Week 5 - Turbulence modelling challenge

Part 1: Explain different turbulence models & why DNS isn't feasible according to Kolmogorov's scale. There are two main models are available to model turbulence which are as follows: 1. First Order Models: First order models assume analogy between laminar & turbulent flows. They assume that the average turbulent flow field is similar to the laminar flow field which results in lower accuracy. It has three subtypes of models based on the number of equations the model is solving. - Zero Equation Models - One Equation Models (Spalart Allmaras model) - Two Equations Models (K-epsilon model & k-omega model) 2. Second Order Models: These models are solving the transport equations additionally to derive Reynolds stress terms in 3D.
As these models are solving additional equations to work in 3D & also PDEs are of the 2nd order, it has the highest accuracy but computationally very expensive. And because of large number of extra equations, these models are sensitive to boundary conditions as well. These models are commonly used in the industries.

This type also has subtypes. - Algebraic Stress Model - Reynolds Stress Model The main difference between first order & second order model is that first order model uses the PDEs of 1st order to derive Reynolds stress terms while the second order models are using the PDEs of 2nd order because of that the accuracy of the second order models are more than the first order models but computationally more expensive.
Detail explanation of each model of First Order Models are as follows: Zero Equation Model: - No PDE is used to solve the turbulent viscosity. - Fails to account for transient behaviour of turbulent viscosity which leads to lower accuracy results. - Directly solves turbulent viscosity using a Mixing length model. - Mixing length model assumes eddy viscosity terms to be dimensionally similar to two scales: Kolmogorov length scales & Kolmogorov velocity scales

One Equation Model: - This model uses one set of equations to solve the turbulent kinetic energy in order to obtain turbulent viscosity. - The derived turbulent viscosity is substituted into the RANS model to solve the turbulence. - Spalart Allmaras Model (S-A model) is one eqation model. This S-A model is specifically designed for internal & external flows when the flow is attached, but not good when flows with strong adverse gradient of detaching flows. Two Equation models: These models solve two PDEs to determine following quantity based on the model used. - Turbulent Kinetic Energy & Turbulent Dissipation Rate (K-epsilon Model) - Turbulent Kinetic Energy & Specific Dissipation Rate (K-omega Model) K - epsilon Model: This model has three different variants: (a) Standard k-epsilon model: - This is the most widely used model in the industries. - It uses wall functions to calculate epsilon near wall. - It is very known model to have very good convergence & memory efficient characteristics. - It is very good model for attached & turbulent flows and also for solving external flow around complex bodies.

Part 2: Objective is to determine which way ball is going to move. The velocity contour graph & vector plot will be presented. Inputs: Air velocity: 60 m/s Following model has been received as input:

Turbulence Model used for the simulation: SST K-omega Model Material: Air Inlet: 60 m/s Initialization: Standard Iterations: 300
Results: CID-post has been used for post-processing the simulation results. Velocity Contour Plot:

from above vector plot, it can be said that the ball will curve downward. The wake region or recirculation region at the back side of ball shows the direction of arrow circulating downward.
The recirculation region also helps the flow seperating from the ball.