Course Content:

Introduction: Examples of turbulent flow, modeling and their applications, Review of fluid mechanics: Mass, momentum and energy equations, boundary layer theory; Theory of turbulent flow: Introduction and statistical description of turbulence, scales of turbulence, energy cascade, Reynolds Equations (SRANS and Unsteady RANS), Reynolds Stress (RS) Equations and closure problems, Turbulent kinetic energy equations, wall bounded, and free-shear turbulent flows, Dynamics of turbulence, coherent and incoherent structures; Review of computational method: Aspects of Finite Difference Equation (FDE) (stability, convergence, order of accuracy, truncation error etc. using modified equations), FDM Solution of Incompressible Viscous Flows (SIMPLE and MAC); Turbulence modeling and simulations: Direct numerical simulation: Accuracy (higher order discretization, scales etc.) and Stability; Large Eddy Simulation: LES filtering, properties of filtering, Explicit and implicit filtering, LES equations, Smagorinsky model and their variants (DSM, SISM), Grid independent LES, Applications to free-shear and wall-bounded flows; Steady/Unsteady Reynolds-averaged Navier–Stokes equations (RANS and URANS) model: (a) Zero equation model, (b) One- and (c) Two-equation models (k-ε, k-ω models), closure models, application for free-shear and wall-bounded flows, range of applicability; Reynolds Stress based modeling and its applications; Probability Density Function (PDF) Modeling: Definitions, Brownian motion, Application to reacting flows (if time permits).

Lecturewise Breakup (Based on 40 lecture)

I. Introduction: [1 lecture]

• Examples of turbulent flow, modeling and their applications.

II. Review of fluid mechanics: [2 lectures]

• Mass, momentum and energy equations, boundary layer theory.

III. Theory of turbulent flow: [13 lectures]

• Introduction and statistical description of turbulence, scales of turbulence, energy cascade.

• Reynolds Equations (SRANS and Unsteady RANS), Reynolds Stress (RS) Equations and closure problems.

• Turbulent kinetic energy equations, wall bounded, and free-shear turbulent flows.

• Dynamics of turbulence, coherent and incoherent structures.

IV. Review of computational method: [5 lectures]

• Aspects of Finite Difference Equation (FDE) (stability, convergence, order of accuracy, truncation error etc. using modified equations), FDM Solution of Incompressible Viscous Flows (SIMPLE and MAC).

V. Turbulence modeling and simulations: [20 lectures]

• Direct numerical simulation: Accuracy (higher order discretization, scales etc.) and Stability.

• Large eddy simulation: LES filtering, properties of filtering, Explicit and implicit filtering, LES equations, Smagorinsky model and their variants (DSM, SISM). Grid independent LES, Applications to free-shear and wall-bounded flows.

• Steady/Unsteady Reynolds-averaged Navier–Stokes equations (RANS and URANS) model: (a) Zero equation model, (b) One- and (c) Two-equation models (k-ε, k-ω models), closure models, application for free-shear and wall-bounded flows, range of applicability.

• Reynolds Stress based modeling and its applications.

• Probability Density Function (PDF) Modeling: Definitions, Brownian motion, Application to reacting flows (if time permits).

References:

1. Fluid Mechanics, F. M. White (7th Edition, McGraw Hill, 2011)

2. Fluid Mechanics, P. K. Kundu, I. M. Cohen and David R. Dowling (5th Edition, Academic Press, 2012)

3. Computational Techniques for Fluid Dynamics, Vol. 1 and Vol. 2, C. A. J. Fletcher, Springer Verlag

4. Computational Fluid Flow and Heat Transfer, Eds. K. Muralidhar and T. Sundararajan, (Narosa Publishers, New Delhi, 2011).

5. Turbulent Flows, Stephen B. Pope (Cambridge University Press, 2000).

6. Turbulence Modeling for CFD, David C. Wilcox, (DCW Industries, Incorporated, 1994).

7. Turbulent Flow, Fundamentals, Experiments and Modeling, Editors: G. Biswas and V. Eswaran, (Narosa Publishing House, New Delhi, 2002).