Boundary Layer Correction of Viscous Flow Through 2 D Turbine Cascades

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Presentation transcript:

Boundary Layer Correction of Viscous Flow Through 2 D Turbine Cascades P M V Subbarao Professor Mechanical Engineering Department A Classical Method Recommended by Schlichting .……

Validity of Inviscid Flow Theory

Cascade Boundary Layer

Losses in 2D Cascades For flow of viscous fluids through two-dimensional cascades, the main object of the investigations has been to find a way to calculate theoretically the loss coefficients of the cascade. They depend on the geometrical and aerodynamic parameters of the cascade. A turbulent boundary layer computation has been incorporated into the inviscid design. This method solves three ordinary differential equations for three independent parameters, the momentum thickness, the shape factor and the entrainment coefficient.

The Displacement Thickness Conservation of mass is applied to this Engineering CV @SSSF:

Momentum Thickness of BL Conservation of Integral x momentum

Physical Interpretation of Momentum and displacement thicknesses Their ratio of displacement thickness to momentum thickness is called the shape factor, is often used in estimation of boundary-layer impact on cascade peformance

BL Correction Equations

Comparison of optimum solidities

Non-Dimensional Variables for Cascade Analysis Non dimensional deflection: Loss Coefficient: Solidity ratio: Reynolds Number:

Non-Dimensional Variables for Cascades : Design Pressure Coefficient: Flow Coefficient:

Wind Tunnel Testing of Cascades

COMPRESSIBLE CASCADE FLOW This is regarded as very important for basic research on cascades, because the aerodynamic coefficients in most cases depend considerably on both the Mach number and the Reynolds number of the blade. The independent variation of Mach number and Reynolds number is achieved by installing the cascade wind tunnel in a tank which can be evacuated from 1 atm down to 0.1 atm. The Mach number range is from M = 0.2 to about 1.1. The blade length L = 300 mm and the blade chord c = 60 mm. For one year an extensive programme of pressure distribution measurements has been carried out on cascade blades at high subsonic speeds.

High Speed Wind Tunnel Testing of Cascades

Effect of Mach Number

Effect of Mach Number

Effect of Mach Number