DESIGN OF PELTON TURBINE

The Pelton wheel is an impulse type water turbine. It was invented by lester Allan Pelton in the 1870s. The Pelton wheel extracts energy from the impulse of moving water, as opposed to water's dead weight like the traditional overshot water wheel.
In the Pelton turbine water jets impacts on the blades of the turbine. The turbine is used to rotate the wheel to produce torque and power.

Design Of Pelton Wheel Turbine

In the Pelton wheel to a rotor or rotating shaft circular disk is mounted. The circular disk consists of cup shaped blades. The cup blades are known as buckets. Those are placed at the circumference with equal spacing. To the wheel nozzles are arranged so the water jet ejects from the nozzle. The nozzles are tangential to the wheel circumference. No of nozzles depends upon the available water head and the operating requirement of the shape. The nozzles placed around the wheel are varying.

The specific speed of a turbine dictates the turbine's shape in a way that is not related to its size. This allows a new turbine design to be scaled from an existing design of known performance. The specific speed is also the main criterion for matching a specific hydro-electric site with the correct turbine type.

(dimensioned parameter), = rpm

where:
• = Power (W)
• = Water head (m)
• = Density (kg/m3)
The formula implies that the Pelton turbine is most suitable for applications with relatively high hydraulic head H, due to the 5/4 exponent being greater than unity, and given the characteristically low specific speed of the Pelton.

Energy and initial jet velocity

In the ideal (frictionless) case, all of the hydraulic potential energy (Ep = mgh) is converted
into kinetic energy (Ek = mv2/2). Equating these two equations and solving for the initial jet velocity
(Vi) indicates that the theoretical (maximum) jet velocity is Vi = √(2gh) . For simplicity, assume that
all of the velocity vectors are parallel to each other. Defining the velocity of the wheel runner as: (u), then as the jet approaches the runner, the initial jet velocity relative to the runner is: (Vi − u). The initial jet velocity of jet is v1

Final jet velocity

Assuming that the jet velocity is higher than the runner velocity, if the water is not to become backed-up in runner, then due to conservation of mass, the mass entering the runner must equal the mass leaving the runner. The fluid is assumed to be incompressible (an accurate assumption for most liquids). Also it is assumed that the cross-sectional area of the jet is constant. The jet speed remains constant relative to the runner. So as the jet recedes from the runner, the jet velocity relative to the runner is: −(Vi − u) = −Vi + u. In the standard reference frame (relative to the earth), the final velocity is then: Vf = (−Vi + u) + u = −Vi + 2u.

Optimal wheel speed

We know that the ideal runner speed will cause all of the kinetic energy in the jet to be transferred to the wheel. In this case the final jet velocity must be zero. If we let −Vi + 2u = 0, then the optimal runner speed will be u = Vi /2, or half the initial jet velocity

Power

The power P = Fu = Tω, where ω is the angular velocity of the wheel. Substituting for F, we have P = 2ρQ(Vi − u)u. To find the runner speed at maximum power, take the derivative of P with respect to u and set it equal to zero, [dP/du = 2ρQ(Vi − 2u)]. Maximum power occurs when u = Vi /2. Pmax = ρQVi2/2. Substituting the initial jet power Vi = √(2gh), this simplifies to Pmax = ρghQ. This quantity exactly equals the kinetic power of the jet, so in this ideal case, the efficiency is 100%, since all the energy in the jet is converted to shaft output.

Efficiency

A wheel power divided by the initial jet power, is the turbine efficiency, η = 4u(Vi − u)/Vi2. It is zero for u = 0 and for u = Vi. As the equations indicate, when a real Pelton wheel is working close to maximum efficiency, the fluid flows off the wheel with very little residual velocity.[2] This basic theory does not suggest that efficiency will vary with hydraulic head, and further theory is required to show this. There are five types of efficiency in Pelton turbine:
Hydraulic
Mechanical
Volumetric
Overall
Wheel efficiency