ENGINEERING TRIPOS PART IIB – 2012/2013

Module 4A10 - Flow Instability

AIMS

This course aims to develop physical insight into the unsteady behaviour of fluid flows through a range of practical examples, videos and demonstrations. The examples are chosen to be appropriate in a wide range of applications and to introduce flow effects not covered in the third year, like the interaction between flexible structures and fluids, rotating flow and the effects of convection and surface tension.

LECTURE SYLLABUS (16L)

Instability of fluid flows (8L, Dr A. Agarwal)

• The break up of a liquid jet in air, surface tension effects, temporal instability, mean droplet size.
• The stability of rotating flows, Rayleigh's criterion; flow between rotating cylinders; different flows according to parameter range, ranging from Taylor vortices to chaotic flow; Görtler vortices, relationship to streamwise vortices in boundary layers;
• Shear flow instability, temporal and spatial; the Kelvin-Helmholtz instability; the effects of viscosity and transition to turbulence.
• Convection due to surface heating, formation of cellular patterns, effect of variations in surface tension.

Absolute and Convective Instability (4L, Dr M. P. Juniper)

• Local instability and global instability
• Phase velocity and group velocity
• Temporal, spatial and spatio-temporal stability analysis

Fluid-structure interaction (4L, Dr M. P. Juniper)

• External flow; Flow-induced oscillations of structures; Vortex shedding, lock-on; Galloping and flutter; Control of oscillations by passive techniques.

OBJECTIVES

On completion of the course students should:-

• Understand that even a fluid flow with nominally steady boundary conditions may be unsteady due to flow instability;
• Be able to analyse the stability of simple flows by determining whether small disturbances grow or decay with time;
• Understand how a liquid jet breaks up under the destabilising influence of surface tension;
• Be able to analyse the stability of inviscid rotating flows, and understand the relationship to streamwise vortices in boundary layer flows;
• Be aware that concepts in modern nonlinear dynamics, including phase space diagrams and chaos, can be useful in the description of fluid flows;
• Be able to analyse the instability of simple inviscid shear flows, including the effects of density stratification and surface tension, to discuss the effects of viscosity and the transition to turbulence;
• Understand the destabilising influence of convection in a fluid heated from below, be able to describe the cellular flow pattern formed (Bénard cells) and the effects of variations in surface tension;
• Be able to discuss external flow around flexible structures, including 'lock-on', galloping and flutter;
• Be able to distinguish between absolutely unstable and convectively unstable flows

REFERENCES

Please see the Booklist for Group A Courses for references for this module.

Last updated: June 2012