**Introduction:**

VOF model is used to model immiscible fluids with clearly defined interface. Numerical study of multiphase fluid flows require mathematical methods for distinguishing interface between two fluids. The volume of fluid (VOF) method is one of such method which takes care of fluid shape in a local domain and reconstructs the interface from volume fraction of one fluid.

It is a surface-tracking technique applied to a fixed Eulerian mesh where Navier Stokes equations which describe the motion of the flow have to be solved separately. The method is based on the solution of a transport equation for variable ‘C’ (often also referred as indicator or colour function) for the liquid phase.

The following mathematical equations are involved in the analysis process:

Cij represents the portion of the area of the cell (i, j) filled with liquid phase and the phase function χ:

where 0 < C < 1 in cells cut by the interface S and C = 0 or 1 away from it.

The VOF method doesn't explicitly track the interface, it reconstructs the interface based on calculation of the volume fraction of fluid. The Color Function also cannot be solved easily. Several methods for the reconstruction of the interface exist, the most popular being PLIC (Piecewise Linear Interface Calculate).

In a 3D space, the interface can be described by:

Where n is the normal vector to the interface and α is a constant line.

α can be solved by root-finding method or analytical formulas α=α(C) and n⃗ has several approaches such as Parker and Yong's method, Least-squarts method etc.

**Geometry:**

The Model is created in Design Modeler. Fig 1 shows the Tank Model. Inlet diameter of the tank 200 mm and pipe diameter between two tanks is 100 and outlet diameter is 50mm.

**Fig.1: Tank Model**

**Meshing:**

Meshing is created in ANSYS according to the following parameters.

Mesh Details:

Nodes: 5284

Elements: 5056

Mesh Type: Quadrilateral.

Thereafter the name selection for the configuration has been done as: inlet and outlet.

Fig.2: Meshed Model

**Fluent Setup:**

**General Settings:**

**1.** Check the mesh.

**2. **Examine the mesh.

Fig.3: Examining Mesh

3. Set the Gravitational Acceleration.

Fig.4: General Setting

Enter -9.81 m/s^{2} for the Gravitational Acceleration in the Y direction.

Models:

1. Enable the Volume of Fluid multiphase model for two phases.

Fig.5: Multi-Phase Model Setting

2. Enable the standard k-e turbulence model.

Fig.6: Viscous Model Setting

** Defining** **Material:**

**Material- Air :** For primary Phase**Material- Air : **Create Edit-Water Liquid

Fig.7: Defining Material

**Define: Phase-Phase 1: Air**

Fig.8: Phase - 1- Air

Phase-Phase 2: Water-Liquid

Fig.9: Phase - 2- Water

**Boundary Condition:**

At Inlet: Velocity Inlet-Mixture - 0.25 m/s.

Fig.10: Defining Velocity at Inlet.

Velocity Inlet: Phase 2 - edit Multiphase: Volume Fraction: 1

At Outlet: Pressure Outlet.

**Solution Initialization:**

Fig.11: Initializing the Solution

** Region Adaptation:**

Fig.12: Region Adaptation Setting

**Select: Adapt**

** Select: Mark**

**Patch:** Volume Fraction in Variable and Hexahedral-r0 in registers to patch.

Fig.13: Patch Setting

**Calculation Activities:** Auto save every 5sec.

Fig.14: Auto-Save Calculation Setting

** Run Calculation:**

Fig.15: Defining No. of Time Steps.

**Results:**

**Volume Fraction after 10 secs:**

Fig.16: Volume Fraction after 10 secs.

Volume Fraction after 20 secs:

Fig.17: Volume Fraction after 20 secs

Volume Fraction after 30 secs:

Fig.18: Volume Fraction after 30 secs

Volume Fraction after 40 secs:

Fig.19: Volume Fraction after 40 secs

Volume Fraction after 50 secs:

Fig.20: Volume Fraction after 50 secs

Velocity Streamline:

Fig.21: Velocity Streamline

Velocity Vector:

Fig.22: Velocity Vector