Turbulence and RANS Modelling

Turbulence and RANS Modelling

A 3 month course which explains everything you need to know about modelling turbulence in CFD simulations

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A Quick Overview

"Turbulence and RANS modeling” is designed to provide a basic understanding of the physics and modeling of Fluid Turbulence. Fluid Turbulence is an omnipresent phenomenon and hence becomes important from a fundamental understanding and engineering perspective.

An overview of fluid turbulence and related difficulties is presented in this course. The course then focuses on the industrial CFD application area, i.e., explains different turbulence models (RANS: k-epsilon, k-omega, etc) used in commercial packages, their strengths, and weaknesses. The knowledge and skills acquired would aid the students to choose the best models for a given flow problem.


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1What is Turbulence?

  • Introduction (omnipresence and applications), 
  • From general nature to definition
  • Governing equations (Vector and Einstein notation)
  • Physical meaning

2From Physics to Modeling

  • Navier-Stokes equations: Difficulties and simplifying assumptions
  • Vorticity and “eddy” Modeling
  • Introduction
  • Why model? From low to high fidelity models
  • How to choose models, an overview

3Reynolds averaging - 1

  • What is averaging in fluid mechanics?
  • Decomposition of variables
  • Averaging of Navier-Stokes equations
  • Outlook to modeling effect of fluctuations


  • Effect of fluctuations and Reynolds Stress tensor
  • A brief detour into tensors
  • Kinetic theory and Gradient Diffusion hypothesis, Knudsen number
    • Difference between molecular and turbulent eddy motion

5Dynamics and scales of Turbulence – part 1

  • Energy cascade in real space
  • Kolmogorov’s theory (small scale dynamics)
  • Correlation functions
  • Space and time scales

6Dynamics and scales of Turbulence – part 2

  • Isotropic (Homogeneous) Turbulence
  • Equations in Fourier space
  • The role of pressure
  • Velocity Spectra
  • Taylor’s hypothesis
  • Spectral view of energy cascade

7Free Shear Flows

  • Energy exchange between the mean flow and turbulence
  • Free Shear Flow
  • Self similarity
  • Round jet
  • Plane flow equations

8Wall-bounded Shear Flows

  • Wall Flows
  • Plane flow equations
  • Log law and importance in modeling
  • Heat transfer in wall flows

9Modeling basics – part 1

  • Turbulent viscosity hypothesis revisited
  • Reynolds Stress analogy
  • Reynolds Stresses equation
  • Closure problem

10Modeling basics – part 2

  • Mixing length model
  • Other algebraic models
  • Turbulent Kinetic Energy models

11Practical models - part 1

  • The k-epsilon model
  • The k-omega model
  • Near wall treatments

12Practical models - part 2

  • Idea of Reynolds Stress models
  • The role of numerical dissipation

Projects Overview

Project 1


Consider the 2D Couette-Poiseuille flow which was a part of a challenge in the course.

We are now going to add two functionalities:

  1. non-uniform wall-clustered mesh
  2. a turbulence model to our laminar flow code.

Choose a suitable distribution (exponential, geometric etc.). Do not exceed 200 grid points. Try different wall resolutions for a mesh independence study (stay in log-layer).

The flow solver will now have to use iterations over “pseudo time” to converge the equations with the model. In the code, the declaration of Arrays a,b,c,d and the TDMA solver all go inside the said iterative process. You might have to use a convergence criteria, such as, stop the loop if consecutive solutions do not change by more that 1e-5. Further, consider using under-relaxation if you encounter solver instability as:

u = r*u + (1-r)*u_old  where r varies from 0 to 1 and “mixes” new and old iteration of velocity

The task is to compare velocity profiles with Cases 1-15 from the given reference.

Project 2


The present project is related to simulating turbulent flow through pipes that are bent by 180 degrees (also known as U-bend pipes).

Background: One of the prominent applications of U-bend pipes is for the internal cooling of turbine blades that work at high temperatures. The U-bend pipes are used as “internal cooling channels” where colder air is circulated that takes the heat away from the blade. Usually, one objective is to estimate (and optimize) the pressure loss associated to the flow turning. It involves recognising the main flow features in the blade (separation, 3D flows etc.). 


Task: In a short* report, compare the flow field obtained from two different turbulence models on the same mesh. Use (i) one of the k-epsilon variants and (ii) the RST model.  Note that the kinematic viscosity has to be 1.725e-05 m^2/s. You can use any CFD solver but, follow the specific steps below:

  1. Create a three-dimensional model of the geometry. 
  2. Create a mesh with a target y+=30 for the walls (we are going to use Wall Treatments).
  3. Use the boundary conditions (BCs) at Inlet as provided in the question. 
  4. Perform the calculations using the two suggested turbulence models. For each of them:
    1. show the residual convergence. Report the computational time taken by the two models and also if you encounter any convergence difficulties.
    2. Streamwise velocity contours and streamlines on the Y-Z symmetry plane,
    3. Velocity profiles on the Y-Z symmetry plane (x/D=0.5). 
  5. Speculate how the pressure loss relates to the separation in this flow configuration?




  • Students and Professionals who are interested and/or would like to enhance their knowledge of Turbulence and CFD. The understanding is beneficial for industry jobs and higher studies (Masters, PhD) in the subject.
  • Pre-requisites: Undergraduate level fluid mechanics, basic calculus, Fourier Transform, basic coding skills (Python/MATLAB), familiarity with CFD software


Ansys Fluent / Python

Python is an interpreted high-level general-purpose programming language. It is used for data processing purposes in this course. Scientific packages have been used.
Ansys FLUENT software contains the broad physical modeling capabilities needed to model flow, turbulence, heat transfer, and reactions for industrial applications. In this course, we use it for a fundamental and advanced aerodynamics case.

Frequently Asked Questions

1Who can take your course?

  • Students and Professionals who are interested and/or would like to enhance their knowledge of Turbulence and CFD. The understanding is beneficial for industry jobs and higher studies (Masters, PhD) in the subject.
  • Pre-requisites: Undergraduate level fluid mechanics, basic calculus, Fourier Transform, basic coding skills (Python/MATLAB), familiarity with CFD software

2What is included in your course?

  • Basic turbulence theory (Introduction, RANS equations, Shear Flows, Dynamics)
  • Modeling: Physical arguments behind various RANS turbulence models (Mixing length, k-epsilon, k-omega, RS models)
  • Hands on exercises, both on self-developed simple codes (simple 2D turbulent flow case) and commercial CFD package.

3What will the student gain from your course?

Better understanding of fluid mechanics, turbulence, modeling, basic scientific coding and commercial CFD software experience. In simple words, you would be able to make informed decisions in your CFD process as compared to someone who just “tests and tries”. This might help you save (critical) time and effort in your professional life. The student will be able to understand what experts are saying/discussing on the subject.

4What software skills are you teaching and how well are these tools used in the industry?

  • Basic scripting and scientific calculation skills (predominately in Python) – Commonly used everywhere
  • CFD software – Commonly used in related companies and academia
  • Basic LaTex

5What is the real world application for the tools and techniques will you teach in this course?

  • Python (or MATLAB): Day to day scripting, plotting, basic number crunching, rapid development of pre- or post-processing tools.
  • CFD software: Engineering design process (design based on flow physics and simulations), R&D in both industry and academia.

6Which companies use these techniques and for what?

Typical industry sectors using CFD (that involves turbulence knowledge) include Automotive, Aerospace, Chemical, Energy and CFD software development companies themselves. To be specific some of the Indian companies are Tata R&D, Mercedes Benz, Rolls Royce, Siemens, GE India, Ansys etc. Major parts of the Engineering design process may be influenced by the CFD simulations, starting from proof of concept to optimization of the product. Python (or alike techniques) are used almost universally for the tasks listed in 5a above.

7How is your course going to help me in my path to MS or PhD?

Fresh (under)graduates may lack (or need a brush up) in concepts on fluid physics, basic coding and/or numerics. This course helps to fill the gap between a typical undergrad knowledge level and high requirements of good Master/PhD programmes. Also, the course might help in grasping the subject swiftly during the MS/PhD programmes. An additional specialized course is always an attraction point for the admissions teams.

8How is this course going to help me get a job?

At the end of the course, the student will be able to demonstrate a good level of technical aptitude in the subject. A practical orientation in the course is ensured to meet the industry skill demands. The student will be one step closer to being an expert in the applications of turbulence models in CFD. More generally, the student will be able to devise flow-component designs on the basis of physical understanding, refine and optimize them using the CFD.


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  • Top 5% of the class will get a merit certificate
  • Course completion certificates will be provided to all students
  • Build a professional portfolio
  • Automatically link your technical projects
  • E-verified profile that can be shared on LinkedIn

Flexible Course Fees

Choose the plan that’s right for you


2 Months Access


Per month for 3 months

  • Access Duration : 2 Months
  • Mode of Delivery : Online
  • Project Portfolio : Available
  • Certification : Available
  • Email Support : Available
  • Forum Support : Available

Lifetime Access


Per month for 3 months

  • Access Duration : Lifetime
  • Mode of Delivery : Online
  • Project Portfolio : Available
  • Certification : Available
  • Individual Video Support : 12/ Month
  • Group Video Support : 12/ Month
  • Email Support : Available
  • Forum Support : Available
  • Telephone Support : Available
  • Dedicated Support Engineer : Available


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