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Understanding Energy and Rotational Dynamics in Turbines

Explore energy and rotational principles in turbines, including equations for centrifugal acceleration, Coriolis effect, and forces in rotating channels. Gain insights into turbine operation and efficiency.

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Understanding Energy and Rotational Dynamics in Turbines

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  1. Energy and Rotalpy Where: E1 = Energy at the inlet of the turbine [J/kg] E2 = Energy at the inlet of the turbine [J/kg] I1 = Rotalpy at the inlet of the turbine [J/kg] I2 = Rotalpy at the inlet of the turbine [J/kg] g = Gravity constant [m/s2] H = Head [m] h = Efficiency [ - ]

  2. Energy and Rotalpy cu u w cm c

  3. Rotalpy along the streamline

  4. Absolute and relative acceleration We assume stationary flow and introduce relative and peripheral velocity: Where: w = relative velocity [m/s] u = peripheral velocity [m/s] w = angular velocity [rad/s] r = radius [m] Centripetal acceleration Coriolis acceleration Relative acceleration

  5. Relative acceleration Centripetal acceleration Acceleration along a streamline

  6. Forces acting in a rotating channel along a streamline

  7. By inserting the equation And rearranging we obtain the following equation:

  8. Rotalpy If we integrate the equation above we get the equation for rotalpy:

  9. Coriolis acceleration Centripetal acceleration Centripetal acceleration Acceleration normal to a streamline

  10. Forces acting in a rotating channel normal to a streamline

  11. We insert the equation for the normal acceleration in to the equation above. We obtain the following equation:

  12. We derive the rotalpy equation above with respect to the normal direction. We obtain the following equation: We insert the equation the equations to the right in to the equation above. We obtain the following equation:

  13. We have the equation below from the derivation from the Rotalpy equation We have the equation below from the derivation from Newton’s second law If we rearrange the equations above we obtain the following equation:

  14. Pump Pump-turbine in turbine mode Francis turbine

  15. w Pump

  16. w Pump-turbine

  17. w Francis turbine

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