US1315232A

US1315232A - Hydeaulic bbaet-tubb

Info

Publication number: US1315232A
Authority: US
Publication date: 1919-09-09
Anticipated expiration: 1936-09-09

Description

L.1F. MOODY.

HYDRAULIC DRAFT TUBE.

APPLICATION FILED ]AN.22 1919.

Patented Sept. 9, 1919.

3 SHEETS-SHEET I.

L. F. MOODY.

HYDRAULIC DRAFT TUBE.

' APPLICATION FILED JAN.22 I919- aaiaaa.

" To all whom it may concern:

Be it known that l, LEWIS PERRY Moon r, a citizen of the United States, residing at Philadelphia, in the county of Philadelphia and State of Pennsylvania, have invented certain new and useful Improvements in "discharging water must have its direction turned into the horizontal and it is essential for good eificiency at the same time to convert the velocity head of the water leaving the runner into pressure head by the time it reaches the point of final outlet, so that the energy of the discharge will be utilised to lowerthe back pressure on the turbine runner with substantial gain in power. v t

3. Since only a limited depth is available in practice below the runner of such a turbine restrictions are imposed upon the dimensions of the draft tube, and in prior constructions'the water has been turned into the horizontal by bending the tube into an elbow or by directly impinging the vertical stream against a horizontal surface. Both of these methods are objectionable in that they necessitate sudden changes in direce tion and velocitypf the water and sharp relative shifting btween parts of the stream retarding and wasting the, .energy of the discharge with a resultant increase in back pressure and a loss of power. Particularly serious losses occur in such constructions when the disturbances are aggravated by imtial non-uniform'flow, such as is the ordinary condition of Water leaving the turbine runner, where there are turbulent eddies and cross currents and often a whirling of the stream as "a whole tending even to form a central cavity.

4. The object of this invention is to provide a draft tube which will gradually and continuously turn the discharge into the horizontal and simultaneously convert its velocity head into effective pressure head without abrupt changes in speed or direction at any point or the formation of wastel n'nmntre manner-rune.

fu-l disturbances. This is accomplished by progressively spreading the discharge downwardand curving it outward into the horizontal plane symmetrically around a central expanding conical core, so that all trans verse elements; of the stream go through substantially the same gradual change in direction and velocity together. The stream lines are thus maintained substantially parallel at each point as in a straight tube and are simply bent outward symmetically around the axis without abrupt change in direction at any part of the stream. Eddies and dis turbances are smoothed out and any whirl- .ing of the stream is usefully expended in expanding it.

5. Simultaneously the velocity of the outflow is lowered by a gradual increase in the transverse sectional area of the tube passage and upon the dimensions of this passage depend the exact rate of this increase and the efiiciency of the draft tube. The importance of the exact .rate of increase in sectional area has been fully demonstrated in the case of straight draft tubes and rules for the most eflicient designs under given conditions have been established. Since in the draft tube of this invention, all the stream elements curve simply from their straight path, all parts of any given transverse plane have nearly the same velocity and the longitudinal streamlines are substantially parallel. With this gradual curvature there are thus maintained conditions of How closely similarto those in a straight tube and'by allowing for the curvature and Specification of Letters Patent. Patented @eept. a, ll@l9. I

Application filed January W, 1919. Serial No. 272,432. I

spread of the new passage its successive cross-sections may be calculated the same as they would befor equal distances'of flow in a straight tube. It is therefore possible to apply the established rules for the rate of increase in area to the new conditions and definitely determine the contour of the curved tube walls for full eiiiciency.

6. Furthermore where the ractical limitations of the installation ma e desirable a shorter, sharper bend of the tube, the resulting variations in flow due to this sharper curve occur in such a regular manner in the draft tube of this invention, that accurate allowance can be made for-them and-elliciency and power maintained.

7. lln the accompanying drawings,

Figure 1 is a central vertical section of a draft tube formed according to this invention' Fig. 2 is a similar diagrammatic view of a straight draft tube;

Fig. 3 is a similar diagrammatic viewof a tube of this invention illustrating a method of determining its dimensions;

Fig. 4 is a horizontal sectional View on line 44 of Fig. 5 of a draft tube of this invention showing the discharge passages to the tail-race;

Figs. 5 and 6 are vertical sections respectively on lines 55 and 66 of Fig. 4, and

Figs. 7 and 8 are diagrammatic views illustrating the manner of applying the .correction to the width of a bent channel and to that of asmall section of a flared pipe or draft tube.

Figs. 9 and 10' are sections illustrating a spiral conduit that may be employed in connection with my improved draft tube.

8. This invention may be advantageously applied to draft tubes molded in a concrete substructure as shown in Fig. 1, where A is the vertical shaft turbine runner, B the sub-structure and C the draft tube showing one embodiment of this invention. The water discharging from the runner A flows downward into the draft tube at 6 in a circular stream of an initial diameter 78 the draft tube is formed as a straight section expanding in diameter to 1011 at 9 with corresponding deceleration of the outflow. B'elw this straight part .the discharge of the stream is turned outward all around the axis DD along the curves 12-13-14 between the conical core E and the spaced confining wall F. The stream is thus spread into the horizontal plane so that the water leaves the tube in a radially outward direction with respect to the axis on all sides, being distributed with substantial uniformity throughout the annular discharge space 20 forming the outlet from the tube.., At the same time the cross sectional area of the stream is progressively expanded to continue the deceleration of the outflow so that simultaneously with the change in direction, the velocity head is converted into effective pressure head, In the embodiment shown in Fig. 1, a short conical draft tube 6 to 9 is used as a transition tube between the runner discharge space and the beginning of the curved tube. The beginning of this curved portion could if desired be placed immediately at the runner discharge and this will in many cases be the preferable arrangment. Where space permits however, such a straight transition tube is of value, since it gives a preliminary reduction of velocity before the entrance into the curved flaring portion and the use of the straight portion is not objectionable if space remains below it to design the fiared part of the tube with sufii-- ciently gradual curvature.

9. In changing the direction of flow it is desirable to keep' the radius of curvature of all water paths as great as possible within the restrictions due to the limited space practically available below the turbine runner. The main curve of the flow 12, 13, 14 is therefore made as smooth and with as gradual transition as possible on lines which begin at the upper end, 12, in a direction tangent to the straight flow line bisecting the radii of the straight tube, and gradually curve into the horizontal direction at the lower end 14, the curvature increasing from the upper end to a maximum degree of curvature at 13 slightly below the middle of the curve and then gradually decreasing 5 again so as to merge into the horizontal plane at the lower end 14. The point of maximum'curvature should be slightly below the middle of the curve since it is desirable to have this point of most rapid curvature occur when the velocity has been reduced -as far as possible. The resulting line 12, 13, 14, partakes somewhat of the nature of a hyperbola, which when revolved around the axis DD generates a frustum of a cone whose section containing the axis is concave away therefrom.

10. The curved discharge passage is formed by surfaces spaced on each side of the cone generated by the line 12, 13, 14, and if this passage had simply to change the direction of outflow these central and side surfaces would be spaced from the main lines 12, 1'3, 14, as shown in dotted lines in Fig. 3, at only sufficient distances to provide a constant cross-sectional discharge area equal to that at section 9, 10, 11, the surfaces of course converging outward to compensate for the constantly lengthening circumference. In order to provide for the desired increase of cross section however, these surfaces must be spaced further apart and the spacing and contour of the central core E and peripheral surfacesF are determined by. reference to established designs for 115 straight draft tubes in the following manner.

11. Starting with point 12 at the middle of the radius of the tube on section 9, 10, 11, the line12, 13, 14 is drawn as above described, its contour being determined to give the most gradual curvatures permitted by the conditions of the installation. Then, (see' Fig. 3) there is laid off along this line from 12 to'41 a certain distance S, stepped off along the curve and at the point 41 a normal to the curve is drawn as-shown at n. The transverse area of the discharge at point 41 will therefore be 2mm, where n, the length of the line n, is the distance beneiaaea tween the central and side surfaces, and r is the mean distance of the line 11/ from the axis 'DD, i. 6., the radial distance from point 41 to the axis D]D. In order to determine the value for n for a most eficient increase in area of the discharge section, it is only necessary to give it such a value that the corresponding cross section will be the same as that for a straight conical draft tube at the same point of flow, i. 2mm will equal alt, where R is the radius a straight tube would have at an equal distance of flow vfrom the section 9, 10, 11; as at point 43, Fig. 3, where line 9 to a3 is equal in length to S, the length of line 12 to ll. Theumost. etlicient value for lit thus determined will be. substituted in the equation Qarnzalfi, and the value of nobtained from' this equation is laid ofl one-half on each side of the central line. By stepping off a series of such points along the axis lDD and the curve 12, 13, 1.4, and similarly obtaining the successive values lit, R", etc.,

n, n,etc., the complete form of the central cone E and side surfaces F will be accurately determined as the surfaces of revolution generated by revolving the curves pass-' ing through the ends of the normals n, a, it, etc., around the vertical axis lD-lD.

12. Experimental researches of the ordinary form of conical draft tube have shown that the best efliciency is obtained when the angle of flare is in the neighborhood of 3 to 49.. One of the advantages of the type of draft tube covered by this application is the fact that when a curved central cone is introduced the water is guided more definitely on all sides, and it becomes possible to increase the equivalent angle of flare of a straight draft tube having areas corresponding to the curved flaring tube, to values considerably above t" without materially reducing the efficiency. lit has been found from tests that the equivalent angle should be kept betweenv about 3 and about'15 to insure good results. A considerable range of values is therefore available without seriously reducing the efficiency. The equivalent conical draft tube is not necessarily made with a single angle from top to bottom .but this angle may be progressively increased from entrance to discharge without requiring any change in the method of design described. The advantage of using a larger angle of flare than the 4 or thereabout, which must be'used with the ordinary type of draft tube, is'that, the velocity can be reduced'within smaller space limits without l seriously increasing the losses of energy.

13. The above method of laying out the design of the draft tube may be applied exactly as described, when the space limitations permit the use of large radii of curvature of the channel center-line at all points. When,

however, it is necessary touse a considerable if this velocity were the same at all points of any such transverse section. This would indeed be very nearly true when the walls of the passage in the direction of the flow have but little curvature. When, however, the curvature is rapid, that is when the radius of curvature is no longer very great in comparison with the transverse width of the assage, the centrifugal force of the water owing in such a curved channel increases. the pressure .on the side of the channel away from the center of curvature, and reduces it on the other, and as a result the velocity decreases on the side having increased pressure and increases on the other side. if the preceding method of design is adhered to for channels having rapid curvature, the average velocity over any transverse section will still decrease in the same manner as in the preceding method. Due to the variation of velocity across the lines of flow, however,the

.velocity at the inner and outer Walls of the 'lhis maxlmum velocity occurs along the wall nearest to the center of curvature of each section. If this correction is not applied, the high velocities along the outer wall of the flaring draft tube instead of continually decreasing at the desired regular rate will either decrease at an insufficient rate, or may even increase, and will then subsequently decrease with undue rapidity.

14. The corrected widths of channel N N etc., from point to point will be greater than the widths n, n, et c., determined by the method given above and the increase will be greater at points of greater curvature so that the resulting enlargement of the tube section correctively decelerates the flow at the outer wall in exact opposition to the acceleration due to the curvature.

15. To explain the matter more clearly,before taking up the magnitude of the correction which is to be applied in a channel of the form above described (that is, one in which the flow is in radial planes having a common axis) let us consider the flow in a simpler form of channel, such as a bend or* elbow in a canal or pipe of uniform rectangular cross section. In the usual design of such a canal or pipe bend, the channel is bounded by two parallel plane surfaces, and by two concentric cylindrical surfaces, the channel being of constant Width measured normally to the. flow at all points. As a result, the unequal distribution of velocity in any cross section, caused by centrifugal force, forces the water flowing on the side nearest 'to the center of curvature of the bend to increase to a considerabl higher value than the velocity in the straight portions ofthe pipeor canal leadin to the bend or away from the bend. his increased velocltv occurs at the very point where high velocity is particularly undesirable, namely, along the wall having the most rapid curvature, and this results in a harmful acceleration and subsequent retardation of the velocity alongthis wall, and gives rise to eddies and consequent losses. of en ergy. In applying the correction here proposed to the design of such a pipe or channel bend in which the purpose of the bend is merely to hange the direction of flow, but to deliver the water into a discharge channel with the same velocity as that existin in the entrance channel, the width norma to the lines of flow at each section of the bent portion of the channel would be increased sufiiciently to maintain a constant velocity at all points of the inner wall, that is, the wall nearest to the center of curvature of the bend. This increase in width would be greater at points having more rapid curvature. In addition to this, the center line of the channel would be designed with curvature graduallyincreasingup' to the center of the bend and then gradually decreasing in a manner similar to that already described in connection with the flaring draft tube. In accordance with this method, the channel will'be widest at the middle of the bend and will taper in each direction to the width of the uniform straight portions of the channel. My method of determining the amount of correction to be applied to the width is based on the assumption of a uniform variation of velocity transverse to the lines of flow; that is, the velocity in a transverse section is assumed to vary in accordance with the straight-line law.

16. Assuming in advance that it is possible to design a bend or elbow in which the losses of head are very small, the sum of the pressure-head plus the velocity-head will be practically constant at all points in the stream. If we design the bend to maintain a constant pressure-head along the inner wall, the velocity-head and consequently the velocity must also be constant at all points of this surface in accordance with the above assumption.

17. From a mathematical investi ation of systems of hyperbolic curves, inclu ing both rectangular hyperbolas and hyperbolas of the third degree (having the equatio w z=a constant) it has been found that in such systems or curves the radius of curvature varies uniformly along a line drawn normal to all of the curves ofsuch a'system. If the hyperbolic curves be'taken to represent flow lines, and if we integrate thedifferential change in pressuredue to the centrifugal force of any elementary stream filament, it is found that the velocity varies uniformly from point to point along all lines normal to the flow. Whether this uniform variation of velocity transverse to the flow be regarded merely as an assumption, or Whether it be regarded as the result of the mathematical investigation described, it will be adopted here for reasons of simplicity.

18. Assuming, then, a uniform variation "of velocity across a transverse section of the above pipe bend or elbow, it is also found, from the above integration for the change in pressure due to centrifugal force, that the rate of variation of velocity across the lines of flow is such that if continued outside the channel the velocity would become zero at a distance from the axis ofthe channel equal to the radius of curvature at the section considered, this zero point of velocity occurring,

however, on the Opposite side of the channel from the center of curvature. Fig. 7 is given to illustrate this point. On the basis of the above considerations, the resulting correction which should be applied to the width of the channel at any point may be found as follows: If we denote by a the original Width which the channel would have had if this width had been kept uniform around thebend, and by N the corrected width of the stream at any section to satisfy the above requirements, then the ratio in which the stream must be widened is given by the following formula:

n p in which p is the radius of curvature of the center line of the channel at the section considered.

19. Now, taking up another form of channel, let us suppose the parallel sides T, T of the above elbow to be changed into an inclined position, as shown by T, T in Fig.

8, so that we now have a wedge-shaped channel which may be considered to be a small section of a large circular stream, similar to that of the draft tube of this invention. If we still consider a case in which the velocity of the water after leaving the bend is the same as the velocity of the water before entering the bend, we have a channel similar to that described in the first part of paragraph 10, namely, a flaring tube in which the average velocity is constant at every section transverse to the flow. For the same considerations as already described, the

width of the channel of Fig. 8 should be tion the distance L..from the middle of any.

corrected to maintain a constant velocity along the surface VV instead of maintaining a constant average velocity around the bend. On account of the form of thischannel, however, we must take into considerasection to the point where the plane of the section intersects the axis DD. The above formula will consequently be changed to the following:

N n H N 12. The amount of widening to be applied at any section of a channel so designed is therefore given by the formula last stated above, in which:

a :original width of channel at any section as obtained from the method given in paragraphs 11 and 12 Fig. N corrected width of channel to allow for curvature.

p :raolius of curvature of center line of channel at section considered. L=olist,ance from center of channel to intersection of the line of the section with the axis of symmetry. (See r Fig. 3.)

21. It is not convenient to solve this formula directly for N since this involves the solution of an equation of the third degree. It may however, be readily solved by first assuming tentative values for N at successive points on the curve 12, 13, 14, for 1nstance where n n 41.", etc., are already determined, and then solving for H the computation being repeated if the resulting value of N diflers appreciably from the tentative value. Successive values of N N N", etc., will then be laid off along thecorresponding n n 91.", etc., and one-half on each side \of the center line. The finally corrected form of channel E, F, Fig. 1, will then be determined as the surfaces of revolution generated by the curves, passing through the ends of lines N N N", etc.-, rotated around the vertical axis D-D.

22. This final correction will maintain a radual and continuous deceleration of veocity along the outer walls and enable the;

tube of this invention to be applied under all practical conditions for turning the flow into the horizontal in a smooth and eflicient manner.

23. In Figs. 4:, 5 and 6, a particular embodiment of the draft tube of this invention is shown in relation to the other elements of the structure. 'The outer walls F of the tube C, are formed within overhang B of the sub-structur'e'B and around this overhang and the discharge annulus 20 are in cross section toward the final outlets at Q on each side of the pier V. This pier in the particular design shown is added for structural reasons to provide additional support for the power house. The curved tube may be combined with a straight transition section in any way dictated by the limitations of specific installations and a spiral or other form of collection tube may be used to receive the water from the outlet 20 and may be designed with further increasing cross section to further convert the velocity into pressure head as shown in Fig. 4.. The spiral collecting or regainlngtube may also begin within the limits of the flared channel here described, spiral walls 25 being inserted in the space between walls E and F as shown in Figs. 9 and 10. Under all circumstances the exact contour of the flaring passages required to give the desired velocity reduction and change of direction may be accurately and readily predetermined.

24. It is obvious that while the invention has been illustrated in connection with its special application to the discharge of a vertical turbine it may be used in a horizontal turbine, or in other connections such as a pump difluser, or a pipe or conduit.

1. A hydraulic conduit comprising guiding passages having central and side surfaces directing the flow in curves symmetrL cally flaring from a central axis and with cross sectional areas increasing gradually in the direction of flow.

2. A hydraulic conduit cbmprising; guiding'passages having central and side surfaces directing the flow in substantially hyperbolic curves symmetrically flaring from a central vertical axis, said passages increasing in cross section in the direction of flow.

3. In a hydraulic conduit, a conical core symmetrically flaring from a central vertical.-

P.XiS and concave aw'ay therefrom in a plane containlng sald axis, 1n com-blnation with a side wall around the said core and spaced therefrom, the linear width of'thespace be{ ing less, but the area of cross section being greater in accordance as. the sections are taken farther from the axis.

4:. In a hydraulic conduit, [a conical core symmetrically. flaring from a central verti-- cal axis and having its sections containing the axis concave away from said axis to its 75 formed the outlet passages G Gr increasing turn the stream lines gradually without abrupt change in direction, and side walls cooperating with said core to form passages iqncreasing in cross section in the direction of 5. The combination with a hydraulic turbine of a draft tube therefrom comprising guiding passages adapted to spread and turn the outflow around a central conical core, a straight transition tube interposed between the turbine runner and said passages.

6. The combination with a hydraulic turbine of a draft tube therefrom comprising a centralconical core, a straight transition tube interposed between the turbine runner and said core, side surfaces extending from said straight tube and cooperating with said core to form a passage in continuation of said tube. 1

7. The combination with a hydraulic turbine of a draft tube therefrom comprising a central conical core, a straight transition tube interposed between the turbine runner and said core, and side surfaces extending from said straight tube and cooperating with said core, said straight tube and the passage between said side surfaces and core in creasing in cross section in the direction of flow.

8. In a hydraulic conduit means for changing the direction of flow comprising a central axial conical core having its sectioncontaining the axis concave away therefrom and cooperating side walls correspondingly convex toward said axis, said core and walls forming between them a radially flaring passage of increasing sectional area in the direction of flow. I

9. In a hydraulic conduit means for changing the direction of flow comprising a central axial conical core having its section containing the axis concave away therefrom and cooperating side walls correspondingly convex toward said axis, said core and walls forming between them a passage gradually increasing in curvature in the direction of flow and then decreasing in curvature from an intermediate maximum.

10. In a hydraulic conduit means for changing the direction of flow comprising a central axial conical core having its section containing the axis concave away therefrom and cooperating side walls correspondingly convex toward said axis, said core and walls forming between them a passage gradually increasing in curvature in the direction of flow and then decreasing in curvature from an intermediate maximum, said maximum beinglocated between the middle and discharge end of said passage.

11. In a hydraulic conduit means for changing the direction of flow comprising a central axial conical core having its section containing the axis concave away therefrom and cooperating side Walls correspondingly convex toward said axis, said core and walls formingbetween them a symmetrical passage radially flaring from the central axis in Substantially hyperbolic line 1 2. In a hydraulic conduit means for changing the direction of flow con'iprising a central axial conical core having its section containing the axis concave away therefrom and cooperating side walls correspondingly convex toward said axis, said core and walls forming between them a symmetrical passage radially flaring from the central axis in substantially hyperbolic lines and having a transverse area increasing in the direction of flow.

13. A hydraulic conduit formed by inner and outer coaxial surfaces of revolution generated by curved generating lines convex toward the axis and spaced to give a regular rate of increase in the cross section of the conduit.

14. A hydraulic conduit formed by inner andouter coaxial surfaces of revolution generated by curved generating lines convex toward the axis and so spaced that the cross sectional area of said passages at any intermediate distance from the entrance end of the conduit is slightly larger than the corresponding section of a straight conical tube of the same entrance and discharge areas.

15. A hydraulic conduit formed by inner and outer coaxial surfaces of revolution generated by curved generating lines convex toward the axis and so spaced that the cross sectional area of said passages at any intermediate distance from the entrance end of the conduit is slightly larger than the corresponding section of a straight conical tube of the same entrance and discharge areas, the amount of excess in area over the straight tube being dependent on the radius of curvature.

16. A hydraulic conduit formed by inner and outer coaxial surfaces of revolution generated by curved generating lines convex toward the axis, and so spaced that the crosssectional area of said conduit at any distance from the entrance end of the conduit has a value between the limits fixed by the areas, at an equal distance from the entrance end, of straight conical tubes of the same entrance area, the sides of which taper at angles of about 3 and 15 with respect to the axis.

17. A hydraulic conduit having guiding passages formed by coaxial surfaces of revolution the outer and inner'surfaces being so curved as to be tangent at one end of the conduit respectively to the walls of a straight pipe and to its axis, and at the other end of the conduit equally spaced from a plane surface normal to the axis.

18. A hydraulic conduit having guiding passages formed by coaxial surfaces of revlltlt ing passageshaving central and side surfaces curving symmetrically from a central vertical axis at all points and formed to maintain acondition of flow at the outer surface equivalent to the corresponding con- .dition-in a conical tube.

20. A hydraulic conduit comprising guiding passages having central and side surfaces curving symmetrlcally from a central vertical axis at all points and formedto maintam a deceleration of flow at the outer surface equivalent to'the corresponding condition in a conical tube.

' 21. A hydraulic conduit formed by inner and outer coaxial surfaces of revolution generated by curvedgenerating lines convex to- Wardthe axis and spaced to give cross sections across the lines' of flow everywhere at least equal to the corresponding cross sections of a conlcal tube, and the cross sections where the conduit curves being in creased beyond such equal relation.

intense 22-. A hydraulic conduit formed by inner and outer coaxial surfaces of revolution generatedby curved generating lines convex to Ward the axis and spaced to give cross sections across the lines of flow based on corresponding cross sections of a conical tube.

23. A hydraulic conduit formed by inner and outer coaxial surfaces of revolution generated by curved generating lines convex to- Ward the axis and spaced to give cross sections across the lines of flow based on corresponding cross sections of a conical tube and increased further in correspondence to the degree of curvature of the lines of flow in the conduit. f

24. A hydraulic conduit formed by inner and outer coaxial surfaces of revolution generated by *curved generating lines convex toward the axis and so spaced that the cross sectional area of said passages at any intermediate distance from the entrance end of the conduit is not less than the corresponding section of a straight conical tube of the same entrance and discharge areas.

25': A hydraulic conduit comprising guiding passages having central and side surfaces curving symmetrically from a central vertical axis at all points and formed to maintain a smooth deceleration of flow at the outer surface.

LEWIS rnnnr noonr.

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