# its CFD Modeling

## 1. Introduction

### 1.1 Phases of Substances

To get physical understanding of matter, phase and interaction between phases are important for any engineers and users before numerical modeling of any fluid related problems. Materials exist in one of phases like solid, liquid and gases. More than two phases can exist together in many fluid flows. For example, water falling the tap: in this case both air and water interact each other through surface tension.
• Matter: It is defined as a physical structure which has mass and volume in space. It has all types of physical elements that exist in the form of atoms. Examples: wood, water, Uranium, salt and dust particles etc.
• Phase: The distinctive form of matter is defined as a phase which is categorized into three main fields.
• Solid: Shape and volume are definite
• Liquid: Volume is definite, but shape depends on type of container
• Gas: Shape and volume depends on type of container or storage device

### 1.2 Definition of Multi phase flow

• It is defined as the fluid flow where the simultaneous flow of materials with two or more thermodynamic phases exist together.
• Example of Multi-phase Flow: Water bubble column, boiling and condensation and cavitating pumps and turbines etc.
• Multi-phase flow consist of two major phases: 1) Particle (dispersed) phase, 2) Continuous (Eulerian) phase

a) Particle phase:

• This phase  consists of bubbles, particles, or drops, and the continuous phase as the fluid in which these particles are generally immersed.
• The particles can be composed of solid, liquid, or gas
b) Continuous (Eulerian) phase:
• It is based on the Eulerian hypothesis of continuous phase
• The continuous fluid can be a liquid or a gas

Example of multi-phase: free water flow in the air

1.3 Interface:

•  Due to difference in chemical or physical structures, a narrow region between phases is observed as demarcation. This is called an interface
• To distinguish two adjacent  phases or matters, a mathematical function for the interface is generally used for numerical (CFD) modeling.

## 2. Applications of Multi-phase flow

•  Application of multi-phase flow in industries: Solid drying systems, Droplet separation, Packed bed reactors, Foam, Packed columns,Mist eliminators, Centrifugal extractors, Sedimentation, Fluidized bed, Cyclone separators, Mixers, Bubble columns, Particulate systems,  Dust collection systems, Precipitators, Solid suspensions
• Natural phenomenon: rain falls, water from from river and oceans
• Dust flow behind the moving car is an example of multi-phase flow

###   2.1 Cleaning of air in Cement Plants

• Cleaning air in cement plants is essential to reduce particle. It is achieved using the cyclone separator
•  Cyclone for cleaning of dust air
•     Cement Cyclone for cement industries

### 2.2 Controlling Solid pollutants from the flue gases of power plant

•  Electrostatic precipitator (ESP) in the thermal power plant is widely used to collect the dusts and unburned carbon particles carried along with the flue gases
• In ESP, electric field is applied between to opposite plates to attract the particles
• Multi-phase flow through electrostatic precipitator (ESP)

### 2.4 Coal combustion in furnaces

• In boiler, the coal particles are carried by the preheated air and supplied to furnaces
• The coal burners are used in asphalt batching plant to help to save the fuel cost. Now,it is also used in boiler,dryer and other industrial
• Multi-phase flow for coal fired boiler and burner
• Pulverized coal burner is where coal and air is supplied  to generate the flame

### 2.5 Cavitation of Pump Impeller

• While pumping the water, the water vapor is formed in the impeller due to lower pressure. That causes the cavitation in the pump impeller
• The cavitation problem is studied by multi-phase modeling
• Scope of multi-phase flow to study cavitation of water pump

## 3. Classifications of Multi-phase Flows

### 3.1 Depending on the number of miscible fluid

• The multi-phase flows are classified based on number of continuous and dispersed phases

### 3.2 Specification of the Fluid Flow Regime

There are numerous types of multi-phase fluid flow according to the physical process and properties of the problem, and these can be classified into three main fields:

### i)  Dispersed Phases or Particle Laden Flows

• Finite numbers of phases spread through the volume of continuous phases such as droplets, drops, particles or bubbles
• Examples of Dispersed Flow:

### Classification of Particle laden flow ( Based on coupling)

• The coupling between the particle motion and its surroundings can be used to classify the character of the multiphase flows
• Dilute, dispersed, and dense flow conditions based on various interphase and intraphase coupling

### ii)  Separated Phases

• More than one immiscible fluid in continuous phases and separated by interface
• Examples of separated flow at static condition

• Presence of both separated and dispersed phases
• Classification based on gas -liquid flow through the pipe

## 4. Basic Terms and Governing Equations

### 4.1 Basic Terms for Multi-phase Flows

1) Void Fraction/Mean Phase Content (εi): The mean phase content (εi) of the ith phase is defined as the time-averaged volume fraction of that phase in a cross-section of the channel

2) Superficial velocity:

• It is the ratio of  volume flow rate of the phase, Vi (m3/s)  to  the channel cross-sectional area, S (m2):
• It is also called the volume flux for ith phase • The total superficial velocity U is calculated as where n is the total number of phases
3) Average phase velocity:The average phase velocity (ui) of the ith phase is calculated as 4) Flow quality: the flow quality xi of the ith phase is defined where is the mass flux of the ith phase ( = /S), as is the mass rate of flow the phase
5) Multi-phase density: it is the mass of the multi-phase mixture per unit channel volume where ρi is the density of the ith phase.

# 5. Multiphase Flow Modeling

### 5.1 Multi-phase Modeling methods

• Following methods are used for multi-phase modeling
•  CFD users must be familiar with advantage and disadvantages of each modeling techniques
• Grid based methods are available in most of commercial CFD solver like  ANSYS FLUENT and COMSOL Multiphysics  as well as in OpenFOAM
• If the concentration of dispersed phase is less than ~10%, the Dispersed Phase Method (DPM) or model of two way coupling can be used to model the multiphase model. This model does not consider the collision between two particles which is accounted in the Decrete Element Method (DEM).
• If the concentration of dispersed phase is greater than ~20%, by volume averaging, the information of the dispersed phase is lost and can be modeled as contentious (Eulerian) phase
•  CFD user must be familiar assumption considered in each multiphase model as per requirement of flow physics in industrial problems.

### 5.3 COMSOL Multiphysics Solvers

1. COMSOL Multiphase_Models_PDF
3. COMSOL_Multiphaseflow_Introduction_Video
• For COMSOL solver, laminar and turbulent multiphase flows except for:1) Two-phase flow with moving mesh , 2) Three-phase flow, 3) Only available as predefined for laminar flow but can be manually changed for turbulent flows

### 5.4  OpenFOAM Models

• In OpenFoam, basic multi-phase solvers for Eulerian-Eulerian, separating flow solver ( interFoam ) and particle flow (Euler-langrage) are available.
• CFD users can customize the Open Foam code for phase change,  interaction between two phases

### 5.5 Modeling of Interpenetrating Continuous Phases

In this method, the different phases are modeled  mathematically considering as interpenetrating continua. For a given volume,  a particular phase cannot be occupied by the other phases. Hence, the concept of volume fraction is introduced to define the phases. Total sum of volume fraction is 1

1) Interface Capturing Method (VOF/LS/CLSVOF):

• This approach is used for a fixed Eulerian mesh
• It is designed for two or more immiscible fluids where the position of the interface between the fluids is necessary
• A mathematical function is used at  the interface to discriminate two adjacent phases
• The volume of fluid  (VOF) method is mass conservative but interface is not sharp (diffusive) and surface tension is not correctly accounted. To overcome this, level set (LS) function is used to get a sharp interface. However the LS approach is mass conservative. To take advantage of each method a combined level set volume of fluid (CLSVOF) approach is used
• In this approach, a single set of momentum equations is shared by the fluids, and the volume fraction of each of the fluids in each computational cell is tracked throughout the domain.
• Applicationfree-surface flows, stratified flows , cavitation, filling, sloshing , the motion of large bubbles in a liquid, the motion of liquid after a dam break, the prediction of jet breakup (surface tension), and the steady or transient tracking of any liquid-gas interface.
• Comparison of interface tracking methods (VOF, LS and CLSVOF)

### 2) The Mixture Model:

• The mixture model is used for two or more phases (fluid or particulate).
• In this model, the phases are treated as interpenetrating continua.
• This model solves  mixture momentum equations using the relative velocities to define the dispersed phases
• Application of the mixture model:  particle-laden flows with low loading (<5%), bubbly flows,  cyclone separators, and sedimentation
• This model can also be used without relative velocities for dispersed phases to homogeneous multi-phase flow

3) The Euler-Euler or Multi-fluid Model

• This model is applicable for two or more interpenetrating phases (fluid-fluid)
• It solves a set of conservative (momentum and continuity) equations for each phase
• Coupling between two phases is obtained bythe pressure and inter-phase exchange coefficients. The inter phase coefficients depends type interactions  like granular flow (fluid-solid) and non-granular (fluid-fluid) flows
• For granular flows (fluid-solid), inter phase properties are obtained based the kinetic theory of gases
• In ANSYS FLUENT, user-defined functions (UDFs) can  used to customize the calculation of the momentum exchange between two phases
• Applications Euler-Euler or Multi-fluid models: bubble columns, risers, two miscible fluids, particle suspension, and fluidized beds etc

## References:

1) Christopher E. Brennen, Fundamentals of Multiphase Flows, Cambridge University Press 2005

### 2 thoughts on “Basics of Multi-phase Flow and its CFD Modeling”

1. The discrimination of phases in the numerical simulation basically relies on the rate of volume or mass. To determine an appropriate mathematical model for fluid flow, factors such as physical process and flow regime have to be described in advance. Several mathematical models have been developed in order to properly simulate fluid flow. The investigation of multiphase flow still has several hindrances due to complexities related to the mathematical models. However, the Navier-Stokes equations might be broadly used to examine multiphase flows, and the capability of hardware in conducting numerical studies, which are reliant on Navier-Stokes equations, is still far from an affirmative solution.

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