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 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 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 kepsiilon model
 Understand the two method for treating wall boundary conditoins: wall functions and lowReynolds 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 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 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 kepsiilon model
 Understand the two method for treating wall boundary conditoins: wall functions and lowReynolds 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 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 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 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. and turbulence modeling. The students will learn how to derive the exact equation for turbulent kinetic energy. Then we go on to the kepsilon 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 lowReynolds number model.
In a second assignment, the students will use STARCCM+ to compute simple twodimensional 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 STARCMM+ 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