## Course Specifications

- Recommended book: Incompressible Flow, by R.L. Panton, 4th ed. John Wiley (2013)
- Instructor: Goodarz Ahmadi (CAMP 267, 268-2322)
- Office Hours: Monday and Wednesday 12:30 – 3:30 pm
- Prerequisites: Graduate Standing

### Course Learning Objectives

- To provide a fundamental understanding of fluid flows in the laminar regime.
- To provide a fundamental understanding of boundary layer flow.
- To familiarize the students with the computational modeling of fluid flows.
- To familiarize the students with the industrial applications of fluid flows.

#### Course Learning Outcomes

**Objective 1**

- Students will be able to formulate and solve fluid flows under the laminar regime.

**Objective 2**

- Students will be able to use perturbation and asymptotic methods and analyze boundary layer flows.

**Objective 3**

- Students will demonstrate a fundamental understanding of computational fluid mechanics.
- Students will demonstrate using the ANSYS-Fluent Code for solving laminar flow problems.
- Students will demonstrate using the CFD code for solving turbulent flows.

**Objective 4**

- Students will understand the concept of stability of fluid motion.
- Students will understand the basics of turbulent flows.
- Students will understand the industrial applications of fluid flows.

### Course Outline

I. REVIEWS OF ENGINEERING MATHEMATICS

- Engineering Mathematics, Differential Equations
- Engineering Mathematics, Partial Differential Equations
- Indicial Notation

II. CONTINUUM FLUID MECHANICS

III. NAVIER-STOKES EQUATION

IV. LOW REYNOLDS NUMBER FLOWS

V. NUMERICAL SIMULATION METHODS

- Finite Difference and Finite Volume Methods
- Introduction to CFD
- Commercial codes (ANSYS-FLUENT)
- ANSYS-Fluent Tutorial Part 1
- ANSYS-Fluent Tutorial Part 2
- ANSYS-Fluent Tutorial Part 3

VI. ASYMPTOTIC METHODS

- Perturbation Method
- Singular Perturbation Theory
- Matched Asymptotic Expansion
- Potential Flows
- Inviscid Shear Flows

VII. BOUNDARY LAYER THEORY

- High Reynolds Number Flows
- Boundary Layer Flows
- Self-Similar Solutions
- Integral Methods
- Free Shear Flows (Jet and Wake Flows)

VIII. STABILITY OF FLUID MOTION

- Linear Instability Theory
- Theory of Small Perturbation and Orr-Sommerfeld Equation
- Nonlinear Stability Analysis

IX. TURBULENT FLOWS

- Introduction to the Physics of Turbulence
- Reynolds Equation
- Phenomenological Theories
- Correlation and Spectrum, Length and Time Scales
- Energy Equation
- Vorticity Dynamics
- Turbulent Jet and Wake Flows

X. TURBULENCE MODELING

#### Evaluation Methods

- Homework 10%
- Exam-1 25%, October 25, CAMP 268, 3:00-4:20 pm
- Final Exam 35%, Final Exam Week
- Projects 30%

### Course Description

ME527 Advanced Fluid Mechanics R-3, C-3.

Prerequisites: Graduate Standing.

Review of engineering mathematics, kinematics of fluid motion, conservation laws, continuity and momentum equations, Navier-Stokes equation, viscous flow theory, simple flows, and low Reynolds number flows. Introduction to computational fluid dynamics. Asymptotic methods, perturbation methods, singular perturbation, and matched asymptotic expansion. Boundary layer theory, similarity solutions, and integral approach. Review of instability of viscous flows. Origin of turbulence. Phenomenological theories of turbulence. Reynolds’ equation, energy, and vorticity transport in turbulence. Introduction to turbulence modeling. The k-e and stress transport models.

### Exam & Homework Policies

#### Exam Policy

Exams will be open books with one book allowed.

#### Homework Policy

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