DESIGN STEPS OF FRANCIS TURBINE

Main components of the francis turbine are sprial case,stay vanes,guide vanes,turbine runner and
draft tube.

The dimensions of these parts are dependent Practically all dimensions, features and characteristics of the desired turbine can be expressed as a function of the specific speed. Hence, specific speed is logical key to design of turbine and choice of turbine.

Ns=(N√P)/H^(5/4)  where,

N=the normal working speed(rpm)
P=power output of the turbine(kw)
H=effective head(m)

Discharge

H=effective head(ƞ_m)
O=overall efficiency(ƞ_h×ƞ_m )

where,
H=head of turbine
uniformly along the circumference to keep the fluid velocity constant in magnitude along its
path towards the stay vane/guide vane.

Draft tube transform velocity head to static head due to its increasing area and will reduce
effect of cavitation.

Tube Theory

P_2/w=P_a/w-H_s-((V_2^2-V_3^2)/2g-h_f )


, P_2/w is less than atm pressure.

Efficiency of draft tube
ƞ_d=(((V_2^2-V_3^2)/2gh_f ))/((V_2^2)/2g)

Where V2,P2 is velocity, pressure at section 2 V3 is velocity at section 3 Pa is atm pressure h_f is loss of energy between sections 2-2 and 3-3 mainly on the design discharge,head and the speed of the rotor of the generators.

Runner Design
The runner of a francis turbine is required is to be designed to develop a known power P when running at a known speed N rpm under a known head H.

The design of the runner involves the determination of its size and the vane angles.

Specific speed
It is determination of water flow rate transported through the turbine.

Q=P/(ƞ_O wH)

where,P=power output of the turbine(kw)
w=ρg(weight of fluid)

Diameter of Runner

At inlet(External)

D_1=√(Q/(〖(K〗_f √2gH)K_t πn))

At outlet(Internal)

D_2=D_1/2

where,
Q=discharge(m^3/s),
K_f=Flow ratio,K_f=V_f1/√2gH
n=B/D(ratio of width to diameter)
K_t=Vane thickness coefficient(<1)


Velocities

Flow Velocity
Flow velocity is the vector field that is used to describe fluid motion in a mathematical manner. The
entire length of the flow velocity is referred to as the flow speed.

At inlet
Vf1=Q/(K_t1 πD_1 B_1 )

At outlet
V_f1/V_f2 =(K_t2 πD_2 B_2)/(K_t1 πD_1 B_1)

Usually,it is presumed
V_f1=V_f2,K_t1=K_t2,B_2=2B_1

where,B_1=Width of runner vane at inlet(m)

B_2=Width of runner vane at outlet(m)

V_f1=V_f2=Velocity of flow(m/s)
V_w1=velocity of whirl(m/s)

Rim velocity(tangential velocity Tangential velocity is the linear speed of something
moving along a circular path(velocity along the rim).

At inlet
U1=(πD_1 N)/60

At outlet
U2=U1/2
where,

D_1=External diameter of runner(m)

N=the normal working speed(rpm)

Whirl velocity
Whirl velocity is the number of times in a second that a turbine can rotate, moving at a speed(velocity
due to rotation).

Vw1=(ƞ_h gH)/U1

where,
ƞ_h=(V_w1 U_1)/gH(hydraulic efficiency)
U_1=Tangential velocity at inlet(m/s)

Power
Wicket gates around the outside of the turbine's rotating runner control the rate of water flow
through the turbine for different power production rates.

P=ƞ_o wQH
Q=discharge(m^3/s)
ƞ_O=overall efficiency(ƞ_h×ƞ)
w=ρg(weight of fluid)


Number of Vanes
Number of Runner vanes
In order to avoid any pulsations,the runner vanes are Often made an odd number.
n=K√D
K=3.7 for slow runner
K=3 for normal runner
K=2.2 for fast runner

D=Runner diameter

Number of Guide vanes
n′=K′√D
K‘=2.5 for α_1 between 10° & 20°
K‘=3 for α_1 between 20° & 30°
K‘=3.5 for α_1 between 30° & 40°

The number of vanes varies from 16 to 24
Vane angle

Quide vane angle(α)
Tanα=V_f1/V_w2

Runner vane angle(θ) from inlet velocity triangle

Tanθ=V_f1/(V_w1-U1)
Runner vane angle(ø) from outlet velocity triangle

Tanø=V_f2/U2
where,U_1=Tangential velocity at inlet(m/s)
U_2=Tangential velocity at outlet(m/s)
V_f1=V_f2=Velocity of flow(m/s)
V_w1=velocity of whirl(m/s)

Design of Spiral Casing
The cross-sectional area of this casing decreases
At any angle q, the radius of casing is



Discharge per unit: Q

Draft tube





Draft tube transform velocity head to static head due to its increasing area and will reduce
effect of cavitation.

Tube Theory
P_2/w=P_a/w-H_s-((V_2^2-V_3^2)/2g-h_f ) , P_2/w is less than atm pressure.

Efficiency of draft tube

ƞ_d=(((V_2^2-V_3^2)/2gh_f))/((V_2^2)/2g)
Where V2,P2 is velocity, pressure at section 2
V3 is velocity at section
Pa is atm pressure
h_f is loss of energy between sections 2-2 and 3-3

Efficiencies

FRANCIS TURBINE

TURBINE

A Machine for producing continuous power in which a wheel or rotor typically fitted with vanes is made to revolve by a fast moving flow of water steam,gas ,air or other fluid .
The kinetic energy of the moving fluid is converted to Mechanical energy by the impulse or reaction of the fluid .
Key parts of a turbine are set of blades that catches the moving fluid ,the shaft that rotates as the blades moves and generator that is driven by the shaft.

TYPES OF TURBINE

• PELTON TURBINE
• KAPLAN TURBINE
• FRANCIS TURBINE

FRANCIS TURBINE

It is the most commonly used turbine used under medium head about 45-400 meter.It is a reaction turbine and is used for the electricity generation and is preferred more in comparison to kalpan and pelton turbines.
The important features of francis turbine is described below.

• Used under medium head 45-400m.
• Used under flow rate between 10-700cubic meter.
• Water enters into the runner Radially and leaves axially and so it is also called Mixed flow turbines
• Curved vanes are used and when water flows
• through the vanes a low pressure is created at oneside and high pressure is created at the other side due to which a lift force is created.
• Vanes have a bucket kind of shape at the outlet so water will hit and produce an impulse force before leaving the runner.
• Both impulse force and lift force will make the runner rotate.So Francis turbine is not a pure

Reaction turbine.

• Runner is connected to a generator with a help of a shaft for electricity generation.
• Arrangement of turbine shaft is fitted inside a casing .
• Flow of water takes place via a nozzle .
• Stay vanes and guide vanes are fitted and the purpose of them is to convert one part of potential energy to kinetic energy .
• Stay vanes directs the water flow into the runner section towards the blades.

WORKING OF FRANCIS TURBINE

As water enter the turbine through the inlet nozzle its velocity will decrease as it moves forward in the turbine but the continuous decrease in the area of spiral casing will not let it happen. Design of spiral casing makes shore that the water strike the each blade of the turbine as a constant speed. Blades are mounted on the runner. Design of the blade is like a thin air foil so when water flow over it low pressure is created at one point and high pressure is created on other side and motion take place from high pressure to low pressure. Lower side of the blade is like a bucket which use the impulse forces of water in the rotation.






If water flow rate change then governing mechanism came into use and change the angle of attack of water on to the blade so the turbine can work properly. After the water passes the blades it enter the draft tube whose continuous increase in area decrease the velocity of the water.

Figure shows the different parts associated with the francis turbine.Francis turbine is placed inside a casing and guide vanes are used as shown in the figure .Water from the penstock enters into the casing and reaches to the turbine blades where the lift force and impulse force rotates the blades .

APPLICATION OF FRANCIS TURBINE

• Electricity production can be estimated by the help of flowrate and head.
• Francis turbine may be designed for wide range of head and flow.
• It has high efficiency.
• They may be used as Pump.

ADVANTAGES

• Easy control on changing head.
• Size of runner and generator is small.
• Small change in efficiency over time.
• Operating head can be utilized even when the variation in tail water level is relatively largewhen compared to the total head.

DISADVANTAGES

• Unclean water can create problem 
• Cavitation is and ever present danger.
• Head 50 percent lower can be harmful effect on the effieciency as well as cavitation danger becomes more serious.