# ES441 - Advanced Fluid Dynamics

**(15 Credits)**

### Aims

To provide an advanced course in fluid dynamics which reflects the research strengths and activities of the Fluid Dynamics Research Centre. The course will build on the material studied in previous courses taught in the School. It will provide students with the opportunity to apply their already existing knowledge to two new fields, while also providing a good foundation and specialist knowledge in two new fields in fluid dynamics and related areas of engineering interest.

### Learning Outcomes

By the end of the module the student should be able to:

- Demonstrate they have advanced their numerical and graphical skills.
- Demonstrate they have advanced their ability to learn new technically demanding material.
- Demonstrate they have improved their time-management skills.
*Aerodynamics of wings and bodies:*

- Understand of the principal physical phenomena involved in flow past wings and bodies and the forces so generated.
- Appreciate the modelling techniques, and their limitations, used to predict aerodynamic characteristics for aircraft design.
- Apply computational techniques to a relevant flow problem.

*Multiphase flows:*

- Describe the fundamental aspects of multi-phase fluid dynamics. They will be aware of the importance and implications of multi-phase flows to areas such as mechanical and civil engineering, oceanography, coastal sedimentary environments, mining, agriculture, geology, food and pharmaceutical industry etc.

*Turbulent flow:*- Understand the current concepts and methods used to analyse, measure and predict turbulent flows of engineering and environmental interest.
- Undertake engineering calculations of turbulent flow.
- Demonstrate a good foundation for pursuing further study on turbulent flow.

### Syllabus

This will depend upon the research focus adopted in each year. Examples of three possible syllabi are:

1) *Aerodynamics of Wings and Bodies*

Low-speed inviscid theory: Review of potential flow, complex potential, conformal transformations, circulation, generation of lift and drag, Kutta condition. Thin-aerofoil theory. Finite-wing theory

Viscous effects: Types of drag, laminar and turbulent boundary layers, transition prediction, separation, wake modelling. High-lift devices. Boundary-layer control and turbulence management.

Computational methods: Panel methods, higher-order techniques, inclusion of viscous effects.

Compressible flow: Introduction to subsonic, transonic and supersonic flow. Potential flow. Swept wings. Calculation of lift and drag.

2) *Multi-phase flows.*

Basic Equations, Transport Properties and Processes

Sediment Properties, Threshold of Particle Movement, Sand Transport by Air, Dune Morphology, Dune Sediments, Dune Dynamics

Geometry of Fluvial Channels, Sediment Transport, Erosion and Deposition, Cohesive Sediments, Coastal Processes

Formation and Break-Up of Fluid Particles, Stability of Jets, Atomization

Pipe Flow of a Suspension, Transport in Pipelines

Non-Newtonian Phenomena, Rheological Characteristics of Materials

Dense Systems (Liquid Slurries, Fluidized Beds)

Mixing in Two-Phase Flows

Two-Phase Flow through Nozzles, Shock Waves in Dusty Gases

3) *Turbulent flow*

Fundamental governing equations: time averaging; Reynolds stresses and equations; turbulent energy equation.

Phenomenological approach: Boussinesq and mixing-length models; applications to pipe flows and boundary layers; viscous sub-layer and law of the wall.

Statistical theory: Integral length scales and microscales; energy spectrum; Komolgoroff's concepts.

Laminar-turbulent transition: basic mechanisms and theoretical modelling; prediction and control.

Coherent structures: basic forms and experimental evidence.

Calculating turbulent flows: Zero-equation models; 2-equation models; stress -equation models; large-eddy simulation; direct numerical simulation.

Control of turbulent flow

**Illustrative Bibliography :**

A History of Aerodynamics and its impact on Flying Machines Anderson, J.D. Cambridge Univ. Press (1997) ISBN 9780521669559

An Album of Fluid Motion Van Dyke, M. Parabolic Press (1982) ISBN 9780915760022

Boundary Layer Theory Schlichting, H. Springer (2000) ISBN 9783540662709

Boundary Layers Young, A.D. Oxford Blackwell Sci. (1989) ISBN 9780632021222

Bubbles, Drops and Particles [electronic resource] Clift, R., Grace, J.R. Academic Press (2007) ISBN 9781420015386

Foundations of aerodynamics : bases of aerodynamic design Kuethe, A.M. Wiley (1997) ISBN 9780471129196

Fundamentals of Aerodynamics Anderson, J.D. McGraw-Hill (2011) ISBN 9780071289085

Modern Compressible Flow Anderson, J..D. McGraw-Hill (2004) ISBN 9780071241366

Physical Fluid Dynamics Tritton, D.J. OUP (1988) ISBN 9780198544937

Race Car Aerodynamics: designing for speed Katz, J. Robert Bentley (1995) ISBN 9780837601427

The Phenomena of Fluid Motions Brodkey, R.S. Dover Publications (1995) ISBN 9780486686059

The simple science of Flight Tennekes, H, The MIT Press (2009) ISBN 9780262513135

Theory of Wing Sections Abbott, I.H. Dover (1959) ISBN 9780486605869

Turbulence Modeling for CFD Wilcox, D.C. DCW Industries (2002) ISBN 9781928729105

Wing Theory Jones, R.T. Oxford University Press (1990) ISBN 9780691085364

Viscous fluid flow White, F.M. McGraw-Hill (2006) ISBN 9780071244930

Fluid mechanics Kundu, P. K. Academic Press (2012) ISBN 9780123821003

Particulates and continuum : multiphase fluid dynamics Soo, S. L. Hemisphere (1989) ISBN 0891169180

Fluid mechanics White, F. M. McGraw-Hill (2011) ISBN 9780071311212