# FSG3131 Kinetic Gas Theory 7.0 credits

#### Kinetisk gasteori

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.

### Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

## Course information

### 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

Project work in groups of 2 students.

Seminars with student project presentations with 2 students per 45 minutes.

### Literature and preparations

#### 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

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

### Further information

#### Course web

No information inserted

SCI/Mechanics

#### Main field of study *

No information inserted

#### Education cycle *

Third cycle

No information inserted

Anders Dahlkild

#### 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.