23.2.2 Steady/Transient Treatment of Particles

The Discrete Phase Model utilizes a Lagrangian approach to derive the equations for the underlying physics which are solved transiently. Transient numerical procedures in the Discrete Phase Model can be applied to resolve steady flow simulations as well as transient flows.

In the Discrete Phase Model dialog box you have the option of choosing whether you want to treat the particles in an unsteady or a steady fashion. This option can be chosen independent of the settings for the solver. Thus, you can perform steady state trajectory simulations even when selecting a transient solver for numerical reasons. You can also specify unsteady particle tracking when solving the steady continuous phase equations. This can be used to improve numerical stability for very large particle source terms or simply for postprocessing purposes. Whenever you enable a breakup or collision model to simulate sprays, the Unsteady Particle Tracking will be switched on automatically.

When Unsteady Particle Tracking is enabled, several new options appear. If steady state equations are solved for the continuous phase, you simply enter the Particle Time Step Size and the Number of Time Steps, thus tracking particles every time a DPM iteration is conducted. When you increase the Number of Time Steps, the droplets penetrate the domain faster.

When solving unsteady equations for the continuous phase, you must decide whether you want to use Fluid Flow Time Step to inject the particles, or whether you prefer a Particle Time Step Size independent of the Fluid Flow Time Step. With the latter option, you can use the Discrete Phase Model in combination with changes in the time step for the continuous equations, as it is done when using adaptive flow time stepping.

If you do not use Fluid Flow Time Step, you will need to decide when to inject the particles for a new time step. You can either Inject Particles at Particle Time Step or at the Fluid Flow Time Step. In any case, the particles will always be tracked in such a way that they coincide with the flow time of the continuous flow solver.

You can use a user-defined function ( DEFINE_DPM_TIMESTEP) to change the time step for DPM particle tracking. The time step can be prescribed for special applications where a certain time step is needed. For more information about changing the time step size for DPM particle tracking, see this section in the separate UDF Manual.

When the density-based solver is used with the explicit unsteady formulation, the particles are advanced once per time step and are calculated at the start of the time step (before the flow is updated).

Additional inputs are required for each injection in the Set Injection Properties dialog box, as detailed in Section  23.3.15. For Unsteady Particle Tracking, the injection Start Time and Stop Time must be specified under Point Properties. Injections with start and stop times set to zero will be injected only at the start of the calculation ( $t=0$). If the In-Cylinder mesh motion is enabled, the start and stop times are replaced by Start Crank Angle and Stop Crank Angle, respectively. The injection specified in this way will be repeated at the starting and stopping crank angle if the simulation is run through more than one cycle. Changing injection settings during a transient simulation will not affect particles currently released in the domain. At any point during a simulation, you can clear particles that are currently in the domain by clicking the Clear Particles button in the Discrete Phase Model dialog box.

For transient simulations, several methods can be chosen to control when the particles are advanced.

• If the Number of Continuous Phase Iterations per DPM Iteration is less than the number of iterations required to converge the continuous phase between time steps, then sub-iterations are done. Here, particles are tracked to their new positions during a time step and DPM sources are updated; particles are then returned to their original state at the beginning of the time step. At the end of the time step, particles are advanced to their new positions based on the continuous-phase solution.

• If the Number of Continuous Phase Iterations per DPM Iteration is larger than the number of iterations specified to converge the continuous phase between time steps, the particles are advanced at the beginning of the time step to compute the particle source terms.

• When you specify a value of zero as the Number of Continuous Phase Iterations per DPM Iteration, the particles are advanced at the end of the time step. For this option, it may be better if the particle source terms are not reset at the beginning of the time step. This can be done with the TUI command define/models/dpm/interaction/reset-sources-at-timestep?.

In all the above cases, you must provide a sufficient number of particle source term updates to better control when the particles are advanced, see Figure  23.6.3.

In steady-state discrete phase modeling, particles do not interact with each other and are tracked one at a time in the domain.

If the collision model is used, you will not be able to set the Number of Continuous Phase Iterations per DPM Iteration. Refer to this section in the separate Theory Guide for details about this limitation.