Parametric Study of Turbine Cascades P M V Subbarao Professor Mechanical Engineering Department Identification of New design Variables.……

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

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

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

Isentropic Flow Calculations : Impulse Turbine U V r1 V a1 V r2 V a2 11 11 22 22

Isentropic Flow Calculations : Reaction Turbine U V r1 V a1 V r2 V a2 11 11 22 22

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.

Irreversible Flow Through Turbine Cascade

The Effect of Solidity on Losses