pelton wheels - walter scott, jr. college of engineeringpierre/ce_old/classes/cive 401...pelton...
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Pelton Wheels
By: Chris Holmes, Amanda Higley, and Nick Hiseler
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." Wikipedia. Wikimedia Foundation, 17 June 2015. Web. 18 Oct. 2015. <https://en.wikipedia.org/wiki/Lester_Allan_Pelton#Inventing_the_Pelton_wheel>.
Lester Allan Pelton http://electrical-engineering-portal.com/lester-allan-pelton-father-hydroelectric-power Figure from Pelton's original patent (October 1880)
https://en.wikipedia.org/wiki/Pelton_wheel
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. 2015. Web. 18 Oct. 2015. <https://en.wikipedia.org/wiki/Pelton_wheel>.
http://img.bhs4.com/4D/5/4D5E0F4CF28BCBF14A02F83836CD68A3468EF8B5_large.jpg
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%.
http://palmerdesign.co.nz/wp-content/uploads/2014/10/3d-printed-pelton-wheel-hand-for-scale.JPG https://upload.wikimedia.org/wikipedia/commons/8/8a/Walchenseewerk_Pelton_120.jpg
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. This turns the wheel and allows for the least waste in energy. These wheels are highly efficient and are ideal for low flow designs.
https://commons.wikimedia.org/wiki/File:Pelton_wheel_turbine_in_Barcelona.jpg
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. http://nptel.ac.in/courses/112104117/chapter_7/7_4.html
The bucket geometry helps to generate maximum power
• The most efficient design for kinetic energy capture would be at 180 degrees
• 𝐹𝑥 = 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
http://www.power.altona.com.br/en-gb/Category/Power+Generation
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 ℎ𝑙 =8𝑓𝑙𝑄2
𝑔𝜋2𝐷5
• For nozzle sizing 𝐴1
𝐴2=
𝑉1
𝑉2
http://cfbt-us.com/wordpress/?p=991
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 = 𝐴𝑛𝑉1
Where
An=area of jet
And equating
𝑉1 = 𝐶𝑣 𝑔𝐻
Where Cv=coefficient of jet velocity
𝑄 = 𝐴𝑛𝐶𝑣 𝑔𝐻
While the wheel spins, it also runs into frictional resistance.
Starting with 𝑉 = 𝑉1 − 𝜔𝑅
Where
𝜔𝑅=rotational velocity
With 𝜔𝑅 = to U and adding a friction constant
𝑉 = (𝑉1 − 𝑈)(1 + 𝑘1𝑐𝑜𝑠𝜃)
Where
k1=frictional resistance coefficient 𝑐𝑜𝑠𝜃=cosine of the angle between the incident and
emergent jets
Pelton wheel sizing
The wheel has to be matched with the force of the jet
• 𝜔𝑡𝑢𝑟𝑏𝑖𝑛𝑒 𝑟𝑝𝑚 =1
2(229.2)
𝑉𝑗𝑒𝑡
𝐷𝑡𝑢𝑟𝑏𝑖𝑛𝑒
• 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
http://www.ebay.com/bhp/pelton-wheel
http://gthec.en.alibaba.com/product/1153230206-211910193/Pelton_wheel_runner_for_water_pelton_turbine_in_hydro_power_plant.html
Using the right nozzle, diameter of wheel, and cup size ensures maximum energy capture
http://ricklyhydro.com/micro-mini-hydro-systems/turbines/pelton-wheel-turbine/
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.
Estimating energy output
Including the relation of wheel momentum, losses from stream
friction, and kinetic head this turns into
𝑃 𝑊𝑎𝑡𝑡𝑠 = 𝐴𝑛𝐶𝑣 𝑔𝐻𝜌𝑈(𝑉1 − 𝑈)(1 + 𝑘1𝑐𝑜𝑠𝜃)
Where
An=area of incident jet Cv=coefficient of jet velocity
g=gravitational constant H=dynamic head
V1=nozzle velocity U=tangential wheel velocity
k=frictional resistance coefficient
Power is generally defined as
𝑃 = 𝑄𝛾𝐻
Where
Q=flow rate 𝛾=weight of water H=dynamic head
(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. These will tell you what range you need to operate in so that output is not interrupted.
http://www.learnengineering.org/2013/08/pelton-turbine-wheel-hydraulic-turbine.html
Maximum output
𝑃𝑚𝑎𝑥 =𝐴𝜌𝐶𝑣
3(2𝑔𝐻)23
2
Where A=area of jet
Cv=coefficient of jet velocity
Minimum torque 𝜏𝑠𝑡𝑎𝑙𝑙 = 𝑄𝜌𝑅𝑉1(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.
To find the maximum efficiency of a given wheel, the following equation is used.
𝐶𝑣2(1 + 𝑘1𝑐𝑜𝑠𝜃)
2
Where
Cv=air resistance factor k1=dynamic wheel constant
The ideal system would have Cv, cos𝜃, and k1 equal to 1 giving 100% efficiency.
Efficiency
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/m3 ]
H = net head [m]
Q = volumetric flow rate [m3 /s] (Johnson et al, 2008)
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.
• https://en.wikipedia.org/wiki/Rubicon_Hydroelectric_Scheme
Rubicon Power Station, Rubicon, Australia
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.
http://disneyandmore.blogspot.com/2015/01/disney-and-more-tribute-to-wdi.html
Geyser Mountain Plan
References
Civil Engineering Terms. “Parts of Pelton Wheel.” Aug. 2012. Web. Accessed 21 Oct. 2015. http://www.civilengineeringterms.com/fluid-mechanics-2/definition-of-pelton-wheel-parts-of-pelton-wheel/ Johnson, Victoria, and Jenna Wilson. "Fluid Flow in a Micro Hydro System." Dec. 2008. Web. Accessed 21 Oct. 2015. http://sei.oregonstate.edu/wp-content/uploads/documents/JWil_VJohn_331%20Special%20Project.pdf Learn Engineering. Web accessed 2015. http://people.rit.edu/rfaite/courses/tflab/Cussons/pelton/pelton.htm Pelton Wheel Water Turbine. G. Cussins Ltd. Web. Accessed 2015. http://www.learnengineering.org/2013/08/pelton-turbine-wheel-hydraulic-turbine.html