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

Concept:

The overall efficiency of a Francis turbine is defined as the ratio of useful power output at the runner shaft to the hydraulic power input from water striking the runner.

Formula:

Hydraulic Power Input = Weight of water per second × Net Head

\( \lambda_0 = \frac{\text{Power Output}}{\text{Hydraulic Power}} = \frac{P}{W \cdot H} \)

 

Explanation:

Parson’s Reaction Turbine

• Parson's reaction turbine is a type of reaction turbine where the steam expansion takes place both in fixed nozzles (or guide blades) and moving blades. This turbine operates on the principle of reaction, which means the steam not only changes its direction but also expands as it flows through the blades, producing an equal and opposite reaction that drives the rotor.
• In Parson's reaction turbine, the steam expands partially in the fixed nozzles (or guide blades), where it gains velocity, and then further expands in the moving blades, where a reaction force is generated. The turbine blades are designed with changing cross-sectional areas to facilitate this expansion and create a reaction force, which rotates the rotor. The velocity diagrams are critical for analyzing the forces and angles in the turbine.

The correct condition for Parson's reaction turbine is:

θ = β, ϕ = α

This condition satisfies the velocity triangle analysis for Parson's reaction turbine. The angles are defined as follows:

• α (Nozzle angle): The angle at which steam enters the fixed blades (or nozzles).
• ϕ (Exit angle of moving blade): The angle at which steam exits the moving blades.
• θ (Entrance angle of moving blade): The angle at which steam enters the moving blades.
• β (Discharge angle of moving blade): The angle which the discharging steam makes with the tangent of the wheel at the exit of the moving blade.

For Parson's reaction turbine, the following relationships hold true:

• The entrance angle of the moving blade (θ) equals the discharge angle of the moving blade (β), as the steam flow is symmetrical relative to the moving blades.
• The exit angle of the moving blade (ϕ) equals the nozzle angle (α), which ensures proper alignment and efficient energy transfer.

Thus, the condition θ = β and ϕ = α is correct for Parson's reaction turbine.

Concept:

Hydraulic efficiency for a reaction turbine is given by:

\( \eta_h = \frac{V_{w1} \cdot u_1}{gH} \)

Given:

\( H = 25~m,~V_f = 2.5~m/s,~\alpha = 10^\circ \Rightarrow \tan \alpha = 0.176,~g = 10~m/s^2 \)

Step 1: Whirl Velocity

\( V_{w1} = \frac{V_f}{\tan \alpha} = \frac{2.5}{0.176} \approx 14.2~m/s \)

Step 2: Tangential Velocity

\( u_1 = V_{w1} = 14.2~m/s \) (since radial vanes, no losses assumed)

Step 3: Hydraulic Efficiency

\( \eta_h = \frac{14.2 \times 14.2}{10 \times 25} = \frac{201.64}{250} = 0.8163 = 81.63\% \)

 

Explanation:

The Degree of Reaction

• The degree of reaction is a critical parameter in the analysis of turbines and compressors. It quantifies the distribution of energy conversion between the rotor and the stator within a stage of a turbo-machine. Specifically, it is defined as the ratio of the enthalpy drop in the rotor to the total enthalpy drop in the stage (which includes both the rotor and the stator).

Mathematical Expression: The degree of reaction (R) is mathematically given as:

R = (Actual enthalpy change in rotor) / (Actual enthalpy change in stage)

Where:

• Actual enthalpy change in rotor: Represents the energy transformation occurring in the rotating blades of the turbine or compressor.
• Actual enthalpy change in stage: Represents the total energy transformation in the entire stage, which includes contributions from both the rotor and the stator.

The degree of reaction also provides insights into the distribution of pressure and velocity changes within a stage. For instance:

• If R = 0, the entire enthalpy change occurs in the stator.
• If R = 1, the entire enthalpy change occurs in the rotor.
• If R = 0.5, the enthalpy change is equally distributed between the rotor and the stator (commonly referred to as a 50% reaction stage).

Explanation:

Kaplan Turbine

• A Kaplan turbine is a type of reaction turbine specifically designed for low-head and high-flow applications. It is a propeller-type turbine with adjustable blades, which allows it to operate efficiently under varying water flow conditions. It is one of the most commonly used turbines in hydroelectric power plants where the available water head is relatively low.

Working Head Range:

• The Kaplan turbine is best suited for a working head range of 5 to 70 meters. This is because it is designed to harness energy from water at low to medium heads while maintaining high efficiency. The adjustable blades of the Kaplan turbine allow it to adapt to changing water flow conditions, making it highly versatile for such applications.

Working Principle:

• The Kaplan turbine operates on the principle of reaction and dynamic action of water. Water enters the turbine through a scroll casing and is directed onto the runner blades by guide vanes. The adjustable guide vanes control the flow of water, ensuring optimal efficiency. The water’s pressure energy is converted into mechanical energy as it flows through the turbine, causing the runner to rotate. The rotation of the runner drives the generator, which converts mechanical energy into electrical energy.

Features of Kaplan Turbine:

• Adjustable Blades: The runner blades of the Kaplan turbine are adjustable, allowing the turbine to maintain high efficiency across a wide range of water flow conditions.
• Reaction Turbine: It operates as a reaction turbine, meaning the water’s pressure energy is partially converted into kinetic energy before it reaches the runner.
• Low-Head Application: It is specifically designed for low-head applications, making it ideal for rivers and dams with small elevation differences.
• High Flow Rate: The Kaplan turbine is capable of handling large volumes of water, making it suitable for high-flow conditions.

Concept:

The overall efficiency η_o of turbine = volumetric efficiency (η_v)× hydraulic efficiency (η_h)× mechanical efficiency (η_m)

\({\eta _o} = {\eta _v} \times {\eta _h} \times {\eta _m}\)

\({{\rm{\eta }}_{\rm{v}}} = \frac{{{\rm{volume\;of\;water\;actually\;striking\;the\;runner}}}}{{{\rm{volume\;of\;water\;actually\;supplied\;to\;the\;turbine}}}}\)

\({{\rm{\eta }}_{\rm{h}}} = \frac{{{\rm{Power\;deliverd\;to\;runner}}}}{{{\rm{Power\;supplied\;at\;inlet\;}}}} = \frac{{{\rm{R}}.{\rm{P}}}}{{{\rm{W}}.{\rm{P}}}}\)

\({{\rm{\eta }}_{\rm{m}}} = \frac{{{\rm{Power\;at\;the\;shaft\;of\;the\;turbine}}}}{{{\rm{Power\;delivered\;by\;water\;to\;the\;runner}}}} = \frac{{{\rm{S}}.{\rm{P}}}}{{{\rm{R}}.{\rm{P}}}}\)

Overall efficiency: \({\eta _o} = \frac{{S.P}}{{W.P}}\)

Water Power = ρ × Q × g × h 

Calculation:

Given:

η_o = 0.8, Head h = 10 m, and Q = 1 m³/s.

\({\eta _o} = \frac{{S.P}}{{W.P}} = \frac{{S.P}}{{\rho \times Q \times g \times h}}\)

\(0.8 = \frac{{S.P}}{{1000 \times 1 \times 9.81 \times 10}} \Rightarrow S.P = 78480\;W \approx 78\;kW\)

Explanation:

Flow ratio

The flow ratio of Francis turbine is defined as the ratio of the velocity of flow at the inlet to the theoretical jet velocity.

\(Flow\;Ratio = \frac{{{V_{f1}}}}{{\sqrt {2gH} }}\)

In the case of Francis turbine,

Flow ratio varies from 0.15 to 0.3

Speed ratio varies from 0.6 to 0.9

Calculation:

\(Flow\;Ratio = \frac{{7}}{{\sqrt {2\times10\times62} }}=0.2\)

Explanation:

Draft tube

It is a conduit which connects the runner exit to the tailrace where the water is being finally discharged from the turbine.

Hence, Draft tube at the exit of a reaction turbine used for the hydroelectric project is always immersed in water.

Function

The primary function of the draft tube is to reduce the velocity of the discharged water to minimize the loss of kinetic energy at the outlet. 

Non-dimensional specific speed is given by

\({N_S} = \frac{{N\sqrt P }}{{{{\left( {gH} \right)}^{\frac{5}{4}}} \cdot \sqrt \rho }}\)

The Francis turbine is a type of reaction turbine, and it can operate over a wide range of water flows and height differences, which makes it suitable for a specific speed value of 1. It is more flexible in terms of operation conditions compared to the Pelton wheel.

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.

So the Kaplan turbine has the highest specific speed.

The classification of the turbine based on the basis of operating head

Type of turbine	Operating head (m)
Pelton	300 m and above
Francis	60 m to 300 m
Kaplan	20 m to 60 m
Bulb	2 m to 20 m

 

The specific speed of a turbine is in the range of

Turbine	Ns
Pelton wheel	10 - 60
Francis	60 - 300
Kaplan	> 300

Concept:

In order to predict the behaviour of a turbine working under a varying condition of head, speed output, etc, the results are expressed in terms of quantities that may be obtained when the head on the turbine is reduced to unity.

The following are three important unit quantities.

Unit speed	Speed of turbine working under  a unit head	\({N_u} = \frac{N}{{\sqrt H }}\)
Unit discharge	Discharge passing through a turbine  which is working under a unit head	\({Q_u} = \frac{Q}{{\sqrt H }}\)
Unit power	Power developed by a turbine   working under unit head	\({P_u} = \frac{P}{{{H^{3/2}}}}\)

Concept:

 In order to predict the behaviour of a turbine working under a varying condition of head, speed output, etc, the results are expressed in terms of quantities that may be obtained when the head on the turbine is reduced to unity.

The following are three important unit quantities.

Unit speed	Speed of turbine working under  a unit head	\({N_u} = \frac{N}{{\sqrt H }}\)
Unit discharge	Discharge passing through a turbine  which is working under a unit head	\({Q_u} = \frac{Q}{{\sqrt H }}\)
Unit power	Power developed by a turbine   working under unit head	\({P_u} = \frac{P}{{{H^{3/2}}}}\)

Calculation:

Given:

\(\frac{N_1}{N_2}~=~\frac{3}{1}\)

∵\({N_u} = \frac{N}{{\sqrt H }}\)

⇒ \(\frac{N_1}{N_2}~=~\sqrt{\frac{H_1}{H_2}}\)

⇒ \(\frac{H_1}{H_2} ~=~\frac{9}{1}\)

Now, \({P_u} = \frac{P}{{{H^{3/2}}}}\)

⇒ \(​​​​\frac{P_1}{P_2}~=~(\frac{H_1}{H_2})^{\frac{3}{2}}\)

⇒ \(​​​​\frac{P_1}{P_2}~=~(\frac{9}{1})^{\frac{3}{2}}~=~\frac{27}{1}\)

Explanation:

Turbines are hydraulic machines that convert hydraulic energy into mechanical energy.

Classification of turbines based on the energy at inlet:

Impulse turbines	Reaction turbines
These have only Kinetic energy at the inlet.	They have both Kinetic energy and pressure energy at the inlet.
Examples: Pelton wheel, Girard turbine, Banki turbine, etc.	Examples: Kaplan turbine, Francis turbine, Propeller turbine, etc

Specific Speed of Turbines:

Type of turbine	Specific Speed (Ns)
Kaplan and Propeller	300 - 1000
Pelton	10 - 35
Francis	60 - 300

 

Head of turbines:

Type of turbine	Head
High head turbines: Pelton turbine	Above 250 m
Medium head turbines: Francis turbine	60 m - 250 m
Low head turbines: Kaplan and Propeller turbine	Below 60 m

Explanation:

The specific speed of a turbine is defined as, the speed of a geometrically similar Turbine that would develop unit power when working under a unit head (1m head). 

Mathematically it is given by:

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

Classification of turbines on the various basis is given in the table below:

Flow	Energy	Head	Specific speed	Example
Tangential	Impulse	High (300 m and above)	Low (0 – 60 RPM)	Pelton Wheel turbine
Radial	Reaction	Medium (30 m to 300 m)	Medium (60 – 300) RPM	Francis turbine
Axial	Reaction	Low (less than 30 m)	High
			(300 – 600) RPM	Propeller turbine
			(600 – 1000) RPM	Kaplan turbine

Concept:

Kaplan Turbine:

Kaplan Turbine is an axial reaction flow turbine and has adjustable blades. When the water flows parallel to the axis of the rotation of the shaft, the turbine is known as the axial flow turbine.

Flow ratio (ψ) for a Kaplan Turbine is given by:

\({\rm{ψ }} = \frac{{{{\rm{V}}_{\rm{f}}}}}{{\sqrt {2{\rm{gH}}} }}\)

Where V_f is the flow velocity at the inlet of the runner and 'H' is the head available.

Calculation:

Given:

ψ = 0.6, H = 20 m.

Taking g = 10 m/s²

\({\rm{ψ }} = \frac{{{{\rm{V}}_{\rm{f}}}}}{{\sqrt {2{\rm{gH}}} }}\)

\(0.6 = {\rm{\;}}\frac{{{{\rm{V}}_{\rm{f}}}}}{{\sqrt {2 \times 10 \times 20} }}\)

V_f = 12 m/s

∴ The velocity of flow at the inlet of the runner is 12 m/s.