MODELING AND ANALYSES OF EVAPORATIVE MODELING AND ANALYSES OF EVAPORATIVE
COOLING EFFICIENCY FOR MIST-FOG SYSTEMSCOOLING EFFICIENCY FOR MIST-FOG SYSTEMS
Ta-Te Lin, Yi-Chung Chang
Department of Agricultural Machinery Engineering,
National Taiwan University,
Taipei, Taiwan, R.O.C.
INTRODUCTION
MODEL DEVELOPMENT
SIMULATION AND ANALYSES
CONCLUSIONS
INTRODUCTIONINTRODUCTION
EVAPORATIVE COOLING AND ITS APPLICATIONS FACTORS AFFECTING EVAPORATIVE COOLING OBJECTIVES
EVAPORATIVE COOLING AND ITS APPLICATIONSEVAPORATIVE COOLING AND ITS APPLICATIONS
FACTORS AFFECTING EVAPORATIVE COOLINGFACTORS AFFECTING EVAPORATIVE COOLING
RELATIVE HUMIDITY AMBIENT TEMPERATURE DROPLET SIZE VENTILATION RATE DROPLET TRAVEL DISTANCE
OBJECTIVESOBJECTIVES
To develop a theoretical model for the calculation of evaporative cooling efficiency base on mass transfer and particle dynamic theories.
To validate the model with existing laboratory data.
To analyze the influences of selected parameters, such as temperature and relative humidity, on the evaporative cooling efficiency of mist-fog systems.
MODEL DEVELOPMENTMODEL DEVELOPMENT
MASS TRANSFER OF DROPLETS PARTICLE DYNAMICS CALCULATION OF PSYCHROMETRIC PARAMETERS
MASS TRANSFER OF DROPLETSMASS TRANSFER OF DROPLETS
dm
dtk A PMg s v
dD
dt
M
M
D
D
P
PN Np v
m
v
p
a
l fsc re
2 2 0 6 1 3 1 2
. / /
The Goering Model:
The Basic Mass Transfer Equation:
Diffusivity
MASS TRANSFER OF DROPLETSMASS TRANSFER OF DROPLETS
D Tv k 5 28 10 6 188. .
Pressure Difference P P Pswb v
Partial Pressure of Air
Pressure Difference
P P Pf atm v
aatmP
gRT
PARTICLE DYNAMICSPARTICLE DYNAMICS
Particle Motion:
a
d X
dt
D
mx 2
2
sin
a
d Y
dt
W D
my 2
2
cos
D D Vdm
dtf e
Drag Force Calculation:
DC AV
fd a p r 2
2
CN
Ndre
re 24
0 5.
CN
Ndre
re 26 38
0 49 0 5 2000 845
.. .
.
Effect of Wind Direction and Droplet Moving Angle:
Effect of Spray Nozzle Gauge Pressure:
PARTICLE DYNAMICSPARTICLE DYNAMICS
arcsin
cos cosV V
Va
r
2
arcsinV
Vx
V V Vx y 2 2 0 5.
V V V V Vr a a cos cos sin sin 2 2
VP
on
l
2
PARTICLE DYNAMICSPARTICLE DYNAMICS
D
F
W
y
y
x
x
Va
VVr
£]
£^
Diagram of Particle Dynamics
CALCULATION OF PSYCHROMETRIC PARAMETERSCALCULATION OF PSYCHROMETRIC PARAMETERS
P eswb
Wet Bulb Saturation Pressure:
Dry Bulb Vapor Pressure:
P P Pv swb atm ( ) / ( . / ) 1 015577
A BT CT DT ET
FT GTwb wb wb wb
wb wb
2 3 4
2
1006 9254
0 62195
.
.
P P
hT Tswb atm
fgwb
Latent Heat of Water:
h Tfg 2502535 259 2385 76424 27316. . ( . )
SIMULATION AND ANALYSESSIMULATION AND ANALYSES
SIMULATION PROCEDURES VALIDATION OF THE MODEL PARTICLE SIZE AND MOVING DISTANCE EFFECT OF TEMPERATURE AND RELATIVE
HUMIDITY
SIMULATION AND ANALYSESSIMULATION AND ANALYSES
SIMULATION PROCEDURES VALIDATION OF THE MODEL PARTICLE SIZE AND MOVING DISTANCE EFFECT OF TEMPERATURE AND RELATIVE
HUMIDITY
SIMULATION AND ANALYSESSIMULATION AND ANALYSES
SIMULATION PROCEDURES VALIDATION OF THE MODEL PARTICLE SIZE AND MOVING DISTANCE EFFECT OF TEMPERATURE AND RELATIVE
HUMIDITY
SIMULATION AND ANALYSESSIMULATION AND ANALYSES
SIMULATION PROCEDURES VALIDATION OF THE MODEL PARTICLE SIZE AND MOVING DISTANCE EFFECT OF TEMPERATURE AND RELATIVE
HUMIDITY
SIMULATION AND ANALYSESSIMULATION AND ANALYSES
SIMULATION PROCEDURES VALIDATION OF THE MODEL PARTICLE SIZE AND MOVING DISTANCE EFFECT OF TEMPERATURE AND RELATIVE
HUMIDITY
0. 000. 050. 100. 150. 200. 250. 300. 350. 400. 450. 500. 550. 60
1 3 5 7 9 11
13
15
17
19
21
23
25
Test Number
Eva
pora
tion
Eff
icie
ncy
( )
MeasuredPredicted
Comparisons between predicted and measured evaporation efficiencies.
Comparisons between predicted and measured final chamber temperature.
20
22
24
26
28
30
32
34
1 3 5 7 9 11
13
15
17
19
21
23
25
Test Number
Fina
l Cha
mbe
r Tem
pera
ture
(C
)
MeasuredPredicted
Droplet evaporation percentage at various moving distances under different temperatures and relative humidities. Initial droplet size is 45 microns
0
10
20
30
40
50
60
70
80
90
100
0.0 0.1 0.2 0.3 0.4 0.5Moving Distance (m)
Dro
plet
Eva
pora
tion
Per
cent
age
(%)
20℃, 80%RH30℃, 80%RH20℃, 50%RH30℃, 50%RH20℃, 30%RH30℃, 30%RH
Effect of droplet diameter and psychrometric parameters on the moving distance.
0.01
0.10
1.00
10.00
100.00
0 50 100 150 200
Droplet Diameter (microns)
Mov
ing
Dis
tanc
e (m
)
20 ℃， 80%
30 ℃， 80%
20 ℃， 50%
30 ℃， 50%
20 ℃， 30%
30 ℃， 30%
Droplet evaporation rate under different relative humidities. Dry bulb temperature is 30 and the initial droplet d℃iameter is 65 microns.
0
5
10
15
20
25
30
35
40
45
50
0 5 10 15 20 25 30 35 40
Time (s)
Eva
pora
tion
Rat
e (1
0-12 k
g/s)
RH 50%
RH 60%
RH 70%
RH 80%
RH 90%
Droplet evaporation rate under different relative humidities. Dry bulb temperature is 30 and the initial droplet d℃iameter is 65 microns.
0
20
40
60
80
100
120
140
160
0 5 10 15 20 25 30 35 40 Time (s)
Tot
al
Eva
pora
tion
(10
-12 k
g)
RH 50%
RH 60%
RH 70%
RH 80%
RH 90%
Evaporation rate of droplet with different initial diameter. Dry bulb temperature is 25 and the relative humidity i℃s 90%.
0
2
4
6
8
10
12
14
0 10 20 30 40 50 60 70 80
Time (s)
Eva
pora
tion
Rat
e (1
0-12 k
g/s) 15 microns
45 microns
65 microns
105 microns
Evaporation rate of droplet with different initial diameter. Dry bulb temperature is 25 and the relative humidity i℃s 90%.
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 Moving Distance (m)
Eva
pora
tion
Rat
e (1
0-12 k
g/s) 15 microns
45 microns
65 microns
105 microns
Evaporation efficiency as affected by droplet diameter and psychrometric parameters. The nozzle height is 1.8m.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 20 40 60 80 100 120 140 160 180 200
Droplet Diameter (microns)
Eva
pora
tion
Eff
icie
ncy
()
20℃， 80%30℃， 80%20℃， 50%30℃， 50%20℃， 30%30℃， 30%
Evaporation efficiency as affected by droplet diameter and psychrometric parameters. The nozzle height is 3.0m.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 20 40 60 80 100 120 140 160 180 200
Droplet Diameter (microns)
Eva
pora
tion
Eff
icie
ncy
()
20℃，80%
30℃，80%
20℃，50%
30℃，50%
20℃，30%
30℃，30%
Droplet evaporation percentage at various moving distances under different temperatures and relative humidities. The nozzle height is 0.9m and the droplet diameter is 65 microns.
5
20
35
50
65
80
95 21
25
29
33
37
0102030405060708090
100
EvaporationEfficiency (%)
Relative Humidity (%)
Temperature(¢ J)
Droplet evaporation percentage at various moving distances under different temperatures and relative humidities. The nozzle height is 0.9m and the droplet diameter is 105 microns.
5
20 35 50 65 80 95
21
25
2933
37
0102030405060708090
100
蒸發效率Evaporation
Efficiency (%)
相對溼度Relative Humidity
(%)
溫度Temperature
(¢ J)
(B)
Droplet evaporation percentage at various moving distances under different temperatures and relative humidities. The nozzle height is 1.2m and the droplet diameter is 65 microns.
51
5
25
35
45
55
65
75
85
95 21
24
27
3033
3639
0
10
20
30
40
50
60
70
80
90
100
蒸發效率Evaporation
Efficiency (%)
相對溼度Relative Humidity
(%)
溫度Temperature
(¢ J)
(C)
FITTING WITH SIMPLE FUNCTIONS
4037.53532.5
3027.525
22.5
Temperature 〔℃〕60
6570
7580
8590
Relative Humidity (%)
10
10
20
20
30
30
40
40
50
50
60
60
70
70
80
80
90
90
100
100
Eva
pora
tion
Eff
icie
ncy
(%)
Droplediameter
(m)
NozzleHeight
（m）
Best fitted function R2 Commonfunction
R2
0.6 z=a+b(lnx)2+cy1.5 0.9908 0.9755
45 0.9 z=a+blnx+cy3 0.9892 0.9718
1.2 lnz=a+bx/lnx+c/lny 0.9973 0.9970
0.6 lnz=a+b(lnx)2+cy1.5 0.9913 0.9703
65 0.9 lnz=a+bx0.5lnx+cy5 0.9952 z=a+blnx+cy 0.9769
1.2 lnz=a+blnx+cy3 0.9853 0.9756
0.6 lnz=a+bx0.5+cy1.5 0.9930 0.9587
105 0.9 lnz=a+bx0.5+cy1.5 0.9930 0.9556
1.2 lnz=a+b(inx)2+cy1.5 0.9915 0.9630
FITTING WITH SIMPLE FUNCTIONS
CONCLUSIONSCONCLUSIONS
A theoretical model to predict evaporative cooling efficiency for mist-fog systems was established based on mass transfer theory and particle dynamics.
The model was validated with experimental data from existing literature and the predicted evaporation efficiency agreed well with the measured values.
The effects of temperature, relative humidity and the size of spray droplet on the cooling efficiency of mist-fog systems were analyzed with the developed model. Useful information can be generated with model simulations as an aid in designing effective mist-fog systems.
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