Study & Analysis of Carnot’s Model for Ideal Machine P M V Subbarao Professor Mechanical...
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Transcript of Study & Analysis of Carnot’s Model for Ideal Machine P M V Subbarao Professor Mechanical...
Study & Analysis of Carnot’s Model for Ideal Machine
P M V Subbarao
Professor
Mechanical Engineering Department
IIT Delhi
A True Concept of Blue Printing…….
A Mathematical Model for (James Watt’s) Steam Engine
expansion
Heat AdditionHeat Removal
Carnot Power Cycle
Goal: To generate Mechanical Power through from heat input !!!
Question: What is the Upper Limit of Engine Performance?
Can You Predict?
Is it essential to try and find out using only on the field Test?
Carnot’s Model for Power Cycle
compressorturbinenet WWW
s
– 2 : Compressor : Isentropic Compression : s2 = s1
2 – 3 : Boiler: Isothermal Heating : T3 = T2
3 – 4 : Turbines : Isentropic Expansion : s4 = s3
4 – 1 : Condenser: Isothermal Cooling : T1 = T4
Carnot’s Model for Power Cycle
Compressor : Isentropic Process
21 hhmW c
CVout
outin
inCV WgzVhmgzVhmQ
22
SSSF: Conservation of mass
inin mm
First Law :
No heat transfer, change in kinetic and potential energies are negligible
ssuming a single fluid entering and leaving…
Use the combined first and Second law statement for a reversible process.
2
1
12
2
1
vdpmhhmqm
Reversible Adiabatic Process:
2
1
21 vdpmhhmWcompressor
02
1
12
vdpmhhm
2 – 3 : Boiler: Isothermal Heating : T3 = T2
No work transfer, change in kinetic and potential energies are negligible
QCV
CVout
outin
inCV WgzVhmgzVhmQ
22
outoutininCV hmhmQ
ssuming a single fluid entering and leaving…
inoutCV hhmQ
3
2
23
3
2
vdpmhhmqm
For reversible constant Pressure & Temperature Process (change of phase)
23
3
2
hhmTdsm
2323max hhmssTm
Turbine : Isentropic Process :s4=s3
No heat transfer. Change in kinetic and potential energies are negligible
3
4
T
inin mmCMSSSF ::
CVout
outin
inCV WgzVhmgzVhmQ
22
CVoutoutinin Whmhm
ssuming a single fluid entering and leaving…
4
3
43 vdpmhhmhhmW outinCV
4 – 1 : Condenser : Isothermal Cooling : T3 = T2
No work transfer, change in kinetic and potential energies are negligible
QCV
CVout
outin
inCV WgzVhmgzVhmQ
22
outoutininCV hmhmQ
ssuming a single fluid entering and leaving…
41min ssTmhhmQ inoutCV
Analysis of Cycle
• First law for a cycle:
WQ
vdpmTdsm
41min23max ssTssTmW net
minmaxminmax
2143 &,
ssTTmW
ssssBut
net
additionHeat of Rate
outputPower Net cycle theof Efficiency
minmaxmax
minmaxminmax
ssTm
ssTTm
in
net
Q
W
max
min1T
T
minmaxminmaxoutput Work Specific ssTT
minmax
MEPvv
vdp
Work done per unit volume of the engine: Mean Effective Pressure
Carnot
inimize the capital & running costs.
Compact and efficient.
Use of Carnot Model for Optimization of Power Plant
A Major Crossroad Confusion: How to go from <6% to 75% Efficiency ???????
Rankine, William John Macquorn (1820-1872)
A MANUAL of the STEAM ENGINE and other PRIME MOVERS 1859 Rankine
• The conventional name work of the thermodynamics by Rankine.
• Rankine is the largest meritorious person who in addition raises the technology of the steam engine to science, the word, " energy " is something due to him.
• Harmony meaning of this work becomes " the manual of the steam engine and the other motive for action machines “.
• The chapter " of thermodynamics " advocated the cyclic process which is called Rankine cycle.
• This was related to the policy of researching the steam engine theoretically, brought the progress of the steam engine.
Rankine, William John Macquorn (1820-1872)• Rankine was born in Edinburgh and trained as a civil engineer.
From 1855 he was professor at Glasgow.• In 1849 he delivered two papers on the subject of heat, and in 1849 he
showed the further modifications required to French physicist Sadi Carnot's theory of thermodynamics.
• In A Manual of the Steam Engine and other Prime Movers 1859, Rankine described a thermodynamic cycle of events (the Rankine cycle).
• This came to be used as a standard for the performance of steam-power installations where a considerable vapour provides the working fluid.
• Rankine here explained how a liquid in the boiler vaporized by the addition of heat converts part of this energy into mechanical energy when the vapour expands in an engine.
• As the exhaust vapour is condensed by a cooling medium such as water, heat is lost from the cycle.
• The condensed liquid is pumped back into the boiler.