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

2

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

3

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 (⇥).

19

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

4

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

5

❖ 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.

6

References on the CFD-DEM Applications

Background

7

Hierarchy of Numerical Models for Particle-Laden Flows

8

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.

9

Details of DEM (Particle-Resolving Model)

❖ Particle-particle interaction models: soft sphere model with collision forces, lubrication, force, buoyancy etc.

10

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

11

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

12

❖ Averaging (coarse graining): converting information from discrete Lagrangian particles to continuum Eulerian field.

Bridging Continuum and Discrete Scales

13

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

14

Challenges in CFD-DEM for Sediment Transport

15

CFD—DEM for sediment transport

CFD—DEM in fluidized bed/liquefaction

16

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.

17

❖ In CFD—DEM applications, the size of CFD mesh is usually much larger than the size of particles.

Unique challenge in modeling sediment transport

18

❖ 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

19

❖ 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

20

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.

21

Methodology—averaging@"s@⌧

= r2"s for x 2 ⌦, ⌧ > 0

"s(x, ⌧ = 0) = "0(x)

@"s@n

= 0 on @⌦

22

equivalent to Gaussian kernel

Methodology—averaging

easy for parallelization

easy for boundary treatment23

Sun & Xiao, IJFM (2015a)

24

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.

25

26

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

27

Test 1: Mesh Convergence

deviation in flowvelocity profiles

Resolve the flow at the boundary is important!

28

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

30

Test 2: Dune Generation

31

flow velocity

Comparison with Experimental Data

32

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

37

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

38

Test Case 4: Wave-Induced Sheet Flow

Validation: fluid velocity

39

Validation: Sediment Flux

40

Test 4: Results

41

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

42

Maximum sediment flux

Zero sediment flux

Micromechanics: Force Network

43

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

2

Test 5: Cutting Transport in Drilling Pipe

45

Drilling bit

Ground

Test 5: Cuttings Transport: Irregular Particles

46

Parallel efficiency test

CFD cells: 13 million.particles: 10 million.

47

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.

48