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Aerodynamics is of fundamental interest in computational aerospace science and engineering. It is taught as a standard undergraduate course on aerospace engineering courses. However, its complexity necessitates to approximate key aerodynamic coefficients through correlations and simplified theories; this is where this course comes into play.

Computational Aerodynamics does not rely on simplified theories and instead employs Computational Fluid Dynamics (CFD) to solve the governing equations of fluid dynamics to replace these approximate theories and correlation-based tools, such as panel methods, lifting-line theory, or other potential flow-based methods. This provides a robust way to capture the linear lift slope regime with additional non-linear effects such as occurrences of laminar separation bubbles and stall. In a similar manner, drag values are no longer based on correlations but rather modelled through transport equations, providing greater accuracy. Coupling CFD with an introduction to Aerodynamics, this module provides the basis for calculating force and moment coefficients and essential flight mechanics stability analysis is reviewed where these force and moment coefficients play a dominant role.

Along the way, classical and advanced concepts in Computational Fluid Dynamics are reviewed, from CAD clean-up and meshing to solving and post-processing, including the use of high-performance computing (HPC) facilities to allow for large aerodynamic calculations to be performed.

• Review of key fluid mechanic and thermodynamic concepts.
• Review of key non-dimensional numbers.
• Calculate lift and drag polars and extracting different type of drags from simulations.
• Simulate viscous flow around aerodynamic bodies, including an extension to separated boundary layer flows.
• Extract key aerodynamic figures such as minimum drag and maximum lift over drag speed.
• Calculate centre of pressure and aerodynamic centre on aerofoils / wings / horizontal stabiliser and rudder and use extracted moments for static stability analysis.
• Perform CFD simulations for aerodynamic devices such as wings, aerofoil sections, flaps, etc. and use appropriate modelling strategy to capture the flow around these.
• Use shock-capturing schemes to resolve shock-waves for compressible flows, such as Riemann solvers.
• Apply mesh motion to simulate rotating domains (propellers, rotors, etc.).
• Automate the CFD calculation through scripting.
• Run automated CFD simulation on an HPC cluster environment.

On successful completion of this module you should be able to:

1. Develop a suitable cleaned CAD geometry and create a suitable volume mesh using commercial pre-processing software packages.

2. Perform aerodynamic simulations using Computational Fluid Dynamics (CFD) and appraise the different modelling techniques available to obtain aerodynamic coefficients, forces and moments and their computational cost / accuracy trade-off.

3. Use high-performance computing (HPC) resources to perform complex aerodynamic flow calculations, which includes setting up automated simulations through scripting to be run on HPC systems.

4. Calculate aerodynamic coefficients from raw CFD data and evaluate their differences to simplified aerodynamic correlations and mathematical theories from the literature.

5. Develop a simulation environment that is able to capture laminar / turbulent and incompressible / compressible flows, including an understanding of shock-wave capturing schemes.

To introduce the concepts of validation and verification methods including the management of computational errors and uncertainties related to simulation of external flows for aeronautical and aerospace applications.

• Mathematical foundations of uncertainty quantification methods and related theories including the definition of consistency, stability and convergence.
• Taxonomies of numerical errors and uncertainties.
• Principles of code verification for external flows.
• Introduction to the method of manufactured solutions.
• Principles of solution verification.
• Principles of the generalized Richardson extrapolation including a method how to report numerical errors in a unified way based a proper grid convergence study.
• Principles of mathematical model validation.
• Statistical approaches to epistemic uncertainty.
• Construction of validation and verification hierarchies.

On successful completion of this module you should be able to:

1. Distinguish and analyse different classes of numerical errors and uncertainties for simulating flows used in aeronautical and aerospace applications.

2. Evaluate the strength and weaknesses of computational approaches related to the potential sources of errors and uncertainties for aerospace applications.

3. Critically evaluate the tools that are available for the quantification of error and uncertainty for simulating external flows used in aeronautical and aerospace applications.

4. Set up reliable simulations through code verification and computational model validation.

To understand the key features of mathematical modelling approaches and computational methods used for simulating flows relevant in aeronautical and aerospace applications.

• Overview of the governing equations of fluid dynamics applicable to external flows including classical and advanced turbulence modelling approaches for aeronautical and aerospace applications.
• CFD methods for low- and high-speed flows used for advanced aerospace applications.
• CFD methods for digital wind tunnel applications.
• State-of-the-art case studies and application examples.

On successful completion of this module you should be able to:

1. Set up the governing equations of external fluid dynamics to simulate external flows in a digital wind tunnel.

2. Collect data with a systematic approach and analyse computational results through numerical methods and models for turbulent flows used in aeronautical and aerospace applications.

3. Evaluate the strength and limitations of computational methods used in the aerospace sector.

4. Propose solutions in conjunction with the current efforts made by industry and academia for improving the state-of-the-art methods in the above applications.

To introduce basic concepts in the discretisation and numerical solution of the hyperbolic systems of partial differential equations describing the flow of compressible fluids.

• Mathematical properties of hyperbolic systems.
• Conservation Laws.
• Non-linearities and shock formation.
• WENO schemes.
• MUSCL schemes Introduction to the Riemann problem.
• Lax-Wendroff scheme.
• Introduction to Godunov's method.
• Flux vector splitting methods.
• Approximate Riemann solvers.
• Explicit and implicit time-stepping schemes.

On successful completion of this module you should be able to:

1. Demonstrate a critical awareness of the mathematical properties of hyperbolic partial differential equations.

2. Recognise the importance of non-linearities in the formation of shock waves.

3. Distinguish the fundamental differences between monotone schemes, WENO schemes for hyperbolic systems.

4. Judge the suitability of various Riemann solvers for various compressible flow problems.

5. Create high-resolution shock capturing schemes for compressible flow problems.

Each computational investigation requires a CAD model from which numerical analyses can be performed. This is true for both CFD and FEA simulations, both of which students are exposed to during their studies on this MSc.

This module combines elements of CAD with an introduction to aerospace structures, focusing in particular on different components on the aircraft, as well as manufacturing philosophies which in turn inform the creation of parts (and CAD models).

Students will learn how to build up various components of an aircraft using CATIA and OpenVSP as the CAD software and will be capable of designing components themselves, based on drawings and technical documents, which they can then use to study numerically the behaviour of the component.

In addition, this module also explores elements of computational geometry, where students will work with and extend a simple Python-based CAD tool to generate parametric CAD components, which can be used in a parameterised computational workflow (e.g. for optimisation studies). 

Students will also work with CATIA's FEA and optimisation workbench, which can be used to construct and check structural components such as the wing, fuselage and empennage of an aircraft and optimise them to reduce weight and maximise stresses within the structure.

• Understand the different design philosophies such as fail-safe, safe-life and damage-tolerant.
• Understand the different structural components that make up aerospace structures.
• Understand the constraints imposed by additional reserve factors on the structural components (limit and ultimate load factors).
• Understand the influence of fatigue on the life expectancy of a structure.
• Create solid models using Catia.
• Create surface models using Catia.
• Create assemblies of different models in Catia.
• Create parametric models in Catia.
• Create FEA simulations of 2D shell and 3D solid parts in Catia.
• Perform optimisation of 2D and 3D geometries in Catia based on FEA results.
• Create quick parametric models of an entire aircraft using OpenVSP.

On successful completion of this module you should be able to:

1. Create CAD models using commercial and industrial leading CAD software packages.

2. Design various components found on aeroplanes from drawings and technical documents.

3. Perform integrated Finite Element Analyses of structural components using Catia.

4. Perform optimisation of structural components to minimise weight of the final assembly using global optimisation methods.

5. Create parametric models that automatically update themselves based on external calculations.

Software engineering is a fundamental tool for computational engineers, and this module exposes you to modern best practices in software engineering, in the context of computational aerospace applications.

Python is used as the programming language, and you are first introduced to basic programming techniques with Python, as well as object-oriented programming, before exploring more advanced DevOps concepts such as version control and test-driven development.

The successful computational engineer of tomorrow requires knowledge of solving partial differential equations (PDEs), solving sparse linear systems of equations, utilising high-performance computing, and optimising designs using algorithm-based and machine learning-based optimisation strategies.

This will allow you to develop codes for bespoke aerodynamic and structural problems for specific PDEs, which are potentially solved using a high-performance computer. On the other hand, you will also be able to develop codes that take outputs from existing CAE solvers and apply either post-processing or optimisation to them.

The computational engineering world has settled on Python as a common denominator, with many engineering packages offering scripting through a Python layer. This module will equip you with the knowledge and confidence to write Python code that connects various tools through efficient and bug-free code.

• Work with Python using both procedural and object-oriented concepts.
• Work with dependencies in Python, including how to install them and work with virtual environments.
• Work with packages commonly used in scientific applications (e.g. numpy, pandas, matplotlib, pyplot, scipy, streamlit).
• Discretise partial differential equations using stable numerical schemes and the finite difference/finite volume method.
• Efficiently compute solutions for sparse linear systems of equations.
• Optimise Python code for speed by introducing just-in-time compilation and parallelisation.
• Optimise solutions using classical algorithm-based approaches such as the Genetic Algorithm and Particle Swarm.
• Develop machine learning-based solutions to enhance scientific applications in the context of optimisation problems using PyTorch.

On successful completion of this module you should be able to:

1. 1. Evaluate and discuss a conceptual understanding of software design methodologies.
2. 2. Discuss a working knowledge of the life-cycle implications in software design, development and test.
3. 3. Demonstrate a systematic understanding of Ada programming language.
4. 4. Use Ada programming language to implement software.

Mathematical modelling and simulation of unmanned aerial vehicles is a vital part of system development. Nowadays COTS components becoming more powerful and can multi-task and carry-out complex computations.You would need to learn the technical skills not only for the modelling and simulation but also the real-time implementation of the algorithms. 

The aims of this course is to provide you with the skills and knowledge necessary to model, simulate and then critically analyse the resultant non-linear motion of unmanned air vehicles using mainly Matlab/Simulink and target compile the algorithms on an embedded flight control system.

 

• Introduction to mathematical modelling and simulation; systems of nonlinear ODEs; equilibrium, linearisation and stability; numerical & computational tools (10 hours).
• Model building; model testing, validation and management; trimming and numerical linearisation (10 hours).
• Control implementation and testing on COTS FCS

On successful completion of this module a student should be able to:

1. Design and implement an example UAV model in terms of their aerodynamic, control, mass and inertia characteristics. Appraise and critically compare the resultant motion.
2. Distinguish the requirements for model testing, verification and validation, and demonstrate their application to an UAV model.
3. Implement and apply selected control laws and carry out simulation-in-the-loop testing. 
4. Communicate and present results of individual work.

This module aims to introduce the fundamentals of dynamics and control for Unmanned Aircraft Systems (UAS). Dynamics-wise both fixed-wing and rotary UAS are covered, including effects of aero (servo) elasticity and introduction to tilt rotors and copters. From a control viewpoint focusing on linear control theory students understand its purpose, strengths and limitations, and relevant characteristics in the context of UAS control. Complemented with a case study on UAS dynamics and control, it provides the underpinning knowledge for the “UAS Modelling and Simulation” and “UAS Autonomous Vehicle Control Systems” modules.

• Overview of dynamics of motion
• Mechanics of flight (performance requirements, forces/moments, dynamics)
• Overview of aero(servo)elasticity effects
• Introduction to tilt-rotor and copters
• Mathematical modelling of typical fixed-wing and rotary UAS
• UAS feedback control system characteristics
• UAS control system stability and performance
• Frequency response methods for UAS Flight Control Design
• Classical and state space control design for UAS

On successful completion of this module a student should be able to:

1. Distinguish the fundamentals of flight dynamics for Unmanned Aircraft Systems (UAS) and their control techniques and properties.
2. Evaluate the physical underpinning of mechanics of flight and convey mathematically dynamics of typical fixed-wing and rotary UAS.
3. Evaluate the characteristics, purposes, and design procedures of UAS control systems;