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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.
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]
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
A steam turbine from MAN SE subsidiary MAN Turbo. In general, the two kinds of turbomachines encountered in practice are open and closed turbomachines. Open machines such as propellers, windmills, and unshrouded fans act on an infinite extent of fluid, whereas closed machines operate on a finite quantity of fluid as it passes through a housing or casing.
A derivation of the general Euler equations (fluid dynamics) is Euler's pump and turbine equation, which plays an important role in understanding impeller performance. This equation can be written in the form: Equation-1.2 (see Figures 1.2.2 and 1.2.3 illustrating impeller velocity triangles)
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,
Fig-4: Velocity Diagram of Pressure compounded Impulse Turbine. The velocity diagram shown in figure 4 gives detail about the various components of steam velocity and Blade velocity. where, symbols have the same meaning as given above. An important point to note from the above velocity diagram is that the fluid exit angle (δ) is 90⁰.