Objectives of this course are to introduce mathematical formulations, physical insights, and numerical
modeling of incompressible turbulent flows.
The following is the progress during Spring 2022 semester. The duration of each lecture is 50 minutes.
[18/01] Chapter 1: Some famous fluid mechanics experiments, overview of the course
[20/01] Motivation, characteristics of turbulent flows
[21/01] Are turbulent flows beneficial/detrimental?
[25/01] Energy cascade, Introduction to index notation
[27/01] Tutorial on index notation. Chapter 2: Need for statistical description,
Reynolds decomposition, rules of averaging
[28/01] Derivation of Reynolds Averaged Navier-Stokes equations (RANS), Reynolds stress,
closure problem
[01/02] Mean passive scalar equation, eddy viscosity and gradient-diffusion hypothesis
[03/02] Energetics of total- and mean-flow
[04/02] Ergodicity hypothesis, Equations for second-order moments of fluctuating velocity
[08/02] Turbulent kinetic energy equation
[10/02] Review of relevant fluid mechanics concepts, derivation of vorticity equation in index notation
[11/02] Vortex stretching mechanism, enstrophy
[15/02] Chapter 3: Experimental observations on round jet — velocity profiles, self-similarity, universal constants, entrainment, Reynolds stress
[17/02] Turbulent boundary layer approximation, self-similarity solution for plane jet, energy budget
[18/02] Simplified TBL approximation and self-similar solutions of Plane wake
[22/02] Mean flow equations and velocity profiles in turbulent channel flow
[24/02] Friction and Reynolds stresses in channel flow, Pipe flows and effect of roughness
[25/02] Chapter 4: Overview of numerical simulations of turbulent flows, Direct numerical simulation
[03/03] Hands-on session 1: Introduction to DNSLab. DNS of channel flow, and write mean velocity profile
[04/03] Hands-on session 2: Exercises on DNSLab. Q-criterion, and write outputs of turbulence quantities and production
[09/03] Mid-semester exam
[22/03] Chapter 3 (contd.) Turbulent boundary layers – Mean velocity profiles, van Driest damping function, log-law and power law
[24/03] Reynolds stresses in TBL, budgets of normal and shear stresses
[25/03] Coherent structures in wall-bounded flows: streaks, streamwise vortices, hairpin vortices, quadrant analysis
[29/03] Chapter 4 (contd.) introduction to RANS models, recap of kinetic theory of gases, mixing length hypothesis
[31/03] Algebraic models: mixing length, Cebeci-Smith, and Baldwing Lomax models
[01/04] Performance of algebraic models in attached and separated flows, Construction of “model” turbulent kinetic energy equation
[05/04] Spalart-Allmaras model
[07/04] Hands-on session 3: Flow over a NACA0012 airfoil at zero degree AoA with Spalart-Allmaras model using ANSYS-FLUENT
[08/04] Hands-on session 3: contd.
[12/04] Formulation of k-epsilon and k-omega models
[19/04] Hands-on session 4: Flow over a NACA0012 airfoil at 4 degree AoA with Spalart-Allmaras, and other models
[21/04] Hands-on session 4: contd. Turbulent flow through a channel and comparison with Johns Hopkins turbulence database
[22/04] Performance of two-equation models to free-shear and attached boundary layer flows
[26/04] Performance of two-equation models to separated flows, Large eddy simulation
[28/04] Term paper presentation
[03/05] Term paper presentation
[03/05] End-semester exam