DPM Breakup and Coalescence -- TAB, Wave Breakup, Stochastic Collision, and Droplet Merging

#+CATEGORY: cfd

#+TAGS: DPM breakup TAB Wave coalescence stochastic-collision droplet-spray atomization

#+MATURITY: growing

DPM Breakup and Coalescence :: TAB, Wave, Stochastic Collision

In spray DPM simulations (droplet particle type), parcels can break into smaller droplets when aerodynamic forces exceed surface tension, and collide with other parcels to merge (coalesce). Fluent ships two breakup models -- TAB (Taylor Analogy Breakup) and Wave (Reitz-DPKH) -- plus a stochastic collision model for coalescence and bouncing. This page gives the full equations, activation, and parameter guidance. These models do not apply to inert particles (shisha PM2.5) but are documented for completeness in the exhaustively comprehensive DPM wiki.

TAB Breakup Model (Taylor Analogy Breakup)

Physical basis

The TAB model (O'Rourke & Amsden, 1987) treats the droplet as a damped spring-mass system. The aerodynamic force deforms the droplet; when deformation exceeds a critical value, the droplet breaks up.

Droplet deformation parameter

where:

• y is the dimensionless deformation (0 = sphere, y_{crit} = breakup)
• \mu is liquid viscosity
• \sigma is surface tension
• \rho_d, \rho_g are liquid and gas densities
• r_d is droplet radius
• \mathbf{u}_g - \mathbf{u}_d is relative velocity

Default constants

Breakup criterion

Breakup occurs when y \geq C_b (= 0.5=). At breakup:

The parent parcel is removed and replaced with child parcels of diameter r_{new}.

Activation

1. Models > Discrete Phase > Interaction 2. In the Droplet Vaporization section:

• Set Particle Type to Droplet
• Enable Breakup
• Select TAB

3. Set Max Number of Breakup Steps (default 20)

When TAB is appropriate

• Low-to-moderate Weber numbers (=We = 10--100=)
• Diesel spray atomization (primary and secondary breakup)
• Water injection into air

When TAB is NOT appropriate

• Very high Weber numbers (> 1000) -- use Wave
• Non-Newtonian liquids
• Viscous liquids (silicone oil, polymer melts) -- deformation is overdamped

Wave Breakup Model (Reitz-DPKH / KH-RT)

Physical basis

The Wave model (Reitz, 1987; Patterson et al., 2001) treats breakup as a Kelvin-Helmholtd instability on the droplet surface. The fastest-growing instability wave strips fragments from the droplet surface.

Instability growth rate

where:

• =We_g = \rho_g |\mathbf{u}_g - \mathbf{u}_d|^2 r_d / \sigma= (gas Weber number)
• =Oh = \sqrt{We_l} / Re_l= (Ohnesorge number)
• =T = We_g / \sqrt{Re_l}= (Taylor number)

Breakup time

where =B_1 = 10= (default constant) and \Lambda is the most unstable wavelength.

Child droplet radius

where =B_0 = 0.61= (default).

Activation

1. Models > Discrete Phase > Interaction 2. Enable Breakup > Wave 3. Set Wave Model Constants:

• B0 (default 0.61)
• B1 (default 10.0)

4. For KH-RT hybrid: enable RT (Rayleigh-Taylor) alongside KH for high-acceleration regimes

Wave vs TAB comparison

Stochastic Collision (O'Rourke Model)

Overview

The stochastic collision model (O'Rourke, 1981) determines, for each parcel at each time step, whether it collides with another parcel, and if so, whether the collision leads to coalescence (merging) or bouncing (elastic/plastic rebound).

Collision probability

where:

• N_p is the number of real particles in the parcel
• =r_{coll} = r_{d1} + r_{d2}= (sum of radii for collision cross-section)
• |\mathbf{u}_{rel}| is the relative velocity between parcels
• V_{cell} is the cell volume
• \Delta t is the time step

Collision outcomes

After collision, the outcome depends on the Weber number:

Coalescence efficiency

The probability of coalescence given a collision:

Activation

1. Models > Discrete Phase > Interaction 2. Enable Collision 3. Set Collision Model to Stochastic 4. Set Colliding Parcels handling:

• Within same injection (default): parcels from the same injection can collide
• Between all injections: parcels from different injections can also collide

5. Set Coalescence toggle (on/off)

Important: parcel number density

The stochastic collision model is only valid when multiple parcels occupy the same cell. If you have too few parcels (e.g., 100 parcels in 10000 cells), most cells will contain 0--1 parcels and no collisions will occur. Requirements:

• At least 10--50 parcels per cell for statistical convergence
• For spray: ensure parcel number density = 10^4--10^6 per m^3 near the nozzle

Bouncing (Collision Without Coalescence)

When coalescence is disabled, colliding parcels bounce off each other. The post-collision velocities are computed from momentum conservation with a restitution coefficient:

Parameters:

• e = restitution coefficient (0 = perfectly inelastic, 1 = perfectly elastic)
• \mathbf{n} = unit normal at collision

Default =e = 0.9= (nearly elastic, appropriate for hard-sphere particles).

Breakup Model Selection Guide

TUI Commands

  define/models/discrete-phase/interaction/breakup-model/
    > tab
    > wave
  define/models/discrete-phase/interaction/breakup-model/tab-constants
  define/models/discrete-phase/interaction/breakup-model/wave-constants
  define/models/discrete-phase/interaction/breakup-model/max-breakup-steps
  define/models/discrete-phase/interaction/collision/
    > stochastic
    > off
  define/models/discrete-phase/interaction/collision/coalescence
    > enable / disable
  define/models/discrete-phase/interaction/collision/restitution

See Also