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Advanced Fluid Dynamics

 

 

PİRİ REİS UNIVERSITY

FACULTY OF ENGINEERING

Mechanical Engineering Programme

2017- 2018 Spring Term Course catalog Form

Advanced Fluid Dynamics

Degree: Bachelor

 

Code

 

 

Year/Semester

 

Local Credits

 

ECTS Credits

 

Course Implementation, Hours/Week

Course

Tutorial

Laboratory

MECH326

3/6

2.0

3

2

-

-

Department

Mechanical Engineering

Instructors

 

Dr. Murat ÖZBULUT

Contact Information

 

mozbulut@pirireis.edu.tr

Office Hours

 

Web page

Pruonline

Course Type

 Elective

Course Language

English

Course Prerequisites

 ENG221, ENG221L

Course Category by Content, %

Basic Sciences

Engineering Science

Engineering Design

Humanities

40

60

-

-

Course Description

Fundamentals:  Molecular motion, continuum hypothesis, introduction to kinetic theory, Mean free path, transport phenomena, kinetic theory for transport equations, Introduction to Cartesian Tensors: Scalars, Vectors and Tensor Notation, Forces Acting on a Surface, Scalar and Vector Products, Kronecker Delta and Alternating Tensor, Gradient, Divergence and Curl Operators, Symmetric and Anti-Symmetric Tensors, Conservation Laws for Fluid Flows: Continuity equation: Mass flux, integral and differential equations, stream function. Momentum equation: Forces, stresses, symmetry of stress tensor; properties of second-order, symmetric tensors; Newtonian fluid; Derivation of momentum equations, boundary conditions; Euler equations, streamline coordinates. Energy equation: First law of thermodynamics, heat transfer, derivation of energy equation. Derivation of entropy equation, implications for transport coefficients. General form of Bernoulli equation. Potential Flows: Complex potentials, Source, Sink, Doublet, Vortex, Transformation of Flows: Conformal mapping, Solutions of the Viscous Flow Equations: Classification of solutions; Unidirectional flows; Similarity solutions; Lubrication theory; Creeping motion, Laminar Boundary Layer: Boundary layer equations; Similarity solution; Free-Shear Flows; Approximate integral solutions; Thermal boundary layer; Asymptotic solutions. Turbulent Flows: Reynolds decomposition, Reynolds stresses, Reynolds equation. Self similar free shear flows; effective viscosity. Turbulent boundary layers; mixing length hypothesis. Turbulence models.

 

Course Objectives

 

The course is designed to teach senior and first year graduate mechanical engineering students the fundamentals of the classical fluid mechanics at an advanced level that is beyond the scope of the first fluid mechanics course. An introduction to the Cartesian tensors and derivation of flow equations in various forms. Solutions to the flow equations using scaling and approximations. Giving a general perspective on viscous fluid flows, boundary layer theory, turbulent flows, unidirectional flows and lubrication theory with applications in engineering.

 

Course Learning Outcomes

 

At the end of this course,  students  will have a complete understanding of the following fundamental topics in engineering:

I.   Be able to use Cartesian tensors to manipulate flow equations;

II. Understand the derivation and physical interpretation of the flow equations;

III. Understand and effectively use the scaling and approximations to obtain analytical solutions

IV. Understand the physical meaning and mathematical  implementation of potential theory and the inviscid flows

V. Understand the boundary layer theory, derivation and solution of the boundary layer equations,

VI. Understand the lubrication theory, its limitations and applications

VII. Understand the concept of flow instability and turbulent flows,

Instructional Methods and Techniques

 

Tutorial Place

Classroom

Co-term Condition

 

Textbook

1. White, F.M., Viscous Fluid Flow, McGraw-Hill, 1994.

2. Kundu, P.K., Cohen, I.M and Dowling, D.R. “Fluid Mechanics” 5th Edition

3. Panton, L. “Incompressible Flows”, 2013, Wiley

Other References

1. An Introduction to Fluid Dynamics by Batchelor G.K.

2. Physical Fluid Dynamics by Tritton, D.J.

3. Boundary-layer Theory by Herrmann Schlichting, Klaus Gersten, with contributions from Egon Krause and Herbert Oertel Jr.

4. Turbulent Flows by Pope, S.B.

 

Homework & Projects

Three problem sets and a term project.

Laboratory Work

 

Computer Use

Commercial CFD tools like FLUENT, CFX, StarCCM will be used in term projects.

Other Activities

-

                   

 

 

Assessment Criteria

Activities

Quantity

Effects on Grading, %

Attendance

 

 

Midterm

1

25

Quiz

 

 

Homework

3

20

Term Paper/Project

1

15

Laboratory Work

 

 

Practices

 

 

Tutorial

 

 

Seminar

 

 

Presentation

 

 

Field Study

 

 

Final Exam

 1

40

TOTAL

 

%100

Effects of Midterm on Grading, %

 

%60

Effects of Final on Grading, %

 

%40

TOTAL

 

%100

 

 

Week

 

Topics

Course Outcomes

1

Introduction to Advanced Fluid Dynamics: Molecular motion, continuum hypothesis

II

2

Fundamentals:Introduction to kinetic theory, Mean free path, transport phenomena, kinetic theory for transport equations.

II,III

3

Introduction to Cartesian Tensors: Scalars, Vectors and Tensor Notation, Forces Acting on a Surface, Scalar and Vector Products

I, II,III

4

Introduction to Cartesian Tensors: Kronecker Delta and Alternating Tensor, Gradient, Divergence and Curl Operators, Symmetric and Anti-Symmetric Tensors

I, III

5

Conservation Laws for Fluid Flows: Continuity equation,  Mass flux, integral and differential equations, stream function.

II,III

6

Conservation Laws for Fluid Flows: Momentum equation: Forces, stresses, symmetry of stress tensor; properties of second-order, symmetric tensors, Newtonian fluid; Derivation of momentum equations, boundary conditions

II, III

7

Conservation Laws for Fluid Flows: Euler equations, streamline coordinates. Energy equation: First law of thermodynamics, heat transfer, derivation of energy equation. Derivation of entropy equation, implications for transport coefficients. General form of Bernoulli equation.

II,III

8

Potential Flows: Complex potentials, Source, Sink

IV

9

Potential Flows: Doublet, Vortex, Transformation of Flows: Conformal mapping

IV

10

Mid-term Exam

I,II, III,IV

11

Solutions of the Viscous Flow Equations: Classification of solutions; Unidirectional flows, Similarity solutions; Lubrication theory; Creeping motion

V, VI

12

Laminar Boundary Layer: Boundary layer equations; Similarity solution; Free-Shear Flows; Approximate integral solutions; Thermal boundary layer; Asymptotic solutions.

V

13

Turbulent Flows: Reynolds decomposition, Reynolds stresses, Reynolds equation. Self similar free shear flows; effective viscosity

V,VI

14

Turbulent Flows: Turbulent boundary layers; mixing length hypothesis. Turbulence models

V,VI

 

 

Relationship between the Course and the Mechanical Engineering Curriculum

 

 

Program Outcomes

Level of Contribution

1

2

3

a

An ability to apply knowledge of mathematics, science, and engineering

 

 

X

b

An  ability to design and conduct experiments, as well as to analyze and interpret data

 

 

 

c

An ability to design a system, component or process to meet desired needs

 

X

 

d

Ability to function on multi-disciplinary teams

 

X

 

e

An ability to identify, formulate, and solve engineering problems

 

 

X

f

An understanding of professional and ethical responsibility

 

 

 

g

An ability to communicate effectively

 

 

 

h

The broad education necessary to understand the impact of engineering solutions in a global and societal context

 

 

 

i

A recognition of the need for, and an ability to engage in life-long learning

 

 

 

j

A knowledge of contemporary issues

X

 

 

k

An ability to use the techniques, skills and modern engineering tools necessary for engineering practice

 

 

X

l

An ability to apply basic knowledge in fluid mechanics, structural mechanics, material properties, and energy/propulsion systems in the context of mechanical engineering design

 

 

X

 

         1: Small, 2: Partial, 3: Full

 

Programme Outcomes & Course Outcomes Connectivity Matrix

 

Course

I

II

III

IV

V

VI

VII

Outcomes

Programme Outcomes

a

X

X

X

X

X

X

X

b

   

 

 

 

 

 

c

 

X

X

 

 

 

 

d

   

 

X

 

 

 

e

X

X

X

X

X

X

X

f

   

 

 

 

 

 

g

   

 

 

 

 

 

h

   

 

 

 

 

 

i

   

 

 

 

 

 

j

   

 

X

X

X

X

k

X

X

X

X

X

X

X

l

X

X

X

X

X

X

X

 

 

 

Prepared by

Dr. Murat Özbulut

Date

01.02.2018

Signature