Performance of Hydraulic Turbines free study material

1. Introduction

Performance of hydraulic turbine refers to how efficiently it converts the energy of flowing or falling water into mechanical energy. It is evaluated using parameters like efficiency, power output, speed, discharge, and specific speed.

2. Types of Efficiencies of Turbine

(a) Hydraulic Efficiency (ηₕ)

It measures how effectively the turbine converts the water energy into runner energy.$$\eta_h = \frac{\text{Power delivered to runner}}{\text{Water power at inlet}}$$

• Losses: friction, turbulence, shock losses
• Important for blade design

(b) Mechanical Efficiency (ηₘ)

It accounts for mechanical losses such as bearing friction.$$\eta_m = \frac{\text{Shaft power}}{\text{Runner power}}$$

(c) Volumetric Efficiency (ηᵥ)

It considers leakage losses.$$\eta_v = \frac{\text{Actual water striking runner}}{\text{Water supplied}}$$

(d) Overall Efficiency (ηₒ)

It represents the total efficiency of the turbine.$$\eta_o = \eta_h \times \eta_m \times \eta_v$$

OR$$\eta_o = \frac{\text{Shaft Power}}{\text{Water Power}}$$

3. Unit Quantities

Unit quantities help compare turbines under unit head (H = 1 m).

(a) Unit Speed (N₁)

$$N_1 = \frac{N}{\sqrt{H}}$$

(b) Unit Discharge (Q₁)

$$Q_1 = \frac{Q}{\sqrt{H}}$$

(c) Unit Power (P₁)

$$P_1 = \frac{P}{H^{3/2}}$$

4. Specific Speed (Nₛ)

Specific speed is a key parameter used to classify turbines.$$N_s = \frac{N \sqrt{P}}{H^{5/4}}$$Ns​=H5/4NP​​

Importance:

• Helps in selecting the type of turbine
• Indicates shape and design of runner

Typical Ranges:

• Pelton turbine → Low (10–60)
• Francis turbine → Medium (60–300)
• Kaplan turbine → High (300–1000)

5. Characteristic Curves of Turbine

These curves show the turbine performance under different conditions.

(a) Main (Constant Head) Characteristics

• Head remains constant
• Plots:
  • Power vs Speed
  • Efficiency vs Speed
  • Discharge vs Speed

(b) Operating Characteristics

• Actual working conditions
• Shows variation of:
  • Efficiency
  • Power
  • Discharge with load

(c) Universal Characteristics

• Used for comparing turbines of different sizes
• Plotted using unit quantities

6. Performance Parameters

(a) Power Developed

$$P = \rho g Q H \eta_o$$

Where:

• ρ = density of water
• g = acceleration due to gravity
• Q = discharge
• H = head

(b) Efficiency vs Load

• Efficiency increases with load up to optimum
• Then decreases due to losses

(c) Runaway Speed

• Speed at zero load
• Important for turbine safety design

7. Governing of Turbines

Governing maintains constant speed despite load changes.

Methods:

• Pelton turbine → Needle valve control
• Francis/Kaplan → Guide vane control

8. Cavitation in Turbines

Definition:

Formation and collapse of vapor bubbles due to low pressure.

Effects:

• Pitting of blades
• Noise and vibration
• Efficiency loss

Prevention:

• Proper installation height
• Use of draft tube
• Maintain pressure above vapor pressure

9. Draft Tube and Its Role in Performance

• Recovers kinetic energy at outlet
• Increases efficiency
• Reduces exit velocity losses

10. Factors Affecting Turbine Performance

• Head of water
• Flow rate
• Blade design
• Mechanical losses
• Cavitation
• Operating conditions

11. Comparison of Turbine Performance

Parameter	Pelton	Francis	Kaplan
Head	High	Medium	Low
Efficiency	High	Very High	Very High
Specific Speed	Low	Medium	High

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