Introduction to Turbulence and Turbulence Modelling

Module aims

The course aims at providing the student with a minimum background knowledge and physical understanding necessary for the critical assessment of turbulent models which the student is very likely to be confronted with in subsequent courses and in industry.

Learning outcomes

 On successfully completing this course unit, students will be able to:

·      describe the basic characteristics of turbulent flows, as well as their practical consequences concerning drag, dispersion of momentum/material/heat, etc;

·    distinguish the differences in the mechanics of important classes of turbulent flows such as boundary free flows and wall flows;

·  operate Reynolds decompositions and work out turbulent mean flow, energy, dissipation, pressure properties;

·      manipulate basic turbulent models and understand their strengths and limitations;

·    operate multiscale/Fourier analysis of homogeneous turbulence and derive the Kolmogorov theory of small-scale turbulence;

·   derive the log-law of the wall in various ways whilst understanding the assumptions made and their limitations;

·   understand the range of applicability of the Taylor frozen turbulence hypothesis fundamental for the interpretation of hot wire anemometry measurements.

· understand and operate various decompositions, mean and fluctuations on the one hand, multiscale/Fourier decompositions of fluctuations on the other, a very widely transferable skill to all types of data and PDE analyses.

·      use fundamental knowledge to investigate and assess new and emerging technologies

·  apply mathematical and computer-based models for solving aerodynamic fluid-flow problems in engineering

Module syllabus

Introduction: basic characteristics of turbulent flows: 3-D, vortex stretching, energy transfer, enstrophy, strain rates, randomness and statistics.
Reynolds decomposition: mean flow turbulence fluctuations and energetics.  Pivotal experimental observation concerning independence of kinetic energy dissipation rate from Reynolds number. The importance of pressure. Brief discussion of practical consequences to do with drag and dispersion of momentum, material and heat.
Examples of simple turbulent flows: two-dimensional free shear flows (jets and wakes), two-dimensional channel flow, turbulent boundary layer, decaying grid flow. Introduce the concept of statistical homogeneity and its consequences. Distinction between wall flows and free shear layers.
The Kolmogorov theory of homogeneous turbulence: The universality theory, the -5/3 law for the energy spectrum and the limitations of universality.
Wall turbulence. The log law. Anisotropic energy spectra and their scalings. Eddy structure of turbulent boundary layers and its relation to spectra.
for numerical simulation
Measurement of turbulent flows. Constant temperature anemometry, Taylor’s frozen flowfield hypothesis, basic uncertainty quantification.

Teaching methods

Lectures, tutorials

Assessments

Examined Assessment
2 hour written examination in January (100%)

Non-Examined Assessment
1 x Progress test (peer marked)

Reading list