The following initial conditions are used to investigate the influence of initial values of inlet variables on the dynamic response characteristics of the cooling tower’s exit water temperature:
Case (a) Three initial inlet air temperatures, i.e., (ta, E)o= 30.0, 32.0 and 34.0 °C, combined with the other initial conditions: (tw, E)o= 38.2 °C, (Wa,
E)o= 22.4 g/(kg dry air), (Ga)o= 12.62 kg/s, (Gw)o= 3.31 kg/s;
Case (b) Three initial inlet air humidity ratios, i.e., (Wa, E)o= 22.0,24.0, and 26.0 g/(kg dry air), combined with the other initial conditions: (ta, E)o= 34.0 °C, (tw, E)o= 38.2 °C, (Ga)o= 12.62 kg/s,(Gw)o= 3.31 kg/s;
Case (c) Three initial inlet water temperatures, i.e., (tw, E)o= 38.0, 40.0 and 42.0 °C, combined with the other initial conditions: (ta, E)o= 34.0 °C, (Wa, E)o= 22.0 g/(kg dry air), (Ga)o= 12.62 kg/s,(Gw)o= 3.31 kg/s;
The mass of water in the sink of cooling tower (Msump) is identically given as 88.5 kg for all the simulation cases. The initial values of the exit variables can be obtained with respect to the initial conditions of inlet variables.
(1) Different initial values of inlet air temperature(ta, E)o
The system matrixes of cooling tower under the initial conditions of case (a) are calculated as below:
Atower;ta;Eẳ30CẳAtower;ta;Eẳ32CẳAtower;ta;Eẳ34C
ẳ
12:0343 0:0251 2:4203 0:0000 0:0000 9:5964 0:0002 0:0000 0:5702 0:1313 3:1079 0:0000 0:0000 0:0000 0:0374 0:0374 2
66 64
3 77 75;
Btower;ta;Eẳ30Cẳ
7:1580 0:0251 0:1633 2:4203 0:0000 0:0000 9:5959 0:0017 0:0002 0:0000 0:5702 0:1313 0:2509 1:7810 3:4163 0:0000 0:0000 0:0000 0:0000 0:0045 2
66 64
3 77 75;
Btower;ta;Eẳ32Cẳ
7:1580 0:0251 0:2823 2:4203 0:0000 0:0000 9:5959 0:0015 0:0002 0:0000 0:5702 0:1313 0:1882 1:7810 2:9005 0:0000 0:0000 0:0000 0:0000 0:0045 2
66 64
3 77 75;
Btower;ta;Eẳ34Cẳ
7:1580 0:0251 0:4100 2:4203 0:0000 0:0000 9:5959 0:0014 0:0002 0:0000 0:5702 0:1313 0:1234 1:7810 2:3646 0:0000 0:0000 0:0000 0:0000 0:0045 2
66 64
3 77 75:
Figure3.20 presents transient responses of the cooling tower’s exit water tem- perature subjected to various disturbances under different initial values of inlet air temperature. The results manifest that the transient response characteristics of the cooling tower’s exit water temperature to the perturbations of inlet air temperature and humidity as well as inlet water temperature will not affected by initial value of inlet air temperature. However, when subjected to the perturbations of water or airflow rate, the initial value of inlet air temperature will impact on the transient response characteristics of the cooling tower’s exit water temperature. As shown in Fig.3.20d, e, the absolute proportionality coefficient of the exit water temperature to the water or airflow rate decreases with the initial inlet air temperature increasing.
(2) Different initial values of inlet air humidity ratios
The system matrixes of cooling tower corresponding to the initial conditions of case (b) are calculated as below:
Atower;Wa;Eẳ22 g=kgẳAtower;Wa;Eẳ24 g=kgẳAtower;Wa;Eẳ26 g=kg
ẳ
12:0343 0:0251 2:4203 0:0000 0:0000 9:5964 0:0002 0:0000 0:5702 0:1313 3:1079 0:0000 0:0000 0:0000 0:0374 0:0374 2
66 64
3 77 75;
Btower;Wa;Eẳ22 g=kgẳ
7:1580 0:0251 0:4539 2:4203 0:0000 0:0000 9:5959 0:0015 0:0002 0:0000 0:5702 0:1313 0:1126 1:7810 2:2641 0:0000 0:0000 0:0000 0:0000 0:0045 2
66 64
3 77 75;
Btower;Wa;Eẳ24 ẳ
7:1580 0:0251 0:3749 2:4203 0:0000 0:0000 9:5959 0:0013 0:0002 0:0000 0:5702 0:1313 0:1320 1:7810 2:4448 0:0000 0:0000 0:0000 0:0000 0:0045 2
66 64
3 77 75;
Btower;Wa;Eẳ26 g=kgẳ
7:1580 0:0251 0:0701 2:4203 0:0000 0:0000 9:5959 0:0010 0:0002 0:0000 0:5702 0:1313 0:1661 1:7810 2:7551 0:0000 0:0000 0:0000 0:0000 0:0045 2
66 64
3 77 75:
The influences of initial inlet air humidity on the transient response of cooling tower’s exit water temperature to various disturbances are shown in Fig.3.21. The results manifest that the initial inlet air humidity will not affect the transient response characteristics of the cooling tower’s exit water temperature when sub- jected to the perturbations of inlet air temperature and humidity as well as inlet
0 0.05 0.1 0.15 0.2 0.25 0.3
0 10 20 30 40 50 60 70 80 90 100
Time (s) Variations of cooling tower's exit water temperature (t'w,L)o
(ta,E)o=30 (ta,E)o=32 (ta,E)o=34 Disturbance Inlet air temperature increases by 1.0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0 10 20 30 40 50 60 70 80 90 100
Time (s) Variations of cooling tower's exit water temperature (t'w,L)o
(ta,E)o=30 (ta,E)o=32 (ta,E)o=34 Disturbance Inlet air humidity increases by 1.0 g/(kg dryair)
(a)Subjected to the disturbance of inlet air temperature (b) Subjected to the disturbance of inlet air humidity
0 0.1 0.2 0.3 0.4 0.5 0.6
0 10 20 30 40 50 60 70 80 90 100
Time(s)
Variations of cooling tower's exit watertemperature (t'w,L)o (t'w,L)o
(ta,E)o=30 (ta,E)o=32 (ta,E)o=34 Disturbance Inlet water temperature increases by 1.0
0 0.2 0.4 0.6 0.8 1 1.2
0 10 20 30 40 50 60 70 80 90 100
Time (s) Variations of cooling tower's exit water temperature (t'w,L)o
(ta,E)o=30 (ta,E)o=32 (ta,E)o=34 Disturbance Water flow rate increases by 1.0 kg/s
(c)Subjected to the disturbance of inlet water temperature (d) Subjected to the disturbance of water flow rate
-0.09 -0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0
0 10 20 30 40 50 60 70 80 90 100
Time (s)
Variations of cooling tower's exit water temperature
(ta,E)o=30 (ta,E)o=32 (ta,E)o=34
Disturbance Air flow rate increases by 1.0 kg/s
(e) Subjected to the disturbance of air flow rate
Fig. 3.20 Responses of cooling tower’s exit water temperature to various disturbances under different initial values of inlet air temperature. a Subjected to the disturbance of inlet air temperature.bSubjected to the disturbance of inlet air humidity.cSubjected to the disturbance of inlet water temperature.d Subjected to the disturbance of waterflow rate. eSubjected to the disturbance of airflow rate
water temperature. However, the transient response characteristics of the cooling tower’s exit water temperature to the perturbations of water or airflow rate will be affected by the initial inlet air humidity. As shown in Fig.3.21d, e, the absolute proportionality coefficient of the exit water temperature to the water or airflow rate increases with the initial inlet air humidity increasing.
0 0.0 5 0. 1 0.1 5 0. 2 0.2 5 0. 3
0 10 20 30 40 50 60 70 80 90 100
Time(s) Variationsofcoolingtower'sexitwater temperature(t'w,L)o
(da,E)o=22.0 g/kg (da,E)o=24.0 g/kg (da,E)o=26.0 g/kg Disturbance Inlet air temperature
increases by 1.0
0 0.0 1 0.0 2 0.0 3 0.0 4 0.0 5 0.0 6 0.0 7 0.0 8 0.0 9
0 10 20 30 40 50 60 70 80 90 100
Time (s) Variationsofcoolingtower'sexitwater temperature(t'w,L)o
(da,E)o=22.0 g/kg (da,E)o=24.0 g/kg (da,E)o=26.0 g/kg Disturbance Inlet air humidity
increases by 1.0 g/(kg dryair)
(a) Subjected to the disturbance of inlet air temperature (b) Subjected to the disturbance of inlet air humidity
0 0.1 0.2 0.3 0.4 0.5 0.6
0 10 20 30 40 50 60 70 80 90 100
Time(s) Variations ofcoolingtower'sexitwater temperature (t'w,L)o
(da,E)o=22.0 g/kg (da,E)o=24.0 g/kg (da,E)o=26.0 g/kg Disturbance Inlet water temperature
increases by 1.0
0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1
0 10 20 30 40 50 60 70 80 90 100
Time(s) Variationsofcoolingtower'sexitwater temperature(t'w,L)o
(da,E)o=22.0 g/kg (da,E)o=24.0 g/kg (da,E)o=26.0 g/kg Disturbance Water flow rate
increases by 1.0 kg/s
(c) Subjected to the disturbance of inlet water temperature (d) Subjected to the disturbance of water flow rate
-0.0 6 -0.0 5 -0.0 4 -0.0 3 -0.0 2 -0.0 1 0
0 10 20 30 40 50 60 70 80 90 100
Time(s)
Variationsofcoolingtower'sexitwater temperature(t'w,L)o (da,E)o=22.0 g/kg (da,E)o=24.0 g/kg (da,E)o=26.0 g/kg
Disturbance Air flow rate increases by 1.0 kg/s
(e) Subjected to the disturbance of air flow rate
Fig. 3.21 Responses of cooling tower’s exit water temperature to various disturbances under different initial values of inlet air humidity.aSubjected to the disturbance of inlet air temperature.
bSubjected to the disturbance of inlet air humidity.cSubjected to the disturbance of inlet water temperature.dSubjected to the disturbance of waterflow rate.eSubjected to the disturbance of airflow rate
(3) Different initial values of inlet water temperatures
The system matrixes of cooling tower under the initial conditions of case (c) are as follows:
Atower;tw;Eẳ38CẳAtower;tw;Eẳ40CẳAtower;tw;Eẳ42C
ẳ
12:0343 0:0251 2:4203 0:0000 0:0000 9:5964 0:0002 0:0000 0:5702 0:1313 3:1079 0:0000 0:0000 0:0000 0:0374 0:0374 2
66 64
3 77 75
Btower;tw;Eẳ38Cẳ
7:1580 0:0251 0:3866 2:4203 0:0000 0:0000 9:5959 0:0015 0:0002 0:0000 0:5702 0:1313 0:1103 1:7810 2:2411 0:0000 0:0000 0:0000 0:0000 0:0045 2
66 64
3 77 75
Btower;tw;Eẳ40Cẳ
7:1580 0:0251 0:1080 2:4203 0:0000 0:0000 9:5959 0:0017 0:0002 0:0000 0:5702 0:1313 0:1943 1:7810 3:0196 0:0000 0:0000 0:0000 0:0000 0:0045 2
66 64
3 77 75
Btower;tw;Eẳ40Cẳ
7:1580 0:0251 0:6700 2:4203 0:0000 0:0000 9:5959 0:0019 0:0002 0:0000 0:5702 0:1313 0:2761 1:7810 3:7749 0:0000 0:0000 0:0000 0:0000 0:0045 2
66 64
3 77 75
The responses of cooling tower’s exit water temperature to various disturbances under different initial values of inlet water temperature are presented in Fig.3.22.
The influence of initial inlet water temperature on the transient response charac- teristics of the cooling tower’s exit water temperature shares the same regular patterns with the influence of initial inlet air humidity on that as shown in Fig.3.21.