Thermodynamics- Vapour Power Cycles

Question 1

What are the impracticalities associated with a Carnot cycle within the saturation dome of a pure substance water?

Answer 1

Limiting the heat transfer processes to two-phase systems severely limits the maximum temperature that can be used in the cycle (must remain under critical point) which limits thermal efficiency (process 1-2). The turbine cannot handle steam with high moisture (low quality) as in process 2-3. Process 4-1 (isentropic compression) involves liquid-vapour mixture and it isn’t practical to design a compressor which handles two phases.

Question 2

Why can’t a Carnot cycle be used for vapour power cycles starting above the saturation dome?

Answer 2

Requires isentropic compression to extremely high pressures and isothermal heat transfer at variable pressures.

Question 3

How can the impracticalities of the Carnot cycle be eliminated for a vapour power cycle?

Answer 3

Superheating the steam in the boiler and condensing it completely in a condenser

Question 4

Describe the Rankine cycle

Answer 4

The ideal cycle for vapour power plants. Doesn’t involve any internal irreversibilities. Has 4 steps of
1-2: Isentropic compression in a pump
2-3: Constant pressure heat addition in a boiler
3-4: Isentropic expansion in a turbine
4-1: Constant pressure heat rejection in a condenser

Question 5

Describe the T-s graph of the ideal Rankine cycle

Answer 5

Has the normal saturation curve. Starts near bottom left on saturation curve. Moves vertically up to a new pressure on liquid side at state 2. Straight diagonal line to higher T and s point on curve. Horizontal line to other side of curve. Line curves upwards to state 3 on vapour side. Vertical line down to same temperature as state 1 (just inside saturation curve). Horizontal line back to state 1.

Question 6

Describe what goes on in the ideal vapour power cycle

Answer 6

Water enters pump at state 1 as saturated liquid. Is compressed isentropically to operating pressure of boiler. Water temperature increases during this compression due to a slight increase in its v. Water enters boiler as compressed liquid at state 2 and leaves as superheated vapour at state 3. This enters the turbine where it expands isentropically and produces work by rotation the shaft connected to an electric generator. Pressure and T drop during this process to state 4 (high quality saturated liquid-vapour mixture) when it enters a condenser. Leaves as saturated liquid and enters pump at state 1.

Question 7

What does the area enclosed on a T-s graph of the Rankine cycle represent?

Answer 7

The net work produced during the cycle

Question 8

What can be steady-flow energy per unit mass equation for the Rankine cycle be reduced to?

Answer 8

(qin-qout)+(win-wout)=he-hi
This is because kinetic and potential energy changes usually small relative to work and heat transfer terms
Think e and i mean end and initial

Question 9

Which types of energy change are 0 for each component of a Rankine cycle?

Answer 9

Pump: q=0
Boiler: w=0
Turbine: q=0
Condenser: w=0

Question 10

What are the conservation of energy relations for each component in a Rankine cycle?

Answer 10

Pump: win=h2-h1 or win=v(P2-P1)
Boiler: qin=h3-h2
Turbine: wout=h3-h4
Condenser: qout=h4-h1
All numbers are subscript and the works are for that specific component.

Question 11

Formula for thermal efficiency of the Rankine cycle

Answer 11

ηth=wnet/qin=1-qout/qin
Uses wnet=qin-qout=work output of turbine-work input of pump
th, net, in and out subscript

Question 12

How can the thermal efficiency of a Rankine cycle be interpreted using its T-s graph?

Answer 12

Ratio of area enclosed by the cycle on the T-s diagram to the area under the heat-addition process

Question 13

Name two common sources of irreversibilities in a vapour power cycle

Answer 13

Fluid friction and heat loss to the surroundings

Question 14

What does fluid friction mean for a vapour power cycle in practice?

Answer 14

Causes pressure drops in boiler, condenser (small) and piping between components. To compensate, water must be pumped to a sufficiently higher pressure than the ideal cycle calls for meaning a larger pump and a larger work input to the pump.

Question 15

What does heat loss from the steam to the surroundings mean in practice for a vapour power cycle?

Answer 15

To maintain the same level of net work output, more heat needs to be transferred to the steam in the boiler to compensate for the undesired heat losses. Therefore cycle efficiency decreases.

Question 16

How does the T-s graph of a real vapour power cycle deviate from that of the ideal Rankine cycle if nothing is done to compensate for irreversibilities?

Answer 16

1-2: vertical line becomes diagonally right so state 2 further up
2-3: horizontal line becomes diagonally down and curve upwards has same gradient as before so state 3 further right
3-4: vertical line becomes diagonally right so state 4 not under saturation curve and is higher
4-1: horizontal line becomes diagonally down, bit curvy from state 4 to saturation curve

Question 17

How does the T-s graph of a real vapour power cycle deviate from that of the ideal Rankine cycle for irreversibilities of pump and turbine alone?

Answer 17

Only 2 differences in processes.
1-2: vertical line becomes diagonally right so state 2 is higher
3-4: vertical line becomes diagonally right from 3 to saturation curve, then curves right once under saturation curve to T at state 1 so state 4 is further right

Question 18

Formula for isentropic efficiency of pump

Answer 18

ηP=ws/wa=(h2s-h1)/(h2a-h1)
Where P, s, a and numbers are subscript
State 2a is actual exit state of the pump
State 2s is the exit state for the isentropic case

Question 19

Formula for isentropic efficiency of turbine

Answer 19

ηT=wa/ws=(h3-h4a)/(h3-h4s)
Where T, s, a and numbers are subscript
State 4a is actual exit state of the turbine
State 4s is the exit state for the isentropic case

Question 20

Basic idea behind all modifications to increase thermal efficiency of a power cycle

Answer 20

Increase the average temperature at which heat is transferred to the working fluid in the boiler, or decrease the average temperature at which heat is rejected from the working fluid in the condenser

Question 21

How does lowering the condenser pressure increase thermal efficiency?

Answer 21

It automatically lowers the temperature of the steam and thus the temperature at which heat is rejected. On the T-s diagram, the lower horizontal line is lowered so greater enclosed area. However the pressure must be at least the saturation pressure corresponding to the temperature of the cooling medium. Also, it increases the moisture content of the steam in the final stages of the turbine which can lead to corroded blades.

Question 22

Why is the steam superheated in a vapour power cycle?

Answer 22

Increases the average temperature at which heat is transferred to the steam. On the T-s diagram, the right vertical line moves right and starts higher so the area enclosed is greater. Both the net work and heat input increase. Also, decreases the moisture content of the steam at the turbine exit. Temperature limited to what the materials can withstand.

Question 23

How does increasing the boiler pressure improve thermal efficiency?

Answer 23

It automatically raises the temperature at which boiling takes place so raises the average temperature at which heat is transferred to the steam. On the T-s diagram, the line from state 2 to 3 is raised meaning state 3 is further left but overall there is an increase in wnet. Does however increase the moisture content of the steam at the turbine exit.

Question 24

Describe the T-s diagram for a supercritical Rankine cycle

Answer 24

Same as normal but process from stage 2 to 3 doesn’t cross saturation curve and goes above it. This line starts with a steep gradient which decreases gradually, then a lot as it approaches the critical point, then nearly straight curving up a bit towards state 3.

Question 25

How does the ideal reheat Rankine cycle work?

Answer 25

The steam is expanded in the turbine in two stages and reheated in between. In the first stage, the steam is expanded isentropically by a high pressure turbine to an intermediate pressure and sent back to the boiler where it is reheated at constant pressure to the temperature of the first turbine stage. Steam then expands isentropically in the second stage using a low-pressure turbine to the condenser pressure.

Question 26

Equations for the heat input and work output of the ideal reheat a Rankine cycle

Answer 26

qin=qprimary+qreheat=(h3-h2)+(h5-h4)
wturb,out=wturb,I+wturb,II=(h3-h4)+(h5-h6)
Numbers are subscript and refer to states on the T-s diagram

Question 27

Describe the T-s diagram of the ideal reheat Rankine cycle

Answer 27

Sam as normal but state 4 becomes 6. Vertical line down from 3 stops at new state 4 (still above saturation curve). Then diagonal line right up to new state 5 (same temperature as 3). Then vertical line down to what is now state 6.

Question 28

What is feedwater?

Answer 28

The water leaving the pump and entering the boiler

Question 29

How does the ideal regenerative Rankine cycle work in practice?

Answer 29

Steam is extracted from the turbine at various points. This steam could have produced more works by expanding further in the turbine but is used to heat the feedwater instead. The device where the feedwater is heated by regeneration is called a regenerator or feedwater heater (FWH).

Question 30

What is the problem between state 2 and the saturation curve in the Rankine cycle?

Answer 30

Heat is transferred to the working fluid at a relatively low temperature lowering the average heat addition temperature and thus the cycle efficiency.

Question 31

What is a feedwater heater?

Answer 31

A heat exchanger where heat is transferred from the steam to the feedwater either by mixing the two fluid streams (open FWHs) or without mixing them (closed FWHs).

Question 32

What are the advantages of regeneration in a Rankine cycle?

Answer 32

It improves thermal efficiency because it raises the average temperature at which heat is transferred to the steam by raising the temperature of the water before it reaches the boiler. Provides a means of deaerating the feedwater (removing air that leaks in at the condenser). Helps to control the large volume flowrate of the steam at the final stages of the turbine (due to large specific volumes at low pressures).

Question 33

How does an open feedwater heater work in a regenerative Rankine cycle?

Answer 33

It is basically a mixing chamber where the steam extracted from the turbine mixes with the feedwater exiting the pump. Ideally the mixture leaves the heater as a saturated liquid at the heater pressure. It is connected to the turbine, the normal pump and sends the saturated liquid to another pump (pump II) which raises the pressure of the water to boiler pressure.

Question 34

Describe the T-s diagram of an ideal regenerative Rankine cycle with an open feedwater heater

Answer 34

Starts at bottom left on sat curve and goes vertically up a bit to state 2. Then normal diagonal to sat curve at new state 3. Then vertically up a bit again to state 4. Then diagonal to sat curve, then horizontal under sat curve, then curve up to state 5. Vertical line down to state 6 (outside sat curve). Extra line curves back to sat curve then horizontal back to state 3. Vertical line down from 6 to 7 which is under sat curve at state 1 temperature. Horizontal line back to state 1.

Question 35

Equations for work and heat in and out of ideal regenerative Rankine cycle with open feedwater heater

Answer 35

qin=h5-h4
qout=(1-y)(h7-1)
wturb,out=(h5-h6)+(1-y)(h6-h7)
wpump,in=(1-y)wpumpI,in+wpumpII,in
y is fraction of steam extracted from the turbine
wpumpI,in=v1(P2-P1)
wpumpII,in=v3(P4-P3)

Question 36

How does a closed feedwater heater work in an ideal regenerative Rankine cycle?

Answer 36

No mixing takes place during heat transfer so the two streams can be at different pressures. Ideally, the feedwater is heated to the exit temperature of the extracted steam, which ideally leaves the heater as a saturated liquid at the extraction pressure. The condensed steam is then either pumped to the feedwater line or routed to another heater or the condenser by a trap. The heater is connected to the turbine, pump I, pump II and a mixing chamber.

Question 37

What does a trap do?

Answer 37

It allows the liquid from the condensed steam (after a closed FWH) to be throttled to a lower pressure region but traps the vapour. The enthalpy of the steam remains constant during this process.

Question 38

Describe the T-s diagram of an ideal regenerative Rankine cycle with a closed FWH

Answer 38

Starts at bottom left on sat curve. Goes vertically up a bit to state 2. Diagonal line to new state 9 (between FWH and mixer) then state 5 (between mixer and boiler) then reaches sat curve, horizontal under sat curve, curves up to state 6. Vertical line down to 7 (outside sat curve). Extra line curves to sat curve, the horizontal to other side of sat curve at state 3 (between FWH and pump II), then vertically up to join diagonal line from 5 at state 4. Vertical down from 7 to 8 (sam temperature as 1 and under sat curve). Horizontal to state 1.

Question 39

What is process heat?

Answer 39

The heat energy that some systems or devices need for their energy input

Question 40

What is cogeneration?

Answer 40

The production of more than one useful form of energy (such as process heat and electric power) from the same energy source.

Question 41

Describe the layout of an ideal cogeneration plant

Answer 41

Has water going into the pump. This goes to the boiler to make steam. The steam turns the turbine. The steam then flows to a process heater instead of condenser so no heat is rejected from the plant as waste heat. Therefore all of the energy transferred to the steam is utilised as either process heat or electric power.

Question 42

What is the utilisation factor of a cogeneration plant?

Answer 42

εu=(Net work output+Process heat delivered)/Total heat input
Equal to (W•net+Q•p)/Q•in
Equal to 1-Q•out/Q•in
Where Q•out is heat rejected in the condenser
All • are above letter and u is subscript

Question 43

What is the utilisation factor of real and ideal cogeneration plants?

Answer 43

Ideal- 100%

Real- 80% and above