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Syllabus for

Academic year
TME226 - Mechanics of fluids  
Strömningsmekanik, fortsättningskurs
 
Syllabus adopted 2020-02-10 by Head of Programme (or corresponding)
Owner: MPAME
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: Second-cycle
Major subject: Mechanical Engineering
Department: 30 - MECHANICS AND MARITIME SCIENCES


Teaching language: English
Application code: 03127
Open for exchange students: Yes
Block schedule: B+

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0120 Written and oral assignments, part A 1,5c Grading: UG   1,5c    
0220 Written and oral assignments, part B 1,5c Grading: UG   1,5c    
0320 Examination 4,5c Grading: TH   4,5c   26 Oct 2020 am J,  05 Jan 2021 pm J,  24 Aug 2021 am J

In programs

MPAME APPLIED MECHANICS, MSC PROGR, Year 1 (compulsory)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
MPNAV NAVAL ARCHITECTURE AND OCEAN ENGINEERING, MSC PROGR, Year 2 (elective)

Examiner:

Lars Davidson

  Go to Course Homepage


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

Lectures. One workshops using Python or Matlab/Octave. In the second workshop, the commercial CFD program STAR-CMM+ will be used (CFD=Computational Fluid Dynamics).,The workshops will be presented in written reports.

Literature

eBook which can be downloaded from the course web page

Examination including compulsory elements

Assignments and written examination


Published: Mon 28 Nov 2016.