Fluent-Adv Turbulence 15.0 L05 Case Studies

1 2014 ANSYS, Inc. April 23, 2014 ANSYS Confidential

15.0 Release

Lecture 5:

Case Studies

Turbulence Modeling Using ANSYS Fluent


Motivation

How do I choose which turbulence model and near-wall modeling approach to use for a given application? Understanding of how turbulence modeling issues affect turbulence

model selection and performance

Observation and comparison of behavior of turbulence models for flows in similar applications Results from a variety of flows will be presented


The Main Objectives

Understand factors affecting turbulence model selection

Compare performance of turbulence models Which models are likely to be accurate in a particular flow How factors besides the turbulence model may affect accuracy


Factors Affecting Turbulence Model Selection

Many factors must be considered. To make the best choice requires an understanding of the available options

This lecture focuses primarily on flow physics and accuracy

Turbulence Model & Near-Wall Treatment

Flow Physics

Accuracy Required

Computational Resources

Turnaround Time Constraints

Computational Grid


Turbulent Flow Feature Space

Thin B.L. flows

Rotating & swirling

flows

Crossflow/Secondary

flows

Rapidly strained flows

Transitional flows &

re-laminarization

Separated &

recirculating flows

Large-scale unsteady

structure

Thick BL, mildly

separated flows

Streamwise vortices

Free shear flows (BL, mixing

layer, wakes, jets

Shocks and shock-

induced boundary-layer

separation

Impinging flows


Turbulence Modeling Challenges

Pressing needs for high-fidelity CFD predictions Tight margin for design improvement Direct simulation still beyond the reach for industrial applications

Difficult to know which model to use or recommend Industrial flows are complex and multi-featured Incurs a considerable cost on both developers and users

There are many other factors affecting CFD predictions Choice of solution domain, boundary conditions, numerical error, etc. Quality of mesh and mesh resolution User error


Modeling Challenges

Yet turbulence modeling is a pacing item for the fidelity of CFD predictions

Higher expectation for the fidelity predictions as CFD technology matures

Widely varying requirements on accuracy

No breakthrough in turbulence modeling for industrial flows

Numerous models spawned over last two decades Theres no single, dominantly superior, universally reliable

engineering turbulence model yet


Other factors: 2D Back-step (Standard k-e )

Accuracy of turbulent flow predictions is also affected by boundary conditions, grid resolution, near wall modeling etc.

Heat transfer predictions along the bottom

Measured by Vogel and Eaton (1980)

SKE with standard wall functions employed



Run X-Velocity

B.C.

Thermal

B.C. Turbulence B.C.

1 Profile Uniform Profile

2 Uniform Uniform Intensity & Hydraulic

Diameter

3 Profile Uniform k = 1, e = 1 Prior to R14.5, values of 1 (in SI units) were the default b.c. for the k-e model. The new defaults (intensity = 5%, turbulent viscosity ratio = 10) are better, but would likely still give results closer to the green curve.



Structured

Quad Pave

Tri w b/l

Tri


Other factors: 2D Back-step (SKE)

30% Growth

Triangular

40% Growth


Other factors: 2D Back-step (RKE)

y+ values must be appropriate for selected near wall treatment

Red line range of y+ appropriate for wall functions

Green Line range of y+ not suitable for wall functions


Spalart-Allmaras Model (SA) Fundamentals transport equation for modified turbulent viscosity,

Advantages robust, very economical natural description of near wall turbulence (optional) accurate for 2D wall bounded flow with mild separation

Drawbacks in the absence of strain merely convects boundary values weak for complex 3D flow

Recommended usage less complex / quasi-2D (external) flows, e.g. airfoils, missiles, slender

bodies

t~


Transonic flow over 2D Bump Case description Transonic flow accelerates over a

bump and decelerates to subsonic speed in trailing edge shock (ONERA 1980)

Shock induced boundary layer separation takes place at Rec=1.4 x 10

7 and Mashock=1.37

Results depend on boundary layer development and trailing edge separation

SA, SKE, RNG and RKE used on 2D quad mesh with good near-wall resolution ( y+ =1 )

Trailing Edge

P total = 95 KPa gage

d

shock

e/c=0.04

Leading Edge

P total = 95 kPa gage

d

c e

shock

e / c = 0.04

shock

shock induced

flow separation

trailing edge


Transonic flow over 2D Bump

Mach number along the lower wall of the channel

Despite its simplicity, SA captures the position of the shock very well whereas Standard k-e fails


Standard k-e Model (SKE) Fundamentals 2-equation Eddy Viscosity Model ( m t = f ( k,e ) )

Advantages well tested, robust, economical reasonable accuracy for a wide range of flows

Drawbacks overly diffusive for many situations needs additional description for near wall turbulence inaccurate for transitional flow regime

Recommended usage doing qualitative comparisons and screenings exploring basic flow pattern converging initial case before switching to other models


Internal Airflow (SKE, RNG, RKE, SST) Case description Flow enters a rectangular domain along the

upper left edge with uin= 4.55 m/s and leaves along the opposite corner (ECBCS Annex 20 air flow in buildings test case, 1993)

Profiles of mean velocity are calculated and compared to experiment at x = 3 m and x = 6 m

Results depend on spreading of inlet jet, near-wall turbulence and interaction of recirculation zones

SKE, RNG, RKE and SST model used on 2D 76K cell quad mesh with B.L. resolution (y+=1)

inlet

outlet

x=6m x=3m

measuring planes


Internal Airflow (SKE, RNG, RKE, SST)

SKE results are consistent with the predictions of other k-e models

x-velocity 3m from inlet x-velocity 6m from inlet

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9

dim

en

sio

nle

ss h

eig

ht

y/H

dimensionless velocity u/u0

Velocity profile in a distance of 3m

SST-grid3 SKE-grid3 RNG-grid3 RKE-grid3 Measurement

Velocity profile in a distance of 6m

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

-0,5 -0,3 -0,1 0,1 0,3 0,5 0,7 0,9

dimensionless velocity u/u0

dim

en

sio

nle

ss

he

igh

t y

/H

SST-grid3 SKE-grid3 RNG-grid3 RKE-grid3 Measurment


RNG k-e Model (RNG) Fundamentals derived by scale-elimination applied to N-S equations modified source terms in e equation analytical formula for turbulent Prandtl numbers Prt = f(m /(m +m t )) Differential-Viscosity option for low turbulent Reynolds numbers option to modify turbulent viscosity to account for swirl

Advantages less diffusive than Standard k-e Model for complex shear flow well suited for flows with low turbulence regions

Drawbacks tends to uncover small scale unsteadiness sometimes difficult to converge

Recommended usage locally transitional flow, e.g. natural convection in buildings


Realizable k-e Model (RKE) Fundamentals derived by enforcing Realizability of k-e, e.g. ui2 0 modified source terms in e equation, new formula for m t

Advantages overall good performance and accuracy strong for (internal) flows with interacting shear layers robust

Drawbacks difficult to converge on rare occasion

Recommended usage default choice for most applications


Turbulent flow past a blunt flat plate was simulated using four different turbulence models. 8,700 cell quad mesh, graded near leading edge and reattachment

location.

Non-equilibrium boundary layer treatment

Blunt Flat Plate

D

000,50Re D

Rx

Recirculation zone Reattachment point

0U

N. Djilali and I. S. Gartshore (1991), Turbulent Flow Around a Bluff Rectangular Plate, Part I: Experimental Investigation, JFE, Vol. 113, pp. 5159.


Blunt Flat Plate: TKE Predictions

Contours of Turbulent Kinetic Energy (m2/s2)

RNG k Standard k

Reynolds Stress Realizable k

0.00

0.07

0.14

0.21

0.28

0.35

0.42

0.49

0.56

0.63

0.70


Blunt Flat Plate: Flow Separation

Experimentally observed reattachment point is at x / D = 4.7

Predicted separation bubble:

Skin Friction

Coefficient Cf 1000

SKE severely underpredicts the size of the separation bubble, while RKE predicts the size exactly.

Distance Along Plate, x / D

RKE results are often better than standard k-e when accurate predictions needed

Standard k (SKE)

Realizable k (RKE)


Standard k-w Model (SKO) Fundamentals uses specific dissipation rate w instead of e

Advantages natural description of near wall turbulence (optional) to some extent can handle boundary layer transition less diffusive than Standard k-e Model

Drawbacks sensitive to inlet and far-field boundary values sometimes under diffusive for complex shear and strain sometimes difficult to converge

Recommended usage wall bounded (external) flow, e.g. airfoils, compressors, turbines without

massive interaction of shear layers prediction of wall heat transfer


SST k-w Model (SST) Fundamentals uses blending of e and w equations for specific dissipation

Advantages overcomes sensitivity to inlet and far-field boundary values natural description of near wall turbulence (optional) to some extent can handle boundary layer transition less diffusive than Standard k-e Model

Drawbacks sometimes under diffusive for complex shear and strain sometimes difficult to converge

Recommended usage wall bounded (external) flow, e.g. airfoils, compressors, turbines without

massive interaction of shear layers prediction of wall heat transfer


NACA 4412 Airfoil Case description

Rec = Uref * C/ = 1.5106

13.87 angle of attack Quadrilateral mesh with

y+ ~= 1

Good test case for the capability of RANS models to predict the separation zone near the trailing edge


NACA 4412 Airfoil Results

Good prediction of separation and velocity profiles in separated zone with SST model

u/Uref

Dis

tan

ce

fro

mw

all

0 1 2 3 4 5 6

0

0.02

0.04

0.06

0.08

0.1

SST

Wilcox 2006

Spalart-Allmaras

v2-f

Experiment


V2F k-e Model (V2F) Fundamentals 4-equation model solving for wall normal fluctuations and relaxation

functions f in addition to k and e

Advantages natural description of near wall turbulence promising results for 3D low-Re boundary-layer flows

Drawbacks high quality high resolution meshing required needs more CPU time and memory than 2-equation models sometimes difficult to converge

Recommended usage in detail analysis of the near-wall behaviour and heat transfer

2v


Impinging Jet Heat transfer Case description

Cooling jet (T0 ) impinges on a hot wall (Twall )

HTC calculated along the wall for nozzle distances H/D = 2 & H/D = 6

Results depend on near-wall turbulence in stagnation zone and boundary layers

SKO and V2F model used on 2D axisymmetric 10K cell quad mesh with B.L. resolution (y+ = 1)

Free jet

Stagnation zone

Boundary Layer

Wall Jet

Twall

?


Impinging Jet Heat transfer (SKO, V2F)

reasonable accuracy with SKO and V2F

Wall Nusselt number distribution H/D = 2

Wall Nusselt number distribution H/D = 6

k-

V2F

Nu* Nu*

V2F

k-


Transition Models Fundamentals Three models that allow for prediction of laminar to turbulent transition Transition SST (Menter and Langtry, 2004) Correlation based model using transport equations and local formulation Uses SST k and w equations plus two additional transport equations (intermittency and Req )

Intermittency Transition (ANSYS, R15.0) A further development based on the Transition SST model Uses SST k and w equations plus one additional transport equation (intermittency) Only model with provisions for crossflow instability

k-kl-w (Walters and Cokljat, 2007) Based on laminar kinetic energy concept Uses k and w equations plus one additional transport equation (laminar kinetic energy)

Advantages The only RANS models that can predict transition

Drawbacks High mesh resolution requirements near walls (y+ = 1)

Recommended usage Boundary layer transition only


VPI Turbine Heat Transfer (SST-T, Walters)

Case Description Hybrid Mesh: 24386 cells Re = 23,000, Uin = 5.85m/s, Tin=20 C, Chord=59.4cm Air: constant cp and r Three inlet turbulence intensities: 0.6%, 10% and 19.5%


VPI Turbine Heat Transfer (Transition SST, k-kl-w) h

, W

/( m

2K

)

Fully

-tu

rbu

len

t Fl

ow

Tran

siti

on

Lam

inar

Blade Pressure Side S

tagn

atio

n h

, W

/( m

2K

)

Fully

-tu

rbu

len

t F

low

Tran

siti

on

Lam

inar

Blade Pressure Side

Stag

nat

ion

s/C s/C

Note: Experiment authors indicated that the instrumentation for the heat flux measurements was inducing early transition in the heat transfer data


Reynolds Stress Model (RSM) Fundamentals transport of Reynolds 6 stresses Rij and e for RANS

Advantages physically more sound than Eddy Viscosity concept, e.g. weak secondary flow along

sharp edges is resolved

Drawbacks even more modeling assumptions required needs additional description for near wall turbulence small gain in accuracy for the majority of applications needs more CPU time and memory than 2-equation models sometimes difficult to converge

Recommended usage complex flow dominated by curvature, swirl and rotation


Secondary Flow in a Triangular Duct

Case description Turbulent flow passes an infinite pipe

with triangular cross section; in each corner a pair of secondary flow vortices pointing to the outside is formed

Secondary flow pattern produced by anisotropy of Reynolds stresses

Results depend on the exact prediction of the 6 different Reynolds stresses

RSM and SST model used on 3D 15K cell quad mesh (3 layer slice) with B.L. resolution ( y+= 1 )

z

y

x

Periodic element m = 0.0138 kg/s W = 2.6 m/s Re = 10000

s = 0.1m

corner

.


Secondary Flow in a Triangular Duct

only RSM is able to resolve the secondary flow pattern in sharp corners

wsecondary (m/s) wsecondary (m/s)

RSM Secondary Flow

Wsecondary /Wmain< 3% SST Secondary Flow

Wsecondary /Wmain< 0.0001%


Flow in a Cyclone Separator Case description

Flow with high levels of swirl Swirl velocity* is calculated and compared

with the measured value at a specific axial position

( Wmax = 1.8 x Uin )

Results depend on accurate modeling of Reynolds stresses equilibrium (rigid body vs. potential flow)

SKE, RNG, RKE and RSM used on 40k cell 3D Hex mesh with wall functions

* Swirl Velocity = Tangential Velocity Component

0.97 m

0.1 m

0.2 m

Uin = 20 m/s

0.12 m


Flow in a Cyclone Separator

Swirl velocity at 0.41 m below the vortex finder

despite swirl option, RNG accuracy worse than RKE and SST; only RSM delivers potential flow vortex


Tip Vortex of a Wing Case description

Finite wing of 4ft x 3ft with rounded tip is mounted in a wind tunnel; a tip vortex separates and is convected downstream (Chow et al., 1997)

The tip vortex tracked for a = 10o and Rec = 4.6 x 10

6

Results depend on B.L. vortex separation and swirling shear layer interaction

RSM, SA, RKE, SST used on 3D 2,3M cell Hex mesh with B.L. resolution

( y+ = 1 )

tunnel wall

wing


Tip Vortex of a Wing Development of pressure coefficient Cp along the core of the tip vortex

RSM does the best job to conserve vortex and swirl


Large Eddy Simulation (LES)

Fundamentals depending on time and space discretization, directly resolves large scale turbulent

eddies eddy viscosity models to account for subgrid turbulence

Advantages accurately resolves large scale turbulent structures

Drawbacks needs additional description for near wall turbulence very sensitive to grid resolution and boundary values alway unsteady; needs lots of CPU time and memory

Recommended usage detailed analysis of unsteady turbulent flow, e.g. turbulent structures behind bluff

bodies, aeroacoustics


Heat Transfer & Wake of Bluff Body Case description

Cold flow heats up and separates along a cylinder

Temperature and mixing of air in the wake of a heated cylinder are calculated at a critical Reynolds number of ReD= 40,000

Results depend on wall heat transfer, flow separation and vortex structure downstream of the cylinder

LES and SST model used on 3D 3million cell hex mesh with B.L. resolution ( y+= 1 )

5000 < Re < 200000: Laminar BL prior to separation ( = 80), wide turbulent wake

3.31 D

3.11 D

D

U0

ReD=40000

g

Courtesy CEA/EDF

P =

600W


Turbulent mixing in wake region is well captured with LES LES results closer to experiment than RANS-SST CPU cost with SST is of order of days CPU cost with LES is of order of weeks

Heat Transfer & Wake of Bluff Body Temperature at x = 0.5m Temperature at x = 1.5m

-800 -500 -321 0 321 500 800 250

500

750

1000

1250

1500

1750

2000

2250

2500

2750

-800 -500 -321 0 321 500 800

250

500

750

1000

1250

1500

1750

2000

2250

2500

2750

Largeur (mm)

Hauteur (mm)

3,0-4,0

2,0-3,0

1,0-2,0

0,0-1,0

Visualisation de

l'chauffement de l'airG=1m50

SST LES Experiment SST LES Experiment


Automobile Rain Gutter Acoustics (LES) Case description

Flow stagnation takes place and unsteady separation at a rain gutter causes noise

Unsteady flow is calculated for U0= 22.35m/s, Dt = 3x10-5s (~5000Hz) and sound pressure levels (SPL) are evaluated using Ffowcs Williams-Hawkings acoustic analogy

Results depend on separating small scale structures, their interaction with main flow and related pressure fluctuations

LES with Smagorinsky subgrid model used on 3D 5Million-cell Hex mesh with B.L. resolution ( y+=1 )

U0 Rain Gutter

Iso-surface of vorticity


Automobile Rain Gutter Acoustics (LES)

Mean flow properties and SPL from unsteady noise sources reasonably well captured by LES

Cp at rain gutter SPL derived by FWH


Detached Eddy Simulation (DES)

Fundamentals depending on time and space discretization, LES resolves large scale turbulent eddies RANS modeling for near wall regions

Advantages accurately resolves large scale turbulent structures in fine grid regions reduces computational effort because in the boundary layer coarser grid spacing can

be used in directions parallel to walls (still need fine resolution normal to wall)

Drawbacks needs additional description for near wall turbulence very sensitive to grid resolution and boundary values alway unsteady; needs lots of CPU time and memory

Recommended usage detailed analysis of unsteady turbulent flow, e.g. turbulent structures behind bluff

bodies, aeroacoustics


Lift and Drag for Airfoil (DES) Case description

Flow over airfoil at a critical angle of attack with transitional B.L. and trailing edge separation (Mellen et al., 2002)

Lift and drag calculated for = 13.3o and Rec=2,1 x 10

6

Results depend on B.L. transition, separation and wake flow

DES with SST used on 3D 370K cell mesh with near-wall resolution of y+= 5

LES would require >10M cell mesh


Lift and Drag for Airfoil (DES)

DES results in very good agreement with experiment

Mean Velocity at Suction Side Lift and drag coefficients

Experiment DES

Cl 1.515-1.574 1.569

Cd 0.021-0.031 0.0313


Simplified Truck Drag Prediction (DES) Case description

B.L. separates on backside of a bluff body (Sovani et al., 2005)

Drag coefficient calculated for ReL = 2 x 106 and zero yaw

Results depend on B.L. separation and character of wake flow

DES with SA used on 12M cell Hex mesh


Simplified Truck Drag Prediction (DES)

Time-dependent and time-averaged drag coefficient

wind tunnel result well captured with DES

Experiment DES

Cd 0.250 0.253


Summary ANSYS Fluent provides a broad range of RANS, LES and hybrid RANS-

LES turbulence models.

The case studies presented here intend to provide an overview of the strengths of the individual models to help show which models are best suited for a given application.

The results of turbulent flow simulations can be affected by factors other than the choice of turbulence model Grid, boundary conditions, near-wall modeling approach,

Additional factors such as the required solution turnaround time and available computations resources also need to be considered when choosing the turbulence model

Fluent-Adv Turbulence 15.0 L05 Case Studies

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