The University of Southampton
Courses

# SESA6061 Turbulence: Physics and modelling

## Module Overview

This module will provide an introduction to the fundamentals of turbulent flow and present strategies of how to solve the turbulence problem. The focus will be on understanding the equations of motion and the underlying physics they contain. The goal will be to provide you with the tools necessary to continue the study of turbulence and the methods available to numerically find solutions for turbulent flows. Topics covered include: what is turbulence; the Reynolds-averaged equations; simple and more sophisticated closure models; challenges for numerical simulations of turbulence, the Reynolds stress equations; simple decaying turbulence; homogeneous shear flow turbulence; free turbulent shear flows; wall-bounded turbulent flows.

### Aims and Objectives

#### Module Aims

• Lay a foundation for their rational prediction and analysis. • Cultivate an appreciation for the importance of turbulence over a range of disciplines. • Introduce tools for analysis of turbulent flows. • Acquaint students with the strategies available to surmount the turbulence closure problem. • Cultivate the skill and insight needed to affect a successful turbulent-flow solution appropriate for the geometry and boundary conditions under consideration.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Fundamental principles of turbulent flows
• Different statistical analysis tools as well as data manipulation methods
• How the full governing equations can be simplified and modelled
• Methods used to compute and model turbulent flows
• Strengths and weaknesses of popular industrial turbulence models
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Understand basic features of turbulence
• Appreciate strengths and weaknesses of methods used to measure turbulent flows
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Study and learn both independently
• Communicate work in oral presentations
• Demonstrate study and time management skills
• Solve problems
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Analyse turbulent flows via various statistical tools
• Critically appraise results from commercial computational fluid dynamics packages

### Syllabus

The nature of turbulence (2 lectures) - Its origin - stability. - Mean and fluctuation quantities. - General features and major effects. Tools for studying turbulence (5 lectures) - Definitions: stationarity and ergodicity. - Statistical tools: probability density function and moments, spectra, correlations. - Time-domain statistics: correlation and spectral functions. - Experimental tools: Hotwire anemometry, PIV. Equations and scales of motion (4 lectures) - Reynolds averaging; momentum and Reynolds stress equations. - Turbulence energy equation. - Vorticity and enstrophy; vortex stretching. - Spatial and time scales. - The energy cascade and Kolmogorov hypotheses. Canonical turbulent flows (6 lectures) Free flows: - Homogeneous isotropic turbulence and homogeneous shear flow. - Self-preserving jets, wakes and mixing layers. Wall flows: - 2D channel flow. - Smooth- and rough-wall boundary layers. Computational strategies: hierarchy of turbulence closures (1 lecture) - Engineering/CFD models: RANS schemes. - 'Numerical experiments': DNS and LES. - Hybrid RANS/LES: DES. - Survey of relevance and limitations. Reynolds-Averaged Navier-Stokes (RANS) models (8 lectures) - Motivation, philosophy, and classification - Modelling canonical flows: Homogeneous isotropic turbulence, 2D wall layers - Industrial models: - Complex geometry, pressure gradients/separation, surface roughness, mean three-dimensionality, compressibility. - Eddy-viscosity/Boussinesq closures: - Algebraic/zero-, one- and two-equation models. - Example: anatomy of the Spalart-Allmaras one-equation scheme. - Limitations of eddy-viscosity closures. - Guidelines for CFD users. Direct Numerical Simulations (DNS) (4 lectures) Numerical issues: - Domain size, resolution requirements - Spectral and high-order finite-difference methods - FFTs, aliasing, modified wavenumber analysis. Examples of classical and recent simulations: - plane-channel, 2D and 3D turbulent boundary layers separation bubbles, shock-boundary layer interaction. Recent developments: - Inflow treatments, and immersed-boundary techniques. Large Eddy Simulations (LES) (2 lectures) - Implicit and explicit filtering; subgrid-scale (SGS) modelling. - Recent developments: dynamic modelling, approximate deconvolution. - Inherent limitations of LES. New frontiers (2 lectures) - Unsteady RANS. - Hybrid RANS/LES methods. Revision (2 lectures)

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### Learning and Teaching

#### Teaching and learning methods

Teaching methods include • Lectures (3 per week) • Supporting material on Blackboard.

TypeHours
Revision123
Lecture27
Total study time150

Pope (2000). Turbulent Flow.

### Assessment

#### Assessment Strategy

Method of repeat year: Can be repeated externally (100% exam) or internally

#### Summative

MethodPercentage contribution
Coursework 15%
Coursework 15%
Exam  (2 hours) 70%

#### Referral

MethodPercentage contribution
Exam  (120 minutes) 100%

#### Repeat Information

Repeat type: Internal & External