Week 5 - Turbulence modelling challenge

Turbulence modelling challenge

Aim: To explain turbulence modelling and run simulation for Golf ball.

Objective:

1. Turbulence modelling.

2. To perform a 3D simulation and explain the recirculation region using velocity vectors.

3. Visualize the wake region.

Theory:

Turbulence is unsteady, irregular fluid motion in which transported quantities (mass, momentum, scalar species) fluctuate in time and space.

As of now there is no sure shot definition for turbulence. Some of charecteristics are:

1. Identifiable swirling patterns characterize turbulent eddies.

2.Enhanced mixing (matter, momentum, energy, etc.) results

3. Fluid properties and velocity exhibit random variations for this statistical averaging results in accountable, turbulence related transport mechanisms.

Some of the turbulence models are :

A ) Zero Equation Model:

1. No PDE is used to solve the turbulent viscosity.

2. It fails to account for transient behaviour of turbulent viscosity which leads to lower accuracy in results.

3. Directly solves turbulent viscosity using a Mixing length model.

4. Mixing length model assumes eddy viscosity terms to be dimensionally similar to two scales mainly Kolmogorov length scales & Kolmogorov velocity scales.

B ) Spalart Allmaras Model (S-A model) (One Equation Model):

1. It uses one set of equations to solve the turbulent kinetic energy in order to obtain turbulent viscosity.

2. The derived turbulent viscosity is substituted into the RANS model to solve the turbulence.

3. This is specifically designed for internal & external flows when the flow is attached, but not good when flows with strong adverse gradient ot detaching flows.

C ) Two Equation models:

The mainly used models are :

1. Turbulent Kinetic Energy & Turbulent Dissipation Rate (K-epsilon Model):

In this K-epsilon (k-ε) turbulence model is used to simulate mean flow characteristics for turbulent flow conditions. It is a two-equation model which gives a general description of turbulence by means of two transport equations (PDEs). The original impetus for the K-epsilon model was to improve the mixing-length model.

2. Turbulent Kinetic Energy & Specific Dissipation Rate (K-omega Model)

It predicts turbulence by two partial differential equations for two variables, k and ω, with the first variable being the turbulence kinetic energy (k) while the second (ω) is the specific rate of dissipation.

It is widely used model industry: mainly in aerospace and turbomachinery.

DNS isn’t feasible according to Kolmogorov's scale:

1. It is more tedious procees for solution to converge

2. It requires very fine meshes which results in more computational resources for a simulation to run. Hence industries dont preffer this method as its inefficient

Procedure:

Geometry:

Import the geometry in fluent.

Meshing:

size : 1mm

Assign the names accordingly

Setup:

Pressure-based

Inlet - 60m/s.

Results:

Velocity contour:

Pressure contour:

Conclusion:

Re-circulation is visualized, it is condition where the flow separates from the body of the obstacle. This creates a low pressure area immediately downstream which sucks fluid back into this region from the main flow with the net result of creating a circulating vortex or pair of vortices.

The wake region behind the ball is captured.

The direction of the ball is going down and the dimples on the golf ball helps to reduce the drag.