PROCEEDINGS

of the Tomsk Technological Institute

of Emperor Nicholas II.

Vol. 18. 1910. No. 2.

V.

A. I. Astrov.

CONCERNING THE WORKS OF Mechanical Engineer A. Ya. MILOVICH

“Designing the Blades of a Francis Turbine by Prof. Pfarr’s Method” and “An Experiment in the Theory of the Suction Pipe.”

1–5.

Concerning the Works of the Mechanical Engineer A. Ya. Milovich

“Construction of the Blades of a Francis Turbine According to Professor Pfarr’s Method”) and “An Essay on the Theory of the Draft Tube”*).

For many years now, the insufficient substantiation of the theory of water turbines has been felt—a theory compelled to liken the motion of the entire mass of water passing through the engine to the motion of a single “average” jet. All attempts to split the moving mass of liquid into separate jets proceeded from the assumption of a complete absence of interaction among them, both in the sense of internal friction and in the sense of deformation of the entire mass. Such a fundamentally incorrect formulation of the theory of water turbines is in full accord with the manner of treating most questions of hydraulics, and is a consequence of the limited range of problems studied by hydrodynamics, of the great complexity of the analysis it employs, and consequently of the need to introduce purely empirical corrections into its conclusions. In recent years attempts have appeared to apply the equations of hydrodynamics to the theory of turbines. These attempts were made first by Professor Prášil (Zurich) and, somewhat later, by Professor Hans Lorenz (Danzig), and are very similar to one another in method of investigation, although they also have certain essential differences. Both of the works by Mr. Milovich under consideration, and especially the second, should be regarded as a continuation of attempts of this kind. It should be noted here that Professor Lorenz’s works, although they appeared in 1905, apparently remained unknown to Mr. Milovich; at least he does not mention them. We shall begin our consideration of the above-named works with the second.

In their main features these works of Mr. Milovich represent a reworking of Professor Prášil’s article “Über Flüssigkeitsbewegungen in Rotationshohlräumen”***), supplemented by certain independent investigations and considerations. The general line of thought is as follows. It is assumed that the motion of a liquid continuous mass is—1) non-vortical and 2) completely symmetric with respect to the vertical axis, so that for

) Bulletin of the Polytechnic Society, 1906, Nos. 1 and 2.
) Ibid., 1907, No. 1.
**) Schweiz. Bauzeitung, 1903, Bd. XLI.

A. I. Astrov.

of all particles lying in a plane perpendicular to the axis at the same distance from it, all the circumstances of the motion are identical. By means of the equations of hydraulics, transformed into cylindrical coordinates, both the streamlines and the surfaces of equal velocity potentials, equal velocities, and so on are considered. Unlike Prášil, Mr. Milovich supplements this examination by studying the surfaces of equal pressure. This addition is essential, and the author makes use of it below in the question of flared mouths.

Proceeding further from the assumption of the absence of both external and internal friction, the proposition is established that if the liquid flows inside a vessel whose walls constitute a surface composed of the streamlines of the flow under consideration continuously following one another, then its actual flow will not differ from the one studied, provided that the conditions of entry into and exit from such a vessel corresponding to this flow are fulfilled. If, at the same time, Professor Prášil (in the work that appeared in print), as well as Professor Lorenz, restrict themselves to indicating vessels that are bodies of revolution with an axis coinciding with the axis of the flow and with a meridian coinciding with one of the streamlines, then Mr. Milovich quite reasonably extends this conclusion to a number of other possible forms, which in general may be obtained by isolating from the flow any bundle of streamlines, even those lying on one side of the axis of the flow, provided only that the conditions of entry and exit are satisfied. In this way there arises the possibility of strictly determining the form of the very widespread at present curved and continuously widening concrete suction pipes. Criticizing the form of Professor Prášil’s suction pipe, i.e. one symmetric with respect to the axis of the flow, the author, together with Professor Pfarr, quite correctly notes that such a pipe would be good if water could escape from beneath it in all radial directions, which in reality the side walls of the discharge channel usually do not allow. However, the method proposed by him of outlining the suction pipe in the form of a bundle of streamlines eccentric with respect to the axis of the flow, improved in comparison with Professor Prášil’s pipe in the sense of outflow from it, is inferior to the latter in the sense of failure to observe the inlet conditions: if the assumption that the water, leaving the turbine runner, which is always made as a body of revolution, moves along surfaces of revolution seems more or less probable and feasible, then the admission that, at the exit from the runner, there will occur precisely that same ...

On the Works of A. Ya. Milovich

but the distribution of velocities, pressures, and so forth, which is necessary for the selected eccentric bundle of streamlines. The introduction of a cylindrical tube in the form of a transition from the runner of the suction tube probably will not always be sufficient to express these discrepancies. In any case, its proper length ought to be clarified. The same technique—the investigation of the flow and the determination of the corresponding form of flow—is applied by Mr. Milovich to another case, namely to the plane flow of a liquid, and in this way he obtains a suction tube enclosed between two parallel and vertical planes, very convenient for execution in concrete. I am not aware that anyone in print has given such a consideration as applied to suction tubes.

In all cases the author devotes great attention to the place where the flow passes from the suction tube into the discharge channel, calculates the loss of energy thereby caused, and attempts to establish certain norms for the proper execution of this part of the turbine installation. Owing to the complexity of the question—the finding of the form of the diffuser that least disturbs the main flow and at the same time sufficiently approximates it to the conditions of motion in the discharge channel, at least in the sense of the pressure distribution—everything considered, though it goes much further than that indicated by Professor Prášil, still by no means has that strict and finished character by which the study of the flow itself is distinguished. For this reason one especially cannot but agree with the author when he says that the whole theory needs experimental verification.

At the end of the work under discussion the author considers the case of rotational, but not vortical, motion in a tube (somewhat differently than the same case is considered in Professor Prášil’s work), and one case of vortical motion in a tube, namely when the vortex lines coincide with the streamlines. The author uses this last consideration to explain the circumstance that in mixed turbines the efficiency coefficient changes little, despite wide limits of variation in discharge. To this circumstance, which the author calls “stability of the efficiency coefficient,” he also devotes attention in the first of the articles mentioned in the title of this note; therefore I shall state my opinion on this matter also in the review of that article.—Finally, the last pages of the work on suction tubes are devoted to a series of interesting analogies between the flows of a drop liquid considered and the forms of horns.

The first work of Mr. Milovich—on the design of Francis runners—is to a considerable degree less independent than the preced-

...and first presents several considerations in favor of the applicability of one of the above-mentioned flows to the profiling of turbine-wheel rims (following Professor Prášil’s idea), and chiefly sets forth, thoroughly and in considerable detail, the rule for designing and determining the shape of the wheel blades adopted by Professor Pfarr, one of the greatest authorities in the construction of turbines. The intelligent and clear exposition of this method, very visual and rather simple, cannot but be credited to Mr. Milovich’s merit before our technical literature. If there is anything to be regretted, it is the absence in the articles of illustrations of this method by an example of the design of a normal and a high-speed wheel (an example is given only for the slow-speed type). Had these examples been given by Mr. Milovich, perhaps this would have made him less insistent in asserting that the surface on which the outlet edges of the wheel blades are situated must be chosen as a surface of equal velocity potential in a flow with one axis of symmetry. This very requirement in the first part of this article is not very convincingly explained solely by the desire to apply the discharge equation without introducing the multiplier characterizing the angle of deviation of the absolute velocity from the normal to this surface; meanwhile, fulfillment of this requirement in a normal turbine, and especially in a high-speed one, is almost impossible and in any case leads to very long blades. I believe that the author would have been more correct had he resolved this question in a less categorical form, leaving its settlement until experimental verification.

As for the first part of this work, it must rather be regarded as an introduction or supplement to the article on suction pipes analyzed above; together with the latter it is in close connection, whereas its relation to the construction of the wheel according to Pfarr is only external and in some cases even contradictory. The author’s attempt to explain this contradiction by an objection to Professor Escher’s objection*) cannot be called convincing: while admitting that the shape of the wheel rims is capable of changing the magnitudes of the velocities, even though they would prove equal when the influence of centrifugal force is taken into account, the author for some reason does not allow that centrifugal force in turn must change that form of the surface of velocity potential which is obtained without the influence of the effect of rotation of the liquid with the wheel.

*) See p. 24 of the separate offprint.

In general, the author perhaps somewhat overestimates the significance of theoretical conclusions for the construction of turbine wheels. Thus, for example, in explaining, as was noted above, in both works the phenomenon of the “stability of the efficiency coefficient” of the Francis turbine, the author dwells exclusively on the forms of flow considered by him and does not at all touch upon such an important factor as the design of the turbine’s regulating device, which in this very question has very substantial significance: turbines with cylindrical gates, as is known, do not exhibit the stability that is observed with the guide apparatuses of Fink, Fodell, and the like.

Leaving aside, however, this essentially understandable enthusiasm for theoretical conclusions, especially in view of the opinion expressed more than once by the author that these conclusions are subject to strict scientific-experimental verification, and leaving aside also a certain incompleteness of practical data and instructions on the construction of wheels, since they do not fully enter into the task of the article, it is necessary to acknowledge in Mr. Milovich’s works major merits, which may be formulated as follows:

1) These articles present a very thorough, clear, and comparatively simple exposition of Prášil’s theory, very successfully supplemented by a critique of the practical proposals of that author, by extension to methods that are not new theoretically but practically useful—the forms of curved suction tubes—and by consideration of plane flow, also accompanied by an indication of its practical applicability.

2) The question of the bell-mouth of the suction tube, i.e. of the place of transition of the flow from the tube into the discharge canal, is raised and posed quite correctly, although not resolved.

3) Both articles undoubtedly represent an independent treatment of all the material, as is evident from a simple comparison of the author’s articles with the sources cited by him.

4) Finally, one cannot fail to note that it is evident from both articles that the author has a sufficiently free command of the apparatus of mathematical analysis.

In conclusion, I can only wish that the author, who has undoubtedly shown by these works the ability and inclination for independent investigations, be placed in such conditions as would allow him both to continue his investigations and to subject them to experimental verification.

Assoc. Prof. Al. Astrov.

November 14, 1907.