Pelton Wheels. By: Chris Holmes, Amanda Higley, and Nick Hiseler

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1 Pelton Wheels By: Chris Holmes, Amanda Higley, and Nick Hiseler

jet hitting the cups in their middle, the slippage made it hit near the edge Surprisingly, the turbine now moved faster Lester Allan Pelton http://electrical-engineering-portal.

2 History Lester Allan Pelton invented the Pelton wheel, an impulse type water turbine in the late 1870 s. Pelton's invention started from an accidental observation some time in the 1870s Pelton was watching a spinning water turbine when the key holding its wheel onto its shaft slipped Instead of the jet hitting the cups in their middle, the slippage made it hit near the edge Surprisingly, the turbine now moved faster Lester Allan Pelton Figure from Pelton's original patent (October 1880) "Lester Allan Pelton." Wikipedia. Wikimedia Foundation, 17 June Web. 18 Oct <

3 History Many similar variations of the wheel existed before Pelton s design, but they were much less efficient. Peloton s design better captured a stream s kinetic energy, rather than relying on pressure head. In previous designs, water left the wheel at a very high speed, meaning little energy was extracted. Pelton s split cup design extracts almost all of the water s impulse energy, leaving it with very little velocity. "Pelton Wheel." Wikipedia. Wikimedia Foundation, 15 Oct Web. 18 Oct <

Today large hydro-electric power plants generate up to 40,000 horsepower with efficiencies

4 History By the time of his death in 1908, Pelton s design was produced for a variety of applications. Today large hydro-electric power plants generate up to 40,000 horsepower with efficiencies greater than 88%.

Main Components of the Pelton Wheel Nozzle used to increase velocity of water jet and direct it to the buckets Spear used to shut off and vary the water jet

5 Main Components of the Pelton Wheel Nozzle used to increase velocity of water jet and direct it to the buckets Spear used to shut off and vary the water jet velocity Buckets evenly spaced double hemispherical bowls positioned to evenly divide the jet. Casing to direct discharge of water (Civil Engineering Terms, 2012)

Pelton wheels are used to capture hydraulic energy at high head and low flow The cupped design is optimal for capturing a high velocity stream of water.

6 Pelton wheels are used to capture hydraulic energy at high head and low flow The cupped design is optimal for capturing a high velocity stream of water. This turns the wheel and allows for the least waste in energy. These wheels are highly efficient and are ideal for low flow designs. bine_in_barcelona.jpg

7 Pelton wheel efficiency depends on the ratio of jet speed to blade speed This graph shows that the optimum jet to blade ratio is at about half. In practice this number is closer to.46. For this reason pelton wheels are typically equipped with lag gears and generator braking mechanisms. This keeps the wheel running at maximum efficiency capturing maximum power.

The bucket geometry helps to generate maximum power The most efficient design for kinetic energy capture would be at 180 degrees F x = ρvq cosθ 1 In order to keep the stream from hitting the back of

8 The bucket geometry helps to generate maximum power The most efficient design for kinetic energy capture would be at 180 degrees F x = ρvq cosθ 1 In order to keep the stream from hitting the back of the adjacent bucket most are designed at 160 degrees A splitting ridge rests in the center of each bucket in order to split the stream into two equal parts

9 Nozzle sizing for high velocity output In order to turn the head into velocity that can be used at the wheel it is necessary to size a pipe with limited head loss At the end of the pipe an appropriate nozzle increases the flow velocity For losses h l = 8flQ2 gπ 2 D 5 For nozzle sizing A 1 A 2 = V 1 V 2

10 Frictional coefficient and nozzle flow coefficient When the stream leaves the nozzle there is a loss due to the friction of air interaction and the sudden change in pressure. Starting with Q = A n V 1 Where A n =area of jet And equating V 1 = C v gh Where C v =coefficient of jet velocity Q = A n C v gh While the wheel spins, it also runs into frictional resistance. Starting with V = V 1 ωr Where ωr=rotational velocity With ωr = to U and adding a friction constant V = (V 1 U)(1 + k 1 cosθ) Where k 1 =frictional resistance coefficient cosθ=cosine of the angle between the incident and emergent jets

2) V jet D turbine Using this equation and a spec for the generator an appropriate wheel can be sized for your needs It is

11 Pelton wheel sizing The wheel has to be matched with the force of the jet ω turbine rpm = 1 2 (229.2) V jet D turbine Using this equation and a spec for the generator an appropriate wheel can be sized for your needs It is important to get the correct sizing given that maximum efficiency happens when the wheel turns at half the speed of the jet ower_plant.html

Using the right nozzle, diameter of wheel, and cup size ensures maximum energy capture After sizing your pelton wheel, the next step is to match it with an appropriate generator.

12 Using the right nozzle, diameter of wheel, and cup size ensures maximum energy capture After sizing your pelton wheel, the next step is to match it with an appropriate generator. Generators come in a wide variety of resistances and outputs. If there is a variable head for your system it is important to use a more advanced generating system with variable speeds and resistances. This can greatly increase the cost of some projects.

13 Estimating energy output Power is generally defined as P = QγH Where Q=flow rate γ=weight of water H=dynamic head Including the relation of wheel momentum, losses from stream friction, and kinetic head this turns into P Watts = A n C v ghρu(v 1 U)(1 + k 1 cosθ) Where A n =area of incident jet C v =coefficient of jet velocity g=gravitational constant H=dynamic head V 1 =nozzle velocity U=tangential wheel velocity k=frictional resistance coefficient

14 (Johnson at al, 2008)

Operational range In order to find an operational range for a specific pelton wheel design, it is necessary to find the maximum output and the stall torque rate.

15 Operational range In order to find an operational range for a specific pelton wheel design, it is necessary to find the maximum output and the stall torque rate. These will tell you what range you need to operate in so that output is not interrupted. Maximum output P max = AρC v 3 (2gH) Where A=area of jet C v =coefficient of jet velocity Minimum torque τ stall = QρRV 1 (1 + c) Where R=radius of turbine rotor c=loss coefficient At maximum output the wheels velocity is theoretically half of the stream velocity. On the other hand if there is not enough resistance from the generator the wheel could reach the stall torque.

16 Efficiency To find the maximum efficiency of a given wheel, the following equation is used. C v 2 (1 + k 1 cosθ) 2 Where C v =air resistance factor k 1 =dynamic wheel constant The ideal system would have C v, cosθ, and k 1 equal to 1 giving 100% efficiency.

17 Efficiency Comparison The power available from a stream of water is determined by: P = η x γ x H x Q where: η = efficiency of turbine γ = specific weight of water [N/m 3 ] H = net head [m] Q = volumetric flow rate [m3 /s] (Johnson et al, 2008)

18 Applications Pelton wheels are ideal in a high velocity, low flow environment. they are best suited for use in supplying hydrologic power to mountainous or hilly areas where small, fast moving streams are common. Rubicon Power Station, Rubicon, Australia

19 Applications Perhaps a more unique application of the Pelton wheel is its use in Disney s Geyser Mountain Project in Irvine, CA. The steep drop guests ride down allows for a significant build up of kinetic energy in the flowing water. Much of this energy is then harnessed using Pelton wheels and recycled back into making the ride run. Geyser Mountain Plan

20 References Civil Engineering Terms. Parts of Pelton Wheel. Aug Web. Accessed 21 Oct Johnson, Victoria, and Jenna Wilson. "Fluid Flow in a Micro Hydro System." Dec Web. Accessed 21 Oct Learn Engineering. Web accessed Pelton Wheel Water Turbine. G. Cussins Ltd. Web. Accessed

Chapter 5 1. Hydraulic Turbines (Gorla & Khan, pp )

Electronic Notes Chapter 5 1. Hydraulic Turbines (Gorla & Khan, pp.91 141) 1. Terminologies Related to A Hydropower Plant Hoover Dam generates more than 4 billion kilowatt-hours of electricity each year,