READ!
ME
Evaporation cooling Thermocompressor design
Steady state: calculate temperature at the cooling
Laval
nozzle Transient: calculation of time course of temper
Motion
steam
Input parameters are i blue cells
Condenser
Evaporated
water
Cooling box
Strana 1
READ!ME
e temperature at the cooling box for given mass flowrate of motion steam
ion of time course of temperature in the cooling box
Strana 2
COOLING-STEADY STATE
Evaporation cooling 70
STEADY STATE COOLING
Thermocompressor design 60
Motion steam parameters Ambient temperature [C] 50
p1[MPa]= 0.62 40 40
Q-[kW]
T1= 157.7967 Area of cooling box walls [m ]
2
30
M [kg/s]= 0.01 100 20 Qch
Condenser , cooling water Heat transfer coef. [W.m-2.K-1] Qzt
10
T5[C] 40 30
0
p5[MPa] 0.007351 Antoine equation lnp=A-B/(C+T) is used 20 22 24 26 28
T-suction [C]
Evaporated water (the compressor suction) Kappa= 1.13 0.115044248
T2[C] p2[MPa] Pe=p1/p2 Pk=p5/p2 fe=Me/Mp fm=Mp/Me Me[kg/s] Qchl[kW]
30 0.00422 147 1.74 1.86 0.54 0.018609 44.662
29 0.00398 156 1.85 1.74 0.58 0.017386 41.727
28 0.00375 165 1.96 1.63 0.61 0.016324 39.178
27 0.00354 175 2.08 1.54 0.65 0.015390 36.937
26 0.00333 186 2.21 1.46 0.69 0.014562 34.949
25 0.00314 197 2.34 1.38 0.72 0.013821 33.171
24 0.00296 210 2.49 1.32 0.76 0.013153 31.568
23 0.00278 223 2.64 1.25 0.80 0.012548 30.114
22 0.00262 237 2.81 1.20 0.83 0.011995 28.789
21 0.00246 252 2.99 1.15 0.87 0.011489 27.574
20 0.00231 268 3.18 1.10 0.91 0.011024 26.457
19 0.00217 286 3.39 1.06 0.94 0.010593 25.423
18 0.00204 304 3.61 1.02 0.98 0.010194 24.465
17 0.00191 324 3.85 0.98 1.02 0.009822 23.574
16 0.00179 346 4.10 0.95 1.06 0.009476 22.742
15 0.00168 369 4.38 0.92 1.09 0.009151 21.963
14 0.00157 394 4.67 0.88 1.13 0.008847 21.233
Strana 3
COOLING-STEADY STATE
70
STEADY STATE COOLING
60
50
40
30
20 Qchl[kW]
Qztraty[kW]
10
0
20 22 24 26 28 30 32
T-suction [C]
Qztraty[kW]
30
33
36
39
42
45
48
51
54
57
60
63
66
69
72
75
78
Strana 4
TRANSIENT
Evaporation cooling : transient
Mass of water in evaporator M= 100 [kg] Initial temperature of water [C] 30
Motion steam parameters Ambient temperature [C] 35
START UP - COOLING
p1[MPa]= 0.62 40 30
T1[C]= 157.7967 Area of cooling box walls [m2] 25
Mp [kg/s]= 0.01 (mass flowrate) 100 20
T [C]
Condenser , cooling water Heat transfer coef. [W.m .K ]
-2 -1 15
10
T5[C]= 40 5
5
p5[MPa] 0.007351 Antoine equation lnp=A-B/(C+T) is used
0
Evaporated water (the compressor suction) Kappa= 1.13 0.115044247787610
t [s]
500 1000 1500 2000 2500
Assuming, that the largest mass of water is in the evaporator tank, the analysis of transient start-up or shut-down
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
This is a ordinary differential equation which must be evaluated numerically if the heat of evaporation is not a co
Nevertheless it will be interesting to compare the numerically obtained results with the analytical solution for r=c
Its your bussines to find out the analytical solution. The numerical solution in the column A is explicit
Time step of numerical integratio 100 [s]
T2[C] p2[MPa] Pe=p1/p2 Pk=p5/p2 fe=Me/Mp r[kJ/kg] Me[kg/s] Qcool[kW]
30 0.00422 147 1.74 1.86 2459 0.018609 45.760
20.30 0.00235 263 3.12 1.12 2485 0.011157 27.727
16.04 0.00180 345 4.09 0.95 2496 0.009489 23.689
13.25 0.00150 414 4.91 0.86 2504 0.008631 21.611
11.29 0.00131 472 5.60 0.81 2509 0.008109 20.346
9.86 0.00119 520 6.16 0.78 2513 0.007764 19.509
8.81 0.00111 559 6.62 0.75 2515 0.007525 18.928
8.01 0.00105 590 7.00 0.74 2518 0.007354 18.513
7.41 0.00101 615 7.29 0.72 2519 0.007229 18.210
6.96 0.00098 635 7.53 0.71 2520 0.007136 17.986
6.61 0.00095 651 7.71 0.71 2521 0.007067 17.817
6.34 0.00094 663 7.86 0.70 2522 0.007015 17.690
6.14 0.00092 673 7.97 0.70 2522 0.006975 17.594
5.98 0.00091 680 8.06 0.69 2523 0.006945 17.521
5.86 0.00090 686 8.13 0.69 2523 0.006922 17.464
5.76 0.00090 690 8.19 0.69 2523 0.006904 17.421
5.69 0.00089 694 8.23 0.69 2524 0.006890 17.388
5.64 0.00089 697 8.26 0.69 2524 0.006880 17.363
5.59 0.00089 699 8.29 0.69 2524 0.006872 17.343
5.56 0.00089 700 8.30 0.69 2524 0.006865 17.328
5.53 0.00088 702 8.32 0.69 2524 0.006861 17.316
5.51 0.00088 703 8.33 0.69 2524 0.006857 17.307
5.50 0.00088 703 8.34 0.69 2524 0.006854 17.300
Strana 5
TRANSIENT
5.49 0.00088 704 8.35 0.69 2524 0.006852 17.295
5.48 0.00088 704 8.35 0.69 2524 0.006850 17.291
5.47 0.00088 705 8.36 0.68 2524 0.006849 17.288
5.47 0.00088 705 8.36 0.68 2524 0.006848 17.285
5.46 0.00088 705 8.36 0.68 2524 0.006847 17.283
5.46 0.00088 705 8.36 0.68 2524 0.006846 17.282
5.46 0.00088 706 8.37 0.68 2524 0.006846 17.281
Strana 6
TRANSIENT
cp[J/kg/K]=4.2
T 50
ART UP - COOLING
45
Q [kW]
40
35
30 Q [kW]
25
20
15
10
5
0
t [s]
0 1000 1500 2000 2500 3000 3500
nt start-up or shut-down can be restricted to the heat balance of evaporator
r(T) is the latent heat of water
of evaporation is not a constant
nalytical solution for r=const.
umn A is explicit. Rewrite it to the more precise implicit form.
Qlosses time [s] T Q [kW]
5 0 30 45.760
9.852 100 20.29519 27.727
11.980 200 16.03936 23.689
13.374 300 13.25164 21.611
14.355 400 11.29045 20.346
15.068 500 9.864078 19.509
15.597 600 8.806755 18.928
15.993 700 8.01349 18.513
16.293 800 7.413488 18.210
16.521 900 6.957082 17.986
16.696 1000 6.608489 17.817
16.829 1100 6.341444 17.690
16.932 1200 6.136417 17.594
17.011 1300 5.978744 17.521
17.071 1400 5.857336 17.464
17.118 1500 5.763762 17.421
17.154 1600 5.691589 17.388
17.182 1700 5.635892 17.363
17.204 1800 5.592891 17.343
17.220 1900 5.559681 17.328
17.233 2000 5.534027 17.316
17.243 2100 5.514205 17.307
17.251 2200 5.498887 17.300
Strana 7
TRANSIENT
17.256 2300 5.487049 17.295
17.261 2400 5.477899 17.291
17.265 2500 5.470826 17.288
17.267 2600 5.465359 17.285
17.269 2700 5.461132 17.283
17.271 2800 5.457865 17.282
17.272 2900 5.455339 17.281
Strana 8
GRAPHS
70
STEADY STATE COOLING
60 Qchl[kW]
Qztraty[kW]
50
40
Q-[kW]
30
20
10
0
20 22 24 26 28 30 32
T-suction [C]
35 50
START UP - COOLING 45
30
40
25 T
35
Q [kW]
30
20
Q [kW]
25
T [C]
15
20
10 15
10
5
5
0 0
0 500 1000 1500 2000 2500 3000 3500
t [s]
Strana 9
