# Lectures - Winter Term

## German / EnglishStrömungslehre 2 / Fluid Dynamics

The lecture offers deeper knowledge on important problems in fluid dynamics, and is divided into the following chapters:

• Conservation equations in fluid dynamics, describing the conservation of mass, momentum and energy (Navier-Stokes equations), stress-strain relations, and thermal and caloric equations of state
• Similarity theory
• Creeping flows
• Potential flows
• Boundary layer theory
• Introduction to turbulent flows
• One-dimensional gas dynamics

Objectives:
The students should be able to analyse and mathematically describe complex theoretical or experimental problems in fluid dynamics, and for simpler problems also perform calculations.

## EnglishGasdynamics

The lecture gives an introduction to thermodynamics and fluid mechanics of compressible media, in particular gases. The structure of the lecture is:

• Introductory repetition of kontinuummechanics fundamentals and a short introduction to the kinetic theory
• One-dimensional streamtube theory for steady nozzle flow, stationary shocks and the compressible, viscous flow
• One-dimensional streamtube theory for linear (acoustic) and non-linear wave propagation, the shocktube (aka the Riemann Problem), and the analogy to the shallow-water flow
• Gas dynamics of combustion: deflagration and detonation
• Introduction to analytical and numerical solution methods

Objectives:
The students will be able to understand the effects and phenomena of compressible flows and to identify them in technical systems. The will be able to perform calculations of steady and transient, one-dimensional flow phenomena and to evaluate the implications for plant or device design. The introduction to numerical solution methods gives a very first foundation for application of specialized simulation software.

## EnglishTurbulent Flows

The lecture gives an introduction to the fluid mechanics of viscous turbulent fluids. Flows can be laminar or turbulent. Laminar flows can be modeled exactly. However, turbulent flows, which are relevant to almost all technical applications, can only be approximated due to their stochastic nature. The lecture analyses the structure of turbulent flows, and built on this highlights the treatment of the most important approaches for the calculation of turbulent flows.

Rough outline:
• Origin of turbulence
• Statistical assessment of turbulence
• Structure of turbulent flows
• Simulation of turbulence - LES and DNS
• Reynolds-averaged equations
• Approaches for turbulence modelling
• Compressible turbulent flows

Objectives:
Understanding of modern methods to evaluate the effects of turbulence

# Lectures - Summer Term

## German / EnglishStrömungslehre 1 / Fluidmechanics

The lecture gives an introduction to the mechanics of fluids and is divided into the following chapters:

• static of fluids
• kinematics of fluids
• streamtube theory of incompressible fluids
• derivation of conservation equations for mass and energy
• Bernoulli equation
• energy equation with external energy and with friction
• momentum theorem
• angular momentum theorem
• streamtube theory of compressible fluids (introduction to gasdynamics)

## EnglishNumerics & Flow Simulation

Voraussetzung "Fluiddynamik" und "Strömungsmechanik"

The course aims to provide a detailed understanding of numerical techniques that are used for fluid flow simulation and to enable the students to understand the strengths and shortcomings of these methods. The first half of the course will focus on numerical techniques and the discretisation of the Navier-Stokes equations; the respective tutorials will apply Matlab to develop a simplified (1D) CFD tool. The second half of the course will teach the basics of the OpenFOAM software and apply this program to solve the flow in canonical geometries.

The course material can be accessed via moodle, for which you need a password. This is the birth date of John von Neumann. The birthday must be formatted like "DDMMYYYY".

The course will cover the following topics:

• Interpolation, numerical integration and differentiation, discretisation of convective and diffusive fluxes, advancing/integration in time, pressure-velocity coupling, 3D-CFD, Reynolds averaged simulations, Large-Eddy Simulation
• Introduction to concepts of OpenFOAM, basics of grid generation, setting up a simple flow simulation, programing a custom solver in OpenFOAM

Upon successful completion of the course, students will have obtained the following skills and knowledge:

• Knowledge of schemes for solving the partial differential equations of fluid mechanics
• Knowledge of the Finite Volume Method
• Knowledge of terms and abbreviations of computational fluid mechanics
• Knowledge and an understanding of discretization schemes for convective and diffusive fluxes
• Knowledge and an understanding of the properties of the above schemes
• Knowledge about schemes for pressure-velocity coupling in incompressible descriptions
• Ability to implement simplified CFD codes in Matlab
• Basic skill set to use 3D CFD programs for solving fluid mechanical problems
• The ability to apply OpenFOAM to solve three-dimensional flow problems
• Knowlege and an understanding of the limitations of CFD approaches, models and numerical schemes
• An understanding of the sources and properties of numerical error (Dissipation/Dispersion)

## Exams

In the courses Strömungslehre 1 / fluid mechanics as well as in Strömungslehre 2 / fluid dynamics a written exam is taken.

In the courses Numerics & Flow Simulation, Turbulent Flows and Gas Dynamics an oral exam is taken.

Registration for all exams is done via the responsible examination office within the given deadlines.

The appointments for the oral exams are made directly with us at the end of the lecture period.

Further details on examination dates, registration deadlines and contact addresses can be found here.

## Contact

Should you have questions regarding lectures, exercises and tutorials, please send a message to the corresponding e-mail address below or contact directly your course instructor:

Contact Gas Dynamics: gasdynamics.cfd [at] uni-due.de

Contact Numerics and Flow Simulation: numerics.cfd [at] uni-due.de

Contact Turbulent Flows: turbulence.cfd [at] uni-due.de

Contact Strömungslehre 1 / Fluidmechanics: fluidmechanics.cfd [at] uni-due.de

Contact Strömungslehre 2 / Fluiddynamics: fluiddynamik.cfd [at] uni-due.de