1. Development of Turbine Cascades
P M V Subbarao
Professor
Mechanical Engineering Department
The Paths Followed by Parson, Prandtl & Schlichting.……

2. Introductory Remarks
The science of practical hydrodynamics and aerodynamics is becoming more and more applied to turbines, pumps, fans, and compressors.
It is of interest to inquire how far the knowledge of aerofoil mechanics is applicable to steam turbines.
In practical steam turbines, it is not possible to use thin aerofoil blades, that is, streamline contours of small curvature.
Almost all steam turbine blades have much greater curvature than aerofoils, on account of the necessity for utilizing the entire head of steam in a practicable number of stages.

3. Preferred Blade Angles
In order to have a large enough rate of change of momentum of the steam jets of these stages, it is necessary to adopt blade discharge angles of not more than about 20 deg.
From considerations of “flow-in” from the preceding nozzles, the inlet blade angles cannot be more than about 90 deg., and in impulse turbines the angle is normally much less.
The nominal “outside angle” of normal turbine blades therefore, instead of being obtuse (as in aerofoils), is about 90 deg. or less.

4. Types of axial turbine design
The process of choosing the best turbine design for a given application usually involves juggling several parameters which may be of equal importance.
These are rotor angular velocity, weight, outside diameter, efficiency,.
This will ensure that the final design lies within acceptable limits for each parameter.
In consequence, a simple model can hardly do justice to the real problem.
However, a consideration of the factors affecting turbine efficiency for a simplified case can provide a useful guide to the designer.

5. Experimental Reaction Turbine @ Messrs. C. A. Parsons and Company, Ltd
Experimental Reaction Messrs. C. A. Parsons and Company, Ltd., Newcastle upon Tyne.

6. The Nomenclature

7. The Cascade Combinations Considered by Messrs. C. A
The Cascade Combinations Considered by Messrs. C. A. Parsons and Company, Ltd

8. Cascade Models for Testing

9. Experimental Data
The primary experimental data required were as follows :-
(1) Initial steam pressure.
(2) Initial steam temperature
(3) Final steam pressure.
(4) Torque (or weight in scale pan of dynamometer).
(5) Revolutions per minute.
(6) Steam consumption.
(7) Mechanical and frictional losses.
(8) Blade tip clearance leakage losses.

10. Curves showing the Effect of Root Pitch

11. Circumferential Pitching of Steam Turbine Blades
A common experiment in steam turbine engineering is to determine the best circumferential spacing of the blades by trial of various pitchings, until the optimum efficiency is obtained.

12. The Gap between Blades

13. “Biplane Effect” on Lift of Aerofoils

14. H. Schlichting’s Approach
The main incentive of cascade flow investigations is that real progress in the flow problems of turbo-machines will be achieved only by a deeper knowledge of complex flow phenomena.
This requires extensive theoretical calculations which, however, need careful correlation with experiments.

15. CASCADE FLOW PROBLEMS :H. Schlichting
The very complex cascade flow problem has been split up as follows:-
Two-dimensional flow through cascades.
(a) Incompressible and inviscid flow.
(b) Incompressible, viscous flow.
(c) Compressible flow.
Three-dimensional flow through cascades.
(a) Secondary flow effects at blade root and blade tip.
(b) Effects due to radial divergence of the blades in cascades of rotational symmetry.

16. INCOMPRESSIBLE CASCADE FLOW
For two-dimensional cascades, the main object of the investigations has been to find a way to calculate theoretically the loss coefficients of the cascade.
The loss coefficients depend on the geometrical and aerodynamic parameters of the cascade.
This is achieved by applying boundary layer theory to the cascade flow.
It is necessary to improve the methods of calculating the incompressible and inviscid flow through a cascade.
These solutions are used in an extensive algorithm of theoretical calculations of loss coefficients.
The information for loss coefficients are generated using a large amount of experimental work.

17. Definition of Cascades by Schlichting
Vr1 s
Vr1 Vf c
=0.5
=0.75

18. Method for Real Turbine
Define Half Travel Point of a fluid particle as
Vfi=Vfe
Vri
Vre V∞

19. The “Tragflügeltheorie”V∞
Fideal lift
Factual lift

20. The “Tragflügeltheorie” at Half Travel Point
The “Tragflügeltheorie” was developed by Ludwig Prandtl.
According to the “Tragflügeltheorie” :
A lifting force is generated at the blades of the runner due to the configuration of the flow stream and the whirling stream, which occur at the Center of Pressure of blade.
Values such as the lift coefficient and the attack angle δ also play a significant role in the design of the blade.
These coefficients can be determined via model tests.
Using these results the profile, the chord and the exact distortion of the blade can be determined.

21. Vri

22. Drag Coefficient