Turbulence and Turbulence Modelling

Module aims

The course provides the basic knowledge and physical understanding necessary for the critical assessment of turbulent models relevant to subsequent courses as well as research and industry. Starting with simple turbulent flows, students learn to rigorously model complex turbulent flows, paying attention to the requirements for simulating turbulent flows as well as the considerations for measuring turbulence.

Learning outcomes

On successfully completing this module, you should be able to: 1. Appraise the basic characteristics of turbulent flows, as well as their practical consequences concerning drag, dispersion of momentum/material/heat; 2. Distinguish the differences in the mechanics of important classes of turbulent flows such as boundary free flows and wall flows; 3. Apply Reynolds decompositions and work out turbulent mean flow, energy, dissipation, pressure properties; 4. Manipulate basic turbulent models and understand their strengths and limitations; 5. Formulate a multiscale/Fourier analysis of homogeneous turbulence and derive the Kolmogorov theory of small-scale turbulence; 6. Derive the log-law of the wall in various ways whilst understanding the assumptions made and their limitations 

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 (and examples of vortical flows which do or do not have this property). 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: derivation from the Navier-Stokes equation of the scale-independence of energy flux in wavenumber space for stationary 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.  Eddy viscosities/diffusivities. Prospects for turbulence modelling and caveats, closure models for numerical simulation.  Measurement of turbulent flows. Constant temperature anemometry, Taylor’s frozen flow field hypothesis, basic uncertainty quantification. AHEP Learning Outcomes: SM7M, SM8M, EA6M, EA5m, EA7M, D9M, P9m, P10m, G2 

Teaching methods

The module will be delivered primarily through large-class lectures introducing the key concepts and methods, supported by a variety of delivery methods combining the traditional and the technological.  The content is presented via a combination of slides, whiteboard and visualizer.Learning will be reinforced through tutorial question sheets, featuring analytical tasks representative of those carried out by practising engineers. 

Assessments

This module presents opportunities for both formative and summative assessment.  
You will be formatively assessed through progress tests and tutorial sessions. 
You will have additional opportunities to self-assess your learning via tutorial problem sheets. 
You will be summatively assessed by a written closed-book examination at the end of the module.
Assessment type Assessment description Weighting Pass mark
Examination Closed-book written examination 100% 50%

You will receive feedback on examinations in the form of an examination feedback report on the performance of the entire cohort.

You will receive feedback on your performance whilst undertaking tutorial exercises, during which you will also receive instruction on the correct solution to tutorial problems.

Further individual feedback will be available to you on request via this module’s online feedback forum, through staff office hours and discussions with tutors.

Reading list

Core

Supplementary

Module leaders

Dr Oliver Buxton