Course11210645374 lectures
Turbulence Modeling
Prof. Vagesh D Narasimhamurthy · IIT Madras
About
Most fluid flows in industry and in nature are turbulent. For example, atmospheric and oceanic flows are turbulent, combustion in an aircraft or IC engine is turbulent, and even human breathing is turbulent. Laboratory experiments of turbulent flows are difficult, expensive and many times impossible! For example, how to measure airflow in a human lung or measure tomorrow’s weather?! Modeling turbulence, therefore, is a pragmatic approach to solve industrial flow problems and understand physics of the fluid flow. This course aims at building fundamentals/theory of various turbulence modeling techniques (from statistical to eddy-resolving methods), their advantages and challenges while implementing them in a computer program or CFD application software.
Prerequisites: PG level fluid mechanics and basic CFD knowledge
Lectures
Week 1
- Introduction to turbulence
- Statistical Analysis: Part - I
- Statistical Analysis: Part - II
- Statistical Analysis Part - III
- Statistical Analysis and Cartesian Tensors
Week 2
- Cartesian tensors and Navier Stokes equation
- Navier Stokes equation and Reynolds decomposition
- RANS equations I
- RANS equations II
- RANS equations III
- RANS equations IV
Week 3
- Reynold's stress: governing equations - I
- Reynold's stress: governing equations - II
- Statistical Stationarity and Homogenity in Plane Couttee Flows - I
- Statistical Stationarity and Homogenity in Plane Couttee Flows - II
- Pressure-strain-rate and redistribution of turbulence in flows - I
- Pressure-strain-rate and redistribution of turbulence in flows - II
Week 4
- Turbulence Kinetic Energy and it’s dissipation rate - I
- Turbulence Kinetic Energy and it’s dissipation rate - II
- Production rate of TKE and Mean TKE - I
- Production rate of TKE and Mean TKE - II
- Turbulent Boundary Layer: Order of Magnitude analysis - I
- Turbulent Boundary Layer: Order of Magnitude analysis - II
Week 5
- Inner and Outer TBL: Order of magnitude analysis - I
- Inner and Outer TBL: Order of magnitude analysis - II
- Inner layer equation, constant stress layer, and inner velocity scaling - I
- Inner layer equation, constant stress layer, and inner velocity scaling - II
- Reynold's Averaged Navier-Stokes (RANS) models - I
- Reynold's Averaged Navier-Stokes (RANS) models - II
Week 6
- Different approaches to solve turbulence closure problem - I
- Different approaches to solve turbulence closure problem - II
- Modelling of turbulent kinetic energy (k): production, destruction, and dissipation rate - I
- Modelling of turbulent kinetic energy (k): production, destruction, and dissipation rate - II
- Standard k-ε model and the model constants - I
- Standard k-ε model and the model constants - II
Week 7
- Standard k-ε model, RNG k-ε model, and Prandlt’s one equation model - I
- Standard k-ε model, RNG k-ε model, and Prandlt’s one equation model - II
- New model k- ε and model constants - I
- New model k- ε and model constants - II
- Introduciton to wall-functions - I
- Introduciton to wall-functions -II
Week 8
- Introduction to wall-resolved simulations - I
- Introduction to wall-resolved simulations - II
- Damping functions for LRN - I
- Damping functions for LRN - II
- Boundary and Initial conditions for RANS simulations - I
- Boundary and Initial conditions for RANS simulations - II
Week 9
- Realizability constraints in eddy-viscoscity models - I
- Realizability constraints in eddy-viscoscity models - II
- Correctors for eddy-viscoscity models - I
- Correctors for eddy-viscoscity models - II
- Reynold’s Stress Modelling (RSM): governing equations - I
- Reynold’s Stress Modelling (RSM): governing equations - II
Week 10
- Dissipation rate and Pressure-Strain rate modelling for RSM - I
- Dissipation rate and Pressure-Strain rate modelling for RSM - II
- Pressure-Strain rate modelling for RSM - I
- Pressure-Strain rate modelling for RSM - II
- Pressure-Strain rate modelling and wall corrections for RSM - I
- Pressure-Strain rate modelling and wall corrections for RSM - II
Week 11
- Introduction to Eddy Resolved Models - I
- Introduction to Eddy Resolved Models - II
- Introduction to Direct Numerical Simulations (DNS) - I
- Introduction to Direct Numerical Simulations (DNS) - II
- Introduction to Large Eddy Simulations (LES) Filtering operation and SGS stresses - I
- Introduction to Large Eddy Simulations (LES) Filtering operation and SGS stresses - II
- Large Eddy Simulations: Filtered Navier-Stokes Equations - I
- Large Eddy Simulations: Filtered Navier-Stokes Equations - II
Week 12
- Large Eddy Simulations: Filters and its types - I
- Large Eddy Simulations: Filters and its types - II
- Large Eddy Simulations: Smagorinsky model - I
- Large Eddy Simulations: Smagorinsky model - II
- LES: Dynamic Smagorinsky model and Scale similarity models - I
- LES: Dynamic Smagorinsky model and Scale similarity models - II
- Numerics in LES and Hybrid models
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Madras
- Department
- Mechanical Engineering
- Teacher
- Prof. Vagesh D Narasimhamurthy
- Level
- Undergraduate
- Language
- English
- Subjects
- Engineering
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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