3.5 Turbines

3.5 Turbines

1. Classification and Working Principles

1. Classification by Head and Flow:

   • Impulse Turbines: High head, low flow rate.

     • Example: Pelton wheel.

     • Energy conversion: Pressure → Kinetic → Mechanical.

   • Reaction Turbines: Medium to low head, high flow rate.

     • Examples: Francis, Kaplan.

     • Energy conversion: Pressure + Kinetic → Mechanical.

2. Classification by Flow Direction:

   • Tangential Flow: Pelton wheel.

   • Radial Flow: Early Francis turbine.

   • Mixed Flow: Modern Francis turbine.

   • Axial Flow: Kaplan, propeller turbines.

3. Working Principles:

   • Impulse Turbine:

     • Fluid (jet) strikes buckets at atmospheric pressure.

     • Entire pressure drop occurs in nozzle.

     • Runner operates in air.

   • Reaction Turbine:

     • Fluid fills runner completely under pressure.

     • Pressure drop occurs gradually across runner.

     • Runner operates submerged.

4. Specific Speed ($N_s$):

   • Dimensionless parameter for turbine selection.

   • $N_s = \frac{N\sqrt{P}}{H^{5/4}}$ (SI units)

   • Low $N_s$: Pelton (10-60).

   • Medium $N_s$: Francis (60-400).

   • High $N_s$: Kaplan (300-1000).

2. Components and Functions

1. Common Components:

   • Runner/Rotor: Rotating part with blades/buckets.

   • Casing: Encloses runner, directs flow.

   • Guide Vanes/Nozzle: Control flow direction and rate.

   • Draft Tube (reaction turbines): Recovers kinetic energy.

2. Pelton Wheel Specific:

   • Nozzle: Converts pressure to high-speed jet.

   • Spear/Needle Valve: Controls jet size.

   • Buckets: Double-cupped, split by splitter.

   • Casing: Protects from splashing, not pressure-tight.

3. Francis Turbine Specific:

   • Spiral Casing: Evenly distributes flow.

   • Stay Vanes: Guide flow to guide vanes.

   • Guide Vanes/Wicket Gates: Adjustable for flow control.

   • Runner: Mixed flow design.

   • Draft Tube: Essential component.

4. Kaplan Turbine Specific:

   • Scroll Case: Similar to Francis.

   • Guide Vanes: Adjustable.

   • Runner: Propeller-type with adjustable blades.

   • Draft Tube: Essential component.

3. Governors

1. Function:

   • Maintain constant turbine speed under varying load.

   • Control flow rate through turbine.

   • Prevent overspeed during load rejection.

2. Components:

   • Speed Sensor: Measures turbine RPM.

   • Controller: Compares actual vs desired speed.

   • Servomotor: Hydraulic/pneumatic actuator.

   • Control Mechanism: Adjusts guide vanes/spear valve.

3. Types:

   • Mechanical Governors: Flyball type.

   • Hydraulic Governors: Most common, more responsive.

   • Electronic Governors: Modern, digital control.

4. Droop Characteristic:

   • Speed decreases slightly with increasing load.

   • Allows parallel operation of multiple turbines.

   • Droop = $\frac{N_{no-load} - N_{full-load}}{N_{rated}} \times 100\%$

5. Isochronous Operation:

   • Constant speed regardless of load.

   • Used for single turbine or master in parallel operation.

4. Cavitation

1. Definition:

   • Formation and collapse of vapor bubbles due to local pressure falling below vapor pressure.

   • Occurs where pressure is lowest (high velocity regions).

2. Cavitation Locations:

   • Suction side of turbine blades.

   • Outlet edges of runner blades.

   • Draft tube (in Francis turbines).

   • Guide vane surfaces.

3. Effects:

   • Material Damage: Pitting and erosion.

   • Performance Drop: Efficiency reduction.

   • Noise and Vibration: Unstable operation.

   • Reduced Life: Component failure.

4. Cavitation Parameter (Thoma's Coefficient):

   • $\sigma = \frac{H_a - H_v - H_s}{H}$

   • Where: $H_a$ = atmospheric head, $H_v$ = vapor pressure head, $H_s$ = suction head, $H$ = net head.

   • Must exceed critical σ to avoid cavitation.

5. Prevention:

   • Keep installation above tailrace level (negative suction head).

   • Smooth surface finish.

   • Optimal runner design.

   • Air injection.

5. Performance Curves

1. Constant Head Curves:

   • Main Characteristic Curve: Unit speed ($N_u$) vs unit power ($P_u$) at constant guide vane opening.

   • Shows performance at constant head.

2. Constant Speed Curves:

   • Operating Characteristic Curve: Head vs efficiency at constant speed.

   • Shows optimal operating range.

3. Iso-Efficiency Curves:

   • Contours of constant efficiency on head-flow or speed-power plots.

   • Identify best efficiency point (BEP).

4. Mushroom Curves:

   • Combined curves showing efficiency, power, discharge vs speed at constant head.

5. Key Parameters:

   • Unit Speed: $N_u = \frac{ND}{\sqrt{H}}$

   • Unit Discharge: $Q_u = \frac{Q}{D^2\sqrt{H}}$

   • Unit Power: $P_u = \frac{P}{D^2 H^{3/2}}$

6. Performance at Off-Design:

   • Efficiency drops away from BEP.

   • Cavitation risk increases at off-design conditions.

   • Turbines operate best near design point.

6. Draft Tube

1. Function:

   • Converts kinetic energy at runner exit to pressure energy.

   • Allows turbine installation above tailrace level.

   • Maintains submergence of runner (reaction turbines).

2. Types:

   • Conical (Straight) Draft Tube: Simple, efficient for small heads.

   • Elbow Draft Tube: Common in medium-head plants, saves excavation.

   • Moody Spreading Tube: Reduces exit velocity efficiently.

   • Simple Elbow Tube: Space-saving but lower efficiency.

3. Energy Recovery:

   • Pressure head recovered = Height above tailrace + Kinetic head recovery.

   • Efficiency: $\eta_{dt} = \frac{\text{Actual pressure recovery}}{\text{Kinetic energy at inlet}}$

4. Design Considerations:

   • Divergence Angle: 5-10° to avoid flow separation.

   • Exit Velocity: Minimize to reduce losses.

   • Submergence: Must prevent air entry and vortex formation.

5. Cavitation in Draft Tube:

   • Can occur at low loads due to pressure pulsations.

   • Causes surging and vibration.

   • Controlled by air admission or proper operating range.

6. Importance for Reaction Turbines:

   • Essential for Francis and Kaplan turbines.

   • Increases net available head.

   • Improves overall turbine efficiency by 2-5%.