Numerical simulation of particleladen channel flow

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Numerical simulation of particle-laden channel
flow
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Hans Kuerten
Department of Mechanical Engineering Technische
Universiteit Eindhoven
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Contents

• DNS of particle-laden flow
• Large-eddy simulation (LES)
• LES of particle-laden flow
• Reynolds-averaged Navier-Stokes
• Conclusions

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1. DNS of particle-laden flow

• Turbulent channel flow
• Particles
• Only drag force
• Elastic collisions with walls

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• Spectral method Fourier-Chebyshev
• 128 x 129 x 128 points
• Second-order accurate time integration
• Fourth-order interpolation for fluid velocity
  at particle position

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Wall concentration
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Explanation for turbophoresis
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Comparison with expansion
St1
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2. Large-eddy Simulation

• Filter with typical size D
• Top-hat filter

D
1/D
x
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Effect on energy spectrum
0
10
DNS
E
-5
10
-10
10
0
1
2
10
10
10
k
z
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Effect on velocity fluctuations
y
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A priori simulations

• Filter fluid velocity as calculated in DNS with
  top-hat filter.
• Solve particle equation of motion with filtered
  fluid velocity

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Effect on turbophoresis
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St1
St5
15
St25
10
5
1
2
3
4
10
10
10
10
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3. Real LES of particle-laden flow

• Subgrid model in Navier-Stokes
• Smagorinsky eddy viscosity
• Dynamic eddy viscosity
• LES grid 32 x 33 x 64

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Subgrid model in particle equation

• Retrieve unfiltered velocity from filtered
• Only possible for scales present in LES grid

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LES velocity fluctuations
y
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Wall concentration
St5
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Concentration in steady state (St5)
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Dispersion (St25)
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Linear velocity interpolation
St5
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Linear velocity interpolation
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First conclusions

• Dynamic model performs better than Smagorinsky.
• Linear interpolation is inaccurate.
• Inverse filtering improves results of dynamic
  model.
• Still discrepancy with DNS results
• A priori results do not agree well with LES.
• Inverse filter is arbitrary.

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Approximate Deconvolution Model (Stolz et al.,
2001)

• Approximate unfiltered velocity in LES
• Add relaxation term for dissipation.
• Deconvolution also in particle equation.

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Dispersion (St25)
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Concentration (St5)
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Drift velocity (St1)
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High Reynolds number simulations

• No DNS of particle-laden flow.
• DNS data of channel flow is available (Moser, Kim
  Mansour) at Re590.
• Particle velocity rms should be close to fluid
  velocity rms at low Stokes number.

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Dispersion (Re590, St1)
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4. Reynolds-averaged Navier-Stokes

• Often used in CFD packages
• Only mean velocity is known and some information
  about turbulence

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• k-e model
• k and e are known
• isotropic

• Reynolds-stress model
• all Reynolds stresses and e are known
• anisotropic

• For both models
• w is constant during time interval
• eddy-turnover time, teck/ e
• crossing trajectories, tc depends on tp

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Results

• a priori obtain RANS quantities from DNS
• a posteriori real RANS simulations performed
  with fluent on fine grid
• same test case as in DNS and LES

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Velocity fluctuations (St1)
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Velocity fluctuations (St1)
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Particle concentration (St1)
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5. Conclusions (LES)

• A priori turbophoresis is changed if eqs of
  motion are solved with .
• Real LES confirms this.
• Inverse filtering improves results.
• Similar results for particle dispersion.
• Inverse ADM gives best results for concentration
  and dispersion.
• Also applicable at higher Reynolds number.

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Conclusions (cont.)

• Linear interpolation of fluid velocity is
  inaccurate.
• Smagorinsky model is inaccurate.
• Inverse filtering hardly improves Smagorinsky
  results.

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Conclusions (RANS)

• Reynolds-stress model gives accurate results for
  particle dispersion if stress tensor is
  accurately predicted.
• k-e model is not accurate because of isotropy of
  velocity fluctuations.
• Turbophoresis is not well predicted since
  preferential concentration cannot be taken into
  account.