Further Developments in Carnotization of Rankine Model

BY

P M V SubbaraoProfessor

Mechanical Engineering DepartmentI I T Delhi

Taming of Non-Isothermal Heat Addition Zones…..

C

C

C

Reassessment Thru Carnot Model

Reheat Cycle

Analysis of Reheat Cycle

• 1—2: Isentropic Pumping

• 2 –3 Constant (High)pressure Heat addition

• 3 –4 Isentropic expansion in HP turbine.

• 4—5 Constant (Low) Pressure Reheating.

• 5 – 6 Isentropic expansion in LP turbine.

• 6 – 1 Constant pressure condensation.

12 hhwp

43, hhw outhp

23, hhq SGin

45, hhq RHin

65, hhw outlp

16 hhqout

inR

netRHRH q

w

.

,

RHinSGin

plphpRH qq

www

,,

4523

126543

hhhh

hhhhhhRH

Analysis of Reheat Cycle

• Consider reheat cycle as a combination of Rankine cycle and horn cycle.

• Cycle 1-2-3-4-5-6-1 = Cycle 1-2-3-4-4’-1 + Cycle 4’-4-5-6-4’.

• Therefore,

’

HornRankineRH www HorninRankineinRHin qqq ,,,

HornoutRankineoutRHout qqq ,,,

inHorninRankine

netHornnetRankine

inRH

netRHRH qq

ww

q

w

,.

,,

,

,

4’ 6

Horn Cycle:

4’ – 4 Isentropic Compression.4 – 5 Isobaric Heat Addition.5 – 6 Isentropic Expansion6 – 4’ Isobaric(thermal) cooling.

45

'4465

45,

4465,

'44,

65,

hh

hhhh

hhq

hhhhw

hhw

hhw

horn

inhorn

nethorn

inhorn

outhorn

inRankine

netRankineRankine q

w

.

,inHorn

netHornHorn q

w

.

,

inRH

inRankine

netRankine

netRH

Rankine

RH

q

q

w

w

.

.

,

,

inRankine

inhornnetRankine

Horn

Rankine

RH

qqw

w

.

., 1

11

inRankine

inhorninRankine

inHorn

Rankine

Horn

Rankine

RH

qqq

q

.

.,

,

1

11

inHorn

inRankine

Rankine

Horn

Rankine

RH

qq

.

.1

1

1

Select appropriate reheat pressure, pRH, such that left hand side is maximum.

11

1

1

.

.

,

,

inRankine

inhorn

inRankine

inHorn

Rankine

Horn

Rankine

RH

qq

q

q

inRankine

inHorn

Rankine

Horn

inRankine

inHorn

Rankine

RH

qq

q

q

.

.

,

,

1

1

1

Mean Temperature of Heat Addition

260

270

280

290

300

310

320

0 2 4 6 8 10 12 14 16

prh, MPa

Tm,in

C

Theoretical analysis of Reheat Cycle

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 2 4 6 8 10 12 14 16

prh, MPa

eff.

fact

orpmax= 15 MPaTmax= 550 0CTsat= 342.20C

Procedure to Determine Optimum Reheat Pressure

• Calculate the efficiency of Rankine cycle, Rankine.

• Calculate mean effective temperature of heat addition, Tm,in using

inm

cCarnotEqRankine T

T

,. 1

i

i

rhinm

cCarnotEqheat T

T

,,.Re

1

• Find out pressure corresponding to Tm,in and entropy at HP turbine exit.

• Add reheating at this pressure and calculate efficiency of the Reheat Cycle.

• Repeat above steps for few iterations.

Mean Temperature of Heat Addition

260

270

280

290

300

310

320

0 2 4 6 8 10 12 14 16

prh, MPa

Tm,in

Cpmax= 15 MPaTmax= 550 0CTsat= 342.20C

Effect of Reheat Pressure

prh/pmax

0.2 0.4 0.6 0.8 1.0

~0.3