History
Figure from Lester Allan Pelton's original October 1880 patent Lester Allan Pelton was born in Vermillion, Ohio in 1829. In 1850, he traveled overland to take part in theDesign
Nozzles direct forceful, high-speed streams of water against a series of spoon-shaped buckets, also known as impulse blades, which are mounted around the outer rim of a drive wheel (also called a ''runner''). As the water jet hits the blades, the direction of water velocity is changed to follow the contours of the blades. The impulse energy of the water jet exerts torque on the bucket-and-wheel system, spinning the wheel; the water jet does a "u-turn" and exits at the outer sides of the bucket, decelerated to a low velocity. In the process, the water jet's momentum is transferred to the wheel and hence to a turbine. Thus, " impulse" energy does work on the turbine. Maximum power and efficiency are achieved when the velocity of the water jet is twice the velocity of the rotating buckets. A very small percentage of the water jet's original kinetic energy will remain in the water, which causes the bucket to be emptied at the same rate it is filled, and thereby allows the high-pressure input flow to continue uninterrupted and without waste of energy. Typically two buckets are mounted side-by-side on the wheel, with the water jet split into two equal streams; this balances the side-load forces on the wheel and helps to ensure smooth, efficient transfer of momentum from the water jet to the turbine wheel. Because water is nearly incompressible, almost all of the available energy is extracted in the first stage of the hydraulic turbine. "Therefore, Pelton wheels have only one turbine stage, unlike gas turbines that operate with compressible fluid."Applications
Pelton wheels are the preferred turbine for hydro-power where the available water source has relatively highDesign rules
The specific speed parameter is independent of a particular turbine's size. Compared to other turbine designs, the relatively low specific speed of the Pelton wheel, implies that the geometry is inherently a " low gear" design. Thus it is most suitable to being fed by a hydro source with a low ratio of flow to pressure, (meaning relatively low flow and/or relatively high pressure). The specific speed is the main criterion for matching a specific hydro-electric site with the optimal turbine type. It also allows a new turbine design to be scaled from an existing design of known performance. (dimensionless parameter), where: * = Frequency of rotation (rpm) * = Power (W) * = Water head (m) * = Density (kg/m3) The formula implies that the Pelton turbine is ''geared'' most suitably 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.Turbine physics and derivation
Energy and initial jet velocity
In the ideal ( frictionless) case, all of the hydraulicFinal 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: − (''V''''i'' − ''u'') = −''V''''i'' + ''u''. In the standard reference frame (relative to the earth), the final velocity is then: ''V''''f'' = (−''V''''i'' + u) + ''u'' = −''V''''i'' + 2''u''.Optimal wheel speed
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 −''V''''i'' + 2''u'' = 0, then the optimal runner speed will be ''u'' = ''V''''i'' /2, or half the initial jet velocity.Torque
By Newton's second and third laws, the force ''F'' imposed by the jet on the runner is equal but opposite to the rate of momentum change of the fluid, so : ''F'' = −''m''(''V''f − ''V''i)/''t'' = −''ρQ'' i + 2''u'') − ''V''i">−''V''i + 2''u'') − ''V''i= −''ρQ''(−2''V''i + 2''u'') = 2''ρQ''(''V''i − ''u''), where ''ρ'' is the density, and ''Q'' is the volume rate of flow of fluid. If ''D'' is the wheel diameter, the torque on the runner is. : ''T'' = ''F''(''D''/2) = ''ρQD''(''V''i − ''u''). The torque is maximal when the runner is stopped (i.e. when ''u'' = 0, ''T'' = ''ρQDV''i). When the speed of the runner is equal to the initial jet velocity, the torque is zero (i.e., when ''u'' = ''V''i, then ''T'' = 0). On a plot of torque versus runner speed, the torque curve is straight between these two points: (0, ''pQDV''i) and (''V''i, 0). Nozzle efficiency is the ratio of the jet power to the waterpower at the base of the nozzle.Power
The power ''P'' = ''Fu'' = ''Tω'', where ''ω'' is the angular velocity of the wheel. Substituting for ''F'', we have ''P'' = 2''ρQ''(''V''''i'' − ''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, ''i'' − 2''u'')">'dP''/''du'' = 2''ρQ''(''V''''i'' − 2''u'') Maximum power occurs when ''u'' = ''V''''i'' /2. ''P''max = ''ρQV''''i''2/2. Substituting the initial jet power ''V''''i'' = , this simplifies to ''P''max = ''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'' = 4''u''(''V''''i'' − ''u'')/''V''''i''2. It is zero for ''u'' = 0 and for ''u'' = ''V''''i''. 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. In theory, the energy efficiency varies only with the efficiency of the nozzle and wheel, and does not vary with hydraulic head.System components
The conduit bringing high-pressure water to the impulse wheel is called the penstock. Originally the penstock was the name of the valve, but the term has been extended to include all of the fluid supply hydraulics. Penstock is now used as a general term for a water passage and control that is under pressure, whether it supplies an impulse turbine or not.See also
*References
External links