Course syllabus
Course-PM
TME085 Compressible flow lp3 VT24 (7.5 hp)
Course is offered by the department of Mechanics and Maritime Sciences
The course is given in English.
Contact details
Examiner
Niklas Andersson
Examiner/Lecturer/Adm
niklas.andersson@chalmers.se
Teaching Assistants
Debarshee Ghosh
Exercises/Computer assignments
ghoshd@chalmers.se
Course purpose
The main objectives of the course are to convey to the students an overview of and familiarity with the field of compressible flows 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 and some experience with typical CFD codes for compressible flows should also be obtained after this course.
Course literature
Text Book
Modern Compressible Flow with Historical Perspective
John D. Anderson
4:th edition
McGraw-Hill
ISBN: 978-1-260-57082-3
the 4:th edition is available at Chalmers Store. If you have an older version of the book that will work just fine.
The course covers essentially everything in chapters 1 to 7. The topic covered in chapter 12 is included but replaced by lecture notes. Selected parts of chapters 16-17 are included.
Summaries of each of the chapters included in the course along with quizzes can be found here:
Additional Documents
|
Document |
Description |
| Formulas, tables, and graphs |
Document including all formulas, graphs and tables that you need for solving the problems in the course. A copy of this document will be provided with the exam. |
| Study guide |
The study guide provides reading instructions for the course text book (Modern Compressible Flow by J. D. Anderson) there are also a set of theory questions and a list of recommended problems for all chapters of the text book included in the course. Theory questions on the exam will be inspired by the theory questions provided in the study guide (might appear as is or in slightly modified form). |
Lecture Notes
|
Document |
Description |
| Lecture 01 |
Chapter 1 - Introduction |
| Lecture 02 |
Chapter 2 - Integral forms of the conservation equations for inviscid flows |
| Lecture 03 |
Chapter 3 - One-dimensional flow |
| Lecture 04 |
Chapter 3 - One-dimensional flow |
| Lecture 05 |
Chapter 4 - Oblique shocks and expansion waves |
| Lecture 06 |
Chapter 4 - Oblique shocks and expansion waves |
| Lecture 07 |
Chapter 5 - Quasi-one-dimensional flow |
| Lecture 08 |
Chapter 5 - Quasi-one-dimensional flow |
| Lecture 09 |
Chapter 6 - Differential conservation equations for inviscid flow |
| Lecture 10 |
Chapter 7 - Unsteady wave motion |
| Lecture 11 |
Chapter 7 - Unsteady wave motion |
| Lecture 12 |
Chapter 7 - Unsteady wave motion |
| Lecture 13 |
Chapter 12 - The time-marching technique |
| Lecture 14 |
Chapter 12 - The time-marching technique |
| Lecture 15 |
Chapter 16 - Properties of high-temperature gases |
| Lecture 16 |
Chapter 17 - High-temperature flows |
| Lecture 18 |
Extra material |
Course design
In the course there are in total 18 lectures and 7 sessions with exercises. There are also four compulsory numerical assignments involving problem solution based on classical formulae and/or numerical methods. One of these assignments, referred to as The Compressible Flow Project, spans over all eight course weeks and includes a literature survey part and a hands-on numerical assignment. The project is done in groups of up to four students and should be presented in form of a technical report at the end of the course. There is also a mandatory oral-presentation session in the end of the course where each of the groups presents their approach to solve their specific problem and their major findings. The numerical tools used in the course consist of a Chalmers-developed in-house code for simulation of 1D compressible flow called CFLOW and the commercial code Star-CCM+ is used for 2D compressible flow simulations. Detailed descriptions of the assignments and the project can be found here.
Learning objectives and syllabus
This course in compressible fluid mechanics will give you knowledge about fluid flows and related engineering methods such that you will be able to:
- conduct industrial development work in the area of high-speed flows
- apply control volume formulations, differential formulations for inviscid flows
- account for basic phenomena and methods for treating compressible flows
After the completing the course, you should be able to:
- Define the concept of compressibility for flows
- Explain how to find out if a given flow is subject to significant compressibility effects
- Describe typical engineering flow situations in which compressibility effects are more or less predominant (e.g. Mach number regimes for steady-state flows)
- Present at least two different formulations of the governing equations for compressible flows and explain what basic conservation principles they are based on
- Explain how thermodynamic relations enter into the flow equations
- Define the special cases of calorically perfect gas, thermally perfect gas and real gas and explain the implication of each of these special cases
- Explain why entropy is important for flow discontinuities
- Derive (marked) and apply (all) the presented mathematical formulae for classical gas dynamics
- 1D isentropic flow *
- Normal shocks *
- 1D flow with heat addition *
- 1D flow with friction *
- Oblique shocks in 2D *
- Shock reflection at solid walls *
- Contact discontinuities
- Prandtl-Meyer expansion fans in 2D
- Detached blunt body shocks, nozzle flows
- Unsteady waves and discontinuities in 1D
- Basic acoustics
- Solve engineering problems involving the above-mentioned phenomena (8.a - 8.k)
- Explain how the incompressible flow equations are derived as a limiting case of the compressible flow equations
- Explain how the equations for aero-acoustics and classical acoustics are derived as limiting cases of the compressible flow equations
- Explain the main principles behind a modern Finite Volume CFD code and such concepts as explicit/implicit time stepping, CFL number, conservation, handling of compression shocks, and boundary conditions
- Apply a given CFD code to a particular compressible flow problem
- Analyse and verify the quality of the numerical solution
- Explain the limitations in fluid flow simulation software
- Report numerical analysis work in form of a technical report
- Describe a numerical analysis with details such that it is possible to redo the work based on the provided information
- Write a technical report (structure, language)
- Search for literature relevant for a specific physical problem and summarize the main ideas and concepts found
- Present engineering work in the form of oral presentations
Link to the syllabus on Studieportalen.
Examination form
The examination is based on a written test (fail, 3, 4, 5), passed assignments; three numerical assignments and one larger project. The project may give up to seven bonus points for the written exam if the deliverables are handed in on time and all the assessment criteria are fulfilled. The exam will be divided into two parts; the first part (20p.) will contain a number of theory questions and the second part (40p.) will contain 4 problems each of which may give 10 points, i.e. in total 60 points.
Grades for the course will be given as follows (P = P_E+P_B where P_E is the number of points on the exam and P_B is the number of bonus points):
| Grade | Range of points |
| Fail | P < 24 |
| 3 | 24 <= P < 36 |
| 4 | 36 <= P < 48 |
| 5 | 48 <= P |
Schedule
Link to course schedule in TimeEdit:
Detailed schedule:
Course week 1
Lecture L01 - Niklas Andersson
2024-01-16 (Tuesday) 13:15-15:00 (HA2)
Chapter 1 - Compressibility, thermodynamics review
TME085_L01.pdf
Lecture L02 - Niklas Andersson
2024-01-16 (Tuesday) 15:15-17:00 (HA2)
Chapter 2 - Conservation laws (integral form)
TME085_L02.pdf
Lecture L03 - Niklas Andersson
2024-01-18 (Thursday) 13:15-15:00 (HA2)
Chapter 3 - 1D isentropic flow, normal shocks
TME085_L03.pdf
Exercise E01 - Debarshee Ghosh
2024-01-18 (Thursday) 15:15-17:00 (HA2)
Chapter 1 - Compressibility, thermodynamics review
Chapter 2 - Conservation laws (integral form)
Problems solved in class: P1.4b, P1.5, P1.7, P2.1 P2.2
Recommended home exercise: E1.3, E1.4, E1.5, E1.7
Ex.y and Px.y denotes text book examples and problems respectively
Lecture L04 - Niklas Andersson
2024-01-19 (Friday) 13:15-15:00 (HA2)
Chapter 3 - 1D flow with heat addition or friction
TME085_L04.pdf
Course week 2
Lecture L05 - Niklas Andersson
2024-01-23 (Tuesday) 13:15-15:00 (HA2)
Chapter 4 - 2D flow (part I): oblique shocks, shock reflection
TME085_L05.pdf
Exercise E02 - Debarshee Ghosh
2024-01-23 (Tuesday) 15:15-17:00 (HA2)
Chapter 3 - 1D flow with shocks, heat addition or friction
Problems solved in class: P3.8, P3.9, P3.10, P1 (exam 2009)
Recommended home exercise: E3.5, E3.9, P3.4, E3.13
Ex.y and Px.y denotes text book examples and problems respectively
Lecture L06 - Niklas Andersson
2024-01-25 (Thursday) 13:15-15:00 (HA2)
Chapter 4 - 2D flow (part II): expansion fans, shock expansion theory
TME085_L06.pdf
Exercise E03 - Debarshee Ghosh
2024-01-25 (Thursday) 15:15-17:00 (HA2)
Chapter 3 - 1D flow with shocks, heat addition or friction
Chapter 4 - 2D flow (oblique shocks & reflection)
Problems solved in class: P3.12, P3.13, P4.1, P4.6, P1 (exam 2014-03-10)
Recommended home exercise: E3.17, E4.1
Ex.y and Px.y denotes text book examples and problems respectively
Lecture L07 - Niklas Andersson
2024-01-26 (Friday) 13:15-15:00 (HA2)
Chapter 5 - Quasi-1D flow (part I): governing equations and fundamental relations
TME085_L07.pdf
Course week 3
Lecture L08 - Niklas Andersson
2024-01-30 (Tuesday) 13:15-15:00 (HA2)
Chapter 5 - Quasi-1D flow (part II): nozzles and diffusers
TME085_L08.pdf
Exercise E04 - Debarshee Ghosh
2024-01-30 (Tuesday) 15:15-17:00 (HA2)
Chapter 4 - 2D flow, shock expansion theory
Chapter 5 - Quasi-1D flow
Problems solved in class: P4.10, P5.1, E4.14, E4.15, P4 (exam 2009)
Recommended home exercise: P5.2, P5.5, E4.6, E4.12, E4.13, E5.7
Ex.y and Px.y denotes text book examples and problems respectively
Consultation C01 - Debarshee Ghosh
2024-02-01 (Thursday) 13:15-17:00 (ES61)
Assignments 1 & 2
Lecture L09 - Niklas Andersson
2024-02-02 (Friday) 13:15-15:00 (HA2)
Chapter 6 - Alternative forms of the flow equations
TME085_L09.pdf
Course week 4
Lecture L10 - Niklas Andersson
2024-02-08 (Thursday) 13:15-15:00 (HA2)
Chapter 7 - 1D unsteady flow (part I): moving normal shock waves
TME085_L10.pdf
Exercise E05 - Debarshee Ghosh
2024-02-08 (Thursday) 15:15-17:00 (HA2)
Chapter 5 - Quasi-1D flow
Chapter 7 - 1D unsteady flow
Problems solved in class: P5.11, P7.2, P7.3, P7.5, P7.8, P3 (exam 2009)
Recommended home exercise: E7.1, E7.2, E7.5, P7.10
Ex.y and Px.y denotes text book examples and problems respectively
Lecture L11 - Niklas Andersson
2024-02-09 (Friday) 13:15-15:00 (HA2)
Chapter 7 - 1D unsteady flow (part II): reflected shock waves
TME085_L11.pdf
Course week 5
Consultation C02 - Debarshee Ghosh
2024-02-13 (Tuesday) 13:15-17:00 (ES61)
The Compressible Flow Project & Assignment 3
Lecture L12 - Niklas Andersson
2024-02-16 (Friday) 13:15-15:00 (HA2)
Chapter 7 - 1D unsteady flow (part III): elements of acoustic theory and finite non-linear waves
TME085_L12.pdf
Course week 6
Consultation C03 - Debarshee Ghosh
2024-02-20 (Tuesday) 13:15-17:00 (E-D2480)
The Compressible Flow Project & Assignment 3
Lecture L13 - Niklas Andersson
2024-02-22 (Thursday) 13:15-15:00 (HA2)
Chapter 12 - Time marching numerical methods (part I): spatial discretization and numerical schemes
TME085_L13.pdf
Exercise E06 - Debarshee Ghosh
2024-02-22 (Thursday) 15:15-17:00 (HA2)
Old exam problems (part I)
Lecture L14 - Niklas Andersson
2024-02-23 (Friday) 13:15-15:00 (HA2)
Chapter 12 - Time marching numerical methods (part II): time integration and boundary conditions
TME085_L14.pdf
Course week 7
Lecture L14 (Extra) - Niklas Andersson
2024-02-27 (Tuesday) 13:15-15:00 (HA2)
Chapter 12 - Time marching numerical methods (part II): time integration and boundary conditions
TME085_L14.pdf
Consultation C04 - Debarshee Ghosh
2024-02-27 (Tuesday) 15:15-17:00 (MT10-13 (HA2))
The Compressible Flow Project & Assignment 3
Lecture L15 - Niklas Andersson
2024-02-29 (Thursday) 13:15-15:00 (HA2)
Chapter 16 - Properties of high-temperature gases
TME085_L15.pdf
Consultation C05 - Debarshee Ghosh
2024-02-29 (Thursday) 15:15-17:00 (HA2)
The Compressible Flow Project & Assignment 3
Lecture L16 - Niklas Andersson
2024-03-01 (Friday) 13:15-15:00 (HA2)
Chapter 17 - High-temperature flows: basic examples
TME085_L16.pdf
Course week 8
Oral Presentation Session - Niklas Andersson & Debarshee Ghosh
2024-03-05 (Tuesday) 13:15-15:00
groups: 1, 2, 3, 4, 6 (EA)
groups 8, 9, 11, 12, 13, 14 (EL43)
The Compressible Flow Project - D3
Note! Mandatory
Lecture L17 - Niklas Andersson
2024-03-07 (Thursday) 13:15-15:00 (HA2)
Aeronautics - part I: thrust and diffusers
Exercise E07 - Debarshee Ghosh
2024-03-07 (Thursday) 15:15-17:00 (HA2)
Old exam problems (part II)
Lecture L18 - Niklas Andersson
2024-03-08 (Friday) 13:15-15:00 (EA)
Aeronautics - part II: flight aerodynamics
TME085_L18.pdf
Course summary:
| Date | Details | Due |
|---|---|---|