BPSC AE Paper 5 (Mechanical) 2012 Official Paper (Previous Year Paper)

Concept:

• Convergent - Divergent nozzles are used to increase the flow of gas to supersonic speeds (as in the case of rockets).
• Their cross-sectional area first decreases and then increases. The area where the diameter is minimum is called the throat.
• As the gas enters the converging section, its velocity increases, considering the mass flow rate to be constant.
• As the gas passes through the throat, it attains sonic velocity (Mach number = 1).
• As the gas passes through the divergent nozzle, the velocity increases to supersonic (Mach number >1)
• The flow rate is maximum for a given nozzle if the flow is sonic at the throat. This condition is achieved by managing the back pressure.
• For the compressible fluid flow, the Mach number is an important dimensionless parameter. On the basis of the Mach number, the flow is defined.

Important Points

Explanation:

Steam Nozzle:

The steam nozzle is a passage of varying cross-sections by means of which a part of the enthalpy of steam is converted into kinetic energy as the steam expands from a higher pressure to a lower pressure. Therefore, a nozzle is a device designed to increase the velocity of steam.

Convergent-Divergent nozzle: Generally, the configuration of the nozzle is of the decreasing area because we deal with the subsonic flow but when the flow becomes sonic or supersonic we have to use the convergent-divergent configuration of the nozzle.

Mach no: It is defined as the ratio of the velocity of flow to the velocity of sound in the same fluid medium under the same conditions.

\({\rm{Ma;}} = \frac{{{{\rm{V}}{{\rm{flow}}}}}}{{{{\rm{V}}{{\rm{sound}}}}}}\)

• Subsonic flow: when the velocity of flow is lower than the velocity of sound in that medium then this flow is called subsonic flow. for subsonic flow Ma < 1
• Sonic flow: when the velocity of flow becomes equal to the velocity of sound. for sonic flow Ma = 1
• Supersonic flow: when the velocity of flow becomes greater than the velocity of sound. for supersonic flow Ma > 1

• In a convergent-divergent nozzle at a point where the velocity of flow becomes equal to the velocity of sound (i.e. Ma = 1) the value of pressure is called critical value because after this value flow becomes supersonic and we have to increase the area of flow to achieve the increase in pressure.

Important Points

At, Mach = 1 the properties of flow is called critical properties & the velocity of flow is called sonic velocity.

Concept:

• Convergent - Divergent nozzles are used to increase the flow of gas to supersonic speeds (as in the case of rockets).
• Their cross-sectional area first decreases and then increases. The area where the diameter is minimum is called the throat.
• As the gas enters the converging section, its velocity increases, considering the mass flow rate to be constant.
• As the gas passes through the throat, it attains sonic velocity (Mach number = 1).
  

As the gas passes through the divergent nozzle, the velocity increases to supersonic (Mach number >1)

• The flow rate is maximum for a given nozzle if the flow is sonic at the throat. This condition is achieved by managing the back pressure.
• For the compressible fluid flow, the Mach number is an important dimensionless parameter. On the basis of the Mach number, the flow is defined.

Concept:

Under thermal equilibrium there are two conditions:

1. There will be no heat transfer i.e. adiabatic process
2. The entropy change will be zero for ideal flow (i.e. reversible process will take place)

Both these conditions leads to the point that the process is reversible adibatic and reversible adibatic process is always isentropic process.

Important Points

The isentropic process is not a practical process hence a term isentropic efficiency comes into the picture which is given as:

${\eta _{isentropic}} = \frac{{actual;enthalpy;drop}}{{isentropic;enthalpy;drop}}$    (for turbines)

${\eta _{isentropic}} = \frac{{isentropic;enthalpy;drop}}{{actual;enthalpy;drop}}$    (for compressors)

Concept:

• Convergent - Divergent nozzles are used to increase the flow of gas to supersonic speeds (as in the case of rockets).
• Their cross-sectional area first decreases and then increases. The area where the diameter is minimum is called the throat.
• As the gas enters the converging section, its velocity increases, considering the mass flow rate to be constant, it attains subsonic velocity (Mach number < 1).
• As the gas passes through the throat, it attains sonic velocity (Mach number = 1).
• As the gas passes through the divergent nozzle, the velocity increases to supersonic (Mach number >1)
• The flow rate is maximum for a given nozzle if the flow is sonic at the throat. This condition is achieved by managing the back pressure.
• For the compressible fluid flow, the Mach number is an important dimensionless parameter. On the basis of the Mach number, the flow is defined.

Concept:

In a converging-diverging nozzle, when the back pressure ratio reaches a critical value, the flow will become choked with the subsonic flow in the converging section, sonic flow at the throat, and supersonic flow in the diverging section.

A further decrease in the back pressure ratio results in the formation of a shock wave within the diverging section.

The location of the shock is such that the pressure at the diverging section exit will equal the back pressure. As the back pressure ratio is decreased further, the shock wave moves downstream of the throat toward the exit of the device as shown below.

Explanation:

Compressor:

• The air compressor used in gas turbines is of rotary type mainly axial flow turbines.
• It draws air from the atmosphere and compressed to the required pressure.

Compressors can be of two types:

1. Positive displacement type Compressor:

• Positive displacement type like reciprocating compressors, Root's blower, and vane - sealed machines.

2. Rotary type Compressor:

• Rotary type like centrifugal and axial flow compressor.

Losses in centrifugal compressor:

• Intel losses : 
• At the inlet of the compressor, major losses occur due to the formation of eddy's, turbulence, and friction.
• Since the entry of fluid in a centrifugal compressor is axially then suddenly fluid is being directed to radially towards blades and due to this off-design condition incidence losses occur.
• Impeller losses:
• Recirculating losses: these losses occur due to flow reversal of fluid at the impeller exit, this backflow of fluid is a function of the vane exit angle.
• Wake-mixing losses: this loss occurs when fluid flow through the passage of blades, and it causes awake in the vanless space of the rotor.
• Slip losses: these losses occur due to the inertia effect of fluid between blade passage, and a component of velocity lost which is called slip in whirl component.
• Diffusor losses :
• When fluid flows through diffusor frictional losses occur in the diffused area due to skin friction coefficient and since the area is decreasing in the direction of flow hence positive pressure gradient is created so back flow losses can also occur in diffusor.

Concept:

Degree of reaction 

• Degree of reaction or reaction ratio (R) is defined as the ratio of the static pressure drop/increase in the rotor (moving blade) to the static pressure drop/increase in the stage (both fixed blade and moving blade) or as the ratio of static enthalpy drop in the rotor to the static enthalpy drop in the stage.
• $Degree;of;reaction = \frac{{Enthalpy;drop;in;Rotor}}{{Enthalpy;drop;in;Stage}}$
• Degree of reaction may also be defined as 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 an impulse turbine, there is no change in the enthalpy in the rotor, so the degree of reaction is zero.
• R = 0.
• And for Parson’s turbine or 50% reaction turbine R = 0.5 and for Hero’s turbine R = 1.

Explanation:

• Vane Compressor is also known as Rotary Vane Compressor or Sliding Vane compressor.

• Vane Compressor used centrifugal motion to generate compressed air.

• Vane Compressor consists of a cylindrical rotor eccentrically placed in the casing.

• This casing has intake and delivery openings which are also known as inlet and outlet port. The inlet port of the casing is bigger as compared to the outlet port of the casing. Rotor has a drum in its center.

• This drum rotates eccentrically with respect to the casing.

• As the center, shaft continues to rotate, and since it is off-center to the cylinder, the succeeding compartments between the vane are smaller and smaller,  being closer to the outer wall.

• The result is a larger volume of air is compressed into a smaller volume and the now-compressed air is released through another valve into a compressor tank or compressor receiver or into the shop air mains.

• If we increase the mass flow rate then we have to increase the rotor rpm only, an increase in mass flow rate does not increase the pressure ratio because fluid is trapped between the same volume again and again so the pressure ratio is not going to change.

The pressure ratio in a vane rotary compressor is independent of the mass flow rate.

Explanation:

Gas turbine blades are given a rake in the direction of motion of blades.

Explanation:

• Operating conditions of gas turbines are such that the high temperature of the gas stream passes over blades and the complex stress is exposed to blades resulting in various degradation mechanisms.
• When degradation mechanisms become active in blades with time, they can reduce service life.
• Most important failure mechanisms in industrial turbine blades are creep damage, fatigue, corrosion, erosion and environmental attack (oxidation, hot corrosion, erosion and foreign object damage).
• Therefore Gas turbine blades are made of nickel-based (neimonic) and cobalt-based superalloys since these materials are able to withstand the combination of high stress and high temperature.

Concept:

• The specific heat capacity of a substance is defined as the quantity of heat energy required to raise the temperature of a given amount of the substance by a certain amount. This property is temperature-dependent for virtually all materials, but the degree to which it varies depends on the specific substance in question.
• Pressure: For ideal gases, changes in pressure do not affect the specific heat capacity. This is due to the assumption that intermolecular forces are negligible in ideal gases, i.e., the gas molecules do not "interact" with one another. In reality, gases do not behave completely ideally. At very high pressures, these assumptions start to break down, and the specific heat capacity might change slightly with pressure. However, for most practical purposes and problems, the impact of pressure change on the specific heat capacity is usually ignored.
• Temperature: The specific heat capacity can change significantly with temperature. As the temperature of a system increases, the molecules within that system gain kinetic energy, meaning they move and vibrate more vigorously. It requires additional energy to increase this kinetic energy further, which leads to an increase in the specific heat capacity. Simply put, it takes more heat to increase the temperature of an already 'hot' system than it does to increase the temperature of a 'cold' system.
• Fuel-Air Ratio: This is the ratio of the amount of fuel to the amount of air in a combustion process. Varying the fuel-air ratio will change the composition of the combustion products and indirectly the temperature of combustion, both of which can impact the specific heat capacity of the products.
• If we increase the fuel-air ratio (more fuel per unit of air), incomplete combustion can occur leading to combustion products like carbon monoxide and soot, along with the regular products of combustion (CO2 and water vapour). These products can exhibit different specific heat capacities compared to the products of complete combustion.
• Simultaneously, a high fuel-air ratio also means a higher combustion temperature, since there's less excess air to absorb the heat. A hotter combustion process will typically result in combustion products with higher specific heat capacities, due to the temperature dependence mentioned earlier.

Concept:

Intercooling:

• It is the stage of multi-compression in a gas turbine.
• After the compression of gas in the first compressor, its pressure and temperature are increase this gas is passed through the intercooler where its temperature decrease.
• The intercooling process is done by passing an extra amount of water or air.
• This gas is again compressed in a second compressor then it is passed into the combustion chamber.
• Intercooling between the stages in the compressor leads to a decrease in the compressor work input therefore it will also help to increase the work ratio of the gas turbine plant resulting in a decrease in the thermal efficiency, but the scope of regeneration will increase.

Work Ratio:

• It is defined as the ratio of net-work to turbine work.
• W_net = W_T - W_C
• _{Due to perfect intercooling, compressor work decreases so net-work increases as turbine work remain constant.}
• _{So work ratio increase .}

Explanation:

Reheating in Gas Turbine:

• In Reheating, heat input will be increased at the same time work output by the turbine will also be increased so from this result it can not be concluded that the thermal efficiency will increase or decrease.
• Reheating is a method of increasing the mean temperature of heat reception which causes an increase in thermal efficiency.
• In this, the gas is again heated after it has expanded in the gas turbine.

Effect of reheating:

• This increases the work output of the turbine by keeping the compressor work constant.
• For a given power output, the fuel consumption rate decreases.
• Work ratio increases.
• Turbine work increases
• Compressor work constant.
• Heat supplied in the system increases
• Heat rejected from the system increases
• Net work output increases
• Mean temperature of heat addition increases
• Scope of regeneration increases
• Cycle efficiency decreases

Work Ratio;

• Here, Work ratio is the ratio of Net Turbine work and Turbine Work. Since Turbine work increases and Compressor work remains constant, Work ratio increases.
• ${r_{wr}} = \frac{{Net;Work}}{{Positive;Work}} = \frac{{{W_T} - {W_C}}}{{{W_T}}} = 1 - \frac{{{W_C}}}{{{W_T}}}$
• So, the Work ratio will be increased definitely

Explanation:

Insulation

• It is defined as a process of preventing the flow of heat from the body by applying insulator materials to the surface which controls the rate of heat transfer.
• The insulating ability of an insulator depends on various factors:
• thickness of insulator
• material of insulator
• surrounding conditions
• temperature difference
• Generally, air packets are present in porous insulating materials.
• Since water which is a more conductive material is replacing air which is a less conductive material, so the overall insulating ability of the insulator will decrease. Most insulators are porous in nature.
• If it has been about Non-porous insulators then the insulating ability will remain unaffected.

Explanation:

• There are three methods of heat transfer between the two systems. They are conduction, convection, and radiation.
• Conduction is a method of heat transfer in solids and heat transfer takes place without the movement of particles.
• Convection is a method of heat transfer in fluids (gases and liquids) and heat transfer takes place due to the movement of particles.
• Radiation is a method of heat transfer where heat is transferred from one place to another without affecting the medium of heat transfer.

Now let's see what happens in a steam boiler:

• A steam boiler is designed to absorb the maximum amount of heat released from the process of combustion.
• Heat transfer within the steam boiler is accomplished by three methods: radiation, convection, and conduction. The heating surface in the furnace area receives heat primarily by radiation.
• The remaining heating surface in the steam boiler receives heat by convection from the hot flue gases. Heat received by the heating surface travels through the metal by conduction
• Heat is then transferred from the metal to the water by convection.

Concept:

According to Fourier’s law, the rate of heat flow, Q through a homogeneous solid is directly proportional to the area A, of the section at the right angles to the direction of the heat flow, and to the temperature difference dT along the path of heat flow.

$Q = - kA\frac{{dT}}{{dx}};$

Calculation:

Given:

k1 = 2k2

As nothing is mentioned about the other variables like Area, Temperature change across the wall so consider this as a fixed parameter.

$Q = - kA\frac{{dT}}{{dx}};$

$Q \propto k$

$\frac{Q_1}{Q_2}=\frac{k_1}{k_2}=\frac{2}{1}=2$

Concept:

Steam pipe: It is used to transfer the steam from boiler to the working component (turbine). For maximum efficiency of component, the steam in the pipe should not be changed its properties (like temperature, pressure, etc.). Therefore, to prevent the temperature losses, we use the insulation over the pipe. 

Insulation: The products (material) which reduces the heat losses to the atmosphere. The conductivity value of insulating material is very less.

If we put inferior insulating material over the pipe then it conduct more heat from steam than superior insulating material to the intermediate surface between two insulating material and steam losses heat to the atmosphere. Therefore, we use superior insulation put over the pipe an inferior over it.  

Explanation:

Kirchhoff’s law:

• Let E be the total emissive power of the body and α be the absorptivity of the body.
• Emissivity (ϵ) is the ratio of the emissive power of a non-black body to the black body.
• ϵ = $\frac{E}{E_b}$
• Kirchhoff’s law also holds for monochromatic radiation, for which
• \(\frac{{{E_{\lambda 1}}}}{{{\alpha {\lambda 1}}}} = \frac{{{E{\lambda 2}}}}{{{\alpha {\lambda 2}}}} = \frac{{{E{b\lambda }}}}{{{\alpha {b\lambda }}}} = \frac{{{E{b\lambda }}}}{1}\)
• ∵ Absorptivity of a black body is one.
• \(\therefore \frac{{{E_\lambda }}}{{{\alpha \lambda }}} = {E{b\lambda }} \Rightarrow {\alpha \lambda } = \frac{{{E\lambda }}}{{{E_{b\lambda }}}} = {\epsilon_\lambda }\)
• Therefore, the monochromatic emissivity of a black body is equal to the monochromatic absorptivity at the same wavelength.
• Eλ = αλEbλ
• According to Kirchhoff’s law, the ratio of total emissive power to absorptivity is constant for all bodies which are in thermal equilibrium with the surroundings. Therefore, it means that the emissivity of a body is equal to its absorptivity.

Stefan-Boltzmann Law

• The thermal energy radiated by a black body per second per unit area is proportional to the fourth power of the absolute temperature and is given by:
• E ∝ T4
• E = σT4
• σ = The Stefan – Boltzmann constant = 5.67 × 10^-8 Wm^-2K^-4

Wien’s displacement law

• For a black body emissive spectrum, the wavelength λmax giving the maximum emissive power at a temperature is inversely proportional to the absolute temperature.
• λ_max = $\frac{c}{T}$
• λ_maxT= c
• Wavelength = $\frac{Speed ~of ~Light}{Frequency}$ ⇒ λ = $\frac{c}{V}$

Concept:

​Total emissive power

• Total emissive power is defined as the total amount of radiation emitted by a body per unit time.
• Emissivity is defined as the ratio of the total emissive power of a body to the total emissive power of a black body. It is denoted by ϵ.
• ϵ = E/Eb

Explanation:

The emissive power of a Black Body depends upon its temperature only, whereas in the case of a Grey Body it depends on emissivity as well as temperature.

Emissivity itself depends on

• Type of Material
• Physical nature of the surface
• Viewing angle
• Wavelength
• Geometry
• Temperature

Hence, we can say that the emissive power of a body depends upon all the above factors.

Important Points

The term "body" generally refers to "Grey Body", we cannot assume it "Black Body" unless or until it is specified.

$E = \in \sigma {T^4}$

${E_b} = \sigma {T^4}$

Concept:

Blackbody

• A blackbody allows all incident radiation to pass into it (no reflected energy) and internally absorbs all the incident radiation (no energy transmitted through the body).
• This is true for radiation of all wavelengths and for all angles of incidence. Hence the blackbody is a perfect absorber for all incident radiation.

Opaque surface 

• The opaque surface doesn't allow the radiations falling on to transmit through it, therefore, the radiations falling upon it will be either absorbed by it or will be reflected back, which means the transmissivity of an opaque surface will be zero.
• So for an opaque surface since τ = 0
• α + ρ + 0 = 1
• hence we get, α + ρ = 1

Concept:

• Thermal radiation is the transmission of heat in the form of radiant energy from one body to another body by the thermal motion of charged particles of matter.

• The mechanism of radiation is divided into 3 phases

• Conversion of thermal energy of the hot source into electromagnetic waves

• Passage of wave motion through intervening medium

• Transformation of waves into heat

• Thermal radiation is limited to wavelengths ranging from 0.1 to 100 µm of the electromagnetic spectrum.

• It includes some portion of UV radiation (0.1 to 0.4 µm), entire visible radiation (0.4 to 0.7 µm), and entire infrared radiation (0.7 to 100 µm)

Explanation:

Critical Pressure/Temperature: 

• It is defined as the pressure/temperature at which liquid flashes into vapour.
• And there does not exist any distinction between the liquid and gaseous phase.
• Degree of freedom at critical pressure is zero.
• At a critical point, dryness fraction is undefined.
• Latent heat becomes zero at critical pressure.
• For water, P_cr = 221.2 bar, T_cr = 374.15°C

Concept:

• The compressed refrigerant vapor travels to the condenser, the condenser is where heat is rejected from the refrigeration system. the high-pressure, high-temperature vapor leaving the compressor undergoes three changes in the condenser.

1. The refrigerant gives up sensible heat in preparation for condensing
2. The refrigerant condenses from a vapor into a liquid, rejecting latent heat
3. After condensing to 100% liquid, the refrigerant subcools and continues to reject sensible heat.

• Sensible heat is defined as a temperature change that can be measured with a thermometer. You can observe changes in outside temperature. by looking at a thermometer or by opening the window and sticking your head out.
• Latent heat, on the other hand, is a temperature change that cannot be measured with a thermometer. Latent heat is therefore also referred as "hidden heat".
• "Subcooling" refers to the amount of sensible heat that is removed from a liquid after it has condensed.

Concept:

• In the evaporator, the refrigerant enters at very low pressure and temperature after passing through the expansion valve.
• This refrigerant absorbs the heat from the substance that is to be cooled so the refrigerant gets heated while the substance gets cooled.
• The refrigerant leaves the evaporator in the vapour state, mostly superheated and is absorbed by the compressor.
• In the compressor, the temperature and pressure both increases.
• After compressor, the refrigerant goes to the condenser where its temperature decreases while pressure is constant.
• So in the entire cooling cycle the pressure and temperature changes.

Concept:

Ideal-gas equation: PV = nR0T

Characteristic gas equation: PV = mRT

Where R is known as Characteristic Gas Constant (or simply Gas Constant) and R0 is Universal Gas Constant.

$R = \frac{{{R_0}}}{M}$where M is molecular weight.

Explanation:

Specific heat:

• specific heat is a quantity of energy required for a unit mass to change the temperature by 1 K or 1°C.
• Specific heat is a function of operating temperature so it increases with an increase in operating temperature but incremental in value is negligible therefore we need to treat it is independent of temperature.
• In the case of **compressible medium-**specific heat is defined on basis of constant pressure, constant volume. But in the case of the incompressible medium, both the specific heats are equal.
• Specific heat is a property of medium which indicates the store or absorb of thermal energy. The more the specific heat more the ability to store energy more.

Important Points 

• Examples: 
• C_water = 4.187 kJ/kg-K.
• C_iron = 0.45 kJ/kg-K
• (C_p)_air = 1.005 kJ/kg-K = 0.24 kcal.Kg^-1.C^-1
• (C_V)_air = 0.718 kJ/kg-K.

NOTE: 1 Calorie = 4.186 Joules

Explanation:

• Heat: It is a form of energy In transit due to temperature differences. It occurs by conduction, convection, and radiation.
• work: Energy transfer associated with a force acting through a distance.
• Thermal conductivity is mainly a function of the motion of the free electrons therefore property of a material, not a path function.
• Thermal conductivity: It is basically the ability to conduct heat from one end to the other by the collision and entropy change by the electrons of the material. Hence it’s the property of the material, hence not a path function
• To find the change in kinetic energy, we directly subtract the final and initial values. It's the energy possessed by the particle due to its motion. Hence is a state function, not a path function

Additional Information

Any characteristic of the system is called the property of the system.

Properties are classified as follows:

• Intensive or intrinsic property: Independent of the mass of the system under consideration.
• Example: Temperature, pressure, density, velocity, all specific properties are intensive properties (specific enthalpy, specific entropy, specific volume).
• Extensive or Extrinsic property: Depends on the mass of the system under consideration.
• Example: Energy, volume, enthalpy.

Important Points 

Thermal conductivity:

• It is a thermophysical property of a material that tells about the ability of a material to allow the heat energy to get conducted through the material rapidly.
• Insulators have very low values of thermal conductivity thereby heat transfer rate.
• Example: Abestos, Refractory brick.

Explanation:

Otto cycle:

(1-2) - Reversible adiabatic compression

(2-3) - Constant volume of heat addition.

(3-4) - Reversible adiabatic Expansion.

(4-1) - Constant volume of heat rejection.

Calculation:

Given:

During  Ideal conditions, we get maximum work output (T₂=T₄)

T₁ = T_Min and T₃ = T_Max

Calculation:

(1-2) Reversible adiabatic compression:

$\left( {\frac{{{T_2}}}{{{T_1}}}} \right) = {\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^{\gamma - 1}}$

(3-4) Reversible adiabatic expansion:

$\left( {\frac{{{T_3}}}{{{T_4}}}} \right) = {\left( {\frac{{{V_4}}}{{{V_3}}}} \right)^{\gamma - 1}}$

In the otto cycle: V₄ = V_1, V₃ = V₂

_{$(\frac{{T_2}}{{T_1}} )=(\frac{{T_3}}{{T_4}})$}

$T_2×T_4=T_3×T_1$

${\left( {{T_2}} \right)^2} = \left( {{T_3} \times {T_1}} \right)$

$\left( {{T_2}} \right) = \left( {\sqrt {{T_3} \times {T_1}} } \right)=\sqrt{T_{max}\times T_{min}}$

Concept:

• There are eight properties of a system, namely pressure (p), Volume (V), temperature (T), internal energy (u), enthalpy (h), entropy (s), Helmholtz function (f) and Gibbs function (g) and h, f and g are referred to as thermodynamic potentials.
• Helmholtz function F = U - TS
• Gibbs free function G = H - TS

Concept:

Specific Fuel Consumption (SFC):

• The fuel consumption characteristics of an engine are generally expressed in terms of specific fuel consumption in kg of fuel per kW-hr.
• It is an important parameter that reflects how good engine performance is.
• It is inversely proportional to the thermal efficiency of the engine.
• Brake-specific fuel consumption (bsfc) and indicated specific fuel consumption (isfc) is the specific fuel consumption on the basis of brake power (bp) and indicated power (IP) respectively.
• $sfc = \frac{{Fuel;consumption;per;unit;time}}{{power}}$

Concept:

• A dual cycle or limited pressure cycle is a thermodynamic cycle for high-speed diesel and hot spot ignition engines.

• Whether heat is added at constant pressure or constant volume in actual applications, depends upon the rate of heat added and the rate at which pressure decreases due to movement of the piston.

• In an ideal cycle, the piston is assumed stationary during heat addition at constant volume, but in practice, this does not happen.

• As the speed of the engine increases, the rate of decrease of pressure due to the movement of the piston increases, and heat addition cannot be assumed at either constant volume or constant pressure.

• In such a case, a better approach for modeling the situation will be to assume heat addition initially at constant volume and then at constant pressure. That is why a dual combustion cycle is used.

• All diesel engines except slow-speed engines use mixed dual cycles.

• This is because in mixed dual cycles the heat input occurs partially at constant volume and partially at constant pressure.

Explanation:

• Fuel may be defined as a substance, which on burning with oxygen produces a large amount of heat.
• Fuel is mainly composed of carbon and hydrogen.
• The energy produced by the burning of fuel in the form of heat is known as Chemical energy.

​

Additional Information 

Classification of fuels:

Liquid fuels:

Liquid fuels are classified as follows:

1. Natural or crude oils: These Oils are further distilled to obtain benzene, diesel, and other Light oils such as kerosene, alcohol, and so on.
2. Distilled artificial oils: These oils include -tar,tar-oil,shale-oil, and natural gas oil.

Important Points 

Various oils obtained from Natural or crude oils are briefed below.

1. Petrol: It is the lightest and the most volatile liquid fuel. It is mainly used for spark-ignition petrol engines. It is obtained by fractional distillation of petrol at 65° C to 220° C .It is also known as gasoline.
2. Kerosene: It is obtained by fractional distillation of crude oil at 345° C to 365° C. It is also known as paraffin oil .it is heavier and less volatile than petrol.it is used for heating and lightning process.
3. Diesel: It is obtained by fractional distillation of crude oil at 345° C to 470° C. It is mainly used in diesel engines and oil fire furnace and boilers.it is also known as heavy fuel.
4. Benzene: It is obtained by redistillation of tar, Which is a by-product collected during the production of coal gas. It is used as an alternate fuel for internal combustion engines. It is less prone to detonation than standard petrol.
5. Alcohol: It is formed by the fermentation of vegetable matter. The calorific value of alcohol lower than of petrol and the cost is higher. It is mainly used for industrial purposes.

Concept:

Pour point

The pour point in that temperatures just about which the oil sample will not flow under certain prescribed conditions. In other words, pour point of a liquid is the temperature below which the liquid loses its flow characteristics.

Important Points

• Flash Point: The flash point of a volatile material is the lowest temperature at which vapors of the material will ignite when given an ignition source.
• Fire Point: The fire point of a fuel is the lowest temperature at which the vapor of the fuel will continue to burn for at least 5 seconds after ignition by an open flame. The main difference in fire and flashpoint is that at the flashpoint a substance will ignite briefly, but vapor might not be produced at a rate to sustain the fire.
• Flashpoint and fire points are related to high-temperature characteristics of the fuel and tell the behavior of fuel at high temperatures.
• Cloud Point: Cloud point is the temperature at which oil becomes cloudy or hazy when oil is cooled at a specified rate.
• Pour Point: It is the temperature at which oil just ceases to flow. The pour point of the liquid is the lowest temperature at which it becomes semi-solid and loses its flow characteristics.
• Cloud point and pour point are related to low-temperature characteristics of the fuel and tells the behavior of fuel at low temperatures.

Explanation:

• Detonation is a rapid and violent form of combustion due to which strong shock wave propagates into the explosion.
• It is the spontaneous combustion of the end gas in the chamber.
• It is generally caused by:
• Excessive heat
• Excessive cylinder pressure
• Improper ignition timing
• Octane Number
• Octane Number is a measure of the quality of petrol.
• It is the percentage of iso-octane in the mixture of iso-octane and n-heptane which has the same knocking properties as the fuel sample.
• Iso-octane chemically being a very good antiknock fuel, is arbitrarily assigned a rating of 100 octane number.
• Normal heptane (C₇H₁₈) has very poor antiknock qualities i.e. readily detonates and is given a rating of 0 octane number. So, if normal heptane (C₇H₁₈) is present in the fuel then it will create knocking which will result in the auto-ignition.

Important Points

• A fuel having higher self-ignition temperature detonates less, n-heptane fuel detonates readily. While iso-octane has little tendency towards detonation.
• Detonation in petrol engines can be reduced by the addition of a small amount of lead ethide or ethyl fluid into the fuel commonly known as doping

Concept:

Ignition Accelerator are small quantities of additives, are added to the final mixture to improve the fuel quality of the CI engine which increases the mixture Cetane Number

• Cetane number of Diesel fuel is the numerical result of an engine test design to evaluate fuel ignition delay
• Organic peroxides are most widely used in the chemical, plastics, and rubber industries. They act as initiators. In addition to serving as a polymerization catalyst, butyl peroxide acts as an ignition accelerator for diesel fuels.
• Commonly used Ignition Accelerator are amyl nitrate, ethyl nitrate, Acetone peroxide, etc.

Explanation:

• Ignition Accelerator are small quantities of additives, are added to the final mixture to improve the fuel quality in CI Engine and increase the rate of pre-flame reaction and reduce the ignition lag.
• The Advantages of Ignition Accelerator is:
• Use to increase fuel Lubricity
• Use to prevent excessive engine wear
• Reduce Ignition Delay Period
• Use to clear the fuel injectors and minimize Carbon Deposits
• Use to increase the Mixture Cetane number
• An example of the Ignition Accelerator that mostly uses is amyl nitrate, ethyl nitrate, etc.

Concept:

• The value of the compression ratio for diesel engines lies between 16:1 to 22:1 whereas for the petrol engine it lies between 6:1 to 12:1.
• Therefore, diesel engines (C.I. Engines) are larger and also heavier than petrol engines (S.I. Engines) because of the large compression ratio in the case of diesel engines.
• Hence, for the same power output, power to weight ratio for diesel engines is lower than petrol engines.
• The reason for the large compression ratio being compression ignition i.e. in diesel engines, ignition takes place by the high temperature developed by the compression since there is no spark plug like in petrol or S.I.Engine.
• Also, the flashpoint at which fuel gets ignited is more in the case of diesel engines so the compression ratio needs to be sufficient enough to produce that self-ignition temperature of the fuel for the combustion to take place.

Compression ratio (r): It is defined as the ratio of volume before compression to the volume after compression.

$r = \frac{{({V_c} + {V_s})}}{{{V_c}}};$

where Vc and Vs are clearance and swept volume respectively.

Important Points

Difference between C.I.Engine and S.I.Engine:

About Tarapur Atomic Power Station:

• Tarapur Atomic Power station is located in Tarapur, Maharashtra.
• It was the first commercial atomic power station of India commissioned on 28th October 1969.
• It was commissioned under 123 agreements signed between India, the United States, and International Atomic Energy Agency.
• The station is operated by the National power corporation of India.

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Explanation:

Breeder Reactor use in Nuclear Power Plant as a nuclear reactor that converts non-fissionable U238  into fissionable Plutonium-239, which can be used as a fuel in the production of nuclear energy.

Working of Breeder Reactor:

1. The core of the breeder reactor contains fissile uranium and plutonium, atoms that split easily and release energy as heat and radiation.
2. Neutrons released during this reaction are absorbed by a Blanket of fertile uranium surrounding the core. Fertile uranium, harder to split than fissile uranium, turns into plutonium when it absorbs neutrons.
3. Conventional reactor use water to transfer heat, a breeder reactor uses liquid Sodium. The sodium does not slow the neutrons are more readily absorbed by the fertile uranium to create plutonium
4. The sodium surrounding the core flows through a heat exchanger, a cluster of thin-walled metal tubes, and transfer its energy to a separate stream of sodium
5. The heat then passes through a steam generator.
6. The steam drives a turbine generating electricity​

​

Explanation:

• Nuclear fission is performed in Nuclear reactors using radioactive fuels such as uranium and plutonium.
• These nuclear fuels naturally occur in solid form.
• To control the chain reaction according to the need small batches of fuel are created in various shapes.
• The shape of the solid fuel doesn't change the result of the reaction.
• Solid fuel for nuclear reactions may be fabricated into various small shapes.
• The amount of fuel does make difference in the time of chain reaction and energy released out of it.

Additional Information

Nuclear reactions are of two types

1. Nuclear fission:- It means the splitting of a heavy nucleus into lighter nuclei with the release of a large amount of energy.

Conversion of nuclear energy

• Fast neutron strikes the nucleus of a heavy atom to cause the sliting of the original nucleus in almost equal fragments.
• Fragment neutron can be made to cause fission of another nucleus and so on, the chain reaction can be maintained.​
• Ex. Nuclear power plants, nuclear bombs.

2. Nuclear fusion:- Two lighter nuclei are combined to be used together to form a heavier stable nucleus. Ex. sun and many stars in-universe.

The energy liberated by fusion is several times that the energy liberated by the fission process.

Common uses of some Radioactive elements:

Enriched uranium:

• U-235 can start a nuclear reaction and sustain it. But that 0.7 percent in naturally occurring uranium isn’t enough to make a bomb or even a nuclear reactor for a power plant.
• A power plant requires uranium with 3 to 4% U-235 (this is known as low-enriched or reactor-grade uranium), and a bomb needs uranium with a whopping 90 percent U-235 (highly enriched uranium).

Uranium enrichment, then, is the process by which a sample of uranium has its proportion of U-235 increased through the process of isotope separation.

Boiling water reactor: BWRs actually boil the water. Water is converted to steam, and then recycled back into the water by a part called the condenser, to be used again in the heat process. We can understand the overall working of the Boiling Water Reactor by the following diagram.

Explanation:

• In Boiling Water Reactor (BWR), water serves the triple functions of coolant, moderator, and working fluid.
• In this case, the steam flow to the turbine is produced directly in the reactor core.
• In the case of BWR because of steam being generated at the reactor itself, there is no need for a heat exchanger.
• Steam is separated and dried by mechanical devices located in the upper part of the pressure vessel assembly.
• That’s why, water serves the triple functions of coolant, moderator, and working fluid.
• So, the coolant used in a boiling water reactor is a mixture of water and steam

Fig shows a schematic diagram of the boiling water reactor power plant.

Explanation:

• Dryness fraction is defined as the ratio of the mass of dry steam and the combined mass of dry steam & mass of water vapour in the mixture. It is denoted by x.

$Dryness;fraction;\left( x \right) = \frac{{mass;of;vapour;\left( {{m_v}} \right)}}{{mass;of;vapour;\left( {{m_v}} \right) + mass;of;liquid;\left( {{m_l}} \right)}}$

• For saturated liquid x = 0
• For saturated vapour x = 1
• The value of the dryness fraction lies between 0 and 1.

Calculation:

Given:

\(x= \frac{{Mass;of;drysteam}}{{Mass;of;drysteam + Masss;of;water;in;suspension}} = \frac{{{m_v}}}{{{m_v} + {m_f}}} = \frac{{0.4}}{{0.4 + 0.6}} = \frac{{0.4}}{1} = 0.4\)

Concept:

Locomotive boiler

• A fire-tube boiler is sometimes called a “smoke-tube boiler” or “shell boiler”.
• This type of boiler was used on virtually all steam locomotives in the horizontal “locomotive” form.
• It has a cylindrical barrel containing the fire tubes but also has an extension at one end to house the firebox.
• The locomotive boiler is mainly used in the train engine which was running on coal.
• A locomotive boiler is a multi-tubular, horizontal, internally fired, and mobile boiler. It consists of a shell or barrel having 1.5 m diameters and 4 m in length.

Features and characteristics of Locomotive boiler

• Internally fired,
• Horizontal,
• Multi-tubular,
• Fire tube,
• Natural circulation,
• Artificial draft,
• Portable boiler

Explanation:

The table shows the effect and the reason:

Explanation:

The turbine is a prime mover that converts the energy of high pressure, high-temperature fluid supplied by the boiler into shaft work with the low-temperature steam exhausted to a condenser. 

The turbine trip is the shutdown of a power generation turbine due to unexpected events like turbine over-speeding, low vacuum in the condenser, etc.

1. The power pant remains hot even after the turbine trip.
2. The system needs to be gradually cooled.
3. The extremely hot steam generated during the turbine trip needs to be condensed.
4. Hence, the cooling water supply to the condenser should be stopped after 15-30 minutes for the overall cold system.
5. The damaging effect of the hot steam on other components of the power plant is also reduced.
6. Cooled also helps in safe and easy repair operations.

Condenser:- It is a device in a steam power plant in which steam condenses and heat released by steam is absorbed by water.

The condensation of steam in a close vessel produces a partial vacuum due to a great reduction in the volume of low-pressure steam.

Concept:

• 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 drop into several stages corresponding to each to which there is a separate set of nozzles in which the partial pressure drop occurs, and a single set of blades connected to a common rotor to extract the kinetic energy gained by the steam in the nozzles
• 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:

Condenser:- It is a device in a steam power plant in which steam condenses and heat released by steam is absorbed by water.

The condensation of steam in a close vessel produces a partial vacuum due to a great reduction in the volume of low-pressure steam.

A thermal power plant converts the energy of fuel into power output or electricity.

1. The working fluid is water which may be in liquid or vapor phase during its cycle of operation.
2. The energy released by burning fuel is supplied to water.
3. Steam is generated at high pressure and temperature.
4. Steam is expanded in the turbine to low pressure.
5. Then, supplied to the reservoir (condenser) to condense the steam into the water using cooling water and condenser.
6. The Condensate water is fed back to the boiler to reuse in the boiler by the pump.

The layout of the boiler is shown below: