15.12.5 Under-Relaxation of the Interphase Exchange Terms

Note that the interphase exchange of momentum, heat, and mass is under-relaxed during the calculation, so that

where $\alpha$ is the under-relaxation factor for particles/droplets. The default value for $\alpha$ is 0.5. This value may be reduced to improve the stability of coupled calculations. Note that the value of $\alpha$ does not influence the predictions obtained in the final converged solution.

Two options exist when updating the new particle source terms $F_{\rm new}$, $Q_{\rm new}$ and $M_{\rm new}$. The first option is to compute the new source terms and the particle source terms, $F_{\rm calculated}$, $Q_{\rm calculated}$ and $M_{\rm calculated}$, at the same time. The second option is to update the new source terms, $F_{\rm new}$, $Q_{\rm new}$ and $M_{\rm new}$, every flow iteration, while the particle source terms, $F_{\rm calculated}$, $Q_{\rm calculated}$ and $M_{\rm calculated}$, are calculated every Discrete Phase Model iteration. The latter option is recommended for transient flows, where the particles are updated once per flow time step.

Figure  15.12.2 shows how the source term, $S$, when applied to the flow equations, changes with the number of updates for varying under-relaxation factors. In Figure  15.12.2, $S_{\infty}$ is the final source term for which a value is reached after a certain number of updates and $S_0$ is the initial source term at the start of the computation. The value of $S_0$ is typically zero at the beginning of the calculation.

Figure 15.12.2: Effect of Number of Source Term Updates on Source Term Applied to Flow Equations

Figure  15.12.2 can be applied to this option as well. Keep in mind that the DPM source terms are updated every continuous flow iteration.