Test: Francis Turbine - Civil Engineering (CE) MCQ

For the maximum efficiency of all the reaction turbines (Including Francis Turbine) angle of absolute velocity vector at the outlet is 90 degree as shown in the figure

General velocity diagram of the reaction turbine

In the case of Maximum efficiency, α2 = 90°, where α2 is the angle of absolute velocity vector at the outlet.

β₁ and β₂ are runner blade angle
α₁ and α₂ are guide vane angle
u1 and u₂ velocity of blade
V_r1andVr2 are relative velocity of water flow
U1 and U₂ are absolute velocity of flow of water
When discharge enters radially and leaves radially.
⇒ 1) β₁ = 90° i.e. runner blade angle at inlet is 90°
2) α₂ = 90° i.e. Guide vane angle at outlet is 90°
3) V_r1 is radial at Inlet
4) V₂ is radial at exist.
∴ For Francis turbine, the absolute velocity is radial at the outlet.
Hydraulic Efficiency of Francis Turbine:

In Francis Turbine the medium head is required generally in the range of (100-500) meters. In Kaplan Turbine very low head is required, generally less than 100-meter

In Francis Turbine medium flow rate is required. In Kaplan Turbine very large flow rate is required

• High-head turbine: In this type of turbine, the net head varies from 150m to 2000m or even more, and these turbines require a small quantity of water. Example: Pelton wheel turbine.
• Medium head turbine: The net head varies from 30m to 150m, and also these turbines require a moderate quantity of water. Example: Francis turbine.
• Low-head turbine: The net head is less than 30m and also these turbines require a large quantity of water. Example: Kaplan turbine.

Concept:
Power developed in a reaction turbine is given by:

Where,
ρ = density of the water (kg/m³)
Q = Discharge through the turbine (m³/s)
H = Head (m)
ηo = the overall efficiency of the turbine 
Calculation:
ρ = 1000 kg/m³
Q = 100 m3/sec
H = 100 m, Efficiency = 80%
Power developed in a reaction turbine is given by:
P =  1000 × 100 × 10 × 100 × 0.80 / 1000
P = 80000 kW = 80000000 W

Impulse Turbine: If at the inlet of the turbine, the energy available is only kinetic energy, the turbine is known as impulse turbine. e.g. a Pelton wheel turbine.
Reaction Turbine: If at the inlet of the turbine, the water possesses kinetic energy as well as pressure energy, the turbine is known as a reaction turbine. e.g. e Francis and Kaplan turbine.
Tangential flow turbines: In this type of turbine, the water strikes the runner in the direction of the tangent to the wheel. Example: Pelton wheel turbine
Radial flow turbines: In this type of turbine, the water strikes in the radial direction. accordingly, it is further classified as

• Inward flow turbine: The flow is inward from periphery to the centre (centripetal type); Example: old Francis turbine
• Outward flow turbine: The flow is outward from the centre to periphery (centrifugal type); Example: Fourneyron turbine

Axial flow turbine: The flow of water is in the direction parallel to the axis of the shaft. Example: Kaplan turbine and propeller turbine
∴ Francis turbine is a radial inward flowing reaction turbine.

Flow ratio
The flow ratio of Francis turbine is defined as the ratio of the velocity of flow at the inlet to the theoretical jet velocity.

In the case of Francis turbine,
Flow ratio varies from 0.15 to 0.3
Speed ratio varies from 0.6 to 0.9
Calculation:

= 0.2

Concept:
The overall efficiency η_o of turbine = volumetric efficiency (η_v)× hydraulic efficiency (η_h)× mechanical efficiency (η_m)

Water Power = ρ × Q × g × h 
Calculation:
Given:
η_o = 0.8, Head h = 10 m, and Q = 1 m³/s.

Since Francis Turbine is a reaction turbine, part of the available head is converted to velocity head. It is not entirely converted to velocity head. The rest of the available head is converted into pressure head.

Smooth flow and flow without separation (eddiless flow) can be ensured when the cross sectional profile of the guide vanes are aerofoil in nature. Aerofoil shape is used in airplane wings to ensure smooth flow too. Rectangular profiles are not effective in guiding the water into the runner. Elliptical profiles will cause more drag, finally ending up with turbine inefficiency.

Considering the velocity diagram of Francis turbine at the inlet for a fast runner, vane angle is an obtuse angle. Whereas, it is right angle for medium runner and an acute angle for a slow runner.

Fast runners have forward curved blades, where slow runners have backward curved blades. The blades shown in the figure are backward curved blades of a runner, which are used for slow runners.