US3299821A

US3299821A - Pump inducer

Info

Publication number: US3299821A
Application number: US391118A
Authority: US
Inventors: David H Silvern
Original assignee: Sundstrand Corp
Current assignee: Sundstrand Corp
Priority date: 1964-08-21
Filing date: 1964-08-21
Publication date: 1967-01-24
Anticipated expiration: 1984-01-24
Also published as: GB1120672A; DE1528836A1

Description

Jan.

D. H. SILVERN PUMP INDUCER Filed Aug. 2l, 1964 3 Sheets-Sheet l Jan. 24, 1967 D. H. SILVERN PUMP INDUCER 5 Sheets-Sheet 2 Filed Aug. 2l, 1954 Pkz-'sswvf Peor/z E amb:

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ow PRESSURE 5105 VHAW? PREssl/k' JFEFEREwc HIGH PPA-'55u46 5105 4 VELOCITY PROFILE PHAT/v5 W vzac/rv 1 u .X f j -13 .r j w w n Y a 4 j W j 1/ l V|l j m w u .mvwbwlo 4 22 2 lla m T az up m. w Ive CW MMR l TR LP E 11M m. Ne www@ iews Ec rMen T o/CN Mu eeuw NP lf. Nr D ADC ills/L Lm .|.6 M E J0 Z/ DO. ow IIA M D na f1 0 @$468 .uw n4 naamw Jan. 24, 1967 D. H. slLvr-:RN 3,299,821

PUMP INDUCER /NLEr et 7 /a x-Low (6PM) ca ao /oa UnitedStates Patent O 3,299,821 PUMP INDUCER David H. Silvem, North Hollywood, Cal., assigner to Sundstrand Corporation, a corporation of Illinois Filed Aug. 21, 1964, Ser. No. 391,118 22 Claims. (Cl. 10S-88) This invention relates generally to pump inducers and more particularly to an axial ow inducer for a hydraulic centrifugal pump.

The general purpose of an inducer is to increase the pressure of the hydraulic fluid from the suction side of the pump and to turn the hydraulic fluid before it enters the pump in the direction of pump rotation. By raising the inlet pressure to the pump, the inducer permits the pump to operate at a higher speed and deliver a greater ow without producing any cavitation in the inlet which would occur in the higher speed ranges if an inducer were not employed. Also, the inducer reduces the work that the radial impeller blades would normally do on the iluid by turning the fluid in the direction of rotation of the pump impeller blades.

Heretofore, inducers have been designed by the trial and error method of testing and redesigning without employing any theoretical formulae which even approximate the actual ow conditions and phenomena in the inducer. This technique has resulted in overdesigning and inducers of excessive length and diameter for a given inlet head and desired outlet head. This inadequacy in prior blade designs is attributed to a lack of appreciation of the hydraulic phenomena in all parts of the inducer and an inability to construct an inducer blade having an optimum configuration in accordance with formulae that,

represent ow phenomena in different portions `of the inducer itself. The ow problems which influence inducer design and have necessitated this overdesigning in the past are cavitation and separation. As the primary purpose of an inducer is to increase the inlet pressure to the pump, it is obviously desirable to employ amaximum blade angle curvature on the inducer to achieve this pressure increase in the shortest possible axial length. In other words, it is desirable to provide a maximum pressure differential across the inducer blades. However,l if this pressure difference across the bladesvbecomes too great, the pressure on the suction side of the blade will go below the vapor pressure of the hydraulic fluid employed and cavitation will result. Similarly, if the pressure on the high pressure side of the blades, i.e the impeller side, -goes too high, the uid flow will decrease on that si-de and even backow which is commonly knownl as separation.

Now the present invention provides an inducer of minimum radius and length for given inlet and outlet pressures :by shaping the inducer blades with a maximum rate of a blade angle change along the length of the inducer within the limitations imposed by cavitation and separation. The maximum blade angle increase is determined by relating the blade angle to certain cavitation and separation criteria and choosing the maximum blade angle which may be employed without producing either cavitation or separation.

It is, therefore, a primary object of the present invention to provide a new and improved pump inducer and method of making a pump and inducer with blades hav ing the maximum blade angle at each axial station along the length of the inducer to achieve a maximum pressure rise without causing cavitation or separation.

Another object of the present invention is to provide a new and improved pump inducer and method of making the same in which the rate of change in blade angle increases along the axial length of a portion of the inducer as the pressure of the hydraulic Huid increases. One of Patented Jan. 24, 1967 ICC the principal reasons Why certain prior art designs of ing the same having blade angles in the suction end ofl the inducer determined by the limitations imposed upon the flow by certain cavitation criterion and having blade angles in the outlet or impeller portion of the inducer determined by certain separation criterion. In the past, inducer design has resulted in overdesigning of the inducer parameters because of the failure to appreciatel that cavitation imposes the greatest limitation on inducer blade angles in the suction portion of the inducer and that the problem of separation imposes the greatest limitation on the blade angles in the outlet end of the inducer. By shaping the blade angles in the suction end of the inducer in accordance with formulae based upon the cavitation limitation and shaping the inducer blade or blades in the outlet or impeller end of the inducer in accordance with formulae :based upon the separation limitation, maximum blade angles throughout the inducer are provided.

A still further object of the present invention is to provide a new and improved pump inducer having blade angles which produce a pressure difference across the blade in the tangential plane which is m times the local pressure (pressure above the vapor pressure of the pumped fluid) in the tangential plane all along the axial length of the inducer where m is in the range of .75 to 1.25. By maintaining the pressure drop across the blade below this value, cavitation will not occur on the low pressure side of the blade. `Of course, the Iblade angle determines the pressure drop'across the blade, so that the blade angle may be defined in terms of these pressure parameters.

Another object of the present invention is to provide a new and improved pump inducer having a hub for supporting the blades with a radius suficient to prevent fluid separation along the entire length of the hub. Another of the problems in inducer design has been separation of the fluid in or backflow along the inducer hub. The velocity of the hydraulic fluid decreases from the tip of the inducer blade to the axis of rotation. At some point along the radius depending upon the blade angle at that particular axia'l station, the uid flow is low enough to canse separation. It is, therefore, important to design the inducer with a hub radius at least as great as the maximum radius which would cause separation at that point. Theoretically, the minimum hub radius which will prevent separation along the fhub varies with the blade angle along the length of the inducer approximately in a sin 218g relationship where t is the blade angle at that axial station. This explains why the conical hub inducer may be employed in this environment as theoretically,vat least, no radius is needed on the hub at the suction end thereof to prevent separation. While conical hub inducers have been known in the past, the hub radii have been arbitrarily chosen and have not been designed in accordance with any predetermined formulae as a function of the separation limitation. However, the principles are applicable to the choice of a 4minimum hub radius in a straight hub inducer, even though they are more critical in the conical hub type.

Other objects and advantages will become readily apparent from the following detailed description taken in connection with the accompanying drawings, in which:

FIGURE 1 is a side elevation of a straight hub inducer having four blades designed in accordance with the principles of the present invention;

FIGURE 2 is a at pattern taken around the hub diameter of the inducer in FIGURE 1;

FIGURE 3 is :a pressure profi-le Ibetween the induce blades;

FIGURE 4 is a diagram of the velocity profile between the inducer blades;

FIGURE 5 is a vector diagram of the relative velocities of the fluid and the blade in the inducer stream line;

FIGURE 6 is a vector diagram of the relative fluid velocity components;

FIGURE 7 is a graph showing the bladeangles at each axial station based on the bow of cavitation and separation limitations for 2, 4, and 8 blades;

FIGURE 8 is a tip development of the inducer blades along the axial length of the inducer;

FIGURE 9 is another embodiment of the present invention employed in a conical hub type inducer with only one of -four blades illustrated; p

FIGURE 10 is a vector diagram of the blade angle at any axial station;

FIGURE 11 is a vector diagram in perspective showing the velocity components and the distance components with respect to the inducer blade at a particular axial station on the inducer;

FIGURE 12 is a curve showing the tluid velocities along the radius of the blade at an axial station;

FIGURE 13 is a curve showing the minimum hub radii lfor any particular blade `angle which will prevent separation .at the inducer hub;

FIGURE 14 is a graph showing the blade angles at each axial station in the em-bodiment of FIGURE 9; and

FIGURE 15 is a graph showing actual performance curves for embodiment shown in FIGURE 9 of the present invention and a radial flow pump without an inducer.

While illustrative embodiments of the present invention are shown in the drawings and -will be described in detail herein, the invention is susceptible of embodiment in many different forms and it should be understood that the present disclosure is to be considered exemplary of the principles of the invention and is not intended to limit the invention to the embodiments illustrated. The scope of the invention -will be pointed out in the appended claims.

EMBODIMENT I Referring to FIGURE 1, wherein a straight hub inducer is shown generally indicated by the numeral 10 incorporating the principles of the iirst modication of the present invention.

Inducer blades

11, 12, 13 and 14 may be cast with or formed separately from and joined to a constant radius hub 17. Each of the

blades

11, 12, 13 and 14 is perpendicular to the axis of rotation 18 of the inducer 10 in the sense that a radial line passing through the tip of the blade at any point along the blade lies in the blade itself.

It should be noted that the inducer 10 shown in FIG- URE 1 is adapted to be driven directly by a centrifugal pump having radially orientated lblades. The inducer is conventionally located to rotate on the axis of rotation of the centrifugal pump in the suction inlet thereof so that the inducer raises the inlet pressure of the lluid to the pump and permits greater pumping speeds Without producing cavitation in the suction section.

Referring to FIGURE 2, wherein the blade development for each of the `four blades is shown taken along the circumference of the hub 17, it should be noted that this merely represents the unrolled configuration of the inside edges of the blades. In FIGURE 2, and throughout the specification, the letter Z represents an axial distance from the inlet or suction end of the inducer 10. The total axial length of 2.18 inches shown in FIGURE 2 is merely exemplary of one embodiment of the present invention for certain design parameters such as flow, inlet the low press-ure side of the blade.

pressure, outlet pressure, the outside diameter of the blades, and the rotational speed of theinducer. It may be readily seen that blade angles increase only slightly for small Values of Z, i.e., nearthe inlet or suction end of the inducer, and then increase very sharply in the intermediate section of the inducer. The increase in blade angles in the intermediate section of fthe inducer permits

additional blades

13 and 14 t-o be employed as the Idistance between the blades cannotbe .less than that required for machining.

Blades

13 and 14 reduce the axial length of the inducer, as the number of blades is inversely proportional to the axial length of `the inducer for any set of given parameters, i.e., those noted above. sharply increasing blade angle in the intermediate section of the inducer thereby provides both the advantage of a faster increase in pressure rise in the fluid and also of providing more room for additional blades, both orf which reduce the over-all length of the inducer for a given inducer radius.

Over the inlet or suction portion of the inducer, i.e., from 0 to about 0.8 in FIGURE 2, cavitation presents the greatest problem and the rate of blade angle change is therefore based upon a cavitation criterion described below, and in the outlet or impeller portion of the inducer, i.e., 0.8 to 2.180 in FIGURE 2, separation is the greatest problem and the rate of change in blade angles in this portion is determined by a separation criterion discussed in detail below, so that the rate of change of blade angle with respect to theI axial distance in each portion does not exceed the more severe of the two limitations.

Blaae angles in embodiment I An expression for the cavitation limitation is obtained by equating the pressure of the suction side, i.e., low pressure side, of the Iblad-e to a value somewhat higher than the cavitation pressure. This determines the maximum bladeangles at every axial station in the suction or inlet portion of the inducer. An expression ttor the separation limitation or criterion is obtained by assuring a positive velocity head on the pressure side of the blade. This expression then limits and defines the blade angles in the impeller or outlet portion of the inducer.

From the general energy and continuity equations, an expression for the axial velocity component of uid owing through the inducer is derived as a function of the change in local pressure and the tip blade angles. This expression for the axial velocity is expanded in terms of the pressure change between adjacent blades. Then the pressure at an vaxial station is equated to the pressure difference across the blade at that station resulting in a denition of the blade angle which will give a maximum pressure rise across the blade without producing cavitation. The basic objective in preventing `cavitation in the suction end of the inducer is to have a maximum blade angle at leach axial station in the inducer which produces a pressure differential between adjacent blades which is equal to or less than a vconstant m times the mean tluid pressure at an axial station. By definition then, m` is the ratio of the pressure rise across a blade at an axial station to the mean uid pressure at that axial station Z where the mean fluid pressure is the net pressure head Po above the vapor pressure of the hydraulic uid plus the change in local pressure APz of the fluid in the stream line. Values of this 4ratio m from .95 to 1.2 have been found to give pump performance closely approximating the theoretical results. However, under centain conditions this range may be extended to m=.75 to 1.25.

FIGURE 3 shows these relationships when APb is the. pressure difference between yadjacent blades, Po is the net pressure above the vapor pressure of the fluid being pumped and APZ is the change in local pressure in the streamline. ',Actually, t-he pressure change across the blade is not constant but in fact dips rather sharply at i In accordance with the desired relationship APb=m[APzl-Pc].

The j To prevent separation at the high pressure side of the blade the pressure change between the blades must be equal to or less than the velocity head of the uid in the streamline times a constant m. This is represented by the equation:

where e=the mass per unit volume C is the average velocity of the fluid between the blades in the streamline as noted in FIGURE 4. The ratio m is then merely the Huid coeicient `and the range of values thereof are approximately the same as the ratio m noted above. By maintaining the pressure change AP,u across the blade below this value, the pressure on the high pressure side of the blade will not become so great that stagnation and backow of the iluid occurs.

Obviously, the use of lower values of m and m' in the analysis will increase the axial length of the inducer to provide a given outlet head because a lesser rate of increase in the blade angles requires a greater inducer length. The over-all effect is then that the flow is turned at a slower rate and the inducer design is more conservative. An equation representing the cavitation limit-ation noted above in terms of blade angles and axial length is developed as follows:

Referring to the vector diagram -of FIGURE 5, U is the rotor velocity in a direction perpendicular to the inducer axis of rotation. As the rot-or has no movement along its axis of rotation, the rotor itself has only a tangential velocity. The velocity of the hydraulic fluid is represented by the absolute velocity component C, the axial velocity WZ and the relative velocity W of the fluid with respect to the inducer blade. The relative velocity W has a tangential component Wu, and the abs-olute velocity C has a tangential component Cu. As the relative velocity W is along the surface of the inducer blade at any point on the blade, the angle indicates the angle of the blade at that axial station on the inducer with a plane transverse to the -axis `of rotation lat that station.

The cavitation analysis sets the restrictions on the inlet blade angle o of the inducer, and on the rate of blade angle change near the inducer inlet. The criteria for cavitation is based on the Euler flow equations and the continuity equation. The equations assume in the following development that the fluid has a zero radial velocity with steady state conditions and negligible body forces in all directions. The body forces, eg., gravity, are small because of the small dimensions of the inducer. These `assumptions apply directly to the tip of the inducer blade as radial flow at this point is prohibited by the tube wall which shrouds the inducer.

The equations for motion in the tangential and axial directions from Stodola 1 in polar coordinates:

where Cr is the absolute radial velocity component, '6P equals partial diiferential pressure, m equals body forces,

is the substantial derivative, r is the radius of the blade at the selected axial point, Z is the axial length at the selected point, and p is the polar angle. Assuming the radial velocity Cr to be zero, neglecting body forces m lsteam and Gas Turbines, :Sitodola-Loewenstein, vol. 2 McGraw-Hill, 1945.

and considering only the incompressible steady state cases, the equations are reduced to:

DCu l DW di T e Tt@ dt dC W,` Tgo- 2 Now since the substantial derivative is the sum of the partial derivatives: f

and neglecting the radial velocity component, the energy equations become:

By definition aca Z- Substituting the continuity equation into these equations,

Ta v which represents the tangential pressure change, and

and substituting the values of -the tangential and axial pressure changes noted above, we obtain:

By assuming that the blade angle does not` change significantly with the polar angle p, compared to the variation of the blade angle with respect to the change in the axial length Z, the right-hand expression drops out. This assumption is accurate as the blades are fairly close together and are assumed parallel. This reduces the above equation, dividing by BZ and rearranging, to:

Now integrating -this derivative over the axial length Z or dZ: r

We arrive at an expression for the change in pressure at any axial station in terms of the axial velocity of the uid and the blade angle at the station:

nAPb: fdP= f- SW3 Z where n=number of blades, and

Since the integral dq: is 21r.

We now have expressions for both the pressure change across the blade APb and the change in local pressure APb and the change in local pressure APZ both in terms of the axial velocity of the fluid WZ and the blade angle. Remembering that our initial cavitation criteria requires that the change in pressure across the blade API, be equal to or less than m times the sum of the local pressure change and the vapor pressure of the hydraulic fluid an expression is readily derived eliminating the unknown pressure parameters and defining the blade angle as a function of the axial length as follows:

-dZ= Po where D=2r,

The above equation gives values of the ratio of axial length to the diameter of the inducer, Z/D, as a function of the blade angle with all other terms being constant, and represents the expanded cavitation criteria represented in FIGURE 7 as

curves

30 and 31 for a two and four blade inducer, respectively. The curves are drawn with m, the ratio of the pressure change across the blade to the local pressure in the stream line, equal to one. The

curves

30 and 31 therefore represent the maximum blade angles at every axial s-tation along the inducer blade without producing cavitation on the suction side of the blade at any point along the inducer. And the slope of the

curves

30 and 31 represent the maximum change in blade angle along the inducer length to prevent this cavitation.

The second limitation on the rate of change in blade angle is the separation criteria noted above. It will be remembered that this criteria maintains the pressure change across the blade equal to-or less than the absolute velocity head times a constant m' and broken down into radial and axial components is:

2 2 Fmfetuma `Now equating this expression for Ithe pressure change AP,J developed above:

2 2 em/(Wz 'Cu 27|'7 COl which reduces to:

This equation gives the blade angle as a linear function of the inducer length Z/D and represents the expanded flow separation expression or criterion. Referring to FIGURE 7,

lines

35, 36 and 37 have a slope developed from the latter equation and represent the maximum blade angle at every axial station which will prevent separation, and the slope of these

lines

35, 36 and 37 define the maximum rate of change of blade angle to prevent separation or backflow on the high pressure or impeller lside of the inducer blades. Assuming that a two blade inducer is desired, it can be seen that the slope of curve 30 is less than the slope of line 35 up to values of Z/D of about .5. Therefore, since the cavitation criterion places the greatest limitation on Ithe rate of change in the blade angle in this suction or inlet portion of the inducer, the blade angles cannot change any faster than the slope of curve 30 from the inducer inlet to the axial position where the length divided by the diameter of the inducer is around .5 inches. It should be noted that the values in FIGURE 7 are merely exemplary for certain given ilow conditions and desired inlet and outlet heads. However, -the rate of blade angle change with respect to the axial length is always constant for a given number of blades using the separation criterion.

The point of intersection of the curves dening the cavitation criterion and the flow separation criterion may be found by equa-ting the slopes of the two curves, and, reduced and rearranged for blade angle;

where is the blade angle defining an axial position on the inducer where the blade Iangles on lone side of the position, i.e., suction side of the inducer, are determined by the cavitation lcriterion and the blade angles on the other side of the position, i.e., impel-ler or outlet portion side, are determined by the separation cirterion curve. The cnossed line in FIGURE 7 indicates the blade angles of an inducer section having two blades, such as the 'suction portion shown in FIGURE l. That is, from the inlet of the yinducer moving axially to a point where the length divided by the inducer diameter is about .5, the rate in change in blade angles corresponds to the change in the slopes of curve 30. It can be seen that for small values lof Z/D the 4blade angle increases only very slightly but in the range of Z/D=.2 to .5 the blade angle increases more rapidly to where the blade angle equals the blade angle i. But beginning at this point the slope of line 30 is greater than the slope of line 35 and therefore curve 35 must dictate the blade yangles `from that point to the outlet end of the inducer as this curve permits an increase in blade angle less rapid than curve 30 in this section.

Following the above design principles, it is possible to increase the blade angles 50% over the blade angle at the inlet end of the inducer without increasing the length of the inducer over that conventionally used in inducer design producing a Ilesser outlet head.

The above analysis assumes that `cavitation and separation 'are most severe at the tip of the inducer blade and therefore the tip selected as the design condition. As the axial length varies as a logarithmic function of the tangential velocity of the fluid Cu, the higher the tangential velocity the longer the required axial length of the inducer. The elfect of the radial position selected as the design point on the required axial length of the inducer is small and in the direction of reducing the required length.

FIGURE 8 represents the actual development of the inducer blades in a straight hub inducer similar to that shown in FIGURE l except with a smaller blade tip rad-ius and longer 'axial length.

9 CONICAI, HUB-EMBODIMENT II Referring to FIGURE 9 wherein a conical hub inducer ygenerally indicated -by the numeral 110 is shown having a conical hub 111 and a blade 112. It should be understood that onlyone blade is-shown on the inducer for the purpose of clarity and additional blades may be e-mployed if space permits. End portion 114 of blade 112 is the inlet end of the :inducer while the end portion 115 of the blade 112 represents the outlet or impel'ler side of the inducer. The const-ant diameter portion 120` of the hu'b 111 is adapted to [be connected to the drive shaft of a radial ow impeller or plump and driven in 1-1 ratio with the pump along a common axis.

The advantage in employing a -conical hub inducer is because of the ygreater area in the inlet or suction end of the inducer lesser inlet velocities may be used.

However, the shape of the conical hub in this type of an inducer accentuates flow problems not 'found in a heavy hub straight inducer such as that shown in FIGURE 1. In the analysis above for the stra-ight hub inducer it was assumed that the fluid traveled at some average axial velocity along the radius of the blade at any axial station, such as radian 121. However, this assumption is not altogether Iaccurate and results in problems in a conical hub inducerV because of the variable `flow areas. And further, in sections of the inducer having small hub radii the velocity of the fluid from the tip to the hub decreases and if the hub has too small a diameter backflow will occur `along the hulb surface. Now ythis separation at the hub surface reduces the eifective llow area through the inducer yand eventually causes cavitation.

Now the analysis below develops the minimum hub radius rh which wil-l prevent separation around the hub surface. Additionally the equations derived for the blade angles take into consideration the varying axial velocity of the fluid along any radiari of the Iblade at any axial station.

From the general energy equation an expression for the axial veloci-ty component as a function of the hub radius and the tip blade angle is derived. This expression for the axial Velocity when substituted into the continuity equation results in an expression `for the hub radius 'as a function of the tip blade angle. Then the pressure at an axial station is equated to the pressure difference across the blade to derive an expression for the blade angles in the suction section as a function of the axial station.

In this analysis an expression for the radial blade angles at a `given axial stat-ion is developed for the axial velocity component, Wz as the function of the iblade or inducer radius. The expression for the axial velocity component is then substituted in-to the continuity equation -for the tlow and integratedto match the flow rate at the inducer inlet. Note that no avera-ge value is assumed Vfor the axial velocity component WZ and was done in the straight hub analysis in modification 1. This analysis therefore is applicable to all ind-ucer hub designs either straight, conical, or other hub configurations.

As the axial velo-city of the uid is now Iassumed to f 10 where the constant is simply the total inlet head which is the same for every streamline and where:

W=relative Velocity f=head rise at any axial station S= potential head U=inducer velocity Now considering only one axial station and concentrating on the radial variations in head rise we can develop the desired relationship between axial velocities and huib radius. Eulers equation of motion in the radial direction 1s:

2 der oTus +R where:

Cr=radial velocity=0 r=radius R=body forces The radial velocity component is neglected as this is very small in relation to the effect of the other variables, neglecting .body forces which are also negligible and the potential head Q/g, the energy equation becomes, when broken down into velocity components:

Referring to FIGURE 1l,

we can find an expression for Wu in terms of WZ as follows:

2 WuZ=WZ2 tan2 =WZ2(%) tan2 Substituting this into the general energy equation for Wu we find:

-ll) Ud U= constant t Iand letting tan t Ut and substituting (g) Ud U Now differenti-ating this expression with respect to lthe absolute velocity of the blade a ldifferential equation in terms of WZ, U and a is obtained, Whioh when solved for WZ is as follows:

which when rearranged results in:

This expression relates the axial velocity of the fluid as a variable with lthe axial velocity of the iluid .at the tip, the velocity of the inducer, and the blade angle at tip. 'Ilhe curve represented by this expression is de- 'veloped in FIGURE 12 for a particular blade tip angle. It can be readily see-n that as the radius approaches zero the axial flow will go below zero resulting in backflow and separation. Therefore, to prevent this separation all along the length of the hub, it is necessary to develop an expression for the poi-nt Where the curve in FIGURE 12 crosses the zero velocity abcissa for Iall blade angles as the blade angles throughout the inducer vary.

To Iarrive at an expression for the rradius of the hub rh in terms of the blade tip angle, t, it is necessary to eliminate the variable WZ and eventually WZt from the above expression. To develop this expression'the continuity equation is employed as follows:

a cos t sin t cost sin Ut Ttw and e: WZtLi-a Utz Substituting this Wz into the continuity integral above and integrating from rh to rt tlhe following expression is arrived at:

[aw-Th2] e b amg C As the above expression still contains the blade tip velocity WZt which varies over the axial length, this does not express a direct relation between the blade tip angle and the hub radius. Therefore to obtain an expression in terms of rh, the hub radius, and the blade angle at the tip t only, it is necessary to select an axial velocity of the fluid at the hub, WZh, in terms of the velocity of the fluid at the tip so that the velocities may be eliminate-d from the expression. For this purpose the axial velocity at the hub is equated to some positive fraction, l/K, of the tip axial velocity; so that Wzh equals WZt/K. The selection of the proper value of K prevents the axial velocity at the lhub from coming too close to zero or negative in which cases the llow would reverse itself -at the hub. A reasonable value for K is about 4, so that the hub axial velocity is theoretically of the velocity of the fluid at the tip, although a margin of safety is allowed to account for trictionfal and boundary layer effects. Now substituting this value of WZ,1 into and then substituting the resulting expression for e into the continuity equation above, the vfinal relation for the hub madiu-s in tenms of the angle of the blade at the tip t is defined by:

This equation is readily solved by trial and error choosing -a valueof t and K in calculating a, band c. rDhe terms Q, .w and rt are known constants from fthe 1volnme flow, r.p.m. and inducer outer diameter. Therefore for each value of t the value of rh is obtained. A

graph illustrating this relationship is shown in FIG- URE 13 where the curve is seen to be similarl to a sin2 t curve and itis a maximum at t equal to 45 degrees. The radius at the inlet `does not intersect the curve of the equation at the inlet angle ,30 unless K equals l, as WZ, equals WZh just before the inlet. "Dherefore a smooth transition curve may be vdrawn as shown in FIGURE 13 to match the inlet with the design equation. The above analysis is concerned only with minimum hub radii to prevent separation at the hub for a given blade angle at any axial station.

The final portion of the analysis in the conical hub inducer embodiment is concerned with the change in blade angle at each axial station to -prevent cavitation. This analysis begins with t-he same basic cavitation criterion as developed in the embodiment 1 but in the development of the cavitation curve similar to curves 30` and 31 the cha-nge or variation in axial-velocities along the radius at each axial station are taken into consideration. Therefore the relationship between blade angle and length at each axial station developed below is applicable to inducers having variable ilow areas.

Beginning with the same basic .cavitation criterion as developed above, that is:

which says that the change in pressure across the blade must be equal to or less than the local pressure of the fluid in the streamline. The nomenclature employed is identical to that we find in the straight hub embodiment.v Integrating this expression at the tip where WZ is largest:

Where Pt equals the pressure at the tip, this equation is identical to that developed in modification 1 except in there the expression Vcould be integrated directly as WZt was assumed to be some average value because of the straight hub desi-gn. However, in this analysis as WZt is not assumed constant over the radius the variable WZt is obtained by solving for e from the integrated form of the continuity equation which -was developed -above with respect to the hub radius:

13 which when solved for WZt results in:

[Th2 Th2] awzb e: i-*"w (www u [Hagi This equation gives values for WZt upon direct substit-ution of the values rh and t in the curver of FIGUR-E 13. The remaining variable PZ is obtained by means of the integrated form of a general energy equation as follows:

which can be solved directly for each value of Wzt and substituted into the integral relationship of (Z/D)t developed above to find the maximum blade angles at each axial station `which will prevent cavitation.

Referring to FIGURE 14, a cavitation curve 130 is developed substituting values into the blade angle integrand expression above for given set of inducer conditions. Thus the curve 130 represents the maximum blade angles in the suction end of the inducer. Again, in the first axial portion of the inducer from approximately zero to two inches in FIGURE 14, which is numerically merely exemplary, there is on-ly a very small change in slope of the cavitation curve which means that the -blade langles in this first or initial portion of the inducer must change very slowly to prevent cavit-ation. However in the intermediate portion of the inducer from about two inches from the suction end to over four inches from the suction end the cavitation curve 130 is seen to turn more rapidly and therebyindicates that the rate of blade angle change in this section may 4be muchfaster than in the first section.

The separation limitation curve 131 noted in FIGURE 14 is developed by the equations noted above in the straight hub inducer of FIGURE l. A consideration of the eifect of variable flow areas has no inuence on the separation limitations and therefore these equations in modification 1 are equally applicable to the conical hub inducer embodiment shown in FIGURE 9. It should be noted that FIGURE 14 shows only a portion of the cavitation curve which intersects the separation curve at the right hand end of the graph. Therefore, in the exemplary .conditions shown in FIGURE 14, for blade angles greater than 35 degrees the slope of the separation limit curve 131 would dictate the rate of change in the blade curvature. That is, the shape of the blades beyond about 4.6 inches from the inlet end of the inducer would be determined by the slope of curve `131.

FIGURE 16 is an actual performance curve of the embodiment shown in FIGURE 9 taking into account axial Velocity variations. Curve 140 represents the net positive suction head, NPSH, plotted against the fluid iiow in gallons per minute, and curve 141 represents the suction specific speed, S, both for a centrifugal pump without an inducer. These curves are to be contrasted with curves 144 and 145 which show the NPSH and a suction specific speed respectively for the same centrifugal pump with an inducer calculated in accordance with the expressions developed above in the conical hub embodiment. Point 146 indicates the suction specific speed design point. It is readily Iapparent that the actual suction specific speed shown in curve 145 closely approximates that the design point 146 at the maximum fiow conditions.

this expression closely approximate the actual flow conditions inthe inducer.

I claim:

1. An inducer for a radial flow pump, comprising; an elongated hub member having an axis of rotation and adapted to be directly driven by said radial flow pump, at least one blade extending around and from said hub member, one axial end of said blade being the suction end thereof, the other axial end of said blade being the outlet end thereof, said blade defining blade angles with transverse planes through said axis of rotation, said blade angles increasing at a rate below a predetermined rate in a first portion of the blade extending from said suction end, said blade angles Vincreasing at a rate above said predetermined rate in a second port-ion of the blade extending from said iirst portion toward said outlet end whereby the blades turn faster in said second portion and permit a reduction in the axial length of the inducer.

2. An inducer for a radial flow pump, comprising; an elongated hub member having an axis of rotation, at least one -blade extending radially from and around said hub member, said blade defining blade angles with planes perpendicular to said axis of rotation, one axial end of said blade being the suction end, the other axial end of said blade being the outlet end, said blade angles increasing in a first portion of said blade extending from said suction end at a rate below a predetermined rate, said blade angles increasing in a second portion of the blade extending from said first portion toward said outlet end at a rate above said predetermined rate, and said blade angles increasing at a constant rate in a third portion of the inducer extending from said second portion to said outlet end whereby cavitation is prevented in said first and second portions and separation is prevented in said third portion.

3. An inducer 4for a radial flow pump, comprising; a hub member having an axis of rotation, at least one blade extending from and around said hub member, said blade defining blade angles with a plane transverse to said axis on every point along said axis, one axial end of said blade being the suction end, the other axial end of said blade being the outlet end, the rate of change of said blade angles in a first portion of said blade extending from said suction end being below a predetermined rate to prevent cavitation, the rate of change of said blade angles in a second portion of the blade extending from the outlet end -being constant at a value to prevent separation of the fiuid.

4. An inducer as defined in claim 3 wherein, the rate of change of said blade angles on the first portion of the blade increases from the suction end of the blade.

5. An inducer as defined in claim 3, wherein, the rate of change of said blade angles in the second portion of the inducer is equal to the highest rate of change of the blade angles in the first portion of the inducer.

6. An inducer for a pump, comprising; an elongated hub member having an axis of rotation, at least one blade extending from and around said hub member, said blade 'defining blade angles with planes transverse to said axis, one axial end of said bladelbeing the suction end, the other axial end of said blade being the outlet end, said blade angles increasing at a rate suflicient to produce a ypressure differential across said blade equal to mI times the local pressure in the streamline of the iiow between the blades in a portion of said blade extending from said suction end thereof whereby cavitation is prevented.

7. An inducer as defined in claim 6, wherein the constant m is in the range of .75 to 1.25.

8. An inducer as delined in claim 6, wherein the constant m is in the range of .95 to 1.1.

9. An inducer for a radial flow hydraulic pump, comprising; an elongated hub having an axis of rotation, at least one blade extending from and around said hub member, said blade defining blade angles with transverse planes across said axis of rotation, one axial end of said blade being the suction end, the other axial end of said blade being the outlet end, a first axial portion of said blade extending from said suction end having increasing blade angles at a rate sucient to produce a pressure rise across the blade equal to m times the local pressure in the fluid streamline for every point along said axis in said rst portion, a second axial portion of said blade extending from said outlet end having increasing blade angles at a rate sufficient to produce a pressure drop across said blade equal to m times the velocity head of the fluid in the streamline for every point along said axis in said second portion, whereby cavitation and separation are prevented throughout the length of the inducer.

10. An inducer for a fluid pump, comprising; an elongated hub member having an axis of rotation, at least one blade extending radially from and around said hub member and having a suction end axially spaced from an outlet end, said blade defining blade angles with planes transverse to said axis, said blade angles increasing at a constant rate in one portion of said -blade sufficient to produce a pressure change across the blade equal to m. times the velocity head in the streamline Where m' is constant, whereby separation is prevented in the inducer.

11. An inducer as dened in claim 10, wherein m has a range of .95 to 1.2.

12. An inducer for a fluid pump, comprising; an elongated hub having an axis of rotation, at least one blade extending from and around said hub member and having a suction end and an outlet end axially spaced therefrom, said hub member having smaller radii adjacent said suction end than adjacent said outlet end, said blade defining Vvblade angles with planes transverse to said axis, said hub having radii between said suction end and said outlet end defined approximately by sin Z where equals the yblade angle in the transverse planes containing said defined radii, whereby separation at the hub is prevented.

13. An inducer for a fluid pump, comprising; an elongated hub having .an axis of rotation, at least one blade extending from and around said hub member and having a suction end and an -outlet end spaced axially therefrom, said blade defining blade angles with planes transverse to said .axis of rotation, the blade angles in a first portion of said blade extending from said suction end increasing at a rate sufiicient to produce a pressure change across said blade equal to m times the local pressure in the fiuid streamline where m is constant, said hub member having smaller radii adjacent said suction end than adjacent said outlet end, the radii of said hub member between said suction end and said outlet end being defined substantially sin 2 where ,8 is the blade angles in the transverse planes containing the defined radii.

14. An inducer as defined in claim 13, and further including a second portion of said blade extending from said outlet end having blade angles increasing toward :said outlet end at a rate sufiicient to produce a pressure change across the blade equal m times to the velocity head of the fluid in the streamline where m is constant, 'whereby separati-on is prevented in said second portion.

15. An inducer for a fluid pump, comprising; an elon- :gated hub member having an axis of rotation, at least one blade extending from and Iaround said hub member and having a suction end and an outlet end spaced axially from said suction end, said blade defining blade angles with planes transverse to said axis, said blade angles increasing in a rst portion of said blade extending from said suction end at a rate defined by;

16. An inducer for a fiuid pump, comprising; an elongated hub member having an axis of rotation, at least one blade member extending from and around said hub member and having a .suction end and an outlet end axially spaced from said system end, said blade defining blade angles with planes transverse to said axis of rotation, a portion of said blade extending from said outlet end ltoward the suction end having blade angles increasing toward said outlet end at a rate defined by;

where zblade angle at an axial station Z, Z=an axial station, D=outside diameter of the blade, n=number of blades, and Y m=constant in the range of 0.5 to 1.5.

17. An inducer for a fiuid pump, comprising; an elongated hub member having an axis of rotation, a blade extending from and around said hub member and having a suction end and anl outlet end spaced axially therefrom, said blade defining blade angles with planes transverse to said Iaxis of rotation, a portion of said blade extending from said suction end having blade angles increasing from said suction end. at rates defined by;

where Z--distance from the suction end, D=diameter of the blade, t=blade angle at the blade tip, o=blade angle at the suction end, Wzt=axial velocity of the fluid at the tip, Pzt=pressure at the tip,

m=constant, n=number of blades, and p=density of the fluid,

whereby cavitation is prevented in said portion.

18. An inducer as defined in claim 17 wherein th-e value `of the axial velocity `at the blade tip is:

Q=volume flow,

w: (angular velocity of the hub),

rt=radius of the bladetip, rh=radius of the hub,

U=velocity of the rotor at the tip,

Itty-:blade angle at the tip,

and the value of WL P q W 2P iii/ PH-P+ 2g 2g sin2 tg where, P=net pressure above the vapor pressure of the fluid.

19. An inducer for a huid pump, comprising; an elongated hub having an axis of rotation, a-t least one blade extending from and around said hub land having a suction end and an outlet end spaced axially therefrom, said blade defining blade angles with planes transverse to said axis, said hub having radii smaller at said s-uction end than at said outlet end, the radius of said hub between sa'id suction end and said outlet end being defined by the relationship:

where Wzt=axial fluid velocity at the blade tip, K=positive constant,

Ut=velocity of the blade at the tip, rh=radius of the hub,

w=angular velocity of the inducer, and

a, b, and c are functions of the blade angle,

whereby the hub has a sufficient radius to prevent separation along the hub surface.

20. An inducer for a uid pump, comprising; an elongated hub h-aving an axis of rotation, at least one blade extending from and around said hub and having a suction end and an outlet end spaced axially therefrom, said blade defining vblade angles with planes transverse to said axis of rotation, said hub having smaller radii `adjacent said suction end than adjacent said outlet end, the hub having radii between said suction end -and said outlet end defined Q=volume ow,

w=angular velocity of the inducer, rt=radius of the blade tip, rh=radius of the hub, K=constant,

t=blade angle at the blade tip,

whereby separation is prevented along the hub.

21. An inducer for a uid pump, comprising; an elonga-ted hub 4member having an axis of rotation, -at least one blade extending from and around said hub member and having a suction end and an outlet end, said blade deiining blade angles with planes transverse to said -axs of rotation, said hub Ihaving smaller radii adjacent said suction end than -adjacent said outlet end, a portion of said blade extending from said suction end having blade 18 angles increasing from said suction end at increasing rates dened by;

: "VvVztzdt au Pz,

gmn sing p where whereby cavitation is prevented in said portion, and the radii of the hub between said suction end and said outlet end being dened by;

K b-rCrlf w-here Wzt=axiial tiuid velocity at the blade tip, Kzconstant,

Ut=velocity of the blade at the tip, rh=radius of the hub,

wzan-gular velocity of the inducer, and a, b, and c are functions of the blade angle,

whereby separation along the hub is prevented.

22. An axial ow inducer for a radial flow pump, comprising: an elongated hub member having an axis of rotation, `at least one blade extending around and from said hub member, said blade defining blade angles with transverse `planes extending through said axis of rotation, one axial end of said blade being the suction end adapted to receive the uid to -be induced and the other axial end of t-he blade being the outlet or discharge end, said blade having increasing Iblade angles from said suction end to said outlet end, the rate of change of said blade Aangles increasing over lat least a portion of the axial length of the inducer from said suction end to said outlet end.

References Cited by the Examiner UNITED STATES PATENTS 907,591 12/1908 Gilday 230-120 1,199,374 9/1916 Hagen 230-120 1,199,375 9/1916 Hagen 230-120 1,509,65 3 9/ 1924 Kaplan 103--115 1,688,808 10/ 1928 Gill 10-3-8'9 1,807,397 5/ 1931 Feehheimer 103-87 1,887,417 11/1932 Mawson 103-89 2,378,372 6/ 1945 Whittle 230-122 2,384,000 9/1945 Wattendref 230-122 2,426,270 8/ 1947 Howell 230-122 2,505,755 5/1950 Canahl et al. 230-122 2,605,956 8/ 1952 Gardiner 230-122 2,698,249 1/ 1961 Caine et al 103-83 3,028,140 4/ 196-2 Lage 103-115 3,059,834 10/1962 Hausammann 230-134-2 3,068,799 12/'1962 Lock 103-113 3,070,061 12/ 1962 Rightmyer 115-34 3,163,119 12/1964 Huppert et al. 103-89 3,168,048 2/ 1965 Toyokura et al. 103-89 FOREIGN PATENTS 801,772 5/ 1943 France.

912,181 4/ 1946 France.

DONLEY I. STOCKING, Primary Examiner.

HENRY F. RADUAZO, Examiner.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3,299 ,821 January 24 1967 David H. Silvern It is certified that error appears in the above identified patent and that said Letters Patent are hereby corrected as shown below:

Column l line 48 "blades" should read blade Column 3 line l5, "the bow of" should read both the Column 4 lines 2l and 25, "0.8", each occurrence, should read 1.8 Column 5 lines 6 to 8 the equation should appear as shown below: mlgCZ 2 same column 5 line 27 column 10, lines 9 and 71 and column l1 line 32, "U", each occurrence, should read u Column 5 line 43 and column 7 lines 16, 62 and 63 "criteria", each occurrence should read criterion Column 5, lines SS to 64, the equations should appear as shown below:

D C 1 1 CrCu l 3P dt I e IBp DW l a-E M Z aZ SSTC SeIW r u Z 0 at rap az same column 5 lines 66 and 73, "m" each occurrence should read U M lines 67 and 68 the equation should appear as shown below:

same column 5 line 72 "p" should read gp Column 6, lines 1l to 13 the equation should appear as shown below:

D() m .LQ L). Cr ar C" rap WZ az same column 6 lines 28 to 32 the equation should appear as shown below same column 6 lines 43 to 45 the equation should appear as shown below:

same column 6 lines 48 to 50 the equation should appear as shown below:

BCOt

same column 6 lines 59 to 62 the equation should appear as shown below:

Column 7 line l "dP/dU" should read dP/dp lipes 4 to 6 the equation should appear as shown below:

same column 7 line 64 "absolute" should read relative lines 67 to 70 the equation should appear as shown below:

2 Z z Wu U' g Column 8 line 48 "slopes" should read vslope line 65 after "tip" insert is Column 9, line 3, cancel "wherein".

Column l0 lines l5 to 18 the equation should appear as shown below:

2 dcr Cu l 8P dt r e Br same column l0 lines 29 to 3l the equation should appear as shown below:

(3) wi U2 W (wu ulz +I du=F=Constant 2 2 2 U same column l0, lines 47 to 50, the equation should appear as shown below:

2 a 2 2 l 2 Q 2 2 l Wu WZ tan -MWZ (Ut) tan St same column 10, lines 52 to 57, the equation should appear as shown below:

tan tv- J l UdU=Constant 2 2 2l U 2Ut t same column l0, lines S9 to 61, the equation should appear as shown below:

same column l0, lines 63 to 65, the equation should appear as shown below:

U 4'2") UdU same column 10 line 67 the equation should appear as shown below:

a2WU2`UZ+W+ffGWZ l) 2d (U21 Constant same column l0 l'nes 73 to 75 the equation should appear as shown below:

Column ll, lines 2 to 6, the equation should appear as shown below:

sn2 at cos2 et C same column ll

lines

36 and 37 the equation should appear as shown below:

Ut rw same column ll lines 43 to 47 the equations should appear as shown below:

e =Wzt aUt2 and substituting in the expression developed above for WZ b+cr2 same column ll lines 52 to 56 the equation should appear as shown below:

Column l2 lines 3 to 5 the equation should appear as shown below:

2 2 2 WZ (Ut -rh w )a K b Crhz same column l2 lines 8 and 9 the equation should appear as shown below:

(5) e I"8:2 (b+C1h2) KIhZ rtzb+ [Grtz-K) Th2 2 Z A 2 aw b+c1^h -K b-l-crh -K same column 12 line Z8 "snzt" should read sin Zt line 44 "are" should read is lines 59 to 63 the equation should appear as shown below:

it' gmn sin Bt same column l2 lines 73 to 75 the equation should appear as shown below:

Column 13 lines Z to 6 the equation should appear as shown below:

ll to l3 the equation should appeal` as shown below: t

2g 2g g 2 Constant inlet head g same column 13 lines 19 to 2l the equation should appear. as shown below:

2 Z P W 2 W Z1; Po t t t p 2g 2g sin2 Bt (2g) same column 13, line 60 "16" should read 15 Column 16, lines 59 to 62 the equation should appear as shown below:

, 2 WZt l -W 2 2 (2c) aUJC Column 17 line l "U" should read u lines 5 to 7 the equation should appear as shown below:

2 2 P P WZ p Ut2p Wzt p l: O x

same column 17 lines 20 to 22 the equation should appear as shown below:

2 2 Wzt WZ w )a same column 17 line 27 and column 18 line 29, "Ut", each occurrence should read ut Column l7 lines 44 to 46 the equation should appear as shown below:

'Haw

b'i'crh2"K Column l8 lines 22 to 24 the equation should appear as shown below:

K b CI'hZ Signed and sealed this 14th day of April 1970.

`(SEAL) Attest:

EDWARD M.FLETCHER,JR. WILLIAM E. SCHUYLER, JR.

Attesting Officer Commissioner of Patents

Claims

1. AN INDUCER FOR A RADIAL FLOW PUMP, COMPRISING; AN ELONGATED HUB MEMBER HAVING AN AXIS OF ROTATION AND ADAPTED TO BE DIRECTLY DRIVEN BY SAID RADIAL FLOW PUMP, AT LEAST ONE BLADE EXTENDING AROUND AND FROM SAID HUB MEMBER, ONE AXIAL END OF SAID BLADE BEING THE SUCTION END THEREOF, THE OTHER AXIAL END OF SAID BLADE BEING THE OUTLET END THEREOF, SAID BLADE DEFINING BLADE ANGLES WITH TRANSVERSE PLANES THROUGH SAID AXIS OF ROTATION, SAID BLADE ANGLES INCREASING AT A RATE BELOW A PREDETERMINED RATE IN A FIRST PORTION OF THE BLADE EXTENDING FROM SAID SUCTION END, SAID BLADE ANGLES INCREASING AT A RATE ABOVE SAID PREDETERMINED RATE IN A SECOND PORTION OF THE BLADE EXTENDING FROM SAID FIRST PORTION TOWARD SAID OUTLET END WHEREBY THE BLADES TURN FASTER IN SAID SECOND PORTION AND PERMIT A REDUCTION IN THE AXIAL LENGTH OF THE INDUCER.