Modelling of nonequilibrium turbulent flows

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Modelling of non-equilibrium turbulent flows
Tania S. Klein Second Year PhD Student
Supervisors Prof. Iacovides and Dr. Craft
School of MACE, The University of Manchester
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Outline of Presentation

• Introduction
• Test Cases
• Turbulence Models
• Results
• Conclusions

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Introduction
Non-equilibrium flows those subjected to rapid
changes Sudden contraction, sudden
expansion Imposed pressure gradients They are
commonly found in the industry Valves, pumps,
heat exchangers, curve surfaces Objective of
this work Test different turbulence models for
several cases in order to evaluate their
performance.
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Test Cases

• Fully Developed Channel Flow
• Homogeneous Constant Shear Flow
• Zero Pressure Gradient Boundary Layer
• Adverse Pressure Gradient Boundary Layer
• Favourable Pressure Gradient Boundary Layer
• Contraction/Expansion Flows

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Fully Developed Channel Flow

• One of the simplest flows
• 2D
• DPcte
• UU(y)

Simulated Cases
ERCOFTAC database
Kawamura Lab
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Homogeneous Constant Shear Flow
SdU/dycte ? U U(y) not wall-bounded
unsteady
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Zero Pressure Gradient Boundary Layer
Simulated Cases

• Still a simple flow
• 2D
• DP0
• UU(x,y)

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Adverse Pressure Gradient Boundary Layer

• Non-equilibrium flow
• 2D
• DP gt 0
• UU(x,y)
• dU/dx lt 0

SJ
MP
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Favourable Pressure Gradient Boundary Layer

• Non-equilibrium flow
• 2D
• DP lt 0
• UU(x,y)
• dU/dx gt 0
• reaches a self-similar prolife

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Contraction/Expansion Flows

• Non-equilibrium flow
• 3D
• dV/dy cte
• dW/dz -cte

a 0
a ?/2
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Turbulence Models
Run with the wall function of Chieng and Launder
(1980)
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Results Fully Developed Channel Flow
General Conclusions

• All models predicted the log law reasonably
  well.
• All models predicted the shear Reynolds Stress
  reasonably well.
• The HJ and TC models best predicted the normal
  Reynolds stresses.

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Results Fully Developed Channel Flow
Re 6500
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Results Fully Developed Channel Flow
Re 6500
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Results Fully Developed Channel Flow
Re 41441
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Results Homogeneous Constant Shear Flow
General Conclusions

• Difficult prediction
• Overall, the SG and the KS model performed best
• The extreme shear values are more difficult to
  predict.

S20v2 S01.68
S10 S016.76
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Results Homogeneous Constant Shear Flow
S20v2 S01.68
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Results Homogeneous Constant Shear Flow
S20v2 S030.75
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Results Zero Pressure Gradient BL
General Conclusions

• The tested turbulence models have shown to be
  sensitive to the inlet conditions, implying bad
  predictions at low Req values.
• The normal Reynolds stresses were better
  predicted by the RST models, as expected.
• One can notice the importance of LRN models for
  the near wall region predictions.

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Results Zero Pressure Gradient BL
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Results Zero Pressure Gradient BL
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Results Adverse Pressure Gradient BL
General Conclusions
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Results Adverse Pressure Gradient BL
SJ
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Results Adverse Pressure Gradient BL
MP
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Results Adverse Pressure Gradient BL
MP
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Results Favourable Pressure Gradient BL
General Conclusions

• The turbulence model which overall better
  predicted these flows was the KS model, although
  it failed to predict the Reynolds stresses.
• The KS and LS models are the only ones expected
  to correctly predict the laminarization process,
  since they possess a term which accounts for the
  second derivative of the mean velocities.
• The RST models best predicted the normal
  Reynolds stresses, specially the TC and HJ models.

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Results Favourable Pressure Gradient BL
K1.5x10-6
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Results Favourable Pressure Gradient BL
K1.5x10-6
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Results Favourable Pressure Gradient BL
K2.5x10-6
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Results Favourable Pressure Gradient BL
K2.5x10-6
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Results Contraction/Expansion Flows
General Conclusions

• No turbulence model was able to correctly
  predict the interruption of the applied strains.
• Overall, the GL and the TC models provided the
  best predictions.
• The eddy viscosity formulations clearly failed
  to predict these flows.

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Results Contraction/Expansion Flows
TR
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Results Contraction/Expansion Flows
GM - a ?/2
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Conclusions

• The Channel flow, which is the simplest flow,
  was reasonably well predicted by all turbulence
  models as well as the ZPGBL cases at high Req
  values.
• The two not wall-bounded cases HCS flow and
  C/E flows were the most difficult to predict
  and the RST models performed better, showing the
  importance of calculating the Reynolds stresses
  through transport equations.
• The APGBL cases could not be well predicted by
  any model at high DP, however the FM model could
  match the U profile.
• The FPGBL cases were better predicted by the KS
  model which evidenced the importance of a
  velocity second derivative term to predict
  laminarization.

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Thank you