Vapour Power Cycles

Power Cycle-Converts heat into workWorking fluid repeatedly performs a

succession of processes

Vapour Power Cycle: Working fluid-Water- undergoes phase changeWorking fluid is alternatively vaporized and

condensed.

Quest for higher thermal efficiencies- innovative modifications to basic vapor power cycleReheat Regenerative Cycles

Steam- most common working fluidDesirable CharacteristicsLow costAvailabilityHigh enthalpy of vaporization• Steam power plants- or Coal plants, Nuclear

plants, Natural gas plants- depending on type of fuel used to supply heat to steam.

• Steam goes through same basic cycle in all

Steam Power Cycle

Carnot Vapor Cycle• Steady Carnot cycle executed

within the saturation dome of a pure substance.

• Fluid is heated reversibly and isothermally in Boiler (4-1)

• Expanded isentropically in a turbine(1-2)

• Condensed reversibly and isothermally in a condenser (2-3)

• Compressed isentropically by a compressor to initial state (3-4)

Impracticalities(1) Isothermal heat transfer to or from two phase system- achievable Limiting heat transfer processes to two-phase systems limits

maximum temperature Limiting max temperature in cycle- limits thermal efficiency.(2) Isentropic expansion process can be approximated closely by a well designed turbine. But quality of steam decreases during the process. Low quality steam = steam with high moisture content. Impingement of liquid droplets on turbine blade causes erosion and

will lead to wear(3) Isentropic compression process involves compression of liquid-vapor mixture to a saturated liquid. Two impracticalities Not easy to control condensation process so precisely ending at

desired quality at state 3 Not practical to design a compressor that handles two phases.

High pressure, high temperature steam

Furnace

Boiler

Air & Fuel

Combustion Products

Turbine Generator

Condenser

Circulating pumpQ2

Wp

Condensate pump

High pressure water

WT

River (Sink)

T2

Q1

STEAM POWER PLANT

Fluid undergoing a cyclic process, • no net change in its internal energy over the cycle • so net energy transferred to the unit mass of fluid as heat

during cycle =net energy transfer as work from fluid. • By first law

∑푄 = ∑푊cycle cycle

푄 − 푄 = 푊 −푊

Heat transferred to working fluid

Heat rejected from the working fluid

Work transferred

from working fluid

Work transferred

into the working fluid

η = = = = 1−

Rankine Cycle

Impracticalities in Carnot Cycle eliminated by

(1) Superheating steam in boiler(2) Condensing completely in condenser

3

4

1

2

Ideal Rankine Cycle

3-4 Isentropic compression in a pump4-1 Constant pressure heat addition in a boiler1-2 Isentropic expansion in a turbine2-3 Constant pressure heat rejection in a condenser

Process 3-4 Water enters pump at state 3 as saturated liquid Compressed isentropically to operating pressure of boiler Water temp increases corresponding to slight decrease in specific

volume here Vertical distance 3-4 is greatly exaggeratedProcess 4-1 Water enters boiler as compressed liquid at state 4 and leaves as

superheated vapor at state 1Process 1-2 Superheated vapor at state 1 enters turbine- expands isentropically-

produces work . Pressure and temperature of steam drop to values at state 2Process 2-3Steam enters condenser At 2, steam is in a saturated liquid-vapor mixture with high quality. Steam is condensed at constant pressure in condenser. Steam

leaves condenser as saturated liquid and enters pump, completing cycle

T-S Diagram Rankine Cycle

3

4

1’

2’ 2

1

1’’

2’’

T

S

Steam approaching turbine may be dry saturated (state 1), wet(state 1’), or super heated (state 1’’)

Fluid approaching pump in any case is – saturated liquid

Steam expands reversibly and adiabatically in turbine from state 1 to state 2 (or 1’ to 2’, or 1’’ to 2’’)

Steam leaving turbine condenses to water in the condenser reversibly at constant pressure from state 2 (or 2’ or 2’’) to state 3

h-S diagram

h

S

1”

2”2

1

1’

2’

p1

p2

3

4

h

s

h-S diagram for Rankine Cycle

The S.F.E.E for boiler (control volume)

2

1

3

4

h

s

h4 + Q1 = h1Q1 = h1-h4

The S.F.E.E for turbine (control volume)h1 = WT + h2WT = h1-h2

h2 = Q2 + h3Q2 = h2-h3

The S.F.E.E for condenser

h3 + WP = h4WP = h4-h3

The S.F.E.E for pump

h-S diagram for Rankine Cycle

Efficiency of a Rankine cycle

η = 푊푄

=푊 −푊

푄=

ℎ − ℎ − ℎ − ℎℎ − ℎ

Work Ratio

Ratio of net work output to positive work output

Work ratio = =

Pump work is small compared to turbine work and sometimes neglected. Cycle efficiency approximately becomes

η =ℎ − ℎℎ − ℎ

Efficiency of Rankine Cycle represented graphically in T-S diagram

3

4

1

2

T

S

3

6 5

Q1 α 1564Q2 α 2563Wnet α 1234

Steam Rate: To express capacity of steam plant Rate of steam flow (kg/h) required to produce unit shaft

output (1kW)

Steam Rate=

Cycle Efficiency/Heat Rate

Rate input (Q1) required to produce unit work output (1kW)

Heat Rate=

Adapted from• (1) Engineering Thermodynamics Text Book –P.K.Nag,5th Edition(2) Thermodynamics-An Engineering Approach-Y.A.Cengel, M.A.Boles

Compiled ByDr.G.R.SabareeshDepartment of Mechanical Engineering