Multiphase Flow Modeling:Terminologies

Terminologies:
The fundamental terminologies used in the study of multiphase flows are as follows:

• Continuous phase or Primary phase: This is basically the carrier fluid, that is present in bulk.

• Dispersed phase or Secondary phase: This is the discrete phase which is usually in the form of  particles, droplets, or bubbles. The secondary phase may or may not have a distinct velocity field i.e. it will at some times follow the continuous phase or at times will have its own velocity field and affect the continuous phase flow.

• Volume fraction:

+ Volume fraction of a dispersed phase: It is defined as the ratio of volume of dispersed phase to the volume of the medium or the total volume. Mathematically represented by

Where  del Vd is the volume of the dispersed phase in  volume del V .
Unlike a continuum, the volume fraction cannot be defined at a point and is defined based on the volume.
+ Volume fraction of a continuous phase: Similarly, defined as the ratio of volume of continuous phase to the volume of the medium or the total volume. Mathematically represented by

where del Vc is the volume of the continuous phase in the volume. By definition the sum of the volume fraction must be unity i.e.

• Densities: In multiphase we have two terms for densities, the bulk density and the material density. The bulk density is defined as the mass of the dispersed phase per unit volume of mixture, mathematically given by,

del Md mass of dispersed phase. This bulk density is related to the material density rho(d) by,

The sum of the bulk densities for the dispersed and continuous phases is the mixture density.

• Velocities: There are generally two terms used to define velocities, the superficial velocity and the phase velocity.

+ Superficial Velocities: It is mostly associated with pipe flow and is the mass flow rate, of the respective phase divided by the pipe area A and material density. So in case of dispersed phase this superficial velocity is given by:

+ Phase velocities: The phase velocity Ud is the actual velocity of the phase. The volume fraction relates the phase velocity with the superficial velocity as follows:

The phase velocity or the bulk density, are generally defined for our convenience purpose in study of multiphase flow and different from the actual velocity and density of the phase. They are obtained by multiplying actual velocity or density with volume fraction.

• Mass concentration of dispersed phase: It is the ratio of the mass of dispersed phase to that of the continuous phase in a mixture.

• Quality: It is the measure of the quantity of dispersed phase in the medium (both the dispersed and continuous phase).

• Phase Loading: It is the ratio of mass flux of the dispersed phase to that of continuous phase.

• Disperse Flows: In such flows the phase loading of dispersed flows is comparatively lower (by mass) than the continuous phase. The bulk of the flow is occupied by the continuous phase and dominates the flow phenomena. In dispersed flow the particle motion is mainly controlled by the fluid forces (like drag and lift).

• Dense Flows: Such flows are generally associated with high phase loadings of dispersed phase. Here the interparticle collisions play a dominant role in the flow field controlling the overall particle motion. The dense flows are classified into two main categories namely,           

+  Collision dominated: Collisions between the particles control the overall flow features.
+  Contact dominated: Continuous particle to particle contact controls the overall flow features.

• Stokes Number: It is a non-dimensional number, given by the ratio of  particle (dispersed phase) relaxation time to the characteristic time scale of the flow. Mathematically represented by:

+ Significance of Stokes Number:
If Stk<<1 , then particles follow the continuous phase flow closely.
If Stk> 1 , then dispersed phase particles will move independent of the continuous phase flow.

coming up... Fundamentals of Multiphase Flow Modeling

Multiphase Flow Modeling

What is a Multiphase Flow?

Multiphase flow is a phenomena of simultaneous flow of mixtures of phases such as gases (like bubbles) in a liquid, or liquid (like droplets) in gases and similar such flows.

By multiphase flow we mean that its a mixture of phase and each phase in it has a distinct velocity field.

Why study Multiphase Flow?

• Multiphase flows are found in various industrial applications like chemical reactors and process flow industries.
• Natural and environmental flows like rivers and cloud formation involve multiphase flows.
• In practical flows it is difficult to isolate single phase isolated flow phenomena.
• Knowledge of multiphase flow physics  is extremely important to conduct any experimental or simulation studies.
• Multiphase flow is a very vast  discipline of study. It involves study of fluid mechanics, heat transfer, mass transfer and energy transfer.

Classification of Multiphase flows:

Multiphase flows are generally classified on the basis of:

• number of phases 
• types of phases 
• size of phases
• the interaction between the phases. 

Based on these parameters they are further classified as follows:

• Dispersed Phase Flow: In this type of flow one of the phases is in the form of discrete elements. There is no connection between these discrete phase elements that may be in the form of particles or droplets. E.g.: Droplets in gas, bubbles in liquid etc. It is thus a mixture of different sized droplets of particles dispersed around a continuous media.                                                               

• Separated Flows: In such types of flows the two phases involved are separated by a distinct line of contact. This basically means that we can travel from one location to another in the same phase and remain in the same medium.  E.g.: Annular flow where there is a liquid layer along the pipe wall and a gaseous inner core. Thus in this flow, one phase can be distinctly separated from another.  

• Gas-Liquid Flows: As the name suggests one of the phases is in gaseous form while the other in liquid state. They can be in different forms like bubbly flow and annular flow.

• Gas–Solid Flows: In such types of flows we generally have gas with suspended solid particles. Granular flows are also among this where particle–particle and particle–wall interactions are more important than the forces due to the interstitial gas. 

• Liquid–Solid Flows: In these types of flows solid particles are carried by liquid, also called as slurry flows. Here the solid particles will not have the distinct velocity field but will generally follow the liquid velocity field.

• Three-Phase Flows: Three-phase flows are also encountered in engineering problems. For example, bubbles in a slurry flow give rise to three phases flowing together. This is an emerging topic for research and computational modeling and is a very advanced and interesting branch of study under multiphase flows.

coming up next... Fundamental terminologies used in study of multiphase flows :

Introduction to CFD - Part V : Solution

Solutions

Once the preprocessing is done, means once we have good mesh, we can import the mesh in specific solver are solve the desired governing equations. This step is called as solution step. The tools which take mesh as input and carryout the solution of selected governing equations are called as solvers. 

In typical solver we will be doing following steps:

a) Selecting the appropriate solvers

i) Pressure based or density based

b) Selecting the mathematical equations to be solved

i) Steady state or unsteady state equations

ii) Compressible of incompressible equations

iii) Laminar or turbulent flow equations

iv) Energy equation

v) Multiphase flow equations

vi) Radiation equations 

           And many more based on the physics you want to simulate

 c) Selecting the material properties

i) Fluid Material (Water, air etc...)

ii) Solid Material (Copper, Aluminum etc...)

d) Assigning appropriate boundary conditions

i) Inlet Boundary:

- Example 1 : Velocity Inlet with 10 m/s and normal to boundary

- Example 2: Total pressure at inlet = 101325 Pa (Gauge)

- Example 3: Mass flow rate at inlet = 12 Kg/s

ii) Outlet Boundary

- Example 1 : Pressure at outlet = 0 (Gauge)

- Example 2 : Mass flow at outlet = 10.2 Kg/s

- Example 3 : 50 % flow is going out of the outlet

iii) Wall Boundary

- Example 1 : Adiabatic and no slip boundary

- Example 2 : Constant temperature 400 K and no slip boundary

iv) Fluid domain conditions

- Example 1 : Working media is air and domain is rotating with 1000 rpm

- Example 2: Working media is water

v) Solid domain conditions

- Example 1 : Heat generation rate in solid = 20 W/m³

           Any many more depending on the problem that you are simulating

e) Selecting the Solutions controls

i) Selecting discritization schemes

- Example : 1^st order for pressure and 2^nd order for density

ii) Selecting under relaxation factors

iii) Selecting pressure correction methods

- SIMPLE/SIMPLEC/PISO

iv) Selecting the CFL number 

f) Providing the initial guess of the solution

g) Putting some monitors for getting idea about if my solution is converged or not

h) Carrying out the solution

 

You may not be in position to appreciate most of the above steps. But all the above steps will be explained in detail in chapters to come. You will come to know the meaning and importance of each and every step written above but the only conditions is you should keep on reading.

The overall idea of task carried out in solver is to solve the selected set of equations with specified boundary conditions for selected materials using selected numerical schemes

The type of numerical scheme and solution strategy will depend on which type of equations we will be solving, which type of boundary conditions we will be using and what type of geometry is involved in the problem.

 

Following chart will give an overall idea about inputs needed for any solver