ENGINEERING TRIPOS PART IIA - 2012/2013

Module 3A3 - Fluid Mechanics II

Courses

1. One-dimensional Compressible Flow : 2 lectures/week, weeks 1-6 Michaelmas term (Prof R.S. Cant)
2. Two-dimensional Compressible Flow : 2 lectures/week, weeks 7-8 Michaelmas term and weeks 1-2 Lent term (Dr J.P. Jarrett)
3. Equations of Fluid Flow and their Numerical Solution : 2 lectures/week, weeks 3-5 Lent term (Prof R.S. Cant)
4. Turbomachinery: 2 lectures/week, weeks 6-8 Lent term (Dr J.P. Longley)

AIMS

To understand fluid flows to a level such that the pressures and resultant forces acting can be estimated in situations involving complex geometries of industrial interest at both subsonic and supersonic speeds. To include the effects of viscosity where relevant.

SYLLABUS

1. One-dimensional Compressible Flow (12L)

• Steady, adiabatic and inviscid flow; speed of sound; reversibility; the stagnation state; the effect of area variation on subsonic/supersonic flow, choking; normal shock waves; flow patterns in nozzles; use of table for isentropic flow and for shock waves.
• Fanno and Rayleigh line processes for the effects of friction and heat exchange.
• Introduction to unsteady flow.Hydraulic analogy to steady compressible flow; speed of waves in shallow water; the hydraulic jump; the venturi flume; weirs.

2. Two-dimensional Compressible Flow (8L)

• Method of characteristics, expansion fan and compression ramp.
• Oblique shock waves, strong and weak solutions.
• Shock-expansion theory
• Potential equation and linearisation. 

3. Equations of Fluid Flow and their Numerical Solution (6L)

• Numerical solution techniques; finite difference approximations; finite volume approximations; order of accuracy, diffusion and dispersion errors; stability considerations for time iterative techniques
• Classification of Equations; numerical solution of the Euler equations and boundary layer equations

4. Turbomachinery (6L)

• Axial-flow and radial-flow turbines
• Axial-flow and radial-flow compressors, fans and pumps
• Velocity triangles, Euler's work equation, SFEE in rotating frame
• Loss generation
• Compressible flow within turbomachinery
• Designs for gas and stream power plant; wind turbines

OBJECTIVES

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

One-dimensional Compressible Flow

• Know the concepts of stagnation temperature and stagnation pressure and be able to determine their values from a knowledge of static temperature, static pressure and Mach number.
• Know how conservation principles determine the behaviour of normal shock waves and be able to use tables to quantify that behaviour.
• Evaluate Mach number of a flow from measurements of Pitot and static pressures.
• Determine flow patterns in nozzles under the assumption of one dimensionality, using tables.
• Know how Mach number and other flow properties change under the influence of friction or heat exchange.
• Quantify, using tables, the effects of friction or heat exchange.
• Know how to construct and interpret x-t diagrams for unsteady ID flow.
• Quantify the behaviour of hydraulic jumps and infinitesimal waves in shallow water.

Two-dimensional Compressible Flow

• Understand the influence of the speed of sound on flow behaviour.
• Apply the two-dimensional method of characteristics for simple flows and flows involving reflection/cancellation.
• Understand the origin of oblique shock waves and their reflection.
• Apply the preceding ideas to practical flows via shock-expansion theory, linearised method of characteristics and linearised potential theory.

Equations of Fluid Flow and their Numerical Solution

• Know how to construct and use numerical solution methods for the equations of fluid flow using finite difference and finite volume approximations
• Know how to estimate the accuracy and analyse the stability of numerical schemes

Turbomachinery

• Identify and understand the operation of different types of turbomachinery.
• Analyse turbomachinery performance.
• Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
• Analyse compressible flow through turbomachines.

REFERENCES

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

Last updated: June 2012

teaching-office@eng.cam.ac.uk