Unit 4 of ME 3003 (Mechanical/Automobile Engineering)

 Unit 4: Hydraulic Turbines for your ME 3003 (Mechanical/Automobile Engineering) course, These are short notes for revision purpose. please refer you Reference book & College study materials for complete study.

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4. HYDRAULIC TURBINES

Hydraulic turbines convert the energy of flowing or falling water into mechanical energy, which is then used to generate electricity in hydroelectric power plants. The study of turbines includes understanding their types, working principles, construction, and efficiency calculations.

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4.1 Layout of Hydroelectric Power Plant (Basic Concept)

A hydroelectric power plant is designed to harness the energy of flowing or falling water to generate electricity. The basic layout includes the following components:

• Reservoir: A large water body that stores water at a height, providing potential energy.
• Penstock: A large pipe that carries water from the reservoir to the turbine. The pressure of the water increases as it flows down through the penstock.
• Turbine: Converts the potential energy of water into mechanical energy.
• Generator: Attached to the turbine, it converts mechanical energy into electrical energy.
• Draft Tube: A pipe that carries water from the turbine to the tailrace. It helps recover energy and ensures the water pressure is low when exiting the turbine.

The general flow of water is from the reservoir, through the penstock, to the turbine, and then to the tailrace.

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4.2 Classification and Selection of Hydraulic Turbines

Hydraulic turbines can be classified based on head (height from which the water falls) and flow rate (amount of water flow). The main classifications are:

1. Impulse Turbines: These turbines are used for high-head, low-flow applications. The water jet strikes the turbine blades at high speed. Pelton Wheel is a typical example.
2. Reaction Turbines: These turbines operate under low head and high flow conditions. The blades work by reacting to both pressure and velocity of the water. Examples include Francis and Kaplan turbines.

The selection of turbines depends on factors like:

• The available head (height of water).
• The flow rate.
• Efficiency requirements.
• Space constraints.

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4.3 Construction and Working Principle of Pelton Wheel

The Pelton Wheel is an impulse turbine used for high-head applications, typically for generating power from waterfalls or rivers with a significant height difference.

• Construction:

  • The Pelton Wheel consists of a wheel with buckets attached to its circumference. Water is directed into the buckets through a nozzle.
  • The nozzle accelerates water into high-speed jets that strike the buckets.
  • The buckets are designed to change the direction of the water jet and capture its energy.

• Working Principle:

  • The high-velocity water jet strikes the buckets, which deflects the water and causes the wheel to rotate.
  • The force of the water jet on the bucket is converted into mechanical energy, which drives the shaft connected to the generator.
  • Since the jet provides all its energy to the wheel (impulse), the pressure of water remains constant as it passes through the turbine.

Efficiency of the Pelton Wheel depends on the proper design of the bucket shape and the angle of the nozzle.

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4.4 Francis and Kaplan Turbines (Derivation for Work and Efficiency)

Francis Turbine:

• Construction: The Francis turbine is a reaction turbine used for medium head (10–200 m) and high flow conditions. It has a radial flow pattern.
• Working Principle:
  • Water enters the turbine radially and flows out axially.
  • The turbine consists of a runner with curved blades. The blades are designed to make use of both the pressure and velocity of the incoming water.
  • The water is directed into the runner, where its pressure is converted into mechanical energy.

Derivation for Work and Efficiency:

• Work done: The work done per second on the turbine is given by the rate of change of momentum.

• The power produced by the turbine is:

  $$P = \rho Q g H$$

  Where:

  • $P$ = Power produced (W)
  • $\rho$ = Density of water (kg/m³)
  • $Q$ = Flow rate (m³/s)
  • $g$ = Gravitational acceleration (9.81 m/s²)
  • $H$ = Head (m)

• Efficiency: The efficiency of the Francis turbine is the ratio of the useful power output to the energy supplied by the water.

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Kaplan Turbine:

• Construction: The Kaplan turbine is a reaction turbine with adjustable blades, used for low head (2–30 m) and high flow applications like in river plants.
• Working Principle:
  • The water flows through the turbine’s blades, which are axial in design.
  • The blades are adjustable to suit varying flow conditions.
  • The water passes through the runner and moves in the axial direction.
  • The efficiency of the Kaplan turbine is higher at low heads and large flow rates.

Derivation for Work and Efficiency:

• The working and efficiency derivations for Kaplan turbines are similar to the Francis turbine.
• The power produced by the Kaplan turbine is: $$P = \rho Q g H$$
• The efficiency is a function of the water head, flow rate, and the turbine's design parameters.

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4.5 Draft Tubes – Types and Construction

A draft tube is a pipe that carries water from the turbine to the tailrace and reduces the pressure at the turbine exit. The draft tube is crucial for maximizing turbine efficiency by allowing the water to expand and recover some energy that would otherwise be lost.

• Types of Draft Tubes:

  1. Conical Draft Tube: Widely used for turbines, it has a conical shape, which helps in controlling the flow and improving the efficiency.
  2. Elbow Draft Tube: Used when there is a need for a sharp bend to direct the water flow to the tailrace.
  3. Straight Draft Tube: Sometimes used for small turbines or where space constraints exist.

• Construction: A draft tube is generally made from concrete or steel, depending on the size of the turbine and the installation conditions.

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4.6 Concept of Cavitation in Turbines

Cavitation refers to the formation of vapor bubbles in the water when the local pressure in the turbine drops below the vapor pressure of the water. When these bubbles collapse, they create shockwaves that can cause damage to the turbine blades, leading to erosion and loss of efficiency.

• Causes of Cavitation:

  • High-speed flow.
  • Low-pressure regions, especially near the inlet or on the suction side of the blades.

• Preventing Cavitation:

  • Ensure proper design of the turbine to avoid low-pressure zones.
  • Use of pressure recovery devices like draft tubes to prevent pressure drops.

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4.7 Simple Problems Related to Calculation of Work Done, Power, Efficiency of Turbines

Example 1: Pelton Wheel Work and Power

A Pelton wheel is used to harness water with a head of 100 meters. The flow rate is 10 m³/s, and the density of water is 1000 kg/m³. Calculate the power generated.

Solution:

• Given:
  • $H = 100 \, \text{m}$
  • $Q = 10 \, \text{m}^3/\text{s}$
  • $\rho = 1000 \, \text{kg/m}^3$

The power generated is given by:

$$P = \rho Q g H = 1000 \times 10 \times 9.81 \times 100 = 9.81 \times 10^6 \, \text{W} = 9.81 \, \text{MW}$$

Thus, the power generated by the Pelton wheel is 9.81 MW.

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Example 2: Efficiency of a Francis Turbine

A Francis turbine operates with a flow rate of 20 m³/s and a head of 40 meters. If the efficiency of the turbine is 85%, calculate the power output.

Solution:

• Given:
  • $Q = 20 \, \text{m}^3/\text{s}$
  • $H = 40 \, \text{m}$
  • Efficiency $\eta = 85\%$

The theoretical power output is:

$$P = \rho Q g H = 1000 \times 20 \times 9.81 \times 40 = 7.848 \times 10^6 \, \text{W} = 7.848 \, \text{MW}$$

Now, accounting for the efficiency:

$$\text{Power Output} = \eta \times P = 0.85 \times 7.848 \, \text{MW} = 6.67 \, \text{MW}$$

Thus, the power output is 6.67 MW.

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4.8 Unit Quantities

Unit quantities are used to simplify the analysis and design of turbines. They are dimensionless values that allow comparison between different turbines regardless of size or scale.

• Unit Speed ($N_u$): Defined as the speed of the turbine at a unit flow rate and head.
• Unit Flow ($Q_u$): A dimensionless quantity representing the flow rate relative to the turbine's size.
• Unit Power ($P_u$): A dimensionless quantity representing the power produced by the turbine.

Unit quantities are useful for turbine design, ensuring turbines are optimized for specific applications and conditions.

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Summary of Key Concepts

• Hydraulic turbines convert the energy of water into mechanical energy.
• Pelton wheels are impulse turbines, while Francis and Kaplan turbines are reaction turbines.
• Work and power in turbines are calculated based on flow rate, head, and efficiency.
• Cavitation is a major concern in turbines and can be prevented by proper design.
• Unit quantities allow for scaling and optimization in turbine design.