From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Detailed analysis of turbine blade design, comparing a conventional form with a new invention using mathematical formulas and calculations.
| Identifier | ExFiles\Box 147\2\ scan0205 | |
| Date | 16th January 1939 guessed | |
| 6 511,278 the following formulæ to be understood, in which the angles A, B, and C, are reproduced. In regard to this :— 5 u = rω = linear blade velocity at any given radius r.{Sir Henry Royce} vw = absolute whirl velocity of fluid. va = axial velocity of fluid. vabs = absolute velocity of fluid. 10 vr{E. S. Voller - Orders} = velocity relative to blades at which fluid enters blades 4. vwr = whirl velocity relative to blades at which fluid enters blades 4. v'r = velocity relative to blades at which fluid leaves blades 4. 15 (Though for simplicity va is shown the same at entry and exit, this is not necessarily always the case, and in general va at discharge will be greater than at entry). Then :— 20 A = tan⁻¹ (va / vw) B = tan⁻¹ (va / vwr) C = tan⁻¹ (va / u) Now, vwr = M where M is the angular momentum of unit mass of fluid about the axis of the machine, and it is a fundamental assumption for this invention that the value of M is constant over any one entry or exit plane. 30 ∴ vwr = vw - u = (M / r) - rω where ω = angular velocity of blade. If it is desired to relate these angles with the conditions at any specific radius R, this can be done by the fact that M = RVw where Vw is the whirl velocity at that radius R.{Sir Henry Royce} 40 The above laws apply to any row of a reaction or impulse turbine which is to yield purely axial flow (vr{E. S. Voller - Orders} in the foregoing case). To ascertain the correct twist the correct B and C are found for different values of r.{Sir Henry Royce} 45 A numerical example will now be given which will serve to indicate the characteristics of a rotor blade form according to this invention as compared with a conventional form hitherto employed, based on 50 u / vw = 1. Data : Wheel mean diameter 30″ Blade length 2″ 55 Mean blade speed 400 feet per second Mean gas speed (whirl) 400 feet per second Mean gas speed (axial) 80 feet per second Conventional blade form hitherto employed (which assumes a constant vw) Inner radius of blades 14″ 60 Outer radius of blades 16″ Blade speed at tip = 16/15 x 400 = 427 ft. per second Blade speed at root = 14/15 x 400 = 373 ft. per second Relative gas speed at tip (whirl) 427 - 400 = 27 ft. per second. (Note : blade is overtaking gas). 65 Angle at tip = 90 + tan⁻¹ (27 / 80) = 108° 40′ Relative gas speed at root (whirl) = 400 - 373 = 27 ft. per second. Angle at root = 90 - tan⁻¹ (27 / 80) = 71° 20′ ∴ Entry angle twisted through 37° 20′ Blade form according to this invention (data as before). Gas speed (whirl) is now inversely proportional to radius; axial velocity constant; 511,278 7 gas speed (whirl) at tip = (15 x 400) / 16 = 375. Blade speed = 427 as before. Relative gas speed at tip (whirl) = 427 - 375 = 52 (note : blade is overtaking gas). 5 Angle at tip = 90 + tan⁻¹ (52 / 80) = 122° Gas speed at root (whirl) = (15 x 400) / 14 = 429 Blade speed at root = 373 (as before) Relative gas speed at root (whirl) = 429 - 373 = 56 10 Angle at root = 90 - tan⁻¹ (56 / 80) = 55° ∴ Entry angle twisted through 67°. 15 Figure 3 illustrates in end view an axial-flow gas turbine rotor blade designed in accordance with the principle of my invention, on the following relationships :— u / vw at mean section = .545. 20 Axial velocity uniform = 48.3% of the whirl velocity at mean section. Blade length is 17.15% of mean diameter of rotor. A = 22° 10′ root; 29° 15′ at tip. B = 33° 20′ root; 64° 40′ at tip. C = 46° 33′ root; 37° 20′ at tip. 25 A corresponding blade as hitherto employed would have had the variation on each side of the mean diameter of about half the above values of B. Figure 4 shows this blade in elevation 30 in the axial direction, on a smaller scale, the blade 7 having leading or inlet edge 8 and leaving or outlet edge 9. In a turbine with blades shaped as 35 above, there is preferably, according to this invention, a clearance space between the nozzle blades and rotor blades, and a typical construction is indicated by diagram in Figure 5. 40 In Figure 5 the nozzle blades 10 have trailing or leaving edges 11 and are mounted on the nozzle diaphragm 12. The parts 12 and 13 are axially extended towards the plane of the turbine wheel 14, so as to form a cylindrical space 45 at 15. The turbine rotor blades 16 have leading or entering edges at 17 and leaving edges at 18. The blades 16 are encircled by the blade shroud ring 19. An edge 20 is presented by the rim 13, close 50 to the ring 19, a small working clearance being provided; the inner wall of the rim of casing opposite the ring 19, may be corrugated as indicated at 20, in known manner, the arrangement having the object of inhibiting fluid flow between the rotor of the turbine and the axial extension of the diaphragm, or the casing. 55 The axial dimension of the space 15 is shown greater than half the chord of the blades 16; it is in any case greater than one quarter. The fluid flow in this space 60 is as nearly as possible that of a free circular vortex, i.e. a concentric flow in which vwr is constant where vw = rotational (whirl) velocity and r = radius. 65 Turning to the construction of a compressor in accordance with the invention, reference is made to Figure 6 and Figure 7. These correspond generally to Figures 1 and 2. Figure 6 shows the rotor blades 70 21 with entering edges 22 and leaving edges 23, and stator blades 24 with like edges 25, 26. With reference to the allied vector diagram, Figure 7, the following are indicated:— 75 va = axial velocity of fluid. u = blade speed. vwr = whirl velocity of fluid relative to blades on discharge from blades 21. 80 v'r = velocity of fluid relative to blades on entering blades 21. v'r = resultant velocity of fluid relative to blades at discharge from blades 21. vwabs = absolute whirl velocity on discharge from blades 21. 85 Then the angles to which the blades are designed, at any given radial station, are shown to be: D = tan⁻¹ (va / u) E = tan⁻¹ (va / (u - vwabs)) 90 F = tan⁻¹ (va / vwabs) | ||