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Axial and tangential components of both absolute and relative velocities are shown in the figure. Static and stagnation values of pressure and enthalpy in the absolute and relative systems are also shown. Velocity triangle for a turbine stage. It is often assumed that the axial velocity component remains constant through the stage.
These equations govern the power, efficiencies and other factors that contribute to the design of turbomachines. With the help of these equations the head developed by a pump and the head utilised by a turbine can be easily determined. As the name suggests these equations were formulated by Leonhard Euler in the eighteenth century. [1]
An example of a velocity triangle drawn for the inlet of a turbomachine. The "1" subscript denotes the high pressure side (inlet in case of turbines and outlet in case of pumps/compressors). A general velocity triangle consists of the following vectors: [1] [2] V = absolute velocity of the fluid. U = blade linear velocity.
The velocity triangle [2] (Figure 2.) for the flow process within the stage represents the change in fluid velocity as it flows first in the stator or the fixed blades and then through the rotor or the moving blades. Due to the change in velocities there is a corresponding pressure change. Figure 2. Velocity Triangle for fluid flow in turbine
The radial component of the fluid velocity is negligible. Since there is no change in the direction of the fluid, several axial stages can be used to increase power output. A Kaplan turbine is an example of an axial flow turbine. In the figure: U = Blade velocity, V f = Flow velocity, V = Absolute velocity, V r = Relative velocity, V w ...
As stated above, some of the air is deflected away from the turbine. This causes the air passing through the rotor plane to have a smaller velocity than the free stream velocity. The ratio of this reduction to that of the air velocity far away from the wind turbine is called the axial induction factor. It is defined as
Usually the flow velocity (velocity perpendicular to the tangential direction) remains constant throughout, i.e. V f1 =V f2 and is equal to that at the inlet to the draft tube. Using the Euler turbine equation, E/m=e=V w1 U 1, where e is the energy transfer to the rotor per unit mass of the fluid. From the inlet velocity triangle,
The power coefficient [9] C P (= P/P wind) is the dimensionless ratio of the extractable power P to the kinetic power P wind available in the undistributed stream. [ citation needed ] It has a maximum value C P max = 16/27 = 0.593 (or 59.3%; however, coefficients of performance are usually expressed as a decimal, not a percentage).