RANS model

A low-cost model solving an equation for the modified eddy viscosity

Eddy-viscosity is obtained from

Mainly for aerodynamic/turbo-machinery applications with mild separation(supersonic/transonic flows over airfoils, boundary-layer flows, etc).

( )( ) 31

3

3

11/~

/~,~

v

vvt C

f f +

=

~


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Standard k SKE A two-equation RANS model

Transport equations for k and :

The most widely-used engineering turbulence model for industrialapplications

Robust Performs poorly for flows with strong separation, large streamline

curvature, and large pressure gradient.

( )

( )k

C Gk

C x x Dt

D

G xk

xk Dt D

k e j

t

j

k jk

t

j

2

21

+

+

=

+

+

=

3.1,0.1,92.1,44.1,09.0 21 ===== k C C C where


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k m o els

+

+

=

+

+

=

=

j

t

j j

iij

jk

t

j j

iij

t

x x f

xU

k Dt D

x

k

xk f

x

U

Dt

Dk

k

2

*

*

*

1

k

specific dissipation rate:

Two-equation RANS models

Fluent supports the standard k- model by Wilcox (1998), and Menters SST k- model (1994).

k- models are inherently low-Re models: Can be integrated to the wall without using any damping functions Accurate and robust for a wide range of boundary layer flows with pressure

gradient Most widely adopted in the aerospace and turbo-machinery communities. Several sub-models/options of k- : compressibility effects, transitional flows

and shear-flow corrections.


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Reynolds-Stress Model RSM)

( ) ( ) ijijT ijijij jik k

ji DF PuuU xuu

t +++=

+

Turbulent diffusionStress-production

Rotation-productionPressure strain

Dissipation

Modeling required for these terms

Attempts to address the deficiencies of the EVM. Anisotropy, history effects of Reynolds stresses. RSM requires more modeling (the pressure-strain is most critical and difficult

one among them). More expensive and harder to converge. Most suitable for complex 3-D flows with strong streamline curvature, swirl and

rotation.


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Near Wall Modeling


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The Structure of Near-Wall

Flows The structure of turbulent boundary layers in the near-wall region:


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Near-Wall Modeling

Wall Functions Wall Integration

Accurate near-wall modeling isimportant to correctly predict frictionaldrag, pressure drop, separation, heat

transfer etc.


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Placement of The First Grid

Point For standard or non-equilibrium wall functions, each wall-adjacent

cells centroid should be located within:

For the enhanced wall treatment (EWT), each wall-adjacent cellscentroid should be located: Within the viscous sublayer, , for the two-layer zonal model:

Preferably within for the blended wall function

How to estimate the size of wall-adjacent cells before creating the grid: , The skin friction coefficient can be estimated from empirical

correlations:

2// f ew cU u =

30030 + p y

1+ p y

u y yu y y p p p p // ++

30030 +

p y


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Near-Wall Modeling:

Recommended Strategy Use SWF or NWF in high Re applications (Re > 10 6) where you

cannot afford to resolve the viscous sub-layer. Use NWF for mildly separating, reattaching, or impinging flows.

You may consider using EWT if:

Near wall characteristics are important. The physics and near-wall mesh of the case is such that y + is

likely to vary significantly over a wide portion of the wall region.

Try to make the mesh either coarse or fine enough to avoid placingthe wall-adjacent cells in the buffer layer (y + = 5 ~ 30).


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Enhanced Wall Treatment

Fully-Developed Channel Flow ( Re t = 590)

For fixed pressure drop cross periodic boundaries, different near-wall mesh resolutions yielded different volume flux as follows

The enhanced near-wall treatment gives a much smaller variationfor different near-wall mesh resolutions compared to the variationsfound using standard wall functions.

y+ = 1 y + = 4 y + = 8 y + = 16

Std. W all fn. 12.68 13.77 16.77 19.08

EW T 18.31 17.58 17.70 18.48


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Inlet/Outlet Conditions

Boundary conditions for k, , w and/or must be specified.

Direct or indirect specification of turbulence parameters:

Explicitly input k, , w, or This method allows for profile definition.

Turbulence intensity and length scale

For boundary layer flows: l 0.4 d99 For flows downstream of grid: l opening size

Turbulence intensity and hydraulic diameter

Internal flows Turbulence intensity and turbulent viscosity ratio For external flows: 1 < m t/m < 10

jiuu

jiuu


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Is the Flow Turbulent?

External Flows

Internal Flows

5

105 x Re along a surface

around an obstacle

,3002h D

Re

UL

Re L where

L = x, D , D h, etc.

20,000 D Re Other factors such as free-streamturbulence, surface conditions, anddisturbances may cause earliertransition to turbulent flow.

Natural Convection

3TLg

Ra where108 1010 Ra


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f b l d l


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GUI for Turbulence Models

Define Models Viscous...

Turbulence Model options

Near Wall Treatments

Inviscid, Laminar, or Turbulent

Additional Turbulence options

RANS Turbulence Model


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RANS Turbulence ModelBehavior and Usage

Model Behavior and Usage

Spalart-Allmaras

Standard k -

RNG k -

Realizable k -

Standard k -

SST k

-

RSM

Economical for large meshes Performs poorly for 3D flows, free shear flows, flows with strong separation Suitable for mildy complex (quasi-2D) flows (turbo, wings, fuselages, missilies)

Robust, but performs poorly for complex flows Suitable for initial conditions, fast design screening and parametric studies

Suitable for complex shear flows involving rapid strain, moderate swirl, vortices,locally transitional flows (e.g. b.l. Separation, massive separation, vortex shedding)

Similar benefits and applications as the RNG model Possibly more accurate and easier to converge

Superior for wall-bounded, free shear, and low-Re flows Suitable for complex b.l flows (e.g. external aero, turbomachinery, vortex shedding) Can predict transition (usually predict to early transition, though)

Similar benefits as SKO, less sensitive to outer disturbances Suitable for wall bounded flows, less suited for free shear flows

The most physically sound RANS model (handels anisotrophy) Computationally expensive and harder to converge Suitable for complex 3D flows with strong streamline curvature, strong swirl(e.g. Curved duct, swirl combustors, cyclones)


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Examples

H t T f B hi d 2D


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Heat Transfer Behind a 2D

Backstep Heat transfer predictions along the bottom Measured by Vogel and Eaton (1980)

SKE, RNG, and RKE models are employed with standard wallfunctions.

Factors affecting


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Factors affecting

accuracy The accuracy of turbulent flow predictions can be

affected by user decisions involving Turbulence model Boundary conditions Grid resolution and near wall modeling

Grid quality

I t f T b l M d l


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Impact of Turbulence Model

k- Results

Impact of Boundary Conditions


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Impact of Boundary Conditions

RunX-Velocity

B.C.Thermal

B.C. Turbulence B.C.

1 Profile Uniform

Uniform

Uniform

Profile

2 Uniform Intensity & Hydraulic

Diameter 3 Profile k=1, =1

Impact of Grid Quality


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Impact of Grid Quality

Structured

Tri w b/l

Quad Pave

Tri

Impact of Near Wall Modeling


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Impact of Near Wall Modeling

y+ values must be appropriate for selected near wall treatment Realizable k- with SWF

Stream Function Contours for


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Stream Function Contours for180 Degree Bend

Spalart-Allmaras Standard k-

RNG k- RSM

Rotating Flow in a Cyclone


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Rotating Flow in a Cyclone

0.2 m

0.97 m

0.1 m

Uin = 20 m/s

0.12 m

Highly swirling flows ( Wmax= 1.8 Uin)

High-order discretization on40,000 cell hexahedralmesh

Computed using a family ofk- models (SKE, RNG,RKE), k- models (Wilcox,

SST) and RSM models

Cyclone Velocity Profiles


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Cyclone Velocity Profiles

04 turbulence

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