Engineering Tripos Part IIB, 4A15: Aeroacoustics, 2018-19
Module Leader
Lecturers
Dr Agarwal, Professor Ann Dowling and Professor Nigel Peake
Timing and Structure
16 lectures + 2 examples classes; Assessment: 100% exam
Prerequisites
3A1 assumed
Aims
The aims of the course are to:
- analyse and solve a range of practical engineering problems associated with acoustics.
Objectives
As specific objectives, by the end of the course students should be able to:
- understand how sound is generated.
- understand how sound propagates in free space and within ducts.
- understand shielding and scattering of sound.
- model sound sources for various aeroacoustic problems and design for low noise.
Content
The students are expected to analyse and solve a range of practical engineering problems associated with acoustics. Examples include modelling of noise sources from jets, fans, wind turbines, vacuum cleaners, etc. and exploring ways to reduce noise either at the source or through acoustic damping. Upon completion of this module, the students would be well placed to pursue research in the area of acoustics and related fields. Students would also be more employable (the topics covered in the course is of interest to GE, Rolls-Royce, Dyson, Mitsubishi Heavy Industries, automobile companies and acoustic consultancies)
Classical Acoustics (5L) (Dr A Agarwal)
- The wave equation and simple solutions
- Impedance
- Energy
- Generalised functions and Green’s function
- Sound from simple sources (monopoles, dipole, compact sources)
Jet noise (3L) (Dr A Agarwal)
- Compact quadrupole
- Sound from a single eddy
- Sound from a random distribution of eddies
- Lighthill’s eighth-power law
- Convection and refraction effects
Sound propagation (2L) (Prof. N. Peake)
- Ray theory
- Snell’s law
- Refraction by temperature gradients
Trailing edge noise (2L) (Prof. N. Peake)
- Scattering and shielding
- Scattering from a source near a sharp edge
- Example: Wind turbine noise and the aeroacoustics of the owl
Duct acoustics (2L) (Prof. A P Dowling)
- Normal modes
- Concept of cut-off modes
- Damping/liner
- Helmholtz resonator
- Example: Thermoacoustic instability
Rotor/Fan Noise (2L) (Prof. A P Dowling)
- Rotor alone noise
- Rotor/Stator interaction noise
- Examples: Aircraft noise, fan and turbine noise
Booklists
Please see the Booklist for Group A Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 01/06/2018 12:07
Engineering Tripos Part IIB, 4A15: Aeroacoustics, 2021-22
Module Leader
Lecturers
Dr A. Agarwal
Timing and Structure
Lent term: 16 lectures + 2 examples classes; Assessment: 100% exam
Prerequisites
No prerequisites. The module would be of interest to students with Aero, Mechnical, Bio or Civil Engineering background.
Aims
The aims of the course are to:
- analyse and solve a range of practical engineering problems associated with acoustics.
Objectives
As specific objectives, by the end of the course students should be able to:
- understand what sound is and how we perceive it
- understand how sound is generated and propagated
- understand the acoustics of a wide range of music and noise production
Content
We will analyse and solve a range of practical engineering problems associated with acoustics. Examples include modelling of noise sources from jets, fans, musical instruments, human voice, kettles, dripping taps, whistling mice, singing flames, etc. We will also study ways to reduce noise either at the source or through acoustic damping. Upon completion of this module, the students would be well placed to pursue academic research in the area of acoustics and related fields or to work in industry (the topics covered in the course is of interest to GE, Rolls-Royce, Airbus, Dyson, Mitsubishi Heavy Industries, automotive companies, music and biomedical industries, and acoustic consultancies).
What is sound and how does it propagate? (5L) (Dr A Agarwal)
- Introduction
- The wave equation
-
Some simple 3D wave fields (plane waves, surface waves and spherical waves)
- Sound transmission through different media
Simples sounds sources (2L) (Dr A Agarwal)
- Pulsating sphere
- Oscillating sphere
- Example: loudspeaker with and without a cabinet
General solution to wave eqn (2L) (Dr. A Agarwal)
- Green's function
- Sound from general mass and force sources (examples, Bliz siren and singing telephone wires)
Jet noise (Dr A Agarwal) (1 L)
- Scaling of jet noise. How much does jet noise increase by if we double the jet's velocity?
- What do jets and tuning forks have in common?
- Lighthill's acoustic analogy
- Sound of aircraft jets and handdriers
Duct acoustics (2 L) (Dr A Agarwal)
- Rectangular ducts (example, sound box)
- Low-frequency sound in ducts
- Circular ducts
- Acoustic liners (Helmholtz resonator, blowing over a beer bottle)
Musical acoustics & everyday things (3L) (Drs A Agarwal)
- String instruments
- Wind instruments
- Brass instruments
- Whistling of steam kettles and Rayleigh's Bird Call
- Acoustics of dripping taps
Vocalisation (0.5 L) (Dr A Agarwal)
- Human speech, singing and overtone singing
- Mice mating calls
Fan noise (1L) (Dr A Agarwal)
- Rotor alone noise
- Rotor-stator interaction noise
Thermoacoustics instability (0.5 L) (Dr A Agarwal)
- Rijke tube experiment (singing flames)
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 21/05/2021 13:24
Engineering Tripos Part IIB, 4A13: Combustion & IC Engines, 2018-19
Module Leader
Lecturers
Prof N Swaminathan and Prof E Mastorakos/Prof G Kalghatgi
Timing and Structure
Lent term. 16 lectures, including 2 examples classes. Assessment: 100% exam
Prerequisites
3A5, 3A6 useful
Aims
The aims of the course are to:
- introduce students to fundamental combustion concepts, and their influence on internal combustion engine preformance and emissions.
Objectives
As specific objectives, by the end of the course students should be able to:
- Understand fundamental concepts in combustion
- Understand combustion issues particularly relvant to gas turbines
- Understand the performance and efficiency characteristics of IC engines
- Understand the formation and aftertreatment of pollutants in IC engines, and tradeoffs with performance
Content
Chemical thermodynamics and equilibrium (1L)
Conservation laws for multicomponent mixture, multispecies equilibrium and calculation method
Chemical kinetics (1L)
Principles of chemical kinetics – law of mass action, activation energy, order & degree of a reaction, hydrocarbon reaction chains , pollutant formation multistep reactions, chemical explosion, chemistry reduction using steady state and partial equilibrium approximations
Applications of chemical kinetics: limit reators (1L)
Common approximations used in combustion analysis – perfectly stirred reactor, plug flow reactor, thermal explosions, autoignition & spark ignition
Laminar premixed flames (1L)
Concepts and measurements, conservation equations in one and multiple dimensions, characteristic time and space scales, Zeldovich number, solution for 1D flame, flame speed and its dependence on mixture composition, temperature and pressure
Laminar non-premixed flames (1L)
Mixture fraction concept and its physical significance, conserved scalar approach, state relationship, simple solution for diffusion flame, droplet combustion as an example for diffusion flame
Pollution from Combustion (1L)
Nature of pollution emitted by combustion and its effect on environment & human health, features of pollution generation chemistry, typical techniques used for emission reduction
Turbulent Combustion (1L)
A brief introduction to turbulent combustion, its importance, applications, and scientific methods used to study turbulent combustion
Introduction to Internal Combustion Engines (1L)
Types of engines – Spark Ignition Engines, Diesel Engines, Homogeneous Charge Compression Ignition (HCCI) Engines; Thermodynamic cycles and Efficiency; Emissions control
Outlook for Energy and Transport (1L)
Transport energy outlook – drivers for change, prospects for alternatives to internal combustion engines and conventional fuels, challenges of full electrification, importance of internal combustion engines and the necessity and potential for improving them
Practical Transport Fuels (1L)
Composition, properties, manufacturing, & specifications
Deposits in Engines and Fuel Additives (1L)
Fuel system, intake system and combustion chamber deposits in SI engines, diesel injector deposits in diesel engines, mechanisms of formation, effects on engine performance and operation, controlling methods
Fuel Anti-Knock Quality and Knock in SI Engines (1L)
Knock and SI engine performance, fuel antiknock quality, RON, MON and octane index, lessons learnt from HCCI studies, future fuel requirements
Insights into knock onset, knock intensity, superknock and preignition (1L)
Knock fundamentals, ignition delay and Livengood-Wu integral, stochastic nature of knock, knock intensity, developing detonation and superknock, difference between preignition and superknock, application of fundamental insights to practical understanding
Fuel effects in compression ignition engines (1L)
Particulate/NOx control and ignition delay, Gasoline Compression Ignition (GCI) engines, fuel effects, advantages, challenges and prospects for GCI, dual fuel approaches to low NOx/low soot combustion
Evolution of future transport energy and implications for future fuels (1L)
Summary of previous 7 lectures. Future fuels and engines
Booklists
Please see the Booklist for Group A Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
Last modified: 19/03/2019 14:43
Engineering Tripos Part IIB, 4A13: Combustion & IC Engines, 2017-18
Module Leader
Lecturers
Prof E Mastorakos and Prof S Hochgreb
Timing and Structure
Lent term. 16 lectures, including 2 examples classes. Assessment: 100% exam
Prerequisites
3A5, 3A6 useful
Aims
The aims of the course are to:
- introduce students to fundamental combustion concepts, and their influence on internal combustion engine preformance and emissions.
Objectives
As specific objectives, by the end of the course students should be able to:
- Understand fundamental concepts in combustion
- Understand combustion issues particularly relvant to gas turbines
- Understand the performance and efficiency characteristics of IC engines
- Understand the formation and aftertreatment of pollutants in IC engines, and tradeoffs with performance
Content
Chemical thermodynamics and equilibrium (1L)
- Mass, energy and atomic species conservation
- Multispecies equilibrium and calculation method
Chemical kinetics (1L)
- Principles of chemical kinetics: law of mass action and activation energy
- Hydrocarbon reaction chains
- Pollutant formation
- Multistep reactions and explosions
- Steady state and partial equilibrium approximations
- Characteristic time and space scales
Applications of chemical kinetics: limit reators (1L)
- Common approximations in combustion analysis:
- Static reactor
- Perfectly stirred reactor
- Plug flow reactor
- Thermal explosions
- Autoignition
Laminar premixed flames (1L)
- Laminar premixed flames: concepts and measurements
- Conservation equations for combustion in one and multiple dimensions
- Characteristic time and space scales, Zeldovich number
- One-dimensional conservation equation and simplified solutions
- Effects of mixture composition, stretch and curvature
Laminar non-premixed flames (1L)
- Laminar diffusion flames: concept and measurement methods
- Characteristic time and space scales
- Conserved scalars and mixture fraction
- One-dimensional conservation equations: co-flow and opposed flow
Kinetics of pollution formation (NOx,CO, particles) (1L)
- Zel'dovich and extended NOx formation chemistry
- Time scales for CO and HC chemistry
- Particle formation and oxidation mechanisms
Flames and Turbulence (1L)
- Characteristic time and space scales
- Regimes of turbulent combustion
- Measurement methods and results
- Approaches to modeling turbulent combustion
Gas turbine combustion - performance and emissions (1L)
- Gas turbine combustion principles
- Emissions and stability in industrial gas turbines and aeroengines
Fundamental concepts in IC engines (2L)
- Overview of energy use in transportation
- IC and reciprocating engine evolution
- Basic concepts and definitions
- Ideal constant volume and constant pressure cycles
- Efficiency, indicated mean effective pressure and torque
Spark ignition engines (1L)
- Basic concepts and definitions
- Valve timing and volumetric efficiency
- Residual gases
- Intake and fuel injection systems
- Combustion in SI engines
- Autoignition and limits to combustion
- Spark timing and optimisation
- Effects of speed and load
- SI engine maps
- Emissions
CI engines - enhancing performance and emissions (1L)
- Compression ignition process parameters
- Combustion under autoignition
- Fuel injection timing, torque and emissions
- Controlling NOx and soot
- CI engine maps
- Principles of turbocharging and relevant physics
- Turbocharger matching
SI engine emissions and aftertreatment (1L)
- Combustion and engine out emissions
- Three way catalysts
- Air-fuel ratio control
- Exhaust gas recirculation
SI engine emissions and aftertreatment (1L)
- Combustion and engine out emissions
- Methods of in-cylinder control of NOx and soot
- Air-fuel ratio control
- Exhaust gas recirculation
- Selective catalytic reduction
- Particulate matter removal
Booklists
Please see the Booklist for Group A Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
Last modified: 03/08/2017 16:06
Engineering Tripos Part IIB, 4A12: Turbulence & Vortex Dynamics, 2017-18
Leader
Lecturers
Prof E Mastorakos and Prof P Davidson
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3A1 assumed; 3A3 useful
Aims
The aims of the course are to:
- introduce the physical basis of turbulence as well as its practical implications for engineers; turbulence is a common feature of fluid flows in the atmosphere and the ocean, in aerodynamics and in chemically-reacting flows such as combustion.
- introduce the basic rules of vortex dynamics, which is identified as controlling energy transfers between different scales in a turbulent flow.
Objectives
As specific objectives, by the end of the course students should be able to:
- be aware of the turbulent nature of most flows of interest to engineers and its influence on the transfer processes involving momentum, heat and mass.
- interpret fluid motion in terms of the creation and transport of vorticity.
- understand energy transfer between mean flow and turbulent fluctuations (Reynolds stresses).
- understand energy transfer between the different scales of turbulence and the mechanism of dissipation.
- be aware of the more common phenomenological models of turbulence currently used by engineers and of their underlying assumptions and limitations.
Content
Turbulence and Vortex Dynamics (16L)
- Introduction to turbulence: Pictures of turbulence. Universality of turbulence in flows as the final result of instabilities. Engineering consequences.
- Some simple illustrations of vortex dynamics: The persistence of rotation (angular momentum) in flows. Another description of fluid dynamics: the vorticity equation. Lift and induced motion, with application to aerodynamics and hovering insects. Swirling flows with application to tornadoes, hurricanes and tidal vortices.
- Basic concepts in turbulence theory: Order from chaos - Reynolds decomposition and Reynolds equation. Kinetic energy - Production and Dissipation. Introduction to the different scales in Turbulence, from the integral scale to Kolmogorov's micro-scale. Wall-bounded shear flows. Vortex dynamics at work at the large and small scales (worms).
- Phenomenological models of turbulence: Prandlt's Mixing length and k - e model: their assumptions and limitations. Other models. What can be expected from these turbulence models in terms of velocity and heat transfer.
- Current trends in industrial fluid mechanics.
Booklists
Please see the Booklist for Group A Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 03/08/2017 16:05
Engineering Tripos Part IIB, 4A12: Turbulence & Vortex Dynamics, 2019-20
Module Leader
Lecturers
Prof E Mastorakos and Prof P Davidson
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3A1 assumed; 3A3 useful
Aims
The aims of the course are to:
- introduce the physical basis of turbulence as well as its practical implications for engineers; turbulence is a common feature of fluid flows in the atmosphere and the ocean, in aerodynamics and in chemically-reacting flows such as combustion.
- introduce the basic rules of vortex dynamics, which is identified as controlling energy transfers between different scales in a turbulent flow.
Objectives
As specific objectives, by the end of the course students should be able to:
- be aware of the turbulent nature of most flows of interest to engineers and its influence on the transfer processes involving momentum, heat and mass.
- interpret fluid motion in terms of the creation and transport of vorticity.
- understand energy transfer between mean flow and turbulent fluctuations (Reynolds stresses).
- understand energy transfer between the different scales of turbulence and the mechanism of dissipation.
- be aware of the more common phenomenological models of turbulence currently used by engineers and of their underlying assumptions and limitations.
Content
Turbulence and Vortex Dynamics (16L)
- Introduction to turbulence: Pictures of turbulence. Universality of turbulence in flows as the final result of instabilities. Engineering consequences.
- Some simple illustrations of vortex dynamics: The persistence of rotation (angular momentum) in flows. Another description of fluid dynamics: the vorticity equation. Lift and induced motion, with application to aerodynamics and hovering insects. Swirling flows with application to tornadoes, hurricanes and tidal vortices.
- Basic concepts in turbulence theory: Order from chaos - Reynolds decomposition and Reynolds equation. Kinetic energy - Production and Dissipation. Introduction to the different scales in Turbulence, from the integral scale to Kolmogorov's micro-scale. Wall-bounded shear flows. Vortex dynamics at work at the large and small scales (worms).
- Phenomenological models of turbulence: Prandlt's Mixing length and k - e model: their assumptions and limitations. Other models. What can be expected from these turbulence models in terms of velocity and heat transfer.
- Current trends in industrial fluid mechanics.
Booklists
Please see the Booklist for Group A Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 23/05/2019 15:52
Engineering Tripos Part IIB, 4A12: Turbulence & Vortex Dynamics, 2025-26
Module Leader
Lecturers
Prof E Mastorakos and Dr J Li
Timing and Structure
Michaelmas term. 16 lectures (including examples classes). Assessment: 100% exam.
Prerequisites
3A1 assumed; 3A3 useful
Aims
The aims of the course are to:
- introduce the physical basis of turbulence as well as its practical implications for engineers; turbulence is a common feature of fluid flows in the atmosphere and the ocean, in aerodynamics and in chemically-reacting flows such as combustion.
- introduce the basic rules of vortex dynamics, which is identified as controlling energy transfers between different scales in a turbulent flow.
Objectives
As specific objectives, by the end of the course students should be able to:
- be aware of the turbulent nature of most flows of interest to engineers and its influence on the transfer processes involving momentum, heat and mass.
- interpret fluid motion in terms of the creation and transport of vorticity.
- understand energy transfer between mean flow and turbulent fluctuations (Reynolds stresses).
- understand energy transfer between the different scales of turbulence and the mechanism of dissipation.
- be aware of the more common phenomenological models of turbulence currently used by engineers and of their underlying assumptions and limitations.
Content
Turbulence and Vortex Dynamics (16L)
- Introduction to turbulence: Pictures of turbulence. Universality of turbulence in flows as the final result of instabilities. Engineering consequences.
- Some simple illustrations of vortex dynamics: The persistence of rotation (angular momentum) in flows. Another description of fluid dynamics: the vorticity equation. Lift and induced motion, with application to aerodynamics and hovering insects. Swirling flows with application to tornadoes, hurricanes and tidal vortices.
- Basic concepts in turbulence theory: Order from chaos - Reynolds decomposition and Reynolds equation. Kinetic energy - Production and Dissipation. Introduction to the different scales in Turbulence, from the integral scale to Kolmogorov's micro-scale. Wall-bounded shear flows. Vortex dynamics at work at the large and small scales (worms).
- Phenomenological models of turbulence: Prandlt's Mixing length and k - e model: their assumptions and limitations. Other models. What can be expected from these turbulence models in terms of velocity and heat transfer.
- Current trends in industrial fluid mechanics.
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 04/06/2025 13:24
Engineering Tripos Part IIB, 4A12: Turbulence & Vortex Dynamics, 2022-23
Module Leader
Lecturers
Prof E Mastorakos and Prof P Davidson
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam. NOTE: The first 8 lectures will be delivered online.
Prerequisites
3A1 assumed; 3A3 useful
Aims
The aims of the course are to:
- introduce the physical basis of turbulence as well as its practical implications for engineers; turbulence is a common feature of fluid flows in the atmosphere and the ocean, in aerodynamics and in chemically-reacting flows such as combustion.
- introduce the basic rules of vortex dynamics, which is identified as controlling energy transfers between different scales in a turbulent flow.
Objectives
As specific objectives, by the end of the course students should be able to:
- be aware of the turbulent nature of most flows of interest to engineers and its influence on the transfer processes involving momentum, heat and mass.
- interpret fluid motion in terms of the creation and transport of vorticity.
- understand energy transfer between mean flow and turbulent fluctuations (Reynolds stresses).
- understand energy transfer between the different scales of turbulence and the mechanism of dissipation.
- be aware of the more common phenomenological models of turbulence currently used by engineers and of their underlying assumptions and limitations.
Content
Turbulence and Vortex Dynamics (16L)
- Introduction to turbulence: Pictures of turbulence. Universality of turbulence in flows as the final result of instabilities. Engineering consequences.
- Some simple illustrations of vortex dynamics: The persistence of rotation (angular momentum) in flows. Another description of fluid dynamics: the vorticity equation. Lift and induced motion, with application to aerodynamics and hovering insects. Swirling flows with application to tornadoes, hurricanes and tidal vortices.
- Basic concepts in turbulence theory: Order from chaos - Reynolds decomposition and Reynolds equation. Kinetic energy - Production and Dissipation. Introduction to the different scales in Turbulence, from the integral scale to Kolmogorov's micro-scale. Wall-bounded shear flows. Vortex dynamics at work at the large and small scales (worms).
- Phenomenological models of turbulence: Prandlt's Mixing length and k - e model: their assumptions and limitations. Other models. What can be expected from these turbulence models in terms of velocity and heat transfer.
- Current trends in industrial fluid mechanics.
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 08/02/2023 17:17
Engineering Tripos Part IIB, 4A12: Turbulence & Vortex Dynamics, 2023-24
Module Leader
Lecturers
Prof E Mastorakos and Dr J Li
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam.
Prerequisites
3A1 assumed; 3A3 useful
Aims
The aims of the course are to:
- introduce the physical basis of turbulence as well as its practical implications for engineers; turbulence is a common feature of fluid flows in the atmosphere and the ocean, in aerodynamics and in chemically-reacting flows such as combustion.
- introduce the basic rules of vortex dynamics, which is identified as controlling energy transfers between different scales in a turbulent flow.
Objectives
As specific objectives, by the end of the course students should be able to:
- be aware of the turbulent nature of most flows of interest to engineers and its influence on the transfer processes involving momentum, heat and mass.
- interpret fluid motion in terms of the creation and transport of vorticity.
- understand energy transfer between mean flow and turbulent fluctuations (Reynolds stresses).
- understand energy transfer between the different scales of turbulence and the mechanism of dissipation.
- be aware of the more common phenomenological models of turbulence currently used by engineers and of their underlying assumptions and limitations.
Content
Turbulence and Vortex Dynamics (16L)
- Introduction to turbulence: Pictures of turbulence. Universality of turbulence in flows as the final result of instabilities. Engineering consequences.
- Some simple illustrations of vortex dynamics: The persistence of rotation (angular momentum) in flows. Another description of fluid dynamics: the vorticity equation. Lift and induced motion, with application to aerodynamics and hovering insects. Swirling flows with application to tornadoes, hurricanes and tidal vortices.
- Basic concepts in turbulence theory: Order from chaos - Reynolds decomposition and Reynolds equation. Kinetic energy - Production and Dissipation. Introduction to the different scales in Turbulence, from the integral scale to Kolmogorov's micro-scale. Wall-bounded shear flows. Vortex dynamics at work at the large and small scales (worms).
- Phenomenological models of turbulence: Prandlt's Mixing length and k - e model: their assumptions and limitations. Other models. What can be expected from these turbulence models in terms of velocity and heat transfer.
- Current trends in industrial fluid mechanics.
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 13/11/2023 20:19
Engineering Tripos Part IIB, 4A12: Turbulence & Vortex Dynamics, 2021-22
Module Leader
Lecturers
Prof E Mastorakos and Prof P Davidson
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam. NOTE: The first 8 lectures will be delivered online.
Prerequisites
3A1 assumed; 3A3 useful
Aims
The aims of the course are to:
- introduce the physical basis of turbulence as well as its practical implications for engineers; turbulence is a common feature of fluid flows in the atmosphere and the ocean, in aerodynamics and in chemically-reacting flows such as combustion.
- introduce the basic rules of vortex dynamics, which is identified as controlling energy transfers between different scales in a turbulent flow.
Objectives
As specific objectives, by the end of the course students should be able to:
- be aware of the turbulent nature of most flows of interest to engineers and its influence on the transfer processes involving momentum, heat and mass.
- interpret fluid motion in terms of the creation and transport of vorticity.
- understand energy transfer between mean flow and turbulent fluctuations (Reynolds stresses).
- understand energy transfer between the different scales of turbulence and the mechanism of dissipation.
- be aware of the more common phenomenological models of turbulence currently used by engineers and of their underlying assumptions and limitations.
Content
Turbulence and Vortex Dynamics (16L)
- Introduction to turbulence: Pictures of turbulence. Universality of turbulence in flows as the final result of instabilities. Engineering consequences.
- Some simple illustrations of vortex dynamics: The persistence of rotation (angular momentum) in flows. Another description of fluid dynamics: the vorticity equation. Lift and induced motion, with application to aerodynamics and hovering insects. Swirling flows with application to tornadoes, hurricanes and tidal vortices.
- Basic concepts in turbulence theory: Order from chaos - Reynolds decomposition and Reynolds equation. Kinetic energy - Production and Dissipation. Introduction to the different scales in Turbulence, from the integral scale to Kolmogorov's micro-scale. Wall-bounded shear flows. Vortex dynamics at work at the large and small scales (worms).
- Phenomenological models of turbulence: Prandlt's Mixing length and k - e model: their assumptions and limitations. Other models. What can be expected from these turbulence models in terms of velocity and heat transfer.
- Current trends in industrial fluid mechanics.
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 17/01/2022 10:14
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