Another important discovery was that despite the fact that turbomachine parameters depend strongly upon details of their individual design, there are some general laws valid irrespective of the particular design features. Already at the beginning of this century, water turbine manufacturers have found a certain relationsship between speed, power, height difference ( - and therefore ) on one hand and the corresponding most suitable dimensions and geometry of the rotor on the other hand. It became common to express these relationsships by means of the concept of specific speed (Baashuus 1905). This is still sometimes used (mainly by the force of tradition), although dimensional analysis made later possible (Eck 1926, Keller 1934) to find better dimensionless parameter - the speed coefficient. Its is expressed in radians (- which is, of course, a dimensionless value, arc length divided by radius length).

Fig.F-20 The effect of the speed coefficient on design of a radial turbomachine: the value of the coefficient determines the position of the optimum operation point. This illustrations presents as an example results for a family of blowers: the blower A with low value of the coefficient is suitable for generating high pressure differences, while the machine E is suitable for for large flow rates. Note (diagram at right) that speed coefficient
also determines the achievable efficiency and size (- and thus price) of the machine.




























In the upper right diagram, Fig.F-20 above presents dependence of relative size of the rotor - nondimensional outlet diameter - and the achievable efficiency = / mech upon the value of the speed coefficient (mech is the mechanical power applied to the driving shaft). It is apparent that the preferable policy is to choose the value of the speed coefficient near to 1.0 rad. This leads to maximum efficiency. For higher flow rates, however, it may be justifiable to select higher a geometry with higher value of the coefficient so that the machine (having smaller is not so large. On the other hand, if it is desirable to generate or process rather high drop in a single stage, it is advisable to select a geometry with lower speed coefficient value.

Fig.F-21
More about characteristics. The derivation in Fig.F-9 was just consideration of basic energetic changes. We may further note that an essential influence upon the shape of the characteristic has the rotor blade exit angle , the magnitude of which its is possible to choose when designing the machine.
Fig.F-22a
Fig.F-22b






Using the relation derived in Fig.F-14,

it is possible to evaluate an idealised lossless characteristic of a pump or blower. Note that in contrast to the simple bent pipe case in Fig.F-14, it is necessary in the case of a rotor to discriminate between the angle at and angle at . The lossless characteristric is a straight line dependent solely upon the exit angle . Fig.F-21 shows three such characteristics, in the relative co-ordinates of Fig.F-19, for three ddifferent values of the angle . Better approximation to real characteristics is obtained according to Fig.F-22a and Fig.F-22b by considering various loss effects that decrease the amount of specific energy that the fluid gains inside the pump. First, it is necessary to subtract from the straight line A of Fig.F-21 the effect of relative rotation of fluid with respect to rotor blades. This rotation (Fig.F-23) causes the real exit angle to become smaller than what would be expected from the blade geometry. As a result, the characteristic changes to B. Then there is the effect of hydraulic losses - those discussed in chapter [D]. Their dependence upon flow is quadratic and results in the shape C. One of the most important influences, however, is then the fact (explained in Fig.F-24) that blades may be exposed to the incoming flow at the proper angle of attack (according to Fig. F-17a)


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This is page Nr. F08 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
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