Dense Discrete Phase Model (DDPM) -- KTGF, Stochastic Collision, DEM, and Dense Particle Flows

#+CATEGORY: cfd

#+TAGS: DPM DDPM dense-discrete-phase KTGF stochastic-collision DEM coalescence fluidized-bed

#+MATURITY: growing

Dense Discrete Phase Model :: KTGF, Collisions, and Dense Particle Flows

The standard DPM assumes dilute particles that do not collide with each other. When the particle volume fraction exceeds approximately 10^{-3}, particle-particle interactions become important. The Dense Discrete Phase Model (DDPM) extends DPM to handle dense flows by incorporating the Kinetic Theory of Granular Flow (KTGF) for stress closure, and optionally stochastic collision models (nozzle model) or deterministic Discrete Element Method (DEM) for explicit collision handling. This page covers when DDPM replaces DPM, the physics at each density regime, and setup instructions.

Density Regimes in Particle-Laden Flow

The appropriate model depends on the particle volume fraction \alpha_p:

Decision flowchart

Shisha applicability check

For your shisha simulation:

• Smoke mass generation rate: ~2--5 mg/min = ~5e-8 kg/s
• Bowl chamber volume: ~0.5 L = 5e-4 m^3
• Particle density: ~1200 kg/m^3
• Steady-state mass concentration: ~1e-4 kg/m^3
• Volume fraction: =\alpha_p = 10^{-4} / 1200 \approx 8 \times 10^{-8}=
• Conclusion: dilute regime. Standard DPM is correct. DDPM is not needed.

DDPM is relevant for fluidized beds, cyclones, pneumatic conveying, and sedimentation -- not for shisha smoke. This page documents it for completeness and for future cases where mass loading increases.

KTGF Physics in DDPM

The KTGF treats the particle phase as a granular material with its own "temperature" (granular temperature \Theta, not thermal temperature). This granular temperature represents the fluctuating kinetic energy of particles due to collisions.

Granular temperature

where \mathbf{c}' is the fluctuating component of particle velocity.

Solids pressure

where g_0 is the radial distribution function (contact probability):

Shear viscosity (granular)

In DDPM, Fluent solves a transport equation for \Theta (or assumes algebraic equilibrium), then uses p_s and \mu_s to compute the particle-phase stress tensor.

Stochastic Collision (Nozzle Model)

In the DDPM stochastic collision approach, particle collisions are modelled statistically rather than resolved deterministically. At each time step, Fluent:

1. For each parcel, computes the collision probability based on local number density, parcel cross-section, and relative velocity 2. Samples a random number; if < collision probability, a collision occurs 3. If collision occurs, samples a random partner parcel 4. Applies momentum exchange using specified restitution coefficients

Collision parameters

Activation

1. Enable DPM with dense phase: Models > Discrete Phase > Dense Discrete Phase 2. Physical Models tab:

• Enable KTGF (granular energy equation)
• Set Collision Model to Stochastic
• Set restitution coefficients

3. Select Nozzle Model for collision partner selection

DEM Collision (Explicit Contact)

For \alpha_p > 0.1 (very dense flows), stochastic collisions become inaccurate because multi-body contacts dominate. DEM resolves each contact explicitly:

Contact model

Normal force (Hertz-Mindlin):

where \delta_n is the overlap, E^* is the equivalent Young's modulus, R^* is the equivalent radius, and \eta_n is the normal damping.

Activation

1. Models > Discrete Phase > Dense Discrete Phase 2. Collision Model = DEM 3. Specify contact model parameters (E^*, \nu, \eta, \mu_f)

Computational cost

DEM is expensive because every particle pair must be checked. Fluent uses a neighbor list (cell-based or linked-cell) to reduce the O(N^2) to approximately O(N \log N). Typical speedup: DEM costs 10--100x more than stochastic collision per time step.

Coalescence

Coalescence is the opposite of collision: instead of bouncing, two colliding droplets merge. This is relevant for spray simulations (DPM droplet type) when droplets collide at low relative velocity.

Coalescence efficiency

where We is the Weber number and We_{crit} is a critical Weber number (typically 5--20).

Activation

1. DPM > Interaction 2. Enable Coalescence 3. Set Coalescence Model to Stochastic or ODE 4. Specify We_{crit} for the ODE model

Setup Instructions for DDPM

Step-by-step

1. Enable DDPM: Models > Discrete Phase > Dense Discrete Phase toggle 2. Select KTGF option:

• Algebraic (faster, equilibrium assumption) for moderate density
• Transport equation (slower, solves granular energy) for very dense flows

3. Set collision model: Stochastic, Nozzle, or DEM 4. Set restitution: =e_n = 0.9= (glass beads), 0.8 (sand), 0.99 (nearly elastic) 5. Set packing limit: =\alpha_{max} = 0.63= (random close packing of spheres) 6. Set interaction frequency: more frequent collision checks = more accurate but slower 7. Inject parcels: same procedure as standard DPM, but with higher parcel-per-cell ratio 8. Run: DDPM requires smaller time steps than standard DPM because collision timescales are shorter

TUI commands

  define/models/discrete-phase/dense-discrete-phase     (enable/disable)
  define/models/discrete-phase/dense-discrete-phase/ktgf/algebraic
  define/models/discrete-phase/dense-discrete-phase/ktgf/transport-equation
  define/models/discrete-phase/dense-discrete-phase/collision-model/
    > stochastic
    > nozzle
    > dem
  define/models/discrete-phase/dense-discrete-phase/restitution-coefficient
  define/models/discrete-phase/dense-discrete-phase/packing-limit

When DDPM Replaces DPM: Decision Summary

For the shisha PM2.5 simulation: standard DPM is the correct choice. Keep DDPM in reserve for any future case where particle loading increases substantially (e.g., injection of dense carrier particles, fluidized bed reactor, or cyclone separator).

See Also