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CM3230 Lecture 9 Page 1
CM 3230 Thermodynamics, Fall 2014
Lecture 9
1. Rankine Cycle (Vapor Compression Power Cycle)
- Contains 4 main units:
- Turbine
- converts enthalpy of working fluid to useful work, e.g. via generator
- ideal case: fluid undergoes isentropic expansion a. outlet pressure is lower than inlet pressure b. adiabatic and reversible process for the fluid
- practical constraints: want outlet stream to be saturated, possibly high quality “wet steam”
- Condenser
- Working fluid changes phase at constant pressure, i.e. inside phase envelope.
- Ideal case: heat exchange is only between working fluid and cooling fluid (i.e. heat lost by working fluid = heat gained by cooling fluid no heat lost to other surrounding)
- Practical/economic issues: a. Since next unit downstream is a compressor, we want the outlet to be completely liquid ( bubbles not good for compressor ) b. But do not want to cool working fluid too far from saturated liquid condition c. Cooling needs to be fast enough for required power delivery ( heat transfer rate depends on temperature difference, etc. transport problem )
CM3230 Lecture 9 Page 3
- Compressor
- Increase the inlet pressure to a much higher outlet pressure
- Ideal case: isentropic (adiabatic and reversible path for the working fluid)
- Practical issues a. Work done by compressor should be much less than work given to turbine ( In some designs, part of the work to drive turbine is used to run compressor.) b. But want outlet pressure high to make the boiler temperature higher ( recall conclusion of efficiency of ideal Carnot cycles )
- Boiler
- Takes compressed working liquid and boils (isobarically, at high pressure) it to superheated condition
- Ideal case: heat gained by working fluid = heat delivered by “fuel source” no heat lost to other surrounding
- Practical issue: the outlet temperature, together with the fixed pressure, has to be at the point such that when the turbine path is accomplished, the working fluid is a high quality steam.
- Fuel sources: combustion, nuclear reaction, others (solar?)
- Boiling rates needs to be fast enough for required power delivery ( heat source depends on heat transfer and reaction rates, etc. transport and kinetics problem )
In class exercise: a) Sketch the equipment diagram of the Rankine cycle (and label the points in the path) b) Sketch the accompanying ᡆ-ᡱ diagram of ideal Rankine cycle c) Fill-in the work/heat “balance sheet” for the paths
CM3230 Lecture 9 Page 7
Example 3.14. Rankine Engine Cycle
Given : ᡆ⡩ = 600°ᠩ, ᡂ⡩ = 10 ᠹᡂᡓ, ᡂ⡰ = 100 ᡣᡂᡓ
Required: ᡵ㕉䙢〩げ,う,ぁ〲ぇ, ―〲ぁ〴〶ぁ〲, compare with Carnot efficiency
Solution: Need:
ℎ㕒⡩ = 䙦^ 䙧^ 〸〴〸】
ℎ㕒⡰ = 䙦^ 䙧^ 〸〴〸】
ℎ㕒⡱ = 䙦^ 䙧^ 〸〴〸】
ℎ㕒⡲ = 䙦^ 䙧^ 〸〴〸】
Then
ᡵ㕉〩げ,う,ぁ〲ぇ = 㐵ℎ㕒⡩ − ℎ㕒⡰㐹 + 㐵ℎ㕒⡱ − ℎ㕒⡲㐹 = 䙦^ 䙧^ 〸】〸〴
ぐ㕉䙢㉷㌀,㊔,㊉㊀㊕ い䙢㊄㊉,ㄠ→ㄗ^ =^
ぐ㕉䙢㉷㌀,㊔,㊉㊀㊕ 〵㕓ㄗ⡹〵㕓ㄠ^ = 䙦^ 䙧
For Carnot efficiency: ᡆ〉 = ᡆ⡩ = 600°ᠩ and ᡆ〄 = 䙦 䙧°ᠩ.
―〰〨ぅぁあぇ =
CM3230 Lecture 9 Page 9
Work and Heat Paths “Balance Sheet” of ideal Rankine Cycle
Unit/Path Shaft Work By Fluid Heat Into Fluid
Turbine: 1 2
Notes: a) 䙦ᡆ⡩, ᡂ⡩䙧 (^) steam table 䙗䙔 㐵ℎ㕒⡩, ᡱ̂⡩㐹 b) (ᡱ̂⡰ = ᡱ̂⡩, ᡂ⡰䙧 (^) steam table 䙗䙔 㐵ℎ㕒ぉ,⡰, ℎ㕒〹,⡰, ᡶ㐹 → ℎ㕒⡰
Condenser: 2 3
Notes: ℎ㕒⡱ = ℎ㕒〹,⡰ ( or less if excess cooling occurs )
Compressor: 3 4
Notes: ℎ㕒⡲ can be obtained from subcooled table, or ℎ㕒⡲ ≈ ℎ㕒⡱ + ᡴ㕈〹,⡱䙦ᡂ⡲ − ᡂ⡱䙧
Boiler: 4 1
