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 ErosionCan I use MRF in a Lagrangian particle erosion simulation?STAR-CCM+ Documentation sections:
Theory > Lagrangian Multiphase Flow > ErosionSimulating Physics > Multiphase Flow > Using the Lagrangian Multiphase Model > Lagrangian Phase Models > Erosion ModelTechnical Forum:
Technical Forum Multiphase Group