TJ 870 Z7 WATER TURBINES Contributions to Their Study Computation and Design BY S. J. ZOWSKI Published by The Engineering Society University of Michigan THE AMERICAN HIGH SPEED RUNNERS FOR WATER TURBINES Looking at a modern American standard runner for a water turbine one is liable to wonder why the design of such runners is considered to be one of the most difficult problems in hydraulic engineering. The forms of the runners are so natural, the buck- ets and their curvature so simple, that "we fail to see where the pretended difficulties are." As is usual in such cases, we forget here again that there is always a direct proportion between the simplicity of a machine and the amount of brainwork and time necessary to produce the same. A brief history of the evolution of the American turbine or a glance at the reports of the numer- ous tests made in the Holyoke testing flume would convince us of this fact. Indeed, the American standard runners, as they are manufactured now, represent a great amount of hard and earn- est work. Hundreds of tedious and expensive experiments, with many a failure and success, had to be made an experience of almost half a century had to be aggregated first, before this mod- ern runner type was produed. The aim was, first, of course, a good efficiency. But this was not all. Already in the early eighties at a time when the Euro- pean engineers still were questioning the advantages of the radial inward flow turbine there were in this country wheels of this type, which yielded efficiencies up to 84%, acording to the tests made in Holyoke. And yet since that time remarkable progress has been made. Following the general tendency of modern en- gineering, the speed and capacity of the turbines had to be stead- ily increased. That for the turbine designer this resulted in new difficulties is evident, as high speed calls for small dimensions, while high capacity calls for large dimensions, and consequently the increase of both is possible only to a certain limit. The purpose of this study is to show how far the American manufacturers of water turbines have come in this respec-t and also to compare the results which were obtained by their various 224635 in runner types. The accuracy of this study is naturally limited by the accuracy of the data, which were accessible to the writer, and which were taken from the guarantees of the different con- cerns. But as these guarantees are based on careful tests made in the Holyoke testing flume, and as these tests are considered official in this country, also the results of the following study can be considered reliable. The comparison at least will be accurate, because, if mistakes in the testing of the wheels be made (and some engineers, especially in Europe, believe that the Holyoke tests are not quite reliable regarding the actual discharge) the same mistakes owuld be made on all runners. NOTATION. To get a proper basis for this study, some of the principal turbine formulae must be recalled and some new ones derived. The notation is the same, which the writer uses in his lectures on water turbines at the University of Michigan. H-P = effective power of the runner. N = speed of the runner in R. P. M. Q = discharge of the runner in cubic feet per second. H net head in feet acting upon the turbine = gross head minus all losses in head race, conduit and tail-race. =. hydraulic efficiency of the turbine, (i c ) H = head lost inside of turbine itself due to friction, whirls and shocks. Di =. mean entrance diameter of runner in feet. B = height of guide case in feet. o-i = angle between entrance speed and peripheal speed at Di. & = bucket angle at Di. Ci = real entrance speed at Di. Wi = relative entrance speed at Di. Vi = peripheral speed at Di. CT =. radial entrance speed at Di radial component of c\, see Figs. I and 2. SPEED. All modern American runners are of the radial inward flow type, working with pressurehead. The definition of the "pres- surehead turbine" or "pressure turbine" (so-called reaction tur- bine) is: "The water enters the runner and flows through the same with a certain pressurehead, as the whole available head is not turned into speed at the entrance. The real entrance speed 5 Ci is smaller than the spouting velocity. A pressurehead is left, to be used for the acceleration of the flow of the water through the runner." The regulation of the hydrodynamic conditions in the runner, for a flow either with or without pressurehead, is possible by the choice of the angles (3^ and 04. If -the entrance into the runner is "shockless," and the dis- charge is "perpendicular" (real discharge speed perpendicular to the corresponding peripheral speed) then = A tgff ~\ \ \ sin ( 8 l ! sin ( ft . a t ) ^ sz /3 t 0.s % Both f t and z/ are functions of the angles a and /3 for a given head. The speed c can naturally never exceed the spouting ve- loicty \/2geH. It would become equal to this velocity if \ sn x cos fl or if ft = 2a t For all angles /3 i which are larger than 204, the speed c 1 will be smaller than the spouting velocity, hence the turbine will be a pressure turbine. For a pressureless turbine the peripheral speed would be This is variable only within very small limits, as cosc^ varies only a little for the values of a t which are used in practice. Hence the peripheral speed of the pressureless turbine is practically given by the head, and consequently the speed N (R.P.M.) can be varied only by variation of the runner diameter D . As prac- tical reasons restrict both the increase and decrease of D 1} the speed of a pressureless turbine is variable only within narrow limits. This is one of the main reasons why nowdays pressure 6 turbines occupy the first place, and pressureless turbines (Im- pulse wheels and Schwamkrug-turbines) are used only when ab- solutely necessary. The speed of the pressure turbine can be varied not only by variation of the runner diameter but also, and very effectively, by variation of the angles ft and o . Combining both means, it is easy to vary the speed of a pressure turbine for a given head and capacity in the ratio of 6 : i. To show how the angles Ol and ft affect the peripheral speed v the factor sin (0i ' sin 0i cos of equation (2) has been represented by a series of curves. Fig- ure 3 gives^the values of this factor for a series of constant bucket angles ft with variable angles o . Figure 4 gives the same values for a series of constant angles o with variable angles ft. For ft = 90 the factor sin (0! aj = i sin 0i cos i for all values of 04. For all angles ft < 90 the value of the rad- ical is smaller than i ; for all angles ft > 90 its value is larger than i. As a low or medium head turbine must, as a rule, be designed for a relatively high speed, all American standard runners, being built for low or medium heads, have ft > 90 and are "high speed runners" Runners with ft = 90 are called "medium speed runners" and those with ft < 90 are called "low speed runners" See Figures 5, 6, 7. Practical reasons, as for instance the necessity of an easy, smooth and yet a short curvature of the bucket, are limiting the increase of ft. The value of ft max 135 will represent good practice and will be found in many of the best American high speed runners. The increase of angle 04 also increases the speed z/i for all angles ft > 90. But to avoid what is called over gat- ing, it is advisable not to assume too high values for 04. Tests show that the capacity of the runner reaches its maximum at a certain gate opening. To open more, is not only useless, but even CO 4 d wrong, as not only the output goes down, but also the efficiency. Although the point of overgating may, by a proper design of the runner, (at the least passage area) be moved upwards, it is not advisable to depend on this too much. Less efficiency than that expected does not disappoint the turbine buyer as much, as when the turbine is found to give less than the expected maximum power. It is not wise to make 04 larger than 40. The hydraulic efficiency may be assumed between 0.82 and 0.84. For e = 0.83, V<# = 5-167 and sin (/?! ax) -7 \/ H sin /?! cos a^ Since for a given runner the value of the radical is a constant, we may write and K v may be called the "speed constant." For 0! = 135, ai = 40, e = 0.83, K v = about 7.0. For giv- en runners, where D lf H and N are known, the speed constants may be calculated as follows : and thus the different runner types may be compared in reference to speed. These constants will also show, whether a further in- crease of the speed is possible or not. Should the speed constant be considerably larger than 7, then it can be assumed with certain- ty that either the guaranteed speed is higher than the best speed (the best speed is the speed at which the runner yields the max- imum efficiency) or that the nominal diameter of the runner is larger than the mean diameter D r CAPACITY. The quantity of water discharging from a given opening in a certain time, say in one sec., is Q = const. X V^ if H is the head at the center of the opening. Hence, for a given opening, 10 Q/V// = constant. We call this constant the "specific discharge" and use for the same the symbol: 1 = = cub. ft. /sec. ( 5) . The specific discharge from an orifice is the discharge in cub. feet per sec. when H = I ft. Take into consideration the entrance area of the runner, Ai = *DiB X 61, where k lt being smaller than i, is a factor, the addition of which is necessary, in order to consider the decrease of the circumfer- ence by the ends of vanes and buckets. The speed of the stream, normal to this entrance area, is the radial speed c r> which, like all speeds of a given runner is in di- rect proportion to -\/H. Cr = fa V/f Passage area X speed of flow normal to the area = discharge. Therefore Q = A^Cr = TTD.Bk.k, V//. Express the width of the guide case in parts of runner diameter D, B = hDt (In runners of the same type k 2 will be nearly the same for all runner sizes.) Then by substitution we obtain Q = irDfktMH = K*DMH, (6) where K q =7rk i k 2 k s . Q Qi ~ A 2 ,/-// - A 2 (7) K q is the "capacity constant" of the runner. The capacity con- stant of a runner is its specific discharge for a runner diameter = i ft. In all runners of the same type K q will be nearly the same, hence the capacity constant is a criterion of the capacity of dif- ferent runner types. FIG. 5. I.OW SPEED RUNNER. FIG. 6. MEDIUM SPEED RUNNER. FIG. 7. HIGH SPEED RUNNER. 12 SPEED AND CAPACITY. Knowing the speed and capacity constants of different runners and runner types, we are not yet able to say to what extent they fulfill the requirements of highest speed zvith highest capacity. We may have two runners with two different values of K q and K v , and yet both runners may be equivalent, when we con- sider capacity and speed together. Another criterion must be in- troduced, which will be a proper combination of K^ and K v . This combination could be made in various ways, but the most conven- ient one was indicated by M. Baashuus and Professor Camerer and may be derived as follows : 7T D l N , *i = ~- = K - V H By substitution we obtain " v i/~^ _ 60 i/ET X Kv \~7f_ 7T X \ 0, The power of a turbine is 550 J > efficiency of turbine. H-P = KQH. As a rule r> is taken , then A: =1/1 1. Q = H-P/KH, and Q t = H-P/KH V// Substitute in the last equation for N, then V H-P whereby z% _ 60 l/Xq AV i/ A" "IT- (9) J^t may be called the "type constant" or "type characteristic"' of the runner. It is a combination of the speed and capacity con- stant, and both determine the type of the runner. The conven- ience of this constant will be apparent, when we write equation 8 in the following form : ~ N \/ H-P ~ K t can be figured directly from the speed, power and head, which data can be obtained easily and seldom differ from actual values. No dimensions of the runner, neither the discharge nor the efficiency need to be known, and yet the efficiency is consid- ered, because the formula Kt = contains K which is a function of rj. Turbines of the same capacity and speed constant, but with different efficiencies, will have a different type characteristic. Hence K t is an absolute criterion for turbines in reference to the aim, "highest speed and highest capacity with best efficiency!' The meaning of K t can be found by assuming H-P = i and "The type characteristic of a runner is the speed in R.P.M. which would be attained by the runner, if it were reduced in all dimensions to such an extent, as to develop I H-P when ^vor king under the head H = i ft." In Germany the term "specific speed" (spezifische Geschwin- digkeit or spezifische Umlaufzahl) and the symbol N s or n s is used for K t . The writer prefers, however, not to use this term for the fol- lowing reasons. The word specific discharge is used for Q = 14 r , the word specific power is used for H-P/H^/H, or for the discharge and power under the head H=i ft. Hence spe- cific speed should denote the speed at H = i ft. TV As NI is used very frequently, the term type characteristic has been chosen for K t . SPEED, CAPACITY AND TYPE CHARACTERISTICS OF THE AMERICAN HIGH SPEED RUNNERS. I. THE DAYTON GLOBE IRON WORKS CO., DAYTON, OHIO. The Dayton Globe Iron Works Co. is the manufacturer of the world known American turbines. The last two types developed by this concern are the New American and the Improved New American turbine. The difference in the design of these two run- ners is seen from figures No. 8, 9, 10, n. In order to increase the capacity, the height has been increased, and the entrance edge inclined. Thus the mean diameter D has been reduced and speed increased, while the minimum passage area at "a" is kept ample. The discharge end of the bucket has also been changed. In order to increase the actual discharge area, and to so decrease the discharge speed, the bucket has been drawn down and shaped spoonlike at the discharge. The radius of the curvature of the spoon at "b" however seems to be rather small. The outward discharge could be made more effective by a larger spoon. Nev- ertheless both the capacity and the efficiency of this runner are very good. The data for a 19" New American runner are: H = 2$ ft. H-P = 8o. N = M 9 . 60 Q = 2128 cub. ft. per min. (a) Speed constant. n.Ft...^. * PI N ^^7339 60 V H 60 1/25 K* = 5.62. Some engineers prefer to express all speeds in parts of the ^pouting velocity FIG. 8. SECTION THROUGH NEW AMERICAN RUNNER. FIG. 9. SECTION THROUGH IMPROVED NEW AMERICAN RUNNER. FIG. 10. NEW AMERICAN RUNNER. FIG. ii. IMPROVED NEW AMERICAN RUNNER. Kv = about 0.7. (6) Capacity constant. 0i = 7.0933. <2i 7.0933 _ "" (c) Type characteristic. 339 Kt = 25 V 7 25 TABLE NO. i. NEW AMERICAN RUNNER. Di Q l H-P! Ni Kv Kci Kt K'v 10 1-95 O.I76 122.4 5-35 2.8l 51.3 0.667 13 2.96 0.264 99-o 5-6i 2.52 50.9 0.700 16 4.80 0.432 80.4 5.6o 2.70 52.8 0.699 19 7.09 0.640 67.8 5-6i 2.8 3 54-2 0.700 22 9.28 0.840 58.4 5-60 2.76 53-5 0.699 25 11.63 1.048 5i-4 5.60 2.68 52.7 0.699 27-5 15-04 1.360 46.6 5-6o 2.87 54-4 0.669 30 18.20 1.648 42.8 5.6o 2.90 55-0 0.699 33 21.60 1.984 39-2 5.63 2.85 55-3 0.703 36 27.50 2.488 35-8 5-62 3-05 56-5 0.702 39 29-83 2.704 32.8 5-59 2.82 54-0 0.697 42 3-024 30.6 5.60 2.72 53-2 0.699 45 40.05 3.624 28.6 5.60 2.84 54-5 0.699 48 46.08 4.080 26.8 5.6i 2.88 54-2 0.700 51 49-27 4.464 25-4 5.65 2.72 53-7 0.705 54 57-93 5.256 23-8 5.6i 2.85 54-5 0.700 57 63-39 5-744 22.6 5-6i 2.81 54-3 0.700 60 73-73 6.680 22.0 5-75 2.85 56.8 0.717 In the same way the constants for the other runner sizes have been calculated and are given in Table No. i. Also the specific speed N l = N/\/H and the specific power H-P = H -L_ - i8 have been added, as both are very convenient characteristics of a runner. They may be used to calculate the speed and power of each runner for any given head. JVi = 339/V25 67.8. H-Pi = 80/25 V25 = 0.64. [At H = 36 this runner would have a speed TV = 67.8 X y 36 = 406.8 R.P.M. and would develop 0.64 X 36 V36 142.2 H-P.] The Improved New American runner, figured in the same way, will be found to have a speed constant which is considera- bly larger than that corresponding to ^=135 and 04 40. As the speed TV (R.P.M.) must be assumed to be correct, (is based on Holyoke tests) and the angles /J x and 04 do not exceed 135 and 40 respectively, (^ is about 135 ; a x seldom exceeds 35), the discrepancy can be due only to the fact that the nom- inal diameter is larger than the mean diameter D^. Measuring several runners, the writer has found that the nominal diameter is taken close to the fillet (see Fig. No. 9). The ratio of the mean to the nominal diameter was found to be about 0.97, for smaller runner sizes. For larger szes this ratio is somewhat smaller. TABLE NO. II. IMPROVED NEW AMERICAN RUNNER. 0i <2i H-Pi Ni Kv K 7-784 29.0 7-30 3-39 81.0 0.911 66 101.80 9-344 26.2 7.26 3-35 80.2 0.905 Table No. II has been calculated with D,=c >-97 X nominal diameter for all sizes. The specific power and speed have been represented by curves, Fig. 12, and they show clearly that the success of the Improved 10 30 40 50 FIG. 12. SPECIFIC SPEED AND SPECIFIC POWER OF THE RUNNERS MANUFACTURED BY THE DAYTON GLOBE IRON WORKS CO. N. A. NEW AMERICAN RUNNER. I. N. A. IMPROVED NEW AMERICAN RUNNER. 20 New American over the New American runner, regarding the aim of highest capacity and highest speed, is remarkable. The dotted curves give the same values, if the nominal diameters are taken as a basis. The average values of the characteristic constants are : New American Improved New American Capacity const. A'a 2.8 3.43 Speed const. Kv.....^ 5.6 7.1 Type characteristic Kt 54. i 79-0 2. THE PLATT IRON WORKS CO., DAYTON, O v SUCCESSORS TO BIERCE CO. To meet the demand of turbines for low, medium, or high heads, this company is manufacturing both radial inward and outward flow, pressure and pressureless tubines. Here only the IMG. 13. VICTOR RUNNER, TYPE A, INCREASED. CAPACITY. Victor turbine Type A for low and medium heads will be taken into consideration. The name under which this turbine generally appears is Cylinder Gate Victor Turbine, as this concern prefers Dj - 10 7G FIG. 14. SPECIFIC SPEED AND SPECIFIC POWER OF THE RUNNERS MANUFACTURED BY THE PLATT IRON WORKS CO. V. S. VICTOR STANDARD CAPACITY RUNNER. V. I. C. VICTOR INCREASED CAPACITY RUNNER. 22 to equip its turbines with the cylinder gate regulating device. There are two patterns of the Victor runner Type A : the Stand- ard Capacity and the Increased Capacity runner. Both have the same speed, but the capacity is different. One of the characteristic features of the Victor runner is its large number of buckets. It is the opinion of the writer, how- ever, that there are no reasons to use so many buckets, either for strength or for efficiency. On the contrary, it is advisable to reduce the number of buckets of low head runners, in order to increase the capacity and avoid small widths of the chutes at the runner hub. Tables III and IV have been calculated in the same way as the preceding tables. TABLE NO. III. VICTOR RUNNER, TYPE A, STANDARD CAPACITY. D l ft H-P* Ni K* K* Kt fC% 12 3-26 0.296 117.4 6.13 3-26 63.8 0.765 15 S.io 0.462 93-8 6.13 3-25 63.7 0.765 18 7-34 0.666 78.6 6.18 3-27 64.2 0.771 21 9-99 0.906 67.2 6.15 3-27 64.0 0.767 24 13-04 1.183 58.6 6.12 3-27 63.7 0.763 27 16.52 1.498 52.0 6. ii 3-27 63.7 0.762 30 20.39 1.849 47-0 6.14 3-26 64.0 0.766 33 24-67 2.237 42. & 6.16 3-26 64.1 0.768 36 29.36 2.662 39-0 6.12 3-26 63.6 0.763 39 34.46 3-124 36.0 6.12 3-25 63.7 0.763 42 39-97 3.624 33-6 6.15 3-27 64.0 0.767 45 45-88 4.160 31-2 6.10 3-26 63.7 0.761 48 52.20 4.741 29.0 6.06 3-25 63.2 0.756 5i If' 93 5-341 27.0 6.00 3-25 62.5 0.749 54 66.07 5-990 25.6 6.01 3.26 62.7 0.750 57 60 73-61 81.56 6.673 7-395 24-4 23.0 6.07 6. 02 3-26 3-26 63.2 62.7 0-757 0.751 TABLE NO. IV. VICTOR RUNNER, TYPE A, INCREASED CAPACITY. D, Qi H-Pt AT, Kv K* Kt K'v 12 3-59 0.325 117.4 6.13 3-59 67.0 0.765 15 5-6i 0.508 93-8 6.13 3.6o 66.8 0.765 18 8.07 0.732 78.6 6.18 3-6o 67.2 0.771 21 10.99 0.996 67.2 6.15 3.6o 67.0 0.767 24 14.35 1.292 58.6 6.12 3.59 66.6 0.763 27 30 33 36 39 18.17 22.43 27.14 32.30 37-91 1.647 2.036 2.461 2.928 3.436 52.0 47-0 42.8 39-0 36.0 6. ii 6.14 6.16 6.12 6.12 3.58 3.58 3-59 3-59 3-59 66.6 67-1 67.2 66.8 66.8 0.762 0.766 0.768 0.763 0.763 23 TABLE NO. IV. Continued. VICTOR RUNNER, TYPE A, INCREASED CAPACITY. A & H-Pi tfi Kv K* Kt K'-i 42 43.96 3.986 33-6 6.15 3-59 67.2 0.767 45 50.46 4-576 31.2 6. 10 3-58 66.7 0.761 48 57-42 5.206 29.0 6.06 3-59 66.2 0.756 Si 64.82 5.877 27.0 6.00 3-57 65.5 0.749 54 72.68 6.590 25.6 6.01 3-59 65.7 0.750 57 80.97 7-342 24.4 6.07 3-58 66.2 0-757 60 89.72 8.135 23.0 6. 02 3-59 65.6 0.751 The average values of the characteristic constants are: Victor Standard Capacity Victor Increased Capacity Capacity const. Kn ................ 3.26 3.59 Speed const. Kv .................. 6.1 6.1 Type characteristic Kt ............ 63.5 66.6 THE JAMES LEFFEL AND co v SPRINGFIELD, o. The James Leffel & Co. manufacture the well known Double wheel, designed originally by James Leffel as a combination of two runners, one being a pure radial, the other a radial and down- ward discharge runner. To increase the capacity this runner had to be bulged out more, and so the new Double wheel was brought out, which, like all high speed runners, discharges both in central and outward direction. The special feature of this Improved Samson Wheel is the partition wall, subdividing the runner into two sections. The upper half is a solid casting, the lower half has steel plate buckets. Although manufacturing reasons such as the wish to use some existing patterns or pattern parts may have been prevail- ing, it is more than doubtful whether the addition of the partition wall is an advantage. Without going any further into this mat- ter, only a few reasons for this opinion of the writer shall be stated. The partition wall increases the friction loss and decreases the effective height of the runner and thus its capacity. Further, it increases the possibility of clogging, and if not built so that it coincides with the corresponding water flow lines, it will decrease the capacity still more. One advantage could be claimed, namely, that the regulation by a cylinder gate will not affect the efficiency of the turbine very much. But this would be true only for a small variation of load, when the cylinder gate closes only the upper part of the runner. FIG. 15. IMPROVED SAMSON RUNNER. 60 70 FIG. 16. SPECIFIC SPEED AND SPECIFIC POWER OF THE RUNNERS MANUFACTURED BY JAMES IvEFFEl, & CO. IMPROVED SAMSON RUNNER. 26 TABLE NO. V. IMPROVED SAMSON RUNNER. Di Q* Jf-P, A r i Kv #, Kt K V 17 671 0.616 92.8 6.86 3-34 72-9 o.86E 20 8.80 0.808 81.4 7.10 3-i6 73-2 0.886 23 11.63 1.064 70.8 7.10 3-17 73-0 0.886 26 14.87 1.368 62.6 7.10 3-17 73-3 0.886 30 19.79 1.816 54-2 7.10 3-17 73-1 0.886 35 26.83 2.464 46.4 7.09 3-15 73-0 0.885 40 35-19 3-232 40.6 7.09 3. 16 73-1 0.885 45 44-54 4.088 36.2 7.10 3-i6 73-2 0.886 50 " 54-99 5.048 32-4 7-05 3-i6 72.9 0.881 56 84.55 6.328 29.0 7.08 3-17 73-2 0.884 62 84.55 7.760 26.2 7.09 3-17 73-i 0.885 68 101.70 9.336 24.0 7.11 3-17 73-3- 0.887 of the characteristic constants are Capacity constant K* = 3.18. Speed constant Kv = 7.07. Type characteristic #1 = 73.1. THE) TRUMP MFG. CO., SPRINGFIEXD, O. The Trump Mfg. Co. is one of the best known turbine manu- facturers, mainly on the foreign market. At the time when European concerns were not willing or prepared to build radial Fie. 17. TRUMP RUNNER. 20 30 40 .50 frO 70 SPECIFIC SPEED AND SPECIFIC POWER OF THE RUNNERS MANUFACTURED BY THE. TRUMP MANUFACTURING CO. TRUMP RUNNER. 28 inward flow turbines, or were only starting to do so, many of .such wheels were installed by -the Trump Mfg. Co. all over the European continent. Like the Samson, the Trump runner has steel plate buckets and in form resembles the other American high .speed runners. TABLE NO. VI. TRUMP RUNNER. >i Q i ' H-Pi Ni Kv #q K* K f * 14 4.12 0.375 96.2 5-89 3.02 58.9 . 0.735 17 6.28 0.570 79-2 5-89 3-13 59-8 0.735 20 10.03 0.801 67.4 5.89 3-6l Co. 4 0.735 23 I3-3I I. 210 58.6 5-87 3-62 64-5 0.732 26 17.21 1.564 51-0 5-78 3-42 63.7 0.721 30 22. 6l 2.135 44-4 5-8o 3-62 65.0 0.723 35 30.86 2.805 38-2 5-8o 3-63 64.1 0.723 40 40.10 3.646 33-6 5-88 3-6l 64.2 0-734 44 48.51 4.410 30.6 5.87 3-62 64-3 0.732 48 57-70 5.247 28.0 5.87 3.61 64.2 0.732 52 63.43 6.158 25.8 5-85 3-37 64.1 0.730 78.59 7.136 24.0 5-87 3-6l 64.1 0.732 61 92.92 8-444 22. 5.87 3-60 64.0 0.732 66 114.28 10.384 2O.4 5-88 3-77 65-7 0-734 The average values of the characteristic runner constants are : Capacity constant K-sD ^J ^ 6 6 6 6 o 6 o o odd do 6 0660 d oo OtCSCHCICN 10 mtovocx) - M S 5 \. & . > ^ MANUFACT'ED BY NAME OF RUNNER TYPE M O CSCSt^MOO lOM r^^ftocivo ^tcO v)v5vDvOto IO ^J- COOOOO M M 00 vO vO to xO M 10 ioto sOt^ O\M Ot^-l^MtO tOOOM VOMO-TJ-OOCO COO cOcOfOcOM* M' CS M 00 CO rO M CO CO CO CO M M M MM 12 I 1 5 JS "TV- - oo<: i ^ e 2 i -S 39 the runner characteristics have been given also in the metric system. For i (ft.) =0.30479 (m), i (cub. ft.) =0.028317 (cub. m.), i (H-P) = 1.01385 (cheval vapeur) = 1.01385 (metric H-P). The following conversion constants are to be used, when con- verting from the foot system into the metric system. a" PN 40 EXAMPLE: 36" Smith runner; see Table XII. Foot system. Metric system. Q! =33.19 0.05I3X33.I9 = L703 Ni =46.4 1/0.552 X46-4 = 84.1 H-P 1 = 3-047 6. 0246 X 3-047= 18.1 K = 3.68 0.552 X 3-68 = 2.032 K? = 7.29 0.552 X 7-29 = 4-025 Kt =81.0 4-447 X8i. =360. FIG. 26. JOIAY MC CORMICK RUNNER. 41 For clearness two sets of curves have been drawn, showing the specific power and speed of the various runner types. In Fig. 27 the curves of the Improved Samson and Trump runner have been omitted, as they would interfere with those of other runners. The curve of the Improved Samson runner, as can be seen from the values of Kq in Table V, would almost coincide with that of the Victor Standard Capacity runner. The curve of the Trump runner with that of the Victor Increased Capacity. The curve of the Leviathan runner has been drawn as dotted line, because the nominal diameters of this runner type s.eem to be larger than the real mean diameters and a correction, like with the Improved New American, could not be made for lack of in- formation. Judging from the value of K t the curve should be in neighborhood of those for the Smith and Improved New Amer- ican runners. For the same reasons, the speed curves of the Leviathan, Im- proved Samson and Trump runners have been omitted in Fig. No. 28. ABBREVIATIONS. S = Smith. I. N. A. = Improved New American. L,. Leviathan. V. I. C. Victor Increased Capacity. V. S. C. = Victor Standard Capacity. N. b. = New Success. N. A. =: New American. M. C. = McCormick. A. H. D. S. = Alcott High Duty Special. R. D. C. = Risdon Double Capacity. At the end it may be emphasized that it was not the intention of the writer to decide which runner type is best. To endeavor to answer such a question would be absolutely wrong. There can not be a runner which would be best for all conditions. In many cases the best efficiency will be the deciding factor, but very fre- quently the variation of the efficiency with the variation of load, and sometimes the maximum capacity or the maximum speed wilj FIG. 27. SPECIFIC POWER OF THE AMERICAN STANDARD HIGH SPEED RUNNERS. 43 determine which is the best runner for a given case. Not seldom, for merely technical reasons, the best runner may be one which for capacity, speed and efficiency occupies a minor position among the other runners. 10 2O 30 4O 50 FIG. 28. SPECIFIC SPEED 01- THE AMERICAN STANDARD HIGH SPEED RUNNERS. 44 AUJS-CHAI/MERS CO., MILWAUKEE, WIS. The manufacture of hydraulic turbines was begun by the Allis-Chalmers Company only six years ago. Following in the beginning the European principle, turbines were designed to suit given conditions and requirements in every instance. But the advantage of standard turbines being fully appreciated, long and exhaustive studies have been made in this direcion by the com- pany's engineers. At the present time, the developing work on Allis-Chalmers standard turbine types is practically completed. In order that all ordinary combinations of speed and capacity may be covered by these "standards," the company is building six different types of radial inward-flow runners for K t = 13 to about 80, and two types of impulse-wheel buckets. Here only the high speed run- ner, Type F, interests us. This type was designed to have at least a type characeristic K t = 68. The first runner of this type, a 3O-in. runner, was tested in the Holyoke testing flume after the first publication of this article in the summer of 1909. The result of this test, although within the expectations of the engineers, was far beyond the anticipations of the company. The following data obtained from the test are interesting. At best efficiency, 82.5%, the turbine developed power at the rate H-P l = 2.28 with a speed Nj== 52. Thus the values of the runner constants are : Allis-Chalmers "Type F." = 3.89 = 6.8 With increased speed, the efficiency went down very slowly, but the output was increased. At speed proportional to N 1 = 59, the power was proportional to H-P^= 2.34. Thus = 3.80 = 7-72 SECOND SECTION A RATIONAL METHOD OF DETERMINING THE PRIN- CIPLE DIMENSIONS OF WATER-TURBINE RUNNERS. S. J. ZOWSKI, ASSISTANT PROFESSOR OF MECHANICAL ENGINEERING. [Copyrighted, 1909, by S. J. Zowski.] The principal dimensions of a water turbine runner are deter- mined from the required speed and capacity and the available head of water. Let D = the mean runner diameter, in feet. v = the corresponding peripheral speed, in feet per second. N = the required rotative speed, in revolutions per minute, then v irDN/6o and D = 6oz/AN (i ) so that when the proper peripheral speed to give good hydraulic performance is known the diameter of the runner follows there- from. Let us assume that the runner is designed in such a w r ay that at its best speed the water discharges from the runner buckets in planes going through the axis of rotation; this is a condition which the turbine designer should always attempt to secure, in order to avoid helical stream lines in the draft-tube. Then the best peripheral speed is given by a simple formula. Denoting the bucket angle by /?, the guide-vane angle by a, as in Fig. i , and the hydraulic efficiency by e n , the formula is : ^x,- where K, = y The curves in Fig. 2 give the values of the second radical for several constant values of bucket angle ft with varying values of * Reprint from Engineering News. Cuts loaned by courtesy of I'.nginecring News. guide vane angle a. The following limits for a and (3 appear reasonable. F IG j SECTION THROUGH RADIAL INWARD-FLOW TURBINE SHOWING RELATION BETWEEN BUCKET AND GUIDE-VANE ANGLES. For a pronounced low-speed turbine /3 = 6o. a = 20; then \ sin (ft -a] \ sin ft cos a = For a pronounced high-speed turbine /3= 135, a = 40 ; then | sin (ft a) \| sin /? cos a ~ For simplicity we will assume that medium-speed runners (/? 90) show a hydraulic efficiency of 84% (giving Ve h g ==5.198), and other types of runner an efficiency of 83% (giving Ve h g =5.167). These values are by no means taken too high for runners of fair design and construction. . Then the speed constant has for the different types the following values : Type of Runner Low-speed ()3 = 60 to 90 ) Medium-speed (P = go) High-speed (/3 = 90 to 135) Speed Constant Kv 4.588 to 5-198] 5.198 (4) 5.198 to 7.006 J 16 EN6.NEWS. Z4- 28 in Degrees. F IG> 2.. CURVES FOR FINDING THE NORMAL PERIPHERAL SPEED OF A TURBINE RUNNER FOR GIVEN BUCKET AND GUIDE-VANE ANGLES. The ordinates give values of i' sin (ft a) \| sin ft cos (i The speed-constant is X sin (ft a) where ^ = hydraulic efficiency; 9 = gravity constant. The desired peripheral speed of the wheel in feet per second is z> = A' v i/ If where // = effective hydraulic head in feet. For very high heads, which naturally will require low-speed runners, it will be wise not to approach the minimum value of /?, but to remain in the neighborhood of 90, for the following reason: The smaller the angle /?, or to be more exact, the smaller the ratio /?/, the smaller is the pressure-head under which the water passes from the guide case into the runner buckets. This reduced pressure will facilitate the separation of the air that is contained in the water, and thus it will facilitate honey-combing of the runner and guide case, so often observed ^ven in turbines otherwise most carefully designed and highly finished. Substituting the values of K v in eq. ( i ) we obtain the follow- ing simple formulas for the runner diameters : Type of Runner Formula for Diameter Low-Speed X V~H Medium-Speed 9 x ] /~H High-Speed X V~H 7 (5) As far as speed alone is concerned, any diameter within the above wide limits could be used. The required capacity, however, will limit the choice considerably. The following considerations deal with the influence of capacity. Let n = number of buckets. n' = number of guide vanes. / = thickness of bucket edge. /' = width of the eddy caused by the guide vane tips and measured on the runner circumference (see Fig. 3). Then the actual entrance area is : where ., n t ri t' and (8) As to the number of buckets used differences of practice will be found among turbine builders. While a few of them use in FlG. 3. SECTION THROUGH GUIDE-VANE AND BUCKET TIP. every case as large a number of buckets as possible, the majority put into a high-speed runner fewer buckets than into a low-speed runner. The following empirical formulas, in which D is ex- pressed in inches, will give satisfactory results. < , Approx. Number Type of Runner ^ of Buckets Low-Speed n = 3.7 }/ D Medium-Speed n = 3.0 ]/' D (9) High-Speed n = 2.2 j / D The number of guide-vanes is very often determined by the simple rule that in every case a few more guide-vanes than buck- ets should be put in (i. e., n' = i.i n to 1.3 n). This rule, how- ever, gives low-speed runners too many guide-vanes, thereby (on account of the small angles a which are used in low-speed turbines) the gate openings become too small and correspondingly the frictional surfaces become relatively large. Therefore it is proper to take account of the guide-vane angle in choosing the number of vanes. The following empirical formulas will give good results. Again taking D in inches, Approx. Number of Guide-vane angle a Guide-vanes 20 and less n' = 2.5 y D 20 to 30 ,,'=3.o|/77 30 to 40 n' = 3.5 I/ D \ -_ 6 Since for manufacturing reasons it is advisable that the num- ber of guide-vanes be even, and possibly divisible by four, it will be best to use an even number of buckets, in order to avoid hav- ing more than one bucket edge coincide with a guide-vane tip at the same time. On this basis the curves in Fig. 4 have beer* drawn. These may be used instead of eq. (9) and (10). OH- 28 20 12 35 31 27 23 > 15 11 7 *=30 \fo40 Num ber a f 6uia ?-Vcrn es a=SO A&~* weci o - ess I \ i \ J 1 ___ i- r - i J J /3-& v fc9, r <7^ \ Num ber o f Bu ckei-3 r ./&- <30 \ 1 r r j \ \ J3- *30to i 35 1 1 r r \ . 1 \ \ r 1 _J R 18 24 250 36 42 48 54 60 66 72 78 84 ( KNQ. NEWS. _ > Diame-Ver of "Runner in Inches. FlG. 4. DIAGRAM GIVING NUMBER OF BUCKETS AND NUMBER OF GUIDE-VANES. FOR DIFFERENT TYPES AND SIZES OF RUNNERS. The eddies caused by the guide-vane tips should be reduced to a minimum. The writer advises strongly to design the guide case in such a way as to get point x (see Fig. 3) outside of the runner circumference. This obviously must be obtained by shap- ing the vane tips properly and by leaving a sufficient clearance between vane and bucket tips. If this is done the entering streams of water will join in a solid ring, and the effect of the eddies on the capacity of the runner will be nullified. The constant K will then have the value. The thickness t varies between %-in. and , T 4-in. for steel plate buckets, and between %-in. and %-in. for cast buckets. The following gives the values of K for three different runner sizes, computed from eq. ( 1 1 ) : * Constant K! -> tf^ m * ^ja Steel plate buckets Cast buckets > j8 60 13 O.QI54 i ft. 90 ii f.= }^ in. 0.9635 t = Y 4 \n. 0.9270 135 0.9671 0.9542 60 25 0.9600 4 ft. 90 21 t = 1 A in. 0.9652 f = 54 in. 0.9652 135 15 0.9649 0.9298 60 33. 0.9557 7 ft. 90 27 t Y 4 in. 0.9744 t = } in. 0.9616 135 19 0.9745 0.9618 For simplicity we shall assume that K 1 has the uniform value 0.93 for all runner types and sizes, with the distinct understand- ing however that in the final computation the exact value is to be introduced, and also, if necessary, the item n' t' be considered. The capacity of the turbine depends very directly on the ratio B/D, or K 2 . As a matter of fact it is this ratio which finally determines the limits for the application of radial inward-flow turbines. Turbine manufacturers are still struggling with the problem of extending these limits in both directions ; therefore no definite maximum or minimum values can be given. Present-day good practice indicates that until further advance is made it is safe to fix the limits of breadth of runner at 1/30 and l /2 the diameter. The minimum value depends on the purity of the water. The maximum value which could be allowed de- pends on the design of the runner, for it is evident that the larger the width of the runner, the more difficult it is to secure the necessary passage area at the point where the water turns from 8 radial to axial direction. In the opinion of the writer it is pos- sible to go somewhat above l / 2 with the ratio of width to diam- eter, but then the runner must be bulged out sufficiently. We have classified all runners under three types with refer- ence to speed. It is customary to make a further classification; with reference to capacity. Here also we distinguish three types. The latter classification is based on the proportions of the runner profile, or the ratios of ( i ) diameter at entrance point of buckets, (2) diameter at exit point of bucket, (3) diameter of neck of draft-tube. These diameters (Fig. 5) will be denoted by D, D', and D" '. Their ratios depend mainly on the factor K z , or B/D. Type L, or the low-capacity type, comprises all runners in which the draft-tube diameter D" is less than the bucket exit diameter D' ', or at most equal to it, and in which B/D lies be- tween 1/30 and y%. Type II., the medium-capacity type, com- prises runners in which D" is larger than D' but smaller than the entrance diameter D, and in which B/D lies between y% and y\. Type III., or the high-capacity type, comprises all runners in which the draft-tube diameter D" exceeds the bucket entrance diameter D, and in which B/D is between y+ and l / 2 , It is self-evident that high heads will require runners of both low-capacity .and low-speed type, while low heads will call for high-capacity high-speed runners. In other words, small values of K 2 naturally go with small values of K v , and large values of K 2 go with large values of K v . Mistakes in this respect are fre- quently made by manufacturers of low-head turbines, when they occasionally build a high-head turbine, by giving the runner buck- ets of such turbines the same entrance angles (/?>9o) as are used on their low-head turbines. This increases the peripheral speed so much that the runner diameter, and consequently the size of the whole turbine, must be increased considerably in order to obtain the required rotative speed. A runner is characterized as to its capacity by the so-called capacity constant, (12) V HD* IO The values of K q for the different runner types can be found as follows : Area X Speed = Discharge ; therefore, Q = -n-K 1 K 2 D-c f (13) where c r is the radial component of the entrance velocity c (see Fig. i). This component is given by Cr = c sin a =i/ e h g si n(-a}cosa sin a = ** H ( J 4) Combining the last two equations, we get Q = - K\ K z A' 8 1/77 D* = A* q 1/77" D* (15) or, K* = irK 1 K2K 3 (16) in which sin ft Sin(l3 -a)cosa sin a In Fig. 6 is drawn a series of curves which give the values of the second radical of eq. (17) for the same angles ft and a for which the curves in Fig. 2 were drawn. Multiplying the appro- priate ordinate taken from Fig. 6 by V^iTJ, we obtain K 3 . The other coefficients (K and K 2 ) having been found previously, eq. (16) at once gives the value of the Capacity Constant K q . Using the same limiting values as before, to define the several types of runner, we find that the Capacity Constant has the following range : Type of runner Range of K* Low-speed low-capacity 0.21 to 0.89] Medium-speed medium-capacity 0.89 to 2.19 \ (18) High-speed high-capacity 2.19 to 4.66] II 0.7 0.6 - ^ 0.4 1 0.3 0.2 #%xx / y X * x X x wor 5 /0 / 16 20 24 28 32 cc in Degrees. 36 40 i 6, CURVES FOR FINDING RADIAL ENTRANCE VELOCITY FO.* GIVEN BUCKET AND GUIDE-VANE ANGLES. The ordinates give values of a) COS a The factor i" 3 = I/ e\\ g ^\ sin (ft a) cos a sin a where ^ = hydraulic efficiency ; g = gravity constant. The radial entrance velocity in feet per second is where H = effective hydraulic head in feet. 12 By introducing these values in eq. (12) and solving for diameter we obtain the following simple formulas: Diam. in terms of discharge Type of runner per i-ft. head Low-speed low-capacity (2.20 to 1.06) \/~0i ) Medium-speed medium-capacity (1.06 to 0.67) ^/~Q[ >- (19) High-speed high-capacity (0.67 to 0.46) -\J~Q[ ) These formulas, together with eq. (5), will determine which range of diameters can satisfy both the requirements as to speed and capacity. Evidently only those diameters are suitable which satisfy both eq. (5) and eq. (19). The procedure can be further simplified by the use of a con- stant which the writer has called Type Characteristic (see Eng. News, Jan. 28, 1909). Its formula is: N X V H-P 60 Jv v X |/5q X V~K Kt = = (20) H i^H TT where H-P 62.42 X turbine efficiency ~ QH 550 For a turbine efficiency of 80%, K==i/n, which may be used as a fair average value for the present purpose. With this figure, and the values of K^ and 'K v , tabulated previously, we obtain the following ranges for the Type Characteristic : Type of runner Type characteristic 7vt Low-speed low-capacity 12 to 28 ] Medium-speed medium-capacity 28 to 44 } (21) High-speed high-capacity 44 to 87 J With these formulas the determination of proper runner type and diameter is very simple. We proceed as follows : From the given values of horsepower output H-P, speed of revolution A 7 , and hydraulic head H, compute the type character- istic K t by eq. (20). If the resulting figure is between 12 and 28, a radial inward-flow turbine is possible, and the runners will have to be of the low-speed, low-capacity type, with B/D = 1/30 to J/6, /?=:6o to 90, and a profile which will fall between profiles A and B of Fig. 5. If the value of K t is between 28 and 44, the runner will have to be of the medium-speed, medium-capacity type, with B/D = Y& to ^4, /? = 9o, and a profile which will fall between profiles B and C of Fig. 5. If the value of K t is between 44 and 87, the runner will have to be of the high-speed, high-capacity type, with B/D = % to J/>. /3 = 9O to 135, and a profile which will fall between profiles C and D of Fig. 5. If the value of K t is smaller than 12, and it does not seem advisable to make B smaller than 1/30 of the diameter, a radial inward-flow turbine is not possible, and an impulse wheel will have to be used. If the value of K t is larger than 87, a multiplex turbine must be built. That is to say, a case for which K t is found to be, say, 174, which is 2 X 87, would require a quadruplex turbine of which each runner is designed for K t = 87. Knowing the type of runner it is easy to find the other prin- cipal dimensions, as now we can not make a mistake in the choice of the rational values for the different constants in our equa- tions. A few words must be added, however, in reference to the draft-tube diameter D". The flow velocity c" at the point where D" is measured, the "upper draft-tube area," is, in properly designed runners, more or less the same as the flow velocity in the discharge area of the runner. This velocity represents a direct loss; but the loss is partly recovered by the conical lower part of the draft-tube. In low-capacity runners there is no diffi- culty in reducing the discharge loss to a minimum in the runner itself. In high capacity runners, on the other hand, larger dis- charge losses must be allowed, as otherwise the runner would have to be bulged out too much. Expressing the discharge- loss measured at the upper draft-tube area in parts of the total head, the following values will represent good practice. Type of runner Low-speed low-capacity Medium-speed medium-capacity High-speed high-capacity Discharge Joss in terms of total head (0.04 to 0.06) H ] (0.05 to 0.08(0.1 ))H \ (22) (o.oS to 0.15(0.2) )HJ 14 NUMERICAL EXAMPLES. The following specimen calculations will illustrate the application of the method set forth in this article : I. Given H = 100 ft. ; H-P = 2500 HP. ; TV = 250 r. p. m. ii X 2500 Assuming 80% efficiency, Q = = 275 cu. ft. per sec. From eq. (20), 250 X V 2500 A't = = 39-55 100 / 100 Comparing this with the sets of values given by eq. (21) we see that the runner has to be of the medium-speed, medium-capacity type, with bucket angle (3 = 90. Therefore, from eq. (5), D = r Take D = 4 ft. The number of buckets is 21, from the chart Fig. 4. The thickness of bucket edge, using cast buckets, is X~ m - The number of guide-vanes (from Fig. 4) is 20, but the guide case shall be designed in such a way that t' = o giving for the free circumferance TT D n t = TT X 48 21 X 1 A == : 45-55 ms - = 12.16 ft. The type characteristic, 39.55, is nearer the upper limit for type ii than the lower limit; assume, therefore, B = l /\ D = I ft., and D" = D =4 ft. Then the free entrance area I X 12.16 = 12 :i6 sq. ft. Consequently, Q 275 12. l6 = 22.62/2. per sec. For ft = 90, c r = c = V ehg H. tan a. Hence, assuming eh = 0.84, tan a - , = = o 435 V e*g H. 51-90 whence a = 23 30'. The upper draft-tube area, if the shaft does not extend into the draft-tube, is *4 v X 4~ = = 12.57 sc l- ft- Consequently the discharge velocity is c" = 275 = 21.86/2. per sec. 12.57 and the discharge loss percentage is 15 22.86* which value is satisfactory, according to eq. (22). II. Given H = $6 ft.; H-P = 4,000 HP.; N = 200 r.p. m., so that Q = 1,222 cu. ft. per sec. It is required that the turbine be capable of sustaining 15% overload. The type characteristic is A- t = 4 -= 143.5 36 j' 36 Comparing with eq. (21) we find that we must use a quadruplex turbine, with runners designed for = 71.8 This requires Type III, and consequently, by eq. (5), Since the value of K is nearer the maximum than the minimum for Type III, take Then the speed constant is TT D N __ TT X 3-75 X 200 _ 6 545 v "~ 60 \/~H 60 v'~3^ Assuming eh = 0.83, y~e^g is found to be 5.167 then, in (P a) sin p cos a From the curves in Fig. 2, we see that we could use /3= 135 = 3I o. or p =I t a = =3 5 3 o'. We choose the former com- bination,' because the turbine must be capable of carrying over- load. For these angles the value of sin ' X sin a \ sin (ft a] cos a is 0.475, from Fig. 6. Consequently the radial entrance velocity c r = 0.475 X V e h g-H = 0.475 X 5-167 X V36 -= 14706. The number of buckets, from Fig. 4, is 15. The guide case being designed so that t' = o, the free circumference is if) ^ I36 ' 3 ins - = Hence, 1 1.335 X B Xi4-7o6= 1222/4, whence B = 1.823 ft. Taking B = 22 ins., the ratio of width to diameter is 22/45 1/2.045, which value is satisfactory. Take into consideration the runner nearest the generator and assume that the shaft projecting from this runner into the draft- tube is 10^2 ins. in diameter; then the upper draft-tube area in square feet is 10) 2 \ J_ 4/144 4 for D" taken in inches. Assuming an allowable draft-tube loss of 0.14, we have := 0.14 H, or c" = V 29 X 0.14 X 36 = 1 8 ft. per sec. the draft-tube velocity. Then the diameter of the draft-tube must be found from i 44 4 or ~ D"* 1222 144 TT x io.5 2 - + - - = 2530.59 sq. ins. 4 4 18 4 whence D" = 56.8 ins. Using 57 ins. for round numbers, the discharge loss is reduced to 0.138}!. The guide case and the regulating device shall be designed so that maximum gate-opening corresponds to the guide-vane angle a = 40. Assuming for the present that eq. (14) for radial entrance velocity is true up to the maximum gate opening we find with the aid of the curves in Fig. 6 that max. c r = 0.618 ^ whereas at normal gate opening we found C T = 0.475 ~\/ehgff. If we further assume that the efficiency remains unchanged, the discharge at maximum gate-opening 40 will evidently be or, in other words, the turbine is capable of 30% overload theoretically. Practically the overload capacity will be somewhat smaller, as the assumptions made are not correct. Formula (14) 17 is valid only for the "normal" gate opening; i. e., that for which the turbine was originally designed and at which the water dis- charges from the runner buckets in planes going through turbine axis. Further, the hydraulic efficiency always is. smaller when the gate opening is different from the "normal" gate opening. This is not the place to go any further into the difficult ques- tion of the variation of speed, discharge and efficiency with vary- ing gate opening. Suffice it to state that, judging from actual tests we may expect in the case at hand that the required over- load, being only half of the overload as figured before, will cer- tainly be obtained, very likely before the gates are opened to the full 40 angle. It is hoped that the above outlined method of computing water turbine runners will be useful to many engineers and will help to eliminate turbines of irrational types and proportions. It goes without saying that the values of the different constants indicated by the writer, must not be adhered to too closely, and that the boundaries between the different types are not sharp, but may be changed more or less according to the designer's preference. Thus it would not make much difference whether a runner of /e t = 43 were designed with D" = D, or with D" somewhat larger than D. T8 TIIK TYPE CHARACTERISTIC OF IMPULSE WHEELS AND ITS USE IN DESIGN. BY S. J. ZOWSKT. [Copyrighted, 1910, by S. J. Zowski.] A previous article by the author, entitled "A Comparison of American High-Speed Runners for Water Turbines,"* the first of this series, gave the method of deriving a characteristic called the Type Characteristic, by means of which a convenient classifi- cation and comparison of existing runners and runner types is obtained. In a second article, entitled "A Rational Method of Determining the Principal Dimensions of Water-Turbine Run- ners, "t the second of this series, the convenience of using the Type Characteristic for computing new runners was demonstrat- ed. Both articles, however, dealt with the radial inward-flow turbine only. But as the type Characteristic renders equally good service with all other turbine classes, it is proposed in this article to investigate the impulse wheel in a similar way. The following notation will be used : c/ = the actual diameter of the jet. In this country only circular noz- zles are used, therefore square jets will not he considered at all in this article, although such jets would not change the theory materially. This is not the nozzle diameter, but the actual diameter of the jet at the contraction, if there is one, or in any case at the minimum section. D =. the nominal wheel diameter, /'. c., the diameter of the circle tan- gent to the center line of the jet, which circle might appropriate- ly be called the "impulse circle." Some engineers call this circle the "Pelton circle," in recognition of Mr. Peltoirs contributions to the development of the impulse wheel. c the velocity of the jet. r = the peripheral velocity of the wheel, measured on the impulse circle. 77 - the net head acting in the nozzle. li-P - the power of the wheel, in horsepowers. ,V = the rotative speed of the wheel, in revolutions per minute. Unless specified otherwise, the foot and the second are the units. * Engineering News, Jan. 28, 1909, pp. 99-102. Michigan Technic, Jan., 1910. t Engineering News, Jan. 6, 1910. Michigan Technic, June, 1910. I 9 DERIVATION OF TYPE CHARACTERISTIC. The jet velocity c may be expressed ni terms of the head as follows : (l) For nozzles of good design and workmanship, the velocity co- efficient / c may be taken as 0.97. The discharge of the nozzle is =6.3/0 V 2g = 3.77 corresponds to the speed constant Kv = 4.588 to 7.006 for radial inward-flow turbines. t The corresponding value of #N for radial inward-flow turbines is 87 to 134. 21 LIMITING RATIOS OF JET DIAMETER TO WHEEL DIAMETER. It is obvious that there will be a certain maximum value for this ratio, because, going for instance to the extreme, a wheel diameter equal to the jet diameter, or d/D = I, would evidently be impossible to use. Therefore there will be a certain maximum value for K t which cannot be exceeded by an impulse wheel using a single jet. A minimum value for K t does not exist, theoretically, as the ratio d/D could be decreased to any desired amount. In practice, of course, we would come to a limit also in this direction, on account of the limitation as to the size of a wheel. But actual problems would never bring us near this limit, as a wheel of given capacity would never be required to have so low a rotative speed (hence low K t ) as to require wheels of diameter too large to be built or operated successfully. We therefore do not need to con- sider the question of the minimum value for K t at all. The question of the maximum value for K t , however, is of great importance for practical application, as this will determine the number of wheels or number of nozzles required for the given power and speed. To answer this question, we need, since K t is a function of d/D, only to find the least wheel diameter that can be used satisfactorily in connection with a jet of given diameter. The sketches, Figs. I, 2 and 3, bring out the chief conditions involved. As bucket B progresses from the position shown in Fig. i, the jet will be split in two parts, one feeding bucket B, the other proceeding with the jet velocity c in its initial direction. When bucket B reaches the position shown in Fig. 3, the water particle which was at m when bucket B separated it from the main jet will have moved to x. Similarly, the water particle which was at n when the bucket separated it from the main jet (Fig. 2) will have moved to y (Fig. 3). These distances are c , t f c n' o' = n'o'X -= o Jr- - ^ 22 The curve xyz, Fig. 3, shows thus the end of the jet which has been cut off from the main jet, in its correct instantaneous posi- tion at the time when the entrance edge of bucket B is at o. As the wheel moves farther, the separated jet will move, too; when the bucket B reaches, for instance, the position of bucket A in Fig. I, the curve xyz (Fig. '3) will be moved to ^\y i s i (Fig. i). These distances are C , /c Ml' P' m p ;<-=/> - = ^j It is apparent that, in order to utilize the entire energy con- tained in the jet, no particle must slip through, without giving up its energy to the buckets. Therefore, the wheel and buckets must be designed so that the last particle of the jet separated by bucket B from the main jet, namely particle z, will reach bucket A and will be fully deflected by bucket A before this bucket, or that point of the bucket at which the last particle should discharge, leaves the sphere of the jet. While it is a simple matter to determine the position of the bucket A at the moment when the last particle reaches it, it is very difficult, if possible at all, to determine the position at which the last particle has just completed its flow through the bucket. A great deal of judgment must be used in this respect, and, there- fore, special care is advised in all cases where only a short time is left for the bucket to remain in the sphere of the jet after the last particle has entered. This time can be increased in two ways: (i) By decreasing the time necessary for the last particle to reach the bucket A. This is secured by decreasing the pitch of the buckets, thus short- ening the sections of jet cut off by the buckets. (2) By increas- ing the total length of time during which each bucket remains in the sphere of the jet, or in other words, by increasing the length of the arc oOj. In decreasing the pitch or increasing the number of the buck- ets, however, we soon come to a limit. From Fig. 4, showing two consecutive buckets in section, it is apparent that the smaller the |<- Length o-f ' Je+ which flows t - r, g . 3. FIGS. 1-3. RELATION' OF BUCKET AND JET IN THREE DIFFERENT POSITIONS. 24 pitch, the larger the angle must be in order that the water may freely discharge from the bucket without hitting the following bucket. But with increasing , the lateral 'component c'of the FIG. 4. PATH OF JF,T DISCHARGING FROM BUCKET. water velocity grows larger, and this means increased discharge (c'Y loss ; hence the wheel efficiency is decreased. Efficiency 25 demands that we should make angle as small and the pitch as large as possible. Allowing a certain discharge loss as the maxi- mum, we cannot reduce the pitch beyond that which corresponds to this discharge loss. Furthermore, practical considerations will not permit using an excessive number of buckets. If, for in- stance, the buckets are bolted to the wheel disk, which is the gen- eral practice in this country, the flanges must have a certain width, thus giving a minimum pitch which may not even be as small as that resulting from the value of the discharge loss that we are willing to allow. In other words, decreasing the pitch of the buckets, for the sake of lengthening the time left for the bucket to remain in the sphere of the jet after the last particle has entered, can be carried only to a certain limit. Beyond this limit the flow conditions of the last particle can be improved only by lengthening the arc oo . This we can se- cure by increasing the height of the arc, i. e., by making the buckets longer. But here again we are not able to go very far, as it is obvious that the buckets cannot be made excessively long in comparison with the wheel diameter. We come thus to a limit also in this direction, and if now the flow conditions are not satisfactory, the last but most effective means will have to be used, namely that of increasing the length of the arc by increas- ing the wheel diameter proper, or decreasing the value of K t . This, it is believed, shows clearly the nature of the impulse- wheel problem, when for a given size of jet the least possible wheel diameter, or the maximum value of K t , is to be determined. MAXIMUM TYPE CHARACTERISTIC. In the summer of 1908 the writer had to deal with this prob- lem quite extensively, when he was developing a type of buckets which were to be used as "standards" and which would reach the minimum value of K t allowable for radial inward-flow turbines, with as few wheels or nozzles as possible. After all means to improve the flow conditions for the last particle, as described above, had been exhausted ; that is to say, after the pitch had been reduced to a minimum and the length of the buckets had been increased to a maximum, the least wheel diameter with which a perfect reaction of the last particle could be obtained was about 10.5 times the jet diameter. With wheel diameter reduced to 9 26 times the jet diameter, about 2% to 3% of the jet would not react fully. On account of the necessity of making several arbitrary as- sumptions in order to be able to find the position of the bucket at the time when the last particle of water has completed its flow through the bucket, the results involve some degree of uncer- tainty in the neighborhood of the critical point. Therefore, the values found by the writer must not be looked upon as being mathematically exact. The question whether the wheel diameter should not be brought below D = io.$d or whether it should be allowed to go FIG. 5. PATH OF LAST PART OF JET. somewhat lower, say, to D = gd, cannot be settled by a general rule, as efficiency is not always the only deciding factor. There will be many cases in practice where the advantages of higher value of K t , and consequently reduced number of wheels or nozzles necessary for the given power and speed, will justify a certain additional loss by imperfect reaction. A loss of 3% will often be allowable to secure these advantages. Therefore, let us establish as limiting values : d (2) ~r ) 2j- = - , making Kt about 5 ; for perfect reaction. i , making Kt about 6; when loss from imperfect reaction can be about 2% to 3%. 27 The writer does not advise trying to carry K t higher than 6, as the loss due to imperfect reaction increases rapidly. It must be borne in mind, however, that even values of 5 or 6 can be ob- tained only by buckets especially adapted for such high values. These buckets must be considerably longer than standard Pelton or Doble buckets, for instance. In these special buckets, which may appropriately be called high-speed buckets, the part X, Fig. 5, is particularly important. The smaller the wheel diameter the more inclined will be the bucket relatively to the jet at the moment when the last water particles enter, and consequently more water will be discharged at part X. This makes it necessary to design this part of the bucket with the same care as part Y, where the first and main part of the jet discharges; the bucket must be kept sufficiently deep at X and the angle kept sufficiently small. Also another point must be mentioned in this connection : Because the increased length of the bucket makes the flow conditions at the entrance in the bucket less favorable, the practice of moving the entrance edge toward the center, as is done on all modern buckets of good design, be- comes a necessity for high-speed buckets. In the article "A Rational Method of Determining the Prin- cipal Dimensions of Water Turbine Runners," it was shown that the minimum value of K t for radial inward-flow turbines is about 12. With favorable conditions, slightly smaller values can be reached, down to about 10. (The Allis-Chalmers Co., of Mil- waukee, has built a radial inward-flow turbine for the Palmer Mountain Tunnel and Power Co. for the following data: H- 350, H-P = 6$o, N = 6oo; these make K t = io.2.). If now the maximum value of K t for impulse-wheels is 6, it is apparent that we can equal the minimum limit of radial inward-flow turbines by using four single-nozzle impulse-wheels, or a four-nozzle wheel ; thus the entire field of requirements for water-turbines can be covered satisfactorily by these two turbine classes alone. The conditions in this direction have been improved recently by the development of two-stage radial inward-flow turbines, a few of which have been in successful operation in Europe. These 28 two-stage turbines extend the field of the radial inward-flow tur- bine in the neighborhood of the minimum limit.* SUMMARY. If the value of K t computed from the given power, head and rotative speed is smaller than 12, but larger than 6, a multiple impulse-wheel must be built. .. If K t is equal to 6, a single impulse-wheel can be built, but in this case an additional loss of 2% to 3%, due to imperfect re- action of some part of the jet, must be reckoned with. If K t is 5 or less, a single impulse-wheel can be used without any additional loss due to imperfect reaction. However, as long as K t is larger than about 4.2, the design must be very careful, and the buckets must be increased in length as compared with the usual standard buckets. Best conditions for the design prevail when K t is between 2.5 and 3.5. After the question of the number of wheels or nozzles has been decided upon, the jet diameter will be found from formula (s). d (in inches) =: 16.1 V H-Pi where H-P^ is the power of one jet per foot of head, in horse- power. The wheel diameter will be found from eq. (12). n 53-67 d ~~KT~ which value must check with that given by eq. (9) : D = 72 T/7? N * A two-stage turbine for H, H-P, N requires runners of N 1/0.5 H-P _ N 1 At =i A = y o Thus, if a single-stage turbine has a runner of Kt = 12, the runners of a two-stage turbine for the same total power, head and speed would be of Kt = y / lTx 12 = 20.184. Or, if we consider 12 as the minimum value of Kt for radial inward-flow runners, we could, in using a two-stage turbine, reach by radial inward-flow turbines a type characteristic as small as 12/1.682 = about 7.2. - 29 NUMERICAL EXAMPLE. Given H = ^oo ft.; H-P = 7,500 H. P. ; N = 400 r. p. m. Determine the arrangement and dimen- sions of the turbine. 750 =0.2778 900 V 900 400 Ni = -=- = 13-333 1/900 K* = 13-333 V 0.2778 = 7.035 This value is too small for a radial inward-flow turbine and too large for a single impulse-wheel. Choosing, therefore, one wheel with two nozzles, or better, two wheels with one nozzle each, K t for each jet will be reduced to which would require buckets of very careful design and some- what elongated shape. On the other hand, if we decide to use four jets, i. e., either four wheels each with one nozzle, or two wheels each with two nozzles, then K t per jet would be reduced to V 4 Both solutions are possible, and in deciding between them the advantages and disadvantages of each should be carefully con- sidered. The first solution will give us a smaller and cheaper unit, but lower efficiency, whereas the second solution will give us a considerably larger unit, which will cost more and require more space in the power-house, but which will have better effi- ciency. (i) The first solution will require a jet of diameter d (in inches) = 16.1 A/" 1 T^ =6 ins ' and a wheel of diameter D (in inches) = 53 ' 6? X 6 =64.79 ins. which checks with D (in feet) = 7 " l/9 = 54 ft- - 64.8 ins. 400 30 (2) The second solution will require a jet of d (in inches) = 16.1 =4.24 ins. and a wheel of D (in inches) = 53-6 7 X 4.243* ns which checks with the value obtained before. If other values for / c , / v and e seem to be more appropriate than 0.97, 0.47 and 0.80, respectively, the general formulas (3) and (7) should be used in computing d and D. 75% FIG. 6. PERFORMANCE; OF IMPULSE WHEELS : VARIATION OF LOSSES AND EFFICIENCY WITH TYPE CHARACTERISTIC. DISCHARGE LOSS. At the end an interesting relation between the discharge loss, the angle 0, the Type Characteristic, and the pitch or number of buckets shall be derived. Assume that the bucket is in such a position that the center of the discharging water stream is on the impulse circle ; then the peripheral velocity of this center v' , is equal to the wheel ve- locity v. v' v /V V 2gH = 0.47 \/2 g H The discharge is, by Fig. 4, Q_= 2 b w' (p sin ft t~) = f c \/~2g~H~ Also, cos p cos ft Substituting the last value in the preceding expression, sin /> - t) = Neglecting t as small compared with p sin 0, we get or, substituting for p its value * D/n in terms of the number of buckets n, ct*nf c n d d / c "'"8" ^T (I3) Since - = - - , this becomes D 53.67 n At a /c tan ^ = : l^l6- In regard to the ratio of , we possess no definite data, as no b satisfactory experiments have been made in this respect. Tur- d bine designers customarily assume b = 2d, or = /^. Putting b this into our equation, and also 0.47 for / v , and 0.97 for / , we obtain a _ n -**t (\A\ 3 2 Thus we see that the minimum possible angle /? is in direct proportion to the number of buckets used and to the value of K if which is a proof of the statement previously made, that for effi- ciency the number of buckets should be made as small as possible, because the discharge loss increases with increasing p. The true or lateral discharge velocity of the water, c' in Fig. 4, is n K\. d c v tan = vtan /3 = 1T/c and the discharge loss, in terms of the energy supplied, is d - - /nKt d , V -f< (15) d For = y 2 and f '= 0.97, we obtain b Discharge loss = ( * * 866 The discharge loss varies as the square of the Type Charac- teristic and as the square of the number of buckets, if the wheel is designed closely according to theory, i. e., if (3 is made exactly equal to the required minimum. NUMERICAL EXAMPLE. Take a 2^-in. jet and assume that, as K t varies, the shape of the buckets is altered so as to get in each case the least discharge loss which can be obtained by using a certain number of buckets (the number of buckets being re- duced to that required in order that loss by imperfect reaction may be zero up to K t = $.o, and 2^2% at K t = 6). Assume further that, at K t = 3 or D = iSd =45 ins., the wheel efficiency is 85%, and that the loss due to bearing friction, resistance and friction in the buckets remains unchanged. Then the following table can be figured : The discharge loss and loss at reaction, and the total efficiency, are plotted in Fig. 6 from this table. 33 O vo rj- ^ co w M o _o; oq oq co oq oo oo t^ '3 d d d d d d d ill oooo-o o > 8 q q q q q dooooo O O JJJ i^ 1 ^^ "^" >OOO