Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Indian Institute of Technology Bombay

Essentials of Turbulence

Indian Institute of Technology Bombay and NPTEL via Swayam

Go to class Write review
Udacity Ad

Master AI & Data—50% Off Udacity (Code CC50)

Learn More → Coursera Ad

All Coursera Certificates 40% Off

Learn More →

Overview

Coursera Flash Sale
40% Off Coursera Plus for 3 Months!
Grab it
ABOUT THE COURSE:Turbulence is a complex and fascinating phenomenon that plays a crucial role in various scientific and engineering disciplines, from aerodynamics and meteorology to astrophysics and industrial flows. This course provides a comprehensive introduction to turbulence, covering its fundamental principles, mathematical modeling, and practical applications.Course Objectives:Understand the physical nature of turbulence and its significance in fluid dynamics.Explore the governing equations of turbulent flows, including the Navier-Stokes equations.Learn about statistical and spectral descriptions of turbulence.Analyze turbulence modeling approaches, such as Reynolds-Averaged Navier-Stokes (RANS), Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS).Study real-world applications of turbulence in engineering, atmospheric sciences, and beyond.INTENDED AUDIENCE: Mtech/PhD students, Thermal and Fluid EngineersPREREQUISITES: Prerequisite degree: BTechPrerequisite courses: Fluid Mechanics, Engineering MathematicsINDUSTRY SUPPORT: ANSYS, GE, Airbus, Tata motors, Boeing, DRDO, ISRO, HAL, Shell and other companies working in CFD

Syllabus

Week 1: Fundamental considerations of turbulence
  • The "despair" in turbulence
  • Why Study Turbulence?
  • Descriptions of turbulence: How to define turbulence?
  • A brief history of turbulence
  • Eras of turbulent studies

Week 2:The nature of turbulence
  • Irregularity, Diffusivity, Large Reynolds numbers, 3D vorticity fluctuations, Dissipation
  • Methods of analysis
  • Origin of turbulence
  • Diffusivity of turbulence
  • Length scales in turbulent flows

Week 3:Equations of fluid motion
  • Nature of turbulent flows
  • Continuity and momentum equations
  • Role of pressure and conserved scalars; vorticity equation
  • Rates of strain and rotation; transformation properties
  • Reynolds number similarity

Week 4:Statistical description of turbulent flows
  • Random nature of turbulence
  • Characterization of random variables; Examples of PDF
  • Joint random variables; Joint PDFs; Conditional PDFs
  • Random processes; Statistically Stationary Random Processes
  • Statistical Stationarity and homogeneity; Wavenumber spectra

Week 5:Mean flow equations
  • Reynolds equations
  • Closure problem
  • Anisotropy
  • Gradient diffusion hypothesis
  • Turbulent viscosity hypothesis

Week 6:Scales of turbulent motion Part A
  • Energy cascade
  • Kolmogorov hypotheses Part 1
  • Kolmogorov hypotheses Part 2
  • Energy Spectrum Part 1
  • Energy Spectrum Part 2

Week 7:Scales of turbulent motion Part B
  • Fourier modes
  • Fourier series representation
  • Projection Tensor
  • The evolution of Fourier modes
  • The kinetic energy of Fourier models

Week 8:Scales of turbulent motion Part C
  • Velocity spectrum tensor
  • Energy spectrum function
  • Kolmogorov spectra
  • Model spectra
  • Dissipation spectra

Week 9:Modeling and simulation
  • Challenges and modeling approaches
  • Modeling cost and ease of use
  • Direct Numerical Simulation: Pseudo-spectral methods
  • Direct Numerical Simulation: Computational cost
  • Turbulent Viscosity Models

Week 10:Large Eddy Simulations
  • Filtering
  • Spectral representation
  • Resolution of filtered fields
  • Filtering rate of strain
  • Smagorinsky model

Week 11:Turbulent flow applications Part A: Free shear flows
  • Round jet: Experimental observations
  • Round jet: Mean momentum
  • Round jet: Kinetic energy
  • Other self-similar flows: Plane jet and plane mixing layer
  • Other self-similar flows: Plane wake and grid turbulence

Week 12:Turbulent flow applications Part B: Channel flow, pipe flow
  • Channel flow: Near-wall shear stress
  • Channel flow: Mean velocity profiles
  • Channel flow: Length scales and mixing length
  • Pipe flow: friction law
  • Boundary layers

Taught by

Prof. Abhilash J. Chandy

Tags

Reviews

Start your review of Essentials of Turbulence

Go to class

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free
Someone learning on their laptop while sitting on the floor.