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

Transcript of Pelton Wheels - Walter Scott, Jr. College of Engineeringpierre/ce_old/classes/CIVE 401...Pelton...

Page 1: Pelton Wheels - Walter Scott, Jr. College of Engineeringpierre/ce_old/classes/CIVE 401...Pelton wheel efficiency depends on the ratio of jet speed to blade speed This graph shows that

Pelton Wheels

By: Chris Holmes, Amanda Higley, and Nick Hiseler

Page 2: Pelton Wheels - Walter Scott, Jr. College of Engineeringpierre/ce_old/classes/CIVE 401...Pelton wheel efficiency depends on the ratio of jet speed to blade speed This graph shows that

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

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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

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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

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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)

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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

Page 7: Pelton Wheels - Walter Scott, Jr. College of Engineeringpierre/ce_old/classes/CIVE 401...Pelton wheel efficiency depends on the ratio of jet speed to blade speed This graph shows that

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

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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

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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

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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

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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

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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.

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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

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(Johnson at al, 2008)

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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.

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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

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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)

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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

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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

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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