### 8.10.2. Particle Under-Relaxation Factors

This parameter applies only to fully-coupled particle phases. Depending on the flow being solved, particles may introduce very large source terms in the hydrodynamic equations. In reacting flows, large source terms may be generated in the mass, scalar, and energy equations. In heavily laden flows, viscous drag may introduce large source terms in the momentum equations.

In some cases, these source terms may have a destabilizing influence on the convergence of the hydrodynamic equations, resulting in oscillations, or in severe cases, divergence. A simple example of the oscillatory behavior is in a reacting flow field containing burning solid particles. Consider the flow field contains an oxidant into which reacting particles are being injected. If there is sufficient particle mass to consume all of the oxidant, then the oxidant mass fraction approaches zero. The next time the particles are injected, there would be no oxidant, and therefore, no source terms would be generated. The oxidant concentration would return to its original value. Therefore, the oxidant concentration may oscillate between zero and its maximum.

It is possible to minimize the oscillations by under-relaxing the particle source terms. This is done as follows:

| (8–4)

where:

#### 8.10.2.1. Under-Relaxation Factor for Velocity, Energy, and Mass

In ANSYS CFX, particle source terms are generated for the momentum, heat and mass transfer equations. The Under-Relaxation factors for velocity, energy, and mass provide damping for the above equation set. In a steady-state calculation, the default value of `0.75` has been found to be sufficiently small to dampen solutions demonstrating oscillating convergence behavior due to particle sources. In a transient calculation, no under-relaxation is imposed, that is the default values of the under-relaxation factors are `1.0`. If convergence problems are found due to the particle transport coupling, this relaxation factor can be reduced. For details, see Convergence Control for Particle Transport.

#### 8.10.2.2. Under-Relaxation Factor for First Particle Integration

This relaxation factor is applied to particles sources into the fluid phase, if no old particle sources exist. By default, this factor is set to `0.75` for steady-state runs and `1.0` for transient runs.

#### 8.10.2.3. Under-Relaxation at Time Step Start

By default, no relaxation is applied to particle sources between time steps in a transient simulation. If convergence problems are found due to the particle transport coupling, this relaxation factor can be reduced.

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