Derived thermodynamic design data for heat pump systems operating on R216

Hera RecorerySystems Vol. 2. No. 4. pp. 317 to 328. 1982

0198-7593 82 040317-12S03.00 0 Pergamon Press Lid

Printed in Great Britain.

DERIVED THERMODYNAMIC DESIGN DATA FOR HEAT PUMP SYSTEMS OPERATING ON R216 J. A. JIANG, S. DEVOTTA, F. A. WATSON, and F. A. HOLLAND Department of Chemical Engineering, University of Salford, Salford M5 4WT. U.K. Abstract--The theoretical Rankine coefficients of performance (COP)R and the compression ratios have been presented for heat pumps operating on R216. These values are listed in tabular form for temperature lifts of 10-75"C and for condensing temperatures of 10-160~C in 5~C increments. Several graphs have been drawn to illustrate the feasilbe operating range for R216 heat pump systems. The derived thermodynamic data can be used for the rapid preliminary design of heat pump systems operating on R216.

NOMENCLATURE

(COP)R Hx

Rankine coeffÉcient of performance of a heat pump system, dimensionless enthalpy per unit mass at state condition X [kJ ks- 1] pressure in the condenser of a heat pump [bar] pressure in the evaporator of a heat pump system [bar] temperature of the working fluid in the condenser [K or °C] temperature of the heat sink fluid from the heat pump system [K or °C] temperature of the working fluid in the evaporator [K or °C] temperature of the heat source fluid to the heat pump system [K or *C] wetness fraction of vapour, dimensionless entropy per unit mass at state condition X [kJ kg- 1 K - i]

PCO PEx

Too TD TEV

Ts X

INTRODUCTION

R216, WHICH HAS the chemical formula C3C12F6, hexafluorodicholoropropane, is one of the potentially useful working fluids for high temperature heat pump systems. Its critical temperature and pressure are 453.1 K and 27.55 bar, respectively. Table 1 presents an abridged version of some physical data for R216.

50.0

-

20.0 t~

10.0

J

<5.0

100°C

/

t~

2.0--

~.,~

50°C

1.0-0.5

I

100

/

t

sM

I

150 200 250 Enthalpy per unit mass H, kJ kg-I

Fig. 1. Pressure against enthalpy per unit mass for R216. 317

I

500

8. 7630 8. 9001 9.0432

259.136 262.434 265.718

1.4168 1.6234 1.8502

114.117 1 12.359

110. 580

0.11159 0.11242

0.11317

12.415

14.446 16.732

1504.5 1489.8 1475.1

1.3854

1.6243

1.8936

50.0

55.0

45.0

8.6316

255.851 1.2295 115.853

0.11067

10.613

1518.7

1.1745

40.0

8.5040

252.569 1.0604

117 • 592

0.10970

9.018

1532.8

0.9892

35.0

8.3785

269.307 0.9092

119.352

0.108b3

7.618

1546.6

0.8275

30.0

8.2595

266.018 0.7741

121.073

0.10747

b. 394

1560.4

0.b871

25.0

8.1408 2 6 2 . 781

0.6545

122.838

0.10623

5. 328

1573.9

0.5660

20.0

8.0278

239.521

4.407

1587.3

0.4624

15.0

0.5490

0.10364

3.b12

IbO0.7

0.3744

10.0 124.567

128.097

0.10223

2.937

1613.8

0.3003

0.10493

•

7.9151

0.3073

129 8 90

0.10075

2.360

1626.8

236.298

kg MJ

0.4564

-3 MJ m

126.341

-I

7. 8066

kJ kg

-i

mass of working fluid

233.077

5.0

m3kg -I

enthalpy of saturated vapourl k8 kg

0.3763

0.2383

0.0

llquid

--3ar vapour

latent heat

7.6988

bar

°C

PV

229.890

PCO

TCO

-3 density kg m

Table 1. Physical data for R216

z

9.1905 9.3464 9.5104 9.6805 9.8641 10.0562 10.2626 10.6811 10.7187 10.9776 II.2575 11.5695

272. 300 275.574 278.849 282.104 285.351 288. 577 2 9 1 . 8 O0 294. 991 298. 141 301.280 304.362

2.3699 2.0631 2. 9814

3.3232 3.8910 4.0854 4.5062 4.9621 5.346I 5.9246 6.4489

106.993 105.148 103.300 101.378 99.441 97.441 95.410 93.295 91.095 88.829 86.434

O. 11435 O. 1 1 4 8 1

0.11516 0.11541 O. 11554 O. 11552 U. 11539 O. 11493 O. 11645 0.1 1412 0.11342

22.150 25.328 28.862 32.781 37.117 41.927 47.230 53. 187 58.687 66.696 74.610

1444.7 1429.0 1412.9 1396.5 1379.8 1362.5 1344.7 1326.4 1307.5 1287.9 1267.6

2.5330

2.9079

3.3237

3.7831

4.2884

4.8434

5.4501

6.1127

6.8343

7.6115

8.4622

65.0

70.0

75.0

80.0

~5.0

90.0

95.0

100.0

105.0

110.0

115.0

kg MJ

269.013

-3 MJ m

2.0990

-I

10B.808

kJ kg

-I

mass of working fluid

O. 11382

bar m3kg -I

enthalpy of saturated vapour -I kJ kg

19 • 291

vapour

latent heat

1460.1

liquid

PV

2.195b

bar

°c

-3

60.0

PCO

TCO

density kg m

Table I (cont.)

r~

t~

0

0

330.0U5

12.0275

51. 023 0.09104

235. 729

970.0

21.4613

165.0

32~.373

11.6588 56.481

0.09552

206. 622

1020.2

19.1177

160o0

326.333

11.1632 01. 127

0.09905

182.623

1058.0

18.0884

155.0

324.045

10.5960 05.288

0.10209

162.296

1091.0

16.5680

150.0

321.553

9.9961

09.017

0.10456

144.835

1122.1

15.1441

145.0

13. 8060

318.905

9.3769

72.432

0.10676

129.458

1150.1

13.8214

140.0

13.2268

316.160

8.7624

75. 004

0.10866

I 15.~98

1170.4

12.5907

135.0

12.7276 313.323

8.1604

18.570

0.11013

103.862

1200.9

11. 4386

19.5991

17.7052

16.3594

15.3166

14.4891

12.2954

11.9126

310.395

130.0

of

kg MJ -I

7.5717

81.331

0.11140

93.098

1224.2

10.3715

125.0

-3

mass

working fluid

307.402

MJ m

enthalpy of saturated vapour -i kJ kg

6.9915

83. 945

0.11250

83.358

i

1246.4

9.3781

-I

120.0

kJ kg

vapour

liquid

bar

latent heat

°C

bar m3kg -I

PV

PCO

-3

TCO

density kg m

Table 1 cont.)

> Z

>

¢D

4.19

55

4.24

4.76

-

4.70

5O

5.40

75

5.33

45

6.19

-

6.12

4O

7.23

70

7.13

35

8.6O

-

8.49

3O

10.53

3.81

10.39

25

13.45

65

13.25

20

18.28

6O

18.O5

15

27.99

0.566

0.462

27.60

20.0

15.O

IO

(Tco-TEv)

c

i I

-

-

3.49

3.86

4.29

4.82

5.46

6.28

7.33

8.73

10.71

13.66

18.62

28.47

0.687

25.0

-

3.21

3.52

3.89

4.34

4.87

5.53

6.35

7.42

8.84

10.83

13.83

18.81

28.87

0.827

30.O

2.96

3.23

3.55

3.93

4.38

4.93

5.59

6.43

7.52

8.96

II.OO

14.O4

19.17

29.29

0.989

35.0

9.19

11.30

14.42

19.74

30.19

1.385

45.0

2.98

3.26

3.59

3.97

4.43

3.00

3.28

3.61

4.00

4.47

4.98 i 5.03

!

5.66 [ 5.72

I

6.51 I 6.58

7.61 I 7.70

9.08

11.14

14.26

19.39

29.88

1.175

40.0

3.O1

3.30

3.64

4.03

4.51

5.08

5.77

6.66

7.78

9.31

11.42

14.65

19.94

30.58

1.624

50.O

3.O3

3.32

3.66

4.06

4.54

5.12

5.83

6.72

7.88

9.40

11.58

14.80

20.19

30.98

1.894

55.0

3.O4

3.33

3.68

4.09

4.58

5.16

5.88

6.79

7.94

9.52

11.68

14.96

20.41

31.33

2.196

60.0

3.O5

3.35

3.70

4.11

4.61

5.20

5.93

6.84

8.03

5.60

11.81

15.12

20.65

31.69

2.533

65.0

3.O5

3.36

3.71

4.13

4.63

5.24

5.97

6.91

8.09

9.69

11.92

15.28

20.87

32.10

2.908

70.O

75.0

3.06

3.36

3.73

4.15

4.66

5.27

6.02

6.95

8.16

9.78

12.O4

15.44

21.13

32.49

3.324

Table2. TheoreticalRankinecoefficientsof ~r~rmance(COP)R ~rarangeofliftsandcondensingtemperatures ~rR216

3.05

3.37

3.73

4.17

4.68

5.30

6 .O5

7 .OO

8.23

9.86

12.15

1 .61

21.37

32.92

3.783

80.0

3.05

3.37

3.74

4.17

4.70

5.32

6.08

7.04

8.28

9.93

12.26

15.25

21.51

33.20

4.288

85.0

iJ

o

g~

o

~n

f-

0

,t~

--4

~

,~

0

~

~

0

~

~

I,-'

0

~

0

~~ ' " ~,o 8

0

1-~

~

I'~

~o

0'~

~,,,.4

,~.

"

h~

t~

h "~

~.

0 0 ,.-4

U'I

~.~

o"

o

b

~

8

~

b

•-

b

~

b

tD

~

,-4 o

.u~

~.~

~

~

~

..~

~

~

~

~

~

~

~

~

~

~

,~.

~

~'~

"-.4

CO

0

~

~

.

~'~

u'~

~

0

U'~

0

~

~

0

~

ij

~

i' ~

~

k-~

0

I~o

.~

.

°

~

~D

I~0

~

0

~

b

0

~ t~

8t~

•

I,~

~

I~

,.,

b

-~

0

~

0

~,~

e~ k,~

I.o

0 e~ .~-

~ 0

~

0

~ ~

~

~

~

.,~

~

Co

~

0

o

~0

~ ~

h "~

h~

~

~o

0

..4

h~

~

~

u~

~

b e-

k,~

~

~

.~

lm ~--'

~

~.~

~

~

"-4

~'~

~

~

,~,

-~

~

~

0

~

0

~

D

3,899

5.092

6.739

9.047

4.160

5.505

7.390

10.O92

14.0OO

19.781

3O

35

40

45

5O

55

.

3.026

3.185

25

-

-

-

-

.

7O

75

.

24.214

17.137

65

-

2.375

2.472

2O

60

1.885

1.940

15

12.354

1.512

0.566

20.0

1.540

0.462

15.0

IO

(Tco-TEV) - C ' , ~

",~bar)

c

.

-

29.393

20,803

14.996

10.982

8.180

6.182

4.733

3.673

2.883

2.288

1.835

1.486

0.687

25.O

11.777

8.900

6.815

5.288

4.151

3.294

2.642

2.139

1.748

1,440

0.989

35.O

35.398

25.053

42.319

29.951

21.591

18.O60 15.811

13.225

9.851

7.445

5.700

4.423

3.472

2.750

2.210

1.789

1.462

0,827

30.0

Table 4. Compression ratios

i

12.464

9.544

7.405

5.813

4.614

3.700

2.996

2.448

2.O16

1,674

1.4OO

1.385

45.O

22,143

35.560 30.238

25.634

18.772i16.494

13.983

10.567

8.O91

6.278

4.928

3.911

3.137

2.540

2.075

1.709

1.419

1.175

40.0

13.O45 11.736

9.212

25.961 i22.544 19.753

19.338 J17.O36 15.125

14.614

5.864

4.748

3.879

3.196

2.653

2,219

1.869

1.585

1.352

2.196

60.0

7.945 ! 7.312

6.306

5.058

4.095

3.345

2.756

2.288

1,914

1.612

1.369

1.894

55.O

11.190 10.122

8.682

6.815

5.409

4.339

3.513

2.870

2.364

1.963

1.642

1.383

1.624

50.O

17.449

13.539

10.628

8.435

6.7661

5.478

4 - 475

3.687

3.O61

2.561

2,157

1 . 828

1.559

1,338

2.538

65.O

9.684

7.767

6.289

5.137

4.232

3.514

2.940

2,476

2.099

1.790

1.536

1.324

2.908

70.0

I

8,878

7.188

5.872

4.837

4.O17

3.360

2.830

2.399

2.046

1.7551

1.514

1.312

3,324

75.O

15.543

13.945

12.201 11.O69

Pco/PEvfor a range of lifts and condensing temperatures for R216

12.599

10.105

8.181

6.684

5.506

4.572

3.824

3.221

2,731

2.329

1.998

1.723

1.494

1.301

3.783

80.0

11.454

9.274

7.576

6.241

5.18~

4.33~

3.651

3,092

2.64~

2.265

1.953

1,693

1.475

1.290

4,288

85.O

to

=

O

=

o

ar)

1.457

1.666

1.912

2.206

2.558

2.982

3.496

4.124

4.896

5.853

7.049

8.559

10.474

15

2O

25

3O

35

4O

45

5O

55

6O

65

7O

75

9.629

7.932

6.586

5.509

4.640

3.934

3.355

2.878

2.482

2.1 2

1.874

1.640

1.441

1.271

5.450

4.843

1.280

95.0

90.0

IO

(Tco-TEv)-C~, ~

~

~<~Co °C

8.896

7.387

6.179

5.204

4.412

3.763

3.228

2.284

2.413

2.102

1.839

1.616

1.425

1.262

6.113

iOO.O

8.259

6.909

5.819

4.933

4.207

3.609

3.113

2.698

2.350

2.056

1.807

1.594

1.411

1.254

6.834

105.O

7.694

6.481

5.494

4.686

4.020

3.467

3.005

2.618

2.290

2.O12

1.775

1.572

1.397

1.245

7.611

IIO.O

7,205

6.108

5.210

4.469

3.854

3.341

2.910

2.546

2.237

1.973

].747

1.553

1.384

1.238

8.462

115.O

125.O

6.769

5.773

4.953

4.271

3.702

3.225

2.822

2.479

2.187

1.936

1.721

1.534

1.372

1.232

6.387

5.477

4.724

4.095

3.567

3.120

2.742

2.418

2.141

1.903

1.697

1.518

1.363

1.226

9.578 10.372

120.O

6.041

5.210

4.516

3.934

3.442

3.024

2.667

2.362

2.099

1.871

1.674

1.503

1.352

1.220

[1.439

130.O

5~734

4.971

4.330

3.788

3.328

2.936

2.600

2.310

2.060

1.842

1.654

1.488

1.343

1.214

[2.591

135.O

145.O

150.O I

155.O

160.O

5.457

4.753

4.158

3,653

3.224

2.854

2.536

2.261

2.022

1.816

1.633

1.474

1.333

1.208

5~208

4.556

4.003

3.531

3.127

2.779

2.477

2.216

1.990

1.790

1.615

1.460

1.324

1.203

4.985

4.380

3.864

3.421

3.040

2.711

2.424

2.177

1.958

1.767

1.598

1.448

1.316

1.199

4°78]

4.218

3.735

3.319

2.959

2.647

2.376

2.138

1.929

1.744

1.581

1.437

1.309

1.194

4~5981

4.O71

3.618

3.226

2.885

2.591

2.330

2,103

1.901

1.724

1.566

1.427

1.302

1.190

[3.821 15.144 16.569 18.O88 19.718

140.O

Table 5. Compression ratios Pco/Pev for a range of lifts and condensing temperatures for R216

/

4~

325

Heat pump systems operating on R216

THERMODYnAMiC

DERIVED

DATA

The operation of a mechanical vapour compression heat pump approximates closely to the Rankine cycle. The Rankine cycle mainly involves four sequential operations, namely, isobaric evaporation, isentropic compression, isobaric condensation and isenthaipic expansion. In general, isentropic compression of saturated vapour results in superheating of the vapour. However, the thermodynamic properties of R216 imply that partial condensation should result on isentropic compression of the saturated vapour over certain pressure ranges. The ideal Rankine cycle with partial condensation is illustrated in Fig. 1, which is a plot of pressure P against enthalpy per unit mass H for R216. With reference to Fig. I, the theoretical Rankine coefficient of performance of a heat pump can be defined as (COP)R -

HI)I -

HI)3

Ht)t

Hs2

-

(1)

The entropy ~bD~of the two-phase mixture at D1 can be related to the entropies of the saturated liquid q5,)3 and of the saturated vapour qSD2by the equation q5,,I = ¢bD3x + ~b,)2(l -- X)

(2)

|55

Tco= IO0°C

1

Pco= 6.115 bor

~:50 ._E

"o

25 =

e 6 E

2o ~o

5

~c

g

O_

~4

15

,-~

o= t~

E

~R 3

8 o

I IJ

0

I

IO

t ....

I

I

I

20 30 40 50 Temperature lift (Tco-TEv}, °C

I

60

I0

70

I ....

I

I

1

I

I

O

IO

20

30

40

SO

Temperature lift (To-Ts), °C wii~ 20°C drop in heot exchangers.

Fig. 2. Compression ratio and theoretical Rankine coefficient of performance against temperature lift for R216 at a condensing temperature of 100°C and a condensing pressure of 6.113 bar.

326

J.A.

JIAN(;

el al.

where x is the liquid fraction of the wet vapour at Dt. Since the compression fl'om $2 to D1 is isentropic 4't, = 4's2.

(3~

The mass liquid fraction x can be calculated from equations (2) and (3). The enthalpy of the two phase mixture at D1 can then be calculated from the enthalpies of the saturated liquid Ho3 and of the saturated vapour HD2 from equation (4). HDI

=

HD3X + HD2 (1 -- x).

Equations (1)-(4) can be used to calculate

(COP)e values

(4) for any desired condensing

temperature Tco and temperature lift (T(,o- TFv) from the saturation properties of R216. The theoretical Rankine coefficients of performance (COP)R and the compression ratios Pco/P~v have been calculated for R216 for temperature lifts of 10-75°C and for condensing temperatures of 15-160°C in 5°C increments. All the basic thermodynamic properties of R216 used in the calculation have been taken from published tables [1]. Tables 2 and 3 list the calculated (COP)R values and Tables 4 and 5, the calculated Pco/PEv values. Figures 2-6 are plotted from the data listed in the tables. DISCUSSION OF DERIVED THERMODYNAMIC DESIGN DATA

Figure 2 shows the variation of the compression ratio Pco/P~:_vand the theoretical Rankine coefficient of performance (COP)~ with temperature lift (Too - T ~ j for a condensing temperature 7"(,0of 100°C, and a condensing pressure Pco of 6.113 bar. If there is

,5

1

/

,ooc

14

i

Condensing temperature

13

-28 26

'

-- 24 ~n

12

--22

E "5

20

&

0 = 30%

II

2 E :6

rco = $o*c

~

,~

9-

Tc0 =

16

o 8--

14

~. "5

o_

-#

7-

12

6-

io

~

E

rco = 14o*c / oE

L)

3p-

~ }

2

-!2

~

_k.._lo 0

Io

20

3o

~=~ro~e

40

50

nift (~-rEv),

60

7o

oc

Fig. 3. Variation of compression ratio and4heorctieal Rankinc coefficient of performance with temperature lift and condensing temperature for R216.

327

Heat pump systems operating on R216 20 0)

E = 50%

I0

r~

~O-TEv) = 5 0 % o I----

.1

I

2

t 3

1

I 4

Compression folio P / P , CO IrV

I

! 5

t

6

dimensionless

Fig. 4. Theoretical Rankine coet~cient of performance against compression ratio showing the influence of temperature lift and condensing temperatures for R216. 18

Temperofure lift

(Too-TEv)= 20°C

\

( reo- rEv) = 3o*c ~ IO!

\

"5 e I-

o

6

=~

4 21

-

(r~o- r~v) = 4 o o c

(reo rcv) = 5o*c \

-

~o

40

(rco ~ ) = 6 0 % \

I 60

[ 80

L I00

1 120

Condensing temperature Tco,

I 140

I 160

*C

Fig. 5. Theoretical Rankine coefficient of performance against condensing temperature for various temperature lifts for R216.

J A. JIAN(; ,'t a,'.

328

r6 15

E

Temperature lift (T~T~,,) : 7 0 o c

12

8°o o65

,

4

40

60

80 t00 "120" Condensing temperature to' °C

140

160

Fig. 6. Compression ratio against condensing temperature for various temperature lifls for R216.

a temperature drop of 10°C in each of the heat exchanger, the effective temperature lift will be reduced by 20°C. Figure 3 shows that Pco/PEv values for a given temperature lift are extremely sensitive to the condensing temperature. In contrast, the (COPJRvalues are almost independent of the condensing temperature. Figure 4. which is a plot of (COP)R against Pco/PLv for various temperature lifts. implies that relatively high coefficients of performance are only possible for relatively low temperature lifts and compression ratios. Figure 5 shows that (COP). increases almost linearly with the condensing temperature for all temperature lifts and then decreases after reaching maxima in the region of Too = 115°C. The maximum is more pronounced for lower temperature lifts Figure 6 shows the variation of compression ratio with condensing temperature for various temperature lifts. Figure 6 clearly indicates the upper limit of the possible temperature lifts resulting from any practical limit to the compression ratio. REFERENCES 1. H. M. Meacock. Refrigerution Processes. p. 170, P e r g a m o n Press, Oxford [1979),