Course syllabus

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TME085 Compressible flow lp3 VT25 (7.5 hp)

Course is offered by the department of Mechanics and Maritime Sciences

The course is given in English.

 

Content

  1. 1  Contact details
  2. 2  Course purpose
  3. 3  Course literature
    1. 3.1  course documents
    2. 3.2  lecture notes
    3. 3.3  suggested solutions for recommended problems
  4. 4  Course design
    1. 4.1  computer assignment 1
    2. 4.2  computer assignment 2
    3. 4.3  computer assignment 3
    4. 4.4  the compressible flow project
  5. 5  Learning objectives
  6. 6  Examination
  7. 7  Schedule

    week 1  week 2  week 3  week 4  week 5  week 6  week 7  week 8

 

1. Contact details

 

Examiner

 

Teaching Assistant

 

2. 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.

 

3. Course literature

The course follows the book Modern Compressible Flow with Historical Perspective by John D. Anderson, which is a classic book in the field that is used for similar courses world wide.

 

Book cover: Modern Compressible Flow by John D. Anderson 4:th edition

  • 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:
  • Summaries and quizzes

 

3.1 Additional Documents

 

additional course 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).

 


3.2 Lecture Notes

 

lecture notes for each of the 17 lectures

Document

Description
Lecture 01

Chapter 1 - Introduction
Compressibility, thermodynamics review
Lecture 02

Chapter 2 - Integral forms of the conservation equations for inviscid flows
Derivation of governing equations
Lecture 03

Chapter 3 - One-dimensional flow
1D isentropic flow, normal shocks
Lecture 04

Chapter 3 - One-dimensional flow
1D flow with heat addition or friction
Lecture 05

Chapter 4 - Oblique shocks and expansion waves
2D flow (part I): oblique shocks, shock reflection
Lecture 06

Chapter 4 - Oblique shocks and expansion waves
2D flow (part II): expansion fans, shock expansion theory
Lecture 07

Chapter 5 - Quasi-one-dimensional flow
Quasi-1D flow (part I): governing equations and fundamental relations
Lecture 08

Chapter 5 - Quasi-one-dimensional flow
Quasi-1D flow (part II): nozzles and diffusers
Lecture 09

Chapter 6 - Differential conservation equations for inviscid flow
Alternative forms of the flow equations
Lecture 10

Chapter 7 - Unsteady wave motion
1D unsteady flow (part I): moving normal shock waves
Lecture 11

Chapter 7 - Unsteady wave motion
1D unsteady flow (part II): reflected shock waves
Lecture 12

Chapter 7 - Unsteady wave motion
1D unsteady flow (part III): elements of acoustic theory and finite non-linear waves
Lecture 13

Chapter 12 - The time-marching technique
Time marching numerical methods (part I): spatial discretization and numerical schemes
Lecture 14

Chapter 12 - The time-marching technique
Time marching numerical methods (part II): time integration and boundary conditions
Lecture 15

Chapter 16 - Properties of high-temperature gases
Properties of high-temperature gases (selected parts)
Lecture 16

Chapter 17 - High-temperature flows
High-temperature flows (selected parts)
Lecture 18

Extra material
Aircraft aerodynamics

 


3.3 Suggested solutions to problems solved in class

 

suggested solutions for problems solved in class

Document

Description
Exercise session 1

Chapter 1 - Introduction

Chapter 2 - Integral form of the conservation equations for inviscid flows
Exercise session 2

Chapter 3 - One-dimensional flow
Exercise session 3

Chapter 4 - Oblique shocks and expansion waves
Exercise session 4

Chapter 4 - Oblique shocks and expansion waves

Chapter 5 - Quasi-one-dimensional flow
Exercise session 5

Chapter 5 - Quasi-one-dimensional flow

Chapter 7 - Unsteady wave motion
Exercise session 6

Old exam problems (part I)
Exercise session 7

Old exam problems (part II)

 

4. 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. A short descriptions of the assignments and the project are given below (a detailed description and instructions can be found here).

4.1 One-dimensional compressible flow with heat addition and friction

In computer assignment 1, you will investigate one-dimensional flows using the 1D solver available in CFLOW. In total five problems should be solved of which two deals with 1D flow with heat addition and three deals with 1D flow with friction.

Instructions for computer assignment 1

4.2 Two-dimensional flow past a symmetrical diamond wedge airfoil

In computer assignment 2, the flow past a symmetrical diamond wedge airfoil will be calculated using the commercial software STAR-CCM+. The geometry and grid generation, as well as the solution of the Navier-Stokes equations that describe the flow, is carried out within the same software.

Instructions for computer assignment 2

4.3 Quasi-one-dimensional flow

In computer assignment 3, you will investigate flow inside a convergent divergent nozzle and the unsteady wave motion in a shock tube using the Q1D solver available in CFLOW. In total, you will investigate four flow cases of which three are nozzle flows and one is the flow in a shock tube.

Instructions for computer assignment 3

4.4 The compressible flow project

The compressible flow project is based on numerical analysis work and is done in groups of up to four students. All numerical work in the project is done in the commercial CFD software STAR-CCM+. The project is a pass/fail-type of course element and an approved project is needed to get the final course grade. The project can result in total seven bonus points for the written exam at the end of the course. However, the maximum number of bonus points will only be rewarded to groups that complete all parts of the project on time and pass the assessment without revision. If you do not hand in your deliverables on time, you will not get any bonus points. If revision is needed, you will still get bonus points but depending on the severity of the revision the total number may be modified.

Instructions for the compressible flow project

 

5. Learning objectives

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:

    1. Define the concept of compressibility for flows
    2. Explain how to find out if a given flow is subject to significant compressibility effects
    3. Describe typical engineering flow situations in which compressibility effects are more or less predominant (e.g. Mach number regimes for steady-state flows)
    4. Present at least two different formulations of the governing equations for compressible flows and explain what basic conservation principles they are based on
    5. Explain how thermodynamic relations enter into the flow equations
    6. Define the special cases of calorically perfect gas, thermally perfect gas and real gas and explain the implication of each of these special cases
    7. Explain why entropy is important for flow discontinuities
    8. Derive (marked) and apply (all) the presented mathematical formulae for classical gas dynamics
      1. 1D isentropic flow *
      2. Normal shocks *
      3. 1D flow with heat addition *
      4. 1D flow with friction *
      5. Oblique shocks in 2D *
      6. Shock reflection at solid walls *
      7. Contact discontinuities
      8. Prandtl-Meyer expansion fans in 2D
      9. Detached blunt body shocks, nozzle flows
      10. Unsteady waves and discontinuities in 1D
      11. Basic acoustics
    9. Solve engineering problems involving the above-mentioned phenomena (8.a - 8.k)
    10. Explain how the incompressible flow equations are derived as a limiting case of the compressible flow equations
    11. Explain how the equations for aero-acoustics and classical acoustics are derived as limiting cases of the compressible flow equations
    12. 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
    13. Apply a given CFD code to a particular compressible flow problem
    14. Analyse and verify the quality of the numerical solution
    15. Explain the limitations in fluid flow simulation software
    16. Report numerical analysis work in form of a technical report
      1. Describe a numerical analysis with details such that it is possible to redo the work based on the provided information
      2. Write a technical report (structure, language)
    17. Search for literature relevant for a specific physical problem and summarize the main ideas and concepts found
    18. Present engineering work in the form of oral presentations

 

6. Examination

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 bonus points are valid for the exam and the two following re-exams. 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 = E + B where E is the number of points on the exam and B is the number of bonus points):


exam points to course grade conversion table

Grade

Range of points
Fail P < 24
3 24 <= P < 36
4 36 <= P < 48
5 48 <= P

An old-exam archive can be found here

 

7. Schedule

Link to course schedule in TimeEdit:

TimeEdit

Detailed schedule:

Course week 1

  • Lecture L02 - Niklas Andersson
  • 2025-01-21 (Tuesday) 15:15-17:00 (HA2)
  • Chapter 2 - Integral form of the conservation equations for inviscid flows
  • Derivation of the governing equations on integral form

  • lecture notes

  • chapter 2 summary, quiz, and movies

Course week 2

  • Exercise E02 - Emil Ellenius
  • 2025-01-28 (Tuesday) 15:15-17:00 (HA2)
  • Chapter 3 - One-dimensional flow
  • 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

  • suggested solutions

  • chapter 3 summary, quiz, and movies
  • Exercise E03 - Emil Ellenius
  • 2025-01-30 (Tuesday) 15:15-17:00 (HA2)
  • Chapter 4 - Oblique shocks and expansion waves
  • 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

  • suggested solutions

  • chapter 4 summary, quiz, and movies

Course week 3

  • Consultation C01 - Emil Ellenius
  • 2025-02-06 (Thursday) 13:15-17:00 (ES61)
  • Assignments 1 & 2

Course week 4

  • Exercise E04 - Emil Ellenius
  • 2025-02-11 (Tuesday) 15:15-17:00 (HA2)
  • Chapter 4 - Oblique shocks and expansion waves
  • Chapter 5 - Quasi-one-dimensional 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

  • suggested solutions

  • chapter 4 summary, quiz, and movies
  • chapter 5 summary, quiz, and movies

Course week 5

  • Consultation C02 - Emil Ellenius
  • 2025-02-18 (Tuesday) 13:15-17:00 (ES61)
  • The compressible flow project & Assignment 3
  • Lecture L12 - Niklas Andersson
  • 2025-02-20 (Thursday) 13:15-15:00 (HA2)
  • Chapter 7 - Unsteady wave motion
  • 1D unsteady flow (part III): elements of acoustic theory and finite non-linear waves

  • lecture notes

  • chapter 7 summary, quiz, and movies
  • Exercise E06 - Emil Ellenius
  • 2025-02-20 (Thursday) 15:15-17:00 (HA2)
  • Old exam problems (part I)

  • suggested solutions
  • Lecture L13 - Niklas Andersson
  • 2025-02-21 (Friday) 13:15-15:00 (HA2)
  • Chapter 12 - The time-marching technique
  • Time marching numerical methods (part I): spatial discretization and numerical schemes

  • lecture notes

  • chapter 12 summary, quiz, and movies

Course week 6

  • Consultation C03 - Emil Ellenius
  • 2025-02-25 (Tuesday) 13:15-15:00 (E-D2480)
  • 2025-02-25 (Tuesday) 15:15-17:00 (HB105)
  • The compressible flow project & Assignment 3
  • Lecture L14 - Niklas Andersson
  • 2025-02-27 (Thursday) 13:15-15:00 (HA2)
  • Chapter 12 - The time-marching technique
  • Time marching numerical methods (part II): time integration and boundary conditions

  • lecture notes

  • chapter 12 summary, quiz, and movies
  • Exercise E07 - Emil Ellenius
  • 2025-02-27 (Thursday) 15:15-17:00 (HA2)
  • Old exam problems (part II)

  • suggested solutions

Course week 7

  • Guest Lecture GL01 - Christian Ibron (FOI)
  • 2025-03-04 (Tuesday) 13:15-15:00 (HA2)
  • Compressible flow in real life
  • Consultation C04 - Emil Ellenius
  • 2025-03-04 (Tuesday) 15:15-17:00 (HA2)
  • The compressible flow project & Assignment 3
  • Consultation C05 - Emil Ellenius
  • 2025-03-06 (Thursday) 15:15-17:00 (HA2)
  • The compressible flow project & Assignment 3
  • Lecture L17 - Niklas Andersson
  • 2025-03-07 (Friday) 13:15-15:00 (HA2)
  • Aeronautics - part I: thrust and diffusers

Course week 8

  • Oral Presentation Session - Niklas Andersson & Emil Ellenius 
  • 2025-03-11 (Tuesday) 13:15-15:00
  • groups: 1 - 11 (EA)
  • groups 12 - 22 (EL43)
  • The Compressible Flow Project - D3
  • Note! Mandatory
  • Lecture L18 - Niklas Andersson
  • 2025-03-13 (Thursday) 13:15-15:00 (HA2)
  • Aeronautics - part II: flight aerodynamics

  • lecture notes

Course summary:

Date Details Due