Pelton Wheel Turbine MCQ Quiz - Objective Question with Answer for Pelton Wheel Turbine - Download Free PDF

Concept:

The pitch diameter of a Pelton wheel is calculated by equating the tangential velocity derived from geometry and speed ratio. The tangential velocity is:

and also

Equating both:

Final Answer:

Explanation:

Pelton Turbine

Definition: A Pelton turbine is a type of hydraulic turbine that operates on the principle of converting the kinetic energy of a high-speed water jet into mechanical energy. It is specifically designed for high-head, low-flow rate applications where water is available at a high elevation and must be utilized for generating power efficiently. The Pelton turbine is a tangential flow impulse turbine, meaning the water jet strikes the buckets tangentially to the wheel's circumference.

Working Principle: The working of the Pelton turbine is based on the impulse principle, where the momentum of the water jet is transferred to the turbine buckets:

• Water from a high elevation is directed through a nozzle to form a high-velocity jet.
• The jet strikes the curved buckets (or blades) mounted on the periphery of the turbine wheel. These buckets are designed in the shape of double cups with a central ridge, which splits the jet into two halves, allowing smooth flow and efficient energy transfer.
• The force of the water jet causes the turbine wheel to rotate, converting the kinetic energy of the water into mechanical energy.
• The used water is then discharged at atmospheric pressure without creating any suction effect.

Key Characteristics of Pelton Turbine:

• It is an impulse turbine where the entire pressure energy of water is first converted into kinetic energy before striking the buckets.
• The flow of water is tangential to the wheel, classifying it as a tangential flow turbine.
• It is suitable for high-head (typically above 300 meters) and low-flow rate conditions.
• The specific speed of a Pelton turbine is relatively low, making it ideal for high-head applications.
• It is highly efficient for its design conditions and can achieve efficiencies up to 90% or higher.

Explanation:

Energy Possessed by Steam Before Entering a Turbine

• Before steam enters a turbine, it primarily possesses thermal energy.
• Thermal energy is the internal energy of a system due to the kinetic energy of its molecules.
• In the context of steam, this energy is manifested as the high temperature and pressure of the steam generated in a boiler.
• In a typical power plant, water is heated in a boiler to produce steam.
• This steam is then directed to a turbine. The high-pressure, high-temperature steam contains significant thermal energy.
• As the steam expands through the turbine, this thermal energy is converted into mechanical energy, which in turn drives an electrical generator to produce electricity.

Explanation:

Hydro Penstock Design

• A hydro penstock is a large pipe or conduit that directs the flow of water from a reservoir or dam to the turbines in a hydroelectric power plant.
• The design of the penstock is crucial in maximizing the efficiency of the hydroelectric power plant, as it directly affects the water flow rate and pressure, which in turn influences the power generation.
• The primary function of the penstock is to transport water from a higher elevation to the turbines at a lower elevation.
• The potential energy of the stored water is converted into kinetic energy as it flows through the penstock.
• This kinetic energy is then used to drive the turbines, which generate electricity.
• The efficiency of this process depends on several factors, including the design and construction of the penstock.

The length and diameter of the penstock directly influence the flow rate and pressure of the water reaching the turbines. Here’s a detailed explanation of why these parameters are so important:

• Length of the Penstock: The length of the penstock affects the head loss due to friction. A longer penstock will have more frictional losses, which reduces the water pressure and flow rate. Properly designing the length to minimize these losses is essential for maintaining high efficiency.
• Diameter of the Penstock: The diameter of the penstock determines the flow capacity. A larger diameter allows more water to flow through with less frictional resistance, leading to higher efficiency. However, increasing the diameter also increases the cost and structural requirements, so an optimal balance must be achieved.

Additional Factors: While the length and diameter are the most crucial aspects, other factors also play a role in the efficiency of the penstock design:

• Material: The material of the penstock affects its durability and resistance to corrosion and pressure. Common materials include steel and reinforced concrete.
• Shape and Alignment: The shape and alignment of the penstock can influence the flow dynamics. Smooth curves and proper alignment minimize turbulence and energy losses.
• Supports and Anchors: Proper support and anchoring of the penstock are necessary to withstand the water pressure and prevent structural failures.

Explanation:

Pelton wheel or turbine

It is a tangential flow impulse turbine. The water strikes the bucket along the tangent of the runner. The energy available at the inlet of the turbine is kinetic energy. The pressure at the inlet and outlet of the turbine is the atmosphere. This turbine is used for high head and low discharge.

The main parts of Pelton wheel are:

• Nozzle and flow regulating arrangement.
• Runners and buckets.
• Casing
• Breaking jet
  When the nozzle is completely closed by moving the spear in the forward direction, the amount of water striking the runner reduces to zero. But the runner due to inertia goes on revolving for a long time. To stop the runner in a short time, a small nozzle is provided which directs the jet of water on the back of the vanes. This jet of water is called a breaking jet.

Jet ratio:

It is defined as the ratio of the pitch diameter (D) of the Pelton wheel to the diameter of the jet diameter (d).

It is given as \(m = \frac{D}{d}\)

Additional Information

• The speed ratio of the Pelton wheel varies between 0.43 to 0.48.
• The value of the jet ratio is generally taken as 12.
• Number of buckets Z, can be found from simple relation, Z = 15 + 0.5m.

Concept:

Pelton wheel:

It is a tangential flow impulse turbine in which the pressure energy of water is converted into kinetic energy to form a high-speed water jet and this jet strikes the wheel tangentially to make it rotate.

Taygun's formula:

It is used to determine the number of buckets on the runner in the Pelton wheel turbine. It is given by the below formula:

\(Z = 15+{ D\over 2d}\)

Where D = Pitch or mean diameter, d = Nozzle or Jet  diameter

Calculation:

Given,

D = 1 m, d = 0.1 m

The number of buckets on the runner by Taygun's formula

\(Z = 15+{ D\over 2d} = 15+{ 1\over 2\times 0.1}\)= 15 + 5 = 20

Explanation:

Specific speed: 

• It is defined as the speed of a similar turbine working under a head of 1 m to produce a power output of 1 kW.
• The specific speed is useful to compare the performance of the various type of turbines.
• The specific speed differs for the different type of turbines and is the same for the model and actual turbine.

\({N_s} = \frac{{N\sqrt P }}{{{H^{\frac{5}{4}}}}}\)

Following are the range of specific speed of different turbines

• The specific speed of Pelton wheel turbine (single jet) is in the range of 10-35
• The specific speed of Pelton wheel turbine (multiple jets) is in the range of 35-60
• The specific speed of Francis turbine is in the range of 60-300.
• The specific speed of Kaplan/propeller turbine is greater than 300.

Important Points

Explanation:

Given;

Total discharge through pelton turbine = 3 m³/s

Area of jet = 0.02 m²

Velocity of jet = 75 m/s

Calculation:

Discharge through jet = 0.02 × 75 = 1.5 m³/s

\(Number\;of\;jet = \frac{{Total\;discharge}}{{Discharge\;through\;on\;jet}}\) = \(\frac{3}{{1.5}}\) = 2 

Concept:

The overall efficiency of the Pelton wheel is given by,

\({η _o} = \frac{{Shaft \;Power}}{{Water\; Power}}\)

Water Power = ρQgH 

Calculation:

Given:

Shaft Power = 800 kW, η_o = 0.8, H = 40 m

ρ = 1000 kg/m3, g =10 m/s2

\({η _o} = \frac{{Shaft \;Power}}{{Water\; Power}}\)

\({0.8} = \frac{{800}}{{Water\; Power}}\)

Water Power = 1000 kW

Water Power = ρQgH 

1000 × 10³ = 1000 × Q × 10 × 40

Q = 2.5 m3/s.

Explanation:

Impulse turbine: 

• If the energy available at the inlet of the turbine is only kinetic energy, the turbine so known as impulse turbine.
• The available energy at the inlet is only kinetic energy if the inlet pressure and outlet pressure is the same equal to atmospheric pressure.
• Example: Pelton Turbine

Reaction Turbine: 

• At the inlet of the turbine, the water possesses kinetic energy as well as pressure energy
• Example: Francis Turbine, Kaplan Turbine

Important Points

Impulse:

Impulse is the sudden change of momentum of an object when the object is acted upon by a force for an interval of time. 

Specific speed:

• It is defined as the speed of a similar turbine working under a head of 1 m to produce a power output of 1 kW.
• The specific speed is useful to compare the performance of the various types of turbines.
• The specific speed differs for a different type of turbines and is the same for the model and actual turbine.
• Specific Speed of Turbine, \({N_s} = \;\frac{{N \times \sqrt P }}{{{H^{\frac{5}{4}}}}}\)
• Where N = speed of turbine, P = power generated, and H = head generated

Calculation:

Given:

P =  kW, N = 300 rpm, H = 100 m

\({N_s} = \;\frac{{300 \times \sqrt {150000} }}{{{{100}^{\frac{5}{4}}}}} = 367.42 = 367\)

Explanation:

Impulse Turbine: 

If at the inlet of the turbine, the energy available is only kinetic energy, the turbine is known as impulse turbine.

Example: Pelton wheel turbine.

Pelton Wheel Turbine:

It is a tangential flow impulse turbine in which the pressure energy of water is converted into kinetic energy to form a high-speed water jet and this jet strikes the wheel tangentially to make it rotate.

The Main parts of the Pelton wheel turbine are:

1. Nozzle and Flow Regulating Arrangement
2. Runner and Buckets
3. Casing
4. Braking Jet
5. Penstock

Draft Tube is not a part of the Pelton wheel turbine, it is the main component of an axial flow reaction turbine.

Additional Information

Reaction Turbine: 

If at the inlet of the turbine, the water possesses kinetic energy as well as pressure energy, the turbine is known as a reaction turbine.

Example: Francis and Kaplan turbine.

Tangential flow turbines: 

Radial flow turbines: 

In this type of turbine, the water strikes in the radial direction. accordingly, it is further classified as

• Inward flow turbine: The flow is inward from the periphery to the centre (centripetal type). Example: Old Francis turbine
• Outward flow turbine: The flow is outward from the centre to the periphery (centrifugal type). Example: Fourneyron turbine

Axial flow turbine: 

The flow of water is in the direction parallel to the axis of the shaft.

Example: Kaplan turbine and propeller turbine.

Explanation:

Number of buckets on a runner: \(Z = 15 + \frac{D}{{2d}}\) 

Given: Jet ratio = 12 i.e D/d =12

Now,

Number of buckets on a runner = 15 + 6

∴ Number of buckets = 21

Important Points

Design parameters of Pelton wheel turbine:

1. Velocity of jet: at inlet \({V_1} = {C_V}\sqrt {2gH} \) where Cv = coefficient of velocity = 0.98-0.99

2. Velocity of wheel: \(u = \emptyset \sqrt {2gH} \) where φ is the speed ratio = 0.43-0.48

3. Angle of deflection: is 165° unless mentioned.

4. Pitch or mean diameter: D can be expressed by \(u = \frac{{\pi DN}}{{60}}\)

5. Jet ratio: \(m = \frac{D}{d}\) (12 in most cases/calculate), d = nozzle diameter or jet diameter

6. Number of buckets on a runner: \(Z = 15 + \frac{D}{{2d}}\) (Tygun formula) or, \(Z = 5.4\sqrt m \), m = 6 to 35

7. Number of Jets: obtained by dividing the total rate of flow through the turbine by the rate of flow through single jet. The number of jets is not more than two for horizontal shaft turbines and is limited to six for vertical shaft turbines.

8. Size of bucket: length of bucket L = 2.5d, width of bucket B = 5d, depth of bucket Db = 0.8d 

Explanation:

Surge tank:

A surge tank is a cylindrical open-topped storage tank that is constructed to the penstocks at a suitable point.

The function of surge tank:

• Surge tanks are tanks connected to the water conductor system.
• It prevents the sudden increase of pressure in the supply line or in the penstock.
• It is placed as near as possible to the turbine.
• It regulates the water flow by increasing and reducing supply as per demands.
• It reduces the length of high-pressure conduits required to resist the water hammer effects.

Centrifugal compressor – Surging

Centrifugal pump – Priming

Pelton wheel – Impulse Turbine

Kaplan turbine – Axial flow

Explanation:

Impulse Turbine: If at the inlet of the turbine, the energy available is only kinetic energy, the turbine is known as impulse turbine. e.g. a Pelton wheel turbine.

Reaction Turbine: If at the inlet of the turbine, the water possesses kinetic energy as well as pressure energy, the turbine is known as a reaction turbine. e.g. e Francis and Kaplan turbine.

Tangential flow turbines: In this type of turbines, the water strikes the runner in the direction of the tangent to the wheel. Example: Pelton wheel turbine.

Radial flow turbines: In this type of turbines, the water strikes in the radial direction. accordingly, it is further classified as:

• Inward flow turbine: The flow is inward from periphery to the centre (centripetal type); Example: old Francis turbine
• Outward flow turbine: The flow is outward from the centre to periphery (centrifugal type); Example: Fourneyron turbine

Axial flow turbine: The flow of water is in the direction parallel to the axis of the shaft. Example: Kaplan turbine and propeller turbine.

Priming: Priming of a centrifugal pump is defined as the operation in which the suction pipe, casing of the pump and a portion of the delivery pipe up to the delivery valve is completely filled up from outside source with the liquid to be raised by the pump before starting the pump.

Surging: A centrifugal compressor is designed to operate between a given evaporator and condenser pressures. Due to variations either in the heat sink or refrigerated space, the actual evaporator and condenser pressure can be different from their design value. This pressure difference cause refrigerant flows to reduce and finally stop or flow in reverse direction. This oscillation of refrigerant flow and the resulting rapid variation in pressure difference gives rise to the phenomenon called “surging”. Surging produces noise and imposes severe stresses on the bearings of the compressor and motor, ultimately leading to their damage.