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52-542: The process of arriving at the modern Francis runner design took from 1848 to approximately 1920. It became known as the Francis turbine around 1920, being named after British-American engineer James B. Francis who in 1848 created a new turbine design. Francis turbines are primarily used for producing electricity. The power output of the electric generators generally ranges from just a few kilowatts up to 1000 MW, though mini-hydro installations may be lower. The best performance

104-406: A design parameter. Stages having 50% degree of reaction are used where the pressure drop is equally shared by the stator and the rotor for a turbine . This reduces the tendency of boundary layer separation from the blade surface avoiding large stagnation pressure losses. If R= 1 ⁄ 2 then from the relation of degree of reaction,| C | α2 = β3 and the velocity triangle (Figure 4.)

156-573: A reservoir is filled by the turbine (acting as a pump) driven by the generator acting as a large electrical motor during periods of low power demand, and then reversed and used to generate power during peak demand. These pump storage reservoirs act as large energy storage sources to store "excess" electrical energy in the form of water in elevated reservoirs. This is one of a few methods that allow temporary excess electrical capacity to be stored for later utilization. James B. Francis James Bicheno Francis (May 18, 1815 – September 18, 1892)

208-427: A vertical shaft, to isolate water from the generator. This also facilitates installation and maintenance. Water wheels of different types have been used for more than 1,000 years to power mills of all types, but they were relatively inefficient. Nineteenth-century efficiency improvements of water turbines allowed them to replace nearly all water wheel applications and compete with steam engines wherever water power

260-436: A wide range of heads and flows. This versatility, along with their high efficiency, has made them the most widely used turbine in the world. Francis type units cover a head range from 40 to 600 m (130 to 2,000 ft), and their connected generator output power varies from just a few kilowatts up to 1000 MW. Large Francis turbines are individually designed for each site to operate with the given water flow and water head at

312-509: Is Q = 3.33 h 1 3 / 2 ( L − 0.2 h 1 ) {\textstyle Q=3.33h_{1}^{3/2}(L-0.2h_{1})} where: Q is the discharge in cubic feet per second over the weir, L is the length of the weir in feet, and h 1 is the height of the water above the top of the weir. He remained at the Locks and Canal Company for his entire career, until retirement in 1884 at

364-479: Is a corresponding pressure change. Another useful definition used commonly uses stage velocities as: h 2 − h 3 = 1 2 ( V r 3 2 − V r 2 2 ) + 1 2 ( U 2 2 − U 3 2 ) {\displaystyle h_{2}-h_{3}={\frac {1}{2}}(V_{r3}^{2}-V_{r2}^{2})+{\frac {1}{2}}(U_{2}^{2}-U_{3}^{2})}

416-404: Is a type of reaction turbine, a category of turbine in which the working fluid comes to the turbine under immense pressure and the energy is extracted by the turbine blades from the working fluid. A part of the energy is given up by the fluid because of pressure changes occurring on the blades of the turbine, quantified by the expression of degree of reaction , while the remaining part of the energy

468-409: Is again very useful when the rotor blade angle and rotor vane angle are defined for the given geometry. The Figure 3 alongside shows the variation of total-to-static efficiency at different blade loading coefficient with the degree of reaction. The governing equation is written as where Δ W 2 U 2 {\displaystyle {\frac {\Delta W}{2U^{2}}}}

520-433: Is defined as the fraction of energy transfer by change in static head to the total energy transfer in the rotor: R = Static pressure rise in rotor Total pressure rise in stage {\displaystyle R={\frac {\text{Static pressure rise in rotor}}{\text{Total pressure rise in stage}}}} Most turbo machines are efficient to a certain degree and can be approximated to undergo isentropic process in

572-405: Is defined as the ratio of energy transfer by the change in static head to the total energy transfer in the rotor: R = Isentropic enthalpy change in rotor Isentropic enthalpy change in stage {\displaystyle R={\frac {\text{Isentropic enthalpy change in rotor}}{\text{Isentropic enthalpy change in stage}}}} For a gas turbine or compressor it is defined as

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624-471: Is equal to that at the inlet to the draft tube. Using the Euler turbine equation, E / m = e = V w1 U 1 , where e is the energy transfer to the rotor per unit mass of the fluid. From the inlet velocity triangle, and Therefore The loss of kinetic energy per unit mass at the outlet is V f2 /2 . Therefore, neglecting friction, the blade efficiency becomes i.e. Degree of reaction can be defined as

676-445: Is extracted by the volute casing of the turbine. At the exit, water acts on the spinning cup-shaped runner features, leaving at low velocity and low swirl with very little kinetic or potential energy left. The turbine's exit tube is shaped to help decelerate the water flow and recover the pressure. Usually the flow velocity (velocity perpendicular to the tangential direction) remains constant throughout, i.e. V f1 = V f2 and

728-455: Is necessary, as these are major parameters affecting power production. Draft tube : The draft tube is a conduit that connects the runner exit to the tail race where the water is discharged from the turbine. Its primary function is to reduce the velocity of discharged water to minimize the loss of kinetic energy at the outlet. This permits the turbine to be set above the tail water without appreciable drop of available head. The Francis turbine

780-422: Is seen when the head height is between 100–300 metres (330–980 ft). Penstock diameters are between 1 and 10 m (3.3 and 32.8 ft). The speeds of different turbine units range from 70 to 1000  rpm . A wicket gate around the outside of the turbine's rotating runner controls the rate of water flow through the turbine for different power production rates. Francis turbines are usually mounted with

832-730: Is substituted as φ and ( tan ⁡ β 3 − tan ⁡ β 2 ) {\displaystyle (\tan {\beta _{3}}-\tan {\beta _{2}})} as tan ⁡ β m {\displaystyle \tan {\beta _{m}}} giving R = ϕ tan ⁡ β m . {\displaystyle R=\phi \tan {\beta _{m}}.} The degree of reaction now depends only on φ and tan ⁡ β m {\displaystyle \tan {\beta _{m}}} which again depend on geometrical parameters β 3 and β 2 i.e.

884-458: Is symmetric. The stage enthalpy gets equally distributed in the stage (Figure 5.) . In addition the whirl components are also the same at the inlet of rotor and diffuser . Stage having reaction less than half suggest that pressure drop or enthalpy drop in the rotor is less than the pressure drop in the stator for the turbine. The same follows for a pump or compressor as shown in Figure 6. From

936-402: Is the enthalpy drop in the rotor and h 01 − h 03 = h 02 − h 03 = ( U 2 V w 2 − U 1 V w 1 ) {\displaystyle h_{01}-h_{03}=h_{02}-h_{03}=(U_{2}V_{w2}-U_{1}V_{w1})} is the total enthalpy drop. The degree of reaction

988-411: Is the stage loading factor. The diagram shows the optimization of total - to - static efficiency at a given stage loading factor, by a suitable choice of reaction. It is evident from the diagram that for a fixed stage loading factor that there is a relatively small change in total-to-static efficiency for a wide range of designs. The degree of reaction contributes to the stage efficiency and thus used as

1040-950: Is then expressed as R = 1 2 ( V r 3 2 − V r 2 2 ) + 1 2 ( U 2 2 − U 3 2 ) U 2 V w 2 − U 1 V w 1 {\displaystyle R={\frac {{\frac {1}{2}}(V_{r3}^{2}-V_{r2}^{2})+{\frac {1}{2}}(U_{2}^{2}-U_{3}^{2})}{U_{2}V_{w2}-U_{1}V_{w1}}}} For axial machines U 2 = U 1 = U {\displaystyle U_{2}=U_{1}=U} , then R = V r 3 2 − V r 2 2 2 U ( V w 3 + V w 2 ) {\displaystyle R={\frac {V_{r3}^{2}-V_{r2}^{2}}{2U(V_{w3}+V_{w2})}}} The degree of reaction can also be written in terms of

1092-838: The Croton River in New York. He also consulted on the dam at Saint Anthony Falls on the Mississippi River . Their son James fought in the American Civil War as a second lieutenant in 1861. He was wounded in the hand at the Battle of Antietam as a captain , and finished the war in July 1865 as lieutenant colonel . Francis was elected as a member of the American Philosophical Society in 1865. In 1845, Francis developed

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1144-470: The Forest Hills , Hyde Park , Franklin park and Roslindale sections of the city that were subject to flooding. Francis stayed active on all levels of involvement in the city of Lowell, and served as an alderman from 1862 to 1864. In 1865, Francis researched and published his findings on cast iron, and its use in structural columns in "The Strength of Cast-Iron Columns". In 1874, Francis served on

1196-694: The South Fork Dam in Johnstown, Pennsylvania, broke, killing over 2,200 people.   Although the report was completed by January 1890, it was immediately suppressed and not released to other ASCE members or the public until mid-1891, two years after the 1889 flood.   Francis himself presented the results of the investigation at the ASCE convention in Chattanooga, Tennessee.  The other three committee members did not attend.  Although Francis’ name headed

1248-607: The American Society of Civil Engineers committee to investigate the cause of the breach of the Mill River dam in Massachusetts .   Also on the committee were engineers Theodore Ellis and William Worthen. The investigation proceeded quickly and its report was published within a month of the disaster. It concluded that no engineer was responsible for the design and that it was the “work of non-professional persons”. “The remains of

1300-551: The age of 69, and remained on as a consultant right up until his death. His son James took over as chief engineer. The rest of his life he spent with his wife Sarah, and their six children in their home on Worthen Street, which was Whistler's old home and now is the Whistler House Museum of Art . Francis was called to duty in 1889 as a member of an ASCE committee to examine the cause of the Johnstown Flood disaster when

1352-452: The age of 77, and is buried at Lowell Cemetery under a massive pillar of cut granite stones, symbolizing the stones used to make the canals. For all his contributions to the world of engineering and his personal generosity, the following are named in his honor: Today, the Francis turbine is the most widely used water turbine in the world, including China's new Three Gorges Dam as the world's second largest hydroelectric power station in

1404-500: The city from great disaster Francis was awarded a massive silver pitcher and a salver by the City of Lowell. In 1886, Francis teamed up with two other civil engineers; Eliot C. Clarke and Clemens Herschel to study and publish their findings in the "Prevention of Floods in the Valley of Stony Brook" which laid out a flood prevention system for the city of Boston . The detailed study reviewed

1456-571: The dam indicate defects of workmanship of the grossest character.” Francis originated scientific methods of testing hydraulic machinery, and was a founding member of the American Society of Civil Engineers and its president in 1880. In 1883, Francis completed his calculation standards for water flow rates, now known as the Francis equation or Francis formula , usually used in fluid dynamics in conjunction with calculating weirs . The equation

1508-406: The design of high-efficiency turbines to precisely match a site's water flow and pressure ( water head ). A Francis turbine consists of the following main parts: Spiral casing : The spiral casing around the runner of the turbine is known as the volute casing or scroll case. Throughout its length, it has numerous openings at regular intervals to allow the working fluid to impinge on the blades of

1560-545: The first sprinkler systems ever devised in the United States. However, any use of the system would flood the entire structure and its contents. It was not until 1875 that Henry S. Parmelee invented a sprinkler head that activated only one head at a time. Francis became fascinated with and tinkered with turbine designs, after Uriah A. Boyden first demonstrated his Boyden turbine in Lowell. The two engineers worked on improving

1612-477: The gates saved the city of Lowell from the devastating floods of 1852, and again in 1936 , 1938 , 2006 , and 2007 by preventing the Merrimack River from entering the canal system. However, arson damage to the wooden gate in the 1970s, and the difficult method of dropping it (by breaking a large chain link) prompted the city to use a more modern steel-beam bulkhead in its place in 2006. For his efforts in saving

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1664-528: The geometry of the turbomachine as obtained by R = V f 2 U ( tan ⁡ β 3 − tan ⁡ β 2 ) {\displaystyle R={\frac {V_{f}}{2U}}(\tan {\beta _{3}}-\tan {\beta _{2}})} where β 3 is the vane angle of rotor outlet and β 2 is the vane angle of stator outlet. In practice V f 2 U {\displaystyle {\tfrac {V_{f}}{2U}}}

1716-436: The guide and stay vanes is to convert the pressure energy of the fluid into kinetic energy. It also serves to direct the flow at design angles to the runner blades. Runner blades : Runner blades are the heart of any turbine. These are the centers where the fluid strikes and the tangential force of the impact produces torque causing the shaft of the turbine to rotate. Close attention to design of blade angles at inlet and outlet

1768-455: The highest possible efficiency, typically over 90% (to 99%). In contrast to the Pelton turbine , the Francis turbine operates at its best completely filled with water at all times. The turbine and the outlet channel may be placed lower than the lake or sea level outside, reducing the tendency for cavitation . In addition to electrical production , they may also be used for pumped storage , where

1820-413: The isentropic process beginning from stator inlet at 1 to rotor outlet at 3. And 2 to 3s is the isentropic process from rotor inlet at 2 to rotor outlet at 3. The velocity triangle (Figure 2.) for the flow process within the stage represents the change in fluid velocity as it flows first in the stator or the fixed blades and then through the rotor or the moving blades. Due to the change in velocities there

1872-458: The late 1840s and early 1850s, completed the 5.6 mile long Lowell canal system, and greatly increased the industrial power of the thriving industrial city's mill complexes. During his work on the Lowell systems, Francis was also consulted on many other water projects nationwide. When New York needed to increase their water supply, he consulted on the construction of the Quaker Bridge Dam on

1924-464: The ratio of isentropic heat drop in the moving blades (the rotor) to the sum of the isentropic heat drops in both the fixed blades (the stator) and the moving blades: R = Isentropic heat drop in rotor Isentropic heat drop in stage {\displaystyle R={\frac {\text{Isentropic heat drop in rotor}}{\text{Isentropic heat drop in stage}}}} In pumps , degree of reaction deals in static and dynamic head. Degree of reaction

1976-432: The ratio of pressure energy change in the blades to total energy change of the fluid. This means that it is a ratio indicating the fraction of total change in fluid pressure energy occurring in the blades of the turbine. The rest of the changes occur in the stator blades of the turbines and the volute casing as it has a varying cross-sectional area. For example, if the degree of reaction is given as 50%, that means that half of

2028-452: The relation for degree of reaction, | C | α2 > β3. Stage having reaction more than half suggest that pressure drop or enthalpy drop in the rotor is more than the pressure drop in the stator for the turbine. The same follows for a pump or compressor. From the relation for degree of reaction,| C | α2 < β3 which is also shown in corresponding Figure 7. This is special case used for impulse turbine which suggest that entire pressure drop in

2080-551: The report, the de facto chairman of the committee was Max Becker, a railroad engineer based in Pittsburgh with virtually no experience in dams or hydraulic engineering.  According to Francis, it was Becker who delayed the release of the report.  A detailed discussion of the South Fork investigation, the participating engineers, and the science behind the 1889 flood was published in 2018. Francis died on September 18, 1892, at

2132-409: The rotating blades of a compressor or turbine , to the static pressure change in the compressor or turbine stage. Alternatively it is the ratio of static enthalpy change in the rotor to the static enthalpy change in the stage. Various definitions exist in terms of enthalpies, pressures or flow geometry of the device. In case of turbines, both impulse and reaction machines, degree of reaction

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2184-400: The runner. These openings convert the pressure energy of the fluid into kinetic energy just before the fluid impinges on the blades. This maintains a constant velocity despite the fact that numerous openings have been provided for the fluid to enter the blades, as the cross-sectional area of this casing decreases uniformly along the circumference. Guide and stay vanes : The primary function of

2236-554: The same principles. S. B. Howd obtained a US patent in 1838 for a similar design. In 1848 James B. Francis , while working as head engineer of the Locks and Canals company in the water wheel-powered textile factory city of Lowell, Massachusetts , improved on these designs to create more efficient turbines. He applied scientific principles and testing methods to produce a very efficient turbine design. More importantly, his mathematical and graphical calculation methods improved turbine design and engineering. His analytical methods allowed

2288-1069: The stage. Hence from T d s = d h − d p ρ , {\displaystyle Tds=dh-{\frac {dp}{\rho }},} it is easy to see that for isentropic process ∆ H ≃ ∆ P . Hence it can be implied R = Δ H  (Rotor) Δ H  (Stage) {\displaystyle R={\frac {\Delta H{\text{ (Rotor)}}}{\Delta H{\text{ (Stage)}}}}} The same can be expressed mathematically as: R = ∫ 3 s s 2 s dh ∫ 3 s s 1 dh or ∫ 3 s s 2 s dp ∫ 3 s s 1 dp {\displaystyle R={\frac {\int _{3ss}^{2s}{\textrm {dh}}}{\int _{3ss}^{1}{\textrm {dh}}}}\quad {\textrm {or}}\quad {\frac {\int _{3ss}^{2s}{\textrm {dp}}}{\int _{3ss}^{1}{\textrm {dp}}}}} Where 1 to 3ss in Figure 1 represents

2340-876: The total energy change of the fluid is taking place in the rotor blades and the other half is occurring in the stator blades. If the degree of reaction is zero it means that the energy changes due to the rotor blades is zero, leading to a different turbine design called the Pelton Turbine . The second equality above holds, since discharge is radial in a Francis turbine. Now, putting in the value of 'e' from above and using V 1 2 − V f 2 2 = V f 1 2 cot ⁡ α 2 {\displaystyle V_{1}^{2}-V_{f2}^{2}=V_{f1}^{2}\cot \alpha _{2}} (as V f 2 = V f 1 {\displaystyle V_{f2}=V_{f1}} ) Francis turbines may be designed for

2392-748: The turbine. And in 1848, Francis and Boyden successfully improved the turbine with what is now known as the Francis turbine . Francis's turbine eclipsed the Boyden turbine in power by 90%. In 1855, Francis published these findings in the "Lowell Hydraulic Experiments". In 1850, Francis ordered the construction of the Great Gate over the Pawtucket Canal to protect the downtown mills from any devastating floods. This project quickly became known as "Francis's Folly", given that no one believed it would work, let alone ever be needed. But less than two years later, in 1852,

2444-441: The vane angles of stator outlet and rotor outlet. Using the velocity triangles degree of reaction can be derived as: R = 1 2 + V f 2 U ( tan ⁡ β 3 − tan ⁡ α 2 ) {\displaystyle R={\frac {1}{2}}+{\frac {V_{f}}{2U}}(\tan {\beta _{3}}-\tan {\alpha _{2}})} This relation

2496-413: The world, with a future installed capacity of 22,500 MW. With the incorporation of the Francis turbine into almost every hydroelectric dam built since 1900, it is responsible for generating almost one fifth of all the world's electricity: Degree of reaction In turbomachinery , degree of reaction or reaction ratio (denoted R ) is defined as the ratio of the change in static pressure in

2548-641: Was a British-American civil engineer, who invented the Francis turbine . James Francis was born in South Leigh , near Witney , Oxfordshire, in England, United Kingdom. He started his engineering career at the early age of seven as he worked as his father's apprentice at the Porth Cawl Railway and Harbor Works in South Wales . When he turned 18, he decided to emigrate to the United States, in 1833. His first job

2600-516: Was available. After electric generators were developed in the late 1800s, turbines were a natural source of generator power where potential hydropower sources existed. In 1826 the French engineer Benoit Fourneyron developed a high-efficiency (80%) outward-flow water turbine. Water was directed tangentially through the turbine runner, causing it to spin. Another French engineer, Jean-Victor Poncelet , designed an inward-flow turbine in about 1820 that used

2652-522: Was born March 30, 1840, and then they had five more children. In 1841 came his first major project for the company. Francis was to analyse how much water each mill factory was using from the company's channel system. Impressed by his abilities, the company named him "Manager of Locks and Canals" in 1845. As manager and chief engineer, Francis was responsible for the construction of the Northern Canal and Moody Street Feeder . These two canals, built in

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2704-760: Was in Stonington, Connecticut , as an assistant to the railway engineer George Washington Whistler Jr. , working on the New York and New Haven Railroad . A year later, James and his boss, Whistler, travelled north to Lowell, Massachusetts , where at the age of 19, he got a draftsman job with the Locks and Canal Company , and Whistler became chief engineer. A few years later, in 1837, Whistler resigned, and went to work on Russia's major railroads. Before departing, he appointed Francis chief engineer, and sold him his house on Worthen Street. In same year, James married Sarah W. Brownell in Lowell on July 12. Their first son, James Jr.,

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