# Francis turbine

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Side-view cutaway of a vertical Francis turbine. Here water enters horizontally in a spiral shaped pipe (penstock) wrapped around the outside of the turbine's rotating runner and exits vertically down through the center of the turbine.

The Francis turbine is a type of water turbine that was developed by James B. Francis in Lowell, Massachusetts.[1] It is an inward-flow reaction turbine that combines radial and axial flow concepts.

Francis turbines are the most common water turbine in use today. They operate in a water head from 10 to 650 meters (33 to 2,133 feet) and are primarily used for electrical power production. The turbine powered generator power output generally ranges from 10 to 750 megawatts, though mini-hydro installations may be lower. Penstock (input pipes) diameters are between 1 and 10 meters (3 and 33 feet). The speed range of the turbine is from 83 to 1000 rpm. Wicket gates around the outside of the turbine's rotating runner adjust the water flow rate through the turbine for different water flow rates and power production rates. Francis turbines are almost always mounted with the shaft vertical to keep water away from the attached generator and to facilitate installation and maintenance access to it and the turbine.

## Development

Francis turbine parts
Pawtucket Gatehouse in Lowell, Massachusetts; site of the first Francis turbine
Francis Runner, Grand Coulee Dam

Water wheels of different types have been used historically for over 1000 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 was available. After electric generators were developed in the late 1800s turbines were a natural source of generator power where potential hydro-power sources existed.

In 1826 Benoit Fourneyron developed a high efficiency (80%) outward-flow water turbine. Water was directed tangentially through the turbine runner, causing it to spin. Jean-Victor Poncelet designed an inward-flow turbine in about 1820 that used the same principles. S. B. Howd obtained a U.S. 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 wheeled powered textile factory city of Lowell, Massachusetts, improved on these designs to create a turbine with 90% efficiency. 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 confident design of high efficiency turbines to exactly match a site's water flow and water pressure (water head) conditions.

## Components

A Francis turbine consists of the following main parts:

Spiral Casing: The spiral casing around the runner of the turbine is known as volute casing. All throughout its length, it has numerous openings at regular intervals to allow the working fluid to impound on the blades of the runner. these openings convert the pressure energy of the fluid into momentum energy just before the fluid impound on the blades. to maintain a constant flow rate despite the fact that numerous openings have been provided for the fluid to gain entry to the blades,the cross-sectional area of this casing decreases uniformly along the circumference.

Guide or Stay Vanes: The primary function of the guide or stay vanes is to convert the pressure energy of the fluid into the momentum 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 as these are the centers where the fluid strikes and the tangential force of the impact causes the shaft of the turbine to rotate and hence electricity is produced. In this part one has to be very careful about the blade angles at inlet and outlet as these are the major parameters affecting the power production.

Draft tube: The draft tube is a conduit which connects the runner exit to the tail race where the water is being finally discharged from the turbine. The primary function of the draft tube is to reduce the velocity of the discharged water to minimize the loss of kinetic energy at the outlet. This permits the turbine to be set above the tail water without any appreciable drop of available head. The purpose of providing a draft tube will be better understood if we carefully study the net available head across a reaction turbine.

## Theory of operation

Three Gorges Dam Francis turbine runner

The Francis turbine 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 in the blades of the turbine, quantified by the expression of Degree of reaction, while the remaining part of the energy 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.

## Blade efficiency

Ideal velocity diagram, illustrating that in ideal cases the whirl component of outlet velocity is zero and the flow is completely axial

Usually the flow velocity (velocity perpendicular to the tangential direction) remains constant throughout, Vf1= Vf2 i.e. and is equal to that at the inlet to the draft tube.Using Euler turbine equation, E/m=e=Vw1U1 where, e is the energy transfer to the rotor per unit mass of the fluid.From the inlet velocity triangle:

Vw1= Vf1 cotα1 and

U1=Vf1(cotα1+cotβ1)

Therefore,

e=V2f1cotα1(cotα1+cotβ1)

The loss of kinetic energy per unit mass becomes V2f2/2.

Therefore, neglecting friction, the blade efficiency becomes

ηb=e/(e+V2f2/2).

i.e. ηb = $\frac {2V_{f1}^2(\cot\alpha_1(\cot\alpha_1+\cot\beta_1))}{V_{f2}^2+ 2V_{f1}^2(\cot\alpha_1(\cot\alpha_1+\cot\beta_1))} \,$

## Degree of reaction

Actual velocity diagram, illustrating that the whirl component of the outlet velocity is non-zero

Degree of reaction can be defined as the ratio of pressure energy change in the blades to total energy change of the fluid.this means that it is basically a ratio indicating the fraction of total change in fluid pressure energy occurring in the blades of the turbine. Rest of the changes occur in the stator blades of the turbines and the volute casing as it has a varying crossectional area.For example,if the degree of reaction is given to be 50% that will mean that half of 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 that will mean that the energy changes due to the rotor blades is zero and this special case pertains to Pelton Turbine.

R=e-1/2(V12-Vf22)/e

Now, putting the value of 'e' from above and using (V21-V2f2=V2f1cotα2 as Vf2=Vf1)

R=1-cotα1/2(cotα1+cotβ1)

## Application

Francis Inlet Scroll, Grand Coulee Dam
Small Swiss-made Francis turbine

Francis turbines may be designed for a wide range of heads and flows. This, along with their high efficiency, has made them the most widely used turbine in the world. Francis type units cover a head range from 20 to 700 meters (100 to 2,300 feet), and their connected generator output power varies from just a few kilowatts up to one gigawatt. Large Francis turbines are individually designed for each site to operate with the given water supply and water head at the highest possible efficiency, typically over 90%.

In addition to electrical production, they may also be used for pumped storage, where 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, etc. act as large energy storage sources to store "excess" electrical energy in the form of water in elevated reservoirs. This is one of only a few ways that temporary excess electrical capacity can be stored for later utilization.

## References

Bibliography

• Layton, Edwin T. "From Rule of Thumb to Scientific Engineering: James B. Francis and the Invention of the Francis Turbine," NLA Monograph Series. Stony Brook, NY: Research Foundation of the State University of New York, 1992.
• S.M.Yahya,page number 13, fig 1.14