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Kursplan för

Läsår
TME225 - Mechanics of fluids
 
Kursplanen fastställd 2011-02-21 av programansvarig (eller motsvarande)
Ägare: MPAME
7,5 Poäng
Betygskala: TH - Fem, Fyra, Tre, Underkänt
Utbildningsnivå: Avancerad nivå
Huvudområde: Maskinteknik
Institution: 42 - TILLÄMPAD MEKANIK


Undervisningsspråk: Engelska
Sökbar för utbytesstudenter
Blockschema: A

Modul   Poängfördelning   Tentamensdatum
Lp1 Lp2 Lp3 Lp4 Sommarkurs Ej Lp
0111 Tentamen 7,5hp Betygskala: TH   7,5hp   22 Okt 2012 em M,  Kontakta examinator,  27 Aug 2013 fm M

I program

MPAME APPLIED MECHANICS, MSC PROGR, Årskurs 1 (obligatorisk)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Årskurs 1 (obligatoriskt valbar)
MPNAV NAVAL ARCHITECTURE AND OCEAN ENGINEERING, MSC PROGR, Årskurs 2 (valbar)

Examinator:

Professor  Lars Davidson


Kursutvärdering:

http://document.chalmers.se/doc/a5b8fc2b-908d-440e-bc5d-c70cc0d85a4c


  Gå till kurshemsida

Behörighet:

För kurser inom Chalmers utbildningsprogram gäller samma behörighetskrav som till de(t) program kursen ingår i.

Kursspecifika förkunskaper

A basic course in fluid mechanics

Syfte

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

Lärandemål (efter fullgjord kurs ska studenten kunna)


  • 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 equations for the turbulence kinetic energy and the turbulent Reynolds stresses

  • Identify the various terms in these equations and describe what role they play

  • Derive the linear velocity law and the logarithmic velocity law for a turbulent boundary layer

  • Recognize the difference between wall-bounded and free shear flows

Innehåll

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 Matlab 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. Turbulence includes short-lived eddies of different size and frequency. The larger the Reynolds number, the larger the difference in size and frequency between the largest and the smallest eddies. This is the very reason why there is no computer large enough at which we can numerically solve the Navier-Stokes equations at high Reynolds number.


The energy spectra and the energy cascade process will be discussed in some detail; in the energy cascade it is assumed that turbulent kinetic energy is transferred from the largest energy-rich turbulent eddies to the smallest eddies. At the small eddies the kinetic energy is transformed into internal energy, i.e. an increase in temperature.


From the instantaneous Navier-Stokes equations the time averaged momentum equation will be derived. In this equation appears a new term, the turbulent Reynolds stress tensor. The students will learn how to derive the exact Reynolds stress transport (RST) equation, as well as the equations for turbulent kinetic energy and mean kinetic energy. The physical meaning of the different terms in the RST equation, such as the production term, the pressure-strain term and the dissipation, will be discussed in some detail.


In a second Matlab assignment, the students will be given a database of instantaneous turbulent flow for fully developed channel flow. The students will compute and analyze various turbulent quantities such as the turbulent Reynolds stresses, the pressure strain term in the RST equation, the two-point correlation, the integral turbulent length scale and the dissipation.


The Department has extensive experimental facilities for fluid dynamics. Two or three visualizations
of turbulent flow will be presented to the students.


.For more information


.Lecturer's homepage



Organisation

Lectures, workshops using Matlab, assignments including written reports, demonstrations in the fluid dynamics laboratory

Litteratur

Lecture notes

Examination

Assignments and written examination


Sidansvarig Publicerad: on 24 jan 2018.