US2258794A - Elastic fluid turbine - Google Patents

Description

Oct. 14, 1941.

5. WAY

v ELASTIC FLUID TURBINE 2 Sheets-Sheet 1 I Filed May 16, 1940 FI I.

IINVENTOR 5 TEWR RT We )4 WITNESSES.

ATTORN EY Patented Oct. 14, 1941 I ELASTIC FLUID TURBINE Stewart Way, Forest Hills, Pa., assignor to West inghouse Electric & Manufacturing Company, East Pittsburgh, Pa., a corporation of Pennsylvania Application May 16, 1940, Serial No. 335,465

13 Claims. (01. 253-39 My invention relates to elastic-fluid turbines and it has for an object to provide-vane elements suitable for elastic fluids moving at superac oustic velocities.

A more particular object of the invention is.

' pression shocks. I While the invention may be employed either for nozzle vanes or for rotor blades or buckets, it is particularly applicable to the first row of rotor blades of the impulse type'and wherein,

usually steam moving at super-acoustic velocities is encountered. A conventional type of turbine is a two-row Curtis impulse stage followed by reaction or Rateau stages, and a substantial fraction of the available energy of the steam is converted into mechanical energy by the Curtis stage; however, as the eficiency of a Curtis stage is relatively lower than a reaction stage, the overall eificiency is reduced on account thereof. With the incorporation of the new type of blading in the first row of rotor blades, or in subsequent rows if super-acoustic velocities should occur therein, the efiiciency is improved on account of the improved performance of the new type of blading in dealing with elasticfluids moving at super-acoustic velocities. With the conventional design, super-acoustic velocities occur only in the first row of blades, so that it issuificient to restrict the incorporation of the new type of blading tothatrow. a H

One reason for the lower efficiency of the initial impulse blading is-bound up with itsgoperation at super-acoustic entering steam velocities. In super-acoustic gas flow, compression shocks occur 'under. certain conditions that result in an increase in entropy, thereby rendering unavailable a certain portion of the energyinitially avail-' able in the steam for doing work. Heretofore,

' impulse blading has been designed withpractically no attention being given to the possible ccurrence of compression shocks in the passages.

Accordingly, a more particular object of my invention is' to improve the efficiency. of the, initial row or rows of impulse blades for handling elastic fluid moving at super-acoustic velocities by having the convex faces thereofiiormed with corner or corners and theconcave faces cooperating with the convex faces to-define flow passages. providthat the latter will be capable of inducing the adjacent stream to turn without other mechanical constraint, and without the occurrence of compression'ghocks. I

A further object of the invention is to provide blade passages with the convex faces having corners to induce turning of the stream in each passage and wherein the passage sections increase in the direction of flow and the corners ar rounded.

A further object of the invention is to provide a row of turbine blades having concave and po-' lygonal convex faces defining blade passages for the reception 'of super-acoustic velocity elastic fluid and wherein the fluid is induced to turn by I the corners, each convex face having three corners to afford a suitably large total turning angle and to provide blades of adequate mechanical strength. V

- The fact that a corner in an expansion environment will induce a compressible medium moving at super-acoustic velocity to turn without other mechanical constraint was observed and analyzed by 'Prandtl-Meyer (see analysis of Prandtl-Meyer found in Aerodynamic Theory by Duran, volume III, division H, chapter 4, section 4, pages 243-246, and Steam Turbines,'Stodola- Lowenstein (1927), volume II, pages 983-5Q-and may be regarded as the Prandtl-Meyer streamline efiectu The present invention has for an object to utilize the means responsible for this efiect'in connection with impulse turbine vane '"velements to improve the efliciency thereof.

Fig. 5 is a diagrammatic ing; and,

' "These and other objects are effected by. my invention as will be apparent from the following description and claims taken in connection with the-accompanying drawings, forming apart of this application, in which:

Figs. 1, 2 and Bare diagrams'illustrative of the Prandtl-Meyer streamline;

Fig. 4-is a diagram showing the theory of operation of the improved blade passage;

view showing certain geometric aspects;

Fig. 6 is a sectional view of the improved bladvelocity turning efiect,- the convex faces .of the vanes or blades having oneor more corners and ing such pressure conditionsabout each corner. the concave faces cooperating with the convex is parallel to the rigid boundary A0, the corner being at 0. When the fluid reaches the corner,

instead of continuing therebeyond in a straight path, it curves therearound and resumes movement in a straight path after angular deflection dependent upon expansion from the region I of higher pressure to the region II of lower pressure, the excess of actual velocity of the stream over the acoustic velocity, the ratio of the actual velocity to the acoustic velocity being known as the Mach number. In Fig. 1, the stream curves from the radius vector GM to the radius vector ON; and the extent of turning depends upon the Mach number of the approaching fluid, the larger the Mach number, the larger theangle of turn and vice versa. In the zone of turning, the flow is along streamlines which have such relation that the component of velocity (v) perpendicular to the radius vector is always equal to the speed of sound at the conditions of pressure and density existing at the vector, this being set forth in Aerodynamic Theory, supra, page 244, as follows:

Thus, in two-dimensional flow around a corner, the component of velocity perpendicular to the radius vector must always equal the speed of sound at the local conditions of pressure and density.

In other words, within the angular limits inand "k is the specific heat ratio (1.30 for superheated steam). Where n is the value of r when 0:0, any curve C (Fig. 3) consisting of combinations of arcs ab of C (where a and!) are any two points on C) or of arcs ab of C with straight line segments, subject to the condition that the 'end points of adjacent arcs on C shall be one and the same point on curve C; such. a curve C is herein referred to as a Prandtl-Meyer streamline. Curve C is a streamline for the irrotationai flow of a frictionless gas (in two dimensions) around a corner, without compression shocks. I

Since it is desirable to have the passage as wide as possible, the streamline which forms the basis of the convex face should be one corresponding to r=0; and, for any given angle 0, such a streamline therefore reduces to a point. The flow field typified by stream lines C is such that along any ray, for 0=constant, the velocity is constant in direction and magnitude, and

p the state quantities of the gas are also constant.

dicated, such limits being dependent upon the Mach number of the approaching fluid and the pressure drop from the region I to region II, an infinite number of radius vectors may be conceived of as existing between the limits; and along each radius vector the conditions of state, such as pressure, temperature and specific volume, are constant. Accordingly, along the radius vector OM, these conditions of state are constant and coincide with .those of the parallel approaching stream, and the same is true with.

respect to the final vector 0N and the stream flowing parallel therebeyond.

As shown, the stream leaves in a parallel path which may be regarded as parallel to a straight gaseous envelope OB. If OB is replaced by struc ture so that the corner becomes .AOB, then there would be definite structural surfaces parallel to the parallel flow streamlines. Such a conforming corner is used with the turbine blades or vanes as hereinafter pointed out.

The definition of a Prandtl-Meyer streamline will be understood from a consideration of the diagrams of Figs. 2 and 3.

Referring to Figs. 2- and 3, in the polar coordinate system, 1' is a function of 0 and defines the curve C as follows:

where Therefore, each flow fleld terminating along a line, for 0=constant, can be joined directly to a uniform fleld of flow of the proper pressure, temperature and velocity. A straight line OB (Fig. 1), therefore, can be used as a part of the boundary of the convex face of the blade passage.

As a Prandtl-Meyer streamline may be entirely curved or comprise straight and curved portions, to take advantage of this in connection with turbine blades or vanes, I provide the convex faces of the latter with corner or corners extending longitudinally thereof to induce turning with preservation of the Prandtl-Meyer streamline flow along the face. Preferably, each convex face is polygonal or comprises flat portions joined by corner portions. Adjacent to the convex face, the flow is made up of straight portions parallel to the flat portions joined by curved portions, the curved portions increasing and the straight portions decreasing in linear extent out? -wardly radially from the convex face until the havior of a super-acoustic gas velocity stream in such a passage may be observed by the Schlieren photographic method, the corner flow phenomenon being manifested either on a ground glass plate or on a photograph by a mutiplicity of lines (Mach lines) radiating from the corners.- Assuming the fluid to enter the right-hand end of the passage with a Mach number of MI. in excess of unity, then it undergoes compression from the initial Mach line Li, L: and Le to the throat sections 0:, O4 .and 0a and expansions from the latter to the final Mach lines L2, L4 and La, the fluid reaching acoustic velocity at the throat sections and moving at super-acoustic velocities at the larger sections 01, 0:, O5 and 01. The fanlike radiating lines at each corner are Mach lines or linesof constant state. The Mach number has maximum values at the outer marginal lines L1 to Le, inclusive, and unity value at 02, and then increases, for example, to M2, greater than unity, at the final line L2 of the comer 02. As indicated, the expansion from the final corner or throat section Os is for a final angle of turning and for a Mach number, the same as at the entrance.

If a passage, such as shown in Fig. 4, having elastic medium passing therethrough at superacoustic velocity, is subjected to Schlieren photographic examination and the fanlike arrangement of radiating lines at each corner does not appear, then this signifies undesired shock or compression losses, that is, the passage would not be functioning to gradually reduce the Mach number at the compression side from a maximum to unity and then gradually increase the Mach number from unity to a maximumat the expansion side.

While the theory of a compressible non-viscous medium is fundamental to the present invention, nevertheless, all real media are viscous; and, for this reason,'certain departures from the theoretical design are necessary. Accordingly, the corners are rounded to accommodate friction, the turning angle to the first throat is restricted to avoid shock at the entrance, and,

I because of friction, the sectional areas gradually increase from the inlet to the exit end of the passage. Having determined a theoretical passage for a non-viscous medium, then with such a passage as a basis, the requisite corner rounding and relationship of passage areas is secured in order to obtain flow without compression shock, the operation of an effective passage being indicated by Schlieren photographic examination. Having determined in this way what modifications should be made to the theoretical passage, then the practical application of the invention merely involves the utilization of such determinations.

In Fig. 6, there is shown a multiplicity of turbine blades l suitable for dealing with steam moving at super-acoustic velocities. The blades have convex faces ll'cooperating with concave faces 12 to define blade passage 13. Each convex face ll, instead of being curved, as heretofore, is polygonal, or made up of a multiplicity of flat portions Hi, l5, l6, and ill joined by corner portions i8, i9, and 2B. The passages defined by the concave and convex faces provide for such expansion or pressure drop about each of 'the corner portions i8, i9, and 20 that the latter induce, without other mechanical constraint, the elastic fluid to be deflected or turned. If the concave faces conformed exactly, they would have Prandtl-Meyer streamline curvature; however, often a circular arc is so close thereto that it may be used Just about as effectively and is preferable for manufacturing reasons.

As shown, the corners l8, l9, and 2B are rounded to the extent required to widen the passage'to accommodate the larger volume of fluid on account'of friction and to reduce shock losses, the sections 01 to 01, inclusive, being made progressively larger. Also, to avoid shocks at the entrance, the turning angledown to the first throat section 02 is made somewhat smaller than that theoretically corresponding to the Mach number.

The importance of avoiding compression shocks can be seen from the following example.

perheated steam flowing with a velocity 1.523 times the acoustic velocity, as would result from expansion fr0m 1200 lb./'sq. in. abs; pressure to 300 lb./sq. in. If a normal compression shock occurs in such a stream there will be an increase fore not convert the energy of the steam as ef-' ficiently' into mechanical work as would be the case if the steam were flowing at the pressures and densities for which the passages are designed. The compression shocks therefore not only give rise to an essential loss of available energy right at the shock, but also render the flow such that energy conversion cannot be so efiiciently carried out in the impulse blading.

For a given blade width and angle of turning, the design of the elastic fluid passage to provide for Prandtl-Meyer streamlines involves consideration of the Mach number, M, which is the ratio ofthe actual to the acoustic velocity, the Mach angle a, which is the calculated angle 0, and the turning angle 11,

which is equal to cz+090. The angles and relations are identifiable from Fig. 5. Assuming elastic fluid to enter at the right with a Mach number of Ml, the Mach angle on is readily ascertained from the relation Y Illavingfound the Mach angle :11, the derived angle 01 is found from the relation and, knowing 01, the turning angle v1 is readily Suppose we have a super-acoustic stream of sufound from the equation:

With three corners, as in Fig. 5', in which'the concave face has been replaced by a circular arc, a total turning angle of 0, a final turning angle of vc=v1, then the remaining turning angles may be made equaland found from the relation Referring to any particular triangular flow field, such as that between L1 and 02, a unique relation exists. between the Mach number at L1 and the turning angle from L1 to 02. Also a relation exists between this Mach number and the ratio of the areas at O1 and O2. Assume that, at 02, the gas has been compressed until the velocity is acoustic and the Mach number is 1'. The maximum and minimum sections are located relatively to one another as determined by the relation between r and 0 for a stream line,

angle that can be secured in a passage with If we had such a compression shock in one throat O2 is theoretically dependent on the Mach number M1 of the entering Jet and the constant-k, as shown by-the equations above. With two throat sections any turning angle up to 180 can theoretically be obtained, since the Mach number at need not be any pre-assigned value, but is determined by halt the turning angle from O2 to 04. From considerations of minimizing the effects 01 wall friction, it is often desirable to use more than two throat sections, though only two are theoretically required, for, by using three throats instead of two, one is sometimes led to a passage with a greaterratio of width to length.- Also, in applying the theoretical passage form in an actual turbine, considerations of blade strength and thinness of leading edge may tend to favor three throats over two.

The fluid at the initial larger area 01 and at super-acoustic velocity undergoes compression with decrease in velocity until the acoustic velocityis reached at the initial corner or throat section 02". From the latter section to the second larger section 03, the stream undergoes expansion with increase in velocity to a superacoustic value, followed by compression and reduction in velocity to the acoustic value at the second corner or throat section 04. and so on for the succeeding larger and smaller sections.

By the use of a multiplicity of. corners, the desiredtotal turning angle is attained with the preservation of Prandtl-Meyer streamline flow in the passages. The calculated passage is shown in dot-and-dash lines in Fig. 6, superimposed on the actual passage.

The threat dimension 04. for the calculated or theoretical passage is the sameas Oz and the entire passage is symmetrical with respect to a median blade rotationplane. The actual passage involves modification of the calculated passage to accommodate friction and avoid consequent compression shocks, the modification involving rounding of the corners, restriction of the initial tuming' angle (vi), the intermediate turning angles 2 to 215) being increased to compensate and progressively opening up the passage. The throat sections 02 and 04 oi the actual passage are advanced upstream from their theoretical locations. The progressive opening up of the passage results in a larger projected opening on the exit plane than on the entrance plane of the wheel, and compensation to equalize the pitch at the inlet and the exit to make possible a practical blade construction may be accomplished by reducing the inlet angle and increasing the exit angle. For example, if the total turning angle is 130, this would give inlet and exit angles of 21, but the passage, with these angles, would have a larger pitch at the exit than at the inlet side. Therefore, to equalize the pitch at both sides, the inlet and exit planes are oriented, without changing the passages, to decrease the inlet angle and to increase the exit angle to the same. ex-

In the example given, the inlet angle a Mach number of 1.95, a nozzle angle of 15, and

Assuming that the concave face is a circular arc, then R= -;=0.808 inch 138 2 sin T and =sin" ==sin' -==30 51' M 1.95 for superheated steam,

k-l E 0.36115 The Prandtl-Meyer functions a and 0 are related by the following equation:

sin a k-1 2 cos M and from which (For a Mach number of 1.95, and k=l.300 the stream may be turned 27 07' in reducing the velocity just to acoustic.)

The half-chord length z1=R sin v1=0.366 inch r (initial Mach 1ine)= =0.367 inch =0.112 inch g= (cos M9 m2 -a.3o17 The first throat dimension should be 0.367 O, (Prandti-Meyer) -OJII? From this, it will be seen that the error introduced in this case on account of the circular arc approximation to the Prandtl-Meyer stream line Applying the law of cosines r; (0.803) +(0.691) 2(0.803) (0.691) cos 20 56.5

(Prandtl-Meyer) 293 and from this and from the relation L il sin oft-1L2 cos A6 0z=78 6 min., and =33 57 min.

In Fig. 5, the angle ODE=-02-a2=57 57 min. Designating DE by x and 0E by u,

:1: cos 67 5'7 lnin.+y cos 20 56.5 min.=0.69l a; sin 67 57 min.=y sin 20 56.5 min.

= (cos 719-103 mechanical constraint.

may be provided utilizing the corner-turning As the sections 01 and 01 are equal, the sections 02,0 and O6 are equal and the sections 03 and 05 are 'equal, the calculation gives the following forthe theoretical passage:

Position Location Opening Deg. Min. 0 188 O2 27 7 112 0a 48 04 162 O4 69 112 O5 89 57 162 0a 110 53 112 O 1 138 188 The calculation is for a theoretical non-viscous elastic fluid; however, as all real elastic fluids are viscous, modifications, as hereinbefore indicated,

'must be made to the theoretical passage to accommodate friction and avoid consequent compression shocks, the modifications being made until the Schlieren picture presents an appearance with good distribution of Mach lines at each corner. The modification involves corner rounding and opening up between corners to obtain restriction of the initial turning angle and progressive opening up of the sections until a satisfactory passage is reached. Such modification would involve relocation upstream of the first and second corner sections and progressive opening of the sections. For example, the modified section positions and section openings may be:

- Position Location Opening Degrees O1 0 0. 185 O1 25 0. 134 0a 48 0. 166 O4 68 0. 146 O5 90 0. 182 O0 111 O. 162 O1 138 0. 218

It is to be understood that the theoretical calculation, as well as the modifications, are given by way of example only to make the invention clearer and to indicate a procedure which may abstraction stage of theCurtis type wherein, in addition to the improved blades ill used in the.

If the initial Mach number is high enough and the total turning angle desired is sufficiently small, fewer corners can accomplish the tuming, but, for mechanical. reasons, with blades having concave and convex faces providing for Prandtl-Meyer streamline flow, 'not less than three corners can effect a total turning angle of the order suggested. On the other hand, the

number of corners should not be excessive in order to avoidlong slender passages which would increase wall friction.

In Fig. '6, the blades Ill providing -Prandtl- Meyer streamline, fiow passages I3 have elastic fluid supplied thereto by suitable nozzles 2| (one being shown) of suitable expansion ratio,

In Fig. 7, there is shown a multiple-velocityfirst moving row, the nozzles 23 are also constructed and arranged so that corners 24 in duce turning of the fiuid stream in the passages, with the result that nozzles of adequate expansion ratio to give the desired super-acousticvelocitywith. a minimum of shock are provided.

be followed to arrive at practical realization from the theoretical basis. It may be possible to attain the ultimate structure by. other methods or the procedure may, at some time, be simplified by being reduced entirely to a calculation basis.

After all, the invention is for aturbine wherein -the blading convex blade faces are polygonal in order to secure Prandtl-Meyer streamline-flow in the blade passages, the passages providing such expansions or pressure drops about the-corners that the latter induce turning Without any other phenomenon, that is, having Prandtl-Meyer streamline flow in the passages, it is first of all necessary to calculate and design the passage for a theoretical non-viscous elastic fluid and then to modify the passage suitably for a real or viscous fluid to accommodate for friction and avoid consequent shock losses. The number of corners provided on the convex face must be such that the required total angle In order that blades.

form, it will be obvious to those skilled in the art that it is not-so limited, but is susceptible of various changes and modifications without departing from the spirit thereof, and I desire, therefore, that only such limitations shall be placed thereupon as are specifically set forth in the appended claims.

What I claim .is: i

1. In a turbine, a row of vane elements having inlet and outlet edges and convex and concave faces extending therebetween and providing pas- F sages for elastic fluid delivered thereto at superacoustic velocity, said passages having the convex faces thereof-formed by flat portions, in

cluding fiat portions extending to the inlet and outlet edges of the vane elements, and three or more corner portions joining successive fiat portions and said passages providing pressure conditions about each corner portion such that the latter is capable of inducing, without other me chanical constraint, turning of the fluid stream in its passage without compression shocks.

2. In a turbine, a nozzle for discharging elastic fiuid at super-acoustic velocity, a row of vane elements having sharp inlet and outlet edges and convex and concave faces extending between the latter and providing passages for elastic fluid delivered thereto by the nozzle, said passages having the convex faces thereof formed by fiat portions, including fiat portions extending to the inlet and outlet edges, and three or more cor'nerportions joining successive fiat portions and said passages providing pressure conditions about each cornerportion such that the of turning may be efiected, while, at the same time, preserving adequate mechanical strength in the blades each of which must be formed with a concave and convex face. For example, with a blade width of 1.5" and the customary turning angle for a row of impulse blades, for example,

from to three corners seem necessary.

latter is capable of inducing, without other mechanical constraint, turning of the fluid stream in its passage without compression shocks.

. 3. In-a turbine, vane elements providing passages for elastic fluid moving at superacoustic velocities and defined by concave and polygonal convex faces the. polygonal convexfaces providrespectively, rection of fiow.

ing fiat portions separated by corners and the comers being rounded, the fiat portions and the corners of each convex face cooperating with the opposed concave face to provide, respectively, maximum and minimum sections of the passage and to provide for convergence of the passage from the maximum sections to the minimum sections and for divergence thereof from the minimum sections to the maximum sections and the corner sections progressively increasing in area from the inlet end to the outlet end of each passage.

4. The combination as claimed in claini 3 wherein the outermost fiat portions of the polygonal face of each blade define, with the concave face, sharp inlet and outlet blade edges.

5. In a turbine, a row of moving impulse blades providing passages for elastic fluid moving at super-acoustic velocities and defined by concave and polygonal convex faces, the passages pro-- viding such pressure conditions about the corners of the polygonal faces that such corners induce turning of the fluid in the passages without other mechanical constraint, the corners of the convex polygonal faces being rounded and the turning angle to the first throat section and defined by the first corner with respect to the concave face being sufficiently less than that corresponding,

to the Mach number of the entering Jet to avoid compression shock at the passage entrance 6. In a turbine, a row of blades for abstracting energy from elastic fluid delivered thereto at super-acoustic velocity; said blades having convex and concave faces providing blade passages and each convex face being polygonal with the corner portions thereof rounded and joining successive fiat portions; the corner portions of the convex polygonal faces defining, with respect to the concave faces, throat sections and the flat portions defining, with respect to the concave faces, maximum sections ahead of, intermediate and following the throat sections of each passage and said throat sections being progressively larger in the direction of flow.

'7. In a turbine, a row of blades for abstracting energy from elastic fluid delivered thereto at super-acoustic velocity: said blades having convex and concave faces providing blade passages and each convex face being polygonal with the corner portions thereof rounded and joining successive fiat portions; the corner portions of the convex polygonal faces defining, with respect to the concave faces, throat sections and the fiat portions defining, with respect to the concave faces, maximum sections ahead of, intermediate and following the throat sections of each passage and said throat and maximum sections, respectively, being progressively larger in the direction 8. In a turbine, a row of blades for abstracting energy from elastic fluid delivered thereto at super-acoustic velocity; said blades having convex and concave faces providing blade passages and each convex face being polygonal to provide three or more corner portions; said corner portions being rounded and joining successive fiat portions of the convex faces; said corner portions of the convex faces defining, with respect to the concave faces, throat sections and the fiat portions defining, with respect to the concave faces, maximum sections ahead of, intermediate and following the throat sections of each passage and said throat and maximum sections,

being progressively larger in the di- 9. In a turbine, a row of blades having concave and polygonal convex faces providing blade passages each having a total turning angle ranging from 115 to 145, each polygonal face having three corner portions joining successive flat portions, the corner portions of each passage being rounded and cooperating with the concaveface thereof to provide throat sections which successively increase in area in the direction of flow and the flat portions of each passage cooperating with the concave face to define maximum sections successively increasing in area in the direction of flow and from which, to the next throat section, thev passage converges and to which, from the preceding throat section, the passage diverges.

10. In a turbine, vane elements having convex and concave faces'providing flow passages for elastic fluid moving at super-acoustic velocity, the convex faces of the fiow passages comprising fiat portions joined by rounded corner portions andproviding, with respect to the concave faces, maximum and minimum sections, which, for each passage, are consecutively displaced angularly as determined by the area ratio of the sections and the exponent k of the isentropicpressure and specific volume relationship of PV: constant and the turning angle to the initial throat section of each passage being sufficiently smaller than the theoretical as determined by the Mach number of the entering elastic fluid to avoid compression shocks at entrance.

11. In a turbine, vane elements having convex and concave faces defining fiow passages for elastic fiuid moving at super-acoustic velocity; the convex face of each flow passage comprising a plurality of flat portions, including flat portions extending to the blade edges, and corner portions for joining'successive fiat portions; said flat and corner portions defining, respectively, with respect to the concave face, maximum and minimum section areas such that fiuid in traversing the passage undergoes compressions from each maximum section to the succeeding minimum section and expansions from each of the latter to the succeeding maximum section, the excess of actual velosity over the acoustic velocity at entrance and the successive compressions and expansions being such that the velocity is reduced to the acoustic at each minimum section and increased to super-acoustic values at maximum sections.

12. In a turbine, a row of impulse blades having concave and polygonal convex faces defining passages for super-acoustic velocity elastic fluid, each of said convex faces having three rounded corners defining, with the concave face, minimum or throat sections for the passage and the fiat portions of the polygonal face cooperating with the ends of the concave face and with portions of the latter arranged lntermediately of the throat sections to provide maximum sections. said sections being consecutively displaced angularly as determined by the ratio of the areas of these sections and the exponent k" of the isentropic pressure and specific volume relationship PV =constant for the elastic fluid employed, and the turning angle to the initial throat section being sufiiciently smaller than the theoretical as determined by the Mach number of the entering elastic fiuid to avoid compression shocks and the throat section areas being made progressively larger in the direction of fiow to accommodate for cooperating with having concave and polygonal convex faces defining passages for super-acoustic velocity elastic fluid, each of said convex faces having a plurality of rounded corners defining, with the concave face, minimum or throat sections for the pas- I sage and the flat portions of the polygonal face the ends of the concave race and with portions of the latter arranged intermediately of the throat sections to provide maximum sections, said sections being consecutively displaced angularly as determined by the ratio of the areas of these sections and the exponent k" of the isentropic pressure and specific volume relationship Pv =constant for the elastic fluid employed and the throat section areas being made progressively larger in the direction of flow to accommodate for friction.

' STEWART WAY.

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