Fluid Mechanics and Thermodynamics of Turbomachinery

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Fan blade design McKenzie. Turbine cascade correlation Ainley and Mathieson. Comparison of the profile loss in a cascade and in a turbine stage. Optimum space-chord ratio of turbine blades Zweifel.

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Velocity diagrams of the axial turbine stage. Thermodynamics of the axial turbine stage. Stage losses and efficiency.

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Types of axial turbine design. Diffusion within blade rows. Choice of reaction and effect on efficiency. Design point efficiency of a turbine stage. Maximum total-to-static efficiency of a reversible turbine stage. Stresses in turbine rotor blades. Flow characteristics of a multistage turbine.

Moore of Virginia Polytechnic Institute and State University, Virginia, for their helpful correspondence and ideas concerning the vexed question of the conserva- tion of rothalpy in turbomachines. Mayhew is thanked for supplying me with generous amounts of material on units and dimensions and the latest state of play on SI units. Thanks are also given to the following organisations for providing me with illustra- tive material for use in the book, product information and, in one case, useful back- ground historical information: Last, but by no means least, to my wife Rose, whose quiet patience and support enabled this new edition to be prepared.

Basic Thermodynamics, Fluid Mechanics: Similitude If you have known one you have known all. The word turbo or turbinis is of Latin origin and implies that which spins or whirls around. However, despite this apparent problem, the study of wind turbines has become an attractive and even an urgent task, not least because of the almost astonishing increase in their number.

It is a matter of expediency to now include the aerodynamic theory of wind turbines in this book and so a new chapter has been added on the topic. Generally speaking, for a given set of operating requirements one type of pump or turbine is best suited to provide optimum conditions of operation.

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Diagrammatic form of various types of turbomachine. One further category should be mentioned.

The Pelton wheel, Figure 1. It is a simple, logical system based upon decimal relationships between units making it easy to use. In US President Ford signed the Metric Conversion Act which coordinated the metrication of units, but did so without specifying a sched- ule of conversion.

Industries heavily involved in international trade cars, aircraft, food and drink have, however, been quick to change to SI for obvious economic reasons, but others have been reluctant to change. SI has now become established as the only system of units used for teaching engineering in colleges, schools and universities in most industrialised countries throughout the world. In this book all numeri- cal problems involving units are performed in metric units as this is more convenient than attempting to use a mixture of the two systems.

However, it is recognised that some problems exist as a result of the conversion to SI units. One of these is that many valuable papers and texts written prior to contain data in the old system of units and would need converting to SI units. A brief summary of the conversion factors between the more frequently used Imperial units and SI units is given in Appendix 1 of this book.

All the other units used in this book are derived from these basic units. The recommended unit of pressure is the pascal Pa which is the pressure produced by a force of 1 newton uniformly distributed over an area of 1 square metre. Several other units of pressure are in widespread use, however, foremost of these being the bar. Much basic data concerning properties of substances steam and gas tables, charts, etc. It is noted that 1 bar equals 10 5 Pa i.

In this book the convenient size of the kilopascal kPa is found to be the most useful multiple of the recommended unit and is extensively used in most calculations and examples. In SI the units of all forms of energy are the same as for work. The unit of energy is the joule J which is the work done when a force of 1 newton is displaced through a distance of 1 metre in the direction of the force, e. The watt W is the unit of power; when 1 watt is applied for 1 second to a system the input of energy to that system is 1 joule i.

The hertz Hz is the number of repetitions of a regular occurrence in 1 second.

Zero on the celsius scale is the temperature of the ice point The static pressure at any point in a liquid at rest is, relative to the pressure acting on the free surface, proportional to the vertical distance of the free surface above that point. The head H is simply the height of a column of the liquid which can be sup- ported by this pressure. This is left for the student to verify as a simple exercise.

This is the formal procedure whereby the group of variables representing some physical situation is reduced into a smaller number of dimensionless groups. When the number of independent variables is not too great, dimensional analysis enables experimental relations between variables to be found with the greatest economy of effort. Dimensional analysis applied to turboma- chines has two further important uses: Several methods of constructing non-dimensional groups have been described by Douglas et al.

The subject of dimensional analysis was made simple and much more interesting by Edward Taylor in his comprehensive account of the subject. It is assumed here that the basic techniques of forming non-dimensional groups have already been acquired by the student. The choice of Q and N as control variables is clearly arbi- trary and any other pair of independent variables such as t and H could equally well Introduction: Similitude 5 F IG.

Turbomachine considered as a control volume. The important point to recognise is that there are for this pump, two control variables. So far we have considered only one particular turbomachine, namely a pump of a given size. To extend the range of this discussion, the effect of the geometric variables on the performance must now be included.

The latter, more direct procedure requires that the variables selected,r,N,D, do not of themselves form a dimensionless group. The func- tional relationships for geometrically similar hydraulic turbomachines are then, 1. For a pump the net hydraulic power,P N equals rQgH which is the minimum shaft power required in the absence of all losses. No real process of power conversion is free of losses and the actual shaft power P must be larger than P N. On this basis, non-dimensional presentation of performance data has the impor- tant practical advantage of collapsing into virtually a single curve results that would otherwise require a multiplicity of curves if plotted dimensionally.

Evidence in support of the foregoing assertion is provided in Figure 1.

Fluid Mechanics and Thermodynamics of Turbomachinery

Within the normal operating range of this pump, 0. This effect is due to cavitation, a high speed phenomenon of hydraulic machines caused by the release of vapour bubbles at low pressures, which is discussed later in this chapter. The non-dimensional results shown in Figure 1. They would also be approximately valid for a range of different pump sizes so long as all these pumps are geometrically similar and cavitation is absent.

Thus, neglecting any change in performance due to change in Reynolds number, the dynamically similar results in Figure 1. Dimensionless head-volume characteristic of a centrifugal pump. A similar arrangement is used in Kaplan turbines, Figure 1. Movement of the vanes is implemented by cams driven from a servomotor.

The lines a and c in Figure 1. Each of these curves represents, in a sense, a different constant geometry machine. Similitude 9 F IG. Introducing the additional variable b into eqn. As is suggested by any one of the curves in Figure 1. The dimensionless form of N s and N sp is the only one used in this book. Alternative versions of eqns. By divid- ing eqn. For a pump, eqn. Likewise, the head developed by each impeller of different diameter D is made equal by adjusting the speed of rotation N.

Since Q and H are constant, N s varies with N alone. For machines handling liquids the lower limit of size is dictated by the phenomenon of cavitation. It may occur at the entry to pumps or at the exit from hydraulic turbines in the vicinity of the moving blades. Range of pump impellers of equal inlet area.

The phenomenon is accen- tuated by the presence of dissolved gases which are released with a reduction in pressure. For the purpose of illustration consider a centrifugal pump operating at constant speed and capacity. By steadily reducing the inlet pressure head a point is reached when streams of small vapour bubbles appear within the liquid and close to solid surfaces.

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Description Fluid Mechanics and Thermodynamics of Turbomachinery is the leading turbomachinery book due to its balanced coverage of theory and application. Starting with background principles in fluid mechanics and thermodynamics, the authors go on to discuss axial flow turbines and compressors, centrifugal pumps, fans, and compressors, and radial flow gas turbines, hydraulic turbines, and wind turbines.

In this new edition,more coverage is devoted to modern approaches to analysis and design, including CFD and FEA techniques. The Best Books of Check out the top books of the year on our page Best Books of Product details Format Hardback pages Dimensions x x Looking for beautiful books?

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