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  • Particles in a Periodic Double Shear Flow - Pre-Analysis & Start-Up

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Pre-Analysis & Start-Up

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In the Pre-Analysis & Start-Up step, we'll review the following:

  • Theory for Fluid Phase
  • Theory for Particle Phase
  • Choosing the Cases

Pre-Analysis:

A particle laden flow is a multiphase flow where one phase is the fluid and the other is dispersed particles. Governing equations for both phases are implemented in Fluent. To run a meaningful simulation, a review of the theory is necessary.

Fluid Phase:

In the simulations considered for this tutorial, the fluid flow is a 2D perturbed periodic double shear layer as described in the first section. The geometry is Lx = 59.15m, Ly = 59.15m, and the mesh size is chosen as

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in order to resolve the smallest vorticies. As a rule of thumb. One typically needs about 20 grid points across the shear layers, where the vorticies are going to develop. The boundary conditions are periodic in the x and y  directions. The fluid phase satisfies the Navier-Stokes Equations:
-Momentum Equations

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\begin

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\rho_f (\frac{d \textbf

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_f}

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+\textbf

_f \cdot \nabla \textbf

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_f + \textbf

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\end

 

-Continuity Equation

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\begin

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\frac

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+ \nabla \cdot (\rho \textbf

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_f)=0
\end

 

where

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$\textbf

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$

is the fluid velocity,

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the pressure,

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the fluid density and

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$\textbf

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$

is a momentum exchange term due to the presence of particles. When the particle volume fraction and the particle mass loading

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are very small, it is legitimate to neglect the effects of the particles on the fluid:

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$\textbf

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$

can be set to zero. This type of coupling is called one-way. In these simulations the fluid phase is air, while the dispersed phase is constituted of about 400 glass beads of diameter a few dozens of micron. This satises both conditions

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and

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One way-coupling is legitimate here. See ANSYS documentation (16.2) for further details about the momentum exchange term.

Particle Phase:

 

The suspended particles are considered as rigid spheres of same diameter d, and density

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. Newton's second law written for the particle i stipulates:

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$m_p \frac{d \textbf

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_p^i}

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$

where uip is the velocity of particle i, Fiex the forces exerted on it, and mp its mass.
In order to know accurately the hydrodynamic forces exerted on a particle one needs to resolve the flow to a scale significantly smaller than the particle diameter. This is computationnaly pro- hibitive. Instead, the hydrodynamic forces can be approximated roughly to be proportional to the drift velocity:
d u ip = v − u ip dt τp
where τp = XX is known as the particle response time. This equation needs to be solved for all particles present in the domain. This is done in Fluent via the module: Discrete phase ?.

 

Expected Results

Under Construction


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