MR-CFD experts are ready for analysis, consulting, training, and CFD simulation in Multi-Phase field.

**Multi-Phase Flow**

Multiphase flow has various application in the industrial procedure. Some of industrial application of multiphase flow is gas sweetening, jet loop reactor, polymer generation mixer, and dryer. It has also application in power generating like droplet combustion, coal combustion, boiling and evaporation, and fuel cells. Some of this application is related to petrochemical and petroleum engineering like multiphase flow inside the oil transfer tubes. Another application of multiphase flow is related to environment and medial application like rain and blood flow inside the vessel.

We are expert in CFD simulation of all multiphase flow models include eulerian-eulerian and eulerian lagrangian model. And also simulating mass transfer between phases than can occur with the following reason like boiling, melting. Solidification, Sublimation. Evaporation, condensation, and cavitation.

Species transport from one phase to another phase will occur due the concentration difference. Species transport usually will solve with mass transfer coefficient and concentration balance like Raoult and Henry.

ANSYS fluent has four modules for modeling of multiphase flow and each model has its advantage, disadvantage, and limitation. These modules are volume of fluid, mixture, eulerian and we steam. Wet steam is available only in compressible fluid flow and density-based model.

In the following you can see a summary of our performed word associated with the multiphase flow which is simulated by ANSYS Fluent software.

Free surface and open channel flow of various spillways

Improving jet loop reactor performance and increasing gas holdup using various method

Predicting entrainment ratio in two-phase ejector

Gas and liquid separator

Particle tracking and particle settling

Gas-oil filling in an automobile fuel tank

Droplet releasing

Droplet pumps

Desalination of Salty water with solar energy

Float body in open channel flow like ships and boats

Multiphase simulation of heat transfer with freezing and melting operations

Water slushing in tank and damn (during vibration and earthquake)

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### Two-Phase Flow

Flows that are separated by one or more interfaces. Examples of such flows can be seen in industrial systems or in natural phenomena such as liquid-gas, liquid-solid or gas-solid two-phase mixtures. The processes of flow and heat transfer of Two-Phase systems are used in various industries such as oil and gas, air conditioning, power boilers, steam turbines, heat exchangers and porous materials. In two-phase liquid-gas flows, a mathematical model is presented to calculate the pressure drop and volume fraction of each phase under different flow patterns. Flow patterns, which illustrate the formation of phases together, play the main role in the rate of heat transfer and pressure drop.

Mathematical models of two-phase flows are presented based on local or microscopic moment variations with temporal averaging. The local momentum model is based on dividing the two-phase flow field into two single-phase regions and the moving interface between them. Solving the governing equations of each phase with appropriate boundary conditions and integrating the solution of the phases in the interface is used to determine the moment variables. In most cases, such a solution is inaccessible due to phase coupling and boundary conditions. However, using this model can be important in determining pressure drop, heat transfer, phase change, dynamics, interface stability, and critical heat flux. In addition, the local moment model is used in bubble growth and decomposition as well as in ice formation and melting. Another important application of the local momentum model is its use in all two-phase flow models using different averaging methods.

Several research projects are discussed two-phase flow and heat transfer simulation in detail are as follow:

#### A. Gas-Liquid Phase

1- Dynamic simulation of absorption cooling system during startup

2- Experimental study of the heat flux initiation of pool boiling in nuclear flow

3- Experimental study of critical heat flux in research nuclear reactors

4- Two-phase flow simulation in a horizontal tube under imbalance thermodynamic conditions

5- Experimental study of convection heat transfer by heat rods in a pool

6- Pressure change in the channels with sudden cross-section change

7- Numerical analysis of two-phase circular flow in horizontal tubes

8- Numerical simulation of fluid droplet formation in the condensation process

9- Numerical simulation of liquid-vapor flow with phase change

10- Influence of gas velocity on the heat flux rate of water pipes in a power boiler

11- Experimental Investigation of Two-Phase Flow Characteristics in Micro Channels

#### A. Gas-Solid Phase (porous)

1- Numerical simulation of imbalance thermodynamic model in porous materials

2- Determination of thermal equilibrium condition criterion during forced heat transfer in a porous channel

3- Direct numerical solution of laminar fluid flow heat transfer inside the porous channel

4- Numerical solution of non-equilibrium heat transfer in porous media

### Governing Equations

The two-fluid model equations are obtained by spatial averaging methods, so it is more suitable for solving two-phase flow where the longitudinal scale of the interface is smaller than the mesh dimensions. In this model two equations of mass and momentum continuity are solved separately for each phase. Transport terms are replaced by structural equations for mass, momentum, and energy, and these experimental relationships are mainly derived from experiments. In this method, no process is performed to determine the position of the interface within the cell, and the interface is represented by the volume fraction of each of the phases in the cell. On the other hand, a VOF-based model for solving two-phase flow problems in which the longitudinal scale of the interface is larger than the grid dimension, such as the flow in the upper part of the spillway, is acceptable but fails in flows where the longitudinal scale of the interface is smaller than the grid dimension. In this method, both phases are considered as mixtures and use Navier-Stokes equations consisting of a continuum equation and a momentum equation. An additional equation, which is the volume fraction diffusion equation, is used to follow the interface. The main advantage of the coupling of the VOF and two-fluid methods is that some flow regimes with completely separated phases do not require a two-fluid model because the VOF method gives them higher accuracy, on the other hand for dispersive flows, the two-fluid model is more accurate. Therefore, if the combination of two-fluid and VOF models is used for flow modeling, it can be analyzed more accurately for flows that include both interface scales, such as two-phase flow over a stepped spillway. The VOF method is activated and reconstructs the interface with high accuracy in positions where the longitudinal scale of the interface is larger than the dimension of the mesh, and in the cases where the longitudinal scale of the interface is smaller than the dimension of the grid, the two-fluid model is activated and the modeling of the flow without is done by a two-fluid model without considering the interface. Thus coupling improves the accuracy of the solution and prevents non-physical results for a two-phase problem.

## VOF

The VOF model is used for multi-phase flow in which the boundary or contact area between two different phases is clearly defined; in fact, in this multiphase model, the different phases do not mix. Free-Surface, laminar flows, jet disintegration phenomena, and movement of large bubbles into the liquid, pool boiling, fluid fall like a waterfall, spillways are some examples of using the VOF model.

### VOF Method Equations

The VOF method has the advantages of easy realization, low computational complexity, and high accuracy. It also detects the liquids fraction in the grid, not the movement of fluid particles. The VOF method is used to obtain the interface, the αk volume fraction of each k phase is traced in a computational cell across the domain, meaning that a fluid volume fraction in the grid is obtained to achieve it. If αk = 1, this indicates that the cell is filled with k phase, αk = 0, it indicates that the cell does not have k phase. For 0 <αk <1, the cell contains the interface between the two phases.

#### Continuity Equation:

𝛻 ∙𝑉 ⃗ = 0

#### Momentum Equation:

#### Diffusion Equation:

The diffusion equation is also applied to follow the interface as follows:

#### Volume Fraction:

The volume fraction function is used to calculate fluid properties at grid points as these relationships:

### Implicit Body Force

The CFD simulations in which the effect of gravity is considered, the Implicit Body Forces model should be applied. In this case, the effect of pressure gradient terms and volume forces on the momentum equation is significant compared to the viscosity and transport terms.

### Sharp

This method is used when the interface between the two phases is completely clear and the phases do not penetrate at all.

### Explicit & Implicit Formulation

The Implicit formulation is more stable and the solution convergence is easier. When the Explicit method is used, the time step size in problem-solving becomes important. This time dependence is defined as a dimensionless number called Courant Number. In the Implicit method, the volume fraction at the current time step is a function of the other values at the same time step, so at each time step, the volume fraction values of the phases have to be solved using the iterative transport equations, which results in more computational time and cost. While in the Explicit method, the volume fraction in the current time step is obtained directly from the values specified in the previous time step and thus does not require the repetition of the transport equations. The Implicit method does not have a Courant Number constraint and is also applicable to both transient and steady problems; however, because of numerical diffusion at the interface, it does not allow accurate prediction of the curvature of the two-phase interface. Therefore, it is not recommended to predict the flow in models with surface tension.

In the Explicit method, the volume fraction in the current time step is calculated based on the values from the previous time step. Hence, in this solution method, there is no need to solve the iteration equation at each time step. The solution is time-dependent using this method. Therefore, this method is applicable to transient models. This method is suitable for simulating high surface tension flows between two phases due to the high accuracy in calculating the interface curvature between the two phases.

### Modified HRIC Discretization Method

One of the discrete methods of the Explicit solution method is the Modified High-Resolution Interface Capturing method which is a method with good stability and low divergence probability. In general, in VOF simulations, upstream views are not suitable for tracking interface or shared surfaces due to their high dispersion nature, and distinct central views are unobtrusive despite the ability to maintain and control the gain at the interfaces. While the Modified HRIC method is a modified NVD composite method that incorporates a nonlinear combination of upstream and downstream perspectives. This method is computationally lighter than the Geo-Reconstant method.

## Mixture

The mixture model is a simplified Eulerian model based on the assumption of a small Stokes number (St≪1). This model is used in multiphase mixtures where the phases have different velocities but are in equilibrium over small spatial longitudinal scales, or in multiphase mixtures with very strong homogeneous coupling and the same velocity for different phases. This model solves a volume fraction transport equation for each defined secondary phase. In terms of flow regime, this model is applicable for the bubble, slurry (Non-Newtonian), and water droplets. The solubility of the soluble particles is also low to moderate and is acceptable to dilute to moderate density in terms of acceptable volume quality. Practical examples of this model include deposition phenomena, cyclone separators, low particle carrier flows, and bubble flows carrying low volume fraction of gas. The mixture model, like the VOF model, has a single fluid perspective, but differs from the VOF model; first, the mixture model allows the phases to penetrate each other, and secondly, the mixture model allows the phases move at different velocities if the concept of Slip Velocity is used. Also, as the phases penetrate in the Mixture model, the amount of drag between every two phases and the relative velocity value of each of the secondary phases can be determined relative to the primary phase.

### Slip Velocity

This option is enabled if the phases in the multiphase Mixture model have different velocities; while the phases have the same velocity and form a homogeneous mixture, this option will not be enabled. In fact, the Slip Velocity or relative velocity equals the velocity of a secondary phase relative to the primary phase.

## Eulerian

The Eulerian multiphase model is one of the most complex models for defining multi-phase flows. This model solves a set of momentum and continuity equations for each of the phases separately, while in the multi-phase Mixture and VOF modeling methods, only the equations for all phases but the primary phase is solved (the equations are not solved for the initial phase). In fact, the basis in this model is that the Navier-Stokes equations were considered separately for each phase. This model achieves the coupling between pressure and phase interaction coefficients. The coupling method depends on the type of phases involved, so that, for example, solid-liquid (granular) flows are used with a difference compared to non-granular fluid flows.

Applications for the Eulerian model include **bubble columns**, **vertical risers**, **particle suspension**, and **fluidized beds**.

In general, the Eulerian model is used for simulation in some cases of two-phase flows, which include the following:

- Simulation of the bubble, droplet, and particle-laden flows with a volume fraction of more than 12 percent of the dispersed phase.
- Simulation of risers and cyclone as gas-solid flow.
- pneumatic transmission simulation for granular solids.
- Simulation of fluidized beds as a gas-solid flow.
- Simulation of slurry flow as a liquid-solid flow.
- Simulation of sedimentation as a liquid-solid flow.
- Particle suspension simulation.
- Simulation of bubble columns.

When activating the Eulerian multi-phase model, all types of phase interactions are activated and the ability to define the problem is established. Interactions between phases include **drag force**, **lift force**, **turbulent dispersion force**, **virtual mass force**, **mass transfer**, and so on.

The **drag** force between the phases or the momentum transfer between the phases, for example, can be due to the velocity difference between the upward bubble flow inside the liquid, which is a very important term in modeling two-phase flows. The phase interaction drag force is obtained by multiplying the number of particles in a single volume of the mixed mixture in the force of the applied drag on a single particle. The drag force acting on a particle according to the formula depends on the drag coefficient. Drag coefficients based on different Reynolds ranges and in different contexts of the problem can be defined based on different relationships such as Schiller-Naumann, Morsi-Alexander, symmetric, grace, Tomiyama. However, these models are mainly valid for stationary systems and are not compatible with turbulent conditions; therefore, the Brucato drag coefficient is used for turbulent conditions.

The **lift** force is due to three processes, including fluid shear due to non-uniform distribution of pressure due to unbalanced sliding velocities, rotation due to forced rotation of bubbles, droplets and particles in a non-uniform flow field, or due to collision with a wall or the collision between the particle and the fluid shear, and the separation phenomenon occur due to the flow of the vortex flow and the resulting transient lateral force on the object. In general, the cut creates the lift force, which is proportional to the product of the reciprocating velocity and the rotation of the continuous phase. This force is used in high concentration ratios such as bubble flows and large shear flows such as intra-tube flows in which the pipe diameter is comparable to the bubble diameter. The lift force factor is based on the Reynolds number and the physical condition of the phases (bubble size), obtained in various relationships including Saffman-mei, Morga, Legendre-Manaudet, and Tomiyama.

**Turbulent dispersion** indicates the interaction between flow turbulence and particle and plays an important role in homogenizing the phase distribution distributed in the continuous phase. The scattering coefficient of turbulence is defined by the size of the bubbles with models such as Lopez-de-Bertodan, Simonin, and Burns.

The **virtual mass force** indicates the force caused by the inertia of the scattered phase when it accelerates, and this force is proportional to the relative acceleration of the phases. This force is significant for the high-density ratio of the dispersed phase, such as bubble flows, as well as for transient flows, and high-acceleration flows.

**Mass transfer** occurs when mass is transferred from one phase to another. Mass transfer is used for phenomena such as cavitation, evaporation and distillation, chemical reactions, welding, and so on.

The Eulerian model can be used in the dense discrete phase model (**DDPM**), boiling model and multi-fluid VOF model. There are several types of welding models, including RPI (Rensselaer Polytechnic Institute) welding, non-equilibrium welding, and critical heat flux. Multi-fluid VOF models combine the Eulerian model with the VOF model and create sharp or dispersed modes to model the interface between phases. The DDPM also shows the combination of the Eulerian model with the discrete phase model and the creation of a Lagrangian perspective on particle tracking. This mode is mainly used in cyclonic separators, fluidized bed, and risers.

In multi-phase models, VOF and mixture only apply the primary and secondary phases without any other adjustment, while to use the Eulerian model, settings must be considered to define the secondary phase. Normally, only the diameter of the secondary particles can be defined. But, if the **granular** mode is used as a combination of solid-liquid or **packed bed** mode, it also defined some properties of solid particles. In granular mode, the granule temperature option indicates the oscillating energy of solid particles, and in packed bed mode, the partial differential equation option indicates its conductivity.

## Eulerian Model in Fluent

The Eulerian multiphase model in ANSYS Fluent allows for the modeling of multiple separate, yet interacting phases. The phases can be liquids, gases, or solids in nearly any combination. A Eulerian treatment is used for each phase, in contrast to the Eulerian-Lagrangian treatment that is used for the discrete phase model.

With the Eulerian multiphase model, the number of secondary phases is limited only by memory requirements and convergence behavior. Any number of secondary phases can be modeled, provided that sufficient memory is available. For complex multiphase flows, however, you may find that your solution is limited by convergence behavior. See Eulerian Model in the User’s Guide for multiphase modeling strategies.

ANSYS Fluent’s Eulerian multiphase model does not distinguish between fluid-fluid and fluid-solid (granular) multiphase flows. A granular flow is simply one that involves at least one phase that has been designated as a granular phase.

Once you have determined that the Eulerian multiphase model is appropriate for your problem (as described in Choosing a General Multiphase Model in the Theory Guide), you should consider the computational effort required to solve your multiphase problem. The required computational effort depends strongly on the number of transport equations being solved and the degree of coupling. For the Eulerian multiphase model, which has a large number of highly coupled transport equations, computational expense will be high. Before setting up your problem, try to reduce the problem statement to the simplest form possible.

Instead of trying to solve your multiphase flow in all of its complexity on your first solution attempt, you can start with simple approximations and work your way up to the final form of the problem definition. Some suggestions for simplifying a multiphase flow problem are listed below:

Use a hexahedral or quadrilateral mesh (instead of a tetrahedral or triangular mesh).

Reduce the number of phases.

Granular

(secondary phase) indicates whether or not this is a solid phase. This item appears only for the Eulerian model.

Turbulence Multiphase Model

contains options for multiphase turbulence models. This portion of the dialog box will appear if Eulerian is selected as the Model in the Multiphase Model Dialog Box.

Mixture

specifies the (default) mixture turbulence model.

Dispersed

specifies the dispersed turbulence model.

Per Phase

specifies the calculation of a set of turbulence equations for each phase.

k- ε Mixture Turbulence Model

The mixture turbulence model is the default multiphase turbulence model. It represents the first extension of the single-phase – model, and it is applicable when phases separate, for stratified (or nearly stratified) multiphase flows, and when the density ratio between phases is close to 1. In these cases, using mixture properties and mixture velocities is sufficient to capture important features of the turbulent flow.

k- ε Dispersed Turbulence Model

The dispersed turbulence model is the appropriate model when the concentrations of the secondary phases are dilute, or when using the granular model. Fluctuating quantities of the secondary phases can be given in terms of the mean characteristics of the primary phase and the ratio of the particle relaxation time and eddy-particle interaction time.

The model is applicable when there is clearly one primary continuous phase and the rest are dispersed dilute secondary phases.

Coupled Solution for Eulerian Multiphase Flows

In multiphase flow, the phasic momentum equations, the shared pressure, and the phasic volume fraction equations are highly coupled. Traditionally, these equations have been solved in a segregated fashion using some variation of the SIMPLE algorithm to couple the shared pressure with the momentum equations. This is attained by effectively transforming the total continuity into a shared pressure. The ANSYS Fluent, Phase Coupled SIMPLE algorithm has been successfully implemented and solves a wide range of multiphase flows. However, coupling the linearized system of equations in an implicit manner would offer a more robust alternative to the segregated approach.

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