turbulent flow examples - university of...
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![Page 1: Turbulent Flow Examples - University of Southamptonsouthampton.ac.uk/~nwb/lectures/GoodPracticeCFD/...Turbulence Apr 2005 Flow configuration: Johnston et al. (1972) ReH = 11,500 Ro](https://reader030.vdocuments.site/reader030/viewer/2022040407/5ea7bf9e7a1c7d44dd772da3/html5/thumbnails/1.jpg)
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Turbulent Flow
Examples
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2d BackstepExperiments conducted at NASA Ames (Driver and Seegmiller, 1985)ReH= 3.74 x 104, α = 0 deg.The flow features re-circulation, reattachment, and re-developing BLComputed using SKE, RNG, RKE, and k-ω models on a fine mesh
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2D Backstep - Skin Friction Coefficient
Std. k-ε Real. k-ε SST k-ω Wilcox k-ω Measured
xr/H 5.8 6.6 6.6 7.3 6.4
Predicted reattachment lengths
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Low-Re Backstep
Re = 5,100Comparison with DNS data of Le and Moin (1994)Comparison of Standard k-ε + 2-layer, Yang-Shih low-Re model and V2F low-Re model
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Low-Re Backstep
Cp Cfx
Pressure coefficient and x-component of skin friction2-layer model less accurate than V2F and Yang-Shih
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XVelocity X
Velocity
XVelocity X
Velocity
X/h = 1 X/h = 3
X/h = 5 X/h = 7
Low-Re Backstep
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X/h = 1
X/h = 3
X/h = 5 X/h = 7
YVelocity Y
Velocity
YVelocity Y
Velocity
Low-Re Backstep
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Low-Re Backstep
Contours of Rey < 200
ε and νt prescribed algebraically for 2-layer model in region where Rey< 200For low Re, much of the flow is in this region2-layer model is not always a good substitute for a low-Re model
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Comparison with experimental data of Monson et al. (1990)
2D U-Bend
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Streamwise Velocity Comparisons
r*
U/Uref
θ = 90
θ = 0
U/Uref
r* r*
U/Uref
θ = 180
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Cp Cp
S/H S/H
InnerWall
OuterWall
Pressure Coefficients
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Standard k-εSpalart-Allmaras
RNG k-ε RSM
Stream Function Contours
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Lessons from 2-D U-Bend
Only the RSM correctly predicts the effects of streamline curvature
Standard k-ε does not predict any separation
RNG k-ε predicts slight separation
Both RSM and Spalart-Allmaras predict significant separation
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Turbulent Vortex Breakdown
Comparison with experimental data of Sarpkaya (1999)2D axisymmetric calculationSimulation courtesy of R. Spall, Utah State University
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AxialVelocity
r/r0
x/r0 = 5
AxialVelocity
r/r0
x/r0 = 8.3
Comparisons of Axial Velocity Profiles
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Comparisons of Swirl Velocity Profiles
SwirlVelocity
r/r0
x/r0 = 5
SwirlVelocity
r/r0
x/r0 = 8.3
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Lessons from Turbulent Vortex Breakdown
k-ε model cannot predict vortex breakdownin high strain rates, turbulent kinetic energy increases and increases turbulent viscosityRNG k-ε model is better (additional strain-rate term, and an ad hoc swirl correction, reduce the turbulent viscosity) but not acceptable
RSM results show significant improvement for this and many otherswirling flow cases
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Axisymmetric Underwater-BodyExperiments conducted (Huang et al., 1976) at DTNSRDCHigh-Re (ReL= 5.9 x 106), incompressible BL flow with a separation at around x/L = 0.92, and reattachment at x/L = 0.97SKE, RNG, RKE, SA, SKO, SST, RSM and Low Re models tried
Different near-wall treatments tried
Modified hull form
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Axisymmetric Afterbody
Spalart-Allmaras model (fine mesh)
Std. k-ε model + 2-layer (fine mesh)No separation
on afterbody
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Axisymmetric Afterbody
Model Separates?Std k-ε nRNG k-ε nReal. k-ε yRSM yS-A y
Cp
Pressure coefficient on coarse mesh (y+ ~ 40) using wall functions
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Axisymmetric Afterbody
Cp
Pressure coefficient on fine mesh (y+ ~ 0.5) using two-layer model
Model Separates?Std k-ε nRNG k-ε nReal. k-ε y?RSM yS-A y
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Axisymmetric Underwater-Body (2)Pressure (Cp) predictions
Static pressure in the separated region is over-predicted by k-εmodels
Skin-friction predictions
The experiment shows the flow separates at x/L = 0.92 and reattaches at x/L = 0.97k-ω models gives too large a separation
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Axisymmetric Afterbody
Spalart-Allmaras gives consistent results on both meshesSeparation not predicted by Standard k-ε on either meshRSM separates on both meshes
Cp on body somewhat overpredicted on coarse mesh“Wall reflection” term, or quadratic pressure-strain term, necessary to obtain coarse mesh separation
Subtle separation illustrates effect of near-wall treatmentRealizable k-ε has smaller separation bubble on fine mesh
Difficult to get grid-independent solutions using wall functions. Would a low-Re formulation work?
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Axisymmetric Afterbody
Cp
Position (m)
Model Separates?
V2F yAbid nLaunder-Sharma nYang-Shih nAbe-Kondo-Nagano n Chang-Hsieh-Chen n
Pressure coefficient on fine mesh using Low-Re models
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Axisymmetric Afterbody
Low-Re models using damping functions do not predict the separation
Durbin’s V2F (4-equation) model predicts separation
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Ota & Kan 151x75 quad mesh
Turbulent Heat Transfer Over a Blunt Plate
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Standard k-ε model Reynolds-Stress model (exact)
Contours of TKE production
Blunt Plate
The standard k-ε model gives spuriously large turbulent kinetic energy on the front face, underpredicting the size of the recirculation
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Blunt Plate
Standard k-ε
Realizable k-ε
Experimentally observed reattachment point is at x/d = 4.7
Predicted separation bubble
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noneqnoneq
Heat Transfer Over a Blunt Plate
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Example: Ship Hull Flow
Experiments: KRISO’s 300K VLCC (1998)Complex, high ReL (4.6 × 106) 3D Flow
Thick 3D boundary layer in moderate pressure gradientStreamline curvatureCrossflowFree vortex-sheet formation (“open separation”)Streamwise vortices embedded in TBL and wake
SimulationWall Functions used to manage mesh size
y+ ≈ 30 - 80Hex mesh ⇒ ~200,000 cells
Contours of axial velocity compared with simulations
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Comparing Contour Plots of Axial Velocity
SKO and RSM models capture characteristic shape at propeller plane
SA RKE RNG
SKE SKO RSM
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0.486 0.482
0.537 0.539 0.538
0.5830.561 0.56 0.557
0.3
0.35
0.4
0.45
0.5
0.55
0.6
S-A SKERNG
RKEKO-SST
KO-Wilc
oxRSM-G
LRSM-SSG
Exp.
w
4.051 4.216 4.145 4.149 4.2 4.258 4.048 4.06 4.056
00.5
11.5
22.5
33.5
44.5
S-A
SKE
RNG
RKEKO-SST
KO-Wilc
oxRSM-G
LRSM-SSG
Exp.
1000
xCT,
CF,
CVP
CTCFCVP
Comparing Wake Fraction and Drag
Though SKO (and SST) were able to resolve salient features in propeller plane, not all aspects of flow could be accurately captured
Eddy viscosity modelRSM models accurately capture all aspects of the flowComplex industrial flows provide new challenges to turbulence models
dAUu
Aw
PAP∫
−=
0
11
VPFT CCC +=
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Flow configuration:
Johnston et al. (1972)
ReH = 11,500
Ro = 0.21
Flow in a Rotating Channel
Represents flows through rotating internal passages (e.g.turbomachinery applications)Rotation affects mean axial momentum equation through turbulent stressesRotation makes mean axial velocity asymmetricalComputations are carried out using SKE, RNG, RKE and RSM models are with the standard wall functions
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Flow in a Rotating Channel
Predicted axial velocity profiles (ReH = 11.500, Ro = 0.21)
Symmetric profiles
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2-D HillMeasured by Baskaran et al. (JFM, Vol. 182, 1987)High-Re (ReL = 1.33 x 106/m) incompressible BL subjected to pressure gradient, streamline curvatureThe main interests are the skin-friction, static pressure, and extent of the BL separation (x=1.1 m)Computed using SA, SKE, RKE, and k-ω models
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Pressure and Skin Friction Distribution
Pressure distribution
The k-ω models predict the Cpplateau very closely
Skin-friction distribution
The k-ω models give an earlier and larger separation than other models
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Axisymmetric Bump
Measured by Bachalo and Johnson (1986)Transonic BL flow with a standing shock and a pocket of BL separation behind the shockMa = 0.875, Rec = 13.6 x 106 at freestreamComputed using S-A, SKE, RKE, KO, SST models
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Axisymmetric Bump (2)
Wall pressure predictions
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RAE 2822 Airfoil
RAE2822 Transonic airfoilMeasured by Cox (1981) (Case 9 in Stanford database)The corrected α = 2.79 deg., Ma = 0.73, Re = 6.5 x 106
Computed using SA, SKE, RKE, and k-ω models on a wall function (coarse) mesh
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RAE 2822 Airfoil Cp Predictions
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RAE 2822 Cf Predictions
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Forces and moment predictions
(α = 2.79, Re = 6.5 x 106, Ma = 0.73)
The shock location predicted k-ω models is slightly upstream of the measured one and the prediction by other models
The two k-ω models gives a slightly lower lift coefficient, but their results are almost identical
RAE 2822 Airfoil Summary
Flow S-A SKE RKE SST k-ω Wilcox k-ω Exp.CL 0.811 0.835 0.820 0.772 0.774 0.803
CD 0.0180 0.0198 0.0189 0.0172 0.0172 0.0168
CM -0.1093 -0.1063 -0.1092 -0.1068 -0.1072 -0.099
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Flow in a Cyclone
40,000 cell hexahedral meshHigh-order upwind scheme was usedComputed using SKE, RNG, RKE and RSM models with the standard wall functionsRepresents highly swirling flows (Wmax = 1.8 Uin)
0.97 m
0.1 m
0.2 m
Uin = 20 m/s
0.12 m
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Flow in a CycloneTangential velocity profile at 0.41 m below the vortex finder
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Iso-surface of instantaneousvorticity magnitude colored by velocity angle
LES Example - Dump Combustor
A 3-D model of a lean premixed combustor studied by Gould (1987) at Purdue UniversityNon-reacting (cold) flow was simulated with a 170K cell hexahedral mesh using second-order temporal and spatial discretization schemes
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Mean axial velocity at x/h = 5
( )150Re10Re 5 ≈= λd
LES Examples - Dump Combustor
Simulation done for:
Computed using RNG-based subgrid-scale model
Mean axial velocity prediction at x/h = 5;
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LES Examples - Dump Combustor
RMS velocities predictions at x/h = 10