simulation of detached flows using openfoam® - hpc … · simulation of detached flows using...
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Simulation of detached flows using OpenFOAM®
A. Fakhari, V. Armenio University of Trieste
A. Petronio IEFLUIDS
R. Padovan, C. Pittaluga, G.Caprino CETENA
Data 08/03/2016
8 April 2016
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Motivation
• Flow separation is an important phenomena in industrial and
environmental applications
• Most of the models having problem to predict the separation and
reattachment poins
Benchmark cases in order
to test applicative meshes:
Flow past a sphere
Flow around Surface-Mounted
cubical obstacle
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Turbulence models:
Numerical scheme
RANS (standard 𝑘 − 𝜀 model )
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standard Smagorinsky : 𝜈𝑒𝑓𝑓 = 𝜈 + 𝜈𝑡
𝝂𝑻 = 𝑪𝒔𝜟 𝟐 𝑺 , 𝑐𝑠 = 𝑐𝑘 2
𝑐𝑘
𝑐𝜀
Smagorinsky with van Driest damping
Δ = 𝑚𝑖𝑛 Δ𝑚𝑒𝑠ℎ,𝑘
𝐶Δ𝑦 1 − 𝑒−𝑦
+ 𝐴+
dynamic Lagrangian
Numerical scheme
Meneveau et al (1996)
Turbulence models:
LES
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Numerical scheme
Second order schemes
Central difference for advective terms
PISO algorithm for LES,
SIMPLE for RANS.
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Problem description
𝑈 = 1,0,0 𝛻𝑈 = 0
𝑅𝑒𝐷 = 2𝑟𝑈 𝜈 = 10000, 𝑟 = 1 𝑚.
𝑙 = 30𝑟
Constantinescu & Squires (2003)
Free slip
Free slip
Flow around sphere
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case 1 case 2 case 3
case 6
𝒚𝒔𝒑𝒉𝒆𝒓𝒆_𝒄𝒆𝒍𝒍+ ≈ 25
3 𝑝𝑟𝑖𝑠𝑚𝑎𝑡𝑖𝑐 𝑙𝑎𝑦𝑒𝑟𝑠
𝒚𝒔𝒑𝒉𝒆𝒓𝒆_𝒄𝒆𝒍𝒍+ ≈ 1
case 4 case 5
𝒚𝒔𝒑𝒉𝒆𝒓𝒆_𝒄𝒆𝒍𝒍+ ≈ 50
𝒚𝒔𝒑𝒉𝒆𝒓𝒆_𝒄𝒆𝒍𝒍+ ≈ 25
𝒚𝒔𝒑𝒉𝒆𝒓𝒆_𝒄𝒆𝒍𝒍+ ≈ 50
3 𝑝𝑟𝑖𝑠𝑚𝑎𝑡𝑖𝑐 𝑙𝑎𝑦𝑒𝑟𝑠
OpenFOAM
Grid:
case 1
case 2
case 4
case 5
case 6
ANSYS ICEM
Grid:
case 3
𝟑𝟎 × 𝟑𝟎 × 𝟑𝟎 cells
𝒚𝒔𝒑𝒉𝒆𝒓𝒆_𝒄𝒆𝒍𝒍+ ≈ 25
Flow around sphere
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Results of simulation with OpenFOAM using standard 𝑘 − 𝜀 model
Flow around sphere
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Results of simulation with OpenFOAM using LES for case 3 Flow around sphere
case 3
𝒚𝒔𝒑𝒉𝒆𝒓𝒆_𝒄𝒆𝒍𝒍+ ≈ 25
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Result of simulation with OpenFOAM using LES (Smagorinsky) for case 6 Flow around sphere
case 6
𝒚𝒔𝒑𝒉𝒆𝒓𝒆_𝒄𝒆𝒍𝒍+ ≈ 1
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Results of simulation with LES-dynLagrangian : our modification and the original of OpenFOAM case 6
Flow around sphere
case 6
𝒚𝒔𝒑𝒉𝒆𝒓𝒆_𝒄𝒆𝒍𝒍+ ≈ 1
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case 3 𝑘 − 𝜀 LES case 3
Flow around sphere
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experiment by Martinuzzi and Tropea (1993)
ERCOFTAC database
𝑹𝒆𝒉 = 𝑼𝑩𝒉/𝝂 = 8 × 104
𝒉 =0.025 m
no slip
periodic
periodic inflow
outflow
no slip
Problem description wall-mounted box
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𝒚+ ≈ 𝟐𝟓 Near wall
𝒚+ ≈ 𝟐𝟓
𝒚+ ≈ 𝟓𝟎
𝒚+ ≈ 𝟓𝟎
case 1
case 2
case 3
case 4
𝟒𝟎 × 𝟑𝟔 × 𝟐𝟒 cells
Refinement box from bottom
Refinement box from bottom
𝒚+ ≈ 𝟔𝟒 Near cube
Grid generated by OpenFOAM
Flow over box
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Results of simulation with OpenFOAM using standard 𝑘 − 𝜀 model Flow over box
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Results of simulation with OpenFOAM using standard 𝑘 − 𝜀 model Flow over box
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Grid generated by ANSYS ICEM
case 1
case 2
case 3
case 4
Flow over box
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Result of simulation with ANSYS CFX using 𝑆𝑆𝑇 𝑘 − 𝜔 model
Flow over box
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Results of simulation with ANSYSCFX using 𝑆𝑆𝑇 𝑘 − 𝜔 model
Flow over box
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Wall-bounded fully developed turbulent flows passing around bluff-bodies. A random noise is added to the specific inlet velocity from a defined turbulence level Inlet { Type turbulenceInlet; referenceField nonuniform fluctuationScale (0.02 0.01 0.01 ) Value nonuniform }
𝑢𝑝+ =
1
𝑘log 𝑦𝑝
+ + 𝐵, 𝑦𝑝+ > 11
𝑦𝑝+, 𝑦𝑝
+ ≤ 11
6𝛅 ×2 𝛅 × 𝟕𝛅 𝟗𝟒 × 𝟏𝟐𝟎 × 𝟏𝟔𝟎 cells
Flow over box
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Simulation with OpenFOAM, using standard Smagorinsky (van Driest damping)
Flow over box
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Flow over box
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Instantaneous Flow field
Vertical cross section
Horizontal cross section
Flow over box
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• Wall bounded flows, at very high Reynolds numbers,
require very fine grid near wall to resolve viscous sub-
layer
• The resolution even for resolved LES (𝑹𝒆𝟐.𝟓) is
comparable to DNS (𝑹𝒆𝟑), using wall function (𝑹𝒆𝟎.𝟔) [Piomelli 2008]
• In applications where wall roughness is the rule rather
than the exception, it does not make sense to describe
the wall boundary in a deterministic sense.
Why Wall layer model?
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Filtered Navier Stokes equation for an incompresible flow:
𝜕𝑢𝑖
𝜕𝑡+𝜕(𝑢 𝑖𝑢 𝑗)
𝜕𝑥𝑗= −
1
𝜌
𝜕𝑝
𝜕𝑥𝑖+
𝜕
𝜕𝑥𝑗𝜈 + 𝝂𝑻
𝜕𝑢 𝑖𝜕𝑥𝑗
Equilibrium stress model:
𝑢𝑝+ =
1
𝑘log 𝑦𝑝
+ + 𝐵, 𝑦𝑝+ > 11
𝑦𝑝+, 𝑦𝑝
+ ≤ 11
𝑢𝑝+ = 𝑢𝑝 𝒖𝝉 = 𝑢2 + 𝑤2 𝒖𝝉 , 𝑘 = 0.41, 𝐵 = 5.1
Wall shear stress: 𝜏𝑤 = 𝜌𝑢𝜏2 →
𝜏𝑤,𝑥 = 𝜌𝑢𝜏2 𝑢
𝑢𝑝
𝜏𝑤,𝑧 = 𝜌𝑢𝜏2 𝑤
𝑢𝑝
Wall layer model
In x direction:
𝜈 + 𝝂𝑻𝜕𝑢 1𝜕𝑥2
= 𝜏 𝑤,𝑥
In z direction:
𝜈 + 𝝂𝑻𝜕𝑢 3𝜕𝑥2
= 𝜏 𝑤,𝑧
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P in the log region:
𝑆 12 =𝑢𝜏𝑘𝑦𝑝
𝑢
𝑢𝑝+𝜕𝑣
𝜕𝑥, 𝑆 32 =
𝑢𝜏𝑘𝑦𝑝
𝑤
𝑢𝑝+𝜕𝑣
𝜕𝑧
P in the viscous layer:
𝑆 12 =𝑢𝜏2
𝜈
𝑢
𝑢𝑝+𝜕𝑣
𝜕𝑥, 𝑆 32 =
𝑢𝜏2
𝜈
𝑤
𝑢𝑝+𝜕𝑣
𝜕𝑧
Why Wall layer model?
𝝂𝑻 = 𝑪𝒔𝜟 𝟐 𝑺
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WMLES for flows with separation Proper Turbulent inflow for LES Applying LES (dynamic Lagrangian) to
simulate flow around wall-mounted cube Applying DES
Future works
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1. Cintolesi C.: OpenFOAM simulations-flow around a Sphere, University of Trieste, report November
(2013).
2. Constantinescu K., Squires K.: LES and DES investigation of Turbulent Flow over Sphere at
Re=10000. Flow Turbulence and Combustion 70: pp. 267-298 (2003).
3. Ferziger J., Peric M. : Computational methods for fluid dynamics, Springer, Third edition (1996).
4. Isaev S. A., Lysenko D. A. (2009): Calculation of unsteady flow past a cube on the wall of a narrow
channel using URANS and the Spalart-Almaras turbulence model, Journal of Engineering Physics and
Thermophysics, Vol. 82, No. 3.
5. Kundu P., Cohen I.: Fluid Mechanics. Elsevier Academic press, Third Edition (2004).
6. MARTINUZZI R., TROPEA C. : The flow around surface-mounted, prismatic obstacles placed in a fully
developed channel flow. Journal of Fluid Engineering, Vol. 115, p. 85 (1993).
7. Meneveau Ch., Lund T., Cabot W. H.: A lagrangian dynamic subgrid-scale model of turbulence, J.
Fluid Mech., vol. 319, p. 353-385 (1996)
8. Morrison F. A.: Data correlation for drag coefficient for sphere, report in Michigan Technology
University.
9. Penttinen O.: A pimpleFoam tutorial for channel flow, with respect to different LES models, project
done as a part of course at Chalmers University of technology (2011).
10. Piomelli U.:Wall-Layer Models For Large-Eddy Simulations, Progress in Aerospace Sciences 44,
volume 44, 437-446 (2008)
11. Shah K.B., Ferziger J.H. : A fluid mechanicians view of wind engineering: large eddy simulation of flow
past a cubic obstacle, J. Wind Eng. Ind. Aerodyn. 67&68, 211–224 (1997).
12. Yakhot A., Liu H., Nikitin N. : Turbulent flow around a wall-mounted cube: A direct numerical
simulation, International Journal of Heat and Fluid Flow 27, 994–1009 (2006).
References