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THERMODYNAMICS

Lecture 7: Thermodynamic cycles– steam cycles

Thermodynamics

Schematic of steam power plant – Clausius-Rankine cycle

Thermodynamics

A cycle of steam machine is following:

V0 V1 V2

p0

p1

1

2

3

4

5

p

V

Stages of a closed cycle:

1 The piston is at rest, vapourgoes from the boiler to a cylinder,pressure increases.

2 The piston moves, vapour isdelivered, constant pressure, volume increases.

3 Vapour access is closed, adiabaticexpansion

4 Opening of the cylinder to the cooler, rapid decrease of pressure, constant volume.

5 Removal of vapour remainder, constant pressure, volume decreases.

The work is performed during processes 2,3 and 5. It assumes thefollowing values;

Thermodynamics

Schematic of steam power plant – Clausius-Rankine cycle

)(21

hhmWt

−= &)(

32hhmQ

cond−= &&

)(34

hhmWp

−= &)(

41hhmQ

boiler−= &&

( ) ( )( )

41

3421

hhhhhh

QWW

in

pt

t −−−−

=−

=η ( )( )

21

321hhhh

QQQ

in

outin

t −−

−=−

=&

&&η

Thermodynamics

Schematic of steam plant – wet Clausius-Rankine cycle

Steam is a working fluid in ideal C-R cycle. Saturated vapour enters the turbine at 8MPa andsaturated liquid exits the condenser at a pressure of 0.008MPa. The net power output of thecycle is 100MW. Determine for the cycle a)thermal efficiency, b) back work ratio, c) mass flow ofsteam in kg/h, d) rate of heat transfer into the working fluid as it passes through the boiler, e) rate of heattransfer from the condensing steam as it passes through the condenser, f) mass flowrate of condensing cooling water, if cooling water enters the condenser at 15C and exits at 35C.

Thermodynamics

Thermodynamics

Clausius-Rankine cycle – effect of boiler and condenserpressure variation

H

C

ideal TT

−= 1η

Increasing boiler pressureincreases efficiency.

Decreasing the condenserpressure increases efficiency.

Temperature of surroundingsis the lowest temperature to which heat can be discharged(pcond<patm)!

Thermodynamics

Ideal Clausius-Rankine cycle vz. Carnot cycle

Thermodynamics

Clausius-Rankine cycle – irreversibilities in turbine and pump

( )( )

sts

t

t hhhh

WW

21

21

−−

==η

( )( )

34

34

hhhh

WW

s

p

ps

p −−

==η

Thermodynamics

Clausius-Rankine cycle – irreversibilities in turbine and pump

Reconsider the vapor cycle of previousexample, but include in the analyssi thatthe turbine and the pump each have theisentropic efficiency of 85%. Determinefor the modified cycle a) thermalefficiency, b) mass flow rate of steam for as net power output of 100MW, d) rateof heat transfer into the working fluid as it passes through the boiler, e) rate ofheattransfer from the condensing steamas it passes through the condenser, f) mass flow rate of condensing coolingwater, if cooling water enters thecondenser at 15C and exits at 35C. Discuss the effects of irreversibilitieswithin the turbine and pump.

Thermodynamics

Clausius-Rankine cycle – superheating and reheating

Thermodynamics

Clausius-Rankine cycle – supercritical cycles

Critical conditionsfor steam:

Pcr=22.09 MPa

Tcr=647,3K

Thermodynamics

Schematic of steam power plant – Clausius-Rankine cycleSteam enters the first-stage turbine at 8MPa and 480C and expands to 0.7MPa. It is thenreheated to 440C before entering the second-stage turbine, where it expands to thecondenser pressure of 0.008MPa. The net power output is 100MW. Determine a) thermalefficiency of the cycle, b) mass flow rate of steam, c) rate of heat transfer from condensingsteam as it passes through the condenser. Discuss the effects of reheat on the vapourpower cycle.

Thermodynamics

Schematic of steam power plant – Clausius-Rankine cycleReconsider the reheat cycle of last example but include in the analysis that each turbinestage has the same isentropic efficiency. If ηt=0.85 determine the thermal efficiency.

Thermodynamics

Clausius-Rankine cycle – regenerative cycles

y=m2/m1

)1)(()(3221

yhhmhhmWt

−−+−= &&

)1)(()(4567

yhhmhhmWp

−−+−= &&

Thermodynamics

Clausius-Rankine cycle – regenerative cycleConsider a regenerative vapour cycle with one open feedwater heater. Steam enters theturbine at 8MPa. 480C and expands to 0.7MPa, where some of the steam is extracted anddiverted to the open feedwater heater operating at 0.7MPa. The remaining steam expandsthrough the second stage turbine to the condenser pressere of 0.008MPa. Saturated liquidexits the open feedwater heater at 0.7MPa. The isentropic efficiency of each turbine stage is85% and each pump operates isentropically. If the net power output of the cycle is 100 MW, determine a) the thermal effciiency, b) mass flow rate of steam entering the first turbinestage.

Thermodynamics

Clausius-Rankine cycle – closed feedwater heaters

Thermodynamics

Regenerative vapour cycle with one closed feedwater heater

( )( )

72

56

hhhhy

−−

=( ) ( )6572

0 hhhhy −+−=

Thermodynamics

Clausius-Rankine cycle – multiple feedwater heaters

Thermodynamics

Clausius-Rankine cycle – binary cycles

Thermodynamics

Clausius-Rankine cycle – cogeneration