Gas and Vapor Power Cycles MCQ Quiz - Objective Question with Answer for Gas and Vapor Power Cycles - Download Free PDF

Concept:

We use the isentropic relations for an ideal Brayton cycle to determine the final temperatures at the end of the compression and expansion processes.

Given:

• Minimum pressure, \( P_1 = 1 \, \text{bar} \)
• Maximum pressure, \( P_2 = 6 \, \text{bar} \)
• Minimum temperature, \( T_1 = 300 \, \text{K} \)
• Maximum temperature, \( T_3 = 1500 \, \text{K} \)
• Ratio of specific heats, \( \gamma = 1.4 \)

Step 1: Calculate temperature at the end of compression (T₂)

The compression process is isentropic. The relation between temperature and pressure is:

\( T_2 = T_1 \left( \frac{P_2}{P_1} \right)^{\frac{\gamma - 1}{\gamma}} \)

Substitute the given values:

\( T_2 = 300 \left( \frac{6}{1} \right)^{\frac{1.4 - 1}{1.4}} = 300 \times 6^{0.2857} \approx 300 \times 1.668 \approx 500 \, \text{K}\)

Step 2: Calculate temperature at the end of expansion (T₄)

The expansion process is also isentropic. The relation between temperature and pressure is:

\( T_4 = T_3 \left( \frac{P_1}{P_2} \right)^{\frac{\gamma - 1}{\gamma}} \)

Substitute the given values:

\( T_4 = 1500 \left( \frac{1}{6} \right)^{\frac{1.4 - 1}{1.4}} = 1500 \times 6^{-0.2857} \approx 1500 \times 0.599 \approx 900 \, \text{K}\)

Explanation:

Regenerative Rankine Cycle

A regenerative Rankine cycle is a variation of the Rankine cycle which increases the thermal efficiency of the system by using feedwater heaters to preheat the feedwater before it enters the boiler. This process reduces the amount of heat required to convert the feedwater into steam, thereby improving the cycle's thermal efficiency. The preheating is accomplished by extracting steam from the turbine and using it to heat the feedwater.

Analyzing the Given Options

1. Option 1: Open feedwater heater (Correct Answer)

   • An open feedwater heater (also known as a direct-contact heater) is a device where extracted steam from the turbine directly mixes with the feedwater. This method of preheating increases the temperature of the feedwater before it enters the boiler, reducing the fuel required for heating and thus increasing the thermal efficiency of the cycle.

2. Option 2: Air preheater (Incorrect Answer)

   • An air preheater is used to heat the combustion air before it enters the boiler. While it improves the boiler's efficiency, it does not specifically increase the thermal efficiency of the Rankine cycle as a whole.

3. Option 3: Evaporator (Incorrect Answer)

   • An evaporator is a component in the boiler where the feedwater is converted to steam. It is a part of the basic Rankine cycle, but it does not contribute to the regenerative process aimed at increasing the cycle's thermal efficiency.

4. Option 4: Economizer (Incorrect Answer)

   • An economizer is a heat exchanger that preheats the feedwater using the residual heat in the flue gases. While it improves the boiler's efficiency by reducing fuel consumption, it is not directly used for regenerative heating to increase the Rankine cycle's overall thermal efficiency.

Explanation:

• The specific work of a turbine means the work output per unit mass of the steam supplied.
• Now if the specific work output of the turbine has to increase it can be increased by increasing the work output for the same mass of the steam supplied.
• The efficiency of the Rankine cycle is given by- η =  1- \(\frac{{{\rm{T_{rejected}}}}}{{{\rm{T_{added}}}}}\) = 1- \(\frac{{{\rm{T_{Turbine\;exit}}}}}{{{\rm{T_m}}}}\)
• Where T_m = Mean temperature of heat addition. By increasing the temperature and pressure, the T_m of the cycle increases so efficiency will increase.
• Increasing superheat at particular pressure will increase the work output from the turbine so, the specific output and exit point of steam from the turbine will shift towards the saturation curve i.e. low moisture content.
• At a fixed maximum temperature higher pressure will increase moisture content due to shifting of expansion in the turbine towards left on the T-S diagram, but if maximum temperature is not fixed then statement 3 will not always be true. 

Explanation:

Given:

T₁ = 300 K, T₂ = 550 K, T₄ = 1250 K, T₅ = 800 K, T₆ = 600 K,

From energy balance across regenerator

T₃ - T₂ = T₅ - T₆

T₃ - 550 = 800 - 600

Тз = 750 K

Now, 

\(\eta=1-\frac{Q_{R}}{Q_{s}}=1-\frac{\left(T_{6}-T_{1}\right)}{\left(T_{4}-T_{3}\right)}=1-\frac{(600-300)}{(1250-750)}\)

\(\eta=1-\frac{300}{500}=0.4 \text { or } 40 \%\)

Explanation:

• Superheating in Rankine cycle increases the cycle efficiency because of increase in mean temperature of heat addition.

• With increase in pressure of boiler, the cycle efficiency increases. So, the given statement is wrong.

• With decrease in condenser pressure, the cycle efficiency increases because of decrease in mean temperature of heat rejection.

• The pressure of turbine outlet is governed by the condenser temperature. Decreasing the cooling water temperature, creates more vacuum in condenser which results in pressure drop and vice-versa.

Additional InformationRankine cycle

• It is the ideal cycle for a vapour power plant.
• It comprises four reversible processes:

The efficiency of the Rankine cycle

• We know that efficiency η of the Rankine cycle is given as,

​\(\eta =1-\frac{T_L}{T_{avg}}\)

• That means to increase the efficiency we should increase the average temperature at which heat is transferred to the working fluid in the boiler.
• Another way would be to decrease the average temperature at which heat is rejected from the working fluid in the condenser.
   

Decreasing the condenser pressure

• Lowering the condenser pressure will increase the area enclosed by the cycle on a T - S diagram which indicates that the net-work will increase.
• Thus, the thermal efficiency of the cycle will be increased.

Superheating the steam to high temperature

• This will increase the net-work output and the efficiency of the cycle.
• It also decreases the moisture contents of the steam at the turbine exit.
• The temperature to which steam can be superheated is limited by metallurgical considerations (620°C)

Increasing the boiler pressure

• Increasing the operating pressure of the boiler leads to an increase in the temperature at which heat is transferred to the steam and thus raises the efficiency of the cycle.

Concept:

Note that the Rankine cycle has a lower efficiency compared to the corresponding Carnot cycle 2’-3-4-1’ with the same maximum and minimum temperatures. The reason is that the average temperature at which heat is added in the Rankine cycle lies between T₂ and T₂^' and is thus less than the constant temperature T2' at which heat is added to the Carnot cycle.

It is very difficult to build a pump that will handle a mixture of liquid and vapor at state 1' (refer T-s diagram; Carnot Vapor Cycle) and deliver saturated liquid at state 2’.

It is much easier to completely condense the vapor and handle only liquid in the pump (Rankine Cycle)

In the Carnot cycle, the compression is wet compression so the pump work requirement is more compare to the Rankine cycle where the pump compresses only the saturated liquid. Thus the specific work output for the Rankine cycle is more than the Carnot cycle for the same maximum and minimum temperature.

Also, the work ratio is defined as the ratio of net-work to the work done in the turbine.

\(r_w=\frac{W_{net}}{W_T}=\frac{W_T-W_C}{W_T}\)

Thus the work ratio is low for the Carnot Cycle.

Explanation:

Concept of Regeneration in the Rankine cycle:

• Regeneration means to take some part of the heat from the expanding steam in the turbine to decrease the overall heat supplied in the process.
• The thermal efficiency of the Rankine cycle can be increased by the use of a regenerative heat exchanger.
• In the regenerative cycle, a portion of the partially expanded steam is drawn off between the high and low-pressure turbines.
• The steam is used to preheat the condensed liquid before it returned to the boiler.
• In this way, the amount of heat added at the low temperatures is reduced and the mean effective temperature of heat addition is increased, thus cycle efficiency is increased.
• At point 2 some amount of steam is taken out for the heating purpose of water.

Effect of Regeneration:

• Decrease in turbine work due to a decrease in the mass flow rate of steam.
• Decrease in heat rejection in condenser due to a reduction in mass flow rate.
• Increased of efficiency and mean temperature of heat addition (T_m).

Concept:

1.  Superheated Rankine cycle :    

• The average temperature at which heat is added to the steam can be increased without increasing the boiler pressure by superheating the steam to high temperatures. Thus, efficiency increases.
• Superheating the steam to higher temperatures has another very desirable effect: It decreases the moisture content of the steam at the turbine exit.

2. Reheat Rankine cycle :

The advantages of using a reheat cycle are

• higher thermal efficiency
•  reduced feed water pump power
•  smaller condenser
•  smaller boiler
•  long life of the turbine
•  less handling of the fuel and firing requirement.

3. Regenerative Rankine cycle

The advantages of Regeneration cycle:

1. Heat supplied to boiler becomes reduced.
2. Thermal efficiency is increased since the average temperature of heat addition to the cycle is increased.
3. Due to bleeding in the turbine, erosion of turbine due to moisture is reduced.

Concept:

The working of closed cycle gas turbine is as follows

Process 1-2: Isentropic compression of gas takes place in the compressor.

Process 2-3: It denotes the heating of gas in the heating chamber at constant pressure.

Process 3-4: In this process, the expansion of gas takes place isentropically.

Process 4-1: This process shows the cooling of gas at constant pressure in the cooling chamber.

• In a closed-cycle gas turbine, the same working fluid is recirculated again and again
• In an open cycle gas turbine, the working fluid is used only one time.

Concept:

In a steam power plant, The energy balance is given as

Heat supplied in boiler - Heat rejected in condenser = Turbine work - Pump work

Calculation:

Given 

Heat supplied in boiler = QS = 3500 kJ/kg

Heat rejected in condenser = QR = 2900 kJ/kg

Turbine work = 1206 kW

Pump work = 6 kW

Net work output = 3500 - 2900 = 600 kJ/kg

Now W  = 600 × m

Here W = 1206 - 6 = 1200 kJ/s

\(\Rightarrow m = \frac {1200}{600} = 2\ kg/s \)

Concept:

• In a simple cycle, after the isentropic expansion in the turbine, steam is directly fed into the condenser for the condensation process. But in the reheat system, two turbines (high-pressure turbine and low-pressure turbine) are employed for improving efficiency.
• Steam, after expansion from the high-pressure turbine, is sent again to the boiler and heated until it reaches a superheated condition. It is then left to expand in the low-pressure turbine to attain condenser pressure. The reheat cycle has been developed to take advantage of the increased efficiency with higher pressures, and yet avoid excessive moisture in the low-pressure stages of the turbine.
• With reheat, the mean temperature of heat addition Tm increases and so efficiency and work output increase but the steam rate decreases.

The ideal reheat Rankine cycle differs from the simple ideal Rankine cycle in that the expansion process takes place in two stages.

• In the first stage (the high-pressure turbine), steam is expanded isentropically to an intermediate pressure and sent back to the boiler where it is reheated at constant pressure, usually to the inlet temperature of the first turbine stage.
• The steam then expands isentropically in the second stage (low-pressure turbine) to the condenser pressure. Thus the total heat input and the total turbine work output for a reheat cycle become:

Q_in = Q_primary + Q_reheat = (h₃ – h₂) + (h₅ – h₄)

W_turb,out = W_turb,I + W_turb,II = (h₃ – h₄) + (h₅ – h₆)

The incorporation of the single reheat in a modern power plant improves the cycle efficiency by 4 to 5 percent by increasing the average temperature at which heat is transferred to the steam.

The average temperature during the reheating process can be increased by increasing the number of expansion and reheat stages.

\({\eta _{Rankine}} = 1 - \frac{{{T_2}}}{{{T_m}}}\)

(Tm is mean temperature)

Explanation:

Dry saturated steam is admitted to a steam turbine following an isentropic process:

From the T-s diagram:

Process 1-2 is an isentropic process.

If Point 1 is at a dry saturated state, Point 2 will fall in a wet region.

Explanation:

Bleeding System

It is the process of removing a certain amount of steam from the turbine at an intermediate stage

Efficiency of a cycle depends on the mean temperature of heat addition

\(\eta = 1 - \frac{{{T_{HR}}}}{{{T_{HS}}}}\)

From the equation it is clear if the T_HS (mean temperature of the heat addition) is higher then efficiency is higher.

Process:

• Steam is removed from the turbine at an intermediate stage point 1 as shown in the figure.
• After removing the steam from the turbine it is mixed with water.
• Since the steam has a higher temperature than water so it raises the temperature of feed water.
• This feed water flows in the boiler where it takes heat and converted it into steam.
• Since the feed water is already heated by bleeding steam so less heat is required in the boiler to convert it into steam.
• It means heat supplied in the boiler is less.

\(\eta = \frac{{work\;done}}{{heat\;supplied}}\)

Due to bleeding less heat is supplied to feed water in the boiler and it increases the mean temperature of heat addition which increases the efficiency.

Concept:

Work ratio: 

• It is defined as the ratio of net work to turbine work.
• The gas turbine is work on the Brayton cycle.
• This cycle consist of  two adiabatic process and two isobaric process.

​

\(Work Ratio=\frac{W_{net}}{W_T}=\frac{W_T-W_C}{W_T}\)

Turbine work is given by,

WT = Cp(T3 - T4)

Compressor work is given by,

WC = Cp(T2 - T1)

Therefore, \(Work ~Ratio=\frac{C_p(T_3-T_4)-C_p(T_2-T_1)}{C_p(T_3-T_4)}\)

\(\Rightarrow1-\frac{T_2-T_1}{T_3-T_4}\)

\(Work~ratio=1-\frac{T_1(\frac{T_2}{T_1}-1)}{T_4(\frac{T_3}{T_4}-1)}\)

Here, \(\frac{T_2}{T_1}=\frac{T_3}{T_4}=r_p^{\frac{\gamma -1}{\gamma}}\)

Therefore, \(Work~ratio=1-\frac{T_1}{T_4}\)

\(Work~ratio=1-\frac{T_1}{T_4}\times\frac{T_3}{T_3}\)

\(Work~ratio=1-\frac{T_1}{T_3}\times\frac{T_3}{T_4}\)

\(Work~ratio=1 - \frac {T_1}{T_3} (r_p)^\frac {\gamma - 1}{\gamma}\)

Explanation:

Rankine cycle:

The Rankine cycle is an ideal cycle because that has two constant pressure and two isentropic processes and all processes are reversible.

There are four processes in the Rankine cycle:

Process 1 – 2: Isentropic compression

• The working fluid is pumped from low to high pressure.

Process 2 – 3: Isobaric heat addition

• The high-pressure liquid enters a boiler where it is heated at constant pressure by an external heat source to become a dry saturated vapor.

Process 3 – 4: Isentropic expansion

• The dry saturated vapour expands through a turbine, generating power.

Process 4 – 1: Isobaric heat rejection

• The wet vapour then enters a condenser where it is condensed at constant pressure and temperature to become a saturated liquid.

Additional Information

• The Rankine cycle efficiency varies from 35 to 45 %
• η_carnot  > η_rankine
• ( W_net )_rankine > ( W_net )_carnot
• Infinite or series of steam extraction will lead to an ideal regenerative cycle called carnotization of Rankine cycle.