Course syllabus for Mechanics of fluids

Course syllabus adopted 2023-02-12 by Head of Programme (or corresponding).

Overview

  • Swedish nameStrömningsmekanik, fortsättningskurs
  • CodeTME226
  • Credits7.5 Credits
  • OwnerMPAME
  • Education cycleSecond-cycle
  • Main field of studyMechanical Engineering
  • DepartmentMECHANICS AND MARITIME SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 03130
  • Block schedule
  • Open for exchange studentsYes

Credit distribution

0120 Written and oral assignments, part A 1.5 c
Grading: UG		1.5 c
0220 Written and oral assignments, part B 1.5 c
Grading: UG		1.5 c
0320 Examination 4.5 c
Grading: TH		4.5 c
  • 28 Okt 2024 pm J_DATA
  • 08 Jan 2025 pm J_DATA
  • 26 Aug 2025 am J_DATA

In programmes

Examiner

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Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

A basic course in fluid mechanics

Aim

The course provides an introduction to continuum mechanics and turbulent fluid flow.

Learning outcomes (after completion of the course the student should be able to)

  • Confidently manipulate tensor expressions using index notation, and use the divergence theorem and the transport theorem.
  • Derive the Navier-Stokes equations and the energy equation using tensor notation
  • Analytically solve Navier-Stokes equations for a couple of simple fluid flow problems and analyze and understand these flows
  • Characterize turbulence
  • Understand and explain the energy spectrum for turbulence and the cascade process
  • Derive the exact transport equation for the turbulence kinetic energy
  • Identify the various terms in this equation and describe what role they play
  • Derive the linear velocity law and the logarithmic velocity law for a turbulent boundary layer
  • Understand and explain model assumptions in the k-epsiilon model
  • Understand the two method for treating wall boundary conditoins: wall functions and low-Reynolds number models
  • Predict turbulent flow in simple geometries using a commercial CFD solver
  • Confidently manipulate tensor expressions using index notation, and use the divergence theorem and the transport theorem.
  • Derive the Navier-Stokes equations and the energy equation using tensor notation
  • Analytically solve Navier-Stokes equations for a couple of simple fluid flow problems and analyze and understand these flows
  • Characterize turbulence
  • Understand and explain the energy spectrum for turbulence and the cascade process
  • Derive the exact transport equation for the turbulence kinetic energy
  • Identify the various terms in this equation and describe what role they play
  • Derive the linear velocity law and the logarithmic velocity law for a turbulent boundary layer
  • Understand and explain model assumptions in the k-epsiilon model
  • Understand the two method for treating wall boundary conditoins: wall functions and low-Reynolds number models
  • Predict turbulent flow in simple geometries using a commercial CFD solver

Content

The students will initially learn the basics of Cartesian tensors and the index notation.

A strong focus is placed on deriving and understanding the transport
equations in three dimensions.These equations provide a generic basis  for fluid mechanics, turbulence and heat transport. In continuum  mechanics we will discuss the strain-rate tensor, the vorticity tensor and the vorticity vector. In connection to vorticity, the concept of  irrotational flow, inviscid flow and potential flow will be introduced.  The transport equation for the vorticity vector will be derived from  Navier-Stokes equations.

Developing channel flow will be analyzed in detail. The results from a
numerical solution is provided to the students. In a Python/Matlab/Octave assignment, the students will compute different quantities such as the increase in  the centerline velocity, the decrease of the wall shear stress, the  vorticity, the strain-rate tensor, the dissipation, the eigenvectors and the eigenvalues of the strain-rate tensor.

In the larger part of the course the students will learn the basics of
turbulent flow. and turbulence modeling. The students will learn how to  derive the exact equation for turbulent kinetic energy. Then we go on to the k-epsilon turbulence model. Two different treatments of wall boundary conditions will be studied. In one of the methods, a coarse grid is used near the wall and assumptions are made for the flow and the turbulence near the wall. This is called wall functions. In the second method, a fine grid is used near the wall and the viscous effects are resolved.Then we must usually modify the turbulence model in order to take the viscous effects into account. This type of model is called a low-Reynolds number model.

In a second assignment, the students will use STAR-CCM+ to compute simple two-dimensional flow cases. For more information

.Lecturer's homepage

Organisation

10 pre-recorded lectures are available  here and at Canvas. Instead of regular lectures, there will be five discussion seminars on Campus. At the discussion seminars, the questions in the appendix K 'TME226 Discussion seminars' in the  eBook will be discussed. Students are encouraged to ask questions.

  • The students will register in six groups (approximately eight in each). Each group will have approximately one discussion seminarevery week.
  • Each discussion seminar will last 30 minutes.
  • Suitable preparation for a discussion seminar

  1. Watch the relevant recorded lecture(s)
  2. Read relevant parts of the eBook
  3. Study the questions in the appendix K 'TME226 Discussion seminars'

At other times, you can post a question on PIazza


Literature

eBook which can be downloaded from the course web page

Examination including compulsory elements

  • Grades. failed, grade 3, 4 or 5
  • Part 1: Two assignments including written presentations. This part is mandatory. Written presentations are part of the examination.
  • Part 2: Discussion seminars. This part is not mandatory.
  • Part 3: Either Quiz or oral exam is mandatory.
  1. Part 3a: Quiz. Students who pass this quiz get grade 3 (passed).  The Quiz exam will be similar to the Quiz 1-10at Canvas related to the Lectures.
  2. Part 3b: Oral exam based on the questions in the Discussion seminars. The teachers will also ask follow-up questions.There we try to test if the student has understood the topic or if he/she only has memorized it. A good understanding gives grade 4 or 5. Three students at the time (90 minutes). Each student will get appox seven randomly chosen questions fromthe Discussion seminars and the Assignments. Grades: failed, 3, 4 or 5.
  3. To get grade 'passed' on the course, you must have grade 3 on either the Quiz or the Oral exam and handing in the two assignment reports.


The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.