Subgrid Transition Model Reference

The Subgrid Transition model allows you to identify very small Lagrangian parcels and transition them to an MMP phase. Mass, momentum, and energy are conserved in the transition. This model is meant to be used as part of a hybrid multiphase approach where the Mixture Multiphase (MMP) model is used alongside the Lagrangian Multiphase (LMP) model.

The Subgrid Transition model transitions small Lagrangian parcels such as aerosolized droplets (mists) to an MMP phase, thereby reducing computational expense. The transitioning from sub-grid size Lagrangian parcels to an MMP phase volume fraction is based on user-defined transition criteria. The Subgrid Transition model accumulates the volume, momentum, and energy of Lagrangian parcels that satisfy the transition criteria and transitions these properties to the MMP phase at each Lagrangian sub time-step.

表 1. Subgrid Transition Model Reference
Provided By	[phase interaction] > Models > Optional Models
Example Node Path	Continua > Physics 1 > Models > Multiphase Interaction > Phase Interactions > [phase interaction] > Models > Subgrid Transition
Requires	An MMP Multiphase simulation with the Lagrangian Multiphase model activated. The MMP phase and the corresponding Lagrangian phase defined. MMP-Lagrangian Phase Interaction with the MMP phase and the corresponding Lagrangian phase selected.
Properties	None.
Activates	Physics Models	None.
	Model Controls (child nodes)	Lagrangian-Eulerian Transition Criteria See Lagrangian-Eulerian Transition Criteria.
	Field Functions	See Lagrangian-Eulerian Transition Criteria Field Functions.

Lagrangian-Eulerian Transition Criteria

Right-Click Actions

New > Particle Diameter Criterion: Creates a new criterion for the transition of small (sub-grid) Lagrangian parcels to an MMP phase based on the diameter of the Lagrangian parcels.
New > Stokes Number Criterion: Creates a new criterion for the transition of small (sub-grid) Lagrangian parcels to an MMP phase based on the Stokes number of the Lagrangian parcels.

New > User Defined Criterion: Creates a new user defined criterion for the transition of small (sub-grid) Lagrangian parcels to an MMP phase.

Particle Diameter Criterion

Defines the Lagrangian-Eulerian transition of sub-grid Lagrangian particles based on the diameter of each particle. The Lagrangian parcels whose diameter is smaller than the host cell size transition onto the MMP phase, maintaining the volume. Lagrangian parcels whose diameter is greater than the host cell size do not transition.

Lower Bound Lagrangian Particle Diameter: Lagrangian parcels with diameters lower than this value will transition to the MMP phase.

Stokes Number Criterion

Specifies a transition criterion that is based on the Stokes number of the Lagrangian parcels. This Stokes number is defined as:

{S t k}_{p} = \frac{ρ_{d} D_{p}^{2} ‖ v_{p} - v_{c} ‖}{18 μ_{c} l}

(305)

where:

$l$ the characteristic length scale.
$ρ_{d}$ is the particle density.
$D_{p}$ is the particle diameter.
$v_{p}$ is the particle velocity.
$v_{c}$ is the continuous phase velocity.
$μ_{c}$ is the dynamic viscosity of the continuous phase.

Critical Stokes Number: Lagrangian parcels with Stokes numbers lower than this value will transition to the MMP phase. The example images below show the behavior of Lagrangian parcels as result of Stokes number. If ${S t k}_{p} ≪ 1$ , parcels trace the flow streamline (green line). If ${S t k}_{p} ≫ 1$ , parcels detach from the flow streamline (red line).
Characteristic Length: The characteristic length scale $l$ in Eqn. (305).

User Defined Criterion: An optional user defined transition criterion. Lagrangian parcels with a value of 1 for this property transition to MMP. Parcels with a value of zero remain as a Lagrangian phase.

注	Lagrangian-Eulerian transition takes place only for those Lagrangian parcels that satisfy all the criteria that are set under the Lagrangian-Eulerian Transition Criteria node.

Lagrangian-Eulerian Transition Criteria Field Functions

The following field function are available with the Lagrangian-Eulerian Transition Criteria node:

Integrated TransitionMark of [phase interaction]: Gives the integrated results for all the defined transition criteria. A value of $1$ indicates which Lagrangian parcels transition to an MMP phase at any given time-step.
TransitionMark of Particle Diameter Criterion of [phase interaction]: Provides the particle diameter criterion transition mark. A value of 1 indicates which Lagrangian parcels satisfy the particle diameter criterion and are candidates for transitioning to an MMP phase at any given time-step.

TransitionMark of Stokes Number Criterion of [phase interaction]: Provides the Stokes number criterion transition mark. A value of 1 indicates which Lagrangian parcels satisfy the Stokes number criterion and are candidates for transitioning to an MMP phase at any given time-step.

TransitionMark of User Defined Criterion of [phase interaction]: Provides the transition mark when a User Defined criterion is used for the Lagrangian-Eulerian Transition Criteria. A value of 1 indicates which Lagrangian parcels satisfy the User Defined criterion and are candidates for transitioning to an MMP phase at any given time-step.

The transition mark field functions register a value of 0 at the end of the simulation time-step, as transition occurs during Lagrangian sub-stepping. You must refer to the track file or a Lagrangian passive scalar to identify parcels with a value of 1.

Mmp-Lagrangian Continuity Source of [phase interaction]: The continuity source term from the subgrid transition of Lagrangian parcels to an MMP phase.

Mmp-Lagrangian Energy Source of [phase interaction]: The energy source term from the subgrid transition of Lagrangian parcels to an MMP phase.

Mmp-Lagrangian Momentum Source of [phase interaction]: The momentum source term from the subgrid transition of Lagrangian parcels to an MMP phase.

Mmp-Lagrangian Component Source of [mixture component] of [phase interaction]: The species component source terms from the subgrid transition of Lagrangian parcels to an MMP phase. This field function is available for multi-component phases only.