Improvement Rankine Cylce

8/12/2019 Improvement Rankine Cylce

1/24

9.1

ME 300 Thermodynamics IISpring 2011

Lecture 9:

Rankine Cycle Improvements

Yonghua Huang

Shanghai Jiao Tong University

Institute of Refrigeration and Cryogenics800 Dong Chuan Road, Shanghai, 200240, P. R. China

Email : [email protected]

Phone: 86-21-34206295


2/24


3/24

9.3

Rankine Cycle Performance Trends

Effect of superheat on performance: Reason: Increase average temperature for heat

addition at a given boiler pressure

increase in performance

T3is limited by THand materials

Question:

Why not increase TBinstead?

Answer:

- Need high steam quality atturbine outlet to avoid corrosion

(want x4> 0.9, better > 0.95)

- Would require higher boiler

pressurematerials, safety


4/24

9.4

Continue Rankine CyclePerformance Trends

Continue effect of superheat on performance: Consequence of superheating:

DTsup (oC) h x4

0 0.186 0.858

54 0.190 0.913

278 0.217 >1.0

Note:

Increasing DTsuphas nota very big effect on thermal

efficiency, but is needed to increase x4to a practical

value!


5/24

9.5


Effect of boiler pressure on performance:

- Increasing boiler pressure

decreases heat input at

relatively constant workoutput

Increase in efficiency

- Upper limit depends on

heat supply temperature

and materials

- Also decreases quality


6/24

9.6


Continue effect of boiler pressure on performance: Assume: TC= 66

oC [pC= psat(TC) = 0.255 bar]

x4= 0.95 [specifies T3]

TB (

o

C) pB(bar) T3(

o

C) h232 29 400 0.246

288 72 506 0.290

343 153 604 0.324

Notes:

T3increases more than Tboilingto maintain x4

maximum pressure dictated by temperature of heat source and

materials

optimal pressure: trade-off between 1stcosts and operating

costs


7/24

9.7


Effect of condensing pressure on performance:

- Lower condenser pressure

increase work output at the

same heat inputIncrease in efficiency

- Lower limit depends on

environmental temperature

- Lowering pressure

decreases qualityMust increase T3to

keep quality constant


8/24

9.8


Effect of condensation temperature, TC, on performance: Assume: TB= 172.3

oC and x4= 0.95

TC (oC) pC(bar) T3(

oC) h

93.3 0.8 552 0.289

65.6 0.255 604 0.32437.8 0.066 670 0.359

Notes:

T3must increase to maintain x4

Tc

is limited by sink temperature

Summary:

Want high Tband low Tc!

Need superheat to get x4> 0.9

Would rather increase Tbthan T3


9/24

9.9

Continue Rankine Cycle Improvements-----Two-stage Cycle with Reheat

Advantages:High quality (or superheated

vapor) existing the turbine without

large superheat

For a given THcan increase Tb

without reducing quality


10/24

9.10

Continue Rankine Cycle Improvements

Overall thermal efficiency:

Multi-staging with Reheat:

Idea: Would rather raise TBthan T3

Consider limit of infinite-stages:

T1 T2 Pnetth

in B R

W W WW

Q Q Q

h

T

s

1

2

i

i+1

TH

TL


11/24

9.11


Supercritical reheat cycle:

For water/steam:

Tcrit= 374oC

pcrit= 22.064 MPa Advantage:

very high heat addition

high h

Disadvantage:

material requirements

(thermal/mechanical stress)

high initial costs


12/24

9.12

Rankine Cycle Improvements

Recall Basic Rankine Cycle:

Tp1= p4

p2= p3

1 4s

3

TL

TC

TB

TH

4

THX

THX

2s

s

Rankine Cycle Improvements:

1.) Reheat: allows increased TB, while maintaining x4> 0.95

2.) Regeneration: reduce the external heat added from 2

2

22

To improve efficiency:1.) Raise average temperature

for heat addition

2.) Lower average temperature

for heat rejection


13/24

9.13


Regeneration:

There are two types of regeneration cycles:

1.) open feedwater heating---direct contact-type heat exchanger

2.) closed feedwater heating

Rankine Cycle with open feedwater heater:

5

6

7

1st-stage

2nd-stage

1

2

3

4

Turbines

.

WP2

.

WT

.

WP1.

QC

Boiler

Condenser

Pump 1

Pump 2

Open Feed-

water heater

.

QB

.

mtot

.

y mtot.

(1-y) mtot


14/24

9.14


Continue Rankine Cycle with open feedwater heater:

T

p1= p7

1TL

TC

TB

TH

4

s

2 3

p4= p5p2= p3 = p6

5

7

66s

7s

Notes: - Choose y so that state 3 is saturated liquid

- Tradeoff: Heat addition from 25 is reduced by (h3h2)

Flow rate through 2ndstage turbine is reduced

- Overall: net results is increase in hth


15/24

9.15



Question: How to determine y?

Answer: Energy balance on feedwater heater

tot 6 tot 2 tot 3

6 2 2 3

6 2 3 2

3 2

6 2

y m h (1 y) m h m h

y h h y h h

y h h h h

h hy

h h

Assumptions: SSSF

Adiabatic

DKE = DPE = 0


16/24

9.16



Overall thermal efficiency:

T1 T 2 P1 P2net

th

in B

tot 5 6 6 7 2 1 4 3

th

tot 5 4

W W W WW

Q Q

m h h (1 y) h h (1 y) h h h h

m h h

h

h


17/24

9.17


Continue Rankine Cycle with open feedwater heater: Assume: TB= 343

oC pB= psat(TB) = 152.8 bar

TC= 66oC pC= psat(TC) = 0.255 bar


Ti [oC] pi[bar] y [-] hth

66 0.255 0 0.324

121 2.05 0.09 0.352

177 9.31 0.16 0.368

232 20.1 0.22 0.367

288 70.05 0.27 0.352

343 152.8 0.32 0.324

In general, optimal Tifor one feedwater heater is Ti= (TBTC)/2

Then, optimal pressure is pi= psat(Ti)


18/24

9.18


Rankine Cycle with closed feedwater heater: Idea: Do not mix the two streams, use heat exchanger

Can operate two streams at different pressures

Two types of closed feedwater heaters possible:

4

5

6

1st-stage

2nd-stage

1

Turbines

.

WP2

.

WT

.

WP1

.

QC

Boiler

CondenserPump 1

Closed Feed-

water heater

.

QB

.

mtot

.

y mtot.

(1-y) mtot

8v

2

7

Pump 2

Steam Trap

8p3p

3v


19/24

9.19


Continue Rankine Cycle with closed feedwater heater:

T

p1= p6

1TLTC

TB

TH

s

2

p2= p3 = p4

p5= p

7

4

6

55s

6s

3p

3v

8p

8v

7


20/24

9.20


Continue Rankine Cycle with closed feedwater heater: Overall thermal efficiency:

T1 T 2 Pnetth,v

in B

tot 4 5 5 6 2 1

th,v

tot 4 3v

T1 T2 P1 P2netth,p

in B

tot 4 5 5 6 2 1 8p 7

th,p

tot 4 3p

W W WWCase V :

Q Q

m h h (1 y) h h h h

m h h

W W W WWCase P :

Q Q

m h h (1 y) h h (1 y) h h y h h

m h h

h

h

h

h

Assuming that v1~ v

7, p

1~ p

7and h

3v~ h

3p, then h

th,v= h

th,p


21/24

9.21


Continue Rankine Cycle with closed feedwater heater: Energy balance on feedwater heater:

v tot 5 7 tot 3v 2

3v 2v

5 7

p tot 5 7 p tot 3p 2

3p 2

p

5 7 3p 2

5 7 3p 2 p v

Case V : y m h h m h h

h hy

h h

Case P : y m h h (1 y )m h h

h hy

h h h h

Since h h h h : y y !


22/24

9.22


Continue Rankine Cycle with open feedwater heater: Assume: TB= 343

oC pB= psat(TB) = 152.8 bar

TC= 66oC pC= psat(TC) = 0.255 bar


T7=T3 [oC] p7[bar] hth

66 0.255 0.324

121 2.05 0.350

177 9.31 0.360

232 20.1 0.344288 70.05 0.293

343 152.8 0.173

Optimal T7for one feedwater heater is still T7= (TBTC)/2

In practice, use multiple feedwater heaters!


23/24

9.23


Rankine Cycle with Reheat and Regeneration:

5

8

1st-stage 2nd-stage

12

3

4Turbines

.WP2

.WT

.

WP1

.

QC

Condenser

Pump 1

Pump 2

Open Feed-

water heater

.

mtot

.

y mtot

.

(1-y) mtot

6

67

Boiler

Reheater

.

QB

.

QR


24/24

9.24


Continue Rankine Cycle with Reheat and Regeneration:

T

p1= p8

1TL

TC

TB

TH

4

s

2 3

p4= p5p6= p7 = p3

5

7

6

6s

8s

8

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Improvement Rankine Cylce