ME639 Course Syllabus

Course Specifications

Textbook: None
Instructor: Goodarz Ahmadi (CAMP 267, 268-2322)
Office Hours: Monday and Wednesday 12:30 – 3:30 p.m.
Prerequisites: ME 527

Course Learning Objectives

1. To provide the students with a fundamental understanding of turbulent flows.
2. To familiarize the students with the stochastic and chaotic nature of turbulence.
3. To provide the students with the tools for modeling turbulent flows.
4. To familiarize the students with the statistical theories of turbulence.
5. To familiarize the student with simulation techniques in turbulent flows.
6. To familiarize the students with applications of turbulence in industry and environment.

Course Learning Outcomes

Objective 1:

Students will demonstrate an understanding of the fundamental physics of turbulent flows.   Students will be able to analyze the transport of moment, energy, and vorticity in turbulent flows.

Objective 2:

Students will be able to analyze turbulent flows in complex regions with the use of commercial codes. Students will be able to analyze simple shear, wall-bounded, and boundary layer flows with the use of phenomenological models of turbulence.  Students will demonstrate an understanding of advanced higher-order modeling of turbulent shear flows.  Students will be able to analyze turbulent flows in complex regions with the use of commercial codes.

Objective 3:

Students will become familiar with the direct and large-eddy simulations of turbulent flows. Students will become familiar with the classical and modern statistical theories of turbulence.

Objective 4:

Students will perform stochastic simulations in their respective fields of interest. Students will become familiar with the applications of turbulence in industry and the environment.

Course Outline

1. Reviews

• Engineering Mathematics, (Slides)
• Indicial Notation, (Slides)
• Fundamentals, (Slides)
• Kinematics, (Slides)
• Conservation Laws, (Slides)
• Linear Instability Theory, (Slides)
• Nonlinear Stability Analysis, (Slides)
• Dynamical Systems, (Slides)
• Introduction to Chaos, (Slides)

2. Physics of Turbulence

• Introduction to Physics of Turbulence, (Slides)
• Reynolds Equation, (Slides)
• Phenomenological Theories, (Slides)
• Correlation and Spectrum, Length and Time Scales, (Slides)
• Energy Equation, (Slides)
• Vorticity Dynamics, (Slides)

3. Turbulent Shear Flows

• Free Shear Flows (Wake Flows), (Slides)
• Free Shear Flows (Jet Flows), (Slides)
• Wall-bounded Shear Flows, (Slides)
• Boundary Layer Flows, (Slides)

4. Turbulence Modeling

• Zero Equation Models, (Slides)
  • Eddy Viscosity
  • Mixing Length Hypothesis, (Slides)
• One and Muti-Equations Models, (Slides)
  • k-e Models
  • Stress Transport Models, (Slides)
  • Higher-Order Modelings, (Slides)
  • Thermodynamical Approach to Modeling, (Slides)

5. Numerical Simulation Methods

• Computational Modeling of TurbulenceCommercial codes (ANSYS-FLUENT)
• Direct Simulations, (Slides)
• Large-Eddy Simulations, (Slides)
  • Subgrid-Scale Modeling

Statistical Theories of Turbulence

• Homogeneous Isotropic Turbulence
  • Karman-Howarth Equations
• Probability Density Function Approach, (Slides)
  • Lundgren’s Theory
  • Chung’s Kinetic Theory of Turbulence
  • Pope’s pdf Model
• Proper Orthogonal Decomposition Method, (Slides)
  • Orthogonal Basis
  • First Order System
  • Navier-Stokes System
  • Low Dimensional Dynamical System
  • Applications to Modeling
• Wiener-Hermite Expansion Method, (Slides)
  • Orthogonal Random Functions
  • Meecham’s Theory
• Kraichnan’s Direct Interaction Theory
  • Infinitesimal Impulse Response
  • Eulerian Direct Interaction Approximation
• Functional Approach
  • Hopf’s Characteristic Functional Theory of Turbulence
  • Lewis-Kraichnan Approach
• Stochastic Methods
  • Coherent Structures
  • Wavelet Transform
  • Stochastic Estimation
  • Pseudo-Flow Visualization

Evaluation Methods

• Homework 10%
• Exam-1 25% (March 15, CAMP 178 4:00-5:15 pm)
• Final Exam 35% (Final Exam Week)
• Project 1 10% (February 22, 2024)
• Project 2 20% (April 23. 2024)

Course Description

ME 639 Advanced Turbulence R-3, C-3.
Prerequisites: ME 527 or equivalent.

Review of viscous flow theory. Review of the instability of viscous flows. Origin of turbulence. Phenomenological theories of turbulence. Reynolds’ equation. Energy budget and vorticity dynamics in turbulence. Free shear and internal flows. Turbulent boundary layer. Introduction to turbulence modeling. The k-e and stress transport models. Recent developments in turbulence modeling, stress transport models, multipoint closure methods, and thermodynamical formulation. Turbulent diffusion, isotropic turbulence, and Karman-Howarth equation. Kraichnan’s direct interaction approximation.Wiener-Hermite expansion approach. Characteristic functional formulation and Hopf’s theory. Lundgren’s probabilistic formulation and Chung’s kinetic theory of turbulence. Direct and Large-Eddy simulation techniques. Proper orthogonal decomposition Techniques. Chaos and dynamical systems, stochastic Estimation, Lagrangian mean approaches.

Exam & Homework Policies

Exam Policy

Exams will be open book.

Homework Policy

Homework will be collected as assigned. Homework will be graded and returned to the students.