Pelton Wheel. Cive 401: Hydraulic Engineering. Melissa James, Robert Jaquet, Scott Kemper 11/19/2014

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1 Pelton Wheel Cive 401: Hydraulic Engineering Melissa James, Robert Jaquet, Scott Kemper 11/19/2014

History of the Pelton Wheel During the 1850s, the hurdy-gurdy wheels were the main water turbines used in the gold and silver fields of California and Nevada and were considered to be the primitive

2 History of the Pelton Wheel During the 1850s, the hurdy-gurdy wheels were the main water turbines used in the gold and silver fields of California and Nevada and were considered to be the primitive design that developed into the Pelton Wheel ( Pelton Waterwheel Collection ). The hurdy-gurdy wheels (given the name after the musical instrument the wheels sounded like when in operation) were made of blocks of wood about four inches thick...cut so that...each one formed a tooth like that of a circular ripsaw (Shortridge, 22). The wheel moved as a water jet hit the teeth tangentially with heads of 40 to 50 feet. This contraption mostly powered small quartz mills and had a low maximum efficiency of 40 percent, which was assumed to be due to the flat surface of the buckets or teeth (Shortridge, 22-23). In order to increase efficiency, the first major alteration to the wheel system transformed the wooden teeth of the hurdy-gurdy into a cup-shaped bucket that discharged water to the side and middle when hit by a rectangular jet of water formed by a slit nozzle. Lester Pelton, known to some as the Father of Hydroelectric Power, encountered the hurdy-gurdy wheels in the gold fields when he worked as a gold miner and millwright and began experimenting on around 40 different types of wheel designs to improve efficiency. He began his work in California at age 20 and continued until his death at age 79 (Csanyi). Many hydroelectric ideas stemmed from the initial designs created by Pelton in the 19 th century. Figure 1 below shows a common image of Lester Pelton. Figure 1. Lester Pelton Source: (Csanyi)

3 Pelton s first successful wheel design was built in Camptonville, California in 1878 ( Pelton Waterwheel Collection ). In the fall of 1880, Pelton received his first patent on the design shown in Figure 2 below. Figure 2. Pelton s First Patent Design Sketches Source: (Shortridge, 24) Coincidentally, a similar design had been patented in 1873 by Nicholas J. Coleman. However, Coleman s patent was misplaced during Pelton s submission and was not discovered again until a few years later by a vengeful foreman, W.G. Dodd, of Rankine, Brayton & Company in San Francisco after a misunderstanding resulted in Dodd losing his spot in the Pelton Water Wheel Company. The misunderstanding was later resolved by the Pelton Water Wheel Company buying up the rights for Coleman s patent. The Pelton Water Wheel Company was cofounded by Brayton of Rankine, Brayton & Company and Pelton himself as a manufacturing company for the new successful wheel turbine design (Shortridge, 24). The Pelton Water Wheel Company quickly jumped up in the ranks as a famous wheel turbine manufacturing company. Improvements to Pelton s original design were made by many contributors, the final major one being made by Pelton Water Wheel Company s competitor, William Doble. Doble noticed how the buckets in the Pelton design were worn down quickly due to the scouring of the sand of the water jet in turbulent flows hitting the buckets. Doble fixed this by essentially creating a double bucket design with the addition of a water splitter, which divides the jet of water in half and minimizes the turbulence and abrasion of the water in the buckets. Doble s revision of the design led to a second stage in the development of Pelton turbines ( Pelton Waterwheel Collection ).

The buckets receive the jet(s) of water from a typically large head source which is then converted into high velocities at the exit nozzle(s) that then strike

Created by Robert Jaquet The force felt by this blade can be found using the momentum equation and applying it to the control volume in equation one through

F Bx = ρ(v j V b )A j [(V j V b ) 1 (V j V b ) 2 ] Eq 1 This can be simplified base on the reasonable assumption that the x component (V j -V b ) 2 is the

F b = 2 ρa j (V j V bx1 )(V j V bx2 ) Eq 2 However, since there is a loss from the consecutive blade pushing a cylinder of water forward and is partially

4 How does a Pelton wheel work? A Pelton wheel is typically a set of 20 buckets (blades) attached to a wheel that can vary in diameter; however, they are usually 10 meters. The buckets receive the jet(s) of water from a typically large head source which is then converted into high velocities at the exit nozzle(s) that then strike the blade. V b 1 F bx ρ H2 0 A j V j V b 2 Figure 4: Force Diagram. Created by Robert Jaquet The force felt by this blade can be found using the momentum equation and applying it to the control volume in equation one through three found below (Julien, 2014). F Bx = ρ(v j V b )A j [(V j V b ) 1 (V j V b ) 2 ] Eq 1 This can be simplified base on the reasonable assumption that the x component (V j -V b ) 2 is the maximum when theta is equal to 180 degrees. This creates a change in sign and the resulting simplification has been made equation 2). F b = 2 ρa j (V j V bx1 )(V j V bx2 ) Eq 2 However, since there is a loss from the consecutive blade pushing a cylinder of water forward and is partially deflected until the full stream is within the blades edges. The resulting total force is shown in equation 3. F b = 2V j A j ρ(v j V b ) Eq 3 Using the force on the blade multiplied with the velocity of the jet the product is the power developed by the blade is shown in equation four. Power = P = V b F b = 2 ρv b A j V j (V j V b ) = 2ρA j (V j 2 V b V j V b 2 ) Eq 4 A Pelton Wheel assembly can extract the energy from the impulse of the water from the cupped blades at a high hydraulic efficiency of 95 percent. The reason for this is that the velocity

5 of the incoming jet is deflected at approximately 175 degrees between two curved blades shown in figures 4 and 5. Five degrees on either side allows the water jets to separate from the consecutive blade moving into the previously occupied space. Separation decreases the resistance from the influx of water which would impede the angular velocity of the wheel. Optimal power is reached when the velocity of the blade, relative to the jet, is one half, proven by differentiating equation four and setting it equal to zero (Julien, 2014). Figure 5: Six Nozzle Pelton Wheel Vertical Crank Shaft (Advanced Design) Source: Swiss National Computing Centre Considering efficeny, the more advanced six jet pelton wheel system portrayed in figure 5 has amoung the highest hydralic efficency at 98 % (SNSC, 2011). An efficency that has the associated complexity and cost can be beneficial if the design life is much longer than a single or double jet acting on the wheel. A design life analysis must be conducted for a numeric estimate to choose the most economical design. The six jet design will have higher outputs of power than the single/double jet for the same discharge and head which over a period of time will make more money. Another aspect that is considered in the design of a hydro-electric powersource is the footprint of the structure that encloses the generator and all the esentails for operations. The vertical shaft has a smaller footprint than a horizontal shaft, however the vertical shaft requires a higher level off the ground for the generator and other euquiptment used in power generation (Atthanayake, 2009). Once the hydraulic energy has been transformed to mechanical shaft work, this enters the generator which will produce the electrical energy needed at peak hours of the day, or continuously throughout the day depending on the regional situation. The most efficiency developed from this process is nearly 90 percent which is from hydraulic energy to mechanical energy to electricity.

6 Gilkes, one of the leading global manufacturers of Pelton wheels, has typical design values shown in figure 6 below. In addition to design values of Pelton wheels, this figure shows how this type of turbine compares with two other types, the Turgo and the Francis. The Pelton wheel is suited for high head and lower discharges, while the Francis can use lower head sources with more discharge. The power will not be sacrificed in either case, the turbine must fit the site where it will be in service. Figure 6: Gilkes Pelton Wheel Power Generated (MW) Versus Discharge ( m3 s ) & Head (m) compared to two hydro-machines

Uses of the Pelton Wheel Since the Pelton wheel works best with high head and low discharge, mountainous areas potentially benefit the most from using them.

7 Uses of the Pelton Wheel Since the Pelton wheel works best with high head and low discharge, mountainous areas potentially benefit the most from using them. An advantage of Pelton wheels over other power generators is that the Pelton wheel is able to generate a good amount of energy from just a small brook, provided the head is large enough. This allows for electricity generating ability in hard to reach areas and third world countries. Due to the compact shape of the Pelton wheel, installation of these systems is much easier, making them more desirable for implementation. An example of a good setup could be the Hongping power station of China, shown in Figure 7 below, using a nearby stream and diverting some flow for use in hydropower. Figure 7. Hongping power station Due to the Pelton wheel s convenient system, the Pelton Water Wheel company says, It is no exaggeration to say that, in this way, a small trout brook with a high head will often furnish as much power as a large stream under a low head, in a much more convertible form and at probably not more that one-fourth the outlay (1909). As opposed to other methods of hydropower, the Pelton wheel avoids many common difficulties that a hydropower plant may experience. The Pelton Water Wheel company also says: All mountainous regions, particularly those in tropical countries, such as Mexico, Central and South America, present conditions which offer the most serious objections to the turbine wheel. The streams furnishing power in such locations are subject to sudden freshets from

8 excess of rainfall, and carry, at such times, grit and sand sufficient to destroy any turbine in a very short time. They also carry roots, leaves and other trash that fill the vanes and choke the wheels to such an extent as to often prevent their running until the obstructions are removed, involving a degree of unreliability that discredits the many advantages such a power ought always to afford. The Pelton Wheel, on the contrary is constructed with a perfectly free discharge, and the buckets will not choke up by anything that may be thrown upon them, thus making it absolutely reliable (1909). For a more hands-on approach, a model of a Pelton wheel was created using a milk jug, some spoons, a long plastic tube (for use as the penstock), a garden hose and a tree. Figure 8 shows what the experiment looked like. Figure 8. Pelton Model By hooking the plastic tube and garden hose together on the tree, the water was then allowed to flow down and cause the wheel to rotate. This was to show how a small amount of water with a high head could be used to make electricity. The following link gives a video of the model in action. During the 15 second video, the wheel makes 32 rotations, so the wheel makes about 2.1 rotations per second or 13.2 rad/s. The average diameter of the wheel was 0.14m. This means the velocity of the bucket was then m/s. Under ideal conditions, a jet velocity will be twice that of the bucket s velocity. In this case, the wheel was under minimal resistance since it was

9 not being operated as a generator. Since there is lower resistance, the velocity of the jet will be assumed to be 1.2 times greater than that of the bucket, or 1.1 m/s. The diameter of the jet was about 0.01m and thus gave an area of 7.85 x10-5 m 2. Using these variables and plugging them into equation four from above gives about 0.03 watts of power. Since this example uses a tree at about 4.6 meters high with a garden hose at a low discharge, this low amount of power generation makes sense.

10 References Atthanayake, U. I. (2009). International Journal of Engineering IJET-IJENS Vol:09 No:09. Retrieved from Csanyi, Edvard. "Lester Allan Pelton The Father of Hydroelectric Power." EEP Electrical Engineering Portal RSS. N.p., 8 June Web. 01 Nov Retrieved from Gilkes. (2014). Pelton Turbine Manufacturers - Gilkes Product Range. Retrieved from Julien, Pierre Y. (10/6/2014). Turbines and Hydro-machinery Handout. CIVE 401. Lecture conducted from Colorado State University, Fort Collins, CO. Pelton Water Wheel Company. The Pelton Water Wheel: The Pelton System of Power Retrieved from PA11&dq=pelton+wheels+in+mountainous+regions&source=bl&ots=mSD8gLZPN8&si g=9l_q957pi495c6houcmql8ez7oc&hl=en&sa=x&ei=ntcviaob4wvyatc8okyaq&ved=0cdyq6aewba#v=onepage&q=pelton%20wheels %20in%20mountainous%20regions&f=false "Pelton Waterwheel Collection." Landmarks. ASME, n.d. Web. 01 Nov Retrieved from pelton-waterwheel-collection. Shortridge, Robert W. "Lester Pelton and His Water Wheel." HydroReview (1989): HydroWorld. HydroWorld. Web. 1 Nov Retrieved from Swiss National Supercomputing Centre. (2011). PRACE Supercomputers, Software and Applications (Image). Retrieved from ?task=article&id=205

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,