Turbulence Modeling

Overview

ABOUT THE COURSE: 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 knowledgeINDUSTRY SUPPORT : ANSYS, GE, Airbus, Altair, ESI, Tata motors, Bajaj Auto, TCS, Boeing, DRDO, ISRO, HAL, CSIR (NAL, SERC), Shell, Reliance petroleum, ONGC, GAIL, etc.

Syllabus

Week 1: Introduction to turbulence theory, statistical analysis (random process, ensemble mean, variance, single- and multi-point statistics, spatial and temporal correlation)

Week 2:Cartesian tensors, governing equations of fluid motion, Reynolds averaged Navier-Stokes (RANS) equations, turbulence closure problem

Week 3:Equation for fluctuating fluid motion, Reynolds stress transport equation, statistical stationarity and statistical homogeneity

Week 4:Turbulence kinetic energy equation; turbulence characteristics: diffusive, dissipative and redistribution; mean kinetic energy equation and turbulence production

Week 5:Turbulent boundary layer: outer layer and inner layer, inertial and viscous sub-layers, inner scaling

Week 6:RANS modeling: Boussinesq approximation, eddy-viscosity, zero-equation modeling, two-equation modeling, standard k-ε model, model constants

Week 7:RNG k-ε model, one-equation modeling, k-ω models, wall-functions

Week 8:Low-Reynolds number (LRN) models, ε boundary conditions, Initial conditions

Week 9:Realizability constraints, Reynolds stress models (RSM): pressure strain-rate modeling (slow and rapid parts), wall-correction, algebraic stress models

Week 10:Direct numerical simulation (DNS), Kolmogorov hypothesis, large eddy simulation (LES): resolved and sub-grid scales, filtered Navier-Stokes equations

Week 11:Filter types, sub-grid scale (SGS) modeling: Smagorinsky model, one-equation kSGS model, dynamic Smagorinsky model

Week 12:Scale similarity models, grid convergence in LES, hybrid RANS-LES approach, detached eddy simulation (DES)