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

2023-11-02T04:10:22.000-0400
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## Summary

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

## Details

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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.
\$\$RateOfChangeOfMomentum = delta(\$ParcelMassFlowRate*\$\$ParticleVelocity)
\$\$RateOfChangeOfMomentum = delta(\$ParcelMass*\$\$ParticleVelocity/\$TimeStep)
where delta() is the change during the impingement.

\$ErosionRate = sum(\$ParcelMassFlowRate*\$ErosionRatio)/mag(\$\$Area)
\$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.

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

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