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)

Abstract

 An AXIAL FLOW AIR COMPRESSOR DESIGN SYSTEM to produce a compressor in which AIR SPRING ENERGY DESIGNATED Esp(1.2). which is generated between PLANES 1. & 2. is fully used between PLANES 2. & 3. The the blade arc width being such that the blades give full static coverage to its OUTLET PLANE 4. The lamina air flow through each FULL STAGE being as follows:-

PLANE 1.- W(1.3). + (va1². + vcm1².)/2.g. + y.p1.v1./(y-1.). =

PLANE 2.- W(2.3). + (va2²).+ vcm1².)/2.g.+ y.p2.v2./(y-1.). + Esp(1.2). =

Plane 3.- (va3².+ vcml².)/2.g. + y.p2.v2./(y-1.).

PLANE ₄.- (_va3².+ vcm1².)/2.g. + y.p2.v2./(y-1.). - End of Rotor. Start of STATORS.

PLANE 5.- y.p2.v2./(y-1.). + (va3².+ vcm1².)/2.g.

PLANE 6.- y.p2.v2./(y-1.). + (va6². + vcm6².)/2.g.

PLANE 7.- ALL VALUES EXACTLY AS ON PLANE 6.

PLANE 8.- y.p8.v8./(y-1.). + (va8². + vcm8².)/2.g.

NOTE:- p. = Air pressure EXCLUSIVE of that due to the presence of Esp(1.2) at PLANE 2.

WHILE NOT BEING STIPULATED, the Mean Mass Flow Values have been arranged such that sets of lamina values become also Mean Mass Flow Values, for EXAMPLE Esp(1.2)_r=x/2. = m Esp(1.2)_r=x. & va2_r=_x/2. = m va2_r=x. etc.

Also:- Va8_r=Max.No./2· and vcm8_r=Max.No./2. = va1_r=Max.No./2. and vcm1_r=Max.No./2. and are constant values for all stages of a compressor.

And (va6_r./vcm6_r.) = (va7_r./vcm7_r.) = (va8_r./vcm_8r.).

Description

[0001] Multi stage axial flow compressors are used 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 required to add kinetic energy alone or kinetic and heat energy to the air while the stator ring of blades change the surplus whirl 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 streamlines but not necessarily all of the same value.

[0002] 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: - (va4². - val².)/2.g. & Heat: - C.(T4. - T1.)-/(y-1.).

Where va4. & va1. = Outlet and Inlet Air Whirl Velocities.

Where T4. & T1. = Outlet and Inlet Air Temperatures.

Where g. = Acceleration Rate due to Gravity.

Where y. = Ratio of the two Specific Heats of Air.

Where C. = The Gas Constant for Air.

[0003] However the use of circular arc cambered aerofoil sections for the rotor blades in engines to obtain higher output has resulted in the blades allowing a third form of energy intermingled with the heat energy to pass the rotor outlet plane. This third form 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 maximum thickness 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 "service life" to prevent them failing.

[0004] The 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 position and to illustrate this:-

[0005] 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 axial movement and then by force move the piston from its central position the distance D.

[0006] If one now calculates the specific volume of the two halves, add together and divide 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.

[0007] 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 whereas 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.

[0008] Thus it will be seen that if the Esp(1.2). 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.

[0009] 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-(1.2). generated in the air through the first portion of the blade ring is constructively used to help drive 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 1.) and the plane which terminates the working length of the blade (Plane 3.) is qiven below:-

[0010] Where W(1.3). = The energy per unit air mass flow required to drive the Plane 1. to 3. portion of the rotor blade ring.

[0011] Where W(2.3). = The energy - Ditto - Plane 2. to 3. - Ditto.

[0012] Where y., C., g., T., and Esp(1.2). are as previously stated.

[0013] Where vcm1. = Axial Air Velocity.

[0014] The above equation with suffices (r=0.) up to (r= Max.No.) apply to lamina streamline values. That is the mean of unit air mass flow if it was disposed equally above and below the lamina streamline.

[0015] Similarly with suffices (r= 1.) 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 W(1.3)., m va2., m v2., m C3., m p2., m T2. etc.

[0016] To show the development of the design system used for the calculation of the rotor blade profile it is necessary 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:-

[0017] 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 arcs, that of the outlet plane being angularly ahead for the same reason as the outer arc. Both arcs are equal in angular extent but the arc 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.

[0018] 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.

[0019] The inner boundary surface joining the two inner arcs, for reason that the compression of the air should be done by the force used to accelerate the air in a tangential direction only, is of a constant arc radius from Plane 1. to Plane 2., (optionally to Plane 3.). Plane 2. being position of minimum angular extent. From Plane 2. to Plane 4. (Outlet plane) both angular extent and arc 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 spirals in the same direction.

[0020] 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 of which could apply to the airstream to the right of the stipulated one. Thus if we use the left side of the airstream 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 shape of the rotor blade (As manufactured).

[0021] 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 offset to the rear of a true radial line which intersects the rotor axis) the airstream is divided by intermediate streamlines into lasser portions of the full air mass flow. For convenience the radial depth on Plane 1. is divided into an even number of equal portions. The outer boundary one is designated (r=0.) and the inner one (r=Max.No.), the inner ones having intermediate numbers. The air mass flowing between the common outer boundary and any one of the others is calculated for Plane 1. and is retained by the streamline to the outlet plane.

[0022] 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 1. to Plane 3. which terminates the working length of the rotor blades, and for this purpose have supplied Drawings Figures 1/2. & 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.

[0023] In both analogies the air container weight and the atmosphere's resistance to movement of the two bodies has been ignored. Each cylinder contains one pound of air at normal static conditions and the solid bodies weigh less than one pound, having velocities much higher than that of the cylinders. The single difference between the two analogies is that the cylinder of the 2^nd. Analogy has an open rear end fitted with a piston and rod, the latter's 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 1. & 2. is retained. The conditions are recorded in Bernoulli type equations at three positions which are 1. 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:-

1. (va12.+ b.vb1².)2.g. + p1.v1./(y-1.). =

2. (va2². + b.vb2².)/2.g. + p2.v2./(y-1.). + (E-(1.2). -(p2.v2.-p1.v1.)/(y-1.).) =

3. (va3². + b.vb3².)/2.g. + p3.v3./(y-1.).

1^st.Analogy :- E(1.2). = vb1.- va1.)(va2.- va1.)-/2.g. = Esp(1.2). Where p2. = p1. = p3. and v2. = v1. = v3. (Exclusive of air pressure due to presence of Esp(1.2). See Figure 1/2.

2^nd.Analogy :- E(1.2). = (vb1.- va1.)(va2.- va1.)-/2.g. = ((p2.v2.-p1.v1.)/(y-1.). + Esp(1.2).). (Exclusive of air pressure due to presence of Esp(1.2).). See Figure 2/2 .

[0024] Where p2. = p3. and v2. = v3. and the ratio (Esp(1.2)./E(1.2).) = ((va3.- va2.)/(va2.- va1.))². = (C3.- 1.)². and the ratio (Ep(1.2)./E(1.2).) = (1.- (-(va3.- va2.)/(va2.- va1.))².).

[0025] Where E(1.2). = (1. + 1/b)(va2.-va1.)²./2.g. Where Ep(1.2). = (1. 1/b)((va2.- val.)².- (va3.- va2.)².)/2.g.

[0026] Where Ep(1.2). = ((v1./v2.)^(y-1.).- 1.).T1.C./(y-1.).

[0027] Where E(1.2). ((v1./vr2.)^(y-1.).-1.).T1.C./2.(y-1.).

[0028] Where vr2. = Specific Volume of the air mass in the rear portion of the cylinder (Adjacent to piston). Where va2. = va1. + (b.(vb1.- va1.)/(1. + b.)) = vb2. and vb2. = vb1.- ((vb1.- va1.)/(1. + b.)) = va2. Where va3. = C3.(va2.- va1.). + va1. and vb3. = vb1.- (va3.- va1.)/b.

[0029] Where Am(1.2). = (va2.-va1.)/t(1.2). = Abm(1.2). = b.(vb1. -vb2.)/t(1.2).

[0030] and Am(2.3). = (va3.- va2.)/t(2.3). = Abm(2.3). = b.(vb2.-vb3.)/t(2.3).

[0031] Where b. = (va2.- va1.)/(vb1.- vb2.). Where va2. = vb2.

[0032] Where C3. = (1.+ (Esp(1.2)./E(1.2).)^1/2.). = (va3.- va1.)/(va2.- va1.).

[0033] Where t(1.2). = 2.P1.(1.- v2./v1.)/(vb1.- va1.). and t(2.3). = P1.(1.-v2./v1.)/(va3.-vb3.).

[0034] Where P1. = Inside length of cylinder at Position 1. of Analogy. (Cylinder head to inside face of Piston).

[0035] 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(1.2). for it is this value which links up all the different kinds of energy.

[0036] To bridge the differences between the formulae of the 2^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 with the tangential blade velocity, and finally to streamline the blank end of the blade which in the analogy would be (P1. - P2) wide at position 3. of the analogy.

[0037] The first being satisfied by adding the value (Ba1.- b.) to b. of the analogy at Position 1. which would disappear at Position 2. The second by changing the straight line operation of the analogy to circular, which allows area's to be specified between concentric lamina 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 tangential blade velocity, thus the Bernoulli type equation of the analogy becomes:-

1.- (va12. + vcm12. + Ba1.vb1².)/2.g. + y.p1.v1./(y-1). =

2.- (va2². + vcm1². + b.vb2².)/2.g. + y.p2.v2./(y-1). + Esp(1.2). =

3.- (va3². + vcm1². + b.vb3².)/2.g. + y.p2.v2./(y-1.). And as (Ba1.vb1².- b.vb22.)/2.g. = W(1.2). And as b.(vb2².- vb3².)/2.g. = W(2.3).

1.- W(1.3)_r. + (va1_r². + vcm1_r².)/2.g. + y.p1_r.v1_r./(y-1.). =

2.- W(2.3)_r. + (va2_r². + vcm1_r².)/2.g. + y.p2_r.v2_r./(y-1.). ⁺ Esp(1.2),. =

3.- (va3_r².+ vcm1_r².)/2.g. + y.p2_r.v2_r./(y-1.). Where W(1.2)_r. = y.Ep(1.2),. + Esp(1.2)r.+ (va2_r².- va1_r².)/2.g.

Where w(2.3)_r. + Esp(1.2),. = (va3_r².- va2_r².)-/2.g. ₌ Ek(2.3)r.

Where (y-1.).Ep(1.2)_r. = Ei(1.2),. = (Ba1_r.- b,.)-.vb1/_r²./2.g.

[0038] And the formula which connects the tangential blade velocity to the air velocities on the Root Streamline are:-

V1 _R. = m vb(1.3)_R. + Maximum m vcm(1.3)_R. See Figure 1/9.

vcm3_R. (va3_R.(V1_R.- va3_R.))^1/2. See Figure 1/9.

In the example Tables 1 D. to 6D. a constant value vcm1_R. has been used which is slightly less than both the two values above.

Where m vb(1.3)_R. = m va(1.3)_R. + X2_R./2.t(1.3)_R.

Where m va(1.3)_R. = ((t(1.2)_R.(va1_R. + va2_R.)) + (t-(2.3)_R.(va2_R. + va3_R.)))./2.t(1.3)_R.

m va(1.3)_R. = C4_R.(va3_R.- va1_R.). + va1 _R.

Limited Angle C°. is taken to be 45°. and the value of the angular difference between the absolute and Relative centre lines of the tail portions (Plane 3. to Plane 4.) is 90°. See Figure 1/9.

[0039] It is also of importance that on the root streamline where V1R. has the minimum velocity, that vb1_R. should have a value not exceeding (V1_R. + va1_R.).

[0040] 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 (V1.) the rotor blade absolute shape continuously in contact with its relative shape on Plane 1. appears to move in an anti-clockwise direction like a pointer of a clock until at the designed speed it reaches the designed speed position. Intermediate to the two positions described above the absolute 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 arc length of one blade pitch.. (See Figure 9/9.)

[0041] 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.

[0042] With 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 1A. had been used for the example the starting plane of the streamlining would have been prior to Plane3.

[0043] The absolute lamina blade circular arc dimensions are measured from an axial line which passes through the blade point at Plane 1. and the axial length dimensions from Plane 1. along the line. Note also that all streamlines in the Synopsis are at a constant radius thus r(1.3).

[0044] Front profile dimension designations are prefixed by the letters Fp and rear profile dimensions Rp. The mean centre line of air mass flow moved circumferentially one half blade pitch so that it can be dimensioned from the above axial line uses the prefix S.

[0045] The blade length is divided into three sections a., b., c. which represent (Plane 1. to 2.)., (Plane 2. to 3.) and (Plane 3. to 4.) and thus:-

Fpa1_r. = Zero. Fpa2,. = t(1.2)_r.(vb1_r.+vb2_r.)/2.

Sa1 _r. = Zero. Sa2_r. = t(1.2)_r.(va1_r. + va2_r.)/2.

Rpa1 _r. = Zero. Rpa2_r. = t(1.2)_r.(va1_r. + va2_r.)/2.

Fpb3_r. = Fpa2_r. + t(2.3),.(vb2,. + vb3_r.)/2.

Sb3_r. = Sa2_r. + t(2.3)_r.(va2_r + va3_r.)/2.

Rpb3_r. = Rpb2,. + t(2.3)_r.(vb2_r. + vb3_r.)/2.

[0046] And in the intermediate positions:-

Fpan_r. = t(1.n)_r.(vb1_r. + vbn_r.)/2.

San_r. = t(1.n)_r.(va1_r. + van_r.)/2.

Rpan_r. = t(1.n)_r.(va1_r. + van_r.)/2.

Rpbm_r. = Rpa2_r. + t(2.m)_r.(vb2_r. + vbm_r.)/2.

Sbm,. = Sa2_r. + t(2.m)_r.(va2_r. + vam_r.)/2.

Fpbm_r. = Fpa2,. + t(2.m)_r.(vb2_r. + vbm_r.)/2. And for blade section c.

Sc4,. = Sb3_r. + t(3.4)_r.va3_r. Scw_r. = Sb3_r. ⁺ t(3.w)-_r.va3_r.

Fpc4_r. = Sc4. ₌ RpC4_r.

Fpcw_r. = Scw_r. + Xw_r./2. Rpcw_r. = Scw_r.- Xw_r./2.

Fpb3_r. ₌ Sb3_r. ⁺ X2_r./2 Rpb3_r. ₌ Sb3,.- X2_r./2.

Where Xw,. = 2.((RF_r².- L(3.w)_r².)^1/2.-(RF_r².- L(3.4)-_r².)^1/2.

And RF_r. = Blade Form Radius = (L(3.4)_r²./X3_r.) + X3_r./4.

And X3,. ₌ X2_r.

[0047] And for axial lengths.

L(1.2),.= t(1.2)_r.vcm1_r. & L(1.n)_r.= t(1.n)_r.vcm1_r.

L(1.3)_r. = t(1.3)_r.vcm1_r. & L(1.m)_r. = t(1.m)_r.vcm1_r.

L(1.4)_r. = t(1.4)_r.vcm1_r. & L(1.w)_r. = t(1.w)_r.vcm1_r.

[0048] And for relative Blade Shape Dimensions.

R Fpa2_r. ₌ Fpa2_r.- t(1.2)_r.V1_r. & R Fpan_r. ₌ Fpan_r.- t(1.n)_r.V1_r.

R Fpb3,. = Fpb3_r.- t(1.3)_r.V_1r & R Fpbm_r. = Fpbm_r.- t(1.m)_r.V1_r.

_R Fpc4_r. = Fpc4_r.- t(1.4)_r.V1_r. & R Fpcw_r. = Fpcw_r.- t(1.W)_r.V1_r.

R Rpc4_r. = Rpc4_r.- t(1.4)_r.V1_r. & R RpcWr.= Rpcw_r.- t(1.w)_r.V1_r.

R Rpb3_r. = Rpb3_r.- t(1.3)_r.V1_r. & R Rpbm,.= Rpbm_r-t(1.m)_r.V1_r.

R Rpa2_r. = Rpa2,.- t(1.2)_r.V1_r. & R Rpan_r. = Rpan_r.- t(1.n)_r.V1_r.

[0049] To relate all the above dimensions together a Drawing has been provided:- Figure 1/1.

Axial Flow Air Compressor Design Procedure - Rotor Blades. i

Notes:

[0050] - 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 the design of a compressor having a specific air mass flow.

[0051] Thus a first requirement before compilation is to know whether 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 1A. 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 halves and fusing together.

[0052] For industrial use due to the high material and manufacturing costs of the former it is usual to use solid blades decreasing in sectional area radially outwards as on Synopsis Table 1 D.

[0053] A study of both the above Synopses shows that to obtain the 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.

[0054] As values which are the mean over various portions of the airflow are required, to simplify their calculation, products (r1_r.vcm1_r.) and (r1_r.vcm1_r.W-(1.3)_r.) have been made to vary at a constant rate radially across the inlet plane. Thus for example m W(1.3)_r=4. = W(1.3)_r=2., m C3₂₌₃. = C3_r=1.1/2., 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.

[0055] If in the case of the example it is required to reduce the axial length of the rotor blade, the way to do it is either increase the number of blades in the ring or alternatively reduce r(1.3)_o. or do both, but certainly not the axial length alone even though it appears uselessly too long.

[0056] If the Synopsis 1A. 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 with advantage be moved up to Plane 2. while still retaining the same circular arc pitch length as Synopsis 1 D. Thus the formulae for Fpbm_r. and Rpbm_r. would require modification to take the streamlining into account thus:-

Fpb3_r. = Fpa2_r. ⁺ t(2.3)_r.(vb2_r. + vb3,.)/2. - (X2,.-X3_r.)/2.

Rpb3,. = Rpa2_r. + t(2.3)_r.(vb2,. + vb3_r.)/2. ⁺ (X2_r.-X3_r.)/2.

Rpbm_r. = Rpa2,. + t(2.m)_r.(vb2_r. + vbm_r.)/2. + (X2_r.- Xm_r.)/2.

Fpbm_r. = Fpa2,. + t(2.m)_r.(vb2_r. + vbm_r.)/2. - (X2,.-Xm_r.)/2.

R Fpb3,. ₌ Fpb3_r.- t(1.3)_r.V1_r.

R Rpb3r. ₌ Rpb3_r.- t(1.3)_r.V1_r.

R Rpbm_r. ₌ Rpbm_r.- t(1.m)_r.V1_r.

R Fpbm,. ₌ Fpbm_r.- t(1.m)_r.V1_r.

Sb3_r. = Sa2_r. + t(2.3)_r.(va2_r. + va3_r.)/2. (Unchanged)

Sbm,. = Sa2_r. + t(2.m)_r.(va2_r. + vam,.)/2. (Unchanged)

R Sbm_r. = Sbm_r. - t(1.m)_r.V1_r.

R Sb3_r. = Sb3_r. - t(1.3)_r.V1_r.

Note:

[0057] - The above dimensions give the blades position and shape on cylinders of constant r1_r. radius which when looking down the stacking line are identical to the blade shapes on the streamlines.

Computation of Stage 1. Synopsis Values.

[0058] The first requirement is the choice of the following values:-V1₀., r(1.3)o., r(1.3)_r., No. of blades in ring., Ratios (P2_r./Z2_r.)., ICAC Standard Atmosphere air conditions., a stipulation of the value of va1_R., a stipulation of the value of the Ratio (vcm1_R./Max.vcm1_R.) From which are derived all other values on either Synopsis 1A. or 1D. (1D. used in example):-

Root Streamline Column applicable to Synopsis 1A. or 1D.

[0059] Ref.No. 9 .- C3_R. = (1. + ((B.- A.)/B.)^1/2.) Where A. = ((P2_R./Z2_R.)^(y-1.).- 1.) Where B. = (((P2_R./(2.Z2_R.- P2_R.))^(y-1.).- 1.)/2.) Where (P2_R./(2.Z2.- P2_R.)) = (1./2.Z2_R./P2_R.- 1.)) Ref.No.10 .- C4_R. = (3.C3_R.- 1.)/(4.C3_R^2.-2.C3_R.) Ref.No.11 .- bR. = (1./(D. + (_D2. + 1.)^1/2.)) Where D. = ((y-1.)(1.- (C3_R.- 1.)².)/2.) Ref.No.14. - vcm1_R. = Ratio-(vcm1 _R./Max.vcm1_R.).Max.vcm1_R. Where Max.vcm1_R. = C3_R.C4_R.V1_R./(1. + b_R.) See also Sheet 9. Ref.No.15. - T1,. = T.-(y-1.)(va1 _R². + vcm1R2.)-/2.g.y.C. Ref.No.16.-p1,. = p.(T1_R./T.)^y/(y-1.). Ref.No.17. - V1_r. = v.(T./T1 _R.)^1/(y-1.) Ref.No.31. - Ep(1.2)_R. = (Ref.No.9.- A.)-.C.T1,./(y-1.) Ref.No.30. - E(1.2)_R. = (Ref.No.9.- B.).C.T1_r./(y-1.) Ref.No.32. - Ei(1.2)_R. = (y-1.).Ep(1.2)_R. Ref.No.12. - Ba1 _R. = b_R. + Ei(1.2)_R.2.g./vb1_R². Ref.No.20. - vb1_R. = V1_R. + va1_R. Ref.No. 5. - V1_R. = r(1.3)_R.V1₀./r(1.3)₀. Ref.No.33. - Esp(1.2)_R. = E(1.2)_R.-Ep(1.2)_R. Ref.No.18. - va2_R. = E(1.2)_R.2.g./(vb1_R.-va1_R.). + va1_R. Ref.No.34 .- Ek(1.2)_R. = (va2_R².- va1 _R².)/2.g. Ref.No.19. - va3_R. = C3_R.(va2_R.- va1 _R.). + va1 _R. Ref.No.36 .- Ek(1.3)_R. = (va3_R².- va1 _R².)/2.g. Ref.No.21. - vb3_R. = vb1 _R.- (va3_R.- va1 _R.)/b_R. Ref.No.26. - m va(1.3)_R. = C4_R.(va3_R.- va1 _R.). + va1_R. m va(1.3)_R. = ((t(1.2)_R.(va1_R. + va2_R.)) + (t(2.3)-_R.(va2_R. + va3_R.)))/2.(t(1.2)_R. + t(2.3)_R.). Ref.No.27. - m vb(1.3)_R. = m va(1.3)_R. + X2_R./2.t-(1.3)_R. Ref.No.28. - t(1.2)_R. = 2.X2_R./(vb1 _R.- va1 _R.). Ref.No.29. - t(2.3)_R. = X2_R./(va3_R.- vb3_R.). Ref.No.38. - T2_R. = T3R.= (Ep(1.2)_R.(y-1.)./C.) + T1_R. Ref.No.39. - p2_R. = p3_R.= p1_r.(T2_R./T1_r.)^y/(y-1.). Ref.No.40. - v2_R. = v3_R. = v1_r.(T1_r./T2_R.)^1/(y-1.). Ref.No.35. - W(1.2)R.= (Ba1_R.vb1_R². -b_R.vb2_R².)-/2.g. Ref.No.37. - W(1.3)_R. = (Ba1 _R.vb1 _R^2. -b_R.vb3_R².)-/2.g. Ref.No.49. - Angle A_R. = Tan.^-1-(va3_R./vcm1R.). Ref.No.50. - Angle B_R. = Tan.^-1((V1_R.-va3_R.)-vcm1_R.). Ref.No.51. - Angle C_R. = Tan.^-1-((V1_R.- m vb-(1.3)_R.)/vcm1_R.). Ref.No.53. - (1.x 14.x 37.)_R= (r(1.3)_R.vcm1_R.W-(1.3)_R.). Ref.No.54 .- (1.x 14.)_R. = (r(1.3)_R.vcm1_R.)

[0060] Continuation - Outer Streamline Column - Synopses Table 1D. & 1A.

[0061] Ref.No. 9. and 10. - Values C3₀. and C4_o. Use formulae given for same values on Root Streamline. Ref.No.11. - b_o. Note :- Root Streamline value used for convenience such that Ref.No.12.-Ba1_o. is below unity. Ref.No.12. - Ba1₀.= b₀.+ Ei(1.2)₀.2.g./vb1₀². Ref.No.13. - va1₀.= V1₀.- V1_R.)/2. + va1₀. Value chosen to keep the value va3o. reasonable low. Ref.No.14. - vcm1₀.= (va1_R².+ vcm1_R².- va1₀².)^1/2. Ref.Nos. 6., 7., 8., 15., 16., 17. , Values T., p., v., T1., P1., and v1. are of the same value as on the Root and all other streamline columns of the same Synopsis. Ref.Nos.30. to 33. - E(1.2)o., Ep(1.2)o., Ei(1.2)o., Esp(1.2)o., Use formulae given for same values on Root Streamline. Ref.No.18. - va2o.= vb2o.= (E(1.2)₀.2.g./(1. + 1/b₀.))^1/2. + va1o. Ref.No.19. - va3₀. = C3₀.(va2₀.- va1₀.) + va1₀. Ref.No.20. - vb1₀.= ((va2₀.- va1₀.)/b₀.) + va2₀. Ref.No.21. - vb3o.= vb1₀.- (va3o.- va1o.)/bo. Ref.Nos.26., 27., 28., 29., 34., 35., 36., 37., 38., 39., 40., 49., 50., & 51. Values m va(1.3)., m vb-(1.3)., t(1.2)., t(2.3)., Ek(1.2)., W(1.2)., Ek(1.3)., W(1.3)., T2. = T3., p2. = p3., v2. = v3., Angle A., Angle B., Angle C. Use formulae given for same values on Root Streamline. Ref.No.53. - (1.x 14.x 37.) = r(1.3)_o.vcm1o.W-(1.3)₀. Ref.No.54. - (1.x 14.) = r(1.3)₀.vcm1₀.

[0062] Continuation - Intermediate Streamline Column -

[0063] Synopsis Tables 1 D. and 1 A.

[0064] Ref.Nos. 9. & 10. - Values C3_r. and C4,. Use formulae given for same values as on Root Streamline. Ref.No.54.-(r(1.3)_r.vcm1_r.). = (Max.Stre.No. - Stre.No.)(r(1.3)₀.vcm1₀.- r(1.3)_R.vcm1_R.)-/(Max.Stre.No.) + (r(1.3)_R.vcm1_R.). Ref.No.14. - vcm1_r. = (r(1.3)_r.vcm1_r.)/r(1.3)_r. Ref.No.13 .- va1_r. = (va1_R². + vcm1_R².-vcm1_r².)- Ref.No.53 .- (1.x 14.x 37.),. = (Max.Stre.No.-Stre.No.)(r(1.3)₀.vcm1₀.W(1.3)₀.- r(1.3)-_R.vcm1_R.W(1.3)_R.)/(Max.Stre.No.). + (r(1.3)-_R.vcm1_R.W(1.3)_R.) Ref.No.37 .- W(1.3),. = .(1.x 14.x 37.)_r./(r(1.3)-_r.vcm1_r.). Ref.Nos. 6.,7.,8.,15.,16.,17 .- Values T.,p.,v.,T1.,p1.,v1. are of the same value as on the Root Streamline Column of the same Synopsis. Ref.Nos.30 to 33 .- Values E(1.2)_r.,Ep(1.2)_r.,Ei-(1.2)_r.,Esp(1.2)_r. Use formulae given for the same values on the Root Streamline. Ref.No.36 .- Ek(1.3)_r. = W(1.3),.- (y.Ep(1.2)_r.). Ref.No.19 .- va3,. = ((Ek(1.3)_r.2.g. + va1_r².)^1/2. Ref.No.18 .- va2_r. = ((va3_r.-va1_r.)/C3_r.) + va1_r. Ref.No.34 .- Ek(1.2),. = (va2_r².- va1_r².)/2.g. Ref.No.20 .- vb1_r. = ((E(1.2)_r.2.g./(va2_r.-va1_r.)) + va1_r. Ref.No.11 .- b_r. = (va2_r.-va1_r.)/(vb1_r.- vb2_r.) Ref.Nos.35.,37.,38.,39.,40.,49.,50.,51 .-Values W-(1.2)_r.,W(1.3)_r., Angle A., Angle B., Angle C. Use formulae for the same values given for the Root Streamline.

[0065] Continuation - Air Mass Flow Mean Values - Synopses Tables 1D. & 1A.

Note:

[0066] - The suffixes applicable to the example would be (r = 1.) to (r = 4.). Ref.No.41 .- Ar1_r. = Pi.(r(1.3)_(r=0.)². -r(1.3)_r².) Ref.No.42 .- m vcm1_r. = m vcm1_(r-x.). = vcm1_(r=x/2). Ref.No.43 .- M1,. = Ar1_r.m vcm1_r./v1_r. Ref.No.44 .- m Ek(1.3)_r. = m Ek(1.3)_(r=x.). = Ek-(1.3)_(r=x/2.). Ref.No.45 .- m Ep(1.2)_r. = m Ep(1.2)_(r=x.). = Ep-(1.2)_(r=x/2.). Ref.No.46 .- m Ei(1.2)_r.= m Ei(1.2)_(r=x.).= Ei-(1.2)_(r=x/2.). Ref.No.47 .- m W(1.3)_r. = m W(1.3)_(r=x.). = W-(1.3)_(r=x/2.). Ref.No.48 .- m T2_r. = m T3_r. ₌ m T2_(r=x.). = T2_(r=x/2.). NOte: - The mean values for m p2_r. and m v2_r. can be calculated from the above temperature if required. Ref.No.52. - Horse Power = H.P._r. = M1_r.m W-(1.3)_r./550. End of Procedure for Stage 1. Synopses Tables 1D. & 1A.

Computation of Plane n. values intermediate between Planes 1. & 2. All Streamline Columns - Blade Section a. Tables 2D. & 3D.

[0067] Ref.No.54. - van_r. = va1_r. + n.(va2_r.-va1_r.)/N. va-(n=0.)_r. = va1,. Ref.No.55. - vbn_r. = vb1_r.- n.(vb1_r.-vb2_r.)/N. vb-(n=0.)_r.= vb1_r. Ref.No.56 .- Ek(1.n)_r. = (van_r².- va1_r².)/2.g. Ref.No.57. - E(1.n)_r.= (((2.vb1_r.)+ ((1/b_r.-1.)-va1_r.)- ((1/b_r.+ 1.)van_r.))(van_r.- va1_r.))/2.g. Ref.No.58 .- Ep(1.n)_r.= E(1.n=x.)_r+ W(2.m=-(M-x.))_r.- Ek(2.m = (M-x.))_r. Where M.No.of Planes = N.No.of Planes... Also Ep(1.n)_r. = E(1.n)_r.(1.- (C3_r.- 1.)².) Ref.No.59. - Esp(1.n)_r. = E(1.n)_r.(C3_r.- 1.)². Ref.No.60. - Ei(1.n),. = (y.- 1.).Ep(1.n)_r.. Ref.No.61 .- W(1.n)r.= (Ba1_r.vb1_r².-Ban_r.vbn_r².)-2.g. Ref.No.62 .- Ban_r. = ((Ba1_r.vb1_r².-(2.g.(E(1.n)_r. + Ei(1.n),. + Ek(1.n.)_r.)))/vbn_r². Ref.No.63 .- t(1.n)r.= ((1.- (T1_r./(T1_r.+ (y-1.).Ep-(1.n)_r./C.))^1/(y-1.).).2.P2_r./((vb1_r.+ vbn_r.)-(va1_r. + van,.))) Ref.No.64 .- L(1.n),.= t(1.n)_r.vcm1_r. Ref.No.65. - Fpan_r. = t(1.n)_r.(vb1_r. + vbn_r.)/2. Ref.No.66. - San_r. = t(1.n)_r.(va1_r. + van_r.)/2. Ref.No.67 .- Rpan_r. = t(1.n)_r.(va1_r.+ van_r.)/2. Ref.No.86. - R Fpan_r. = Fpan_r. - t(1.n)_r.V1_r. Ref.No.87 .- R San_r. = San_r. - t(1.n)_r.V1_r. Ref.No.88 .- R Rpan_r. = Rpan_r. - t(1.n)_r.V1_r.

Computation of Plane m. values intermediate between Planes 2. & 3. All Streamline Columns - Blade Section b. Tables 3D., 4D. & 5D.

[0068] Re.No.68 .- vam_r. = va2_r. + m.(va3_r.- va2_r.)/M. Ref.No.69 .- vbm_r. = vb2_r. + m.(vb2_r.-vb3_r.)/M Ref.No.70 .- Ek(2.m)_r. = (vam_r².- va2_r².)/2.g. Ref.No.71 .- Esp(2.m),. = Ek(2.m)_r. - W(2.m),. Ref.No.72 .- W(2.m)_r. = b_r.(vb2_r^2.- vbm_r².)/2.g. Ref.No.75 .- Espm_r. = Residual Air Spring Energy existing at Plane m. = Esp(1.2)_r. = Esp-(2.m)_r. Ref.No.73 .- t(2.m)_r. = L(2.m)_r./vcm1_r. Ref.No.74 .- L(2.m)_r. = D_r.((Sin.(Tan.^-1-(vam_r./vcm1_r.)) -(Sin.(Tan.^-1(va2_r./vcm1_r.))). Ref.No.74A .- D_r. (Radius) = L(2.3),./(Sin.-(Tan.^-1.(va3_r./vcm1_r.)) -(Sin.^-1.(Tan.^-1.-(va2_r./vcm1_r.)). Ref.No.76 .- Fpbm_r. = Fpa2_r. + t(2.m)_r.(vb2_r. + vbm_r.)/2. Ref.No.77..- Sbm_r. = Sa2_r. + t(2.m)_r.(va2_r. + vam_r.)/2. Ref.No.78 .- Rpbm_r. ₌ Rpb2,. + t(2.m)_r.(vb2_r. ⁺ vbm_r.)/2. Ref.No.90 .- R Fpbm_r. ₌ Fpbm_r.- t(1.m)_r.V1_r. Ref.No.91 .- R Sbm_r. = Sbm_r.- t(1.m)_r.V1_r. Ref.No.92 .- R Rpbm_r. ₌ Rpbmr.- t(1.m)_r.VI_r. Ref.No.89 .- L(1.m)_r. = L(1.2)_r. ⁺ L(2.m)_r.

Computation of Plane w. values intermediate between Planes 3. & 4. All Streamline Columns - Blade Section c. Tables 5D. & 6D.

[0069] Ref.No.79 .- L(1.w)_r.= L(1.3)_r.+ + w.L(3.4)_r./W. Ref.No.79A .- L(3.4)_r. ₌ L(1.4)_r.- L(1.3)_r. Ref.No.79B .- L(1.4)_r. = vcm1_r.t(1.4)_r. Ref.No.79C .- t(1.4)_r. = (P1_r.- t(1.3)_r.(va3_r.- m va-(1.3)r.))/(V1r.- va3_r.). Ref.No.83 .- rw_r. = b./2.a. + ((b./2.a.)². + c./a.)-^1/2.

[0070] 

Where a. = 2.Pi./No. of Blades.

Where b. = (Xw_outer.+ Xw_inner.) Where inner & outer refer to two adjacent streamlines which enclose an area.

Where c. = (2.Pi.rw_outer²./No. - (Ar_inner.-Ar_outer.)-.2./No. - b.rw_outer.). Commence with the outer pair of which the outer Ar_r=0. = Zero. and continue inwards using the first calculated inner radius as the outer of the next pair and so on. The individual area of the first set is:-(Ar2_r=1. - Ar_r=0.).

[0071] Ref.No.80 .- Fpcw_r. ₌ Fpb3_r.+ w.t(3.4)_r.va3_r./W. - (X3_r.- Xw_r.)/2. Ref.No.81 .- Scw_r. ₌ Sb3_r. + w.t(3.4)_r.va3_r./W. Ref.No.82 .- Rpcw_r. = Rpb3_r. + w.t(3.4)_r.va3_r./W. ⁺ (X3_r.- Xw_r.)/2. Ref.No.96 .- R Rpcw_r. = Rpcw_r.- (V1_r./vcm1_r.).L-(1.w)_r. Ref.No.95 .- R Scw_r. = Scw_r.- (V1_r./vcm1_r.).L-(1.w)_r. Ref.No.94 .- R Fpcw_r. = Fpcw_r.- (V1_r./vcm1_r.).L-(1.w)_r. Ref.No.84 .- Xw_r. ₌ 2.((RF_r².- L(3.w)_r².)^1/2.- (RF_r².-L(3.w)_r².)^1/2.). Ref.No.93 .- RF_r. = Form Radius = (L(3.4)-_r²./X3_r.) ⁺ X3_r./4. Where in the example X3_r. = X2_r.

Computation of Plane w. values intermediate between Planes 3. & 4. All Streamline Columns - Blade Section c. Tables 5D. & 6D.

Note:

[0072] - In the example the streamlining of all blade sections start at Plane 3. Thus with the exception of the energy value Ei(1.2)_r. and the introduction of the value (Ba1_r.- b_r.) to take it into account 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 1A. it could start earlier with Plane 2. being a maximum upstream position.

[0073] In the case of Synopsis 1A. it would be advantageous for reason of material stress to use the same root section as for 1 D. but on the blade tip section use Plane 2. as the starting position of the streamlining. In between it could be varied from the plane of one to the other.

[0074] The streamlining will not affect the energy change between Plane 2. and Plane 3. providing the value (X2_r.- Xb_r.)/2 is subtracted from the front and added to the rear profile through blade section b. similarly as is due on section c.

Rotor Blade Design Procedure applicable to Rotors which follow Stators. - Synopsis Stage 2. Tables17D.

Notes:

[0075] - To provide for the matching of the airflow through a multiple number of stages it will be noted that the Stage 1. Synopsis has made the two products (r(1.3)_r.vcm1_r.W(1.3)_r.) and (r(1.3)_r.vcm1_r.) to vary in value at a constant rate radially across the inlet plane, such that the mean streamline values are also the mean values of the air mass flows which at the inlet plane are symetrically disposed on the plane. Thus W(1.3)_r=x/2. equals m W-(1.3)_r=x., Ek(1.2)_r=x/2. equals m Ek(1.2)_r=x. etc.

[0076] This provision is made to apply to all stages with a further proviso that the two values va1. and vcm1. 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.

[0077] The following formulae have been provided to calculate the new values:-

Ref.No.41 .- Ar1_R. = Stage 1. Ar8_R. & r(1.3)R. Stage 1. r8_R.

[0078] Ref.No.41 .- Ar1_r. = Pi.(r(1.3)₀. - r(1.3)_r².). Ref.No. 1 .- r(1.3)_R. = (r(1.3)₀².- Stage 1.Ar₈R./Pi.)^1/2. Ref.No. 1 .- r(1.3),. = r(1.3)_o. - (Str.No.)(r(1.3)_o. -r(1.3)_R.)/(Max.Str.No.). Ref.No.5 .- V1,. = r(1.3)_r.V1o./r(1.3)o. Ref.No.43 .- M1_r. = Ar1_r.m vcm1_r./m v1_r. Ref.Nos. 9.,10.,30.,31.,32.,33.,35.,38.,39., & 40. - C3_r.,C4_r., E(1.2)_r., Ep(1.2)_r., Ei(1.2)_r., Esp(1.2)_r., W(i.2)_r., T2_r., p2_r., v2_r., Formulae for their derivation are as used for Stage 1. Synopsis.

Rotor Blade Design Procedure applicable to Rotors which follow Stators. - Synopsis Stage 2. Table 17D.

[0079] Ref.No.54 .- Stage 2.(1.x 14.)o. = r8o.vcm8o. Stage 2.(1.x 14.)_R. = r8_Rvom8_R. Stage 2.(1.x 14.)_r=M.No./2. = r(1.3)-_r=M.No./2.vcm1_r=M.No./2. Ref.NO.54 .- Stage 2.(1.x 14)_r.= (1.x 14.)₀. - ((r-(1.3)₀. -r(1.3)_r.)((1.x 14.)₀. - (1.x 14.)_R.)/(r(1.3)₀. -r-(1.3)_R.)). Ref.No.14 .- vcm1_r. = (1.x 14.)_r./r(1.3)_r. Ref.No.13 .- va1_r. = (Stage 1.(va1_r². + vcm1_r².) -vcm1_r².)^1/2. Ref.Nos.15.,16.and 17 .- T1_r.,p1_r.and v1_r. = T8_r.,p8_r.and v8_r. Note: - It has been assumed that the blade strength is capable taking an equal load as the 1^st.Stage so W(1.3)_RMR. of the 2^nd.Stage has been made equal to that of the 1^st.Stage. W-(1.3)₀. of the 2^nd.Stage has olso been made equal to W(1.3)_o. of the 1^st.Stage. Thus:-Ref.No.37 .- W(1.3),. = (1.x 14.x 37.)_r./(1.x 14.),. Ref.No.53 .- (1.x 14.x 37.)_r. = (1.x 14.x 37.)_0.+ (r(1.3)o.- r(1.3)_r.)(2.((1.x 14.x 37.)o.- (1.x 14.x 37.)_RMR.)/(r(1.3)₀. -r(1.3)_R.). Where (1.x 14.x 37.)o. = r(1.3)o.vcm1o.Stage 1.W(i.3)o. And (1.x 14.x 37.)_RMR. = r(1.3)-_RMR.vcm1 _RMR.Stage 1.W(1.3)_RMR. Ref.No.36 .- Ek(1.3)_r. = W(1.3)_r.- y.Ep(1.2)_r. Ref.No.19 .- va3_r. = (Ek(1.3)_r.2.g. ⁺ va1_r².)^1/2. Ref.No.18 .- va2_r. = (va3_r.- Va1_r.)/C3_r. + va1_r. Ref.No.34 .- Ek(1.2)_r. = (va2_r^2.- Va1_r².)/2.g. Ref.No.11 .- b_r. = (va3_r.- va1_r.)/(vb1_r.- vb3_r.) Ref.No.12. - Ba2_r. ₌ b_r. + Ei(1.2)_r.2.g./vb1_r². Ref.No.20. - vb1_r. = (E(1.2)_r.2.g./(va2_r.- va1r.)) + va1_r. Ref.No.21. - vb3_r. = vb2_r.- (va3_r.- va2_r.)/b_r. Ref.No.26. - m va(1.3)_r. = ((va3_r.- va1_r.).C4_r.) + va1_r. Ref.No.27. - m vb(1.3)_r. = m va(1.3),. +X2_r./2.t-(1.3)_r. Ref.No.28 .- t(1.2)_r. = 2.X2_r./(vb1_r.- va1_r.). Ref.No.29. - t(2.3)_r. ₌ X2_r./(va3_r.- vb3_r.). Ref.No.42. - m vcm1_r=_x. = vcm1_r=x/2. Ref.No.44. - m Ek(1.3)_r=x. ₌ Ek(1.3)_r=x/2. Ref.No.45. - m Ep(1.2)_r=x. ₌ Ep(1.2)_r=x/2. Ref.No.46. - m Ei(1.2)_r=x. ₌ Ei(1.2)_r=x/2. Ref.No.47 .- m W(1.3)_r=x. ⁼ W(1.3)_r=x/2. Ref.No.48 .- m T2_r=x. = T2_r=x/2. Ref.No.49. - Angle A_r. = Tan.^-1.(va3_r./vcm1_r.) Ref.No.50. - Angle B_r. = Tan.^-1((V1_r.- va3_r.)-/vcm1_r.) Ref.No.51 .- Angle C_r. = Tan.^-1.((V1_r.- m vb(1.3)-_r.)/vcm1_r.) Ref.No.52. - Horse Power = M1_r=x.m W(1.3)-_r=x./550.

[0080] Axial Flow Air Compressor Design Procedure.

Stator Blade Design Procedure - Notes. Tables 7D. to 16D.

[0081] 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 follows:-Inlet Plane 5.

[0082] This plane except for being divided by a different number of blades is exactly as the preceding rotor outlet plane.

Planes 6. & 7.

[0083] Air conditions at these two planes are exactly alike. Except for allowing for the rotation of the air, dimensions are also alike.

Outlet Plane 8.

[0084] 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 1. Thus before calculating any Stator conditions it is required first to compile the Stage 2. Synopsis.

Planes intermediate between the above planes.

[0085] The planes which divide the length L(5.6)_r. are designated by the letter m.

[0086] The planes which divide the length L(7.8)_r. are designated by the letter n.

[0087] 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 vcm5. such that the ratios va6_r./vcm6_r., va7_r./vcm7_r. and va8_r./vcm8_r. are of the same value.

[0088] The function of the rear portion of the blades is to reduce the air velocities va7_r./vcm_r. via van_r./vcmn_r. to va8_r./vcm8_r. while changing the surplus of kinetic energy into heat energy. by diffusion.

[0089] An assumption has been made that the levelling out of air temperature radially outwards is effected between Planes 7. & 8. which though not exactly true is only untrue quantitatively.

StatOr Blade Design Procedure - Continued.

Outlet Plane 8.. Tables 8D. & 16D.

[0090] Ref.No.3 .- m T8_r. = m T2_R. + m Ek(1.3),.(y-1)-./y.C. Ref.No. 4 .- m p8,. = m p2_R.(m T8_r./m T2_R.)^{y/(y- 1)}. Ref.No. 5. - m v8,. = m v2_R.(m T2_R./m T8_r.)^{1/(y- 1)}. Ref.No.22 .- T8_r. ₌ m T8_r. Ref.No.23 .- p8_r.= m p8_r. Ref.No.24 .- v8_r. = m v8_r. Ref.No.37 .- r8_r. (r8₀².- Ar8_r./Pi.)^1/2. Ref.No. 7. - Ar8_r. = M8_r.m v8,./m vcm8_r. = m Z8_r.H8_r.No. Ref.No.63 .- (37.x 21.)₀. = r8o.vcm8o. Where vcm8₀. = (vcm1₀.- vcm1_RMR.)(r8₀.-RM8_R.)/(r1₀.- RM1 _R.). + vcm1 RMR. Ref.No.63 .- (37.x 21.)_R. = 2.(vcm1_RMR.RM8_R.). - (37.x 21.)₀. REf.No.63 .- (37.x 21.)_r. = ((37.x 21.)o- (37.x 21.)_R.)(r8_r.-r8_R.)/(r8₀.- r8_R.). + (37.x 21.)_R. Ref.No.21 .-vcm8r. = (37.x 21.)_r./r8_r. Ref.No.62 .- (41.x 2.)_RMr. = ((37.x 21.)₀.+ (37.x 21.),.)/2. Ref.No. 2 .- m vcm8_r. = (41.x 2.)_RMr./RM8_r. Ref.No.20 va8_r. = ((va1_r². + vcm1_r².).- vcm8_r².)^1/2. Ref.No. 1 .- m va8_r. = ((va1_r². + vcm1_r².).- m vcm8_r².)^1/2. Ref.No.41 .- RM8_r. = (r8o.⁺ r8_r.)/2. Ref.No.17 .- m P8,. = 2.RM8_r.Pi./No. = Ref.No.18 .- m Z8_r. Ref.No.34 .- P8,. = 2.r8_r.Pi./No. = Ref.No.35 .-Z8_r. Ref.No.58 .- Rv8_r. = (va1_r². + vcm1_r².)^1/2. = Ref.No.5 8.- m Rv8_r. Ref.No.56 .- L(7.8)_r. = X7_r./2.Tan.Ø(7/8)_r. Ref.No.52 .- Ø(7/8)_r. = (Cos^-1((1. + (1. z(7/8)-_r.)Rt(7/8)_r./2)/(1. ⁺ Rt(7.8)_r.))/2. Ref.No.50 .- z(7.8)_r. = ((1/y)+(1/Rt(7/8)_r².) --(1/y.Rt(7/8)_r².))^1/2. Ref.No.49 .- Rt(7/8)_r. ₌ Rv7_r./Rv8_r. Ref.No.58. - Rv8,. = (va8_r².+ vcm8_r².)^1/2. Ref.No.58 .- m Rv8_r. = (m va8_r²./+ m vcm8_r².)-^1/2.

[0091] Ref.No.57 .- L(5.8)_r. = (L(5.7)_r.⁺ L(7.8)_r. Ref.No.55 .- t(7.8)_r. = L(7.8)_r./m vcm(7.8)_r. Ref.No.59 .- m vcm(7.8)_r. = (vcm7_r. + vcm8_r.)/2. Ref.No.60 .- M8_r. = As Stage 1. Rotor Plane 1. Ref.No.43. - m Q8_r. = Tan^-1(m va8_r./m vcm8_r.) Ref.No.44. - Q8,. = Tan^-1(va8_r./vcm8_r.) Ref.No.53 .- SFp8_r. ₌ Tan.Q8r.L(5.8)r.+ X7_r./2. Ref.No.54. - SRp8_r. ₌ SFp8_r. Ref:No.61. - Ry_r. ₌ L(7.8)_r./Sin.(2.Ø(7/8)_r.) Ref.No.62 .- (41.x 2.)_r. = RM8_r.m vcm8_r. Ref.No.63 .- (37.x 21.)_r. = r8_r.vcm8_r.

Note:

[0092] - The slight difference in the values of va8_r., vcm8_r. to the values of va1r., vcm1_r. on the Stage 2. Synopsis is accounted for by the slight changes of air mass flow governed by the intermediate streamlines.

Inlet Plane 5. Tables 7D. & 9D.

Note:

[0093] - 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.

[0094] Ref.No.2. - m vcm5_r. = As Ref.No.42. of the Stage Synopsis. Ref.No. 1. - m va5_r=No. = (m EK(1.3)_r=No..2.g. ^{+ V}a1 _r=No./2.².)^1/2. Ref.No. 1. - m va5_r=No. ⁼ va3_r=No./2. Ref.No. 3. - m T5_r.= As Ref.No.48. of the Stage Synopsis. Ref.No. 4. - m p5_r.= m p5_r=No.₌ p1_r.(m T2_r=No./T1_r.)^y/(y-1.). Ref.No. 5. - m v5_r. = m v5_r=No. = v1_r.(T1_r./T T5_r=No.)^1/(y-1.) Ref.No. 7. - Ar5_r. = M1_r.m v5_r./m vcm5_r. REF.No.37. - r5_r. = (r5₀².- Ar5_r./Pi.)^1/2.. Ref.No.41. - RM5_r. = (r5₀.+ r5_r.)/2. Ref.No.17. m P5_r. = 2.Pi.RM5_r.iNo. Ref.No.18 .- m Z5_r. ₌ m P5_r. Ref.No.34. - P5_r. = 2.Pi.r5_r./No. Ref.No.35. -Z5_r. = P5_r. Ref.No.36. - X5_r.= Zero. Ref.No.19. - X5_r.= Zero. Ref.No.42. - H5,. = (r5_o.- r5_r.) Ref.No.43. - m Q5_r.= Tan.^-1 (m va5_r./m vcm5_r.) Ref.No.44. - Q5_r. = Tan.^-1.(va5_r./vcm5_r.) Ref.No.53. - SFp5_r. = Zero. Ref.No.54 .- SRp5_r. = Zero. Ref.No.33. - m vcm(5.m)_r. = vcm5_r. Ref.No.58 - Rv5r.= (va5_r^2. + vcm5_r².)^1/2. Ref.No.58. - m Rv5_r. = (m va5_r². + m vcm5_r².)-^1/2. Ref.No.58. - Rvx5_r. = Rv5_r. Ref.No.58. - m Rvx5_r. = m Rv5_r.

Plane 6. & 7. - Tables 8D. & 13D.

[0095] Ref.No.58 .- Rv6_r. = (va6_r². + vcm6_r².)^1/2. = Rv7_r. = Rv5_r. Ref.No.58 .- m Rv6_r. = (m va6_r². + m vcm6_r².)^1/2. = m Rv7_r. = mRv5_r. Ref.Nos.43. & 44 .- m Q6_r. & m Q7_r. & Q6_r. & Q7_r. are exactly as m Q8_r. & Q8_r. Ref.No. 1 .- m va6_r. = m va7_r. = Sin.m Q8_r.m Rv6r. Ref.No. 2 .- m vcm6_r = m vcm7r.= Cbs.m Q8_r.m Rv6_r. Ref.No.20 - va6_r. = va7_r. = Sin.Q8_r.Rv6_r. Ref.No.21 .- vcm6_r. = vcm7_r. = Cos.Q8_r.Rv6_r. Ref.No.2 - T6_r. = T7_r. = T5_r. R ef.No.2 3 .- ^p6r.^{= p}7r.^{= p}5r. Ref.No.24 .- v6_r. = v7_r. = v5_r. Ref.No.37 .- r6_r.= r7_r. = r8_r. Ref.No.41 RM6_r.= RM7_r.₌ RM8_r. Ref.No.34 .- P6_r. = P7_r. = P8_r. Ref.No.17 .- m P6_r. = m P7_r. = m P8_r. Ref.No. 7 - Ar6_r. = Ar7_r. = M5_r.m v5_r./m vcm6_r. Let RMR. = (r=Max.No._2.) Ref.No.35 .- Z6_RMR.= Z7_RMR·= v6_RMR.vcm8_RMR.P6_RMR./vcm6_RMR.v8_RMR. Ref.No.35 .- Z6_RMR-1.- ⁼ 2.((Ar6_RMR.-Ar6_RMR-1.)-/(r6_RMR-1-r6_RMR.).No.)- Z6_RMR. Ref.No.35 .- Z6_RMR-2. = 2.((Ar6_RMR-1.- Ar6_RMR-2.)/(r6_RMR-2-r6_RMR-1.).No.)- Z6_RMR-1. Ref.No.35 .- Z6_RMR+1. = 2.((Ar⁶_{R MR+1}.-Ar6_RMR·)/(r6_RMR·-r6_RMR+1.).NO.)- Z6_RMR. Ref.No.35 .- Z6_RMR+2. = 2.((Ar⁶_{R MR+2}.-Ar6_RMR+₁.)/(r6_RMR+1.-r6_RMR+₂.).No.)- Z6_RMR+1.- Ref.No.35 .- All values of Z6 apply to Z7. with identical suffices. Ref.No.18 .- m Z6_r. = m Z7_r. = Ar6_r./No.H6_r. Ref.No.17 m P6_r. = m P8_r. Ref.No.19 .- m X6_r. = m X7_r. = m P6_r.- m Z6_r. Ref.No.39 L(5.6)_r = X6_r/(((vcm6,: vcm5_r.)-t(va5,.- va6_r.)) -(va8_r./vcm8_r.)). Ref.No.39 .- L(5.6)_r. = Rp_r.(Sin.Q5_r.- Sin.Q6_r.). Ref.No.64 .- Rp_r. _ (X6_r./(((vcm6_r.- vcm5_r.)/(va5_r.- _va6r._))-- (va8_r./vcm8_r.))(Sin.Q5_r.- Sin.Q6_r.)) Ref.No.38 .- t(5.6)_r. = L(5.6)_r./m vcm(5.6)_r. Ref.No.33 .- m vcm(5.6)_r.= (((Rv5_r²/2.)(U6_r.-U5_r.) ⁺ (Rv5_r²./4.)(Sin.(2.U5_r.) - Sin.(2.U6_r.)-)/(va5_r.- va6r.)). Where U6r.= ((Pi./2) - Q6_r.) and U5_r.= ((Pi./2) - Q5r.) Where Q6_r. and QS_r. are in Radians. Where Rv5_r. = (va5_r^2. + vcm5_r.²)^1/2. Ref.No.31 .- L(6.7)_r. This length is optional. Ref.No.30.-t(6.7)_r.= L(6.7)_r./vcm6,. Ref.No.39 .- L(5.7)_r. = L(5.6)_r. ⁺ L(6.7)_r. Ref.No.38 .- t(5.7)_r. = t(5.6)_r. ⁺ t(6.7)_r. Ref.No.53 .- SFp6_r. = Tan.Q6_r.L(5.6)_r. Ref.No.53 .- SFp7_r. = Tan.Q6_r.L(5.7)_r. Ref.No.54 SRp7_{r =} SFp7_r. + X6_r. Where X6_r. = Z7r. Ref.No.54 .- SRp6_r. = SFp6_r. + X6_r. Ref.No.36 .- X6_r. ₌ X7,. ₌ (P6_r.- Z6_r.)

Tables 7D & 9D to 12D. Planes m. - Intermediate between Planes 5. & 6.

Note:

[0096] - 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 Qm_r. and Qm_r. 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 were discarded.

[0097] The second method which was applied to the example is to use the values m Qm_r., Qm_r., 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 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 Rvxm_r. to the value of m Rvm_r. And as m vcmxm_r. = m vcm5_r.Ar5_r./Arm_r. (Where Arm_r. = No.Hm_r.m Zm_r.), m vaxm_r. = Tan.m Qm_r.m vcmxm_r.

[0098] Ref.No.43. - m Qm_r.= m Q5_r. - m(m Q5_r.- m Q6_r.)/M. Ref.No.44. - Qm_r. = Q5_r.- Q6_r.)/M. Where Qm_r.= Tan^-1.(vam_r./vcmm_r.) Ref.No. 1. - m vam_r. = Sin.m Qm_r.m Rv5_r. Where m Qm_r.= Tan^-1.(m vam_r./m vcmm_r.). Ref.No. 2. - m vcmm_r. = Cos.m Qm,.m Rv5_r. Where m Rv5_r. = ( m va5_r². + m vcm5_r².)^1/2. Ref.No.20. - vam_r. = Sin.Qm_r.Rv5_r. Ref.No.21. - vcmm_r. = Cos.Qm_r.Rv5_r. Where Rv5_r. = (va5,². + vcm5_r².)^1/2. Ref.No.2A. - m vcmxm_r. = m vcm5_r.Ar5_r./No.Hm_r.m Zm_r. Ref.No.1A. - m vaxm_r. = Tan.m Qm_r.m vcmxm_r. Ref.No. 7. - Arm_r. = No.Hm_r.m Zm_r.

Planes m. - Intermediate between Planes 5. & 6. Tables 12D to 9D.

[0099] Ref.No.20A .- vaxm_r. = Sin.Qm_r.Rvxm_r. Ref.No.21A .- vcmxm_r. = Cos.Qm_r.Rvxm_r. Where Rvxm_r. = Rvm_r.m Rvxm_R./m Rvm_R. Where R.= (r=Max.No.) Ref.No.37. - rm_r.= (Rx_r².- (L(5.6)_r.- L(5.m)_r.)².)-^1/2+(r6_r.- Rx_r.). Where Rx_r.= (L(5.6)_r²./2.(r6_r.- r5_r.).). + (r6_r.- r5_r.)/2. Ref.No.39. - L(5.m)_r.= = L(5.6)_r.(va5_r.- vam_r.)-/(va5_r.- va6_r.). Ref.No.39. - L(5.m)_r.= (Rp_r.(va5_r.- vam_r.))IRvS_r. Where Rp_r. = L(5.6)_r.Rv5_r./(va5_r.- va6_r.). Ref.No.36. - Xm_r.= (Rp_r.(Cos.Qm_r.- Cos.QS_r.)) - (L(5.m)_r.Tan.Q6_r.). Ref.No.17. - m Pm_r.= = RMm_r.2.Pi./No. Ref.No.41. - RMm_r.= (rm₀. + rm_r.)/2. Ref.No.34. - Pm_r. = rm_r.2.Pi./No. Ref.No.35. - Zm,. = (Pm_r.- Xm_r.). Ref.No.18. - m Zm_r=4 = (Zmo.⁺ Zm_r=4.)/8. + (Zm_r=1. + Zm_r=2. + Zm_r=3)/4. m Zm_r=3.= (Zmo.+ Zm_r=3.)/6. + (Zm_r=1. + Zm_r=2.)/3. m Zm_r=2.= (Zm₀. + Zm_r=2.)/4. + (Zm_r=1.)/2. m Zm_r=1.= (Zmo.⁺ Zm_r=1.)/2. Ref.No.19. - m Xm_r.= m Pm_r.- m Zm_r. Ref.No.33 .- m vcm(5.m),.= ((Rv5_r²./2.)(Um_r-U5,.). + (Rv5_r²./4.)(Sin.(2.U5_r.) - Sin.(2.Um_r.)-)/(va5_r.- vam_r.). Where Um_r.= ((Pi./2)- Qm_r.). and U5_r. ((Pi./2)-Q5r.) Where Qm_r. and Q5_r. are in Radians. Ref.No.38. - t(5.m)_r. = L(5.m)_r./m vcm(5.m)_r). Ref.No. 7. - Arm_r. = No.Hm_r.m Zm_r. and Ref.No.43.- Hm_r.= (rmo.- rm_r.) Ref.No.53. - SFpm_r. = Sin.Q6_r.L(5.m)_r. Ref.No.54. - SRpm_r. = SFpm_r. + Xm_r.

Planes n. - Intermediate between Planes 7. & 8. Tables 8D.,14D.,15D.

[0100] Ref.No.58. - Rvn_r. = Rv7_r. - n.(Rv7_r.- Rv8_r.)/N. Ref.No.58 .- m Rvn_r. = m Rv7_r. - n.(m Rv7_r.- m Rv8_r)/N. Ref.No. 1 .- m van_r. = m va7_r.- n.(m va7_r.- m va8_r.)/N. m van_r = Sin.m Q8_r.m Rvn_r. Ref.No. 2 .- m vcmn_r. = m vcm7_r. - n.(m vcm7_r.- m vcm8_r.)/N. m vcmn_r. = Cos.m Q8_r.m Rvn_r. Ref.No.20 .- van_r. = va7 _r.- n.(va7_r.- va8_r.)/N. =
Sin.Q8_r..Rvn_r. Ref.No.21 - vcmn_r. = vcm7_r.- n(vcm7_r.- vcm8_r.)-/N. = Cos.Q8_r.Rvn_r. Ref.No.22 .- Tn_r=M.No./2.= Tn_RMR.= T7_RMR·+ (y-1.)(Rv7_RMR2.-Rvn_RMR2.)/y.2.g.C. Ref.No. 3 .- m Tn_r=M.No. ⁼ Tn_RMR. Ref.No.22 x.- Txn_r. = T7,. + (y-1.)(Rv7_r².- Rvn_r².)-/y.2.g.C.

Note: - For streamlines whose number is less than the Streamline (r=M.No./2) = RMR. the value n.(Tn_RMR.- Txn_r.)/N. should be added to Txn,. For streamlines whose number is greater the value n.(Txn,.- Tn_RMR.)/N. should be subtracted from the value Txn_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. - Tn_r. = Txn,. + n.(Tn_RMR.- Txn_r.)/N. _Ref._No. ₃. - _{m Tnr}. _{= m} Tn_r=x. = Tn_r=x/2. Ref.No. 4 m pn_r. = m p7_r.(m Tn_r./m T7_r.)^y/(y-1). Ref.No. 5 .- m vn_r. = m v7_r.(m T7,./m Tn_r.)^1/(y-1) Ref.No.23 .- pn_r. = p7_r.(Tn_r/T7_r.)^y/(y-1). Ref.No.24. - vn_r. = v7_r.(T7_r./Tn_r.)^1/(y-1).

Planes n. - Intermediate between Planes 7. & 8. Tables 14D. & 15D.

[0101] Ref.No. 3. - m Tn_r. = m Txn_r. ⁺ n.(m Tn₂._RMR. - m Txn_r)/N. Ref.No.22. - Tn_r. = Txn_r. + n.(Tn_RMR. - Txn_r.)/N. Ref.No.23. - pn_r.= p7_r.(Tn_r/T7_r.)^y/(y-1). Ref.No.24. - vn_r.= v7_r.(T7_r./Tn_r.)^1/(y-1). Ref.No. 4 .- m pn_r. = m p7_r.(m Tn_r./m T7_r.)^y(y-1)-

[0102] Ref.No. 5. - m vn,. = m v7_r.(m T7_r./m Tn_r.)^1/(y-1)- Ref.No. 7. - Arn_r. = M5_r.m vn_r./m vcmn_r. Where M5_r. = M4_r. Ref.No.37. - rn_r. = r7_r. = r8_r. Ref.No.42. - Hn,. = H7,. = H8_r. Ref.No.35. - Zn_RMR. = Zn_r=M.No/2.= z7_RMR·vcm7_RMR·vn_RMR·/vcmn_RMR.v7_RMR· Ref.No.35. - Zn_r=1.= 2.((Arn_r=₂.- Arn_r=1.)/No.-(Hn_r=2.-Hn_r=1)) - Zn_RMR. Ref.No.35 .- Zn_r=o.= 2.(Arn_r=1/No.Hn_r=1)-Zn_r=1. Ref.No.35. - Zn_r=3.= 2.((Arn_r=3.- Arn_r=2.)/No.-(Hn_r=3.-Hn_r=2)) - Zn_r=2. Ref.No.35. - Zn_r=4.= 2.((Arn_r=4.- Arn_r=3.)/No.-(Hn_r=4.-Hn_r=3.)) - Zn_r=3. Ref.No.36. - Xn_r. = Ph_r.- Zn,. Ref.No.34. - Pn_r.= 2.Pi.rn_r.No. Ref.No.52. - φ(7/n)_r.= Tan.^-1(A_r./(Ry_r.2.A_r.- A_r².)-^1/2). Where Ry_r. = L(7.8)_r./Sin.(2.φ(7/8)_r.). And A,. = (X7_r.- Xn_r.)/2. Ref.No.56. - L(7.n)_r. = Ry_r.Sin.(2.φ(7/n)_r.). Ref.No.55 .- t(7.n)_r.= L(7.n)_r./m vcm(7.n)_r. Ref.No.59 .- m vcm(7.n)_r. = (vcm7_r. + vcmn_r.)/2. Ref.No.17 .- m Pn_r. = 2.Pi.RMn_r./No. Ref.No.18 .- m Zn_r. = Arn_r./No.Hn_r. Ref.No.19 .- m Xn_r. = m Pn_r.- m Zn_r. Ref.No.57 .- L(5.n)_r. = L(7.n),. + L(5.7)_r. Ref.No.53 .- SFpn_r. = Tan.Q7_r.L(5.n)_r. + (X7,.-Xn,.)/2.

[0103] 

[0104] Ref.No.41. - RMn,. = RM7,. = RM8_r.

Claims

1. The COPYRIGHT FOR THE BLADE SHAPE DESIGN SYSTEM described on Sheets i3. to 37., Tables 1.A., & 1.D. to 20.D. and Figures of the PATENT SPECIFICATION OF A REPEATABLE AXIAL COMPRESSOR STAGE OF COMPRESSION which LIMITS THE EXISTENCE OF THE ENERGY DESIGNATED Esp. to the AXIAL WORKING LENGTH defined by the DIMENSION DESIGNATED L(1.3).

2. The PATENT reserving to us the SOLE RIGHT TO DESIGN, MANUFACTURE, AND USE ROTOR BLADES HAVING SHAPES which are defined by SETS OF DIMENSIONS OBTAINED BY USE OF THE ABOVE SYSTEM which can be identified by the SUDDEN CHANGE IN DIRECTION OF THE BLADE CENTRE LINE AT PLANE 3. which using a SYNOPSIS AS TABLE 1.D. is at a maximum on the ROOT STREAMLINE decreasing with the decreasing thickness of the blade on PLANE 2. radially outwards, and if using SYNOPSIS as TABLE 1.A. would be the same as TABLE 1.D. on the ROOT STREAMLINE but depending on the rate of taper of blade thickness on PLANE 2. could increase or decrease up the blade.

Drawing