The influence of the initial conditions on the transient response characteristic of the refrigeration system is investigated by using the state-space model. Three simula- tion cases (Please see Table3.1) are performed for this investigation. The initial conditions listed in Table3.1are all measured data based on which the rest initial conditions can be obtained including the shell wall temperature of evaporator
-150 -100 -50 0 50 100 150
0 8 1 6 2 4 3 2 4 0 4 8 5 6 6 4 7 2 8 0
Time(s)
Responses of compressor power (Ncom: W) or chiller's cooling capacity (Qc: W)
0 0.02 0.04 0.06 0.08 0.1
Responses of chiller's COP (COP)
Responses of compressor power Responses of chiller's cooling capacity Responses of COP
Fig. 3.14 Responses of compressor power, cooling capacity, and COP of the chiller to step increase of coolantflow rate of condenser by 0.1 kg/s
(ðtegịo) and condenser (ðtcgịo), the exit coolant temperature of condenser (ðtcw;Lịo), and the exit cold carrier temperature of evaporator (ðtew;Lịo).
(1) Simulation case (a)
In the simulation case (a), the response calculations are done with step distur- bances under three initial temperatures of inlet cold carrier of evaporator (i.e., ðtew;Eịo = 24.6, 29.3, 36.2 °C). The corresponding system matrixes for the refrig- eration system (Achiller,Bchiller,Cchiller,Dchiller) under the different initial conditions of simulation case (a) are calculated, respectively, as follows:
For the initial condition ofðtew;Eịo ẳ24:6C::
Achiller ẳ
5:2500 0 5:2454 0 0 0
0 1:4962 2:0831 0 0 0
1:0247 0:2026 1:4299 0 0 0
0:0541 0 0 31:2970 0 31:2579
0 0 0 0 2:1785 1:8934
0 0 0 4:4929 0:1508 4:7945
2 66 66 66 66 4
3 77 77 77 77 5
;
0 200 400 600 800 1000 1200 1400 1600 1800
0 8 16 24 32 40 48 56 64 72 80
Time (s) Responses of compressor power (Ncom: W) or chiller's cooling capacity (Qc: W)
-0.2 -0.1 0 0.1
Responses of chiller's COP (COP)
Responses of compress or power Responses of chiller's cooling capacity Responses of COP
Fig. 3.15 Responses of compressor power, cooling capacity, and COP of the chiller to step increase of refrigerantflow rate by 0.01 kg/s
Table 3.1 Experimental initial conditions for model simulation Simulation case (a)
Study purpose: Investigations into the dynamic response characteristics of the exit cold carrier temperature of evaporator under different initial temperatures of inlet cold carrier of evaporator ðtew;Eịo.
(tew, E)o= 24.6 °C (tew, E)o= 29.3 °C (tew, E)o= 36.2 °C Compressor inlet temp.:
24.1 (°C)
Compressor outlet temp.:
56.1 (°C)
Compressor inlet temp.:
28.2 (°C)
Compressor outlet temp.:
61.5 (°C)
Compressor inlet temp.:
34.5 (°C)
Compressor outlet temp.:
67.8 (°C) Other initial conditions shared:
Evaporating temp.ðtkịo = 16.3 (°C); Cold carrierflow rate of evaporatorðGewịo= 1.45 (kg/s);
Condensing temp.ðtkịo= 36.7 (°C); Inlet coolant temp. of condenserðtcw;Eịo= 29.3 (°C);
Coolantflow rate of condenserðGcwịo= 1.16 (kg/s); Refrigerantflow rate ðGrmịo = 0.13 (kg/s).
Simulation case (b)
Study purpose: Investigations into the dynamic response characteristics of the exit cold carrier temperature of evaporator under different initial temperatures of inlet coolant of condenser ðtcw;Eịo
(tcw, E)o= 29.6 °C (tcw, E)o= 40.7 °C (tcw, E)o= 49.7 °C Compressor inlet temp.: 21.9
(°C)
Compressor outlet temp.:
51.5(°C)
Condensing Temp.:
ðtcịo= 37.1 (°C)
Compressor inlet temp.: 22.2 (°C)
Compressor outlet temp.: 57.5 (°C)
Condensing
Temp.:ðtcịo = 49.5 (°C)
Compressor inlet temp.: 22.4 (°C)
Compressor outlet temp.:
59.7 (°C)
Condensing Temp.:
ðtcịo= 55.2 (°C) Other initial conditions shared:
Evaporating temp.ðtkịo = 18.8 (°C); Cold carrierflow rate of evaporatorðGewịo = 1.45 (kg/s);
Inlet cold carrier temp. of evaporatorðtew;Eịo = 24.1 (°C); Coolantflow rate of condenser ðGcwịo= 1.16 (kg/s); Refrigerantflow rateðGrmịo = 0.13 (kg/s)
Simulation case (c)
Study purpose: Investigations into the dynamic response characteristics of the exit cold carrier temperature of evaporator under different initial refrigerantflow rateðGrmịo
(Grm)o=0.176 kg/s (Grm)o=0.199 kg/s (Grm)o=0.238 kg/s Other initial conditions shared:
Evaporating temp.ðtkịo= 15.1 (°C); Inlet cold carrier temp. of evaporatorðtew;Eịo = 24.7 (°C);
Cold carrierflow rate of evaporatorðGewịo = 2.14 (kg/s); Condensing temp.ðtcịo = 41.2 (°C);
Inlet coolant temp. of condenserðtcw;Eịo= 33.4 (°C); Coolantflow rate of condenser ðGcwịo= 2.14 (kg/s);
Compressor inlet temp.:ðtcom;Eịo = 23.7 (°C); Compressor outlet temp.ðtcom;Lịo= 71.3 (°C)
Bchiller ẳ
0 0 0 0 26:7888
0:5870 1:7765 0 0 0
0:2026 0:2879 0 0 0
0 0 0 0 56:8612
0 0 0:0454 6:4199 0
0 0 0:1508 0:3203 0
2 66 66 66 66 4
3 77 77 77 77 5
;
Cchiller ẳ
0 1:0000 0 0 0 0
0 0 0 0 0 0
0 0 0 0 1:0000 0
0 0 0 0 0 0
136:6685 0 0 124:5601 0 0
172:2758 0 0 124:5601 0 0 0:3644 0 0 0:3221 0 0 2
66 66 66 66 66 64
3 77 77 77 77 77 75
;
Dchiller ẳ
0 0 0 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 0
0 0 0 0 24760 0 0 0 0 181230 2
66 66 66 66 66 64
3 77 77 77 77 77 75 :
For the initial condition ofðtew;Eịo ẳ29:3C:
Achillerẳ
4:9140 0 4:9092 0 0 0
0 1:4962 2:0831 0 0 0
0:9591 0:2026 1:3642 0 0 0
0:054 0 0 31:4166 0 31:3771
0 0 0 0 2:1785 1:8934
0 0 0 4:5100 0:1508 4:8116
2 66 66 66 66 4
3 77 77 77 77 5
;
Bchillerẳ
0 0 0 0 27:6178
0:5870 0:7468 0 0 0
0:2026 0:7649 0 0 0
0 0 0 0 57:9874
0 0 0:0454 5:2185 0
0 0 0:1508 0:0166 0
2 66 66 66 66 4
3 77 77 77 77 5
;
Cchillerẳ
0 1:0000 0 0 0 0
0 0 0 0 0 0
0 0 0 0 1:0000 0
0 0 0 0 0 0
135:8178 0 0 125:9451 0 0
172:1875 0 0 125:9451 0 0 0:3027 0 0 0:2712 0 0 2
66 66 66 66 66 64
3 77 77 77 77 77 75
;
Dchillerẳ
0 0 0 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 0
0 0 0 0 27540 0 0 0 0 184820 2
66 66 66 66 66 64
3 77 77 77 77 77 75 :
For the initial condition ofðtew;Eịo ẳ36:2C:
Achillerẳ
5:1311 0 5:1264 0 0 0
0 1:4962 2:0831 0 0 0
1:0015 0:2026 1:4066 0 0 0
0:0541 0 0 33:5511 0 33:5114
0 0 0 0 2:1785 1:8934
0 0 0 4:8168 0:1508 5:1184
2 66 66 66 66 4
3 77 77 77 77 5
;
Bchiller ẳ
0 0 0 0 28:2526
0:5870 1:3140 0 0 0
0:2026 0:4129 0 0 0
0 0 0 0 59:3983
0 0 0:0454 4:9352 0
0 0 0:1508 0:0366 0
2 66 66 66 66 4
3 77 77 77 77 5
;
Cchiller ẳ
0 1:0000 0 0 0 0
0 0 0 0 0 0
0 0 0 0 1:0000 0
0 0 0 0 0 0
136:1326 0 0 126:4971 0 0
172:4500 0 0 126:4971 0 0 0:3017 0 0 0:2711 0 0 2
66 66 66 66 66 64
3 77 77 77 77 77 75
;
Dchiller ẳ
0 0 0 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 0
0 0 0 0 27920 0 0 0 0 189320 2
66 66 66 66 66 64
3 77 77 77 77 77 75 :
Figure3.16shows the influences of the initial inlet cold carrier temperature on the transient response characteristics of the exit cold carrier temperature subjected to different step disturbances. As seen from the simulation results, the propor- tionality coefficient of the exit cold carrier temperature to step disturbance of the inlet coolant and inlet cold carrier temperature is not affected by the initial condition of the inlet cold carrier temperature. However, the absolute proportionality coeffi- cient of the exit cold carrier temperature to step disturbance of the coolant, the cold carrier, and the refrigerantflow rate will increase with the increase of the initial inlet cold carrier temperature.
(2) Simulation case (b)
In the simulation case (b), the transient response characteristics of the exit cold carrier temperature to step disturbances are investigated under different initial values of the inlet coolant temperature of condenser (i.e., ðtcw;Eịo = 29.6, 40.7, 49.7 °C). The corresponding system matrixes for the refrigeration system (Achiller, Bchiller, Cchiller, Dchiller) under the different initial conditions of simulation case (b) are obtained, respectively, as follows:
For the initial condition ofðtcw;Eịo ẳ29:6C:
Achillerẳ
5:4059 0 5:4015 0 0 0
0 1:4962 2:0831 0 0 0
1:0552 0:2026 1:4604 0 0 0
0:0541 0 0 30:6431 0 30:6037
0 0 0 0 2:1785 1:8934
0 0 0 4:3989 0:1508 4:7004
2 66 66 66 66 4
3 77 77 77 77 5
;
Bchillerẳ
0 0 0 0 25:4475
0:5870 4:0857 0 0 0
0:2026 0:1826 0 0 0
0 0 0 0 54:7588
0 0 0:0454 5:8103 0
0 0 0:1508 0:1772 0
2 66 66 66 66 4
3 77 77 77 77 5
;
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
1 5 9 13 17 21 25 29 33 37 41
Time(s) Responses of the exit cold carrier temperature of evaporator ()
(tew,E)o=24.6 (tew,E)o=29.3 (tew,E)o=36.2 Disturbance The inlet coolant temperature of condenser ( tcw,E) has a step increase by 1.0
-0.025 -0.02 -0.015 -0.01 -0.005 0
1 5 9 13 17 21 25 29 33 37 41
Time(s)
Responses of the exit cold carrier temperature of evaporator ()
(tew,E)o=24.6 (tew,E)o=29.3 (tew,E)o=36.2
Disturbance The coolant flow rate of condenser ( Gcw) has a step increase by 0.1kg/s
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 8 16 24 32 40 48 56 64 72 80
Time(s) Responses of the exit cold carrier temperature of evaporator ()
(tew,E)o=24.6 (tew,E)o=29.3 (tew,E)o=36.2 Disturbance The inlet cold carrier temperature of
evaporator (tew,E) has a step increase by 1.0 .
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0 8 16 24 32 40 48 56 64 72 80
Time(s) Responses of the exit cold carrier temperature of evaporator ()
(tew,E)o=24.6 (tew,E)o=29.3 (tew,E)o=36.2 Disturbance The cold carrier flow rate of evaporator (Gew) has a step increase by 0.1 kg/s
-0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0
0 8 16 24 32 40 48 56 64 72 80
Time (s)
Responses of the exit cold carrier temperature of evaporator ()
(tew,E)o=24.6 (tew,E)o=29.3 (tew,E)o=36.2 Disturbance The refrigerant flow rate ( Grm) has a step increase by 0.01 kg/s
Fig. 3.16 Transient response characteristics of the exit cold carrier temperature of evaporator under different initial temperatures of inlet cold carrier of evaporator (Simulation case (a))
Cchiller ẳ
0 1:0000 0 0 0 0
0 0 0 0 0 0
0 0 0 0 1:0000 0
0 0 0 0 0 0
138:7992 0 0 125:3369 0 0
172:3632 0 0 125:3369 0 0 0:4796 0 0 0:4220 0 0 2
66 66 66 66 66 64
3 77 77 77 77 77 75
;
Dchiller ẳ
0 0 0 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 0
0 0 0 0 21140 0 0 0 0 174530 2
66 66 66 66 66 64
3 77 77 77 77 77 75 :
For the initial condition ofðtcw;Eịo ẳ40:7C
Achiller ẳ
5:7379 0 5:7351 0 0 0
0 1:4962 2:0831 0 0 0
1:1204 0:2026 1:5255 0 0 0
0:0549 0 0 27:8795 0 27:8393
0 0 0 0 2:1785 1:8934
0 0 0 4:0015 0:1508 4:3031
2 66 66 66 66 4
3 77 77 77 77 5
;
Bchiller ẳ
0 0 0 0 23:4127
0:5870 6:3773 0 0 0
0:2026 0:7205 0 0 0
0 0 0 0 50:2580
0 0 0:0454 3:0071 0
0 0 0:1508 0:2246 0
2 66 66 66 66 4
3 77 77 77 77 5
;
Cchiller ẳ
0 1:0000 0 0 0 0
0 0 0 0 0 0
0 0 0 0 1:0000 0
0 0 0 0 0 0
153:9727 0 0 128:0791 0 0
175:1204 0 0 128:0791 0 0 0:5498 0 0 0:4505 0 0 2
66 66 66 66 66 64
3 77 77 77 77 77 75
;
Dchiller ẳ
0 0 0 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 0
0 0 0 0 19840 0 0 0 0 160180 2
66 66 66 66 66 64
3 77 77 77 77 77 75 :
For the initial condition of ðtcw;Eịo ẳ49:7C:
Achillerẳ
5:1288 0 5:1268 0 0 0
0 1:4962 2:0831 0 0 0
1:0015 0:2026 1:4067 0 0 0
0:0553 0 0 27:9825 0 27:9421
0 0 0 0 2:1785 1:8934
0 0 0 4:0163 0:1508 4:3179
2 66 66 66 66 4
3 77 77 77 77 5
;
Bchillerẳ
0 0 0 0 23:0057
0:5870 8:1105 0 0 0
0:2026 0:9936 0 0 0
0 0 0 0 48:3970
0 0 0:0454 3:2998 0
0 0 0:1508 0:0873 0
2 66 66 66 66 4
3 77 77 77 77 5
;
Cchiller ẳ
0 1:0000 0 0 0 0
0 0 0 0 0 0
0 0 0 0 1:0000 0
0 0 0 0 0 0
160:7841 0 0 128:8777 0 0
176:4054 0 0 128:8777 0 0 0:4320 0 0 0:3420 0 0 2
66 66 66 66 66 64
3 77 77 77 77 77 75
;
Dchiller ẳ
0 0 0 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 0
0 0 0 0 22640 0 0 0 0 154250 2
66 66 66 66 66 64
3 77 77 77 77 77 75 :
Figure3.17gives the transient responses of the exit cold carrier temperature to step disturbances under different initial inlet coolant temperatures in the simulation case (b). The results manifest that the initial value of the inlet coolant temperature
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
1 5 9 13 17 21 25 29 33 37 41
Time(s) Responses of the exit cold carrier temperature of evaporator ()
(tcw,E)o=29.6 (tcw,E)o=40.7 (tcw,E)o=49.7 Disturbance The inlet coolant temperature of condenser (tcw,E) has a step increase by 1.0
-0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0
1 5 9 13 17 21 25 29 33 37 41
Time (s)
Responses of the exit cold carrier temperature of evaporator ( )
(tcw,E)o=29.6 (tcw,E)o=40.7 (tcw,E)o=49.7
Disturbance The coolant flow rate of condenser ( Gcw) has a step increase by 0.1 kg/s
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 8 16 24 32 40 48 56 64 72 80
Time (s) Responses of the exit cold carrier temperature of evaporator ( )
(tcw,E)o=29.6 (tcw,E)o=40.7 (tcw,E)o=49.7 Disturbance The inlet cold carrier temperature of evaporator ( tew,E) has a step increase by 1.0 .
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0 8 16 24 32 40 48 56 64 72 80
Time (s) Responses of the exit cold carrier temperature of evaporator ()
(tcw,E)o=29.6 (tcw,E)o=40.7 (tcw,E)o=49.7 Disturbance The cold carrier flow rate of evaporator ( Gew) has a step increase by 0.1 kg/s
-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0
0 8 16 24 32 40 48 56 64 72 80
Time (s)
Responses of the exit cold carrier temperature of evaporator ()
(tcw,E)o=29.6 (tcw,E)o=40.7 (tcw,E)o=49.7 DisturbanceThe refrigerant flow rate (Grm) has a step increase by 0.01 kg/s
Fig. 3.17 Transient response characteristics of the exit cold carrier temperature of evaporator under different initial temperatures of inlet coolant of condenser (Simulation case (b))
produces little influence on the response characteristics of the exit cold carrier temperature subjected to the perturbations of the inlet coolant and inlet cold carrier temperature, but it may affect that subjected to the perturbations of the coolant, the cold carrier, and the refrigerant flow rate. Basically, the absolute proportionality coefficient of the exit cold carrier temperature to step disturbance of the coolant, the cold carrier, and the refrigerant flow rate will decrease with the increase of the initial value of the inlet coolant temperature.
(3) Simulation case (c)
In the simulation case (c), the transient response characteristics of the exit cold carrier temperature to step disturbances are investigated under different initial refrigerantflow rates (i.e.,ðGrmịo = 0.176, 0.199, 0.237 kg/s). The corresponding system matrixes for the refrigeration system (Achiller,Bchiller,Cchiller,Dchiller) under the different initial refrigerantflow rates are listed as below:
For the initial condition ofðGrmịoẳ0:176 kg/s:
Achillerẳ
6:0491 0 6:0430 0 0 0
0 2:5387 3:4000 0 0 0
1:1805 0:3306 1:8418 0 0 0
0:0736 0 0 30:9453 0 30:8924
0 0 0 0 3:1105 2:5852
0 0 0 4:4404 0:2059 4:8521
2 66 66 66 66 4
3 77 77 77 77 5
;
Bchillerẳ
0 0 0 0 27:3712
0:8614 7:8559 0 0 0
0:3306 1:0027 0 0 0
0 0 0 0 55:1646
0 0 0:0837 4:9467 0
0 0 0:2059 0:1208 0
2 66 66 66 66 4
3 77 77 77 77 5
;
Cchillerẳ
0 1:0000 0 0 0 0
0 0 0 0 0 0
0 0 0 0 1:0000 0
0 0 0 0 0 0
187:6315 0 0 168:6454 0 0
234:5960 0 0 168:6454 0 0 0:1947 0 0 0:1681 0 0 2
66 66 66 66 66 64
3 77 77 77 77 77 75
;
Dchillerẳ
0 0 0 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 0
0 0 0 0 34640
0 0 0 0 175820 2
66 66 66 66 66 64
3 77 77 77 77 77 75
;
For the initial condition ofðGrmịoẳ0:199 kg/s:
Achiller ẳ
5:6901 0 5:6831 0 0 0
0 2:5387 3:4000 0 0 0
1:1204 0:3306 1:7715 0 0 0
0:0833 0 0 31:6092 0 31:5499
0 0 0 0 3:1105 2:5852
0 0 0 4:5349 0:2059 4:9466
2 66 66 66 66 4
3 77 77 77 77 5
;
Bchiller ẳ
0 0 0 0 27:8736
0:8614 5:2382 0 0 0
0:3306 0:4395 0 0 0
0 0 0 0 55:0432
0 0 0:0837 5:8096 0
0 0 0:2059 0:1608 0
2 66 66 66 66 4
3 77 77 77 77 5
;
Cchiller ẳ
0 1:0000 0 0 0 0
0 0 0 0 0 0
0 0 0 0 1:0000 0
0 0 0 0 0 0
212:1554 0 0 188:9406 0 0
265:4966 0 0 188:9406 0 0 0:1580 0 0 0:1345 0 0 2
66 66 66 66 66 64
3 77 77 77 77 77 75
;
Dchiller ẳ
0 0 0 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 0
0 0 0 0 38890 0 0 0 0 175440 2
66 66 66 66 66 64
3 77 77 77 77 77 75 :
For the initial condition ofðGrmịoẳ0:237 kg/s:
Achillerẳ
5:5747 0 5:5665 0 0 0
0 2:5387 3:4000 0 0 0
1:0874 0:3306 1:7487 0 0 0
0:0995 0 0 30:7540 0 30:6831
0 0 0 0 3:1105 2:5852
0 0 0 4:4103 0:2059 4:8220
2 66 66 66 66 4
3 77 77 77 77 5
;
Bchillerẳ
0 0 0 0 27:8087
0:8614 4:9823 0 0 0
0:3306 0:2998 0 0 0
0 0 0 0 54:5852
0 0 0:0837 5:5628 0
0 0 0:2059 0:0092 0
2 66 66 66 66 4
3 77 77 77 77 5
;
Cchillerẳ
0 1:0000 0 0 0 0
0 0 0 0 0 0
0 0 0 0 1:0000 0
0 0 0 0 0 0
253:9461 0 0 226:1909 0 0
317:1475 0 0 226:1909 0 0 0:1506 0 0 0:1282 0 0 2
66 66 66 66 66 64
3 77 77 77 77 77 75
;
Dchillerẳ
0 0 0 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 0
0 0 0 0 39850 0 0 0 0 173980 2
66 66 66 66 66 64
3 77 77 77 77 77 75 :
Figure3.18presents the transient responses of the exit cold carrier temperature to step disturbances under different initial refrigerantflow rates in the simulation case (c). As known from Fig.3.18, the absolute proportionality coefficient of the exit cold carrier temperature to the perturbations of the inlet coolant temperature or the cold carrierflow rate increases with the initial value of the refrigerantflow rate, and the change trend is opposite for the perturbations of the coolant flow rate.
However, the response characteristics of the exit cold carrier temperature to the perturbations of the inlet cold carrier temperature or the refrigerantflow rate are affected little by the initial value of the refrigerantflow rate.