Lect24 - Lecture notes 24 PDF

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Summary

Vapor Power Systems Power plants work on a cycle that produces net work from a fossil fuel (natural gas, oil, coal) nuclear, or solar input. For Vapor power plants the working fluid, typically water, is alternately vaporized and condensed. Consider the following Simple Vapor Power Plant Consider sub...

Description

Vapor Power Systems Power plants work on a cycle that produces net work from a fossil fuel (natural gas, oil, coal) nuclear, or solar input. For Vapor power plants the working fluid, typically water, is alternately vaporized and condensed. Consider the following Simple Vapor Power Plant

Consider subsystem A, each unit of mass periodically undergoes a thermodynamic cycle as the working fluid circulates through the four interconnected components 155

For the purpose of analyzing the performance of the system, the following cycle describes the basic system

Consider each process separately applying conservation of energy For steady-state, neglecting KE and PE effects, conservation of energy applied to a CV yields 1 dE Q& CV W&CV 2 ) + g ( z in − z out ) = − + (hin − hout ) + 1 / 2(Vin2 − Vout m& dt m& m& Q& CV W&CV 0= − + (hin − hout ) m& m&

156

1Æ2 Turbine (adiabatic expansion) Q& W& out + ( h1 − h2 ) 0= − & m m& wout

1

W&out (+)

W& out = = ( h1 − h2 ) m&

2Æ3 Condenser (no work)

2

2

− Q&out W& 0= − + ( h2 − h3 ) m& m& qout

Q& out = = ( h2 − h3 ) m&

Q& out (−)

3

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3Æ4 Pump (Adiabatic) Q& − W& in + ( h3 − h4 ) 0= − & m m&

4 3

W&in (−)

W&in win = = ( h4 − h3 ) m& 4Æ1 Steam Generator (no work) Q& in W& 0= − + ( h4 − h1 ) & m m&

1

Q& in (+)

Q& in qin = = ( h1 − h4 ) m &

4

Rankine Cycle Thermal Efficiency net work out (W& out / m& ) − (W& in / m& ) wout − win η = = = & Qin / m& qin heat input ηRankine =

( h1 − h2 ) − ( h4 − h3 ) h1 − h4 158

Back Work Ratio (bwr) work input (pump) W& in / m& w = = in bwr = work output (turbine) W&out / m& wout bwr =

h4 − h3 h1 − h 2

Ideal Rankine Cycle - no irreversibilities present in any of the processes: no fluid friction so no pressure drop, and no heat loss to surroundings 1. 2. 3. 4.

Steam generation occurs at constant pressure 4Æ1 Isentropic expansion in the turbine 1Æ2 Condensation occurs at constant pressure 2Æ3 Isentropic compression in the pump 3Æ4 Pboiler With superheating Pcondenser

159

Note: For an ideal cycle no irreversibilities present so the pump work can be evaluated by 4  W& p     m&  int = − ∫3 vdP   rev

if the working fluid entering the pump at state 3 is pure liquid, then 4 W& p   = ∫ vdP = v3 ( P4 − P3 ) win =   int 3  m&  rev The negative sign has been dropped to be consistent with previous use of win

160

Factors Affecting Cycle Efficiency η =

wout − win qin − qout q = = 1 − out qin qin qin

Recall: for a reversible heat addition process q = ∫ Tds Consider qin at the boiler and qout at the condenser

T qin

1

1

qin = q4 →1 = ∫ Tds

Tin

4

4

= shaded area s

Define mean temperature for process 4 Æ 1 1

Tin =

∫ Tds

4

s1 − s4

1

1

4

4

∴ qin = ∫ Tds = Tin ∫ ds = Tin (s1 − s4 )

161

3

qout = q2 →3 = ∫ Tds

T

2

3

qout

= Tout (s2 − s3 ) = shaded area

2

Tout s

Noting s2 − s3 = s1 − s 4 , the Ideal Rankine cycle thermal efficiency is η Ideal Rankine

= 1−

qout Tout ( s 2 − s3 ) Tout = − 1 = − 1 Tin qin Tin (s1 − s 4 )

Note: this is identical to the Carnot Engine efficiency which is also a reversible cycle

The back work ratio is bwrIdeal Rankine

=

w in v3 ( P4 − P3 ) = ( h1 − h2 s ) w out

162

Increase Rankine Cycle Efficiency η Ideal

= 1−

Rankine

T out Tin

Cycle efficiency can be improved by either: - increasing the average temperature during heat addition (Tin ) - decreasing the condenser temperature (Tout) Increase the amount of superheat (4Æ1’) ’ 1

2

’

Amount of superheating is limited by metallurgical considerations of the turbine (T1 < 670C) Added benefit is that the quality of the steam at the turbine exit is higher

163

Increase boiler pressure (4 Æ 1’) ’

’ ’

Disadvantages: - Requires more robust equipment - Vapor quality at 2’ lower than at 2

164

Decrease Condenser Pressure (2’ Æ 3’)

’ ’

’

Tout is limited to the temperature of the cooling medium (e.g., lake at 15C need 10C temperature difference for heat transfer so Tout >25C) Disadvantages: - Note: for water Psat(25C)= 3.2 kPa lower than atmospheric, possible air leakage into lines - Vapor quality lower at lower pressure not good for turbine

165

The most common method to increase the cycle thermal efficiency is to use a two-stage turbine and reheat the steam in the boiler after the first stage

net work out wout − win ( w1→2 + w3→4 ) − w5 →6 η = = = (q6→1 + q2→3 ) heat input qin

η Rankine = w / reheat

( h1 − h2 ) + ( h3 − h4 ) − ( h6 − h5 ) ( h1 − h6 ) + ( h3 − h2 )

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