FSG3131 Kinetic Gas Theory 7.0 credits
This course is aimed for postgraduate students with their focus on fluid mechanics. The course is an introduction to the kinetic theory of gases. The continuum mechanical equations of fluid dynamics are derived from a kinetic theory approach where the gas is considered a large system of discrete particles, the molecules. The equations of fluid dynamics are shown to result in the continuum limit, but the kinetic theory of gases applies also for micro and nano flows and for rarefied gases. Some basic problems of fluid mechanics are considered in cases when ordinary continuum theory of the gas does not apply.
Information for research students about course offerings
The course is usually given every second year, depending on the number of expected participants.
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Content and learning outcomes
Course contents
After completing this course the student should be able to:
- Give the kinetic theory definitions of the macroscopic continuum properties/variables of a gas.
- State the requirements on a fluid flow for the continuum assumption to be a reasonable approximation.
- Describe the concepts of cross-section and mean free path in a gas and derive an expression for the mean free path.
- Use the mean free path concept to derive an approximate expression for viscosity and heat conductivity in a gas in terms of kinetic variables.
- State the Boltzmann equation and, make an interpretation of the different terms involved.
- State the Maxwellian distribution and when it is valid.
- Give examples of some typical kinetic effects not described by the Navier-Stokes equations.
- Give the main principles of a Direct Simulation Monte-Carlo Simulation (DSMC).
- Describe in broad outline the Chapman-Enskog method to derive the Navier-Stokes equations from the Boltzmann equation at small Knudsen numbers, in particular how viscosity and heat conductivity can be found from the molecular interactions.
Intended learning outcomes
The student will be able to describe the connection between the continuum mechanical Navier-Stokes equations for a gas and the kinetic theory description of a gas in thermal non-equilibrium. Also, the student will be able to describe some effects typical to gases at Knudsen numbers of order one or larger, a limit not covered by the Navier-Stokes equations.
Course disposition
About 10 hour lectures.
Project work in groups of 2 students.
Seminars with student project presentations with 2 students per 45 minutes.
Literature and preparations
Specific prerequisites
Admitted to PhD-program
Recommended prerequisites
An advanced course in fluid mechanics on undergraduate level is recommended.
Equipment
No information inserted
Literature
Course literature
Gombosi, T.I.
Gaskinetic Theory, Cambridge University Press, 1994
Dahlkild, A.A. and Söderholm, L.H.
Lecture notes in kinetic gas theory, 2011
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
P, F
Examination
- INL1 - Assignment, 1.0 credits, grading scale: P, F
- PRO1 - Project work, 3.0 credits, grading scale: P, F
- TEN1 - Oral exam, 3.0 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
INL1 Assignment1,0 hp (P, F)
PRO1 Project work 3,0 ho (P, F)
TEN1 Oral exam 3,0 hp P, F
Lists of typical questions at examination are available for the oral exam.
Other requirements for final grade
The following items have to be approved in order to obtain a pass on the course:
- Project work and 4-page report on a DSMC-simulation
- Oral examination on kinetic theory of gases
Opportunity to complete the requirements via supplementary examination
No information inserted
Opportunity to raise an approved grade via renewed examination
No information inserted
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course web
Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.
Course web FSG3131Offered by
Main field of study
This course does not belong to any Main field of study.
Education cycle
Third cycle
Add-on studies
No information inserted
Contact
Anders Dahlkild