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

Explanation:

Diaphragm in Steam Turbines

• In the context of steam turbines, a diaphragm refers to a separating wall or partition that is positioned between successive rotors of the turbine. The diaphragm carries stationary nozzles or guide blades, which are essential for redirecting and controlling the steam flow to the moving blades of the rotor downstream. This helps in converting the thermal energy of the steam into mechanical energy efficiently.

Working Principle: The diaphragm is a crucial part of the steam turbine's internal design. After the steam passes through the moving blades of the rotor, it needs to be redirected to the next set of moving blades. The diaphragm achieves this by holding the guide blades or nozzles that direct the steam flow appropriately. The stationary nozzles accelerate the steam and guide it into the next set of moving blades at an optimal angle, ensuring efficient energy transfer and minimizing losses.

Construction:

• The diaphragm is typically constructed from high-strength materials capable of withstanding the high-pressure and high-temperature conditions present in steam turbines.
• It is precisely engineered to ensure proper alignment of the stationary nozzles with the moving blades of the turbine rotor.
• Sealing mechanisms are often incorporated into the diaphragm design to minimize steam leakage and enhance overall efficiency.

Role of the Diaphragm in Steam Turbines:

• Separates successive turbine stages to maintain the desired pressure and thermal conditions for each stage.
• Holds the stationary nozzles or guide blades that direct steam flow efficiently onto the moving blades.
• Contributes to the aerodynamic efficiency of the turbine by ensuring smooth steam flow transitions between stages.
• Helps reduce steam leakage, enhancing the turbine's overall performance and efficiency.

Advantages of Using Diaphragms:

• Improved efficiency due to optimized steam flow direction and reduced leakage.
• Enhanced durability and reliability of the turbine by maintaining proper alignment and minimizing wear on components.
• Flexibility in designing multi-stage turbines with different pressure levels and steam velocities.

Applications: Diaphragms are commonly used in multi-stage steam turbines across various industries, including power generation, petrochemical processing, and marine propulsion systems.

Explanation:

De Laval Steam Turbine

• A De Laval steam turbine is a type of impulse steam turbine that uses a single-stage nozzle to accelerate steam to high velocity before it strikes the turbine blades. The kinetic energy of the steam is converted into mechanical work as the steam passes through the turbine rotor, leading to energy output.

In a steam turbine, the work done per unit mass is equal to the change in kinetic energy of the steam:

\( W = \frac{1}{2} m (V_1^2 - V_2^2) \)

Calculation:

Given:

Inlet velocity, \( V_1 = 30~\text{m/s} \)

Outlet velocity, \( V_2 = 10~\text{m/s} \)

Mass, \( m = 1~\text{kg} \)

Now,

\( W = \frac{1}{2} \times 1 \times (30^2 - 10^2) = \frac{1}{2} \times (900 - 100) = \frac{1}{2} \times 800 = 400~\text{N·m} \)

Explanation:

Critical Pressure Ratio in a Convergent Nozzle

• The critical pressure ratio of a convergent nozzle is defined as the ratio of the outlet pressure to the inlet pressure of the nozzle when the flow through the nozzle reaches its maximum mass flow rate per unit area. This ratio is a critical parameter in the design and operation of convergent nozzles, particularly in applications involving compressible fluid flow, such as in turbines, jet engines, and various industrial processes.

Convergent nozzle:

• A convergent nozzle is a device used to accelerate a fluid by decreasing its cross-sectional area. When a compressible fluid, such as a gas, flows through a convergent nozzle, the velocity of the fluid increases as the cross-sectional area decreases, in accordance with the principle of conservation of mass and energy. The relationship between the pressure, velocity, and density of the fluid is governed by the isentropic flow equations for compressible fluids.
• The critical pressure ratio occurs when the flow at the throat of the nozzle (the point of smallest cross-sectional area) reaches the speed of sound, also known as the Mach number equal to 1. At this point, the flow is said to be "choked," and the mass flow rate through the nozzle becomes maximum for the given inlet conditions. Any further decrease in the outlet pressure below this critical value will not increase the mass flow rate.

The critical pressure ratio of a convergent nozzle is the ratio at which the flow becomes choked and mass flow rate per unit area is maximum.

At this point, further decrease in outlet pressure does not increase the mass flow rate.

\( \left(\frac{P_2}{P_1}\right)_{\text{critical}} = \left(\frac{2}{\gamma + 1} \right)^{\frac{\gamma}{\gamma - 1}} \)

Where \( \gamma \) is the ratio of specific heats, \( P_1 \) is inlet pressure, and \( P_2 \) is outlet pressure.

Explanation:

Mach Number Across a Normal Shock Wave

• A normal shock wave is a sudden and nearly discontinuous change in the flow properties of a compressible fluid (usually a gas) that occurs when the flow transitions from supersonic to subsonic speeds. The Mach number (M) is a crucial parameter in this context, defined as the ratio of the fluid velocity to the speed of sound in the medium.
• In an adiabatic and steady flow situation, the Mach number cannot increase across a normal shock wave. This behavior is governed by the fundamental principles of gas dynamics and is mathematically expressed using the Rankine-Hugoniot relation.

Rankine-Hugoniot Relation

• The Rankine-Hugoniot relation is a set of equations derived from the conservation laws of mass, momentum, and energy across a shock wave. These equations describe the relationship between the pre-shock and post-shock states of the fluid. Specifically, they ensure the continuity of mass, momentum, and energy across the shock front. Here’s how the Rankine-Hugoniot relation explains why the Mach number cannot increase across a normal shock wave:

1. Conservation of Mass:

The mass flow rate is conserved across the shock wave. Mathematically, this is expressed as:

ρ₁U₁ = ρ₂U₂

where:

• ρ₁, ρ₂: Densities of the fluid before and after the shock
• U₁, U₂: Velocities of the fluid before and after the shock

2. Conservation of Momentum:

The momentum equation across the shock wave is given by:

P₁ + ρ₁U₁² = P₂ + ρ₂U₂²

where:

• P₁, P₂: Static pressures before and after the shock

3. Conservation of Energy:

The total energy (including internal energy and kinetic energy) is also conserved across the shock wave, expressed as:

h₁ + (U₁² / 2) = h₂ + (U₂² / 2)

where:

• h₁, h₂: Specific enthalpies before and after the shock

4. Implications for the Mach Number:

Combining these conservation equations reveals that the post-shock Mach number (M₂) is always less than 1 (subsonic), while the pre-shock Mach number (M₁) is greater than 1 (supersonic). This means the flow transitions from supersonic to subsonic across the normal shock wave.

In essence, the Rankine-Hugoniot relation establishes the fundamental physics that prevents the Mach number from increasing across a normal shock wave. Instead, the Mach number decreases as a result of the increase in pressure, temperature, and density, and the decrease in velocity

Explanation:

To calculate the velocity of steam at the outlet of the nozzle, we will use the principle of energy conservation, specifically the Steady Flow Energy Equation (SFEE). The SFEE states:

h₁ + (v₁²/2) = h₂ + (v₂²/2)

Here:

• h₁ = Specific enthalpy at the inlet (kJ/kg)
• h₂ = Specific enthalpy at the outlet (kJ/kg)
• v₁ = Velocity at the inlet (m/s)
• v₂ = Velocity at the outlet (m/s)

\( \frac{V_2^2}{2} - \frac{V_1^2}{2} = \Delta h \Rightarrow V_2 = \sqrt{V_1^2 + 2\Delta h} \)

Calculation:

Given:

Enthalpy drop, \( \Delta h = 50~\text{kJ/kg} = 50000~\text{J/kg} \)

Inlet velocity, \( V_1 = 5~\text{m/s} \)

Substitute into equation:

\( V_2 = \sqrt{5^2 + 2 \times 50000} = \sqrt{25 + 100000} = \sqrt{100025} \approx 316.2~\text{m/s}\)

Explanation:

Simple Impulse Turbine (De Laval Turbine):

• It is the first working impulse turbine.
• It consists of a single set of the nozzle and moving blades. Therefore, total pressure drop from boiler pressure to condenser pressure takes place in a single nozzle which gives high rotational speed exceeding pressure limit of 3000 rpm.
• These turbines are mostly used in small power and high-speed purposes.

Additional Information

Concept:

• In general, based on the working principle, both the pressure and velocity of steam drops in the moving blades of the reaction turbine. In the case of an impulse turbine, there is no drop of pressure in the moving blade. It can be seen in the following diagram.

Compounding is done to decrease the high rotational speed of simple impulse turbines to bring it down to the practical limit required for electricity generation. There are two ways of compounding i.e. pressure compounding and velocity compounding.

In pressure compounded impulse turbine (or Rateau turbine), the total pressure drop is planned for more than one stage and each stage consists of a set of nozzles and moving blades, as the enthalpy in each stage is decreased, it decreases the rotational speed.

Whereas in velocity compounded impulse turbine (or Curtis turbine), the total velocity drop is arranged in more than one stage and each stage consists of a set of fixed and moving blades. There is a single nozzle in which total pressure drop takes place and the high velocity obtained is converted into work in more than one stage.

How the pressure and velocity of steams drop for a pressure compounded and a velocity compounded impulse turbine can be seen from the following figure.

Explanation:

• There is no drop of pressure in the moving blade after coming out of the nozzle and is equal to atmospheric pressure generally.
• The absolute velocity of the steam decreases as it proceeds further in the moving blade.

• Both the pressure and velocity of steam drops in the moving blades of the reaction turbine.

It can be observed from the following diagram.

Note: V₁ and V₂ are absolute velocities and V_r1 and V_r2 are the relative velocities component here.

Additional Information

Compounding is done to decrease the high rotational speed of simple impulse turbines to bring it down to the practical limit required for electricity generation. There are two ways of compounding i.e. pressure compounding and velocity compounding.

1. In pressure compounded impulse turbine (or Rateau turbine), the total pressure drop is planned for more than one stage and each stage consists of a set of nozzles and moving blades, as the enthalpy in each stage is decreased, it decreases the rotational speed.
2. In velocity compounded impulse turbine (or Curtis turbine), the total velocity drop is arranged in more than one stage and each stage consists of a set of fixed and moving blades. There is a single nozzle in which total pressure drop takes place and the high velocity obtained is converted into work in more than one stage.

The pressure and velocity variation of pressure compounded and a velocity compounded impulse turbine can be seen from the following diagram.

Concept:

\({\rm{P}} = \frac{{2{\rm{\pi NT}}}}{{60}}\)

where, P = power developed in Watt ; N = speed in rpm, T = Torque (moment of momentum) in N-m.

Calculation:

Given:

N = 600 rpm; T = 15.915 kN-m ⇒ 15.915 × 10³ Nm ;

\( P = \frac{{2 × \pi × 600 × 15.915 × {{10}^3}}}{{60}}\)

P = 0.999 MW = 1 MW.

Concept:

Degree of reaction is the ratio of enthalpy drop in the rotor to the enthalpy drop in a stage.

 i.e. \({\rm{R}} = \frac{{{\rm{Static\;enthalpy\;drop\;or\;rise\;in\;rotor}}}}{{{\rm{Stagnation~enthalpy\;drop\;or\;rise\;in\;stage}}}}\)

Or, \(R = \frac{{static\;pressure\;drop\;or\;rise\;in\;rotor}}{{stagnation\;pressure\;drop\;or\;rise\;in\;stage}}\)

In the case of impulse turbine, there is no change in the enthalpy in the rotor, so the degree of reaction is zero.

R = 0.

Concept:

Impulse Turbine Working:

In the impulse turbine pressure drops and the velocity increases as the steam passes through the nozzles. When the steam passes through the moving blades the velocity drops but the pressure remains the same.

The fact that the pressure does not drop across the moving blades is the distinguishing feature of the impulse turbine. The pressure at the inlet of the moving blades is the same as the pressure at the outlet of moving blades.

In the case of a reaction turbine, the moving blades of a turbine are shaped in such a way that the steam expands and drops in pressure as it passes through them. As a result of the pressure decrease in the moving blade, a reaction force will be produced. This force will make the blades to rotate.

Velocity Compounded Impulse Turbine:

The velocity-compounded impulse turbine (Curtis stage turbine), is composed of one stage of nozzles as the single-stage turbine, followed by two rows of moving blades instead of one. These two rows are separated by one row of fixed blades attached to the turbine stator, which has the function of redirecting the steam leaving the first row of moving blades to the second row of moving blades. In the Curtis stage, the total enthalpy drop and hence pressure drop occur in the nozzles so that the pressure remains constant in all three rows of blades.

Velocity is absorbed in two stages. In fixed (static) blade passage both pressure and velocity remain constant. Fixed blades are also called guide vanes.

Velocity is absorbed in two stages. In fixed (static) blade passage both pressure and velocity remain constant. Fixed blades are also called guide vanes.

Concept:

Impulse Turbine:

• In impulse turbine, steam coming out at a very high velocity through the fixed nozzle strikes the blades fixed on the periphery of a rotor.
• The blades change the direction of the steam flow without changing its pressure.

Impulse-Reaction Turbine:

• In an impulse reaction turbine, steam expands both in fixed and moving blades continuously as the steam passes over them.
• The pressure drop occurs continuously over both moving and fixed blades.
   

Explanation:

• Compounding of steam turbines is the method in which energy from the steam is extracted in a number of stages rather than a single stage in a turbine.
• A compounded steam turbine has multiple stages i.e. it has more than one set of nozzles and rotors, in series, keyed to the shaft or fixed to the casing, so that either the steam pressure or the jet velocity is absorbed by the turbine in number of stages.
• Compounding of steam turbines are done, where rotor speed (flow speed) is reduced in steps, this prevent over speeding of turbine, which could lead to mechanical failures of turbine blades.

Concept:

• In general, based on the working principle, both the pressure and velocity of steam drops in the moving blades of the reaction turbine. In the case of an impulse turbine, there is no drop of pressure in the moving blade. It can be seen in the following diagram.

Compounding is done to decrease the high rotational speed of simple impulse turbines to bring it down to the practical limit required for electricity generation. There are two ways of compounding i.e. pressure compounding and velocity compounding.

In pressure compounded impulse turbine (or Rateau turbine), the total pressure drop is planned for more than one stage and each stage consists of a set of nozzles and moving blades, as the enthalpy in each stage is decreased, it decreases the rotational speed.

Whereas in velocity compounded impulse turbine (or Curtis turbine), the total velocity drop is arranged in more than one stage and each stage consists of a set of fixed and moving blades. There is a single nozzle in which total pressure drop takes place and the high velocity obtained is converted into work in more than one stage.

How the pressure and velocity of steams drop for a pressure compounded and a velocity compounded impulse turbine can be seen from the following figure.

Explanation:

Throat:

1. The section of the minimum cross-sectional area is known as the throat. These are designed to be obtained the desired pressure ratio as well as the maximum discharge transfer. 
2. Flow velocity at the throat of nozzle operating at designed for maximum pressure ratio is the velocity of sound.
3. Flow velocity if it designed for the maximum discharge then,

• Up to the throat, the flow velocity is subsonic.
• Flow velocity after the throat is supersonic.​

​So, Flow velocity at the throat of a converging-diverging nozzle is Sonic when it designed for the maximum discharge.

Additional Information

Mach number (M):

We can say the speed of sound can be equated to Mach 1 speed. The Mach number due to the local speed of sound is dependent on the surrounding mediums in specific temperature and pressure. Flow can be determined as an incompressible flow with the help of the Mach number. The medium can either be a liquid or a gas. The medium can be flowing, whereas the boundary may be stable or the boundary may be traveling in a medium that is at rest.

M = \(\frac{u}{c}\)

Where, u = Local flow velocity, c = Speed of sound

Its classification: