Francis turbine

Aim:

To study the performance characteristics of Francis turbine.

Apparatus:

1. Francis turbine test rig
2. Tachometer
3. Dead weights

Formulae:

1. Input power, `P_{i}=\gamma QH`   kW
2. Output power, `P_{o}=\frac{\piDNT}{60,000}`    kW
3. Efficiency, `\eta = (\frac{P_{i}}{P_{o}})` X `100`
4. Unit discharge, `Q_{u} = \frac{Q}{\sqrt{H}}`
5. Unit speed, `N_{u} = \frac{N}{\sqrt{H}}`
6. Unit power, `P_{u} = \frac{P_{o}}{H^{\frac{3}{2}}}`
7. Specific speed, `N_{s} = \frac{N\sqrt{P}}{H^{\frac{5}{4}}}` (at maximum efficiency)

where,
γ = Specific weight of water = 9.81   kN/m³
Q = Discharge in m³/sec = `= \frac{C_{d}a_{1}a_{2}\sqrt{2gH}}{\sqrt{a_{1}^{2}-a_{2}^{2}}}`
C_d = Coefficient of discharge of orificmeter
a₁ = Cross-sectional area of the pipeline in m² = `\frac{\pi d_{1}^{2}}{4}`
a₂ = Cross-sectional area at throat in orificemeter in m² = `\frac{\pi d_{2}^{2}}{4}`
d₁ = Diameter of the pipeline in m
d₂ = Throat diameter of the orficemeter in m
h = Head difference between throat and inlet in orificemeter in m = 10(p₁ - p₂)
p₁ = Pressure gauge reading at the inlet section in kg/cm²
p₂ = Pressure gauge reading at the throat of orificemeter in kg/cm²
H = Water supply head in m = 10(P)
P = Delivery pressure in kg/cm²
D = Diameter of the brakedrum in m
N = Turbine speed in r.p.m
T = Net brake load in N = 9.81(T₁ - T₂ + T₀)
T₀ = Weight of the hanger in kg
T₁ = Dead weight placed on hanger in kg
T₂ = Spring balance reading in kg

Theory:

Francis turbine is a mixed flow type of reaction turbinein which water enters the runner radially at its outer periphery and leaves axially at its center. It is used in medium head dams to convert hydraulic energy in to mechanical energy and electrical energy.



Francis turbine test rig consists of a spiral casing, an outer bearing pedestal and rotor assembly with runner, shaft and brakedrum, all mounted on a suitably sturdy cast iron base plate. A straight conical draft tube is provided for the purpose of regaining the kinetic energy from exist water. A transparent hollow perspex cylinder is provided in between the draft bend and the casing for the purpose of observation of flow at exit of runner. A rope brake arrangement is provided to load the turbine. Output of the turbine can be controlled by adjusting the guidevanes for which a hand wheel is provided. The net supply head on the turbine is measured by a pressure gauge and vacuum gauge.

Procedure:

1. Prime the pump with water.
2. Keep the gate opening(100% and 75%) to the required position. Open the gate valve.
3. Start the motor. Allow the water in to the turbine and turbine starts to rotate.
4. By maintaining constant gate opening, load the turbine by placing dead weights on the weight hangerfixed to brakedrum with rope.
5. Note down the following readings after placing each dead weight on the hanger:
 a) Delivery pressure, P
 b) Speed of the turbine, N measured with tachometer
 c) Presuure gauge readings, p₁ and p₂, corresponding to orificemeter
 d) Load placed on weight hanger, T₁
 e) Spring balance reading, T₂
6. Repeat the procedure to obtain atleast 5 sets of readings by varying the load for each gate opening.

Observations:

Diameter of brakedrum, D = .......... m
Coefficient of discharge of orificemeter, C_d = ..........
Diameter of the pipeline, d₁ = .......... m
Throat diameter of the orificemeter, d₂ = .......... m
Weight of the hanger, T₀ = .......... kg

Table:

SNo.	Percentage of gate opening	P (kg/cm2)	H (m)	T (sec)	p1 (kg/cm2)	p2 (kg/cm2)	h (m)	T1 (kg)	T2 (kg)	N (r.p.m)	Q (m3/sec)	Pi (kW)	Po (kW)	η	Nu	Pu	Qu
1
2
3
4
5

Graphs:

1. Q_u Vs N_u:

2. P_u Vs N_u:

3. η Vs N_u:

Precautions:

1. Sufficient time should be given for the flow to become steady - uniform.
2. Priming of the pump should be done to avoid development of air bubbles.

Result:

The performance characteristics of Francis turbine have been studied and the
 a) Maximum efficiency, η_max = .......... %
 b) Specific speed of the turbine, N_s = ..........