Simcenter STAR-CCM+ How to calculate the impingement pressure of Lagrangian particles on a wall

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The total force calculation comprises of discrete and continuous phase when the discrete phase is significant. The following...


The total force calculation comprises of discrete and continuous phase when the discrete phase is significant. The following steps describe a way to calculate the pressure exerted by the Lagrangian particles on wall.

The impingement pressure on a face is defined by:
$ImpingementPressure = sum(dot($$RateOfChangeOfMomentum, $$Area))/mag2($$Area)
where the sum() is over all parcels impinging on the given face.

There is no $$RateOfChangeOfMomentum field function, you must define it.
- In steady simulations,   
   $$RateOfChangeOfMomentum = delta($ParcelMassFlowRate*$$ParticleVelocity)
- In unsteady simulations,
   $$RateOfChangeOfMomentum = delta($ParcelMass*$$ParticleVelocity/$TimeStep)
where delta() is the change during the impingement. 
Comparing with the steady and unsteady expressions for erosion rate
- In steady simulations,   
$ErosionRate = sum($ParcelMassFlowRate*$ErosionRatio)/mag($$Area)
- In unsteady simulations,
$ErosionRate = sum($ParcelMass*$ErosionRatio/$TimeStep)/mag($$Area)
As the erosion rate is defined as the mass of wall material eroded per unit area per unit time (kg/(m2-s)*erosion ratio), you can see the analogy (we are using a similar equation but with different units).
 $ImpingementPressure <-> $ErosionRate
The erosion ratio is dimensionless and comes from built-in methods; to get the force units, a user field function for erosion ratio is created as below: 
$ErosionRatio = dot(delta($$ParticleVelocity), $$Area)/mag($$Area)
provided $ParcelMassFlowRate or $ParcelMass remain unchanged during the impingement.

The final question is how to calculate delta($$ParticleVelocity). You must write a user field function to define it. The $$ParticleVelocity upon which it is based is the incoming one. You must work out the outgoing one from it. For example, with pure elastic rebound you have:
$ErosionRatio = -2*dot($$ParticleVelocity, $$Area)/mag($$Area)

A track file and a simulation file, saved with STAR-CCM+ v8.04, are attached to this article to illustrate the above procedure.

See also :
Best Practices for Lagrangian Erosion
Can I use MRF in a Lagrangian particle erosion simulation?

STAR-CCM+ Documentation sections:
Theory > Lagrangian Multiphase Flow > Erosion
Simulating Physics > Multiphase Flow > Using the Lagrangian Multiphase Model > Lagrangian Phase Models > Erosion Model

Technical Forum:
Technical Forum Multiphase Group


KB Article ID# KB000034868_EN_US



Associated Components

Design Manager Electronics Cooling In-Cylinder (STAR-ICE) Job Manager Simcenter STAR-CCM+