US2505755A - Axial flow compressor - Google Patents

Description

y 1950 c. DE GANAHL ETAL 2,595,755

AXIAL FLOW coupmsson Filed June 10, 1946 ENTRANCE FUT' .STATOR ROTOR 4 Sheets-Sheet 1 EXIT ENTRANCE S'ITITOR INVENTORS an de GHNfll/L 1 L ROOT 3m ATTORN EY5 M y 2, 1950 c. DE GANAHL ETA]. 2,505,755

AXIAL FLOW CDHPRESSOR Filed June 10. 1946 4 Sheets-Sheet 2 E/VDPfl/VCE- 574701? R0701? I E X I 7-6 7/7701? T 533.33 T 594.07 I T 582.40 P l.0926 P =l.5936 P =L488l T 528.46 Tax 577. 76 P Pax- 'r -54aa5 l l T75 5825! P I.I474 P 1.55:5 (-600 as, so,

INVENTORS 65 d8 GfiNflI/L JUSEP/I Col Fl IND HUGO F. BAJCI/ Em ATTORNEYS 4 Sheets-Sheet 3 EXIT- JT/JTOR May 2, 1950 c. DE GANAHL EI'AL AXIAL now COMPRESSOR 4 Sheets-Sheet 4 Filed June 10, 1946 /W/// ////l///// //////l./

/////Jr/// ///////J FLOW INVENTOR5 57/ a:

ATTORNEYS Patented May 2, 1950 UNITED STATES PATENT OFFICE AXIAL FLOW COMPRESSOR Application June 10, 1946, Serial No. 675,626 Claims. (Cl. 230-122) This invention relates to axial flow compressors for compressing air or other compressible fluid.

A single stage axial flow compressor, as distinguished from a centrifugal compressor, consists essentially of a compressor casing and a rotor comprising a central shaft or hub carrying a set of vanes or blades, the casing carrying a set of stationary blades constituting entrance stator blades and an additional set of blades which may be characterized as exit stator blades, the air flow being in a generally axial direction. A single stage compressor includes only one set of rotor blades associated with a set of entrance stator blades and with a set of exit stator blades. In a multistage compressor there are several sets of rotor blades and corresponding sets of stator blades.

This invention relates to improvements in axial iiow compressors, the compressor being either a single stage or a multistage compressor. The principal objects of this invention include the provision of rotor and stator blades forming fluid ducts for conducting the fluid in a generally axial direction through the compressor, and the provision of blades of this character so formed or shaped that the compressed fluid is directed axially in the exit stator with the fluid pressure substantially constant from the root to the tip portions of the blades, the configuration of the compressor blades also being such that the fluid velocity does not have any radial component at any point. Also the pressure 01' the fluid as it is directed axially in the exit stator may have a value that is substantially constant from the root to the tip portions of the exit stator blades. Our invention makes it possible to provide an axial flow compressor having numerous advantages, including the following:

a. The compressed fluid, as it flows axially in the exit stator ducts, has substantially the same pressure at all radially spaced points between root and tip portions of the blades forming the exit stator ducts and accordingly the tendency to cross current flow from a relatively high pressure region to a relatively low pressure region can be avoided.

b. The over-all dimensions may be reduced for a given air capacity and pressure rise.

0. Only a few stages of compression need be employed to produce the required increase in pressure; pressure ratios per stage may be in the order of 1.5 to 1.6 with high efficiencies approaching 90% or better.

d. The blades can be made much longer for a given diameter, thus greatly increasing the mass flow for a given diameter rotor.

. The rotational speed of the rotor is greatly reduced, thereby reducing the stored energy in the rotor and the tension forces in th material.

I. The weight and cost of the compressor can be reduced to a minimum because of simplification of manufacture and the fact that the over-all dimensions may be reduced to a minimum for a given capacity.

The design of axial flow compressors has heretofore been based almost entirely on airfoil theory which involves two assumptions, 1. e.. that the fluid is incompressible, or in other words the density is constant throughout a stage, and that the axial fluid velocity is constant through the various stages.

In the conventional type of axial flow compressor, the energy put into the air by the rotating blades produces a pressure rise in the rotor and also imparts whirl velocity to the air, this whirl velocity being converted into a further pressure rise by the stator blades. The conventional type of axial flow compressor is based on airfoil theory, airioils being used for both the rotating blades and the stator blades. At the tip the velocities should be kept below the valulns which would produce shock waves or local sonic velocities. At the root, stalling of the blades must be avoided, and accordingly the lift coefficient that can be applied at the root is limited. Since the pressure rise at the root should be kept as nearly equal as possible to the pressure rise at the tip, the limit of the pressure rise available is determined by the stalling of the blades at the root, and, for high efficiencies, by operating the blades at lift coeflicients with low drag values. These two factors restrict the length of the blade that can be used and likewise the capacity of the machine. first rotor stage, the flow of air is directed with the direction of motion of the rotor in order to reduce the velocity relative to the rotor blades and also to approach symmetry of velocity diagrams in the rotor and the stator blades; that is to enable the rotor to add an amount of whirl velocity equal to that which can be taken out by the succeeding stator blades.

We have found that a greatly improved axial flow compressor can be made if the basic assumptions of the airfoiI theory (1. e.. that the fluid is incompressible and that the axial fluid velocity is constant for the various stages) are In the entrance stator ahead of the ignored and the rotor and stator blades are constructed or formed in the manner hereinafter described whereby substantially constant pressure is obtained at all radially spaced points between the root and tip portions of the blades where the fluid flows axially, the blades also being preferably formed so that the fluid velocity does not have any radial component at any point.

In general, the principal object of this invention may be attained by forming the rotor and stator blades so that the same amount of energy per unit of compressible fluid is transmitted by the rotor to the fluid at the root portion of the rotor blades as at the tip portion of the rotor blades, even through the circumferential speed of the rotor blade tips is substantially greater than the circumferential speed oi the root portions of the rotor blades. The required configuration of the rotor and stator blades to accomplish this purpose may be determined with the highest degree of precision by first selecting appropriate exit angle for all entrance stator ducts and for all rotor ducts at all concentric zones or regions between the root and tip portions of the blades.

The amount of energy imparted to the fluid by the rotor is a function of the circumferential speed of the rotor and of the velocity of the fluid entering the rotor, and according to this invention the entrance stator blades and the rotor blades are shaped so as to provide progressively decreasing rotor entrance velocity from root to tip to compensate as completely as may be desired-for the increase in circumferential rotor speed between the root and tip of the rotor blades, whereby the root portions of the rotor blades, travelling at relatively low circumferential speed, may impart to the fluid entering the rotor at higher velocity than at the tip, the same amount of energy, the exit portions of the rotor blades being correspondingly shaped to insure this result at the rotor exit so that as the compressed fluid flows axially in the exit stator, it may have the same pressure at all radially spaced points in the exit stator.

In a compressor embodying this invention. there is a pressure stage, or amultiplicity of pressure stages, in which each stage is a combination of an entrance stator, a rotor, and exit stator.

In succeeding stages, the entrance stator to the next stage becomes a part of or is contiguous with the exit stator of the preceding stage. The iiow is axial between stages. i. e., the flow is purely axial as the fluid enters the entrance stator from the exit stator. The rotor blades and stator blades are preferably made of thin sheet metal and these blades are not airfoils. The spaces between the blades form channels which are either converging to form nozzles or diverging to iorm diii'users, as hereinafter explained. The cross sectional area of th channel or duct is proportional to the sine oi the angle the blade makes with a plane normal to the rotor axis. The solidity, i. e., the circumferential spacing of the blades, determines the angle of divergence or the angle of convergence of the duct, depending on whether the duct is a diffuser or a nozzle.

In the axial flow compressor of our invention. the entrance stator directs the fluid against the direction of rotation of the rotor rather than with this direction of rotation as in the conventional axial flow wmpressor, thereby increasing the relative velocity between the rotor blades and the entering air thus greatly reducing the re- I quired speed of the rotor as compared with the conventional compressor.

The angle of the blades at the rotor entrance is adjusted to be streamlined with the flow from the entrance stator. The channels formed by the blades in the rotor are dliiusers having the greatest area ratio at the root and the smallest at the tip.

According to one embodiment of our invention, the circumferential velocity at the exit of the entrance stator and the circumferential velocity at the entrance of the exit stator can be kept equal.

The angle between the airflow leaving the em trance stator and the plane normal to the rotor axis is greatest at "the tip and decreases toward the root. This progressive change in angle tends to increase the relative velocity between the rotor and the entering airflow from tip to root, compensating properly for the decreased rotor velocity toward the root of the blades. The entrance stator and the rotor are so formed that the rotor puts into the air the same amount of energy at the tip as it does at the root so that as the fluid is directed axially in the exit stator, there will be the same pressure and velocity from tip to root. To accomplish this end, the direction of the airflow is bent through a lesser angle of are at the tip than at the root. This increases the ratio between exit and entrance area at each radius of the rotor towards the root, again properly compensating for the decreased rotor velocity at the root. It also increases the amount of whirl velocity delivered to the airflow at the root, further compensating for the decreased rotor velocity at the root.

The entrance to the exit-stator is adjusted to be streamlined with the flow from the rotor at each radius, and is bent through an arc to pure axial flow on leaving the exit stator. The angle between the airflow entering the exit stator and a plane normal to the axis of the compressor is largest at the tip, and decreases towards the root, providing the necessary difference of ratio between exit area and entrance area at each radius to convert the different velocities into pressure.

The general conditions above described can be repeated through succeeding stages.

In the accompanying drawings, we have illustrated in diagrammatic form, elements of an axial flow compressor embodying our invention. In these drawings:

Fig. 1 represents a development of a cylindrical section taken at or near the tip portion of the stator and rotor blades;

Fig. 2 represents a similar development of a cylindrical section taken at the root of the stator and rotor blades;

Fig. 3 is a vector diagram showing typical fluid velocity conditions obtaining at several points in a duct formed by the tip portions of the rotor and stator blades of a compressor representing one embodiment of our invention;

Fig. 4 is a vector diagram showing typical fluid velocity conditions obtaining at several points in a duct formed by the root portions oi the rotor and stator blades of the embodiment of our invention to which Fig. 4 is applicable;

Fig. 5 is a longitudinal section of a portion of a single stage compressor embodying our invention;

Fig. 6 is an elevation of a rotor blade; and

Figs. 7 and B are fragmentary elevations of stator blades of a compressor embodying our invention.

assures In Figs. 1 and 2 of the accompanying drawings. a pair of entrance stator blades are shown at l and I. a pair of rotor blades at 2 and I and a pair of exit stator blades at I and I. These Figs. 1 and 2 thus illustrate in diagrammatic form a single stage of an axial flow compressor and it will be understood that in a multistage compressor, the exit stator blades are extended to form the entrance stator for the next succeeding set of rotor blades. Figs. 1 and 2 show, respectively, the tip and root circumferential sections of the same pairs of stator and rotor blades and accordingly the same reference characters for the blades are used in both of these figures. The stator and rotor blades are preferably made of thin sheet metal stamplngs. the sheet metal being of uniform thickness throughout. All blades in any entrance stator are identical in shape and size and would accurately fit each other if placed close together. This is also true for any rotor set or any exit stator set.

Figs. 5-8. inclusive, show an entrance stator blade I. a rotor blade 2 and an exit stator blade 8. The stator blades l and 3 have their tip portions secured to an outer casing 4 and their root portions secured to stationary members 5 and 6. The rotor blades 2, 2', etc., are secured to a hub 1 fixed to the compressor shaft 8.

The rotor and stator blades define ducts extending from the root to the tip and also extending in a generally axial direction through the rotor and stator blades. Each set of rotor blades and stator blades consists of blade elements bent to form ducts or channels and because of the fact that all of the blades in each set are identical in shape, consecutive blades are "parallel" in the sense that they are equidistant at all points from each other as measured along a circumferential direction. The cross sectional flow areas of the ducts formed by the blades are at all points proportional to the sine of the angle that the duct axis makes with a plane normal to the axis of the rotor.

The entrance stator blades I and l are shaped to form a nozzle or in other words, so that the cross sectional area normal to the duct axis at the exit of the entrance stator is smaller than the corresponding cross sectional area at the entrance to the entrance stator. The duct defined by each pair of rotor blades. as illustrated in the accompanying drawings. is a diffuser for the cross sectional area normal to the duct axis at the rotor exit is larger than the cross sectional area normal to the duct axis at the rotor entrance. Each pair of exit stator blades likewise defines a diffuser and these exit stator blades are shaped so that they direct the fluid axially.

The thermodynamic conditions of flow between two curved blades that are parallel in the sense above defined are such that the fluid temperature, pressure, and velocity conditions at the entrance and exit portions of the duct are determined solely by the ratio of the cross sectional areas normal to the duct axis at the entrance and exit respectively, if the shape of the ducts is such as to maintain streamlined flow between the entrance and exit. The angle of divergence (or convergence) between any pair of consecutive blades of the form described above is determined entirely by the circumferential distance between these blades, this distance being constant throughout the length axially) of any pair of blades as explained above. Thus the cross sectionalarea of the duct defined by any pair of blades is a function of the shape of the blades,

6 whereas. the angle of divergence (or convergence) is a function of the circumferential distance between the blades and these two factors are entirely independent of each other.

In Figs. 1 and 2, the air or other compressible fluid is shown entering the entrance stator duct in a direction parallel to the axis of the rotor, the air at th s point having a temperature Tm, a vuelocity Vin and a pressure Pm. The air leaves the entrance stator nozzle with a velocity v1: which may be considered as having an axial component vlxn and a circumferential component vlxc- It will be understood that the rotor section or element illustrated in Figs. 1 and 2 is moving in the direction indicated by the arrow A, with" respect to the stationary entrance stator and exit stator, and in Fig. i the arrow u represents the reverse of the circumferential velocity or speed of the rotor tips. The velocity of the air entering the rotor. V2, is the vectorial sum of the velocity Vlx and the reverse of the rotor speed a. The air leaves the entrance stator nozzle at an angle with respect to a plane normal to the rotor axis, this angle being designated on: in Fig. l and it will be noted that the direction of the air entering the rotor duct at the rotor entrance, as indicated by the arrow V2n, is parallel to the rotor blades at this point, thus provid ng streamlined flow into the rotor. In other words, as the air enters the rotor duct which is travelling at high speed in the direction indicated by the arrow A in Fig. 1, the air is not immediately subjected to any impact by the rotor blades. As the air progresses in the rotor duct, however. its

- direction of flow is progressively changed by the curved rotor blades. the air being discharged from the rotor duct in a direction indicated by the arrow V2, (relative to the rotor). The air discharged from the rotating rotor ducts enters the stationary ducts formed by the exit stator blades and the direction of flow into the exit stator is represented by the arrow V3" which represents the vector sum of the velocity Va. and the rotor circumferential velocity n. It will be noted that the air entering the exit stator in the direction indicated by the arrow V311 flows parallel to the exit stator blades at this point, thus providing streamlined flow into the exit stator. It will also be noted that the air entering the exit stator may be said to have a circumferential velocity component vf nr and an axial component Vim.

To illustrate the manner of selecting appropriate operating conditions, it may be assumed that the compressor is in an airplane traveling at 1:500 feet per second; that the temperature of the air is To -620 R. where R. denotes Rankine or Fahrenheit absolute) and that the static pressure is Po=1 atm. 2116 lbs. per square foot). It may be assumed that under these conditions.

. the air wiil enter the compressor at a velocity Vin 300 feet per second, and in any event the mouth or entrance of the compressor may be designed or adjusted so that the velocity of the air entering the compressor will be 300 feet per second when the plane is travelling at a speed in the neighborhood of 500 feet per second. An appropriate value is selected for the tip diameter of the rotor. Thus, for purposes of illustration. it may be assumed that the tip diameter is 0:54", that the root diameter is 34.77" and the R. P. M. or N is 2543 revolutions per minute. With the tip and root diameters determined, the R. P. M. of the rotor is such as to produce a Mach number of a r flow of approximately .788 entering the rotor tip, a satisfactory value.

The entrance stator blades may have their tip portions formed so that in this region the entraneestator ductsareshapedtoiormnonies directing the air against the direction of movecircumi'erential velocity 21X 2543X 27 it"w-W fir-I560. (I)

whereNrepresentstherotorR. P.1d. andr the radius of the compressor rotor at the tip portion of the rotor blades.

The total temperature Tn at the entrance to the entrance stator is u it. per sec.

1 Po To where A: being the ratio or 1.4, for air, and therefore 8.6 p 1 1.1474 atm.

The actual temperature oi the air entering the entrance stator. Tm, is

The actual pressure of the air entering the entrance stator, Pm. is

= 1.0926 atms.

with these values of Toand Pin and Via. the airflow in pounds per second per square ioot o! ernrance-stator entrance area is la ln ln W ln A 1X300X 1.0926X2116 53.3X533.33

=24.40 lbs/sq. ftJsec.

For known or assumed values of 'in. the total temperature or the entering air, morn-i, the

' total temperature of the outgoing air, the angles au. as. as: and flu determine the temperatures. pressures and velocities (and their components) at the corresponding points in the compressor.

ment oi the rotor. The rotor blades will have a g spouse The circumferential velocity component of the air leaving the entrance stator is This can he proved by combining the energyequations 7-! n= II+T and -8 n= T..+ By subtraction,

Tn-T K='v t. With the geometry in Fig. 1

7 T T,'+e'+2aVl. 003 n and V1: 608 air=V1se so that W=V1T+u=+2uvm (1 substituting in (9) (Tn-Tn) K=u +2uV1ze solving for vino gives Likewise the circumferential velocity component of the air entering the exit stator is Vine The derivation is similar to that above proved but using the energy equations TI rs= E 11 n T: (2) by subtraction (rn-Tn)K=v ..'1"If (13) since with the geometry in Fig. 1

W=WJ+u=-2w cos and V3; cos flu= ia so that V;=l 3?+u=2uv,.. (14) By substituting in (13) (Try-Tn) K=u--2uV2u solving for V2 gives T T Vi,.,=- 1 (15 and as Vm=u-Vm T T ine Adding the Equations A and B we find: isc+ IIe or Kilt (TnTn) v1,l( 1 VI (0') It iollcws from Equation 0 that according to our invention, the sum of uvm and uvm is a and solving for T1:

Whether or not V1 is equal to vlnc, then, as indicated above (see Equations A, B and C), the sum of uVm and uVam must remain a constant and Vlxc and Vine depend upon the value of T'r2 alone.

As stated above, the entrance stator blades and rotor blades provide progressively decreasing rotor entrance velocities from root to tip to compensate as completely as may be desired for the increase in the circumferential rotor speed (u) between root and tip of the rotor blades, K

whereby the root portions of the rotor blades travelling at relatively low circumferential speed may impart to the fluid entering the rotor at higher absolute velocity than at the tip, the same amount of energy, the exit portions oi the rotor blades being correspondingly shaped to insure this result at the rotor exit, so that as the compressed fluid flows axially in the exit stator, it may have the same pressure at all radial points in the exit stator.

The energy equation shows the energy relation above described, uVm being the energy relation at the rotor entrance and uviine that at the rotor exit.

To have the same energy imparted to the fluid entering the rotor from root to tip we must have z llmzcl =c| and 'uvlnel =62 Thus t t r r (a constant) (D) Also, as stated above, the air flow in pounds per second per square foot of entrance stator entrance area is ln la la Thus the air flow at the entrance of the entrance stator is independent of the radius, or in other words, it is the same at all radial points of the entrance of the entrance stator. This means that the flow of air is vortex free as it enters the compressor. It is well known that it the flow of air is vortex free, i. e., irrotational (assuming an ideal compressible fluid), it remains vortex free throughout its motion. Accordingly, in the compressor of our invention the flow of air remains vortex free as it passes through the cornpressor (assuming ideal conditions). It follows from this fact that in the compressor the product of the circumferential component of the fluid velocity at the exit of the entrance stator (Vim) and the circumferential velocity of the rotor (u) is constant at all radial points between the root and the tip. Likewise the product of the circumferential component of the fluid velocity at the entrance of the exit stator (V3nc) and the circumferential velocity of the rotor (14) is constant at all radial points from root to tip. Hence the ratio of is constant from root to tip. Where Vi=c=Vm, then this ratio is 1. However, when a value 01' Tu is chosen which results in values of Vm and V3m: that are not equal, then the ratio of vine to Vino, of course, has a value other than 1.

It will be noted that in a typical embodiment of our invention (see, for example, Figs. 3 and 4), the ratio lze is the same at all points between the root and the tip. Thus in Figs. 3 and 4 this ratio at the root is and at the tip Also, at the root (Figs. 3 and 4) uVm-=386.3 X 360.97=139443 and at the tip:

uVi==600 232.4:139440 The choice oi the ratio is constant from root to tip, for this condition prevents cross flow (i. e. radial flow) at all points.

The constancy of the ratio i ille in any one compressor design shows that 11 multbeoouetanttromroottotipaeieeaeilyleen Similarlyweflnd: bytakinetheratio of (A) to (8).:iving 'lhmthevalueeoivm.vmand'rnaredeterwmmkmm mama. minate toranyradialcalcuiation ofthe required mm chm n m 'l'hevalue o! for anyradial pointigzivenby V". L I-l in. .=tan l -|(1- 1 (F) to: the oompreeeor. The smaller root involves in supersonic flow. where A ain similarly we ilnd T KT T )6 q.-=tm h ,(1 1} I (K) is the larger positive root of u where l I v. i T T I T I III) I fi TL)("FH 41 To derive this equation. we have 13 the Foam" root of n. T, T. u+V.' WRT a) -(T:,) m )+(fi) the adiabatic relation between pressure and tem- (L) perature (see Equation 3) We have aieo i8 KT 1' 7.'.'=K(Tn--T1. =K1'fl(1 (a) Fm-{ 1 1} (M) he v...=- vr.'-v..-.' when aeehowninmmlaudz. 0 u Substituting Equation a m- P;

is the larger positive reairootot II r 15;) M

II in l n The angle n and the corresponding rotor angle Using the continuity equation an producing streamlined now into the rotor,

areeeentobereletedby theequation W-- (see Equation 6) RT l0 m tan Gi rm ton n.

beeauoei'rommJweeeethat V w-Yl-Jlm -f and because Via=Vu Bin '1: v

mstituting the above values of P1: Vm in this a q.-u+ a, last equation. equarins, and rearranzins, we have v WE on Renee dividinl, 1222 AL" tan. v n) n) Fri) 42?... f ADO 811100 similarly II V $13M a (see Fig. 1 tan m- 't and M118 Equation 18 by vino We have m q Ll /K' T 1' tan a1.- ,(1-- )1 m and u. n an '80 ine no theta: theman a m (Q) l Tn( r Intheabove l ouatiom G. .LLand N. the ex- 73 u ponentt are simple whole numbers (a and o) betor air. However, ii I: is not equal to 1.4, there will he a similar equation. The exponent k-l andthe exponent kl O! the two real positive roots. one is larger than TH? and one less than this value. The lesser one involves a supersonic value of T1; which is extraneous to the subject matter of this invention. The greater root will come out to be greater than which is the subsonic value for T11.

The angles w=90, m. in, "2:, Zia and u=90 thus determined will insure a constant ilow across the compressor from root to tip of the blade without cross flow, and that the pressure at the exit of the exit stator is constant from root to tip.

The determination of the pressure, temperature, and velocity conditions obtaining at the exits X1. X1 and X3, assuming streamlined flow, can be made by employing the usual thermodynamic relations. The ordinary method of making such computations is cumbersome because it involves a trial and error procedure. The solution can be simplified by utilizing a "8 table giving the ratio of the total pressures to the pressures at the exits, as

P n P r: 'n l: r II or I: for various assumed values of T1, Pr and outlet areas Ar: and A2: and As:-

To find the conditions at the exit of the entrance stator and assuming an adiabatic process Tis= T11 in The equation of conservation of energy Yields Vi==1/ 0 P( ri l=) 'J 1'l it) and by the geometry of the velocities the axial 14 and circumferential velocity components are determined Il VII Bin ll- IM lnoia in ine ile u ll =1 laa'+ ina Theentranceansletotherotor hisa gcniometric i'unction of Van. Vm or Val sin q,

ino cos I! V For the case where Vm=0. V2ns=via and ino 252 The total temperature Tr: of the rotor which is the same throughout the duct is found by using the equation of conservation oi energy the thermodynamic adiabatic relation gives u T F? P "(7'1 With Vm=Vm and for example T-rz. P-rs W known, an A2=Ao sin z==sin "a: has to be assumed that results in a known The procedure, explained above, has to he repeated ior diii'erent "2: until the computation gives the desired Vm.

From

WRIT I, sin a KP PIE/P3: 18 found 11 In+ K For the cue where Vim-0, vlu=viu Van-u. Therefore To show a numerical calculation to get a conand v... os1.aa W

M a" -1014.3 Jew.

TH: il-l"? m -1.812 tin.

For theeinmle condition stunt exit pressure throughout the exit oi the exit otutor, an extreme high 14, say 792.1 tt./sec. was

mumed and the computation made for the folgo To and Ti: we have T T C Z) where m= =236 To find V1: we have Vis=V n- Tu) :JEWRY? -351.1 Jew. The axial velocity component The circumferential velocity component,

Via =VuXO08 Ii: =351.1 X .5000 =17 i'tJaeo.

For the rotor aeotion tor which Van 304.0 M all ma 17 26' 30" A =ein a =.29974 cos q.=.95401 for example, then Accordinaly with this value of Van, we try various values oi "a: so am. Vm shall equal 618.57. 25 For example, with This value is sumciently close to the desired value. The computations required for -u=21 85' are carried through below in detail.

A,,=sin 21 '=0.36786 cos 21 35 =0.9299

From B-tabie,

= 1.4643 otm.

. with the value of -u=21 35', then VI:- X sin I! 681.6 X .3679 243.39 ftJseo.

v... 24a.ao I. i q. 300.1 .1-

ton

I nu'I' ToflndPunote thatmisalwaysQOandsin "3:=1=43:

%-1.0202 from B-table These detailed calculations are sufliclent to draw all of the points on curves representing u=792.l ft./sec. and 1==60 and pressure Pa==1.4881.

Similar calculations can be made for 1: from 90 to 40 and all values tabulated for u=792.l !t./sec.

The next step is to assume a dlil'erent u, say u=600 ft./sec. The problem is: What values of 1: etc., will produce with this value of u the same values of P31, T31, Vs: as "11:60" produced for u=792.1 it./eec.? The condition Vm=Vm must still hold.

In order to do this, we use the following two relations which are generally true when vlzo= Vane 11 r| (A) Titand (B) n V Using (Bi with Tr3=587.3, the value for u=792.l. and Tn=540.83 the entrance value, we have Tn-|-Tr1=1128.14 TnT-1=46.48 Then V1,.-' %x12ooo=2s2.4 ftJsec.

ino in u so that ia lu= 0o 32-4 Using (A),

Ta a

4B of these nine: M In In? fig/ eg, Wenowtry uni? 51'.

cos 5: 51'=.00390 Knowin thevelueaoimmdm,whlcharo theamefromroottotip toavaluefor which checks with the required value 282.4 for vino.

ila vl-Xfl n ll =385.3X-79705=307.1 fit/B66.

V 307.1 tan ag m m- We now have to find the right "3a from which all the 2:: values will develop. Try m=46 30'.

Knowing that T'r: must be 587.31 and Pr: must be 1.5315 in order to get the same P3: as before From the 8 table ELI-PA- P P" 1.0590

Hence,

p -P -if gg-rmz etm.

I max In 15 =838.5 X .6884 =233-0 ftJseo.

This value is sumciently close to the desired value. 232.4 ftJsec.

Va...=V,,.=Vi. sin a =338.5X.7254=245.6 ft./sec.

We also have VnXsin 21=V11=V3M so that sin s,,-= :'=i%g% =.5554 and a== 33 44' 30" We should find that Tn=587.3 ii. calculations are correct.

At a radius at which u=600 ft./sec. (which can be considered the tip, Fig. 3)

and at a radius at which u=386.3 ft./sec. (which can be considered the root. Fig. 4, having a diameter of 34.77 as assumed above) The same method as explained for u=600 was used, that is, to find values of on: etc. that produce with this value of u=386.3 the same values of Par. Tiix, Viix, as Gl1=52 51' produced for u=600 or 1==6(l" produced for u=792.l, while the condition must still hold in this example.

An examination oi. Fig. 3 and Fig. 4 will show the values listed above for a tip where the radius and R. P. M. are such that u=600 it./sec. and a root where the R. P. M. is the same but the radius is such that u=386.8 ftJsec. These values apply to the case where the condition that Vwc=V3nc has been imposed, i. e., the circumferential velocity at the exit of the entrance stator equals the 20 circumferential velocity at the entrance to the exit stator.

In Figs. 1 and 2, the entrance stator blades are shown at 1 and 1, the rotor blades at 2 and 2' and the exit stator blades at 3 and 3' as explained above, and the dotted line in each figure represents the center line or axis of the duct formed by the stator and rotor blades. In Figs. 3 and 4. the center line or axis of the duct formed by the blades is likewise illustrated by a dotted line. In each figure of the drawings, vertical dot and dash lines represent the entrance stator exit 1:, the rotor entrance and exit 2n and 21;, respectively, and the exit stator entrance 3n. In Figs. 3 and 4, vertical lines also indicate the entrance stator entrance 1n and the exit stator exit 31:, the latter denoting that portion of the exit stator at which the fluid is directed axially by the exit stator blades. At this point in the exit stator, the angle of the exit stator blades with respect to a plane normal to the axis of the compressor, "ex, is 90. The blades of the entrance stator and of the exit stator preferably consist of thin sheet metal of uniform thickness and the rotor blades may also be formed of thin sheet metal of uniform thickness throughout, although in some instances, it is appropriate to have the rotor blades of greater thickness near the middle portion of the rotor than at the rotor entrance and exit. This latter construction is desirable where the solidity o! the rotor blades is such that the rotor ducts would not constitute diffusers extending from the rotor inlet to the rotor outlet unless the blade thickness is increased near the central plane of the rotor. Figs. 1 and 2 illustrate a construction in which the stator blades have the same solidity as the rotor blades but it is to be understood that this condition is not essential, for in some instances it is desirable to have one or more of the stator elements comprising blades having a. solidity different from that of the rotor blades. In general it may be stated that a single stage or multistage compressor embodying our invention comprises entrance and exit stator elements and a rotor element interposed between these stator elements, the sf ator and rotor blades all forming fluid ducts extending from the root to the tip portions of the blades and in a generally axial direction through the stator and rotor blades, the entrance stator blades being shaped to provide axial flow of the fluid into the entrance stator and the exit stator blades being shaped to direct the fluid axially. Also, according to our invention, the entrance stator has an exit angle n: having a value that is a function of the total temperature at the entrance oi' the entrance stator, T-ri, the temperature of the fluid as it leaves the entrance stator. Tu, and the circumferential component oi. the velocity of the fluid as it leaves the entrance stator, Vlxc, as set forth in Equation F, and the rotor has an exit angle n having a value that is a function of the total temperature in the rotor, T'ra, the temperature at the rotor exit, Tax, and the circumferential component of the fluid velocity at the rotor exit Vm as set forth in Equation H. with the rotor and exit stator having entrance angles (211, 310) having values providing streamlined flow of the fluid into the rotor and from the rotor into the exit stator, with vile constant and vine determined by Equations A and C.

goon-no 21 For maklna a typical computation of-the several blade angles it may be assumed that I no is chosen to give the type 0! compressor desired, 1. e., the desired degree of reaction. Thus, it

the de ree of the reaction at the center of the rotor blade, i. e. for a u o! 500 feet per second, where u at the tip is 600 feet per second and u at the root is 386.3 feet per second, is approximately 60%. with the entering conditions as indicated in Figs. 3 and 4 of the drawings we have, for W='24.4:

and then 22 when substituted in the Equation 1" (for u) give for the tip and for the root "l:=tlll .5052

Similarly when these values are substituted in the equation for T2: we have for the tip the solution of which is n and for the root the solution 01' which is These values of i so To when substituted in the Equation H (for m) give for the tip "z==tan- 1.1982 88 =50.15

and for the root Similarly for the root values we have from 60 and from Equation A Tr2=56L02 and then Substituting these values in the equation for T1: we find for the tip the solution 0! which is and for the root Tn .99777 T" +.01293-0 the solution 01' which is These values for (pointing toward the axis because Vm: is negative, -215.3).

For the condition of streamlined flow of the fluid into the rotor and from the rotor into the 45 exit stator we have the condition that ise so which gives tan can at the tip and for the root In like manner the values or "an may be determined from Equation Q with the following results:

At the tip spasm" At the root m=24fl2 Corresponding values of the blade entrance and 08 exit angles can be found in the manner set forth above for any other value of it along the blade. In the typical computation set forth above the angles 11 and a: for the root and tip were computed by the direct Equations F and H and "an 70 and "in deduced for the root and tip by using the Equations P and Q which define the condition for streamlined flow of the fluid into the rotor and into the exit stator. It will be understood, however. that the angles "an and Zn may I. be determined by the direct Formulas K and M acoavu respectively. Thus, using Equations M and N, the value for has for its solution at the tip In Tn .96950 and :n=tan- .65789 at the tip, i. e., the same angle determined from Equations H and Q.

At the root has for its solution & .98780 sivins "an=tan- 45956 at the root 1. e., the same angle determined above, by using Equations H and Q.

Similarly the angles "11 and In may be determined by the direct formulas F and M and then the angles "In and s; may be deduced by using the Equations P and Q.

As explained above, our invention makes it possible to provide an axial flow compressor in which the pressure of the fluid as it flows axially in the exit stator has substantially the same value from the root to the tip portion the exit stator.

Furthermore the fluid velocity does not have any radial component at any point in the compressor. The entrance stator blades and the rotor blades are shaped so as to provide progressively decreasing rotor entrance velocity from root to tip to compensate as completely as may be desired for the increase in circumferential rotor speed between the root and the tip of the rotor blades, whereby the root portions of the rotor blades, travelling at relatively low circumierential speed, may impart to fluid entering the rotor at higher absolute velocity than at the tip, the same amount of energy, the exit portions oi. the rotor blades being correspondingly shaped to insure this result at the rotor exit. Thus the rotor and stator blades are or such shape that the rotor and stator ducts accommodate the vortex i'ree flow oi the fluid through the compressor. A characteristic of our compressor is that the velocity of the fluid entering the entrance stator and as it is directed axially in the exit stator is truly axial in direction, (1. e., without any circumferential velocity component and without any radial velocity component) the magnitude of the velocity oi the fluid entering the entrance stator being constant from root to tip and likewise the magnitude or the fluid velocity as it is directed axially in the exit stator is constant from root to tip. At the rotor entrance and exit, however, the fluid has a velocity varying progressively from root to tip and which may be regarded as the resultant oi circumi'erential and axial velocity components. at least one of these components varying vely from motto tip.

It will be understood by those skilled in the art that the equations set forth above and appearing in the appended claims are based on the assumption of an ideal compressible fluid and that in the design of any speciflc compressor embodying our invention the usual slight modiflcation oi the theoretically correct blade shapes may be made to compensate as completely as may be desired for the fact that the compressible fluid does not have the precise physical properties oi the assumed ideal fluid.

It is to be understood that our invention is not limited to the particular illustrative embodiments illustrated in the accompanying drawings and described in detail above, but includes such modifications thereof as fall within the scopeo! the appended claims.

We claim: y

1. An axial flow fluid compressor comprising entrance stator blades, rotor blades, and exit stator blades, all forming fluid ducts extending from the root to the tip portions of the blades and extending in a generally axial direction through the stator and rotor blades, the blades 0! the entrance stator being shaped to provide axial flow oi the fluid into the entrance stator, the exit stator blades being shaped to direct the fluid axially, the entrance stator having an exit angle n varying progressively from root to tip and having the value Wen-1&0 a 1 lzc where l: Tl

is the largest real positive root of i J r.. Ti,) V1 V' Tn) o T11 11 K Tr: KP the exit stator having an entrance angle "In varying progressively from root to tip and having the value where & n

is the largest real positive root of k+1 2 (sf-(eve may with varying progressively from root to tip and having the value and an exit angle "a varying progressively from root to tip and having the value whereby streamlined flow oi the fluid is provided as the fluid enters the rotor and as it enters the exit stator and whereby the velocity or the fluid as it leaves the rotor varies progressively from root to tip and consists of eircumierential and axial components each varying progressively from root to tip, and the pressure 0! the fluid as it is directed axially by the exit stator is constant from root to tip.

'2. An axial flow fluid compressor comprising entrance stator blades, rotor blades. and exit stator blades, all forming fluid ducts extending Irom the root to the tip portions of the blades and extending in a generally axial direction through the stator and rotor blades, the blades of the entrance stator being shaped to provide axial flow of the fluid into the entrance stator, the exit stator blades being shaped to direct the fluid axially, the entrance stator having an exit angle "1x varying progressively from root to tip a and having the value the exit stator having an entrance angle 3n varying progressively from root to tip and having as the value where is the largest real positive root of 1 2 the rotor having an entrance angle in varying progressively from root to tip and having the is the largest real positive root of ine r 1 2 (M Tm T KT,-a {if and an exit angle "a; varying progressively from root to tip and having the value K 1 TI! in TI) 2 n is the largest real positive root oi a= n"{ where ise ile

Ina

constant from root to tip and whereby streamlined flow oi the fluid is provided as the fluid enters the rotor and as it enters the exit stator and whereby the velocity of the fluid as it leaves the rotor varies progressively from root to tip and consists of circumferential and axial components each varying progressively from root to tip, and the pressure 01' the fluid as it is directed axially by the exit stator is constant from root to tip.

3. An axial flow fluid compressor comprising entrance stator blades, rotor blades, and exit stator blades, all forming fluid ducts extending from the root to the tip portions of the blades and extending in a generally axial direction through the stator and rotor blades, the blades of the entrance stator being shaped to provide axial flew of the fluid into the entrance stator, the exit stator blades being shaped to direct the fluid axially, the entrance stator having an exit angle a1: varying progressively from root to tip and having the value with where &

' is the largest real positive root of I the rotor having an exit angle "2; varying progressiveiy from root to tip and having the value K n I: '4 ag =tall I: 1 1

V... I 0 where In n is the largest real positive root or n+1 2 I (h) (la) 1 -L 1/ n with Inc constant from root to tip and Vise- 17.5 K v20 1 and V =(TTI TT1) 1 III 2 withrthe rotor having an entrance angle 2n varyval V T) ing progressively irom root to tip and having the 27 and with the exit stator having an entrance angle an varying progressively from root to tip and having the value ine whereby streamlined flow of the fluid is provided as the fluid enters the rotor and as it enters the exit stator and whereby the velocity oi the fluid as it leaves the rotor varies progressively from root to tip and consists of circumferential and axial components each varying progressively from root to tip, and the pressure of the fluid as it is directed axially by the exit stator is constant from root to tip.

4. An axial flow air compressor comprising entrance stator blades, rotor blades, and exit stator blades, all forming fluid ducts extending from the root to the tip portions of the blades and extending in a generally axial direction through the stator and rotor blades, the blades of the entrance stator being shaped to pr'vide axial flow oi the air into the entrance stator, the exit stator blades being shaped to direct the air axially, the entrance stator having an exit angle a varying progressively from root to tip and having the air is the larger real positive root of isa the exit stator having an entrance angle can varying progressively from root to tip and having the 40 N h2 K Vm-2u( 1 isa and the rotor having an entrance angle n varying progressively from root to tip and having the a value and an exit angle or: varying progressively from root to tip and having the value n= f ft ten whereby streamlined flow oi the air is provided as the air enters the rotor and as it enters the 7g exit stator and whereby the velocity 01' the air as it leaves the rotor varies progressively from root to tip and consists of circumierential and axial components each varying progressively from root to tip, and the pressure of the air as it is directed axially by the exit stator is constant from root to tip.

5. An axial flow fluid compressor comprising entrance stator blades, rotor blades,-and exit stator blades, all forming fluid ducts extending from the root to the tip portions or the blades and extending in a generally axial direction through the stator and rotor blades. the blades or the entrance stator being shaped to provide axial flow oi the fluid into the entrance stator, the exit stator blades being shaped to direct the fluid axially. the entrance stator having an exit angle an having the value the exit stator having an entrance angle as varying progressively from root to tip and having the value KT r,

where is the largest real positive root 01' I 1 2 t (e. eve-sea "y 43 with lll constant from root to tip and v (T -T K in I 1 2 ice and the rotor having an entrance angle as varying progressively from root to tip and having the value ise ise tan and an exit angle as; varying progressively from root to tip and having the value o as it leaves the rotor varies progressively from root to tip and consists of circumferential and axial components each varying progressively from root to tip, and the pressure of the fluid as it is directed axially by the exit stator is constant irorn root to tip.

is the larger real positive root of H1 T l: ise Tr 1 =0 11 11 ri KPT,

the rotor having an exit angle an varying progressively from root to tip and having the value where ise with the rotor having an entrance angle on varying progresively from root to tip and having the value and with the exit stator having an entrance angle d-3n having the value fl In-tan VI tan.

whereby streamlined flow of the fluid is provided as the fluid enters the rotor and as it enters the exit stator and whereby the velocity of the fluid as it leaves the entrance stator varies progressively from root to tip and consists of circum- Ierential and axial components each varying progressively from root to tip, and the pressure of the fluid as it is directed axially by the exit stator is constant from root to tip.

7. An axial flow fluid compressor comprising rotor blades and exit stator blades, all forming fluid ducts extending from the root to the tip portions of the blades and extending in a generally axial direction through the rotor and exit stator blades, the blades of the exit stator being shaped to direct the fluid axially, the exit stator having an entrance angle as varying progressively from root to tip and having the value ine where Zia 11 is the largest real positive root of m 2 ,,)i-i 1,,)F 1( [UL WRJT 0 T11 T73 K Tn It 1 where V,"- rig?!) K and the rotor having an entrance angle as varying progressively from root to tip and having the value and an exit angle as: varying progressively from root to tip and having the value whereby streamlined flow oi the fluid is provided as the fluid enters the rotor and as it enters the exit stator and whereby the velocity of the fluid as it leaves the rotor varies progressively from root to tip and consists of circumferential and axial components each varying progressively from root to tip, and the pressure 01 the fluid as it is directed axially by the exit stator is constant from root to tip.

8. An axial flow fluid compressor comprising entrance stator blades and rotor blades all forming fluid ducts extending from the root to the tip portions of the blades and extending in a generally axial direction through the entrance stator and rotor blades, the blades of the entrance stator being shaped to provide axial flow into the entrance stator, the entrance stator having an exit angle a1: varying progressively from root to tip and having the value ri l: Pi 1 tan n) 1 where (In n and the rotor having an entrance angle din varying progressively from root to tip and having the value l1!- a,,,-tan tan 1:

and an exit angle or: varying progressively from root to tip and having the value fl3 =t8l1 Y5:

whereby streamlined flow oi the fluid is provided as the fluid enters the rotor and whereby the velocity of the fluid as it leaves the entrance stator varies progressively from root to tip and 3 consists of circumferential and axial components REFERENCES CITED each varylnz W 1mm mt The following references are of record in the the absolute velocity of the fluid as it leaves the me of this m rotor is axial.

9. An axial flow fluid compressor according UNITED STATES PATENTS to claim 1 characterized by the ratio Number Name Date V 1,688,808 Gill Oct. 23, 1928 1,887,417 .Mawson Nov. 8, 1932 i 958 145 Jones May 8, 1934 being equal to 1. I I

10, An axial now fluid compressor according 1097390 De my 1937 to claim 4 characterized by the ratio mint?" 2.320.783 McIntyre June 1, 1943 m 2,370,372 Whittle June 12, 1945 8 being equal to i. u

CARL nl: GANAHL. JOSEPH G. COEF'IN. HUGO I". 35808.

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