Development of Turbine Cascades P M V Subbarao Professor Mechanical Engineering Department Its Group Performance, What Matters.……

Single Blade Turbine is Useless

The Gap between Blades CHORD, C

Parallel Cascades Vs Turbine Cascades

The group of Aerofois An important point to be examined is whether the crowding together of steam/gas turbine blades has effects similar to those noticed in aeroplane practice. A biplane is stated to have less lifting effect than a monoplane of the same wing surface.

“Biplane Effect” on Lift of Aerofoils

Cascades : A Group of Turbine Blades The biplane arrangement is analogous to the circumferential pitching of steam/gas turbine blades. Additional wing surfaces in series (one behind the other), analogous to avoiding of pressure compounding in a turbine. The reasons for grouping may have some bearing on turbine blading efficiency.

Nomenclature of Turbine Cascades

Solidity: the first Step in Cascade Design One of the important aspects of cascade design is the selection of the blade solidity. Defined as the ratio of chord or axial chord to blade spacing. A minimum allowable value is usually desired from the standpoint of reducing weight, cooling flow, and cost. An increase in the blade spacing eventually results in decreased blade efficiency due to separated flow. An optimum solidity cascade should be a fully attached flow with maximum blade spacing. The gas dynamic factors affecting solidity are The requirements of velocity diagram The blade loading

Solidity: the first Step in Cascade Design One of the important aspects of cascade design is the selection of the blade solidity. Defined as the ratio of chord or axial chord to blade spacing. A minimum allowable value is usually desired from the standpoint of reducing weight and cost. An increase in the blade spacing eventually results in decreased blade efficiency due to separated flow. An optimum solidity cascade should be a fully attached flow with maximum blade spacing. The gas dynamic factors affecting solidity are The requirements of velocity diagram The blade loading

Pressure Distribution on A Single Aerofoil

Cascade Velocity Diagrams & Surface Static Pressure Distribution

The area between the two curves represents the total blade force acting on the flow in the tangential direction. Thus, where c x is axial chord, p p is pressure side static pressure, p s is suction side static pressure. Define axial solidity  x as The Cause to be Created

Considering two-dimensional flow through the cascade of unit height between two blades, then the tangential force F exerted by the fluid as it flows from blade inlet to exit is given as: The effect to be Achieved

Combined Cause & Effect Substituting cause equations into effect equation yields

Real Flow Vs Solidity The pressure drop across a turbine stage produces the useful work. A small portion of this available energy that is not converted to work is denoted as a loss. The primary cause of losses is the boundary layer that develops on the blade and end-wall surfaces. Other losses occur because of shocks, tip-clearance flows, windage (disk friction), and flow incidence. One of the more important and difficult aspects of turbine design is the prediction of the losses.

Losses : An Irreversible Flow Through Turbine Cascade

The Effect of Solidity on Losses

The Nomenclature by C. A. Parsons

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

Cascade Models for Testing

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

Experimental Data The primary experimental data required were as follows :- (1) Initial stream pressure. (2) Initial stream temperature (3) Final stream 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.

Curves showing the Effect of Root Pitch

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.

Selection of Solidity for a Selected Blade V fi =V fe V ri V re V∞V∞ Define Half Travel Point of a fluid particle as

The “Tragflügeltheorie” V∞V∞ F ideal lift F actual lift

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.

V ri

Drag Coefficient

Zweifel Loading Coefficient A very widely used tangential loading coefficient, is introduced by Zweifel. Zweifel loading coefficient  z, relates the actual and ideal blade loading, is based on an ideal loading. Ideal loading is defined as static pressure on the pressure surface to be constant and equal to the difference of inlet total pressure and the static pressure on the suction surface, which is to be constant and equal to the exit static pressure. In equation form,

Simplified Relations for Solidity