cui force calculation

8/13/2019 Cui Force Calculation

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Martin-Luther-UniversittHalle-Wittenberg

Force calculation when particle nearcontact using lattice Boltzmann method

M.Sc. Yan Cui

Prof. Martin Sommerfeld


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Outline

Project description

Lattice Boltzmann Method

Particle near contact Force calculation

Separate scheme

Cut-back method

Lubrication force

Validations Numerical-Numerical

Numerical-Experiment

Simulation of my project

Grid resolution

Plug flow

Shear flow

Particle rotation under plug & shear flow

What will do next?


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Introduction to dry powder inhalator

Nowadays different drugs are appliedthough inhalation.

The drugs are in form of fine liquiddroplets or solid particles(powders).

The size of the particles needs to berather smallin order to ensure thatthey are transported up to the alveoliof the lung.

One solution: coating of larger carrierparticles with the fine agent particles.

Adhesion forcebetween large andsmall particles can be adjusted bysurface treatment.

Using LBMfor analyze the detachmentof the agent particles.


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Sketch map of detachment

dispersion


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Objectives of the simulations

Application of a high resolution Lattice-

Boltzmann-Method with multi-level grid

refinement

Determination of the fluid dynamic forces acting

on small agent particles (~ 5 m) attached to the

surface of a larger carrier particle (~ 100 m)

Identification of the detachment of agent particlesin dependence of adhesion forces, flow conditions and

location on the surface

Different flow conditions for fixed carrier particle:

laminar and turbulent plug flow and shear flow

Homogeneous isotropic turbulence

Determination of the maximum adhesion force

to guaranty agent particle detachment

Flow conditions

similar to those

expected in an

inhaler

Results used for defined

surface modification


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Lattice Boltzmann Method

The Lattice-Boltzmann-Method simulates the motion of a fluid on a microscopic levelsolving the discretised distribution function f(x, v, t), describing the number of fluid

elements at a given location and time having the velocity v.

macroscopic flow system

Discretised Lattice-Boltzmann-Equation (single relaxation time, BGK):

),(),(),(),( )0( txftxfttxftttvxf iiiii

Collision termPropagation term

0

2

2

2

2

2

2

2

2

2

2

1

1

1

1

1

Discrete velocity directions in the D3Q19-model

Bounce-back boundary

condition for curved walls

Momentum exchange yields

forces on the particle

equilibrium Maxwell distribution)t,x(f )0(i


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Particle force calculation

Particle force = Force(fluid nodes near particle surface)

Solid nodes

Fluid nodes

Fluid nodes near particle surface


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Separate scheme

When two particles are near contactless than one grid spacing, the codeitself will recognize two particles as

one particle. Because there are notenough fluid nodes surround oneach particle.

One solution: not only accumulatingthe fluid nodes near particle surface,

but also accumulates those solidnodes near another particle surface.

Defect: those solid nodes do nothave any fluid property, during theaccumulation, those nodes will

become a vacuum which may causetremendous force.


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Separate scheme

A modified approach: we give thosesolid nodes near another particlesurface the equivalent equilibrium

equations, and set the velocityconstant(equal to the particlevelocity).

After that, the very large forcedisappeared, we can get a more

reasonable force for each particle.

Is it enough?

Solid nodes near another particle surface

Fluid nodes near particle surfaceFluid nodes

Solid nodes


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Surfaces near contact

N.-Q. Nguyen and A. J. C. Ladd in 2002 [1] find that whentwo particle surfaces come within one grid spacing, fluidnodes are excluded from regions between the solid surfaces,

leading to a loss of mass conservation.

=

= 0

Although the sums and are zero for any

closed surface, when two particles are close to contact some

of the boundary nodes are missing and the surfaces are nolonger closed. In this case 0and mass conservation isno longer ensured.

If the two particles move as a rigid body, mass conservationis restored. But for soft matter systems, the leak of mass

conservation should be taken into consideration. Solution: Enforce mass conservation, particle-by-particle, by

redistributing the excess mass among the boundary nodes.[1] N.-Q. Nguyen and A. J. C. Ladd, Lubrication corrections for lattice-Boltzmannsimulations of particle suspensions, Physical Review, E 66, 046708 (2002).


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Cut-back-method

Later Burkhard Dnweg and A. J. C. Ladd [2] write that analternative idea is to ensure that there is always at least onefluid node in the gap between the particle surfaces.

E-Jiang Ding and Cyrus K.Aidun in 2003 [3] introduce a cutback method for dealing with particle near contact. They turnthe blue nodes (solid nodes) into fluid nodes, so the shape ofparticle is maintained by the red line.

[2] B. Dnweg and A. J. C. Ladd, Lattice Boltzmann simulations of soft matter systems,Advances in Polymer Science, 221:89-166 (2009).

[3] E-Jiang Ding and Cyrus K. Aidum, Extension of the lattice-Boltzmann method for directsimulation of suspended particles near contact, J.S.P, Vol. 112, Nos. 314 (2003).


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Modified cut-back-method

An modified approach is:

Cut only one particle, retain the full geometry of the other one.

For the cut-particle, we use an extrapolation bounce back

boundary condition to give back some part of the geometry.

Firstly, turn those blue nodes into fluid nodes. Secondly, measure the distance between the green nodes

and the original surface, set it as q (0 1 grid spacing).

Thirdly, travel to the reversed direction, and only travel 1-q

grid spacing, so now the geometry should be on the yellowline


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Numerical-numerical validation

Robyn Larsen, Dmitry Eskin, Jos Derksen, Liftand drag onagglomerates attached to walls,ICMF 2010.

In the first part of this paper, they study the lift and dragforce acting on the particle attached to the wall, with theshear flow and the immersed boundary condition in LBM.

We use the variable-distance-bounce-back boundarycondition, so its a good validation between these twonumerical methods.

Immersed boundary LBM:

Treat the boundary as deformable with high stiffness.

Small distortion yield a force to restore the boundary intooriginal shape.

The body force term is used to mimic the presence of boundary.


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Problem definition

Variable to get: dimensionless lift and drag force.

Changed variable: domain size, length, width and

height(comparable to the diameter of particle). Fixed Re number: 0.012.

Analytical solution of Leighton & Acrivos: L*=9.22, F*=32.1.

PE

R

I

O

D

I

C

Moving Wall

Non-Slip

PE

R

I

O

D

I

C


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Results


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Numerical-Experiment validation

Stationary particle in a wall-bounded linear shear flow.

The problem of lift force on a particle sitting on the wall in aboundary layer has been considered experimentally.

Hall and Mollinger and Nieuwstadt measured lift force on asmall stationary particle in contact with the wall. In all casesconsidered the particle was sufficiently small to be entirely inthe viscous sublayer of the turbulent boundary layer. Owingto turbulence, the lift force was fluctuating in time and they

obtained time-averaged lift coefficient

for varying particle size.

Later Muthanna obtained lift force on

a stationary spherical particle attached

to a wall in a laminar linear shear flow. The present results for the stationary

particle touching the wall in a linear

shear flow can be compared with these experimental results.


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Simulation-Experiment validation

In the beginning, I introduce non-dimensional lift force, +,

and particle radius, +, as follows:

+ =

+ =

, is the shear velocity

Initial condition:

Two-level-grid-refinement

20 cells along the particle diameter


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i l i i lid i


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Simulation-Experiment validation

The lift coefficients obtained by Hall and Mollinger areconsiderably higher than those obtained in our simulation.

It should be noted that the measurements of Hall and

Mollinger are for a particle sitting on a wall in a turbulentboundary layer. Nevertheless the orders of magnitude higherlift force measured in their experiments cannot be explainedby the present simulations.

Experiments of Muthanna in a linear shear flow are more

relevant to the present simulations. Their lift coefficients areconsiderably smaller than those measured in a turbulentboundary layer, but they are still larger than the computedlift coefficient. As pointed out by these authors, accuratemeasurement of lift force on small particles in wall-bounded

flows is a challenging problem.


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G id l ti


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Grid resolution

Change the grid resolution on the agent particles => 6 gridspacing along the diameter

G id l ti


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Grid resolution

Change the domain length x => 60 grid spacing

G id l ti


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Grid resolution

Change the domain length y/z => 50 grid spacing

G id l ti


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Grid resolution

Pa amete st d


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Parameter study

Force vector (plug flow)


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Force vector (plug flow)

Plug flow


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Plug flow

Plug flow


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Plug flow

Plug flow


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Plug flow

Plug flow


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Plug flow

Plug flow


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Plug flow

Plug flow


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Comparing different Re:

Plug flow

Plug flow


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Comparing different size of agent particles:

Plug flow

Diameter_of_Agent_Particle => Feffect. Because 1 N

= 1 kgm/s^2, the force is relate to the mass of particles.

Plug flow


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Comparing different coverage rate:

Plug flow

Plug flow


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Comparing different coverage rate:

Plug flow

Coverage_Rate => Band_of_Feffect. This is because of the

gap between agent particles. If the gap is too large, the flowdisturbance between particles will increase; if the gap is tiny, the

flow will mostly influence on the top of agent particles, but less

impact in the gap, because there are less space for the flow.

Force vector (shear flow)


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Force vector (shear flow)

Shear flow


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Shear flow

Shear flow in 3D and its projection on

Feffect-x and Feffect-z:

Shear flow


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Shear flow

Shear flow in Feffect-x projection:

Shear flow


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Shear flow

Comparing plug flow and shear flow in

Feffect-x projection(same Re):

Shear flow


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Shear flow

Shear flow in Feffect-z projection:

Shear flow


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Shear flow

Comparing different Re with shear flow in

Feffect-z projection:

Shear flow


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Shear flow

Comparing different Re of Shear flow 3D:

Particle rotation


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Particle rotation

1

2 3

4

8 5

7 6

1

2 3

4

Particle rotation


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Comparing different Re under

Rotation_Plug flow:

1

2 3

4

Particle rotation


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1

2 3

4

8 5

7 6

Rotation_Shear flow:

Particle rotation


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1

2 3

4

8 5

7 6

Comparing Rotation_Plug flow and

Rotation_Shear flow:

What will do next?


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Form of multi-layer agent particles

Problem: the form of agglomerate using the tree structure. Soevery particle has only one father. However, in multi-layer,

the particle from second layer may have 2 or 3 contact to thefirst layer particles, which means it has 2 or 3 fathers. This isnot allowed during modeling.

Turbulent effect

Theoretically in LBM, the velocity should be


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Thanks for attention!

cui force calculation

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