MTF256 Turbulent Flow (7.5 hec)

Prerequisites

A basic fluid dynamic course and, preferably, TME075 Mechanics of Solids and Fluids. (or a corresponding course)

Aim of the course

The aim of the course is to introduce students to the phenomenon of turbulence and to provide them with some elementary tools for dealing with it.

Course content

This course will provide an introduction to the fundamentals of turbulent flow. The focus will be on understanding the averaged equations of motion and the underlying physics they contain. Topics covered include:
  • what is turbulence?
  • instability and transition
  • derivation of the Reynolds stress transport equations
  • discussion of the physical meaning of the different terms in the Reynolds stress transport equations
  • Simple shear flows, for example boundary layers, jet and wakes.
  • Elements of experimental work in turbulence
  • Some basic concepts for describing turbulence flow such as turbulent length and time scales, two-point correlations and energy spectra will be introduced.

Learning outcome

After completion of this course, the student should be able to
  • Recognize turbulence as a multi-scale phenomenon with wide separation between the length and times scales of those containing the energy and those at which it is dissipated.
  • Distinguish between non-turbulent unsteady flows and turbulent flows.
  • Derive the exact transport equations for the Reynolds stresses using Cartesian tensor notation.
  • Identify the various terms in these equations and describe what role they play
  • Explain the closure problem
  • Understanding basic properties of simple shear flows
  • Reduce the RANS equations for mean velocity, turbulence energy and Reynolds stress by order of magnitude analysis to forms applicable to simple turbulent shear flows, including jets, wakes and boundary layers.

Organization

Two or three lectures per week will be given. One project and one laboration should be carried out by the students.
  • Project: The students will be given data from a numerical simulation (DNS). The data will be analyzed. The students will be given instantaneous three-dimensional data from a DNS (Direct Numerical Simulation) of channel flow. The following quantities will be computed and analyzed:
    • Time histories
    • Time averaging
    • Histogram/probability density
    • Mean flow
    • The time-averaged momentum equation
    • Wall shear stress
    • Resolved stresses
    • Fluctuating wall shear stress
    • Production terms
    • Pressure-strain terms
    • Dissipation
    • Two-point correlations
  • Experimental investigation of a simple shear flow

Course literature

  • Lecture notes.

Examination

A written examination is given at the end of the course. To pass the course the student must get grade 3 on the written exam.

Written presentation of the project is part of the examination. It must be uploaded to the student portal before deadline (see Time table).

The experimental investigation is compulsary

To get grade 4 or 5 in the course the written project must be handed in on time.

1-7 points can be given for the project (the maximum on the exam is 50). These will be added to the result of the written exam (provided grade 3 or more was achieved on the written exam).

This page can be found on

www.tfd.chalmers.se/~lada/turbulent_flow/



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