Content

This module provides an introduction to the relationship between the microscopic and macroscopic descriptions of thermodynamics and fluid mechanics. The module is equally divided between the two main microscopic approaches, kinetic theory and statistical mechanics, each of which has its place for solving different types of problem. If you have ever wondered about the interpretation of viscosity and thermal conductivity at a molecular level; why the Lewis number is taken as unity for combustion calculations; how to estimate the rate of a gaseous chemical reaction; why the speed of sound in a gas isn’t faster (or slower); what are the interpretations of heat, work and entropy at a molecular level; how you can estimate the specific heat of a gas just by counting, how the conservation equations of fluid flow can be derived from microscopic considerations; what the Boltzmann distribution is and why it is so important; why the no-slip boundary condition is such a good approximation for continuum flow; when the Navier-Stokes equations lose their validity; how gases behave under highly rarefied conditions; how to set about calculating the surface temperature of the space shuttle during re-entry; and many other allied phenomena; then you should find many things to interest you in this module.

The main objective is to obtain a good physical understanding of the relationship between the microscopic and macroscopic viewpoints of thermodynamics and fluid mechanics. At first exposure, this can be a profound experience as it gradually emerges that the macroscopic thermo-fluid-dynamic behaviour of gases can be explained, almost in its entirety, by the results of collisions between molecules. On completion of the module students will have a good appreciation of the microscopic basis of a wide range of macroscopic phenomena.

Kinetic theory and statistical mechanics are complementary theories which are used to give quantitative estimates of macroscopic phenomena, often by using quite simple mathematics. Students will be equipped with the tools to estimate, from microscopic data, many macroscopic thermodynamic properties which would otherwise need to be obtained experimentally. They will also be in a position to construct their own simple molecular models to provide working solutions to specific problems where no data exists. To this end, the lectures will stress the importance of physical understanding backed up by simple mathematical modelling.

More accurate and advanced calculations require a more formalised and complex mathematical approach. Examples occur in rarefied gas dynamics where the fluid cannot be treated as a continuum and the Navier-Stokes equations no longer apply, and in statistical mechanical calculations where inter-molecular forces dominate. Although the lectures will not address such topics in detail, a further objective is to put the student in a position where he or she is ready to assimilate the more advanced literature in both kinetic theory and statistical mechanics.

GAS KINETIC THEORY Dr A J White (7 lectures + 1 examples class)

• Elementary kinetic theory
  Intermolecular forces and molecular models, Density, Pressure, Internal energy, Kinetic and thermodynamic temperature, Specific heat capacity, Molecular degrees of freedom, Equipartition of energy, Rôle of intermolecular forces, Imperfect gases.
   
• Transport properties and chemical equilibrium
  Collision rates, Mean free path, Viscosity, Thermal conductivity, Prandtl number, Mixtures of different gases, Diffusion, Schmidt and Lewis numbers, Chemical equilibrium, Law of mass action.
   
• Molecular velocity distributions
  Velocity distribution functions, Effect of collisions, Maxwell-Boltzmann distribution, Statistical averages, Nonequilibrium velocity distributions, Boltzmann’s equation, Relaxation time to equilibrium.
   
• Molecular gas dynamics
  Derivation of mass, momentum and energy conservation equations from kinetic theory, Isentropic flow, Navier-Stokes equations, Rarefied gases, Knudsen number, Boundary slip, Collisionless flow and heat transfer.

STATISTICAL MECHANICS Dr A M Boies (7 lectures + 1 examples class)

• Introduction to Statistical Mechanics
  Motivation, microstates, statistical analogues of entropy, the Boltzmann relation, probability examples and averaging procedures.
   
• The Partition Functions
  Microcanonical, canonical and grand canonical ensembles, the system partition function and its relation to thermodynamic properties, the single-particle partition function.
   
• Quantum Mechanics and Energy States
  Key results from quantum mechanics, the de Broglie wavelength, the Schrodinger equation and its solution for a particle in a box, density of energy states and energy levels, degeneracy.
   
• The Ideal Gas Model
  The statistical basis of the ideal gas, the high temperature limit and the Boltzmann distribution, the Sackur-Tetrode equation, temperature-dependence of specific heats (vibrational, rotational and electronic excitation energy modes), the equipartation of energy.
   
• Relationship to Thermodynamics and Probability
  Statistical interpretation of heat and work transfers and the First Law. Thermodynamic probability and property fluctuations.
   
• Other Statistical Models
  Other counting methods, the Einstein crystal and the rubber band model.

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 04/06/2025 13:24

Content

This module provides an introduction to the relationship between the microscopic and macroscopic descriptions of thermodynamics and fluid mechanics. The module is equally divided between the two main microscopic approaches, kinetic theory and statistical mechanics, each of which has its place for solving different types of problem. If you have ever wondered about the interpretation of viscosity and thermal conductivity at a molecular level; why the Lewis number is taken as unity for combustion calculations; how to estimate the rate of a gaseous chemical reaction; why the speed of sound in a gas isn’t faster (or slower); what are the interpretations of heat, work and entropy at a molecular level; how you can estimate the specific heat of a gas just by counting, how the conservation equations of fluid flow can be derived from microscopic considerations; what the Boltzmann distribution is and why it is so important; why the no-slip boundary condition is such a good approximation for continuum flow; when the Navier-Stokes equations lose their validity; how gases behave under highly rarefied conditions; how to set about calculating the surface temperature of the space shuttle during re-entry; and many other allied phenomena; then you should find many things to interest you in this module.

The main objective is to obtain a good physical understanding of the relationship between the microscopic and macroscopic viewpoints of thermodynamics and fluid mechanics. At first exposure, this can be a profound experience as it gradually emerges that the macroscopic thermo-fluid-dynamic behaviour of gases can be explained, almost in its entirety, by the results of collisions between molecules. On completion of the module students will have a good appreciation of the microscopic basis of a wide range of macroscopic phenomena.

Kinetic theory and statistical mechanics are complementary theories which are used to give quantitative estimates of macroscopic phenomena, often by using quite simple mathematics. Students will be equipped with the tools to estimate, from microscopic data, many macroscopic thermodynamic properties which would otherwise need to be obtained experimentally. They will also be in a position to construct their own simple molecular models to provide working solutions to specific problems where no data exists. To this end, the lectures will stress the importance of physical understanding backed up by simple mathematical modelling.

More accurate and advanced calculations require a more formalised and complex mathematical approach. Examples occur in rarefied gas dynamics where the fluid cannot be treated as a continuum and the Navier-Stokes equations no longer apply, and in statistical mechanical calculations where inter-molecular forces dominate. Although the lectures will not address such topics in detail, a further objective is to put the student in a position where he or she is ready to assimilate the more advanced literature in both kinetic theory and statistical mechanics.

GAS KINETIC THEORY Dr A J White (7 lectures + 1 examples class)

• Elementary kinetic theory
  Intermolecular forces and molecular models, Density, Pressure, Internal energy, Kinetic and thermodynamic temperature, Specific heat capacity, Molecular degrees of freedom, Equipartition of energy, Rôle of intermolecular forces, Imperfect gases.
   
• Transport properties and chemical equilibrium
  Collision rates, Mean free path, Viscosity, Thermal conductivity, Prandtl number, Mixtures of different gases, Diffusion, Schmidt and Lewis numbers, Chemical equilibrium, Law of mass action.
   
• Molecular velocity distributions
  Velocity distribution functions, Effect of collisions, Maxwell-Boltzmann distribution, Statistical averages, Nonequilibrium velocity distributions, Boltzmann’s equation, Relaxation time to equilibrium.
   
• Molecular gas dynamics
  Derivation of mass, momentum and energy conservation equations from kinetic theory, Isentropic flow, Navier-Stokes equations, Rarefied gases, Knudsen number, Boundary slip, Collisionless flow and heat transfer.

STATISTICAL MECHANICS Dr A M Boies (7 lectures + 1 examples class)

• Introduction to Statistical Mechanics
  Motivation, microstates, statistical analogues of entropy, the Boltzmann relation, probability examples and averaging procedures.
   
• The Partition Functions
  Microcanonical, canonical and grand canonical ensembles, the system partition function and its relation to thermodynamic properties, the single-particle partition function.
   
• Quantum Mechanics and Energy States
  Key results from quantum mechanics, the de Broglie wavelength, the Schrodinger equation and its solution for a particle in a box, density of energy states and energy levels, degeneracy.
   
• The Ideal Gas Model
  The statistical basis of the ideal gas, the high temperature limit and the Boltzmann distribution, the Sackur-Tetrode equation, temperature-dependence of specific heats (vibrational, rotational and electronic excitation energy modes), the equipartation of energy.
   
• Relationship to Thermodynamics and Probability
  Statistical interpretation of heat and work transfers and the First Law. Thermodynamic probability and property fluctuations.
   
• Other Statistical Models
  Other counting methods, the Einstein crystal and the rubber band model.

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 23/05/2019 15:49

Aims

The aims of the course are to:

• develop the basic ideas necessary to understand some advanced concepts in aerodynamics.
• cover the aerodynamic effects that constrain an aircraft design.

Objectives

As specific objectives, by the end of the course students should be able to:

• have an appreciation of the aerodynamic factors likely to feature in the designs of new aircraft.
• have an understanding of the behaviour of boundary layers over swept wings in compressible flow.
• estimate the position of laminar-turbulent transition.
• estimate wing drag, and to be familiar with techniques for avoiding turbulent flow.
• have sufficient knowledge to be able to predict the different supersonic zones on a wing.
• understand how the basic physics can be integrated into the design of an aircraft.
• understand how to make design trade-offs.
• have a basic appreciation of the impact of aviation on the environment and possible responses.

Content

This course aims to develop the basic ideas necessary to enable the student to understand some advanced concepts in aerodynamics. In particular the course will cover the aerodynamic effects that constrain an aircraft design. The course will highlight those factors determining the configuration of aircraft for different duties relating them to the effect of compressibility at transonic speeds, the control of boundary layers to benefit from laminar flows and the estimation of aerodynamic loads on the aircraft structure. Coursework will illustrate basic physics, via transonic airfoil design and the integration of these basics via a study of the trade-offs made in producing a design for a given specification. The course will end by reviewing the environmental impact of aviation and show how aircraft design might change to reduce this impact.

Introduction to transonic wings (3L, Dr J P Jarrett)

• Review of 3A3 material: boundary layers and drag estimation;
• Transonic flow about two-dimensional aerofoils;
• Shock-boundary layer interaction;
• Supercritical aerofoils with delayed shock-induced drag rise.

Transonic aerofoil design (4h coursework, Dr J P Jarrett)

This coursework section will allow the interactive design of a transonic aerofoil profile on a workstation in the DPO. The aim is to consolidate the lecture material and illustrate how the various design constraints compete in practice.

Advanced aerodynamics (3L, Dr J P Jarrett)

• Aerodynamic challenges of high-speed flight
• Airframe/Intake integration
• Stability of swept wing aircraft
• Practical swept wing design
• Delta and slender ogival wings
• Vertical / short take-off and landing

Aviation and the environment (6L, Dr CA Hall)

The impact of air transport on the environment; the relationship between technology, operational practice, regulation and economics.

• Basic modelling
• The environment - overview of atmospheric chemistry, fluid dynamics & mixing; the greenhouse effect; radiative forcing.
• Airframe - aircraft range & endurance, the Breguet equation; ML/D payload, fuel and structure weight; choice of fuel. Why do airplanes fly at the altitude they do? Payload and fuel efficiency.
• Engine - simple modelling of a high-bypass ratio turbofan engine. Cycle efficiency and propulsive efficiency, trading production of NOx and CO2.
• What would an airplane look like if optimised to reduce environmental impact?

Greener by Design (Coursework, Dr CA Hall)

The coursework consists of a choice of one from three case studies, based on the simple modelling above to study from the perspective of environmental impact the trade-offs associated with (A) design range;(B) cruise altitude;and (C) engine overall pressure ratio. It is intended that the case studies will be spreadsheet based.

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 08/10/2018 18:42

Aims

The aims of the course are to:

• develop the basic ideas necessary to understand some advanced concepts in aerodynamics.
• cover the aerodynamic effects that constrain an aircraft design.

Objectives

As specific objectives, by the end of the course students should be able to:

• have an appreciation of the aerodynamic factors likely to feature in the designs of new aircraft.
• have an understanding of the behaviour of boundary layers over swept wings in compressible flow.
• estimate the position of laminar-turbulent transition.
• estimate wing drag, and to be familiar with techniques for avoiding turbulent flow.
• have sufficient knowledge to be able to predict the different supersonic zones on a wing.
• understand how the basic physics can be integrated into the design of an aircraft.
• understand how to make design trade-offs.
• have a basic appreciation of the impact of aviation on the environment and possible responses.

Content

This course aims to develop the basic ideas necessary to enable the student to understand some advanced concepts in aerodynamics. In particular the course will cover the aerodynamic effects that constrain an aircraft design. The course will highlight those factors determining the configuration of aircraft for different duties relating them to the effect of compressibility at transonic speeds, the control of boundary layers to benefit from laminar flows and the estimation of aerodynamic loads on the aircraft structure. Coursework will illustrate basic physics, via transonic airfoil design and the integration of these basics via a study of the trade-offs made in producing a design for a given specification. The course will end by reviewing the environmental impact of aviation and show how aircraft design might change to reduce this impact.

Introduction to transonic wings (3L, Dr J P Jarrett)

• Review of 3A3 material: boundary layers and drag estimation;
• Transonic flow about two-dimensional aerofoils;
• Shock-boundary layer interaction;
• Supercritical aerofoils with delayed shock-induced drag rise.

Transonic aerofoil design (4h coursework, Dr J P Jarrett)

This coursework section will allow the interactive design of a transonic aerofoil profile on a workstation in the DPO. The aim is to consolidate the lecture material and illustrate how the various design constraints compete in practice.

Advanced aerodynamics (3L, Dr J P Jarrett)

• Aerodynamic challenges of high-speed flight
• Airframe/Intake integration
• Stability of swept wing aircraft
• Practical swept wing design
• Delta and slender ogival wings
• Vertical / short take-off and landing

Aviation and the environment (6L, Prof CA Hall)

The impact of air transport on the environment; the relationship between technology, operational practice, regulation and economics.

• Basic modelling
• The environment - overview of atmospheric chemistry, fluid dynamics & mixing; the greenhouse effect; radiative forcing.
• Airframe - aircraft range & endurance, the Breguet equation; ML/D payload, fuel and structure weight; choice of fuel. Why do airplanes fly at the altitude they do? Payload and fuel efficiency.
• Engine - simple modelling of a high-bypass ratio turbofan engine. Cycle efficiency and propulsive efficiency, trading production of NOx and CO2.
• What would an airplane look like if optimised to reduce environmental impact?

Greener by Design (Coursework, Prof CA Hall)

The coursework consists of a choice of one from three case studies, based on the simple modelling above to study from the perspective of environmental impact the trade-offs associated with (A) design range;(B) cruise altitude;and (C) engine overall pressure ratio. It is intended that the case studies will be spreadsheet based.

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 12/09/2024 15:22