Teaching language: English
Open for exchange students
Block schedule:
A
Course module 

Credit distribution 

Examination dates 
Sp1 
Sp2 
Sp3 
Sp4 
Summer course 
No Sp 
0111 
Examination 
7,5c 
Grading: TH 

7,5c







21 Oct 2013 pm M, 
13 Jan 2014 pm V, 
26 Aug 2014 am M 
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:
Professor
Lars Davidson
Course evaluation:
http://document.chalmers.se/doc/4ba6c44eb4344916abb41553550d9f65
Go to Course Homepage
Eligibility:
For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.
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 NavierStokes equations and the energy equation using tensor notation
 Analytically solve NavierStokes 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 wallbounded and free shear flows
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 strainrate 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 NavierStokes 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 strainrate tensor, the dissipation, the eigenvectors and the eigenvalues of the strainrate tensor.
In the larger part of the course the students will learn the basics of turbulent flow. Turbulence includes shortlived 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 NavierStokes 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 energyrich 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 NavierStokes 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 pressurestrain 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 twopoint 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
Literature
Lecture notes
Examination
Assignments and written examination