ENGINEERING TRIPOS PART IIA - 2012/2013

Module 3A1 - Fluid Mechanics I

Courses:

1. Incompressible Flow: 2 lectures/week, weeks 1-5 Michaelmas term (Dr. W.R. Graham)
2. Boundary Layer Flow :2 lectures/week, weeks 6-8 Michaelmas term, weeks 1-2 Lent term (Dr. J.R. Dawson)
3. Applications I - Airfoils and Wings: 2 lectures/week, week 3-6 Lent term (Prof. W.N. Dawes)
4. Applications II - Aerodynamics of Road Vehicles : 2 lectures/week, weeks 7-8 Lent term (Dr. H. Babinsky)

AIMS

There are four themes to this paper. The first concerns two-and three- dimensional flow fields for the basic case of inviscid incompressible fluids. The course aims to develop an understanding of when and where fluid flows can be modelled as incompressible and inviscid. It develops simple analytical and computational methods to solve such flows and aims to build up physical understanding through a range of practical examples. Then the effects of viscosity are introduced and boundary layer flows are discussed in some detail. These ideas are brought together in two applications sections, which consider the aerodynamics of aircraft wings and road vehicles.

SYLLABUS

1. Incompressible Flow (10L)

• Irrotational flow and the velocity potential.
• Two-dimensional flow:stream function and streamline; complex potential; sources, sinks and vortices; superposition of elementary sources to determine real flows; panel method; circulation and lift; use of images.
• Three-dimensional flow:sources and sinks; vorticity in 3D, Kelvin's circulation theorem.
• Viscous effects: Navier Stokes equation, vorticity equation.

2. Boundary Layer Flows (10L)

• The boundary layer equations.
• Laminar boundary layers, similarity solutions
• Thwaites method, numerical methods.
• Turbulent boundary layers, the log law.
• Turbulent boundary layers with roughness
• Pipe flows

3. Applications I - Airfoils and Wings (8L)

Two-dimensional aerofoil flows :

• modelling assumptions;
• vortex sheet panel method;
• thin aerofoil theory;
• lumped parameter modelling;
• viscous effects and stall.

Three dimensional wing flows:

• general features;
• panel methods in 3D;
• lifting line theory;
• lumped parameter modelling;
• wing stall;
• sweep effects.

4. Applications II - Aerodynamics of Road Vehicles (4L)

• Review of fundamental concepts : bluff-body aerodynamics, friction vs pressure drag, 2 and 3 dimensional bodies, ground effect
• Drag of passenger cars ; boat-tailing, tail shapes, skirts
• Lift/downforce: spoilers, wings, diffusers
• Drag of haulage vehicles: tractor/trailer junction, trailer shape effects, cross-wind stability .

OBJECTIVES

On completion of the course students should be able to;-

Incompressible Flow

• Know when and where fluid flows can be modelled as irrotational.

For two-dimensional flow:

• Use the complex potential to determine the velocity and pressure distribution in simple geometries eg. corner flow.
• Superimpose elementary solutions to calculate velocity and pressure distributions in a range of practical flows.
• Know that the panel method leads to an efficient computational scheme.
• Understand the relationship between circulation and lift.
• Use images to investigate ground effects and the influence of wind-tunnel walls.

For three-dimensional flow:

• Use elementary solutions to calculate velocity and pressure in some simple three-dimensional flows.
• Use vortex dynamics to explain the development of simple three-dimensional flows.

For viscous flow:

• Understand the implications of viscosity for fluid flows.

Boundary Layer Flows

• Understand the coupling between the viscous - dominated near-field flow and the inviscid far-field.
• Understand classical and integral solution techniques.
• Understand the difference between laminar and turbulent flows and transition.

Applications I - Airfoils and Wings

• Understand the nature of flow around an aircraft.
• Understand the interaction between lift and induced velocity.
• Estimate the lift and drag of aircraft wings
• Qualitatively understand the effects of viscosity.

Applications II - Aerodynamics of Road Vehicles

• Describe the physical features of the flow around a road vehicle
• Understand the origins of the aerodynamic forces on the vehicle
• Explain how the aerodynamic forces are affected by the vehicle shape.

REFERENCES

Please see the Booklist for Part IIA Courses for references for this module.

Last updated: July 2012