GB2250322A - Axial flow air compressor blade - Google Patents
Axial flow air compressor blade Download PDFInfo
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- GB2250322A GB2250322A GB8920415A GB8920415A GB2250322A GB 2250322 A GB2250322 A GB 2250322A GB 8920415 A GB8920415 A GB 8920415A GB 8920415 A GB8920415 A GB 8920415A GB 2250322 A GB2250322 A GB 2250322A
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
- F04D—NON-POSITIVE-DISPLACEMENT PUMPS
- F04D29/00—Details, component parts, or accessories
- F04D29/26—Rotors specially for elastic fluids
- F04D29/32—Rotors specially for elastic fluids for axial flow pumps
- F04D29/321—Rotors specially for elastic fluids for axial flow pumps for axial flow compressors
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- Mechanical Engineering (AREA)
- General Engineering & Computer Science (AREA)
- Pharmaceuticals Containing Other Organic And Inorganic Compounds (AREA)
- Acyclic And Carbocyclic Compounds In Medicinal Compositions (AREA)
- Structures Of Non-Positive Displacement Pumps (AREA)
Description
:)heet I.
-1 223032C TITLE:- Axial Compressor lotor Blades 3pecifically 3haped to confine the existence of the Energy Designated Esp. to within their,Axial Working Length defined by the Dimension 1&1.3).
IN=. "TO:- Foede -Ack iliggleton. Nationality British AD'IU,,,5-:):Every '7,treet, IPI,',LSCN BB9 7LZ. Lancs.
,UTDi- Mrs. Constance Fenwick, Nationality British ADD'Z-;,"-',7): - The )tone House, Poole in I-Tharfdale, L7321 IJZ.
Uest Yorkshire.
AND:- Mrs. Judith Trafford. Nationality British AD',D-Z-,'.33:- 4. Betton lise, East AytonjY013 91RT.
Scarborough, North Yorkshire.
do hereby ieclare the invention for which we pray that a patent may be granted to us, and the method by which it is to be performed, to be particularly described in and by the follcwirU statement:- I-
Multi stage axial flow compressors are usQd to effect the compression of large air mass flows to high pressures. Each individual stage comprising of a ring of rotor blades followed with running clearance between by a ring of stator blades. The rotor blade ring is re4uirei to add kinetic energy alone or kinetic and heat energy to the air while the stator ring of blades change the surplus whi:-1 velocity kinetic energy into heat energy. The blade shape and speed of rotation being arranged also to maintain a constant value axial air velocity along all st-eaxalinea but not necessurily all of the same value.
Sheet 2.
Thus the difference between each-stage inlet and outlet plane is that at the outlet plane of a stage the area of flow is reduced relative to- the reduced specific volume of the air and the temperature increased relative to the energy added. A truly designed rotor blade is thus only required to add two forms of energy to the air thus:- Kinetic:- (va4 2. - vaI 2.)/2.g. & Heat:- G..(T4. - TI.)/(y-I.).
Where va4. & val. = Outlet and Inlet Air Whirl Velocities.
Where T4. & TI. = Outlet an& Inlet Air Temperatures.
Where g. = Acceleration Rlate due to Gravity.
Where y. = Ratio of the two Specific Heats of Air.
Where C. = The Gas Constant for Air.
However the use of circular are cambered. aerofoil sections for the rotor blad-es in engines to o'btainhigher output has resulted in the blades _allowing a third form of energy interaingled with the heat energy to pass the rotor oiitlet pl;me. This third.. forx of energy for which I have used- the definition letters Esp. (Air Spring Energy) is generated together with the heat energy between the Inlet Plane and Plane 2. whichis the plane where the blade attains its maxiaum thicleess and if unused between Plane 2. and the Outlet Plane cannot be changed by the following Stators into Heat Energy. The only way. this unwanted energy can dissipate itself is by causing the blades it passes between and other components (Combustion chambers etc.) to vibrate. A result of which is that they either fail because of fatigue or have to be given a limited. 'Iservice lifelt to prevent them failing.
Tle unwanted form of energy Esp. is made to exist whenever the plane which divides_the airflow into two equal mass flow halves is made to move away from its normal central positioiiL and to illustrate this:- 1 3heet 3.
Consider a cylinder containing one pound of air at normal temperature, pressure and specific volume divided by a piston in the mid position into two equal halves. The piston being integral with a rod in the axial position which extends through both cylinder end plates fitted with air seals, the only constraint to axial movement being the air at each side of the piston. Secure the cylinder to prevent- jaxlal movement and then by force move the piston from its central position the distance D.
If one now calculates the specific volume of the two halves, add together and -livide by two to get the mean value it will be seen to be unchanged from its original value. Calculate the temperature similarly, add and divide and again no change. Calculate the pressure similarly, add and divide and this time the mean air pressure is. greater than the original value, and this is the only indication of the presence of the energy Esp. When the piston is released- it will spring back and beyond the central position and oscillate until the energy is, dissipated in the form of heat caused by friction between the rubbing surfaces.
In the compressor it will be the stators which are caused to vibrate and the heat generated will be at the root- of the blades the strumming of which will also cause unwanted sound. The heat causing the degeneration of the blade material and thus failure at a much lower stress,than that which it was, designed to withstand. This form of energy exists in both. piston and turbine motivated engines but whe.-eas in the former it exerts itself in line with the gas flow and is thus innocuous in the latter is transverse to it and malignant.
Thus it will be seen that if the -Esp(J.2). is used to help; drive the second portion of the rotor blade ring, besides being more efficient in compressing the air will be better from a structural point of view.
Sheet 4.
A specific. embodiment of the invention is thus rotor blade rings, each blade of which has a precisely calculated. shape such that the energy Esp(I.2). generated in the air through the first portion of the blade ring is constructively used to helpdrive the second portion thus eliminating itself from the air flow. The Bernoulli type equation which identifies. the various forms of energy involved in the action between the inlet plane (Plane I.) and the plane which terminates the working length of the blade (Plane 3.) is given below:
2 2 (Plane I.) W(I.3). + (vaj. + vemI.)/2.g. + Y.C.TI./(y-I.).
2 2 (Plane 2.) W(2.3). + (va2. + vemI.)/2.g. + Y.C.T2./(y-j.). + Esp(I.2).
2 2 (Plane 3.) (va3. + vemI.)/2.g. + y.C.T2./(y-I.).
Where 'Y[.(I.3). = The energy Per unit air mass flow required to drive the Plane I. to 3. portion of the rotor blade ring.
Where W(2,3). = The energy - Ditto - Plane 2. to 3. - Ditto.
1 Rhe re y., G. 9 g. 9 T., and Esp(I. 2). are as previously stated. Where vemI. = Axial Air Velocity.
The above equation with suffices (-r=O.) up to (r= Max.No.) apply to lamina streamline values. That is the mean of unit air mass flow if it was disposed equally abibve and below the lamina streamline.
Similarly with suffices (r= I.) up to (r= Max.No.) it applies to the mean values of the air mass flowing between, the common outer boundary streamline (r= 0.) and the streamline whose designation is used as the suffix. TO distinguish between the two sets of values, those of the latter equations.have m. positioned one letter space between in- front thus:- m KI.3). m va2., m v2., m C3.. 9 m p2. 1 m T2. etc.
1 Sheet 5.
-he To show the development of the design system used for -VI calculation of the rotor blade Profile it isnecessary to postulate the four boundary surfaces and two end planes which. together form the absolute shape of an individual air stream flowing between a single pair of blades- All six are of a different shape, so to simplify a little, for an example will use that of a compressor having a constant value outside diameter, thus:- The inlet and outlet plane outer edges are both equal in radius and angular extent. That at the outlet plane due to the air whirl velocity being angularly ahead in the direction as of the rotation of the blades, of the inlet plane. Similarly the inside edges are both a-rcs, that of the outlet plane being angularly ahead for the same reason as the outer are. Both arcs are equal in angular extent but the are at the outlet plane is at a larger radius than that at the inlet plane. Dependent on the type of blade used to provide for reason of material stress a sectional area decreasing radially outwards, the inside arcs can be at an equal, greater, or lesser axial distance apart than the outer arcs. Thus the axial projection of both end planes are sectors of their respective annulus.
The outer boundary surface that joins the two above planes together is of constant arc radius but not of angular extent, the latter being of minimum extent at Plane 2. The surface also spiralling at a varying rate from inlet to outlet plane.
The inner boundary surface joining the two inner arcs, for reason-that the_oompression of the air should be done by the force used to aepelerate the air in a tangential direction only, is of a constant wro 'radius trom Plane I. to Plane 2. 9 Optionally to Plane 3.). Plane 2. being position of minimum angular extent. From Plane 2. to Plane 4-(outlet Plane) both angular extent and are radius increase at rates which are related to each other to maintain from Plane 2. a constant cross sectional area airstream to the outlet plane. Additional to the foregoing and similarly to the outer surface it soirals in the same direction.
Sheet 6.
If we now look on the inlet plane of a compressor whose direction of rotation is anti-clockwise and visualise the airstream described above to be situated on the top half of the vertical centre line, the surface of the airstream to the left would be the rear absolute profile of the blade to the left and the airstream surface to the right would be the front absolute profile of the blade to the right of the airstream. The reasoning f th e of which could apply to the airstream to the right o stiDulated one. Thus if we use the left side of the streamline to the right and the right side of the stipulated one, together they delineate the absolute shape of the blade to be dimensioned from which is developed the relative sha-oe of the rotor blade (As manufac-tured).
As it is required for purposes other than aerodynamic (To stack the centroids of all the lamina blade sections on or near a straight line which is off 2>et to the rear of a true radial line which intersects the rotor axis), the airstream is divided by intermediate streamlines into lesser portions of the full air mass flow. For convenience the radial depth on Plane I. is divided into an even number of equal portions. The outer boundary one is designated (r=O.) and the inner one (r= Max.No.), the inner ones having intermediate numbers. The air mass flowing betweenthe common outer houndary and any one of the others is calculated for Plane I. and is retained by the streamline to the outlet plane.
At this stage it is necessary to explain the action between the blade (Solid body) and the air passing between the blades during the period of time it takes the air to travel from Plane I. to Plane 3. which terminates, the working length of the rotor blades. and for this purpose have supplied Drawings Figuras 1/2.
?/2. which illustrate two analogies. In both analogies the air container at all positions should be axially in line but have been drawn offset to allow dimensioning.
Sheet 7.
In both analogies the air container weight and the atmosphere's resistance to movement of the two bodies has heen ignored. Each cylinder contains one pound of air at normal sta-,ic conditions and the solid bodies weigh less than one pound, having velocities much higher than that of the cylinders. The single difference beteen the two analogies is that the cylinder of the 2 nd. Analogy has an open rear end fitted with a piston and rod, the latterts purpose being to prevent the solid body making contact with the cylinder. The piston being fitted with a mechanism to allow only irreversible movement up the cylinder so that any compression of the air effected between Positions I. & 2. is retained. The conditions are recorded in Bernoulli type e4uations at three positions which are I. The instant of time when the solid body makes contact with the cylinder or rod. 2. The instant of time when the cylinder and solid body attain an identical speed.
3. The instant of time that the cylinder or rod lose contact with the solid body, thus:
2 2 I. (vaj + b.vbI.)/2-g. + PI.vI./(y-I.).
2 2 2. (va2 + b.vb2.)/2.g. + P2.v2./(y-I.). + (E(I.2).
(p2.v2.- PI.VI.)/(y-I.).) 2 2 3. (va3.+ b.vb3.)/2.g. + p3-V3./(y-I.).
I St. Analogy:- E(I.2). = (vbI, vaj.)(va2.- vaj.)/2.g. = Esp(I.2). Where p2.= PI.= P3. and v2.= vI.= v3. (Exclusive of air pressure due to presence of Esp(j. 2)., ' 'See Figure 1/2.
2 nd. Analogy:- E(I.2).= (vbI.- vaI.)(va2, vaI.)/2.g.= ((P2.v2, PI-VI. )/(y-I.). + Esp(I.2).). (Exclusive of air pressure due to presence of Esp(I.2).). See Figure 2/2. Where p2.= P3. and v2.= v3. and the ratio (Esp(I.2)./E(I.2).) 2 ((va3.- va2.)/(va2, vaI.)). = (C3, 1.)2. and the ratio (Ep(I.2)./lP,(I. 2).) = (I.- ((va3.- va2.)/(va2, vaj.))2.).
Where EI.2). 2. /2. g.
= (I.+ I/b)(va2- vaI.) Where Ep(J.2). = (I.+ I/b)((va2- vaI.)2._ (va3.va2.) 2.)/2.g. Where 1,p(j.2). = ((VI./v2.)(Y-,').- I.).TI.C./(y-I.). Where E(I. 2). = ((vI./vr2.)(Y-,).- I.)-TI.C./2.(y-I.).
Sheet 8.
Where vr2. = Specific Volume of the air mass in the rear DOrtion of the cylinder (Adjacent to piston). Where va2. = vaI. + (b.(vbI, vaj.)/(I.+ b. )) = vb2. and vb2. = vbI, ((vbI, vaI.)/(I.+ b.)) = va2. Where va3. = C3. (va2, vaj.). + vai. and vb3. = vbj.- (va3.- vaI.)/b. Where Am(I.2). = (va2.- vaI.)/t(I.2). = Abm(I.2). = b.(vbI. - vb2.)/t(I.2). and Am(2.3). = (va3.- va2.)/t(2.3). = Abm(2.3). = b.(vb2.- vb3.)/t(2.3). Where b. = (va2vaI.)/(vbI, vb2.). Where va2. = vb2.
1/2 Where C3. = (I.+ (Esp(I.2).pz(I.2).) (va3.- vaI.)/( va2- vaj.).
Where t(I.2). = 2.PI.(I.- v2./VI.)/(vbI, vaj.).
and t(2.3). = PI-(I, v2-/VI.)/(va3, vb3.).
Where PI. = Inside length of cylinder at Position 1. of Analogy.
(Cylinder head to inside face of Piston).
At this time it is necessary to single out the value C3. which has a unique part to play in the design of an axial compressor rotor blade which uses up the malignant Air Spring Energy Esp(I.2). for it is this value which links up all the different kinds of energy.
To bridge the differences between the formulae of the nd. Analogy and the new design system it is first necessary to account for the extra power required for full cycle operation. The second requirement is to provide for specified air mass flows. and thirdly to connect the foregoing withthe tangential blade velocity, and finally to streamline the blank end of the blade which in the analogy would be (PI. - P2) wide at position 3. of the analogy.
The first being satisfied by adding the value (BaI, b.) to b. of the analogy at Position I. which would disappear at Position 2. The second by changing the straight line operation of the analogy to circular, whichallows area's to be specified between concentric lamina 3 -3heet 9.
streamlines which together with the addition of axial air velocity defines air mass flow. The third. by linking the axial and tangential air velocities together and to the tangentiil bla-e velocity, thus the Be_. noulli type eluation of the analoey becomes:- 2 2 2 I, (vaj. + VOMI. + BaI.vbI.)/2.g. + y.pI.VI. ' /(Y-I.).
2 2 2 2,-(va2. + VOMI. + b.vb2.)12.g. + y.P2.v2.,/(y-I.).+ Esp(I.2 2 2 2 3- (va3. + VOMI. + b.vb3.)/2.e. + y.P2.v2./(y-I.). Ai,d as (BaI.vbI 2._ b. vb2 2. ' /2.g. = 1-1(1.2).
2._ 2. R(2.3).
And as b.(vb2 vb3) /2. g. = 1, 2, 2 2 W(I.3),.+ (vaI. + VCMI)12.g. + 2 2 W2.3).+ (va2. + VOMI)/2.r. + v.,)2 v2 j(y-I.). + r r r r r Esp(I.2) r = 3, (va3 r 2.+ vcM, r 2.)/2.g. + y.p2.,.v2,,.l(y-I.).
2 2 he.-.-e W(JJ)r.= y-Ep(I.2)r.+ --,'sp(I.2) r.+ (va2 r._ vaI r /12.
2 2 Where-W(2 T' 3)r. + -1sp(I.2)r. = (va3, va2 r)/2.c. = Ek(2.3)r.
2 Whe-e = ','i(I.2).r. = (BaIr, br.).vbI r. /2. g.
Alj-.i the formula which connects the tangential blade velocity to the air velocities on the.loot Streamline are:- f- 1)!r See Figure 1/9.
vb + 1 aximum m vcm(I.3) :-PC R 0 - I ("ri = (v-3 R R- v.13 R)) In tl,e 2ables ID. to 6D. a coii-3t.ant v-alu,3 vomj,,. has been used which is ilightly less than both the two values above.
See Figure 1/9.
w11..re m vb(I.3) R. = m va(I. 3) R. + X2 R /2.t(I.3) R 6 whe-e m va(I.3) ((t(I.2)R.(vaIR.+ va2R.)) + (t(2.3).,.(va2,,. + va3 R /2. t(I - 3) R m va(I.3) R C4R.(va311, vaI R) + vaI R 0 Limiting Angle Co. is taken to be 45. and the value -f the angular difference between the absolute and. -elative centre lines of the tail po. ..tions (Plane 3. to Plane 4.) is 900. 3ee Ficure 1/9.
Sheet 10.
It is also of importance that on the root streamline where VI R has the minimum velocity, that vbI R sh-ould have a value not exceeding (VI R.+ val R) With reference to surge conditions it should be noted that the rotor blade shape (As manufactured) when stationary is also its.absolute shape. Thus in the run up to the designed speed (VI.) the rotor blade absolute shape continuously in contact with its relative shape on Plane I. appears to zLcLve in an anti-clockwise direction-like a pointer of a clock until at the designed speed it reaches-the designed speed positiox-, Intermediate to the two positions described above the abzolute shape passes through a third position-where it is disposed axially. This is the position where surge conditions would arise if the relative blade shapes did not give full static coverage to the inlet plane. Thus-in a front view of a compressor the rotor blade at all radii should have a minimum are length of one blade pitch.. (See Figure 9/9.) it will also be seen that for industrial use where protection can be given to prevent ingestation of foriegn bodies it would be advantageous to use finer pitched blades than would be used for aircraft engines.
Wa-th regard to streamlining it should be noted that as. in the analogy where the piston is locked tothe cylinder at Position 2. to retain the compression of the air to Position 3. so also does the blade of the compressor attain its maximum thickness at Plane 2. and in the example given retains this thickness to Plane 3. from which it is streamlined to a point at Plane 4. It should be noted however that if required it could have been commenced at Plane 2. If the Synopsis IL. had been used for the example the starting plane of the streamlining would have been prior to Plane3.
z Sheet II.
The absolute lainina blade circular ara;diinensions are measured from an axial line which passes through the blade point at P1ane I. and the axial length dimensions from Plane I. along the line. Note also that all streamlines,in the synopsis are at a constant radius thus r(I.3).
Front profile dimension designations are prefixed by the letters Fp)and rear profile dimensions Rp-A.. The mean centre line of air mans flow moved circumferentially one half blade pitch-so that it, can be dimensioned froin the above axial line uses the prefix S.
The blade length is divided into three sections aL, 9 b..2 a. whicl. represent (Plane I. to 2.)., (Plane 2. to 3.) and (Plane 3. to 4.) and thus,:- FpaI Zero. Fpa2r.= t(I.2)r#(vbIr.+ vb2r.)/2.
r SaI r. Zero. Sa2 r t(I.2),.(v-.iLI,.+ va2r.)/2.
RpaIl. Zero. Rpa2 r t(I.2).r.(vaI:ro+ va2ro)/2.
Fpb3r= Fpa2 r.+ t(2.3).ro(vb2 r& + vb3 r,')/2.
Sb3 = Sa2.+ t(2.3)r.(va2r.+ va3r.)/2.
r r Rpbl.=Rpb2.+ t(2.3)r.(vb2r.+ vb3..)/2_ r r And in the intermediate positions:- Fpan..= t(I.n),.vbj,.+ vbn r.)/2.
Sax.= t(I.,n)r.(-vaIr.+ vani.)/2_ r r RPanr.= t(I.n)r.(vaI.+ van,.)/2.
r r RPbIn r Rpa2 r.+ t(2.ja):r.(vb2 r.+ vba r.)/2 Sba r Sa.2r.+ t(2.a)r.(va2r.+ vaia,.)/2.
Fpbm r Ppa2 r.+ t(2.m):r.(vb2 r.+ vbm)/2.
Sheet 12.
And for blade section c.
Sc4r. Sb3r.+ t(3.Cr.va3r. Sewr.= Sb3r.+ t(3.w)..va3 r Fpe4r. SC4r. = IRPO4r.
Fpew Sew.+ XW./2. Rpew sew XW /2.
r r:r r r, Fpb3r. Sb3r.+ X2 r./2. -!pb3r.= Sb3r--- X2r./2.
Where Xw r.+ 2. F r 2. - L(3.w) r 2.) I/2._ (-RF r 2._ L(3.4)r 2.) 1/2 2 And RF.= Blade Form Radius = (L(3.4) /X3r.) + X3r.A.
And X3 r.= X2 r - And for axial lengths.
L(I.2) r- t(I.2)r-vOmIr. & L(I.n) r.= t(I.n),.vcmj.,.
L(I.3)r.= t(I.3)r.vcmI:r. & L(I.m)r.= t(I.m)r.vcmjr.
L(I.4)r- t(I.4)r-vemI,- & t(I.w):r.vemIr.
And for Relative Blade Shape Dimensions.
R Fpa2 r - = FPa2 r -- t(I.2)r-VIr.
lq FPb3r. = FPb3r, t(I.3)r-VI..
R FPe4r. = Fpo4., t(I.4)r-VI..
R RPO4r. = Rpo4r--- t(I.4)r-VI..
R Rpb3r. = Rpb3r, t(I.3)r-VI.. & R RPbm.,= Rpbmr, t(I.m):r.VIrs Rpa2r. = Rpa2 r -- t(I.2)r.VIre & R Rpan r.= 1Rpan., t(I.n) r VI r TO relate all the above dimensions together a Drawing has been provided:- Figure I/I- & R FPan r.= Fpan., t(I.n.),.VI r & R PPIbMr.= FPbm r t(I.m) r Viro R Fpew r Ppow r t(I.w)r.vi r R Rpow r -Rpow r t(I.W)r.viro Skeet 13.
Axial Flow Air Compressor Design Procedure - Rotor Blades. Notes:- A Synopsis is not compiled for any specific air mass flow but to provide relationships between the dimensions of the air duct and rotor blades to the large number of different air and blade velocities and air conditions which simplify t1te design of a compressor having a specific air mass flow.
TILUS a first requirement before compilation is to know wkether it is for airplane or industrial use. If the former, to facilitate maximum blade loading, the area contained within the rotor blade profile is made to increase in a direction radially outwards as on Synopsis Table IA. The decrease in material sectional area in the same direction for reason of material stress being effected by coring which would be facilitated by making the blades in kalves and fusing together.
For industrial use due to the kigk material and manufacturing costs of the former it is usual to use soli& blades decreasing in sectional area radially outwards as on Synopsis Table ID.
A study of both the above Synopses,shows that to obtain t1te maximum air mass flow through a given area inlet plane, the axial air velocity on the root streamline should be the maximum value and the air whirl velocity a minimum value. The resultant energy of both causing the drop in air pressure from static to inlet plane.
As values which are the mean over various portions of the airflow are required, to simplify their calculation, products (rl:,.vcmI..) and (rI r - vcmI r W(I-3)".) have been made to vary at a constant rate radially across the inlet plane. Thus for example m W-I-3),=,-= W(I-3),=2'9 a C32=3' C"3r=I.I!29 etc. This however is not mandatory and could be different providing the resultant air pressure drop is a constant value over the whole inlet plane.
If in the case of the example it is required to reduce the axial length of the rotor bladeq the way to do it is either increase the number of blades in the ring Skeet 14.
Notes:- Continued. or alternatively reduce:r(I-3)0. or do botk, but certainly not the axial length alone even thougk it appears uselessly too, long. If the Synopsis IA. had been used for the example the blade thickness would have increased. radially outwards thus necessitating a longer length for streamlining at all radii except at the root. The starting positions of the tapering could witk advantage be moved up to Plane 2. while still retaining the same circular are pitch length as Synopsis ID. Thus the formulae for Fpbur- ancl RRbm, would. require modification to take the streamlining into account thus:- Fpb3r--- Fpa2 r. + t(2.3),-(vb2 r vb3r.)/2. - (X2 r -- X3r.)/2.
Rpb3r.= Rpa2r. + t(2.3) r (vb2 r vb3r.)/2. + (X2r, X3r.)/2.
Rpbmr.= Rpa2r. + t(2.ia) (Vb2 vbm)/2. + (X2 XM)/2.
r r r Fpbx Fpa,2. + t(2.iiL),.(vb2 vbin,.)/2. - (X2 Xmr.)/2.
r r r R FPb3r. = FPb3 t('.3)r-VIr.
R RPb3r. = Rpb3r, t(I.3).r.VIr.
R RPblia:, - = -RpbX r- t(I.X)X..vir.
R Fpbar. = Fpbar, t(I.m)..VI..
Sb3r. = Sa2r.+ t(2.3),-(va2 r.+ va3r.)/2. (Unchanged) Sbn r. = Sa2r.+ t(2.iii):,.(va2 r.+ Yam:,.)/2. (Unchanged) R Sba r Sbmr. - t(I.a):r.VI:C.
R Sb3, Sb3, - - t(I.3)r-VI:E.
r r Note:- The above dimensions give the blades position and shape on cylinders of constant rI r. radius which when looking down the stacking line are identical to the blade shapes on the streamlines.
1 0 Sheet 15.
Computation of Stage I. Synopsis Values.
The first requirement is the eh-oice of the following values:- VIO.9 -r(I.3)0.9 r(I.3),. No. of blades in ring., 7atios (P2 r /Z2.r.)., ICAC Standard Atmosphere air conditions., a stipulation of the value of vaj.., a stipulation of the value.R of the Ratio (vemI,/iax.vcmj).From which are derived all other R values on either Synopsis ID. or ID. (used as an example):- Root Streamline Column applicable to Synopses IA. or ID.
1/2.Ref.No. 9, C3n -- (I.+ ((B.- A.)/B.) Where A.= ((P27 (Y-I-)._I.
/Z 2, Where B.= (((P2 R./(2.Z2 1 -- P2 R)) (Y-,').- 1.)/2.).
Where (P2./(2.Z2 - P2 (I.A2.Z2, I.
R :,. /P 2 Ref.NO.I0, G4 R.= (3.C3 I.V 1 (4.C3 2.- M3,.) R 2 1/2 Ref.No.II, b_. = (I./(D.+ (D. + I.) 2 Where D. = ((y-I-)(I, (C3 I.).)/2.).
Ref.No.14, vcmI Ratio(v=I).llax.vcmI R'= /ax. vcmI R 'i R W-here Max.VemI C3 -C4 VI AI.+ b.). See also Sheet 9.
11.,L Z1 11 2 2 Ref.No.15- TI.. = T.- (y-I.).(vaj.... + vemI R.)/2.g.Y.C.
Ref.NO.I6- PI r - = P.(TIr./T.)y/(y-,').
Ref.NO-I7, vIr. = v.(T./TI r) IAY-i.)_ Ref.NO-31- EP(I.2).. = (,ef-No.9.A.)-C-TI -/(y-I.). r Ref.NO-30- E(I.2) = (Ref-NO-9, B.)-C-TIr./(y-I.).
R Ref.NO.32, EiI.2) R = (y-I.).EP(I.2) R 2 Ref.No.12, Baj R b R.+ Ei(I.2) R.2.g./vbI R -P Ref.No.20, vbI R VI R.+ vaj R.
Ref-No. 5..- VI R. = r(I.3) R VIO./r(I.3)0.
Ref.No-33- Esp(I.3) R.= E(I.2) R -- EP(I.2) R Ref.No.18_ va2 '.= vb2 E(I.2) R.2.g./(vbI R- vaI -R + vaI R' rR 'R Sheet 16.
Continuation - Rvot Streamline Column - Synopses ID. &- IA.
2 2 Ref.No.34-- Ek(J.2)-,, (va2.- Val.)/2-g- R q ?ef.No.Ig.- va3,:,.
C3,,. (va.2. - vaj). + vaj.
--- R R D - 1 2 2 -'ef.No.36.-:,k(I.3) R - (va.3 R._ vaI R.) /2. g.
Ref.NO.2I, vb3 = vbI, (-va3 val /b R R R R Ref.No.26, m va(I.3),.= C4. (va3 vaj + vaj R R R R) -1 m va(I.3)--,.= ((t(I.2) R (vaI R.+ va2 R + (t(2.3) R-( -va2 R.+ va3-R.)))/2.(t(I.2) R.+ t(2.3) R') Ref.NO.27, m vb(I.3) R.= m Va(I.3) R + X2 R /2.t(I.3) R - Ref.No.28- t(I.2):- = 2-X2 /(vbI- vaI 1 R Ref.No.29- t(2.3) X2 /(va3 -- vb3 - - R' R R) Ref.NO-38, T2 R T3 R = (Ep(I. 2) 'R (Y-I.)./C.) + TID.
ef.No.39.- P2.= P32.= PIr.(T2-0./T1r.)y/(y-,'). R Ref.No.40- v2,,,.= V3 R.= VI..(TI../T2)IAy-i.).
2 2 Ref-NO-35- W(I.2),.= (BaI R vbI R b R vb2 R.)/2.g.
2 2 Ref-NO-37, W(I.3) R - = (BaI R vbI R. - b IR - vb3 'R.) /2. g.
Ref.No-49, Angle A,.= Ref-NO-50 - Angle B R = 13 - Angle ef.No.51. liR- = 14-X Tan (va3 R. /Vcrn,R Re f I -NO.53, (I.x Ref.No-54- (I.x Tan. (VIR -va3 R)/vmi R-) Tan.-1((VI R m vb(I.3) R)/vcmi R)' 37. (:r(I. 3) R ' VOMI R 11(1.3) R') 14.)R. = (r(I.3)R VCMI R') z Sheet J7.
Continuation - outer Streamline Column - Synopses Table ID. & I.A...
Ref.Nos. g. and I0, Values C30. and C40. Use formulae given for same values on Root Streamline.
Ref.NO-II, b 0' Note:- Root Streamline value used for convenience such that Ref-NO-I2, BaJO. is below unity.
Ref.No.12, BaI.= b + Ei(I.2)0.2.g./vbIO 2 0 0 Ref.NO-I3, vaI0- (VIT- VI R)/2. + vaI R Value chosen to keep the value va3 0 reasonably low.
2 2 2 11/2 Ref.NO-I4, vemI,.= (vaj R. + VOMI R._ vaI 0.) Ref.17os. 6, 7-, 8., 15., 16., 17. Values T. 9 P., V., TI., PI., and vI. are of the same value as on the Root and all other streamline columns of the same Synopsis.
Ref-Nos-30 to 33, E(I.2)o., IEP(I.2)o., Ei(I.2)o., Esp(I.2)c,., Use formulae given for same values on Root Streamline. 1/2 Ref-NO.IB.- va2 0.= vb20.= (E(I.2)0.2.g./(I.+ I/bo.)) + vaj Ref.NO-I9 - va30.= C30.(va20.vajo.) + vaIo.
Ref.No.20, vblo.= ((va20.- vaIO.)/bc).) + va20.
Ref.NO.2I.- vb30.= vb10, (va30, vaI,.)/bo.
Ref.Nosi.26., 27-, 28., 29., 34-, 35., 36., 37-, 38., 39-, 40-, 49.Y 50.9 & 51. Values m va(I.3)-9 m vb(I.3).q t(I.2)., t(2.3)., Ek(I.2). W(I.2).7 Ek(I.3). W(I.3)., T2.= T3-, p2.= P3., v2.= v3.. Angle A., Angle B., Angle C. Use formulae given for same values on Root Streamline.
Ref.No-53, (I.x 14.x 37.) = r(I.3)0.vemIO,'(I.3)0.
Ref.No-54, (I.x 14.) = r(I.3)0-vcmIO.
Sheet 18.
Continuatiox.- Intermediate Streamline Columx SynoPsis,Tables ID. and IA.
Ref.Nos. 9. & JO--- Values C3 r - and C4r. Use formulae given for same values as on Root Streamline.
Ref.No-54, (r(I.3),.vcmI,.). = (Yiax-Stre.No. - Stre.No.)(r(I.3)0.v--inIO.- r(I.3) R. veraj R)/(Max.stre.No.)+ (r(I.3) R VOMI R).
Ref-No-14- vcr'I,. = (r(I.3)r.vcixI:r.)/r(I.3):r.
2 2 1/2 Ref-NO-I3, vaIr. = (vaj.+ vcmj._ vemI R R Ref-No.53- (I.x 14-X 37.)r. = (Max-Stre-NO, Stre.NO.)( r(I.3)0.vcmlo.W(1.3)0.- -r(I.3) R. vemI R W(1 - 3) R May,Stre.No.). + (r(I.3) R VeMI R W.(I.I) R.) Ref-NO-37, W(I.3)._ = I(I.X 14.x 37.),./(r(I,.3-):,.vcmI,.) Ref.Nos- 6.,7. Y8. Y15. 16.,17, Values, T. yP. v. TI. gpI. vI. are of the came value as ox the Root Streamline Column of the same Synopsis.
Ref.Nos.30 to 33, Values E(I.2)r. lEP(I.2)r.lE'(I.2):r. 1Esp(I.2).r.
Use formulae given for the same values on the Root Streamline.
Ref.No-36.- Ek(I.3).. = W(I.3)r- (y.EP(I.2).r.)_ Ref.NO-I9, va3r. = ((Ek(I.3)r2Q.g. + vaI r 2.)J/2.
Ref-NO.I8, va2 r - = ((va3-- vaI.)/C3-.) + vaj.
2 2 Ref-No-34, Ek(I.2).. = (va2 r._ vaj r.)/2.g.
Ref.No.20, vbIr. = ((E(I.2),.2.g./(va2 r - vaj r + vaI r Ref.No.II, b.. =.(va2 r, vair.)/(YbI r, vb2 r.).
Ref. Nor.,. 35. 37-,38. 39-,40. 49.,50.,51 - - Values. W-(,.2):r. qW(I. 3)r. 9 Angle A., Angle B., Angle C. Use formulae for the same values given for the Root Streamline.
Sheet J9.
Continuation - Air Mass Flow Mean Values - Synopses Tables ID. IA.
Note:- The suffixes applicable to the example would be to (r 4-)- 2 Ref.No-41.- ArI r Pi.(r(I.3.) (r=O.) r(I.3)r Ref.No-42..- m veml = m VCMI (r=x.) vcla,(,=,/2)' Ref-NO-43-- MI Arj,m vcmj:,./vI Ref-No-44-Ref.No-45.-- Ref.NO-46.- Ref-No-47-- Ref.No-48.- NOte:- The from m W(I.3 m T2 - = m Ek(I.3).r.= m Ek(I - 3) (r=x. Ek(I. 3) (r=x/2.
m Ep(I.2).r.= m Ep(I.2) (.=X.).= Ep(I.2)( r=x/2.) m Bi(I.2) m Ei(J.2) Ei(I.2) r (r=x.)= (r=x/2.) m Y(I.3)(r=x )r.) = W(I.3) (r=x/2.) m T3 m T2 T2 r (r=x.) (r=x/2.) mean values for m p2r. and m v2 r can be calculated the above temperature if required.
Horse Power = H.P.r.= MIr.m W(I.3).r./550.
End of Procedure for Stage I. Synopses Tables ID. & IA.
Sheet 20.
Computation of plane n. -values intermediate between Planes I. & 2.
All Streamline Columns - Blade Section a. Tables 2D. & 3D.
Ref.No-54- van vai n.(va2,.- vaj,.)/N. va(n=O.),.= vaj r Ref.No-55- vbn,.= vbI,.- n.(vbj.--- vb2..)/N. vb(n=O.):r.= vbjr.
2 2 Ref.No-56- Ek(I.n)...= (van r._ Vai r.)/2.g.
Ref-NO-57, E(I.n) r.= (((2.vbj,..)+ I.)-van.))(van,.- vaj..))/2.g.
r - Ref.No-58, EP(I.n)..= E(I.n==%)-+W(2.m=(M-x.)) r Where M-NO.Of Planes N-No.of Planes...
Also EP(I.n)..= E(I.n)..(j._ (C3.- 1.) 2. 2 Ref.No.59.- Esp(I.n)..= E(IMr.(C3r, I.) Ref-No.60---Ei(i.n).. = (Y-- I.)-EP(I.n) Ref.No.C. W(I.n).= (BaI vbj 2 - - Ban. vbn 2.) /2. g.
r r r r Ref-No.62- Ban ((Baj..vbI 2._ (2.g.(E(I.n),.+ Ei(I.n) + r r Ek(I.n)..)))/vbn. 2 ef.No.63.- t(I.n):r.= ((I.- (TI../(TI..+ (Y-I-)-EP(I.n)./C.
IAyi.) -).2.P2../((VbI:,.+ vbn,.)- (vajr.+ van:r.))) nef-NO.64.- L(I.n).= Ref.NO.65- Fpan.= r t(I.n):,.vemi..
t(I.n),.(vbj,.+ vbn:r Ref.No.66, San r t(I.n),.(vaI, + van t(I.n).(vaI.+ van Ref.No.67- Rpan. = r Ref.No.86, R Fpin r Fpax r t(T.n) VI Ref-No.87, R San r. = San Ref.NO-88, R Rpan - = Rpan t(i.x)rvi Sheet No 21.
Computation of ?lane m. valuesinteriLediate between Planes 2. & 3.
All Streamline Columns - Blade Sectiox b. Tables 3D. 4D. & 5D.
Re.NO.68, vam. = va2.+ m.(va3:- va2r.)/Ji.
Ref.NO.69, vbjn r vb2r.+ m.(vb2 r - vb3,)M 2 2 Ref.NO-70, Ek(2.1n)r. = (vam r._ v;L2 r.)/2.g.
Ref.NO.7I, E5P(2.m):r. = Ek(2.m)r. W(2.in)r.
2 2 Ref.NO-72, W(2.m).r. = bo(vb2 r vba r.)/2.g.
Ref.No-75, Esptre = Residual Air Spring Energy existing at Plane m. = Esp(I.2) r - Esp('.x):r Ref-NO.73, t(2.x)r = L(2.m)./veiRI.
Ref-NO-74- L(2.in):r. = Dr.((Sin.(Tan. -I. (Vamro/vclair.)) (Sin.(Tan.-,(va2,/vcaI,.))). -I.
Ref-NO-74A, D r.4(Radius) = L(2.3)rj(Sin.(Tan. '(va3r./vcxI:r.)) (Sin.,--'(Tan.-"(va2./vcmI_.)).
Ref-NO.76, Fpbxr.= Fpa2r.+ t(2.a)r(vb2 r.+ vbm r.)/2.
Ref-NO-77, Sbier. Sa2r.+ t(2.m)..(va2 r.+ vam r.)/2.
Ref-NO-78, Rpbar. Rpb2r.+ t(2.ia)r.(vb2.+ vbYar.)/2. r Ref.No.90.- R Fpbar. = Fpbjar.- t(I.m)r.VIro Ref.No.91.- R Sba r = Sbar, t(I.in).r.VIro Ref-No.92, R Rpbxr- = Rpbm., t(I.m)roVIr_.
Ref.No.89, L(I.M)r'. = L(I.2):r.+ L(2.ja)r.
Sheet 22.
or Coliputation of Plane w. values intermediate between, Planes 3. & 4.
All Streajaline CO1wnns - Blade Section C. Tables 5D. & 6D.
Ref.No-79, L(I.w) r L(I.3)r.+ w.L(3.4),./W- Ref.No-79A, L(3.4) = L(I.4).L(I.3)..
Ref-NO-79-B-- L(I.4) = vclal -t(I.4)..
Ref No-79C, t(I.4).. = (PI r (VI r:r Ref.No.83.- rw r.= b/2.a. + ((b.,./2,a.). 2. + 1/2 where a. = 2.P:L./No. of Blades.
Where b--, = (Xwouter'-'- Xwinxer') Where inner & outer refer to two adjacent strearLlines which enclose an area.
Where a. = (2.Pi.rw Outer 2 INO. - (Ar inner Ax outer').2./No. - b.rw outer' Commence with the outer pair of which the outer Ar r=O:- Zero. and continue inwards using the first calculated inner radius.as.the outer of the next pair and so on. The iitclividual area of the first set is:(Ar2 r=I - AX r=O).
Ref-10.80, Fpow FPbl.+ WA(3.4)r-/Wi. - (X3, Xw.)/2.
r r r r Ref-NO.8I, Sow Sb3. + w-t(I.4):r r ' P; - Ref.No.82, Rpew Rpb3r+ W.t(3,.4)r./W7. + (X3,r,.- Xw.)/2.
r r Ref.No.96.- R R r RPcw r. - (vi r JvoxIr).L(I.w)r Ref.No-95.- R Saw Sow. - (V1 JvcaIrw).L(I.w) r Ref-NO-94, R FPcv Fpew r r 2 2 1/2 2 Ref.No.84- Xw= 2.((RP r._ LD-w)r.)._ L(3. 4) r 2.) 1/2.
2 Ref.NO.93, RF r.= Forla Radius= (L(3.4)r. A3.r.)+ X3r,A Yhere in the example Xl.= X2 r r Sheet 23- Computation of Plane w. values intermediate between Planes 3. All Streamline Columns - Blade Section-" Tables.5D. & 6D.
Note:- In the example the streamlining of all blade sectioxa start at Plane 3. Thus with the exception of the energy value Ei(I.2) and the introduction of the value (BaIr.- br.) to take it into aecount which does not affect the blade absolute and relative profile dimensions, the formulae of the analogy and those up to Plane 3. used for the example are alike. However particularly in the case of Synopsis IA. it could start earlier with Plane 2. being a maximum upstream position.
In-the case of Synopsis IA. it would be ad-vantageous.for reason of material stress to use the same root section as for ID. but on.the blade tipsection use Plane 2. as the starting position of the streamlining. In between it could be varied fie.x the plane of one to the other.
Vie streamlining will not affeat the energy change between Plane 2. and Plane 3. providing the value (X2r-- Xb r')/2 issubtracted from the front and added to the rear profile throughblade section b. similarly as is done on section c.
Sheet 24.
Rotor Blade DesigA Roced_ure applicable to Rotors which follow Stators. Synopsis Stage 2. Tables17D. Notes:- To provide fOr the matching of the airflow througa- a multiple number of stages-it will be noted that the Stage I-. Synopsis has made the two Products (r(I-3.)rvcmIr-If.-(I-3)r) and (r(I.3)r-vemIr) to vary in value at a constant rate radially across the inlet plane, such that the mean streamline valuesare also the mean values, of the air mass, flows which at the inlet plane are.3ymetrically disposed on the plane. Thus W(I-3) r=x/2 equals m W(I.3) r=x, 1, Ek(I.2) r=x/2. equals a Ek(I. 2) r=M. etc.
This provision isnLade to apply to all stages with a further proviso that the two valuesvaj. and vcxj. on the mean streamline of the full air mass flow are the same for all stages. However due to the repositioning of the full air mass mean streamline each stage the values of the lesser portions do change slightly each stage.
The following formulae have been provided to calculate the new values:Ref.No.4I, ArI R = Stage I. AA R - & r(I.3) R Stage I. r8 R. 2 Ref.No.4IArIr. = Fi.(t(I.3)0. r(I.3)r 2 Ref.No. I, r(I.3) R Cr(I.3), Stage I.Ar8 R. pi.)1/2.
Ref.No. I- r(I.3):r r(I.3)0. (Str.No.)(r(I.3), r(I.3) R)/(max.str.NO.).
Ref.No. 5---VIr. = r(I.3)rVIC./r(I.3)0.
Ref.No-43---MI.. = A-.rI:r.m voinIr./m vIr.
Ref-Nos. 9;.,IO.,30.,3I.932.,33.-i35.138.,39.y & 40, C3r.C4:C.9 E(I.2) p ELDI.2):,#, Ei(I.2)r.l Esp(J.2),.q W(i.2)r_q r T2 r., P2:r.,, v2 r.,, Formulae for their derivation are as used for Stage I. Synopsis.
Sleet 25.
Rotor Blade Design Procedure applicable to Rotors which follow Staters. Synopsis Stage 2. Table 17D.
A Ref.No-54, Stage 2.(I.x 14.)0. = r80.vcm80.
Stage 2.(I.x 14.)R. = A R vcm8 R Stage 2.(I.x 14.)r=M.No. /2. = r(I.3)r=M NO.2vcln,r=Y,.No./2 Ref.NO-54, Stage 2.(I.x 14.)r.= (I.-x 14.)0. ((r(I.3)0. - r(I.3).r.)((I.x 14.)0. - (I--X 14.) R)/(r(I.3)0.
r(I.3) R))' Ref.No.14- vemI_. (I.x 14.).ro/r(I.3)r.
2 2 2 1/2 Ref.No.13, vaI (Stage J.(vaj r. + vemI r VOMI r.) Ref.Nos.15.,I6.and 17, TI r gpI,.and vIr. = T8r.,p8r.and v8 r.
Note:- It hasbeen assumed that the blade strength is capable taking an equal load as.the I St. Stage so W(I.3) RMR' of the nd'Stage has been made equal to that of the IstStage. W(I.3)0. of the 2ndStage has olso been made equal to W(J.3)0. of the Ist-Stage. Thus:- Ref.No.37, W(I.3).. = (I.7C 14.x 3Mr-AI..x 14.)r.
Ref.NO-53, (I.x 14.x 37.)r. = (I.x 14.x. 37.)o.+ Cr(I.3)0, r(I.3):r.
)(2.((I.x 14.x 3MO, (I.:x 14.x 37.) RKR)/(r(I.3)0. - r(I.3) R) Where (I.x 14-X 37.)b.r(I.3)0.vcmIO.Stage I.W(i.3)0.
And (I.:x 14.x 37.) r(I.3) VCMI Stage I.Y(I.3)RMR nm.n M111 171 rL Ref.No.36, Ek(I.3).. = WC.3)r, y.Ep(I.2)r.
Ref.No.I2, -va3 r.. = (Ek(I.3):r..2.g. + -vaI r 2.)1/2 Ref.NO.I8, -:.va2 r -- = (va3r, vaIr.)/C3... + vaIr.
2 2 Ref-NO-34- EgI.2),.. = (va2 r._ vaI r.)/2. g.
Ref.No.II, br. = (va3 r - vaj...)/(vbIr- vb3,.-) -Sheet 26.
Rotor Blade Design Procedure applicable to -Rotors which follow Stators. Synopsis Stage 2... Table 17D._ Ref.No.12.- Ba2 r - = br. + Bi(I.2) r 2.g./vbj., 2 lqef.No.20.- vbI r = (E(I.2)r-2.g./(va2r- vaj..)) + vaI r vb3 - = vb2, (va3 - va2_.)/b.
r r r r r m va(I.3)r = ((va3r, vaIr.)-C4r-) + vajr.
m vb(I-3),. = m va(I.3),. + X2r./2.t(I-3)r.
t(I.2) r 2.X2.r../(vbI r - Val r).
t(2-3)_r. X2 m VCMI Ref.No.21.lqef.NO.26.Ref-No.27-T?ef.No.28.T?ef No. 29 - Ref.No.42.- T?ef.No-44 - m Ek(I.3).,=, -?ef.NO.45-Ref-No.46, P,ef-NO-47, Ref-NO-48, Ref.No-49.Jef No. 50. Ref-NO- 5IRef-NO-52, m Ep(I.2),=x.
m m m T2 T2 Angle A Angle B Angle Cr. = Horse Power ./(va3r--- vb3,.).
vcmj r=X/2 Ek(I.3) r=x/2 EP(I.2) r=x/2 Ei(I.2) r=x/2 W(I.3) r=x/2 r=X/2 Tan. -I. (va3,./vcmI,.).-.- Tan. -I. ((Vir, va3 r)/vcmir.)- Tar.. -It. ((V-T r.-',a Vb( 3)r.)/vemIr).
= NI, I r=xm W(I.3)r=x/550.
Sheet 27.
* Axial Flow Air Compressor Design Procedure.
Stator Blade Design Procedure - Notes. Tables 7D. to 16D.
The axial length of the stators is divided into two parts by a short length interposed for the adjustment of total length for mechanical reasons. The basic planes being as fpllows:- Inlet Plane 5 This plane except for being divided by a different nuxber of blades is exactly as the preceding rotor outlet plane.
Planes 6. & 7. Air conditions at these two planes are exactly &like. Except for allowing for the rotation of the air, dimensions are also alike.
Outlet Plane 8. Except for differences in the radial positions of the intermediate streamlines and number of blades the dimensions of this plane are identical to the following Rotor Blade Plane I. Thus before calculating any Stator conditions it is required first to compile the Stage 2. Synopsis.
Planes intermediate between the above planes. The planes which divide the length L(5.6).,. are designated by the letter m. The planes which divide the length L(7.8),. are designated by the letter n.
The function of the first portion of the blades is to move the streamlines radial position so that at Plane 6. they are axially in line with their position on Plane 8. A second requirement is to change the proportions of va5 and vCm5suelt that the ratios va6 r./vom6r.9 va7r- /vem7r' and va8 r/vcm8 r. are of the same value.
The function of the rear portion of the blades is to reduce the air velocities va7r./vcm r. via van r./Vcmn ?. to va8 r./Vcx8 r.
while changing the surplus of kinetic energy into heat energy.
by diffusion.
An-assumption has been made that the levelling out of air temperature radially outwards is effected between Planes 7- & 8. whickthougk not exactly true is only untrue quantitatively.
Sheet 28.
StatOr Blade Design Procedure - Continued.
Outlet Plane 8.. Tables 8D. & 16D.
Ref.No. 3- m T8. = m T2 + m Ek(I.3),.(y-I)./y.C.
r R Ref.No. 4- m p8r. = m p2 R (m T8r./in T2 R)Y/(Y-I).
Ref.No. 5- m v8,- = m v2 R.(m T2 R' /m T8r.) IAy-i) Ref.No.22- T8 r - = Ref.No.24- v8r. = Ref.No.37- r8.. = m v8 (r8 0 2 Ax8 r. /,:,i.)1/2.
m T8 Ref.No.23, p8,.= m p8r.
Ref.No. 7, Ar8r. = M8r.m v8,./m vcm8,. = m Z8r.H8 r No. Ref.No.63- (37.x 21.)0. = r80-vem80 Where vcm80.= (vcmio.- vcmj RMR)(r80, 1948 R)/ (ri T_ 311 R.). + vemI RMR Ref.No.63- (37.x 21.) R 2. (vemI RMR IN8 R.). - (37.x 21.)0. Ref.No.63, (37.x. 2I.)r. = ((37-x 21.)0, (37.x 21.)R.)(r8:r -A R.)/(:r80---r8R). + (37-x 21.) R Ref.NO.62, Ref.NO.20, Ref-No. I, Ref.No.4I, Ref-NO-I7, Ref-No-34, Ref.No.58- v=8 r. = (37.x 21.) r -/r8r. (4I.x 2.) Rmr - = ((37-X 2I.)o.+ (37-x 21.)r. )/2.
m vcm8 r. = (4I.x 2.) RMr /RM8 r.
2 2 2 va8 r ((-vai r. + VOMI.), vcm8 2 2 2 m va8r. = ((vaI r. + vemI r m v=8 r W r. = (r8 0.+ r8 r.)/2.
m P8 r 2.-RK8 r Pi./NO. Ref-NO-I8- m Z8.
P8 r 2.x8 r Pi./No. Ref-NO.35- Z8 r Rv8r. (vaI, 2.+ vemi:r 2 1/2 Ref.No.5 Rv8 cr, r Sheet 29.
Stator Blade Design Procedure - Continued.
Outlet Plane 8..
Tables 8D. & 16D.
Ref.NO.561, L(7.8) r = X7r./2.Tan.0(7/8) r Ref.No.52c- A7/8) r =(Cos-I W-+ (I-+ z(7/8)r.)Rt(7/8)r./2)1i' (I.+ Rt(7.8) r))/2.
Ref-No.50- z(7.8) r = ((IIY)+ (I/Rt(7/8) r 2.
(I/Y.RtW8) r 2.)) 1/2.
Ref.No.49, Rt(7/8)r. = Rv7r./Rv8r.
2 2 1/2 Ref.No.58, Rv8 (va8 r. + vcm8 r.) 2 2 1/2 Ref.No.58, m Rv8 - = (m va8 r. /+ m v=8 r.) Ref.No.57- L(5.8) = L(5.7)r.+ L(7.8)r. r Ref-NO-55t(7.8)r. = L(7.8)r-/m vem(7.8)r.
Ref.No.59, m vem(7.8),. = (vom7r + vcm8r.)/2.
Ref.No.60, Ref.No.43, Ref.No.44,- Ref.No-53, Ref.No-54 - Ref.No.61, Ref.No.62, (41.x 2.) r =nM8 r m VOM8 r.
Ref.NO.63, (37.x 21.) r =r8,.vcm8 r.
slight difference in the values of va8 r -, vcm8 r the values of vaI r ' VOMI r. on the Stage 2.
Synopsis is accounted for by the slight changes of air mass flow governed by the intermediate streamlines.
Note:- The to M8 r - = As Stage I. Rotor Plane 1.
m Q8r. = Tan-,(m va8r./m vcm8.r.) Q8r. Tan-I(va8r./vem8r.) SPp8 Tan.Q8 -L(5.Cr.+ X7r./2.
r r SFAr' Ry r L(7.8)r./Sin.(2.(7/8)r.) SRp8 r Sheet 30.
Stator Blade Design Procedure - Continued.. Inlet Plane 5- Tables 7D. & 9D.
Note:- Plane 5. outer and inner boundary radii together with the radial positions of the intermediate streamlines are exactly the same as on Plane 4. of the preceding rotor blades.
Ref.NO.2. In.vcm5,.= AG.Ref.No.42. of the Stage Synopsis.
2 1/2 Ref.No. I, m va5.=No. (m. EEK(I.3) r =No - 2. g. + vaj r=No. /2..) Ref.No. I, m va5.=No. = va3 r=No./2.
Ref.No. 3, m T5r--- As Ref.NO-48. of the Stage Synopsis.
Ref-No. 4- m P5r.= m P5r=No. P1r. (in T2 r=110. /TI r.)yAy-i.) IAy-i.) Ref.No. 5- m v5r--- M V5 vI_.-(TI /T T5 To.) & r =No & - r =1 Ref.No. 7, Ar5r. = REF.NO.37- r5r. = D- e f. No.41- IIII..m. v5,./m vcm5,.
2 Cr50 Ar5r-Pi.) 7M5r = (r50.+ r5rs)J/2.
Ref.NO-I7. m P5r - = 2.Pi.RJ5:,./NO. Ref.No.18, m Z5r. = m P5r.
ef.NO.34- P5r -- 2.Pi.r5,./NO. Ref.No-35- Z5.. = P5r.
-Ref.NO-36,X5.., -Zero. Ref-No-19, X5 Zero.
r Ref.No.42, H5r.= (r5,- r5r.) Ref.NO.43, m Q5,.= Tan. -I (m va 5,./m vcm5,.) Ief.No-44, Q5.. = Tan. va5r./WM5r.) Ref.NO-53, SFP5,.= Zero. IRef.No-54-- SRP5_. = Zero.
Rgf.No.'3.- m vom(5.m),- = vcm5:r.
2 2 1/2 -ef-NO-58.-. IRV5.- (va5. + vein 5 r 2 2 1/2 Ref.No-58- m Rv5 r = (m va5,.+ m vcm5,.) Ref.No-58, Ref.NO.58- Rvx5r. = R1v5...
m Rvx5 - = m Rv5r.
T z c Sheet 31.
Stator Blade Design Procedure - Continued.
Plane 6. & 7. - Tables.8D. & 131).
2 2 1/2 Ref.No.58, Rv6 (va6 r. + vcm6 r. = Rv7r.= Rv5r.
2 2 Ref.NO.58- L' Rv6 -. = (m va6 r. + a vcm6 r.)1/2. = m Rv7r= x.Rv5r Ref.Nos-43. & 44- a Q6r. & a Q7r & Q6r. & Or. are exactly as a Q8r & Q8r.
Ref-No. I, a va6 11.= m va7r. = Sin.m Q8 r m Rv6 r - Ref-No. 2. a vcm6,.= a vcm7.= cos.aa Q8a Rv6.
r r r Ref.NO.20, va6 va7,o= Sin.Q8..Rv6.
r Ref.No.21, vcm6,-= vcm7,.= Cos.Q8reRv6r Ref-NO.22, T6 -. = T7r.= T5r. Ref.NO.23, p6,.= P7r, = P5r.
Ref.NO-24, v6r.= V7.r.= V5r.
Ref.NO-37- r6 r- r7r = -r8,. Ref.NO.4I, RM _r.= R7r.= RM8r Ref.No-34- P6 r- P7r.= P8r. Ref.No.I7., a P6 r.= a P7r.= a P8 r.
Ref.No. 7, Ar6:r.= Ar7r--- M5rm V5ro.m VOM6r.
Let RMR. = (r=Max.NoJ2.) Ref.NO.35- Z6 RMR - Z7 RKR= v6 RKR vcm8 RMR P6 RMR /vcm6 W V8 RMR Ref-NO-35, Z6 LUIM-I 2.((Ar6 RMR, AA RMR-I.) /(1.6 RMR-I-_ r6 RM R).NO.) - Z6 RMR Ref.No.35.- Z6 RMR-2.= 2. ( (Ar6 RMR-I. Ar6 RMR-2.)l(r6 RMR-2.--- r6 RMR-I -).NO.) - Z6 IRM R-I - Ref.No.35,, Z6 RMR+I.= 2. ((Ax6 IMR+I - - Ar6 RMR).Z(r6 RMR_ r6 RMR+I.).NO.) - Z6 RMR Ref.NO.35- Z6 RMR+2..= 2.((Ar6 RMR+2._ Ax 6 RMR+I.)/(r6 RMR+I.
r6 WR+2.).NO.) - Z6 RMR+I.
Ref.No-35- All values of Z6 aPPlY to Z7. with identical suffices.
Sheet 32.
)t,ator Bla-te Design Procedure - Continuet.
Planes 6. & 7. - Tables 8D. & 13D.
1 1ef.1To.I8- m Z6r--- m Z7r. = AA /No.H6 r -ef.NO-I7.- m P6 r.= m P8 r I ef.lo.19.- m X6 r'= m X7r,= m P6 r, m Z6 r lef-NO-39.- L(5.6) r = X6.a/(((6 r- VOM5r.)Ava5r--- v-a61..)) (va8,./vcm8,.)).
"ef.No.39- L(5.6)r.= Sin.,6,).
ef.No.64.- RP...= (X6_../(((vem6 vcm5.r.)/(va5X.#- va6r))va8r/vcm8r))(Sin..5r- Sin.,6,.)) -ef.No-38- t(5.6)r. = L(5.6)r'/m vem(5.6),# )ef.NO-33- m vem(5.6)_.= (((,,v5 2. 2.) (U6 U5:r + ( "v5 2 A.X Sin.(2.1T5_..) - Sin.(2X6..W(va5r--- va6r.)).
Where U6..= ((Pi.,/2) Q6r.) an.L U5 r= ((Pi.11/2) - Z5r.) Whe:,e 'li6r. and Q5.ro are in -adians.
L 2. 2. 1/2.
Whe re ?Y5:.. = (-va5 r + Vom5:r tef - No.31. - L(6.7)r# This length is optional.
ef.'tgo.30.- t(6.7):,#= L(6.7),#/vcm6...
Ref.No-39, L(5.7)r, = L(5.6)r+ L(6.7)r& ef-NO-38.- t(5.7)r# = t(5.6).re+ t(6.7)r ef.1To.53.- SFp6,.= Tan.Q6.oL(5.6).. ef.No.53.- UP7. Tan..6:r.L(5.7):r.
ef.NO-54.- 3-1P7. = SFP7r+ X6 r. Where X6.r.= Z7r -.ef.1To.54- 3-P6.. = SFP6.r.+ X6 r Ref.No-36, X6 r = X7r--- (P6 r, Z6r.) Sheet 33..
Stator Blade Design Procedure - Continued. planes m. - Intermediate between Planes 5. & 6.. Tables 7D.jand 91). to 12D. Note:- There are two ways of plotting the inner lamina profiles of the various areas of airflow, the first of which is to arrange a constant rate of change of the values m m r. and Qmr. and a constant rate of change of the value Xm r. in a radial direction. It is then possible using the required areas of airflow in a Quadratic Equation to calculate the exact values of rm, r. to enable the inner lamina profiles to be plotted. Initially this was done but the curves were inconsistant in form and for that reason discarded.
The second method which was applied to the example is to use the values m Q;mr.q Q.
pr and Xm r. as before and arrange a curve of constant arc radius whose radius centre would lie on a.radial line intercepting Plane 6. of the inner streamline, and in a similar way for the other streamlines. The latter curves are thus the mean of the calculated ones. The effect of the latter when the area Arxm r - is greater is to slow down the value of m Rvxm r. to m Rvm r. and if less to speed up the value m Rv=.. to the value of m Rvm And as m vcmxm m vcm5r-Ar5r/Armr. (Where Arm = No. 11M r m Zm r.)5 m vaxm r. = Tan.m Qn:rom vcmxmr.
Ref.No-43, m Qm - = m Q5,r. - m.(m Q5.- m Q6..)/M.
r -Ref.No-44.- QM Q5 M.(Q5r.- Q6r.)1M. Where Qmr.= Tan.-I(vamr./vemm r) r r Ref.No. I, m vam r. = Sin.m Qmr-m Rv5r.
-?,ef.No. 2, m vcmm.. = Cos.m QPirom 'v5:,.
Where m Qm r.= Tan. -I. (m vam r/ m vomm r.) - 2 2 Where m Rv5r. = (m va5,. + m vcm5.r)1/2..
ef.NO.20.- vam r. = Sin.Qmr.Rv5r.
Tef-NO.2I.- vemm Cos.Qmr. Rv5r.
2 2 1/2. Where '.1v5r. = (va5,. + vcm5,.) Ref.NO.2A, m vcmxm,-= m vcm5...Ar5,./No.Hm,.m Zmr.
Ref.No.IA, m vaxm. = Tan.m Qm m vcmxm.
r r. r Arm r - = N6.Hm r m Zm r.
Sheet 34- Stator Blade Design Procedure - Continued.
Planes m. - Intermediate between Planes 5- & 6.; Tables J2D. to 9.D.
Ref-NO.20A- vaxm r Sin.Qm.-."1-vxm r r Ref.No.21A- vcmxm r. = COS.QMr-R= r fhere Rvxm Rvm m Rvxia./m Rvm. I.There r R R 2 2 1/2.
Ref.NO-37, rmr.= (Rxr,._ (L(5.6) r, L(5.m)..).).+ (r6.r.- Rx.).
Where U! r.= (L(5.6):r 2 J2.(r6r--- r5,.)-).+ (r6.- r5r.)/2.
Ref.No-39, L(5.m).r.= L(5.6)r-(va5 - vam..Mva5.- va6,.). r Ref.NO.39, L(5.m).r.= (Rpr.(va5r--- vam.. /,Rv5...
I.There RP = L(5.6)r-Rv5r-Ava5 r.) r. - va6 Ref.No.36, Xmr.= (RPr.(Cos-Qn r- Cos.Cr.)) - (L(5.m).#Tan.Q6 Ref. No-17, m Pm,.=:U,,1m,.2.Pi.,/No. Ref.No.4I.,- IREM..= (rmo+ xmr.)/2. Ref. NO.34, Pmr. = fm,.2.Pi./1o. Ref-NO-32, Zm_.= (Pm., Xmr.).
Ref.No.I8, m ZM r=4= (Zmo.+ ZM r=4.)/8. + (ZM r=I + ZM r=2 + ZM r=3)/4 m ZM r=3= (Zmo+ ZM r=3)/6 + (ZM r=I + Zin r=2)/3 m ZM r=2= (Zmo.+ ZM r=2)/4. + (Zm.=I)/2. m ZM r=,= (Zm 0 + Zmr=j-)/2.
1 Ref.NO.I9- m Xm r.= m Pm r - m ZM -1 2.
ef.NO.33, m vcm(5.m) ((Rv5 2J2.)(Um., U5r.). + (Rv5 A.)( r r Sin.(2.U5r.) - Sin. (2.Um,.))/(va5.,.- vam:,.).
Where Um r.= ((PiJ2)- Qmr.). and IT5r--- ((PiJ2)- 0,5r.) 11 QP1r and Q5 are in Radians.
Ref.No.38, t(5.m)-- = LD.M).-/m vem(5.m),.
Ref.No. 7- Arm r.= No.Hm r m ZM r. and Ref.No.43- Hm r - = (rm c). - rmr. ) Ref-NO-53, SFPm,.= Sin.Q6 rL(5.M)r. Ref.NO.54- SIRpm_.= 'Fpmr.+ Xm r.
Z Sheet 35.
Stator Blade Design Procedure - Continued. Planes n. - Intermediate between Planes 7- & 8. Tables 8D.J4D.J5D.
Ref.No._58, Rvn r - = R-v7r. - n.(R-Y7,.- Rv-8....)/N.
Ref.NO-58, it RYn m RT7 n.(m RY7r--- a Rv8r.)/N.
Ref.No. I, m van.. = m va7r. - n.(m va7r--- a mit8r.)/N.
a van... = Sin.m Q8 r. a Ryn r - Ref.No. 2.- a vcmn -- = & vcm7.r. - n.(a vca7:r,- a vca8,.)IN.
jia vean r, = G05-m Q8.om Rv%.
Ref.No.20, van - - = va7r--- n.(va7,,- va8,#)/N. = Sin.Q8:&Rvn...
Ref.NO.2I- vemn.= vcm7,.- n(vcm7,.- vc&8,.)/N. = Cos.Q8..Rvn.. 2 Ref.No.22, Tn Tn T7 + (Y-I.)(RV7 r=M.No./2= RMR RMR RMR 2 Rvn PAR)/y.2.g.C.
Ref.No. 3, a Tn r=M.NO Tn RMR 2 2 Ref.No-22x.- T=.= T7 (y-I-)(RY7 r Rvn r,.)/y-2.g.C.
- r Ref-NO-3x, zt T= r:x - =" T= r=x/2' Note:- For streamlines whose number is less than the Streamline (r=M.NO. /2) = RMR. the value n.(Tn RMR--- T=..)/N. should be added to T= r - For streamlines whose nuaber is greater the value n.(Txnr,- Tn RMR---)IN. should be subtracted from the value T= r. It will thus be seen that in the temperature levelling out the surplus heat is presumed to move radially outwards between Planes 7- and 8.
Ref,No.22, TA_. = T-M r - + n. (Tn ERR - T=r -) /K - Ref.No- 3, a Tn - - = a Tn r=x - = Tn r=x/2' Ref-NO. 4-- m Pn,- = a k7r-(m Tnr./ma T7,r IAY-I-) Ref-No- 5-- m vnr- = m v7r-(m T7,./x Tn..) Ref.No.23.- Pn - = P7r.(Tn -/T7r-)Y/(Y-") r r Ref-No.24-- vnr' = v7r.(T7r'/Tnr')I/(Y-I.)' 0 Sheet 36.
Stator Blade Design Procedure - Continued.
Planes n. - Intermediate between Planes 7. & 8. Tables 14D. & 15D.
Ref.No. 3_.- m Tn r m T= r. + n.(m Tn 2. RDIR: - m T=.)IN.
Ref'.No.22.- Tn r Txn r. Tn. (Tn IRMR Txn,.)IN.
Ref.No.23.- pn r = P-7,-(Tn,./T7,.)Y/(Y-I.).
Ref.No.24.- vn. = v7r.(T7 /Tnr.)I//(Y-I.).
r r Ref-No- 4-- m Pn,- = m P7 -(m Tn r /m T7,o)y/(Y-,')' r Ref.No-5.- m vnr' = m v7r'(m T7r'/m Tnr.)I/(Y-I.
Ref.No.7---Arn r. = Y15..M vn,./m vemn r. Where M5r.
Ref.NO.37, rn r. = r7r. = r8r.
Tef.NO.42.- Hn r - = H7r. = H8r = M4r.
Ref.No.35, R0 R r=MIax.No./2 RM R PMR RY1 R R Zn. = Zn. = Z7. v=7. -vn 1.1re--myl -1r7 Ref.NO.35- Zn r=I 2.((Arnr =2 o- Arn r=I)/NO-(Hn r=2- Hn r=i.)) - Zn RYL R Ref.No.35, Zn r=o 2.(Arn.=,./llo.Hn r=i -) -- Zn r=I Ref.No.35- Zn r=3 2.((Arn r=3- Arn r=2)/No.(Hn r=3 Hn. =2)) - Zn r=2.
Ref.No-35- Zn r=4 = 2. ( (Arn r=4 Arn -,=3)/NO("n,=4.- Hn r=3)) - Zn r=3 Ref.NO.36, xn,.= Pn..- Zn.. Ref.No-34- Pn r.= 2.Pi.rn r INO.
-1. 2 1/2.
Ref.NO-52, V(7/n),.= Tan. (A r./(Ry r.2.A r, A r Where Ry r.= L(TA).. /Sin. (2.0(7/8) r)' And A r - (X7 r - - Xn r.)/2.
Ref.No-56, LP.n)r.= -!-y..Sin.(2.0(7 /n)r ef.No.55, t(7.n)_.= LP.n)../m vom(7.n).# Ref.NO.59- m vcm(7.n),. = (vcrfl7r.+ vcmnr)/2.
Sheet 37.
Stator Blade Design Procedure - C'Ontinued.
Planes x. - Intermediate between Planes,7-. & 8. Tables I4D--& I5D Ref.No-17-- m Phr- = 2.Pi.RMn r -INO.
Ref.No.I8.- m Zn r - = Arn r- /No.Hn r Ref.No.19.- m Xn - = a Pnj.- m Z.n r r r Ref.No-57.- L(5-n) L(7.n).r,+ L(5-7)ro r Ref.No.53,-- SFpn Tan.Q7r.L(5.n - + (X7ro- Xa)/2.
)r r Ref-NO-54- SRpn SFPn r + Xn r Ref.No.41.:- Wn FM7r, = RM8 r Sheet 38.
Claims (5)
1.3 110 L(3.4) PLANE 4_ RhC4.
- 2-5'2b(o R RhcL.
2.3n42 R R6 c 4.
B, 1005 FJoc4-l F, c 4 442 R - - - 1 Sheet 80.
TABLE 20D.
Dimensions of Air Duct and Stators Plane 5.
(r = 0.). m=2 m--3 m=4-m=5 m=6 n. M-0m=1 0 -0-781 -1618.25,07.3443 -44-23.54-41 0- -0251.0520.0805 -JJ06 -[4-21 -1-7-2> 0.0942.1C28 -3156 -302.2 rm. r h. io.oFo io.oo -)o.ooo lo.ooo to-000 lo-DoD Plane 5.
(r = L).
n. rri--0 m= 1 m-- 2 m=3 m=4. -m=5 m=6 L (Slm.). c) -o8o8 -261 -103G)B?) -164C4 SF 0.0232- -0'751,4 [9E] 0 -0q0-3 rm. r n. q.ú q.52%2 17.5346 9.544 q.55;1:3 g. 1571 q-5G14 ;t95 -- Plane 5.
(r = 2J. - m= 1 m= 2 m--3 m = 4. nn-- 5 m-- 6 m= 0 rrn").'-c) L (5 -0-785; -164-1 -2562-35,42 -4-575.5651A S FD - -0)q3.0404 -0651 -3779(.-4'301 -5 R 0 -0q02.1769 '214qR -0873 r M. r n. c) -3183 q-04 plan -5. -- (r =3j, n. m-- 0 m= 1 m= 2 m:. 3 m= 4 m= 5 m= 6 L(5.m). 0 -0-784.1647 -25e --3584t. - r77L(:> 0 -0192 -031q -0501 -32T7 - 099 9 -1114 S 0.0919 -17(.- -252cl -92 l,aeo -S- --- 8. 978 - -g-. -6 2 _d 2 8.6951, r m. r n. 8.607- P t a n e 5.
(r = 4.-.). rn= 1 rn= 2 m=3 m= 4 m=5 m=6 D - m= 0 - L (5.M). 0 -.07-34 r2 5 9 -2&4-. -05.1p&j94 - r-, -3-05 W7 9 A rrp rn. C.) -018Gq (=>60 2394-2-9 -34-'P>I2> -3895 -1(:160 -2197 -76!9-255'. 8.26q2 8.1qI - 0.-23-75 Iql 77 1 Sheet!BI.
r T ABLE 20D.
jp Inches See Tables 7D. to 16D.
Plane 6. Plane n=2 n=3 Plane 8.
M-7 m=8 7. n=4. n=S' Ti=0 t-l=1 G4-93 -757b- (.0336 [.076 1.6812,5 I-S-7111 2-DL7L:,- 2.2241 '2086 -24-33 -3320 -4-925 -5810 -6646 -7506 -8430 W-000 10.000 10.000 10,.00010.C)D() 10.000 1c)-DOC);0-000 Planc6. Plane Plane8.
rriz 71 m= 8. 7. i n= 1. n= 2. n =
3. n =
4.. n =
5.
n = 0.
694-5 --7'196 q20-7)-4-023 1.933-3 2.02-72 2.221L 1 )c16G -22q7.2C45; -11-226.5121 -517-7cl.(jS-75.^785.,l -4.84-8.522G -55-7&.6759 -7185 -7ZcB2 -7-700.7855 9.5641 9-56l q-565;J 9.5651 9.5651 9-5651 q-5651 Plane6. Plan n= 2 n= 3 Plane 8.
m=7 m=8 7. n=4 n=5 n=0 n= 1 6771 -7920 6664 1-3742 1-6099 1-9155 2,016<i 2-224) -1668 -1991 -21S4 -3590 -521-7.60715 -'70--94- 4--797 -?060 -5211? -62C10 -66>2.61,3377 -7034- 9.1 1333 7.1333 9.1333 q-1333 9,13: C1.1 gs q.)333 3 Ptane6. Plane n=2 n=3 Plane 8.
m=7 m= 8 7. ', -.1 n=0 n=l n'= 4... n = 5 68 c? 1 -8065.8078 1.319 5 1.5 66 9 V7 8 6 0 2. DO 11 2.22& 1 -1335; -156-3 -156,6 -277G -3518 -416,7 -4950 -4.9G2 -5726 -5C?L.2 -40&6;6C),9 -600 8.7026 8.7050 8.7050 97050 8.-7050 8--705;0,S.,-7D50 t 9,70JO Plane6. Pianel n=2 n=3- Plane 8.
m=7 m=8 7. n=4 n=5 n=0 n=1 Pn -65,82.7703 J7c778 1.3062 JJ7-74.G5 1-qgb,0 2.224-1 1,3 8.2777 8.280 8.2iO 8.2804 2.2806 8.2806 9,2906 BS.'2806
2-69)o F,C4.
- 2. 5266 R Fbe L.
0 13.15!B"7a 1. 5 5 4.1 FLAME4- y ?=.58?7 L(J-41 S.1005.. Sc-L- 2.3-744,2 P. - s c- L. - 3.1()05. 1 Rbc44.
Priority Applications (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| GB8920415A GB2250322A (en) | 1989-09-08 | 1989-09-08 | Axial flow air compressor blade |
| EP19890312535 EP0416186A3 (en) | 1989-09-08 | 1989-11-30 | Axial compressor rotor blades specifically shaped to confine the existence of the energy designated esp. to within their axial working length defined by the dimension l (i.3) |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| GB8920415A GB2250322A (en) | 1989-09-08 | 1989-09-08 | Axial flow air compressor blade |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| GB8920415D0 GB8920415D0 (en) | 1989-10-25 |
| GB2250322A true GB2250322A (en) | 1992-06-03 |
Family
ID=10662808
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| GB8920415A Withdrawn GB2250322A (en) | 1989-09-08 | 1989-09-08 | Axial flow air compressor blade |
Country Status (2)
| Country | Link |
|---|---|
| EP (1) | EP0416186A3 (en) |
| GB (1) | GB2250322A (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6945723B1 (en) | 2000-09-21 | 2005-09-20 | L'oréal | Packaging and application device |
| FR2814651B1 (en) | 2000-10-03 | 2003-08-15 | Oreal | PACKAGING AND APPLICATION DEVICE COMPRISING A COMPRESSIBLE APPLICATION ELEMENT FOR APPLYING THE PRODUCT AND HOUSING FOR RECEIVING THE APPLICATION ELEMENT LOADED IN PRODUCT |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB741797A (en) * | 1953-12-21 | 1955-12-14 | Sulzer Ag | Rotors for centrifugal pumps, blowers and compressors |
| GB944166A (en) * | 1960-03-02 | 1963-12-11 | Werner Hausammann | Rotor for turbines or compressors |
| GB1599633A (en) * | 1978-04-17 | 1981-10-07 | Hodgson D I | Aerofoils |
| GB2104975A (en) * | 1981-08-31 | 1983-03-16 | Gen Motors Corp | Airfoils for land vehicle fans |
-
1989
- 1989-09-08 GB GB8920415A patent/GB2250322A/en not_active Withdrawn
- 1989-11-30 EP EP19890312535 patent/EP0416186A3/en not_active Withdrawn
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB741797A (en) * | 1953-12-21 | 1955-12-14 | Sulzer Ag | Rotors for centrifugal pumps, blowers and compressors |
| GB944166A (en) * | 1960-03-02 | 1963-12-11 | Werner Hausammann | Rotor for turbines or compressors |
| GB1599633A (en) * | 1978-04-17 | 1981-10-07 | Hodgson D I | Aerofoils |
| GB2104975A (en) * | 1981-08-31 | 1983-03-16 | Gen Motors Corp | Airfoils for land vehicle fans |
Also Published As
| Publication number | Publication date |
|---|---|
| GB8920415D0 (en) | 1989-10-25 |
| EP0416186A3 (en) | 1991-07-24 |
| EP0416186A2 (en) | 1991-03-13 |
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Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| WAP | Application withdrawn, taken to be withdrawn or refused ** after publication under section 16(1) |