Lagrangian Particle Model
Tracking discrete particles through a fluid flow opens up a broad class of engineering problems that cannot be addressed with fluid-only simulations. FLOW-3D products include a Lagrangian Particle Model that tracks individual particles as they move through the fluid domain, exchanging momentum, heat, mass, and electric charge with the surrounding flow. Particles can represent solid grains, liquid droplets, gas bubbles, massless tracers, and more, and can interact with each other, with the fluid, and with solid geometry in the same coupled simulation.
Particle Classes
Seven particle classes are available, each representing a distinct physical type or function:
- Mass particles are solid spheres with user-defined density and diameter, such as dust, sand, powder, inclusions, or other solid particulates.
- Fluid particles are liquid droplets whose physical properties match the primary fluid. They can be used to model sprays, atomization, and droplet-laden flows. Fluid particles can solidify and re-melt, and can evaporate and condense when the two-fluid phase change model is active.
- Gas particles are compressible bubbles governed by the ideal gas equation of state, whose size changes dynamically with local temperature and pressure. When a gas particle escapes the free surface, it adds its volume to the surrounding gas region. The underlying bubble and phase change model has been reorganized and simplified, consolidating the adiabatic and thermal bubble models into a single ideal gas equation of.
- Void particles are a specialized class used to track collapsed bubble regions, making them useful for identifying potential porosity defects in casting and other processes.
- Probe particles are diagnostic particles that record and report flow variable values at their location. They can be stationary or moving and can be of any other particle class.
- Marker particles are massless tracers with no physical properties, used to visualize flow patterns and track fluid pathlines.
- User particles are up to ten fully customizable classes defined through user-defined functions, each carrying three configurable attributes.
Each material particle class (mass, fluid, gas, user) supports multiple species of different sizes and densities within the same simulation. A macro-coefficient option allows a single simulated particle to represent a cloud of identical physical particles, reducing computational cost in regions of high concentration without sacrificing accuracy.
VOF to Particles: Small fluid droplets generated at the point of impact are automatically converted from VOF representation to fluid particles, improving mass and momentum conservation in regions subject to breakup.
The VOF-to-Particles capability is available across the product family. Small fluid ligaments and droplets that are difficult to track accurately with the VOF method are automatically converted to fluid particles when certain conditions are met. Particle motion is then handled by the Lagrangian Particle Model, and particles are converted back to VOF representation when they reenter the fluid. This improves mass and momentum conservation for fluid regions subject to breakup and can allow higher time steps in many simulations..
The Lagrangian Particle Model interface in FLOW-3D CAST provides a streamlined setup experience for casting-specific particle workflows.
Particle Physics and Coupling
The motion of each particle is governed by Newton’s second law. Forces acting on a particle include gravity, pressure (buoyancy), drag, and added-mass. The particle drag coefficient is computed as a function of the local particle Reynolds number and particle concentration. Heat transfer between particles and the surrounding fluid is available for all material particle classes, enabling thermal equilibration, melting and solidification, and droplet evaporation to be captured within the simulation.
By default, particle motion is influenced by the fluid but has no effect on it. When two-way coupling is enabled, momentum exchange between particles and fluid is solved implicitly, capturing the feedback from the particles on the surrounding fluid field. This is important in applications where particle concentrations or masses are significant enough to alter the flow field.
Discrete Element Method (DEM)
The Discrete Element Method is an extension of the Lagrangian Particle Model that applies to solid (mass and solidified fluid) particles. When enabled, DEM adds particle-particle collision and friction physics to the simulation, resolving normal, tangential, and rotational contact forces between particles and between particles and solid geometry. Particles using DEM can also displace fluid volume as they move, an important effect for coupled fluid-particle flows with moderate to high particle concentrations.
DEM is well suited to applications where the physical interactions between individual solid particles matter, such as granular flow in hoppers and separators, rock stability assessment on riverbanks, and stormwater grit separation. In applications where particle concentrations are low or particle-particle contacts are infrequent, the standard particle model without DEM is typically sufficient and computationally less expensive.
DEM Grit Separator: Solid particles are tracked through a cyclonic separator using the DEM model, capturing particle-particle and particle-wall interactions to evaluate separation efficiency and system performance.
The Discrete Element Method is an extension of the Lagrangian Particle Model that applies to solid (mass and solidified fluid) particles. When enabled, DEM adds particle-particle collision and friction physics to the simulation, resolving normal, tangential, and rotational contact forces between particles and between particles and solid geometry. Particles using DEM can also displace fluid volume as they move, an important effect for coupled fluid-particle flows with moderate to high particle concentrations.
DEM is well suited to applications where the physical interactions between individual solid particles matter, such as granular flow in hoppers and separators, rock stability assessment on riverbanks, and stormwater grit separation. In applications where particle concentrations are low or particle-particle contacts are infrequent, the standard particle model without DEM is typically sufficient and computationally less expensive.
Applications
The Lagrangian Particle Model supports a wide range of applications across the FLOW-3D product family:
- Spray and atomization for tracking droplet formation, transport, and impact in coating, cooling, and combustion processes
- Powder and particle transport for modeling solid particles through process equipment including mixers, fluidized beds, classifiers, and conveyors
- Bubble dynamics for simulating gas bubble motion, growth, and collapse in bubble column reactors, degassing systems, and cavitating flows
- Additive manufacturing for tracking metal powder particles through melt pool dynamics in laser powder bed fusion and directed metal deposition processes
- Inclusion tracking in casting for following non-metallic inclusions or porosity-forming bubbles through filling and solidification to identify defect locations
- Granular flow and particle separation for simulating dense solid particle flows in hoppers, separators, and channel protection systems using DEM
- Pollutant and sediment tracking for following suspended particles through water and environmental flows to assess transport, deposition, and separation
- Flow visualization and diagnostics for seeding marker or probe particles to reveal flow structures, recirculation zones, and residence time distributions
Application Example: Metal Powder Bed Fusion
In laser powder bed fusion, a laser scans across a bed of metal powder particles, selectively melting and fusing them to build up a solid layer. FLOW-3D AM simulates this process using a two-stage simulation approach:
- The particles model with DEM is used to simulate solidified metal particles settling under gravity, to generate a powder bed.
- The settled particles are converted to a solidified fluid, which are heated/melted/re-solidified by one or more laser heat sources.
The example below shows the melting of stainless steel 316 particles on a copper substrate, with velocity vectors in the melt pool and temperature field of the solidified track shown alongside the 3D powder bed geometry.
Melting Stainless Steel 316 Particles simulated in FLOW-3D AM. Top: 3D view of the powder bed with velocity vectors in the melt pool. Bottom left: Temperature field of the solidified track. Bottom right: track geometry after solidification.
Application Example: Produced Water Separator
Produced water separators must reliably separate oil, water, and gas while also managing entrained sand, across a range of flow rates and inlet conditions, behavior that is difficult to predict with hand calculations alone. FLOW-3D HYDRO simulates the internal hydraulics of a 3-phase separator, capturing flow through a perforated baffle, sand baffle, vortex breakers, and spillover weir. The oil phase is modeled using the Dispersed Multiphase Model, while sand is tracked using Mass Particles within the Lagrangian Particle Model, allowing sand settling and accumulation along the vessel floor to be resolved alongside the oil-water separation.
3-phase separation of oil, water, and sand simulated in FLOW-3D HYDRO, showing internal hydraulics through a perforated baffle, sand baffle, vortex breakers, and spillover weir as the phases stratify and sand settles along the vessel floor.