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Here we present the fluid courses in our MSc programme in Applied Mechanics. It is a combined programme of solids and fluids. Students get a general background in both solids and fluids. By choosing elective courses, they can specialize in either solids or fluids; students can also choose elective courses in both areas and they will then acquire a suitable background in multi-physics solid and fluid mechanics.
 
Full course programme

 
the
FLUiDS COURSES
Division of Fluid Dynamics
 
 
Mechanics of Fluids
Computational fluid dynamics
Compressible flow
Heat Transfer
Turbulence modeling
Project in Applied Mechanics
Turbomachinery
Gas turbine technology
Multiphase flow
CFD with Opensource Software
MSc project

 

Web page by I Ljungström

ilj/ /flowsim.se
www.flowsim.se

TME075
 
Mechanics of solids and fluids
September to October

The course provides an introduction to the mechanics of continuous media. A strong focus is placed on deriving and understanding the general field equations in three dimensions. These equations provide a generic basis for solid mechanics, fluid mechanics and heat transport.
 
 

 
Assignment 2: Eigenvalues of the viscous shear stress tensor

The role of constitutive equations in distinguishing the different types of problems will be emphasised. The students will learn the basics of Cartesian tensors and the index notation. They will also study the solutions to boundary-value problems using a general purpose code.
 
 
 more information on this course
1^st Lecturer's www/Chalmers
2^ndLecturer's homepage
2^nd Lecturer's www/Chalmers
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.TME225
 
Mechanics of Fluids
September to October

This course will provide an introduction to turbulent flow. The focus will be on understanding the averaged equations of motion and the underlying physics they contain.
 
One project should be carried out by the students. In this project the students will be given DNS data of fully developed channel flow. From these data the turbulent stresses, two-point correlations, Probability Density Functions (PDFs), integral length scales etc. will be computed and analyzed.
 

Assignment: Probability density function of streamwise fluctuating velocity.

.MTF072
 
Computational fluid dynamics
November to December

We start by carrying out a detailed derivation of the finite volume method. First, the diffusion equation (heat conduction equation) is treated in one and two dimensions. After that, we carry on to convection-diffusion problems. For the convective part, we discuss different discretization schemes where a delicate balance between numerical accuracy and numerical stability must be considered.
 
The Navier-Stokes equations are discussed for both compressible and incompressible flow. In incompressible flow special problems arise from the pressure-velocity coupling which leads to pressure oscillations. Two different methods to solve this problems are discussed in some detail.
 

Many turbulence models are based on the eddy-viscosity concept, where additional transport equation are solved for two scalar quantities. The most well-known models are the k-eps and the k- omega model. Near the walls the grid must be refined in order to resolve the strong gradient prevailing there. A couple of years ago one was forced to, due to limited computer resources, use approximate treatment of the walls in the form of wall functions. In industry these are still often used. However, often more accurate treatments are used, such as low-Reynolds number models.
 
 
 
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Lecturer's homepage
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.TME085
 
Compressible flow
end of January to mid-March

Compressible flow effects are encountered in numerous engineering applications involving high speed flows, e.g. gas turbines, steam turbines, internal combustion engines, rocket engines, high-speed aerodynamics, high speed propellers, gas pipe flows, etc. In fact, modern society with its dependence on fast ground and air transportation would not function without compressible flow. Special phenomena such as compression shocks, entropy layers, expansion fans, flow induced noise etc are of fundamental scientific importance and directly affect the performance and endurance of these engineering applications.

The main objectives of the course are to convey to the students an overview of the field of compressible flows (including aero-acoustics) and the importance of this topic in the context of common engineering applications. This means that the student should acquire a general knowledge of the basic flow equations and how they are related to fundamental conservation principles and thermodynamic laws and relations. The connections with incompressible flows and aero-acoustics as various limiting cases of compressible flows should also become clear. A general knowledge of the status of commercial CFD codes for compressible flows should also be obtained after this course.
 
 
 
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.MTF270
 
Turbulence modeling
mid-March to end of May

Reynolds stress models (both transport models and algebraic ones) will be discussed in some detail. The pressure-strain term is an important part in these models which must be modelled. Different approaches for modelling this term will be discussed. We will also discuss non-linear eddy-viscosity models. This type of models is often a good compromise between modelling accuracy and numerical stability.
 
 

 
Assignment 4: Resolved streamwise normal stresses
 

Slightly more than half of the course will be devoted to unsteady simulations such as Large Eddy Simulations (LES), hybrid LES-RANS and DES (Detached Eddy Simulations). In unsteady simulations the dependent variables are split into a modelled part (small turbulent fluctuations) and a resolved part (turbulent scales which are resolved by our numerical method). The big advantage of unsteady simulations is that only a small part of the turbulence is modelled (the small, modelled scales) and thus dependence on the turbulence modelling is weak, and the accuracy of unsteady simulations is consequently high. The disadvantage with unsteady simulations is that since a large part of the turbulence is resolved, we must solve the equations in transient mode (i.e. time dependent). This is one of the main reasons why unsteady simulations is very expensive; we have increased the number of independent variables from three variables in steady flow (x, y and z) to four variables in unsteady flow (x, y, z and t).
 
 
 
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.TME130
 
Project in Appliced Nechanics
mid-March to end of May

The aim of the course is to provide the student with an opportunity to apply knowledge in mathematical modelling using computational and experimental techniques. The learning environment is organized in such a way that an emphasis is put on practicing communication skills and developing experience working in teams.
 
The course is subdivided into two learning blocks, a shorter introductory block introducing the necessary theory for the specialization, and a longer block with a stronger emphasis on the project working form. The two learning blocks are ended with reporting and presentation sessions.
 

Rig for studying linear cascade
 
 
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.TME210
 
Turbomachinery
September to October

The course gives a broad introduction to the field of turbomachinery. This is primarily done by describing the work principle and the underlying theory of a number of turbomachinery components

The equations describing the energy transfer between the fluid and the rotating component are applied to centrifugal and axial pumps, fans, axial compressors, gas and steam turbines, hydraulic turbines and wind turbines. Aerodynamic loss sources and design constraints are discussed for the various machines being analyzed

 

Employers with an interest in turbomachinery come from a wide range of fields: energy and power generation (hydropower, wind power, nuclear), process industry, automotive industry.

Two labs will complement the learning process:
  1. Use of a commercial design tool to preliminary design and analyse a radial pump
  2. Hydraulic turbine lab. Study visits to a hydraulic power plant and a turbomachinery manufacturer are planned. The course lays the foundations for an efficient study of the course gas turbine technology (MTF171).
 
 
 
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.MTF114
 
Heat Transfer
end of January to mid-March

The course comprises heat transfer through conduction, convection and radiation. Heat transfer in heat exchangers is part of the course as an example of an important industrial application. Energy conservation is also a central issue, both when using engineering methods and when deriving the governing equations. Energy conservation is the 'tool' that is used to couple different heat transfer modes, or heat transfer in different spatial regions. The heat conduction part of the course comprises one- and two-dimensional steady and transient heat conduction. We study both simple cases where analytical solutions may quite easily be derived, and more complicated cases where empirical correlations or numerical methods must be used.

 
Computer exercise with STAR-CCM+: The convective heat transfer in a staggered tube cross-flow heat exchanger. Cold fluid (dark blue) enters from the left, and is heated by the hot tubes. A symmetry boundary condition is applied at top and bottom.

Heat transfer through convection (both forced and natural) is a big subject. We derive and study the energy equation both for laminar and turbulent flows. A number of external configurations - like convective heat transfer for a flat plate, a cylinder, and tube bundles - are studied. We also study convective heat transfer for internal configurations such as pipes and channels. In the end of the course there is a thorough treatment of thermal radiation. We define emission, absorption, radiosity etc. Thermal radiation from gray surfaces, black body radiation, view factors, radiation, absorption and reflection are some of the phenomena that are treated. For industrially applied problems in heat transfer one must in general use numerical methods. The commercial CFD code (Computational Fluid Dynamics) STAR-CCM+ is used in the exercises and in a project work to study conduction and convection. The results are compared with analytical and empirical correlations.
 
 
 
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Web page by I. Ljungström

ilj/ /flowsim.se
www.flowsim.se

MTF171
 
Gas turbine technology
November - December

Gas turbines are the primary source of propulsion for aircraft and find a widespread use in power generation as well as marine applications. Within the course, aspects ranging from cycle studies and performance calculations to analysis of individual components are approached. The ambition is that the student shall become familiar with different gas turbine concepts and their operation. Knowledge necessary to design and analyse more advanced turbomachines is taught in the course.
 

The course starts with a general overview of the gas turbine system and its field of application. The needs, as given by a jet engine or a power generation system, and the implications by these on the engine cycle are treated. Furthermore, the requirements on the components in order to fulfill these cycle requirements are illustrated. Different design principles for the components, such as compressors, turbines, nozzles etc., are described and what requirements are most important for the final system performance.
 
 
 
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TME160
 
Multiphase flow
November - December

Multiphase flow is the simultaneous flow of a mixture with two or more phases. They are frequently encountered in many of our day to day activities. Also, numerous industrial and energy conversion processes rely on the flow of multiphase mixtures.
 
Multiphase Flow occupies a central position in Fluid Mechanics and is fundamental to a wide array of scientific and engineering disciplines. The aim of this course is to learn some of the the basic concepts in describing multiphase flows, their phenomena, and implications for modeling.
 

 
Rising bubbles in water. How should such phenomena be described?

The course starts by discussing the nature of multiphase flows and mathematical tools to describe this nature. The continuum assumption and the various ways of taking averages relating to multiphase flows is discussed. These assumptions and averages are then employed to derive the governing equations describing multiphase flows. After the rigorous derivation of the equations, implications, practical modeling, and various engineering assumptions are discussed.
 
Along the way, many examples, phenomena, and applications are discussed. The course is completed with a computer lab.
 
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FTME055
 
CFD with OpenSource software
September - December

The course gives an introduction to the use of OpenSource software for CFD applications. A major project work in OpenFOAM forms a large part of the course. The project may be defined according to the student's special interests. The result of the project should be a detailed tutorial for a specific application or library of OpenFOAM. The tutorials will be peer-reviewed and graded by the students, and the tutorials thus form a part of the course. The tutorials will be made available as OpenSource, as a contribution to the OpenFOAM community. To pass the course the student must do the project and peer-review the tutorials from the other projects. There will also be some compulsory minor tasks.

The course is open to PhD students, final year master students, and industrial participants. Industrial participants pay a fee.
 
Master students are graded, which is based on the project, the report, the presentation, and the peer-review.
 
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MSc project
 

The MSc project can be either 30hec (20 weeks) or 60hec (40 weeks); in the latter case, the course programme is reduced by 30hec. A 30hec-project is usually carried out during the spring of the second year, but it can be started in summer/autumn. The MSc project can be done at the Department, in the industry (in Sweden or abroad) as well as at a research institute (in Sweden or abroad).
 

 

 
 
 
 
 
 
 
 
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