READ!ME

Evaporation cooling Thermocompressor design

Steady state: calculate temperature at the cooling box for given mass flowrate of motion steam

Transient: calculation of time course of temperature in the cooling box

Input parameters are in

Cooling box

Evaporated water

Condenser

Motion steam

Laval nozzle

Strana 1

READ!ME

Thermocompressor design

Steady state: calculate temperature at the cooling box for given mass flowrate of motion steam

Transient: calculation of time course of temperature in the cooling box

blue cells

Strana 2

COOLING-STEADY STATE

Evaporation cooling

Thermocompressor designMotion steam parameters Ambient temperature [C]

p1[MPa]= 0.62 40

T1= 157.7967 Area of cooling box walls [m2]

M [kg/s]= 0.01 100

Condenser (the compressor output), cooling water Heat transfer coef. [W.m-2

.K-1

]

T5[C] 40 30

p5[MPa] 0.007351 Antoine equation lnp=A-B/(C+T) is used

Evaporated water (the compressor suction) Kappa= 1.13 0.11504425

T2[C] p2[MPa] Pe=p1/p2 Pk=p5/p2 fe=Me/Mp fm=Mp/Me Me[kg/s]

30 0.00422 147 1.74 1.86 0.54 0.018609

29 0.00398 156 1.85 1.74 0.58 0.017386

28 0.00375 165 1.96 1.63 0.61 0.016324

27 0.00354 175 2.08 1.54 0.65 0.015390

26 0.00333 186 2.21 1.46 0.69 0.014562

25 0.00314 197 2.34 1.38 0.72 0.013821

24 0.00296 210 2.49 1.32 0.76 0.013153

23 0.00278 223 2.64 1.25 0.80 0.012548

22 0.00262 237 2.81 1.20 0.83 0.011995

21 0.00246 252 2.99 1.15 0.87 0.011489

20 0.00231 268 3.18 1.10 0.91 0.011024

19 0.00217 286 3.39 1.06 0.94 0.010593

18 0.00204 304 3.61 1.02 0.98 0.010194

17 0.00191 324 3.85 0.98 1.02 0.009822

16 0.00179 346 4.10 0.95 1.06 0.009476

15 0.00168 369 4.38 0.92 1.09 0.009151

14 0.00157 394 4.67 0.88 1.13 0.008847

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Q-[

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Strana 3

COOLING-STEADY STATE

Qchl[kW] Qztraty[kW]

44.662 30

41.727 33

39.178 36

36.937 39

34.949 42

33.171 45

31.568 48

30.114 51

28.789 54

27.574 57

26.457 60

25.423 63

24.465 66

23.574 69

22.742 72

21.963 75

21.233 78

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T-suction [C]

STEADY STATE COOLING

Qchl[kW]

Qztraty[kW]

Strana 4

TRANSIENT

Evaporation cooling : transientMass of water in evaporator M= 100 [kg] Initial temperature of water [C]=

Motion steam parameters Ambient temperature [C]

p1[MPa]= 0.62 40

T1[C]= 157.7967 Area of cooling box walls [m2]

Mp [kg/s]= 0.01 (mass flowrate) 100

Condenser (the compressor output), cooling water Heat transfer coef. [W.m-2

.K-1

]

T5[C]= 40 5

p5[MPa] 0.007351 Antoine equation lnp=A-B/(C+T) is used

Evaporated water (the compressor suction) Kappa= 1.13 0.115044248

Assuming, that the largest mass of water is in the evaporator tank, the analysis of transient start-up or shut-down can be restricted to the heat balance of evaporator

M.cp.dT/dt = - Me.r+S.k.(Te-T), where Me is the mass flowrate of evaporated water and r(T) is the latent heat of water

This is a ordinary differential equation which must be evaluated numerically if the heat of evaporation is not a constant

Nevertheless it will be interesting to compare the numerically obtained results with the analytical solution for r=const.

Its your bussines to find out the analytical solution. The numerical solution in the column A is explicit. Rewrite it to the more precise implicit form.

Time step of numerical integration 100 [s]

T2[C] p2[MPa] Pe=p1/p2 Pk=p5/p2 fe=Me/Mp r[kJ/kg] Me[kg/s]

30 0.00422 147 1.74 1.86 2459 0.018609

20.30 0.00235 263 3.12 1.12 2485 0.011157

16.04 0.00180 345 4.09 0.95 2496 0.009489

13.25 0.00150 414 4.91 0.86 2504 0.008631

11.29 0.00131 472 5.60 0.81 2509 0.008109

9.86 0.00119 520 6.16 0.78 2513 0.007764

8.81 0.00111 559 6.62 0.75 2515 0.007525

8.01 0.00105 590 7.00 0.74 2518 0.007354

7.41 0.00101 615 7.29 0.72 2519 0.007229

6.96 0.00098 635 7.53 0.71 2520 0.007136

6.61 0.00095 651 7.71 0.71 2521 0.007067

6.34 0.00094 663 7.86 0.70 2522 0.007015

6.14 0.00092 673 7.97 0.70 2522 0.006975

5.98 0.00091 680 8.06 0.69 2523 0.006945

5.86 0.00090 686 8.13 0.69 2523 0.006922

5.76 0.00090 690 8.19 0.69 2523 0.006904

5.69 0.00089 694 8.23 0.69 2524 0.006890

5.64 0.00089 697 8.26 0.69 2524 0.006880

5.59 0.00089 699 8.29 0.69 2524 0.006872

5.56 0.00089 700 8.30 0.69 2524 0.006865

5.53 0.00088 702 8.32 0.69 2524 0.006861

5.51 0.00088 703 8.33 0.69 2524 0.006857

5.50 0.00088 703 8.34 0.69 2524 0.006854

5.49 0.00088 704 8.35 0.69 2524 0.006852

5.48 0.00088 704 8.35 0.69 2524 0.006850

5.47 0.00088 705 8.36 0.68 2524 0.006849

5.47 0.00088 705 8.36 0.68 2524 0.006848

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C]

START UP

Strana 5

TRANSIENT

5.46 0.00088 705 8.36 0.68 2524 0.006847

5.46 0.00088 705 8.36 0.68 2524 0.006846

5.46 0.00088 706 8.37 0.68 2524 0.006846

Strana 6

TRANSIENT

30 cp[J/kg/K]= 4.2

Assuming, that the largest mass of water is in the evaporator tank, the analysis of transient start-up or shut-down can be restricted to the heat balance of evaporator

M.cp.dT/dt = - Me.r+S.k.(Te-T), where Me is the mass flowrate of evaporated water and r(T) is the latent heat of water

This is a ordinary differential equation which must be evaluated numerically if the heat of evaporation is not a constant

Nevertheless it will be interesting to compare the numerically obtained results with the analytical solution for r=const.The numerical solution in the column A is explicit. Rewrite it to the more precise implicit form.

Qcool[kW] Qlosses time [s] T Q [kW]

45.760 5 0 30 45.760

27.727 9.852 100 20.29519 27.727

23.689 11.980 200 16.03936 23.689

21.611 13.374 300 13.25164 21.611

20.346 14.355 400 11.29045 20.346

19.509 15.068 500 9.864078 19.509

18.928 15.597 600 8.806755 18.928

18.513 15.993 700 8.01349 18.513

18.210 16.293 800 7.413488 18.210

17.986 16.521 900 6.957082 17.986

17.817 16.696 1000 6.608489 17.817

17.690 16.829 1100 6.341444 17.690

17.594 16.932 1200 6.136417 17.594

17.521 17.011 1300 5.978744 17.521

17.464 17.071 1400 5.857336 17.464

17.421 17.118 1500 5.763762 17.421

17.388 17.154 1600 5.691589 17.388

17.363 17.182 1700 5.635892 17.363

17.343 17.204 1800 5.592891 17.343

17.328 17.220 1900 5.559681 17.328

17.316 17.233 2000 5.534027 17.316

17.307 17.243 2100 5.514205 17.307

17.300 17.251 2200 5.498887 17.300

17.295 17.256 2300 5.487049 17.295

17.291 17.261 2400 5.477899 17.291

17.288 17.265 2500 5.470826 17.288

17.285 17.267 2600 5.465359 17.285

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Q [kW]

Strana 7

TRANSIENT

17.283 17.269 2700 5.461132 17.283

17.282 17.271 2800 5.457865 17.282

17.281 17.272 2900 5.455339 17.281

Strana 8

GRAPHS

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T-suction [C]

STEADY STATE COOLING

Qchl[kW]

Qztraty[kW]

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T [

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t [s]

START UP - COOLING

T

Q [kW]

Strana 9