The University of Southampton
Courses

# FEEG3011 Introduction to Turbulence and Mixing

## Module Overview

The basic concept of mass, scalar, heat and chemical reaction in fluids are introduced. The major focus is advanced numerical and experimental methods and practical applications, including atmospheric boundary layer, bluff body aerodynamics, numerical models of scalars and modelling chemical reaction in CFD packages.

### Aims and Objectives

#### Module Aims

To provide students with an understanding of the principles of mass, scalar, heat and chemical reaction in fluids; Be able to describe the fundamental concepts and associated modelling approaches; Be able to choose appropriate numerical techniques to solve real engineering problems using bespoke or commercial codes.

#### Learning Outcomes

##### Knowledge and Understanding

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

• Fundamental principles, including Fick’s Law, diffusion equation, convection equation, convective-diffusion equation [T, AE];
• Basic principles of turbulence mixing, point source of scalar dispersion, and chemical reaction in fluids (T, AE);
• The theoretical background (T,AE) and practical issues associated with modelling (T,AC);
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Use commercial packages to define, analyse, and solve a class of engineering problems (D, A);
• Communicate work in written reports (D, A).
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Solve basic equations of scalar dynamics using numerical methods [T, AC]
• Use a commercial package with an appreciation of modelling limitations, to demonstrate importance of validation and engineering interpretation of results (T,AE,AC);
• Describe likely levels of uncertainty and confidence associated with the analysis (T, AE, AC).• Describe likely levels of uncertainty and confidence associated with the analysis (T, AE, AC).

### Syllabus

Overview of turbulence and mixing: Outline, examples of mass and scalar transport problems. Introduction to turbulence: Introduction to turbulence and the mathematical description of turbulence. Atmospheric boundary layers and turbulence: Turbulence (gustiness) at different height level, broad range of frequencies in the fluctuations. Similarities in neutral and non-neutral atmospheric boundary layer. Effect of topography, change of terrain (e.g. internal boundary layer). Fick’s law and diffusion equation; convection equation, Convective-Diffusion Equation: Derivation of diffusion equation, convection equation, understanding the physics behind these equations. Derivation of convection-diffusion equation. Understanding the Peclet number. Presenting realistic engineering examples. Dispersion in turbulent flows: Scalar transport equations. Gaussian distribution of concentration and its use in operational plume and puff models. Introduction to Lagrangian particle models and CFD approaches. Source term estimation. Field Experiments: Planning and conducting field experiments, types of sampling instruments and tracers used. Advantages and disadvantages of field and wind tunnel experiments. Time series data analysis, sampling and filtering. Evaluation of concentration fluctuations, turbulence and correlation. Interpretation of results and industrial experiences: Assessing model performance: use of experimental data, metrics and evaluation of accuracy and uncertainty. The confidence and trust that can be placed in numerical and experimental results. Examples of case studies. Numerical Procedures in commercial codes: Finite Differencing methods, explicit and implicit schemes, solution procedure, Reynolds averaging, turbulence mixing coefficient. Practical modelling using case study: Solve a steady 1D convection-diffusion equation with Dirichlet boundary conditions at both ends. The aim is to demonstrate the properties of the discretisation schemes for a simple problem which has an analytic solution, considering various Peclet numbers. Chemical reaction in fluid flows and it modelling: Dealing with multi-scales problems of chemical reactions in turbulent flows, and their modelling, centring on simple "reactors" ie stirred tanks and plug flow reactors and look at the interplay of fluid residence times in the reactor to simple low order reactions. Bluff body aerodynamics and hydrodynamics: Flow separation, re-attachment, flat plate normal to flow, rectangular cylinder, circular cylinder, building shape blocks, pressure distribution at various Re numbers, free-stream turbulence effects. Revision (3 lectures) Computing Lab Sessions: 1 summative assignments with 2 support lab sessions (Weeks 4 -5) 1 summative assignments with 3 support lab sessions (Weeks 6 - 8).

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### Learning and Teaching

#### Teaching and learning methods

Teaching methods include: Lectures (3/week) Computing lab sessions (5 in total) Blackboard tutorials

TypeHours
Revision9
Tutorial5
Completion of assessment task10
Preparation for scheduled sessions18
Lecture36
Follow-up work36
Wider reading or practice36
Total study time150

#### Resources & Reading list

R B Stull (1988). An Introduction to Boundary Layer Meteorology.

F Pasquill and FB Smith (1983). Atmospheric Diffusion study of the dispersion of windborne material from industrial and other sources.

H Tennekes and JL Lumley (1972). A First Course in Turbulence.

### Assessment

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#### Summative

MethodPercentage contribution
Coursework 10%
Coursework 10%
Examination 80%

#### Referral

MethodPercentage contribution
Examination 100%

#### Repeat Information

Repeat type: Internal & External

### Linked modules

Pre-requisites: FEEG1003 Thermofluids or FEEG2003 Fluid Mech or SESA2022 Aerodynamics or SESS2015 Hydrodynamics & Seakeeping

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