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Velocity Triangle for Turbo-machinery BY P M V Subbarao Professor Mechanical Engineering Department I I T Delhi.

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Presentation on theme: "Velocity Triangle for Turbo-machinery BY P M V Subbarao Professor Mechanical Engineering Department I I T Delhi."— Presentation transcript:

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2 Velocity Triangle for Turbo-machinery BY P M V Subbarao Professor Mechanical Engineering Department I I T Delhi

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4 U V ri V re V ai UV ri V ai Inlet Velocity Triangle U V re V ae Exit Velocity Triangle

5 U V ri V ai V re V ae ii ii ee ee V ai : Inlet Absolute Velocity V ri : Inlet Relative Velocity V re : Exit Relative Velocity V ae :Exit Absolute Velocity  i : Inlet Nozzle Angle.  i : Inlet Blade Angle.  e : Exit Blade Angle.  i : Exit Nozzle Angle.

6 VaVa VrVr V rc VwVw U VfVf

7 U U U V ri V re V ai V ae V ni Flow through Blades

8 Fluid Dynamics of Blades

9 The stream is delivered to the wheel at an angle  i and velocity V ai. The selection of angle  i is a compromise. An increase in  i, reduces the value of useful component (Absolute circumferential Component). This is also called Inlet Whirl Velocity, V wi = V ai cos(  i ). An increase in  i, increases the value of axial component, also called as flow component. This is responsible for definite mass flow rate between to successive blade. Flow component V fi = V ai sin(  i ) = V ri sin(  i ). The absolute inlet velocity can be considered as a resultant of blade velocity and inlet relative velocity. The two points of interest are those at the inlet and exit of the blade. U V ri V ai V re V ae ii ii ee ee

10 If the stream is to enter and leave the blades without shock or much losses, then relative velocity should be tangential to the blade inlet tip. V ri should enter at an angle  i, the inlet blade angle. Similarly, V re should leave at  e, the exit blade angle. A blade is said to be symmetric if  i =  e. The flow velocities between two successive blade at inlet and exit are V fi & V fe. The axial (basic useful) components or whirl velocities at inlet and exit are V wi & V we. U V ri V ai V re V ae ii ii ee ee

11 Impulse Turbine

12 Newton’s Second Law for an Impulse Blade: The tangential force acting of the jet is: F = mass flow rate X Change of velocity in the tangential direction Tangential relative velocity at blade Inlet : V ri cos(  i ). Tangential relative velocity at blade exit : -V re cos(  e ). Change in velocity in tangential direction: -V re cos(  e ) - V ri cos(  i ). -(V re cos(  e ) + V ri cos(  i )). Tanential Force, U V ri V ai V re V ae ii ii ee ee

13 The reaction to this force provides the driving thrust on the wheel. The driving force on wheel Power Output of the blade, Diagram Efficiency or Blade efficiency:

14 U V ri V ai V re V ae ii ii ee ee

15 Define Blade Speed Ratio, 

16 For a given shape of the blade, the efficiency is a strong function of  For maximum efficiency:

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18 Impulse-Reaction turbine This utilizes the principle of impulse and reaction. There are a number of rows of moving blades attached to the rotor and equal number of fixed blades attached to the casing. The fixed blades are set in a reversed manner compared to the moving blades, and act as nozzles. The fixed blade channels are of nozzle shape and there is a comparatively small drop in pressure accompanied by an increase in velocity. The fluid then passes over the moving blades and, as in the pure impulse turbine, a force is exerted on the blades by the fluid. There is further drop in pressure as the fluid passes through the moving blades, since moving blade channels are also of nozzle shape. The relative velocity increases in the moving blades.

19 U V ri V ai V re V ae ii ii ee ee p vava vrvr The reaction effect is an addition to impulse effect. The degree of reaction

20 First law for fixed blades: First law for moving blades:

21 If the stream is to enter and leave the blades without shock or much losses, then relative velocity should be tangential to the blade inlet tip. V r1 should enter at an angle  1, the inlet blade angle. Similarly, V r2 should leave at  2, the exit blade angle. In an impulse reaction blade, V r2 > V r1. The flow velocities between two successive blade at inlet and exit are V f1 & V f2. The axial (basic useful) components or whirl velocities at inlet and exit are V w1 & V w2. U V r1 V a1 V r2 V a2 11 11 22 22

22 Newton’s Second Law for an Impulse-reaction Blade: The tangential force acting of the jet is: F = mass flow rate X Change of velocity in the tangential direction Tangential relative velocity at blade Inlet : V r1 cos(  2 ). Tangential relative velocity at blade exit : -V r2 cos(  2 ). Change in velocity in tangential direction: -V r2 cos(  2 ) – V r1 cos(  1 ). -(V r2 cos(  2 ) + V r1 cos(  1 )). Tangential Force, U V r1 V a1 V r2 V a2 11 11 22 22

23 The reaction to this force provides the driving thrust on the wheel. The driving force on wheel Power Output of the blade, Diagram Efficiency or Blade efficiency:

24 First law for fixed blades: First law for moving blades:

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26 Losses in nozzle, Nozzle blade loss factor, 

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28 For a given shape of the blade, the efficiency is a strong function of U/V a1  For maximum efficiency:


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