Multiphase Flow Modeling in COMSOL

Contents

Categorization

The multiphase flow interfaces

Dispersed multiphase flow models

Separated multiphase flow models

Multiphase flow and multiphysics

Dispersed multiphase flow models

For bubbly flows with a large number of relatively small bubbles

For emulsions and aerosols (droplets in gas)

For large numbers of solid particles in fluids

For macroscopic multiphase flow (almost always required)

Separated multiphase flow models

For bubbles, droplets, phase boundaries, or particles that are relatively few and of the order of magnitude of the model domain

For multiphase flow in microfluidics

For free surfaces in otherwise single-phase fluids that are also in macroscopic systems

Categorization

Dispersed multiphase flow models Separated multiphase flow models

Categorization

Volume fraction field, 0 < f < 1

Phase field, ff = 1 (red)f = -1 (blue)

Interfacedescribedin detail

Continuous phase

Dispersedphase

Isosurfaces

Dispersed multiphase flow

Separated flow multiphase flow

Laminar and turbulent multiphase flows except for:

Two-phase flow with moving mesh

Three-phase flow

Only available as predefined for laminar flow but can be manually changed for turbulent flows

The Multiphase Flow Interfaces

Dispersed Multiphase Flow

Process industry

Chemicals, pharmaceuticals

Food and household supplies

Environmental sciences: Hydrogen technologies

Cooling systems and refrigeration

And more…

Defense and space

Gas-liquid systems for fuel, hydrogen-oxygen

Advanced cooling systems

And more…

Applications of Dispersed Multiphase Flow

Hydrogen/water separator modelVera et al, COMSOL Conference, Milano 2012

Bubbly flow model:

Defines one dispersed phase, the gas phase, and one continuous phase, the liquid phase

The relative bubble velocity is described with an equation that balances the drag and pressure gradient

The momentum balance is defined for the continuous phase, while the pressure field is the same in the two phases

Relatively “inexpensive” two-phase flow model

Dispersed Multiphase Flow Models: Bubbly Flow

Mixture multiphase flow model:

Defines one dispersed phase and one continuous phase

The relative velocity of the dispersed phase is described with an equation that balances the drag and pressure gradient

The momentum balance is defined for the mixture, while the pressure field is the same in the two phases

Relatively “inexpensive” two-phase flow model that can also handle phases with small differences in density

Dispersed Multiphase Flow Models: Mixture Model

Euler-Euler multiphase flow model:

Defines dispersed and continuous phases

Separate momentum balances are defined for the different phases

Accounts for possible acceleration of the dispersed phase, while the mixture and bubbly flow models assume terminal velocity for bubbles, droplets, or particles

Accurate but relatively “expensive” multiphase flow model, which can be used for all cases of dispersed multiphase flow

Dispersed Multiphase Flow Models: Euler-Euler

By nature, dispersed models are approximate in relation to the scale of the interface between phases

There is no additional loss of accuracy in combination with turbulence models

Turbulence models introduce a drift diffusion term in the dispersed phase, in addition to the eddy diffusivity contribution to viscosity

Dispersed Multiphase Flow Models and Turbulence

Strengths

A large combination of possible descriptions is available for laminar and turbulent flow

Adaptable: Dispersed flow models may contain almost arbitrary interactions within and between phases, which are relatively easy to define in COMSOL Multiphysics

Relatively easy to tweak and define models

Can be combined with other physics phenomena

Weakness

The model equations are “nasty” and require good initial guesses and initial conditions to converge

Dispersed Multiphase Flow in COMSOL

Turbulent bubbly flow in a photo bioreactor with different separator plate configurations. Ramirez et al, COMSOL Conference, Curitiba 2014

Separated Multiphase Flow

Microfluidics in different fields and industries

Biotech and medical technology

Material science, such as electronics and semiconductors

Chemicals

Space and defense

And more

Larger scale flows to track interfaces between phases and free surfaces

Polymers: for extrusion and mold filling

Chemicals: mixers and reactors

Applications of Separated Multiphase Flow

NanoSat fuel delivery system. Influence of surface tensionMcDeWitt et al, COMSOL Conference, Boston 2010

Two-phase flow with moving mesh:

A workhorse in microfluidics and free surface computation in rotating machinery

The interfaces between different phases are domain boundaries, where surface tension effects may be defined as boundary conditions

Very accurate for separated multiphase flows when topology changes do not occur

Separated Multiphase Flow Models: Moving Mesh

Topology changewhen this snaps

Two-phase flow with level set:

The interface between different phases is represented by an isosurface of the level set function

Surface tension effects are added as sources and sinks over the thin volume around the isosurface that represents the interface between phases, i.e., as body forces

Allows for topology changes but requires a relatively dense mesh at the interface between phases

Separated Multiphase Flow Models: Level Set

Two-phase flow with phase field:

The interface between phases is represented by an isosurface of the phase field function

The method contains a more accurate representation of the surface dynamics compared to the level set method

Surface tension effects are added as sources and sinks over the thin volume around the isosurface that represents the interface between phases, i.e., as body forces

Allows for topology changes but requires a relatively dense mesh at the interface between phases

Separated Multiphase Flow Models: Phase Field

Moving mesh

Phase field

The main purpose is to describe the approximate position of the interface between phases on a relatively large length scale compared to that of surface tension effects

Accuracy in the description of the interface between phases is lost when turbulence models are combined with separated multiphase flow models: Surface tension effects cannot be properly described

Separated Multiphase Flow Models and Turbulence

Strengths

Accurate: Effects of surface tension and contact angles are taken into account in a strict way

Can be combined with other physics phenomena; for example, Marangoni effects

Relatively easy-to-use

Weakness

Computationally, relatively expensive compared to the standard volume of fluids (VOF) method

Separated Multiphase Flow in COMSOL

Separated multiphase flow:

Two-phase flow

Three-phase flow

Dispersed multiphase flow:

Ready-made two-phase flow interfaces

Relatively easy to extend to three-phase flow

Combination of dispersed and separated flows can also describe three-phase flow

Applicable for macroscopic models

Particle tracing can also be used for descriptions of solid particles and droplets in fluids and can be combined with multiphase flow models to describe three-phase flow

Applicable for both microfluidics and macroscopic flows

Sometimes referred to as Euler-Lagrange models

Possible Multiphase Flow Combinations

Multiphase Flow and Multiphysics

Taylor cone

Voltage applied between anode and cathode

Electrolyte with anions and cations

Thin layer of separated charges at the air-liquid interface subjected to forces from the electric field

The thin film with a net charge is displaced by the electric field

The thin film displaces the whole liquid with the help of surface tension and viscous forces

Multiphase Flow and Electrokinetic Flow

++

+

--

Chargeseparation

Cathode

AnodeLiquid

Air

Outletorifice

Inlet

Laminar flow in both air and water

Phase field method for tracking the air-water interface

Structural mechanics for the deformation of the solid whisker

Moving mesh keeps track of the deformation of the fluid domain due to structural deformation of the whisker

Two-Phase Flow and Fluid-Structure Interaction (FSI)

Water

Air

Whisker

Deforming domain only in the subdomain that is deformed by the whisker

Laminar flow in the two fluid subdomains

Solid mechanics in the solid subdomain

Phase field in the two fluid subdomains with initial conditions for air and water

Multiphysics:

Fluid-structure coupling on the solid’s outer boundary

Two-phase flow in the two fluid subdomains

Two-Phase Flow and Fluid-Structure Interaction (FSI)

Waterinitially (green)

Air, initially(blue)

Fluid Flow and Structural Deformation

Flow field, phase boundary, and structural deformation

Moving Mesh

Phase boundary, structural deformation and moving mesh

Two-Phase Flow and Fluid-Structure Interaction (FSI)

Alternative witha thin shell instead of a whisker as obstacle

Contact Uscomsol.com/contact