using particle-resolved simulations to ... - wuhan university
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Using Particle-Resolved Simulations to Probe the Physics in Sediment Transport
Heng XiaoAssistant Professor
Aerospace & Ocean Engineering, Virginia Tech
武汉⼤学,2017年12月25日
基于离散元的泥沙输运模拟研究
肖恒弗吉尼亚理⼯⼤学航空与海洋⼯程系
Acknowledgement
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孙瑞博⼠ @Virginia Tech 2013—2017 Postdoc @ Scripps Institute of Oceanography, UCSD
Current Research Interests❖ Model-form uncertainty in
turbulent flow simulations
❖ Bayesian inference; machine learning.
❖ Dense particle-laden flows, sediment transport
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observations
samples sample mean baseline
DNS (Breuer et al. 2009)
(a) Prior velocities ensemble
(b) Posterior velocities ensemble
Figure 5: The prior and posterior ensembles of velocity profile for the flow over periodic hill
at eight locations x/H = 1, · · · , 8 compared with benchmark data and baseline results. The
locations where velocities are observed are indicated with crosses (⇥).
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training with machine learning
algorithms
prediction withML-assisted RANS simulation
separated flows
attached boundary layers
(a) training: DNS data ofelementary flows
free shear flows
(c) prediction: complex, realistic flows
(b) trained discrepancy functions
(e.g., random forests, or neural network)
data: features qresponses corrections to
RANS Reynolds stress
query: feature q'
other flow categories ... ...
q'Tree T
q'
S1 S2 S3
BL1 BL2BL3
FS1 FS2 FS3
training with machine learning
algorithms
prediction withML-assisted RANS simulation
separated flows
attached boundary layers
(a) training: DNS data ofelementary flows
free shear flows
(c) prediction: complex, realistic flows
(b) trained discrepancy functions
(e.g., random forests, or neural network)
data: features qresponses corrections to
RANS Reynolds stress
query: feature q'
other flow categories ... ...
q'Tree T
q'
S1 S2 S3
BL1 BL2BL3
FS1 FS2 FS3
Further Details
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More detailed results can be found in the manuscripts listed below, available from my webpage.
http://www.aoe.vt.edu/people/faculty/hengxiao.html
Software is made open-source at:
https://github.com/xiaoh/sediFoam
References on the CFD-DEM Solver
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❖ R. Sun and H. Xiao. SediFoam: A general-purpose, open-source CFD-DEM solver for particle-laden flows with emphasis on sediment transport. Computers and Geosciences, 89, 207-219, 2016.
❖ R. Sun and H. Xiao. Diffusion-Based Coarse Graining in Hybrid Continuum–Discrete Solvers: Theoretical Formulation and A Priori Tests. International Journal of Multiphase Flow, 77, 142-157, 2015.
❖ R. Sun and H. Xiao. Diffusion-Based Coarse Graining in Hybrid Continuum–Discrete Solvers: Applications in CFD–DEM. International Journal of Multiphase Flow, 72, 233-247, 2015.
❖ H. Xiao and J. Sun. Algorithms in a robust hybrid CFD–DEM solver for particle-laden flows. Communications in Computational Physics, 9(2), 297-323, 2011.
❖ R. Sun, H. Xiao, H. Sun (2017). Realistic representation of grain shapes in CFD--DEM simulations of sediment transport: A bonded-sphere approach. Advances in Water Resources, 07, 421-438.
❖ R. Sun, H. Xiao, H. Sun (2018). Investigating the settling dynamics of cohesive silt particles with particle-resolving simulations. Advances in Water Resources. 111, 406-422.
❖ R. Sun and H. Xiao (2016). Sediment micromechanics in sheet flows induced by asymmetric waves: A CFD-DEM study. Computers and Geosciences, 96, 35-46.
❖ R. Sun and H. Xiao (2016). CFD-DEM simulations of current-induced dune formation and morphological evolution. Advances in Water Resources, 92, 228-239.
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References on the CFD-DEM Applications
Background
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Hierarchy of Numerical Models for Particle-Laden Flows
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Interface-Resolved Particle-Resolved Two-fluid model
1000 1,000,000
Capabilities of Each Model Category❖ Interface-resolving model: very few particles; study
drag models. ~1 cm scale.
❖ Particle Resolving models: can study small-scale bed-form; requires drag model etc. 1 m scale.
❖ Two fluid model: need particle-phase constitutive model to account for collisions. Tens of meter scale.
❖ Morphological models: km scale, e.g., Delft3D.
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Details of DEM (Particle-Resolving Model)
❖ Particle-particle interaction models: soft sphere model with collision forces, lubrication, force, buoyancy etc.
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other fluid forces, e.g.,drag, lift, buoyancy
collision forces
liquid squeezed outparticles approachingeach others
lubricationforces
(b1)
(b2)
(b3)
particle-to-fluid interaction forces
(a)
(c)
(b)
❖ Equations of fluid motion:
fluid volume fraction
interaction force
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particle centroid method (PCM)
"f,k = 1� "s,k
"s,k =
Pnp,k
i=1 Vp,i
Vc,k
r · ("sUs + "fUf ) = 0
@ ("fUf )
@t+r · ("fUfUf ) =1
⇢f
��rp+r ·R+ "f⇢fg + Ffp
�
Details of DEM (Particle-Resolving Model)
Methodology—Numerical Model❖ Equations of particle motion:
mkdui,k
dt= f col
i,k + ffpi,k +mkgi
Soft-sphere model: particle collisions modeled as spring-dashpot model in both normal and tangential directions
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❖ Averaging (coarse graining): converting information from discrete Lagrangian particles to continuum Eulerian field.
Bridging Continuum and Discrete Scales
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particle centroid method (PCM)
"s,k =
Pnp,k
i=1 Vp,i
Vc,ksolid volume
fraction
Implementation Details❖ CFD solver: OpenFOAM (OpenCFD)
❖ DEM solver: LAMMPS (Sandia National Laboratories)
❖ Coupling of the two solvers, including particle-fluid interaction forces, data exchange, averaging algorithm are implemented based on OpenFOAM.
❖ Code is open-source. Available at: https://github.com/xiaoh/sediFoam
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Challenges in CFD-DEM for Sediment Transport
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CFD—DEM for sediment transport
CFD—DEM in fluidized bed/liquefaction
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CFD—DEM in seepage flow in geotechnical engineering
Unique Challenges in CFD-DEM for Sediment Transport
❖ Most of the critical phenomena occur in the boundary layer. Must resolve the boundary layer adequately!
❖ This lead to stringent requirements on the mesh resolution: cell size can be comparable to particle size.
❖ Lubrication, added mass, lift force are important. The carrier (water) has comparable density as the dispersed phase.
❖ Accounting for these forces can make numerical simulations unstable.
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❖ In CFD—DEM applications, the size of CFD mesh is usually much larger than the size of particles.
Unique challenge in modeling sediment transport
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❖ Limitations when using coarse mesh: not adequate to resolve the fluid flow at the boundary layer
Fluid flow not resolved!
❖ Challenge: find the averaged Lagrangian particle information (e.g., particle volume fraction εs, velocity Us, fluid-particle interaction force Ffp) when using fine mesh to resolve fluid flow.
Unique challenge in modeling sediment transport
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❖ Averaging (coarse graining): converting information from discrete Lagrangian particles to continuum Eulerian field.
Challenges in Resolving Boundary Layer
new averaging method
(diffusion-based)
CFD mesh at the boundary
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particle centroid method (PCM)
"s,k =
Pnp,k
i=1 Vp,i
Vc,k
Diffusion-based averaging algorithm❖ The diffusion-based averaging algorithm solved the
problem to convert Lagrangian particle data to Eulerian field, and it has several advantages:
❖ 1. Theoretically rigorous (equivalent with Gaussian-kernel).
❖ 2. Easy to implement.
❖ 3. Easy to use for arbitrary mesh shape.
❖ 4. Easy for parallelization and boundary treatment.
❖ 5. Do not increase computational cost significantly.
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Methodology—averaging@"s@⌧
= r2"s for x 2 ⌦, ⌧ > 0
"s(x, ⌧ = 0) = "0(x)
@"s@n
= 0 on @⌦
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equivalent to Gaussian kernel
Methodology—averaging
easy for parallelization
easy for boundary treatment23
Sun & Xiao, IJFM (2015a)
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Regimes of Sediment TransportFlat bed in motion:
Re < 500; Ga(hf/dp)2 < 2000.
Small dune:100 < Re < 1000;
103 < Ga(hf/dp)2 < 2×104.
Vortex dune:800 < Re < 104;
104 < Ga(hf/dp)2 < 106.
Flat bed with suspended sediment transport
Objective of This Research
❖ Show the capability of CFD-DEM to simulate sediment transport in a wide range of regimes.
❖ Should not specify a prior the regime!
❖ The regime should emerge as simulation results.
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Mesh resolution 16 x 16 x 8
Domain size (m) 32dp x 32dp x 16dp
Number of particles 9341
Reynolds number 300
Galileo number 8.5
Fluid viscosity (m2/s) 5.0E-06
Fluid density (kg/m3) 1000
Particle diameter (mm) 0.5
Particle density (kg/m3) 2500
The mesh resolution and domain size are in streamwise direction, vertical direction, and
lateral direction, respectively.
flow velocity
Test 1: Flat Bed in Motion
Test 1: Results
sediment transport rate height of movable bed
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Test 1: Mesh Convergence
deviation in flowvelocity profiles
Resolve the flow at the boundary is important!
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deviation in sediment transport rate
Test 1: results
fluid height
The feature of the flow is consistent with Poiseuille flow.29
flow velocity profiles
interface at -2.5
Test 2: Generation of DunesDune type Vortex dune
Mesh resolution 120 x 160 x 60Domain size (m) 311dp x 38.4dp x 80dp
Number of particles 263,000Reynolds number 6000Galileo number 30
Fluid viscosity (m2/s) 1.5E-06Fluid density (kg/m3) 1000
Particle diameter (mm) 0.5Particle density (kg/m3) 2500
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Test 2: Dune Generation
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flow velocity
Comparison with Experimental Data
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Vortex dune
CFD—DEM experiment interfaced-resolved model
Dune height 7 dp 4~8 dp 5 dp
Wave length 162 dp ~150 dp 156 dp
Migration velocity 0.015 Ub 0.01~0.03 Ub 0.026 Ub
vortex dune
CFD—DEM
experiment
Space-Time Evolution of Dunes
small dune vortex dune
tub/H
x/dp x/dp
tub/H
The CFD—DEM model is capable of predicting the generation and migration of dunes.33
Test 3: Suspended Sediment Transport
Test 3: Suspended Sediment Transport
Mesh resolution 140 (streamwise) x 65 (vertical) x 60 (lateral)
Domain size (m) 240dp (streamwise) x 80dp (vertical) x 120dp (lateral)
Number of particles 330,000
Reynolds number 36000~50000
Fluid viscosity (m^2/s) 1.0E-06
Fluid density (kg/m^3) 1000
Particle diameter (mm) 0.5
Particle density (kg/m^3) 2500
Suspended Sediment Transport
sediment transport rate coefficient of friction
Test Case 4: Wave-Induced Sheet Flow
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Mesh resolution 80 (streamwise) x 120 (vertical) x 40 (lateral)
Domain size 139dp (streamwize) x 278dp (vertical) x 80dp (lateral)
Particle diameter 0.27 mm
Number of particles 256000
Velocity -0.9~1.3 m/s
Period 5 s
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Test Case 4: Wave-Induced Sheet Flow
Validation: fluid velocity
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Validation: Sediment Flux
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Test 4: Results
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Sediment transport rate
The motion of the sediment particles predicted by the CFD—DEM model, is consistent with the experimental
measurements.
Movable bed height
Micromechanics: Volume Fraction
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Maximum sediment flux
Zero sediment flux
Micromechanics: Force Network
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Test 5: Cuttings Transport in Drilling Pipes
44Figure 1: Directions of fluid flow (drag) and particle settling (gravity) for (a) vertical wells and (b) deviated(i.e., horizontal or highly inclined) wells.
correlations obtained from experiments often give satisfactory results [e.g., 8–10]. For deviated
wells (particularly those with inclination angle between 30�and 60�), however, the performances
of empirical correlations are much less satisfactory. Due to the complex physics, the critical ve-
locity depends nonlinearly on a large group of parameters. More variables enter the correlation,
and different mechanisms dominate in different inclination angles. Consequently, formulating an
empirical relation valid in a wide operation range covering several flow regimes becomes more
challenging. Techniques such as pipe rotation [e.g., 11–15] which further increases the difficulty
of the prediction and modeling efforts.
Currently two approaches are used to predict critical velocities: empirical approach and mech-
anistic approach. In the empirical approach, the critical velocity is estimated from formulas ob-
tained from dimensional analysis and experiments. Commonly used empirical models for cuttings
transport in deviated wells include those of Larsen et al. [16], Peden and co-workers [17], and
Rubiandini [18], among others. However, a comparative study by Ranjbar [19] found that differ-
ent models often give predictions with significant discrepancies, even for the experimental case
examined in the original publication based on which the model was derived. This is not surprising
because of the highly complicated processes and large number of parameters involved (the curse
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Test 5: Cutting Transport in Drilling Pipe
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Drilling bit
Ground
Test 5: Cuttings Transport: Irregular Particles
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Parallel efficiency test
CFD cells: 13 million.particles: 10 million.
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Conclusions❖ 1. CFD—DEM model is adequate in the numerical
simulation of various sediment transport problems.
❖ 2. The diffusion-based coarse graining algorithm is crucial in the CFD—DEM simulation of sediment transport.
❖ 3. The CFD—DEM model has good parallel efficiency for large and complex problems.
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