ME421/521                            Advanced Fluid Dynamics                                     Fall 2020

Instuctor: Prof. Dr. Metin Muradoglu

Office:     Eng. 248

E-mail:    mmuradoglu@ku.edu.tr

Lectures: Tue/Th/Fri  15:00-15:50 via Zoom

Office Hour: Thursday 14:00-15:00 or by appointment

TA: TBA

Requirements: Mech 301 or equivalent and strong background in differential calculus

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. Creeping flows, boundary layer theory, unidirectional flows and lubrication theory with applications in engineering and biological systems. Introduction to potential flow, turbulence and turbulent flows.

Learning Outcomes
Upon successful completion of this course, a student will:

– be able to use Cartesian tensors to manipulate flow equations;

– understand the derivation and physical interpretation of the flow equations;

– understand and effectively use the scaling and approximations to obtain analytical solutions;

– understand the boundary layer theory, derivation and solution of the boundary layer equations;

– understand the lubrication theory, its limitations and applications;

– understand the concept of flow instability and turbulent flows;

– be able to use modern computational tools and interpret the results.

Tentative Schedule:

 

Lectures	Topic	Text
2 lectures	Fundamentals: Molecular motion, continuum hypothesis, introduction to kinetic theory	1.1-1.5 (Vincenti&Kruger)
3 lectures	Introduction to Cartesian Tensors
2 lectures	Preliminary Concepts: Eulerian and Lagrangian descriptions, pathline, substantial derivative, fluid particle acceleration	Chapter 1 (White)
6 lectures	Conservation Laws for Compressible Viscous 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.	Chapter 2 (White)   Chapter 4 (Kundu &Cohen)   Chapter 5 & 6 (Panton)
7 lectures	Solutions of the Viscous Flow Equations: Classification of solutions; Unidirectional flows; Similarity solutions; Lubrication theory; Creeping motion; Swimming at low Reynolds numbers.	Chapter 3 (White) Chapter 5 (Kundu &Cohen)
2 lectures	Potential Flows: Introduction to complex potential, basic potential flows and superposition, conformal mapping
4 lectures	Laminar Boundary Layer: Boundary layer equations; Similarity solution; Free-Shear Flows; Approximate integral solutions; Thermal boundary layer; Asymptotic solutions.	Chapter 4 (White) Chapter 16 (Kundu &Cohen)
2 lectures	Turbulent Flows: Introduction to turbulence and turbulent flows; Energy cascade and Kolmogorov’s hypothesis; Closure problem and modeling.	Chapter 6 (White)

Grading:

1)Homework, Quizzes and Projects     30%

2)Midterm Exam                                      35%

3)Final Exam                                             35%

Text Book:

Viscous Fluid Flow (strongly recommended and available in bookstore)

by Frank M. White, 3rd edition .

Fluid Mechanics

by Pijush K. Kundu, Ira M. Cohen,Academic Press, 2nd edition .

Incompressible Flow

By R.L. Panton , John Wiley&Sons.

Physical Gas Dynamics (only the first chapter)

By Vincenti and Kruger, Krieger Publishing Co.

Additional References:

An Introduction to Fluid Dynamics

By G.K. Batchelor, Cambridge university Press

Phsical Fluid Dynamics

By D.J. Tritton, Clarendon Press, Oxford, 1988.

Boundary-layer Theory

By Herrmann Schlichting, Klaus Gersten, with contributions from Egon Krause and Herbert Oertel Jr.   translated by Katherine Mayes

Turbulent Flows

By S.B. Pope, Cambridge University Press

Time commitment and ECTS credit:

Activity	Number	Time (hrs)	Predicted Total Work Load (hrs)
Lectures	2×14=28	1.25	35
HWs and Project	14	5	70
Lab	0	0	0
Midterm Exam	1	25	25
Final	1	30	30
Total Work Load			160
ECTS Credit: Total Work Load (hrs)/30* = 5.3 ~ 6
*  30 hours of work load  is assumed to be 1 ECTS credit