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SG2214 Fluid Mechanics 7,5 hp

Course memo Autumn 2024-50872...

Version 2 – 08/20/2024, 6:21:37 PM

Course offering

Doktorand (Start date 26 Aug 2024, English)
TTEMM (Start date 26 Aug 2024, English)

Language Of Instruction

English

Offered By

SCI/Mechanics

Course memo Autumn 2024

Headings denoted with an asterisk ( * ) is retrieved from the course syllabus version Spring 2022

Content and learning outcomes

Course contents

Introduction, tensors, kinematics. Continuum mechanical conservation laws for mass, momentum and energy. Laminar viscous flow. Laminar boundary layers. Vorticity dynamics. Two-dimensional irrotational flow. Introduction to turbulent flow.

Intended learning outcomes

  1. The student should be able to identify, apply and/or present derivations of mathematical models of fluid mechanical phenomena and make relevant approximations.
  2. The student shall for simplified cases be able to apply the derived models (numerically or theoretically) and be able to interpret the result.
  3. The student should show an ability to relate obtained data, observed phenomena and processes in a laboratory environment to the theoretical description of fluid mechanics.
  4. The student should get a fundamental preparation in order to be able to work with fluid mechanical problems as an engineer.

Learning activities

Lectures (L1-14) and recitations (R1-R14)

The course contents will be presented in 14 lectures and 14 recitations divided into the 6 parts:

Part 1. Equations of motion

Part 2. Exact and approximate solutions

Part 3. Boundary layers

Part 4. Flow at low Re

Part 5. Flow at high Re

Part 6. Turbulence

You may prepare for each lecture by reading Kundu & Cohen (4th edition) and/or Kundu, Cohen & Dowling (5th , 6th edition). Detailed reading instructions can be downloaded from Canvas.

Lab

A mandatory experimental lab (Self-similar boundary layer lab with a fauvourable pressure gradient) is scheduled in the Fluid Physics lab, Teknikringen 8. Detailed lab instructions can be downloaded from Canvas. You can sign up in Canvas (under “People” tab). 

Detailed plan

Activity

Location

Teacher

Topic

Section

L1

27/8, 10-12,  D34

SB

Mass conservation and material derivate

1. Equations of motion

R1

27/8, 13-15, E35

JC/CW

Tensors and Cartesian component notation

 

L2

30/8, 13-15, U41

SB

Momentum conservation, stress tensor and Cauchy's equations of motion

 

R2

30/8, 15-17, E51

JC/CW

Macroscopic balances

 

L3

2/9, 8-10, D34

SB

Velocity gradient tensor and Navier-Stokes equations

 

R3

3/9, 15-18, E35

JC/CW

Normal/shear strain rates, rotation rate, stress tensor Tutorial homework 1.

 

L4

4/9, 13-15, V34

SB

Characteristic scales, non-dimensionalization, self-similarity

2. Exact and approximate solutions

R4

6/9, 15-17, Q21

JC/CW

Solutions in Cartesian coordinates

Due Homework 1

L5

TBA

SB

Asymptotic expansions and lubrication theory 

 

R5

10/9, 15-17, Q15

JC/CW

Solutions curvilinear coordinates 

Tutorial homework 2.

 

L6 11/9, 10-12, E51 SB Conservation of energy   

R6

12/9, 10-12, E33

JC/CW

Heat transfer problems

 

L7

17/9, 15-17, D34

JC

Laminar boundary layers, Blasius solution

3. Boundary layers

R7

18/9, 10-12, D3

JC

Boundary layer problems

 

L8

18/9, 15-17, U31

JC

Pressure gradient, separation Falker-skan solutin

 

R8

19/9, 15-17, E51

JC

More boundary layers problems. Tutorial Homework 2.

 

L9

23/9, 8-10, D34

SB

Creeping flow equations and flow physics at low Reynolds number

4. Flow as low Re

See lab group schedule.

R9

24/9, 15-17, E51

JC/CW

Exact solutions to Stokes equations

 

L10

25/9, 10-12, E3

SB

Stream function and biharmonic equations 

 

R10

30/9, 10-12, U21

JC/CW

Stokes drag and other problems.

 

L11

1/10, 15-18, D34

SB/JC/CW

Vorticity dynamics

Tutorial homework  3.

5. Flow as high Re

Due Homework 2

R11

2/10, 10-12, Q21

JC/CW

Solutions to vorticity equation 

 

 

L12

3/10, 10-12, U51

SB

Irrotational flows

 

R12

7/10, 8-10, Q21

JC/CW

Potential flow problems 

 

L13

7/10, 10-12, Q21

SB

Reynolds averaged equations

 6. Turbulence

R13

8/10, 15-17, E51

JC/CW

Problems on turbulence

 

L14

9/10, 13-15, U41

SB

Turbulent channel flow

 

R14

11/10, 8-10 D34

JC/CW

Turbulent channel flow. Summary

 

Exam

25/10, 8-12, D1

 

Written

 

Re-exam

19/12, 8-12, U31

 

Written

 

Preparations before course start

Recommended prerequisites

The student should have good knowledge in linear algebra and calculus in more than one variable, vector analysis, Gauss and Stokes theorems and solution of elementary partial differential equations, basic knowledge of fluid mechanics phenomena, computer programming in e.g. Matlab.

Literature

The book by Kundu & Cohen & Dowling, Fluid Mechanics (6:th ed.), Elsevier AP. You can download E-book (5:th edition) from KTH library. 

Examination and completion

Grading scale

A, B, C, D, E, FX, F

Examination

  • INL1 - Assignments, 3.0 credits, Grading scale: P, F
  • TEN1 - Examination, 4.5 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

INL1: Written assignments and participation and reporting of laboratory exercise

TEN1: Written exam.

Examiner decides, in consultation with KTH's coordinator for students with disability (Funka), about any adapted examination for students with documented, permanent disability. The examiner may allow another examination form when re-examining individual students.

The section below is not retrieved from the course syllabus:

INL1 - Assignments, 3.0 credits

Three sets of mandatory homework (HW) assignments can be download from Canvas (under “Assignments” tab). Upload your assignment on CANVAS from a PDF-file before deadlines (see Detailed plan for when HW are due).

Homework 1:  Max 3p bonus on 1st exam
Homework 2:  Max 5.5p bonus on 1st exam
Homework 3:  Max 3.5p bonus on 1st exam

A mandatory experimental lab in the Fluid Physics lab, Teknikringen 8. 

TEN1 - Examination, 4.5 credits

The grade scale is A-F according to (may be adjusted)

40 ≤ Points --> Grade A
35 ≤ Points < 40  --> Grade B
30 ≤ Points < 35  --> Grade C
25 ≤ Points < 30--> Grade D
20 ≤ Points < 25 --> Grade E
Points = 19 --> Grade Fx
Points <19 --> Grade F

Maximum number of points on the exam is 50+12, including bonus from homeworks. The points obtained from the homework problems can only be used to get a higher grade than E, they cannot be used to pass the exam. The grade Fx can be upgraded (through an oral exam) to E within six weeks after the exams have been corrected. There is a re-exam in December, but with no possibility to receive a Fx (i.e. Fx=F in re-exam). 

Other requirements for final grade

  • INL1, Assignments/laboratory exercise, 3,0 hp, P/F
  • TEN1, Examination, 4,5 hp, A-F

Grading criteria/assessment criteria

Learning outcomes 1 & 2

E

By written presentations of solutions, possibly in cooperation with classmates, to at least one of the problems for each of the three homework assignments.
At a written exam show the ability to clearly formulate a model and present a solution to basic fluid mechanical phenomena and/or to present coherent derivations of fluid mechanics theory.

D-A

By the requirements for E and showing larger width by solving more problems from the homework assignments and/or at the written exam deal satisfactory with more problems/derivations and/or show larger depth by solving and analysing homework assignments/exam problems with excellence and explain the results.

Learning outcome 3

E

By preparing for and execute the experimental lab in the course and submitting a lab

report.

Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

No information inserted

Round Facts

Start date

Missing mandatory information

Course offering

  • Doktorand Autumn 2024-50872
  • TTEMM Autumn 2024-51795

Language Of Instruction

English

Offered By

SCI/Mechanics

Contacts