Multiphase—Lagrangian Approach

Multiphase flows are found in a wide variety of industrial processes, some examples of which are internal combustion engines, liquid, or solid fueled combustors, spray driers, cyclone dust separators, and chemical reactors. Multiphase in this context refers to one thermodynamic phase, be it a solid, a liquid, or a gas, interacting with another distinct phase.

In many of these multiphase processes, there are large separations in physical scales between the phases which make a calculation of a full size device impractical or impossible. For example, in a typical heavy duty diesel engine there can be approximately 10⁷ distinct particles with a wide range of diameters, temperatures, and compositions, making a full Eulerian description at the very least impractical—the particles have diameters on the order of micrometers and the cylinder bore is in the order of ten centimeters. Processes which have a large number of diameter classes or a broad distribution of states (such as temperature) can often be more easily modeled using a Lagrangian frame of reference. The Lagrange multiphase flow models in Simcenter STAR-CCM+ are designed to simulate and track the flow path of dispersed particles in a continuous phase including the associated heat and mass transfer phenomena such as droplet evaporation.

Lagrangian numerical methods can be used in conjunction with Eulerian numerical methods to describe these situations where individual particle dynamics impact the solution on the scale that is resolved in the Eulerian field. Typically, a Lagrangian reference frame is used to describe the evolution of individual particles as they traverse the domain. The equations of change are written following an individual particle. Particles are not resolved on the Eulerian field, they are subgrid and the interaction between the phases is modeled.

A Lagrangian phase can also interact with porous media. See Volume Partitioning for the relationship between porous media and Eulerian and Lagrangian phases.

In general, the continuous phase drives the motion of the dispersed phase. The continuous phase itself is affected by the dispersed phase, as particles occupy volume, and can exchange momentum, heat, and mass with the continuous phase. The strength of the interactions depends on the size, density, and number of dispersed particles.

If the flow is laminar, each particle that is released from a point follows a smooth unique trajectory, that is, the motion of the particle is deterministic. If particles are released to a turbulent carrier flow, each of them has their own random path due to interaction with the fluctuating turbulent velocity field.

If the dispersed phase is volatile, soluble, or reactive, mass transfer occurs between the phases. These effects are accompanied by interphase heat transfer that can also arise due to the interphase temperature differences. Interphase mass transfer causes size changes in the dispersed particles. Even if the initial size distribution is uniform (monodispersed), these effects produce a variable-size (polydispersed) population. The size changes can also be produced by fluid-dynamic forces acting on the dispersed particles causing them to break up into smaller particles. Collisions between particles can also produce the opposite effect, that is, size increase due to coalescence or agglomeration. When dispersed particles hit a wall, the result can be bouncing or shattering, depending on the impact conditions.

Applications with high volume fractions of particles, such as fluidized beds, packed beds, or pneumatic transport, the effect of inter-particle interaction is important. For these applications, Simcenter STAR-CCM+ offers the discrete element method (DEM) that is incorporated into the Lagrangian multiphase framework. DEM is specifically designed to model granular material. In general, DEM particles are solid particles that experience additional contact forces, which enter the Lagrangian momentum equations. In addition to the linear momentum equation, the conservation of angular momentum must be fulfilled for a DEM particle.

Simcenter STAR-CCM+ provides a modeling framework that is able to encompass all of the above phenomena. The framework is based on a Lagrangian-Eulerian approach [655] where the conservation equations of mass, momentum, and energy for the dispersed phase are written for each individual particle in Lagrangian form. This approach allows to calculate the trajectory of each individual particle. The governing equations for the continuous phase are expressed in Eulerian form and they are modified to take into account the presence of the dispersed phase. For flows involving a small number of dispersed particles, it is possible to solve a set of the Lagrangian equations for every particle. However, if the number of particles is large, a statistical approach is more practical. In this statistical approach, the total number of particles is represented by a smaller number of computational parcels. Each of these parcels represents a group (cluster) of particles that share the same properties. The number of particles in a parcel must be large enough so that the properties of the full population of particles are well represented. Also, the number of parcels that are used in the simulation must be large enough to represent the properties of the full population of particles.