The prac tical difficulty in utilizing such high velocity steam jets efficiently in a "simple" steam turbine will soon be apparent. Simple mathematical theory shows, and experiment confirms, that the proportion of energy in a jet of steam which can be converted into useful work on the turbine shaft, depends mainly on the relation which is made (by the designer) to exist between the linear velocity U of the "vanes" or "blades," and
that of the jets impinging on them. In other words, the efficiency of a turbine depends mainly on the ratio called the "velocity-ratio,"
usually denoted by the symbol a. Figure 3 shows a curve (A) of the "blading" efficiency obtainable from a "simple" turbine of the type shown in figure (i). Losses due to windage, eddies and friction in the turbine itself, and to friction of bearings, etc., will absorb some of the power developed, so that the "brake" efficiency at the driving end of the shaft will be considerably less.
Here it may be noted that the expression "efficiency of a turbine" must be carefully understood, as it is liable to mis interpretation. If the energy of the steam jet is, say A units of work and out of this the turbine usefully delivers B units to the coupling at the driving end, then the brake efficiency of the plants exceed about 36.o% so that the overall efficiency is about (0.36 X 0.85) X 100=30.5% from fuel to brake horse power. This comparatively low figure is not due to imperfections in the plant owing to incorrect design, but to a fundamental law of thermodynamics which places a limitation on the thermodynamic efficiency of any engine, however perfect, designed to convert the heat of fuel into motive power. For further information upon this aspect of the problem of the utilization of the heat energy in fuel, see THERMODYNAMICS.
To resume, it will become apparent from fig. 3 that the best efficiency for this type of blading is obtained at a "velocity ratio" of about 0-45, that is to say, when the velocity of the blades is about half the velocity of the steam jets. Referring to Table I. it will be observed that with an ordinary boiler pres sure of, say, 175
absolute, and a final exhaust pressure of 1
absolute, the jet velocity is of the order of 4,000 feet per second. If the blade velocity is to be 0.45 of this, it will be about (0.45 X 4,000)=1,80o ft. per sec.
The centrifugal forces on a turbine wheel and blades operating at this mean blade velocity will be very great, and the conse quent centrifugal stresses also. A rim speed of 1,80o feet per sec. would be that of a 0" wheel revolving at 41,000 revolutions per minute. The maximum stress in a disc at this speed would be of an order which is not practicable so that a turbine consist ing of a single wheel can only have a poor velocity ratio, and is only suitable for small outputs for which efficiency is of secondary importance. The speed of revolution is necessarily high, and
such turbines have therefore to be coupled to the machines they drive through some form of speed-reducing gear, usually of the mechanical type, with double helical gear wheel teeth.
The "simple" type of steam turbine or steam "windmill" was first perfected by the great Swedish Engineer Gustav C. P. de Laval in 1887 after several years of preliminary work. It ranks as a great achievement inasmuch as, within the limitations just described, it is a perfectly practical solution of the problem, worked out moreover in days when reliable data on the proper ties of steam were practically non-existent.
If the mean blade speed of a simple steam "windmill" such as the de Laval, is less than about half the circumferential velocity of the steam jets, the latter will not be slowed down sufficiently in the space following the moving blades, and some of their energy will be wasted. In other words, the velocity of the steam will not be In fact, this principle of "pressure-compounding" or using several "simple" turbines in series is an essential feature of all modern steam turbines of large output and high economy, because it per mits reasonable blade velocities to be adopted, without sacrifice of efficiency. (Parsons' original io h.p. steam turbine and dynamo may be seen in the Science Museum, South Kensington, London.) Application of Parsons' Principle.—The application of this principle may best be grasped by considering its application (at a minimum. In order to provide means for recovering the energy in the residual velocity, about the year 1898, Curtis developed in the United States of America a system known as "velocity com pounding." In this arrangement he fitted additional guide blades to re-direct the steam on to further rows of moving blades. Figure 4 illustrates a series of such additional rows. The char acteristic feature is that the fall in steam pressure is confined to the nozzles, the steam flowing through the remaining blades at constant pressure, but with ever diminishing velocity, because of the energy absorbed by the wheel and transmitted to the tur bine coupling. It might be supposed these rows could be made sufficiently numerous to extract the whole energy economically in a single pressure stage, i.e., that pressure compounding would be unnecessary. Unfortunately, however, reversal of the direc tion of the motion of steam at high velocity is accompanied by loss of energy and this, together with frictional losses, soon im poses a limit to the number of reversals which can be efficiently employed. The "two-row" Curtis wheel has been employed widely but the 3-row Curtis wheel is so inefficient that it is now seldom used except in small auxiliary turbines or sometimes in marine astern turbines where efficiency is less important.