Syllabus for |
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| TME225 - Mechanics of fluids |
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| Syllabus adopted 2014-02-20 by Head of Programme (or corresponding) |
| Owner: MPAME |
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7,5 Credits |
| Grading: TH - Five, Four, Three, Not passed |
| Education cycle: Second-cycle |
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Major subject: Mechanical Engineering
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Department: 42 - APPLIED MECHANICS
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Teaching language: English
Open for exchange students
Block schedule:
B
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0111 |
Examination |
7,5 c |
Grading: TH |
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7,5 c
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30 Oct 2014 am M, |
05 Jan 2015 pm M, |
25 Aug 2015 am M |
In programs
MPAME APPLIED MECHANICS, MSC PROGR, Year 1 (compulsory)
MPNAV NAVAL ARCHITECTURE AND OCEAN ENGINEERING, MSC PROGR, Year 2 (elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
Examiner:
Professor Lars Davidson
Course evaluation: http://document.chalmers.se/doc/bdf20b72-cd41-4aed-864b-4d7c889b8800
Go to Course Homepage
Eligibility:
In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement:
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.
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 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
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 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.
.For more information
.Lecturer's homepage
Organisation
Lectures, workshops using Matlab, assignments including written reports
Literature
Lecture notes which can be downloaded from the course web page
Examination
Assignments and written examination
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