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Fire cooling performance by water sprays using medium and small-scale model experiments with scaling relaxation
Journal Pre-proof Fire cooling performance by water sprays using medium and small-scale model experiments with scaling relaxation Futoshi Tanaka, Wataru Mizukami, Khalid A.M. Moinuddin PII:
S0379-7112(19)30079-7
DOI:
https://doi.org/10.1016/j.firesaf.2020.102965
Reference:
FISJ 102965
To appear in:
Fire Safety Journal
Received Date: 11 February 2019 Revised Date:
5 February 2020
Accepted Date: 5 February 2020
Please cite this article as: F. Tanaka, W. Mizukami, K.A.M. Moinuddin, Fire cooling performance by water sprays using medium and small-scale model experiments with scaling relaxation, Fire Safety Journal (2020), doi: https://doi.org/10.1016/j.firesaf.2020.102965. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Futoshi Tanaka: Conceptualization, Methodology, Software, Formal analysis, Data curation, Writing - Original draft, Supervision. Wataru Mizukami: Validation, Investigation, Data curation, Visualization. Khalid A.M. Moinuddin: Conceptualization, Methodology, Writing- Reviewing and Editing.
1
Fire cooling performance by water sprays using medium and
2
small-scale model experiments with scaling relaxation
3
Futoshi Tanakaa*, Wataru Mizukamib, and Khalid A.M. Moinuddinc
4 5 6
a
7
3-9-1 Bunkyo, Fukui-shi, Fukui 910-8507, Japan
Mechanical Engineering, Faculty of Engineering, University of Fukui
8 9 10
b
Mechanical Engineering, Graduate School of Engineering, University of Fukui
3-9-1 Bunkyo, Fukui-shi, Fukui 910-8507, Japan
11 12
c
13
P.O. Box 14428, Melbourne, Victoria 8001, Australia
Center for Environmental Safety and Risk Engineering, Victoria University
14 15
*
16
Tel: +81-776-27-9817, Fax: +81-776-27-8748
17
Email: [email protected]
18
Postal address: Mechanical Engineering, Faculty of Engineering, University of Fukui,
19
3-9-1 Bunkyo, Fukui-shi, Fukui 910-8507, Japan
Corresponding author:
20 21
1
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Abstract
23
The fire cooling performance by water sprays is investigated in medium and small-scale fire cooling
24
experiments. The scaling relationships considered are the fire diameter, spray height, heat release
25
rate, spray angle, flow rate, working pressure, and droplet diameter. Full-cone-type spray nozzles of
26
different sizes are used in both scale experiments. Although spray conditions (spray angle, flow rate,
27
pressure, and droplet diameter) satisfying the scaling relationships are used, when the geometrical
28
scaling of the nozzles is not sufficient, the water spray mass flux distributions generated by the
29
nozzles do not fulfill the scaling relationship. To resolve this problem, we propose a new scaling
30
relaxation for scaling the fire cooling effect of water sprays even under incomplete scaling
31
conditions in the water spray mass flux distributions. In the scaling relaxation, we propose an
32
effective plane in which the group of water droplets collides with the fire plume, and assume that
33
only the water droplets passing through the effective plane contribute to fire cooling. Based on the
34
experimental data, we show that scaling with sufficient accuracy is possible by normalizing with the
35
spray flow rate directly contributing to the fire cooling. The scaling accuracy tends to decrease with
36
the increasing spray angle.
2
37
Keywords:
38
Fire cooling
39
Water sprays
40
Scaling relaxation
41
Model experiments
42
3
43
Nomenclature
44
Acup
opening area of the cup (m2)
45
b
half-width of Gaussian distribution (m)
46
Cpi
specific heat of each gas component species (kJ/(kg·K))
47
Cp_gas
specific heat of mixed exhaust gas (kJ/(kg·K))
48
D
fire source diameter (m)
49
Dd
diameter of the smoke duct (m)
50
Dv
volumetric diameter of droplet (mm)
51
Dv,0.5
median volumetric diameter of droplet (mm)
52
E'
net heat of combustion per unit volume of oxygen (MJ/m3)
53
E"
net heat of combustion per unit volume of oxygen consumed in the burning of carbon
54
monoxide (MJ/m3)
55
g
gravitational acceleration (m/s2)
56
H
relative humidity in percent (%)
57
∆H
heat of combustion (MJ/kg)
58
krad
correction factor for a radiative heat release rate (–)
59
L
length from burning surface of a fire to a spray head, characteristic length (m)
60
Lp
length from burning surface to effective interaction area (m)
61
Lw
length from spray head to effective interaction area (m)
62
Mcup
mass of water received by the cup (kg)
63
Me
molecular weight of the exhaust gas mixture (kg/kmol)
64
ms
mass flow rate of smoke in the smoke duct (kg/s)
65
mwe
actual delivery water spray mass flow rate (kg/s)
66
m″w
water spray mass flux (kg/(m2·s))
67
P
pressure (kPa)
68
PH2O
water vapor pressure (kPa)
69
Pw
working pressure of water spray (MPa)
70
Q
desired heat release rate (kW)
71
Qchem
chemical heat release rate measured by the oxygen consumption method (kW)
72
Qconv
convective heat flow rate (kW)
73
Qcool
rate of fire cooling by water sprays (kW)
74
Qgas
theoretical heat release rate estimated from mass flow rate of fuel (kW)
4
75
Qloss
rate of heat loss (kW)
76
Qrad
radiative heat release rate (kW)
77
qrad
radiative heat flux (kW/m2)
78
R0
universal gas constant (kJ/(kmol·K))
79
Re
gas constant of the exhaust gas mixture (kJ/(kg·K))
80
Red
droplet Reynolds number (–)
81
r
radius coordinate for water mass flux distribution (m)
82
re
radius of effective interaction area (m)
83
rrad
distance from fire center to the face of a radiometer (m)
84
S
scale ratio (–)
85
Se
effective interaction area (m2)
86
T
temperature (K)
87
∆T
rise in temperature (K)
88
t
time (s)
89
∆tcup
discharging time (s)
90
us
velocity in the smoke duct (m/s)
91
Va
volume flow rate of ambient air drawn from the hood (m3/s)
92
Vs
volume flow rate in the smoke duct (m3/s)
93
Vw
spray flow rate (L/min)
94
X
mole (volume) fraction (–)
95
Y
mass fraction (–)
96
Zf0
virtual origin (m)
97
x, y, z
the axes of coordinates (m)
98 99
Greek letters
100
Ω
spatial distribution function (–)
101
α
plume angle (°)
102
β
correction factor in the smoke duct (–)
103
γ
empirical constant for drop size distribution (–)
104
η
combustion efficiency (–)
105
θ
spray angle (°)
106
ρs
density of smoke (kg/m3)
5
107
σ
empirical constant for drop size distribution (–)
108
oxygen depletion (–)
109
χrad
radiative fraction (–)
110 111
Superscripts
112
A
gas components without water vapor in the gas analyzer
113
AW
gas components with water vapor in the gas analyzer
114
DT
dew point temperature
115
S
gas components in the smoke duct
116
°
gas components in the ambient air
117 118
Subscripts
119
CO
carbon monoxide
120
CO2
carbon dioxide
121
H 2O
water vapor
122
N2
nitrogen
123
O2
oxygen
124
amb
ambient condition
125
m
medium scale
126
s
small scale
127
6
128
1. Introduction
129
130
In the 1970s, Heskestad derived a set of scaling relationships for the thermo-fluid dynamic
131
interaction of water sprays with fires in geometrically similar spaces based on the Froude modeling
132
concept [1]. Subsequently, the scaling relationships proposed were used to evaluate fire extinction
133
similarity on 1:10, 1:3 and 1:1 scale fire experiments with water sprays in a large space, and the
134
effectiveness of the scaling theory was validated [2–3].
135
136
Yu investigated the effect of droplet size on the scaling relationships derived by Heskestad for
137
applying the scaling relationships to the extinguishment phenomenon by water mist with a low
138
Reynolds number based on the droplet diameter (Red ≤ 1) [4]. The finding from this investigation
139
indicated that droplet size for low Reynolds number conditions should be scaled with the 1/4-power
140
of length scale, instead of the 1/2-power found for high Reynolds number conditions. Later,
141
Jayaweera and Yu confirmed the droplet size scaling requirement for low Reynolds number
142
conditions with a series of fire cooling experiments [5, 6]. This improvement was warranted as the
143
scaling relationships derived by Heskestad were developed for sprinklers with significant inertia
7
144
compared to gas flow (Red > 1). Furthermore, Yu derived a general rule for the scaling of the
145
diameter of a droplet under a wide range of droplet Reynolds numbers, and validated this general
146
rule [7]. After improving the scaling relationships, Yu et al. conducted a series of fire suppression
147
experiments to evaluate the efficacy of physical scaling of water mist suppression of a gas fire, pool
148
fire and solid combustible fire in enclosures [8-10]. These experiments were conducted using full
149
and 1:3 scale enclosures. The results showed that water mist cooling and fire development could be
150
reasonably reproduced during enclosure fires by physical scaling based on Froude modeling.
151
Furthermore, Yu et al. presented an evaluation of the scaling of fire extinguishment by water mist in
152
a large industrial machinery enclosure [11]. Four fire scenarios were selected using full and 1:2 scale
153
enclosures. Based on the obtained results, they concluded that the scaling relationships for water
154
mist fire suppression could be used to determine the fire extinguishing performance of full-scale
155
water mist protection.
156
157
In addition to Yu’s research to evaluate the efficacy of physical scaling of water mist, many model
158
scale experiments have been conducted for fires in large structures with water sprays where
159
full-scale fire experiments were difficult. For example, many model-scale studies have been
8
160
conducted on the influence of water sprays installed in tunnels on fires. Ingason carried out 1:23
161
model scale tunnel fire tests with a water spray system in order to capture the basic behavior of water
162
sprays in a longitudinal tunnel flow [12]. Li and Ingason conducted 1:15 model scale tunnel fire tests
163
to clarify the effectiveness of an automatic sprinkler system in a tunnel with longitudinal ventilation
164
[13]. Furthermore, Li and Ingason examined how the combustion products were released while a
165
water sprinkler system was active, using a 1:4 scale model tunnel [14].
166
167
Heskestad proposed the use of geometrically similar nozzles in order to preserve the spray
168
trajectories [2, 3]. Many model scale experiments with water sprays have been conducted using
169
geometrically similar nozzles following the suggestion of Heskestad in addition to satisfying scaling
170
relationships for the working pressure, spray flow rate, and average diameter of droplets. In principle,
171
when the spray trajectory is preserved, the scaling of the water spray mass flux distribution on a
172
floor is automatically satisfied.
173
174
In model scale fire experiments with water sprays, it is necessary to satisfy the scaling relationships
175
concerning geometric similarity including the nozzle, heat release rate of the fire, working pressure
9
176
of the water spray nozzle (determining the initial speed of water droplets), spray flow rate, average
177
diameter of droplets, and water spray mass flux distribution on a floor, and it is quite challenging to
178
fulfill all scaling relationships. In order to prepare a particularly geometrically accurate scaled-down
179
nozzle, a special nozzle must be developed or selected from a number of existing nozzles. As a result,
180
it is quite challenging, or the geometrical similarity of the nozzles must be compromised.
181
182
If geometrically similar nozzles following the suggestion of Heskestad can’t be used, inconsistency
183
in the scaled water spray mass flux distribution on a floor may occur. In this study, we propose a
184
new scaling relaxation to estimate the fire cooling performance in the medium scale from that in the
185
small scale under the condition of inconsistency in the scaled water spray mass flux distribution in
186
medium and small-scale models. In the new scaling relaxation, the actual delivery water spray mass
187
flow rate is used for evaluating the fire cooling performance at medium and small scales.
188
10
189
2. Experimental method
190
In this study, a series of medium and small-scale fire experiments with water sprays were conducted
191
to evaluate the fire cooling performance by water sprays, and Froude’s scaling relationships were
192
applied to the experiments on both scales to evaluate the performance of similarity. Table 1 shows
193
the scaling relationships based on the Froude modeling [1–7]. As the Reynolds number of the flow
194
around a droplet was greater than unity under our experimental conditions, we chose the 1/2 power
195
of scale ratio as per the scaling of droplets [7].
196
Table 1 Scaling relationships for characteristic parameters [1–7].
Unit
197
Scaling (S = scale ratio)
Heat release rate (HRR)
Q [kW]
Q full
=
S
Velocity
u [m/s]
u
=
S
3
full
5/2
Q model
1/2
u
5/2
model
=
S
t full
=
S
T [K]
T full
=
S T model
Pressure
P [kPa]
P
=
S P
Spray flow rate
V w [L/min]
V w full
=
S
Mass flux
m'' [kg/(m s)]
2
m'' full
=
S
Median diameter
D v,0.5 [mm]
D v,0.5 full =
S
Volume flow rate
V [m /s]
V
Time
t [s]
Temperature
full
full
V
model
1/2
t model
0 1
5/2 1/2 1/2
model
V w model m'' model D v,0.5 model
198
199
2.1. Overview of the experimental apparatus
200
Figure 1 shows the experimental apparatus used for this study. The apparatus was constructed as a 11
201
semi-open space, which was 1.6 m wide, 1.6 m deep, and 2.3 m high, and comprised of a hood, a
202
smoke duct and a suction fan for collecting and exhausting the gas including combustion products, a
203
water tank for receiving water spray droplets, a fire source, a water spray equipment, and a gas
204
analyzer system. The size of the hood was 1.6 m in width, 1.6 m in depth, and 1.1 m in height. The
205
upper part of the hood was made of stainless-steel plate of 1.0 mm in thickness and 0.2 m in height,
206
and the lower part of the hood was made of a calcium silicate board of 5 mm in thickness and 0.9 m
207
in height. The smoke duct connecting the hood with the fan was 0.25 m in diameter and made of
208
galvanized steel plates of 0.5 mm in thickness. The size of the water tank for receiving and
209
collecting water spray droplets was 1.5 m in width, 1.5 m in depth, and 0.6 m in height, and was
210
made of stainless-steel plate of 2.0 mm in thickness.
211
212
In the medium and small-scale experiments, two sizes of propane gas burners with inner diameters
213
of 0.155 and 0.08 m, respectively, were used as the fire source, and the rims of the gas burners were
214
made of steel pipe with thicknesses of 5 and 4.2 mm, respectively. The propane gas burners were
215
filled with many ceramic balls of 5 mm in diameter. The burning surfaces of the fire sources were
216
placed directly below a water spray head. During the experiments, the mass flow rate of propane gas
12
217
was regulated by a mass flow controller (model 3660, KOFLOC) to ensure a constant value.
218
219
The length from the spray head to the burning surface of the fire sources was used as the
220
characteristic length, L, in the scaling theory. Equation (1) is the definition of scale ratio, S. S =
221
Lm Ls
(1)
222
The parameters Lm and Ls indicate the characteristic lengths of medium and small scales measured as
223
Lm = 1.33 m and Ls = 0.67 m, respectively. The scale ratio between the medium and small scales was
224
2:1.
225
226
We used the oxygen consumption method developed by Parker [15] and Janssens [16] to measure
227
the heat release rate (HRR) of a fire during ‘free burning’ and water spray activation. In the
228
preconditioning process, the sampling gas drawn from the smoke duct was passed through the first
229
air tank, a cooling bottle filled with water for removing large soot and dust, a hand-made
230
dehumidifier for reducing the relative humidity of the sampling gas, and a filter for completely
231
removing soot, and then collected in the second air tank. Sensors were installed in the first and
232
second air tanks for measuring the relative humidity and gas temperature in the tanks. Furthermore, a
13
233
sensor was also placed in ambient air for measuring the relative humidity and temperature in the air.
234
The water cooling during the pretreatment process has the problem of CO and CO2 dissolution, so if
235
the smoke includes no large soot and dust, water cooling should not have been used in the
236
pretreatment process. In fact, for the clean-burning propane gas in our study there was no need for
237
the water cooling.
238
239
The hand-made dehumidifier consisted of a gas flow section with many fins cooled with ice water.
240
The gas with high humidity was cooled, and its humidity was reduced by condensation. The dew
241
point temperature of the hand-made dehumidifier incorporated in the preconditioning system was
242
about 5 °C. The O2 gas analyzer (POT8000, Shimadzu Corporation, gas analyzer based on the
243
paramagnetic principle) and CO/CO2 gas analyzer with a built-in thermo-electric dehumidifier
244
having the gas dew point temperature of 3.5 °C (CGT7000, Shimadzu Corporation, gas analyzer
245
based on the infra-red (IR) absorption method and Beer-Lambert law) drew the preconditioned gas
246
from the second air tank and measured the concentration of the sampling gas. The dew point of the
247
sample gas entering the O2 and CO/CO2 analyzers was 5 °C and 3.5 °C, respectively.
248
14
249
The oxygen consumption method developed by Parker [15] assumes that the sampling gas is
250
completely dehumidified before being introduced into a gas analyzer. Unfortunately, our hand-made
251
dehumidifier in the preconditioning process could not completely remove all the water vapor from
252
the sampling gas; the dew point temperature was 5 °C for the O2 gas analyzer and 3.5 °C for the CO2
253
and CO analyzer, so we estimated the volume fractions of the completely dehumidified sampling
254
gases assuming that slight water vapor remained in the sampling gases in the second gas tank after
255
the dehumidifier as follows:
X
Ao O2
=
256
X
Ao CO2
X OAW 2
(1 − X ) DT 5 H 2O
=
257
X = A O2
258
A X CO =
AW X CO 2
(1 − X
(2)
o
DT 3.5 H2O
)
(3)
XOAW 2
(1− X ) DT 5 H2O
A XCO = 2
259
o
AW XCO 2
(1− X
DT 3.5 H2O
AW X CO
(4)
)
(5)
260
(1 − X
261
where
XHDT2O5
262
and 3.5 °C, respectively, and
DT 3.5 H 2O
)
and
(6)
XHDT2O3.5
are the volume fractions of water vapor at dew point temperatures of 5
XkAW is the volume fraction of sampling gases with slight water vapor 15
263
measured by the gas analyzers.
264
265
The transport delay time from the flame location through the exhaust collection and sampling probe
266
to the preconditioning system was several seconds (about 5 seconds or less). In the preconditioning
267
process, as the first and second air tanks with the internal volume of 1.5 L and the water cooling tank
268
with air space of about 0.7–0.8 L were used under the sampling gas flow rate of 5 L/min, a large
269
time delay occurred. The preconditioning process with several air tanks can be modeled as a primary
270
delay system under the assumption that the gas concentration in the air tanks is always uniform.
271
Figure 2 indicates the estimated time lag of the preconditioning system and the estimated time lag of
272
the combined preconditioning system and O2 gas analyzer (POT8000). For instance, when gas with a
273
concentration of 100% is introduced to the preconditioning system, the time delay is about 61
274
seconds for reaching a 90% concentration at the output of the preconditioning system. The time
275
delays of the CO2 and CO gas analyzer and the O2 gas analyzer are 30 seconds (CGT7000; 90%
276
response time) and 45 seconds (POT8000; 90% response time), respectively. When we combined the
277
O2 gas analyzer (POT8000) with the preconditioning system during O2 measurement, we found that
278
the time delay for obtaining a 90% response is about 108 seconds. The time delay for obtaining a
16
279
99% response is about 208 seconds. The non-response time from the ignition to the response of the
280
gas analyzers to the gases concentration has been corrected by shifting the time curve of the gas
281
concentration for estimating the chemical heat release rate of fire.
282
283
The mass flow rate of the exhaust gas in the smoke duct was estimated from the rise in temperature
284
in the smoke duct and velocity measured by a thermocouple and a Pitot tube, respectively, installed
285
in the smoke duct as shown in Fig. 1. Leakage or escape of combustion products from the exhaust
286
collection system was not reliably investigated in our system and might have occurred, particularly
287
for the weak fire conditions subjected to spray. Radiative heat flux from the fire was measured by a
288
water-cooled radiometer (RE-4, Tokyo Seiko Co., Ltd.) which was installed 1 m away from the fire.
289
17
290 291
Fig. 1. Schematic of the experimental apparatus: the water spray, fire source, and gas analyzer
292
systems (unit: m).
18
Gas concentration [%]
100 Preconditioning 90% response 61 s
Precon. + O 2 Analyzer 90% response 108 s
50 Input Preconditioning Precon. + O 2 Analyzer
0 0
60
120
180
Time [s] 293 294
Fig. 2. Time delay during gas concentration measurement estimated by the model of a primary delay
295
system.
296
297
2.2. Chemical heat release rate measured by the oxygen consumption method
298
The oxygen consumption method requires the mole (volume) fractions of oxygen, carbon dioxide,
299
carbon monoxide and water vapor to calculate the heat release rate. The mole fractions of the
300
incoming ambient gases and the gases drawn into the analyzers are defined in the same way as those
301
by Parker and Janssen [15, 16]. In Eqs. (7)-(11), the superscripts °, S, and A of the mole fractions
302
indicate the gas components in the ambient air, the smoke duct, and the gas analyzers, respectively.
303 19
304
The chemical heat release rate, Qchem, of the fire source is calculated using Parker’s method as
305
follows [15]:
306
A E "− E ' 1 − φ X CO Qchem = φ − A E ' 2 X O2
307
1 − φ A X Hs 2O o o A Va = Vs 1 − X O2 φ + X O2 A X CO2 + X CO + X O 1 − X Hs 2O 2
308
where E' is the net heat of combustion per unit volume of oxygen (propane: 16.7 MJ/m3, derived
309
from ∆HO2 = 12.77 MJ/kg referred to 25 °C), and E" is the net heat of combustion per unit volume of
310
oxygen consumed in the burning of carbon monoxide (23.1 MJ/m3, derived from ∆HO2,CO = 17.69
311
MJ/kg referred to 25 °C) [17, 18]. The volumetric flow rate of the ambient air drawn from the hood
312
is estimated by Eq. (8). Va and Vs are the volume flow rate referred to standard conditions (25°C, 1
313
atm). The volume fraction of water vapor,
314
immediately after being sampled from the smoke duct in this study. No condensation was observed
315
in the first gas tank or sampling hose even during water spray activation. Oxygen depletion, , is
316
defined as:
317
o 1 − X CO − X Ho 2O 2 X Oo2 − X OA2 A A 1 − X CO − X CO 2 φ= X OA2 X Oo2 1 − A A 1 − X CO − X CO 2
o E ' X O2 Va
(7)
XHs 2O
−1
(8)
, in Eq. (8) was measured in the first gas tank
(9)
20
X Oo2
o XCO 2
318
The initial volume fractions of oxygen,
319
These were measured as the gas concentration of dehumidified air through the preconditioning o
process. Here,
321
X Oo2
322
X Oo2 = X OA2 1 − X Ho 2O
323
o A X CO = X CO 1 − X Ho 2O 2 2
o XCO 2
o
(
o
(
, refer to the incoming air.
o
X OA2
320
and
, and carbon dioxide,
and
A XCO 2
are defined as the initial concentrations of dehumidified air. Then,
are given by:
)
(10)
)
(11)
324
Equations (10) and (11) are substituted into Eq. (9) for and into Eqs. (7) and (8) for the heat
325
release rate of a fire when water vapor is trapped in the preconditioning process.
326
327
In this study, the temperature and relative humidity were measured to estimate the volume fraction
328
of water vapor at three locations. The first location was in the ambient air, the second location was in
329
the first gas tank immediately after being sampled from the smoke duct, and the final location was in
330
the second gas tank after dehumidification. The measurements of the temperature and relative
331
humidity were made every minute. A commercially available thermo-hygrometer was used for the
332
measurements. The temperature and relative humidity were measured by a thermistor element and a
333
ceramic resistor, respectively. From the temperature and relative humidity in the ambient air and
21
334
inside the first gas tank, the volume fractions of water vapor in the ambient air,
335
smoke duct,
X H2O = 336
XHs 2O
, and in the
, were estimated using the following equation:
PH2O H Pamb 100
PH2O
XHo2O
(12)
337
where,
338
relative humidity in percent. The saturated vapor pressure of water was estimated by the equation of
339
the vapor pressure-temperature relationship for saturated water vapor developed by Wagner and
340
Pruß as follows [19]:
341
PH O T ln 2 = c ( a1Θ + a2 Θ1.5 + a3Θ3 + a4 Θ3.5 + a5Θ4 + a6 Θ7.5 ) Pc T ,
342
with Θ = 1-T/Tc, Tc = 647.096 K, Pc = 22.064×103 kPa, a1 = -7.85951783, a2 = 1.84408259, a3 =
343
-11.7866497, a4 = 22.6807411, a5 = -15.9618719, a6 = 1.80122502.
is the saturated vapor pressure of water, Pamb is the ambient pressure, and H is the
(13)
344
345
In the steady-state combustion state, both the temperature and the relative humidity in the first gas
346
tank became almost constant in the averaging period, therefore, the precision index of average
347
became small. On the other hand, the bias limits of the thermo-hygrometer were expected to be in
348
the range of B∆T = ±1 K for the thermistor thermometers and B∆H = ±7% for the ceramic resistance
349
hygrometers. Since the precision index of average was small and negligible, uncertainty of the
22
350
volume fraction of water vapor can be estimated from the bias limit only, and it was about
351
±0.2% estimated from Eq. (14):
∂X H2O ∂X H2O = B∆H + B∆T ∂H ∂T 2
U X H O = BXH O 2
2
352
U XH O 2
=
2
(14)
353
354
355
The volume flow rate in the smoke duct, Vs, was defined as follows:
Vs = β
π 4
Dd2us
(15)
356
where us and Dd are the smoke velocity measured by the Pitot tube at the center of the smoke duct
357
and the diameter of the smoke duct, respectively. The volume flow rate in the smoke duct, Vs, was
358
converted to the volume flow rate referred to standard conditions (25°C, 1 atm) and substituted into
359
Eq. (8). A correction factor, β, was used for estimating average velocity in the smoke duct from the
360
center velocity measured by the Pitot tube. The correction factor was estimated from the velocity
361
distribution in the smoke duct as β = 0.852 by separate calibration experiments.
362
363
In the calibration experiments, the velocity distribution consisting of 13 measurement points in the
364
duct was measured under the same ventilation condition of the hood in the medium scale without the
365
fire source. The correction factor was estimated as the ratio of the volume flow rate obtained from
23
366
the velocity profile in the duct and the volume flow rate obtained from the velocity at the center of
367
the duct. In the fire experiments, the flow velocities at the center of the duct were about 4.0 and 2.3
368
m/s in the medium and small scales, respectively. The Reynolds number of the flow in the duct was
369
6.7×104 in the medium scale and 3.8×104 in the small scale, and both Reynolds numbers were of the
370
same order of magnitude and in a sufficiently turbulent state. When the Reynolds number of the flow
371
was in the same order, it could be expected that there was no significant change in the velocity
372
profile in the duct, so the correction factor measured in the medium scale was also used in the small
373
scale. Furthermore, the effect of buoyancy inside the duct under the fire condition on the correction
374
factor was neglected as the flow was in a sufficiently turbulent state.
375
376
2.3. Radiative heat release rate
377
Radiative heat release rate is the radiative component of Qchem. Figure 3 shows a schematic
378
representation of the distribution of radiative heat flux for estimating the radiative heat release rate.
379
If it is assumed that spatial and temporal variations of radiation from a fire can be separated, the
380
distribution of radiative heat flux, qrad (θ, φ, t), measured rrad away from the fire is given by Eq. (16):
381
′ ( t) qrad (θ,ϕ,t) =Ω(θ,ϕ) qrad
(16)
24
382
where, q’rad (t) is the radiative heat flux measured by the water-cooled radiometer installed rrad away
383
from the fire, Ω (θ, φ) indicates the spatial distribution function, and θ and φ are elevation and
384
azimuth angles, respectively. If the fire is assumed to radiate as a point source, the radiative heat
385
release rate can be estimated by Eq. (17), based on the time curve of the radiative heat flux, q’rad (t): 2 2 ′ ( t ) ∫∫ Ω (θ ,ϕ ) rrad Qrad ( t ) = ∫∫ qrad (θ ,ϕ, t ) rrad sinθ dθ dϕ = qrad sinθ dθ dϕ
ϕ ,θ
386
ϕ ,θ
(17)
387
The value of the surface integral of the spatial distribution function Ω (θ, φ) of the radiation can be
388
expressed as follows using a correction factor, krad: 2 2 4π rrad krad = ∫∫ Ω (θ ,ϕ ) rrad sin θ dθ dϕ
ϕ ,θ
389
(18)
390
When the correction factor, the radiative heat flux measured by the water-cooled radiometer, and the
391
distance from the fire to the radiometer were used, the time variation of the radiative heat release rate
392
was estimated as follows:
393
2 ′ ( t) Qrad ( t ) = 4πrrad krad qrad
394
The correction factor, krad, was derived under the assumption that the time integral of the radiative
395
fraction of Qchem over the average period in ‘free burning’ agrees with the time integral of the
396
radiative heat release rate based on the point source assumption over the same period as shown in Eq.
397
(20):
(19)
25
krad = 398
χ rad ∫ Qchem ( t ) dt ave 2 rad ave
4π r
∫
′ ( t ) dt qrad
(20)
399
where, the value of the global radiative fraction of a propane fire was selected as χrad = 0.29 [18].
400
The distance from the fire to the radiometer was set as rrad = 1.0 m in all fire experiments.
401
402
The correction factor obtained during ‘free burning’ was used to estimate the radiative heat release
403
rate during water spray activation. For the estimation of the correction factor, it was assumed that the
404
spatial distribution function Ω (θ, φ) of the radiation and the global radiative fraction of fire, χrad, did
405
not change during the water spray activation. However, in reality, the latter assumption was not
406
sufficiently valid during the water spray activation. For example, work by White et al. [20] has
407
suggested that the radiative fraction of fire is not constant and reduces when fires are suppressed
408
with water spray owing to the reduction in flame temperature. Furthermore, they confirmed this by
409
direct measurements of the radiative fraction of fire suppressed by nitrogen dilution of the oxidizer.
410
When the oxygen volume fraction in the ambient air with nitrogen dilution was in the range of 0.155
411
to 0.21, the color of the propane flame was yellow indicating soot incandescence. The radiative
412
fraction corresponding to the yellow flame ranged from 0.19 to 0.32 [21]. In our fire experiments,
413
except for the extinguishing condition, since the flame color was observed to be yellow during the
26
414
water spray activation, it can be assumed that the radiative fraction ranged from 0.19 to 0.32. The
415
measurement system used in our study was unable to sense the changes in the radiative fraction
416
during the water spray activation. Therefore, in the estimation of the radiative component of Qchem
417
during the water spray activation, the decrease in prediction accuracy was considered by widening
418
the range of the bias limit B of the global radiative fraction of a propane fire in the uncertainty
419
analysis. Based on work by White et al. [21], the bias limit Bχ of the global radiative fraction of a
420
propane fire was assumed to be Bχ = 0.10. In other words, the radiative fraction was assumed as χrad
421
= 0.29±0.10. As a result, the range of uncertainty has been significantly broadened in the radiative
422
component of Qchem.
423
424
2.4. Convective heat flow rate and heat loss by heat transfer
425
Convective heat flow rate is the convective component of Qchem. The convective heat flow rate of the
426
fire, Qconv, was measured during the fire experiment with and without water sprays. The convective
427
heat flow rate was estimated by the following equation:
428
Qconv = ms Cp _ gas ∆Tgas
429
where, ms, Cp_gas, and ∆Tgas are the mass flow rate of the smoke flowing through the smoke duct, the
(21)
27
430
specific heat of the mixed exhaust gas at constant pressure, and the rise in temperature of the smoke
431
flow in the smoke duct adjacent to the hood, respectively. The specific heat of the mixed exhaust gas
432
was evaluated by a simple mass weighted average of the specific heat of each gas component species
433
(N2, O2, CO2, CO, H2O) dependent on the temperature of the smoke based on the data in
434
NIST-JANAF Thermochemical Tables [22]:
Cp _ gas = ∑YC i pi i
435 436
(22)
The mass flow rate in the smoke duct was defined as follows:
ms = ρsVs = 437
Pamb Vs Re (Tamb + ∆Td )
(23)
438
The mass flow rate was calculated from the smoke density, ρs, and the smoke volume flow rate, Vs.
439
The molecular weight of the exhaust gas mixture, Me, in the smoke duct can be estimated by the
440
following equation derived by Janssens [16]:
441
M e = 18 + 4 1 − X HS 2O
442
where
443
relative humidity and temperature in the first gas tank immediately after being sampled from the
444
smoke duct. The gas constant of the exhaust gas mixture was calculated from the universal gas
445
constant and the molecular weight of the exhaust gas mixture as:
(
X Hs 2O
)( X
A O2
A + 4 X CO + 2.5 2
)
(24)
is the volume fraction of water vapor in the smoke duct, which is estimated from the
28
Re =
446
R0 Me
(25)
447
448
In this study, we installed three thermocouples on the surface of the hood. The approximate value of
449
the rate of heat loss, Qloss, through the hood could be roughly estimated based on the surface
450
temperature by the classical theory for natural convection. When we estimated the rate of heat loss,
451
Qloss, we found that it was 2% or less of Qchem during water spray activation (Qloss ≤ 5% of Qchem
452
during ‘free burning’), therefore, we ignored the rate of heat loss through the surface of the hood.
453
454
2.5. Size distribution of water spray droplets and estimation of droplet diameter
455
In this study, we measured the size distribution of water spray droplets and evaluated the median
456
volumetric diameter, Dv,0.5, from their size distribution. The diameters of spray droplets were
457
measured by using an immersion method [23, 24]. The spray droplets were captured in a small dish
458
containing castor oil and photographed with a microscope and a digital camera, and the diameters of
459
the spray droplets were measured from the photograph. Figure 4 shows an example of the droplets
460
photographed and the measurement of the radius of the droplets. The location where the spray
461
droplets were captured was the same as the burning surface of the fire source. The number of spray
29
462
droplets measured for spray nozzles TG1 and TG03 (refer to Table 2) were 662 and 622 droplets,
463
respectively, to estimate the size distribution and the median volumetric diameter of the spray
464
droplets.
465
466
Figure 5 shows the size distributions of the water spray droplets in the medium and small-scale
467
experiments. The black and red solid lines show the droplet size distributions by cumulative volume
468
fraction (CVF) as measured and prescribed, respectively. The cumulative volume fraction
469
distribution can be prescribed for a water spray as a combination of log-normal and Rosin-Rammler
470
distributions [25]:
471
ln Dv′ 2 Dv 1 Dv ,0.5 1 dD′ exp − v 2π ∫0 σ Dv′ 2σ 2 CVF(Dv ) = γ D 1 − exp −0.693 v D v,0.5
σ= 472
2 2π ( ln 2) γ
=
(D ≤ D ) v
v,0.5
(D > D ) v
v,0.5
(26)
1.15
γ
(27)
473
where Dv,0.5 is the median volumetric droplet diameter and γ and σ are empirical constants.
474
Rosin-Rammler and log-normal distributions are smoothly joined if the relationship between
475
empirical constants γ and σ fulfills the relational expression as shown in Eq. (27). In this study, the
476
parameters γ = 2.6 and σ = 0.442 were determined from the comparison in Fig. 5.
30
Spatial distribution function Ω
qrad (θ, φ, t)
z
y
x Point source χQchem
rrad
q’rad (t) Radiometer
477 478
Fig. 3. Schematic representation of the distribution of radiative heat flux for estimating the radiative
479
component of the chemical heat release rate.
480 481
Fig. 4. Example of the droplets photographed and measured.
482 31
1
CVF [-]
0.8 0.6 0.4 Measured Prescribed γ = 2.6
0.2 0 0
200
400 600 Diameter [µm]
800
1000
483 484
(a) Medium scale: Dv,0.5 = 418 µm
1
CVF [-]
0.8 0.6 0.4 Measured Prescribed γ = 2.6
0.2 0 0
200
400 600 Diameter [µm]
800
485 486
(b) Small scale: Dv,0.5 = 295 µm
487
Fig. 5. Droplet size distributions.
488
489
32
1000
490
3. Experimental conditions
491
Table 2 presents the experimental conditions in the fire cooling experiments. The parameters listed
492
in Table 2 are the fire diameter, D, the desired heat release rate, Q, the water spray conditions in both
493
the medium and small scales, and the nozzle height from the burning surface of a fire source, L,
494
defined as the characteristic length. The heat release rates listed in Table 2 were calculated from the
495
heat of combustion of propane gas (∆H = 46 MJ/kg) [18] and the mass flow rate of propane gas
496
assuming 100% combustion efficiency. However, practically, since the values of the heat release rate
497
measured by the oxygen consumption method were smaller than the values listed in Table 2, the
498
combustion efficiency varied in a range from 83 to 98% in the fire cooling experiments. Water spray
499
nozzles UniJet TG1 and TG03 made by Spraying Systems Co., which can satisfy the scaling
500
relationships of the spray angle, flow rate, working pressure, and droplet diameter, were selected
501
under the medium and small scales. However, it is to be noted that TG1 and TG03 are not
502
geometrically similar and as mentioned earlier, it is challenging to commercially source
503
geometrically similar nozzles. The values in parentheses in Table 2 are ideal values derived from the
504
scaling relationships as shown in Table 1. The ranges of the mass flow rate of the exhaust gas in the
505
smoke duct during ‘free burning’ and water spray activation were from 0.15 to 0.19 kg/s in the
33
506
medium scale and from 0.11 to 0.13 kg/s in the small scale. The mass flow rate of the exhaust gas
507
was determined considering the sensitivities of the gas analyzers and differential pressure gauge for
508
the Pitot tube installed in the smoke duct. Furthermore, the mass flow rate of the exhaust gas was set
509
in a way that the average mass flux of the exhaust gas on the suction area (1.6×1.6 m2) in the hood
510
fulfilled the scaling relationship in the medium and small scales. The lowest possible mass flow rate
511
was chosen so as not to affect the spray transport and fire entrainment behaviors.
512
513
In this study, a full-scale (large-scale) fire was postulated as a fire in a tunnel with the ceiling height
514
of 8 m. It was assumed that a water spray was installed under the ceiling (spray height, L = 8 m) and
515
the heat release rate of a fire ranged from about 1.5 to 3.5 MW (corresponding to a small vehicle fire
516
in the tunnel). The flow rate and the droplet median volumetric diameter of the water spray were
517
assumed to be 80 L/min and about 1 mm, respectively. Based on these conditions in full scale, the
518
experimental conditions in the medium and small scales were determined as shown in Table 2. The
519
scale ratio of the medium and small scales to full scale corresponds to 1:6 and 1:12, respectively.
520
The scale ratio between the medium and small scales was 2:1.
521
34
522
Table 2 Experimental conditions in medium and small-scale fire cooling experiments. Scale
M edium
Small S = 2
Fire diameter, D (m)
0.155
0.08 (0.078)
42.9
7.6 (7.6)
34.7
6.1 (6.2)
26.0
4.6 (4.6)
17.4
3.1 (3.0)
Nozzle type
TG1
TG03
Orifice diameter (mm)
0.94
0.51
Spray angle, θ (°)
54
54 (54)
Spray flow rate, V w (L/min)
0.91
0.16 (0.16)
Working pressure, P w (M Pa)
0.36
0.19 (0.18)
Droplet diameter, D v,0.5 (mm)
0.418
0.295 (0.296)
Spray height, L (m)
1.33
0.67 (0.67)
Heat release rate, Q (kW)
523 524
35
525
4. Results and Discussion
526
527
4.1. Distributions of water spray mass flux
528
To identify the distribution characteristics of the water spray nozzles, the distributions of the water
529
spray mass flux discharged from the nozzles TG1 and TG03 were measured. The conditions of the
530
water sprays are listed in Table 2.
531
532
Figure 6 shows the arrangement of the cups measuring the water spray mass flux distribution.
533
Circular plastic cups with inner and outer diameters of 0.056 and 0.062 m were used in the medium
534
scale. On the other hand, square aluminum cups with outer and inner sides of 0.015 and 0.0126 m
535
were used in the small scale. The cups were arranged on a board set up under the nozzle at intervals
536
of every 0.062 and 0.031 m in the medium and small scales, respectively. The heights between the
537
top surface of the cups and the discharging hole on the nozzle face were set to the same heights from
538
the fire source surface, that is, 1.33 and 0.67 m, respectively. A similar technique was used by
539
Mahmud et al. [26] for the water flux measurements.
540
36
541
In the measurement of the water spray mass flux distribution, the activation periods of water spray
542
discharging were continued for 4 and 10 mins for nozzles TG1 and TG03, respectively. The water
543
spray mass flux, m''w, was estimated from the mass of water received by the cup, Mcup, the opening
544
area of the top surface of the cup, Acup, and discharging time, ∆tcup. Equation (28) defines the water
545
spray mass flux:
mw'' = 546
M cup Acup ∆tcup
(28)
547
The orientation of the nozzle tip incorporated in the spray head was changed 90 degrees clockwise
548
every time and measurements were made four times (0, 90, 180, and 270 degrees, with the x axis as
549
0 degrees). The distributions of the water spray mass flux were evaluated as the average distributions
550
of these four measurements. Figure 7 shows the averaging distributions of the water spray mass flux
551
in the medium and small scales. The intersection of the x and y axes in Fig. 7 indicates the position
552
directly below the spray nozzle and the origin of the coordinates in Fig. 1. The averaging
553
distributions of the water spray mass flux showed concentric distributions in both scales, though the
554
pattern was not fully circular. More non-circular patterns were also observed by Mahmud et al. [26].
555
556
Figure 8 shows a comparison of the curves of the water spray mass flux in the medium and small
37
557
scales. These curves were depicted as the average distribution in the circumferential direction of the
558
water spray mass flux distributions obtained from cups arranged every 45 degrees shown in Fig. 6.
559
The measurement uncertainty at a 95% confidence level of the water spray mass flux at each
560
measurement location was estimated and included as error bars in Fig. 8. In an appendix section, we
561
discuss the details of the uncertainty analysis. The water spray mass flux in the small scale was
562
scaled up to match the medium scale using the scaling relationship shown in Table 1. Even though
563
the water flow rate, working pressure, and droplet diameter were selected to scale satisfactorily, as
564
shown in Table 2, the scaled-up water spray mass flux around the center for the small scale was
565
smaller compared to the medium scale. In model experiments of fire phenomena interacting with
566
water sprays, in addition to the scaling of the nozzle operating conditions, simultaneously satisfying
567
scaling of the water spray mass flux distribution is challenging.
568
38
y
x Cup interval
569 570
Fig. 6. Arrangement of the cups for measuring the water spray mass flux distribution.
571 572
(a) Medium scale (0.91 L/min)
39
573 (b) Small scale (0.16 L/min)
575
Fig. 7. Averaging distributions of the water spray mass flux in the medium and small scales.
Spray mass flux S1/2m''w [kg/m2s]
574
Medium (TG1) Small (TG03) S = 2
0.1
0.05
0
0
0.2
0.4 r-axis Sr [m]
0.6
0.8
576 577
Fig. 8. Averaged water spray mass flux distributions scaled on the radius axis.
40
578
4.2 Time history of heat release rate in fire cooling experiments
579
Figures 9 and 10 show the time curves of the heat release rate in the medium and small scales in the
580
fire cooling experiments. In the case of Q = 7.6 kW, since the water flow rate of the spray nozzle of
581
TG03 was gradually increased after 960 s to examine the water flow rate needed for fire extinction,
582
the time history of data after 960 s is omitted in Fig. 10(a). The omitted data is not required for our
583
further analysis. In these figures, Qchem, Qconv, and Qrad are the chemical heat release rate estimated
584
by the oxygen consumption method, the convective heat flow rate calculated from the rise in
585
temperature and the mass flow rate of smoke flowing in the duct, and the radiative heat release rate
586
estimated from the heat flux measured by the radiometer, respectively. The fire cooling rate by water
587
sprays, Qcool, was defined as follows based on the energy balance:
588
Qcool = Qchem − Qconv − Qrad − Qloss
589
where Qloss denotes the rate of heat loss which was transferred from the smoke flow to the hood and
590
lost to the ambient air. In this study, the rate of heat loss, Qloss, was neglected since its value was
591
small, especially during water spray activation. Qgas, shown by the chain line, indicates the
592
theoretical heat release rate estimated from the mass flow rate of propane gas and its heat of
593
combustion assuming 100% combustion efficiency. In other words, Qgas indicates the desired heat
(29)
41
594
release rate defined as experimental conditions, such as the gas flow rate.
595
596
Table 3 shows multiple respective primary data during ‘free burning’ and water spray activation.
597
The combustion efficiency was defined as η = Qchem/Qgas. Since these values were evaluated as
598
average values, a time range of averaging is also shown in Table 3. The value of η in the case of the
599
heat release rate of 17.4 kW in the medium-scale experiment was measured to be about 4–11%
600
lower than the value of η in the other larger fire cases in the medium scale. Similarly, the value of η
601
in the case of the heat release rate of 7.6 kW in the small-scale experiment was measured to be about
602
4–15% lower than the value of η in the other smaller fire cases in the small scale. As the value of η
603
of 7.6 kW in the period of water spray activation was the same as that of ‘free burning’, we can be
604
confident that it was not due to the influence of water spray. When we considered the range of
605
uncertainty in Qchem, we found that the range in Qchem of 17.4 and 7.6 kW overlaps with Qchem in the
606
other fire cases. Furthermore, since the measurement accuracy of the oxygen consumption method
607
itself is about 10% [16], Qchem in the 17.4- and 7.6-kW cases was judged to be appropriate data.
608
609
In the literature, the value of η in the case of propane gas burning is 0.95 [18]. The average values of
42
610
η in all Qchem during ‘free burning’ were 0.90 and 0.90 in the medium and small scales, respectively,
611
and were close to that in the literature. The uncertainty range of η in the small scale was larger than
612
that in the medium scale. The average values of η in all Qchem cases during the water spray activation
613
were 0.91 and 0.87 in the medium and small scales, respectively, and were close to those during
614
‘free burning’. The convective heat flow rate and radiative heat release rate, Qconv and Qrad,
615
decreased in the period of water spray activation. The convective component, Qconv, decreased
616
because the droplets behaved as a heat sink through heat absorption and evaporation. The radiative
617
component, Qrad, decreased because the small droplets attenuated thermal radiation through a
618
combination of scattering and absorption.
619
620
In the cases of Q = 42.9 and 7.6 kW in the medium and small scales, respectively, the flame on the
621
fire source during the water spray activation continued to burn stably like ‘free burning’. Since the
622
flow rates of water spray were small, the buoyancy produced by the flame was sufficiently stronger
623
than the momentum of the downward flow induced by the droplets discharged during the water
624
spray activation.
625
43
626
In the case of Q = 34.7 kW (medium scale), the tip of the flame was occasionally cracked by the
627
downward flow induced by water sprays. However, after cracking the flame immediately returned to
628
the stable burning condition. In the case of Q = 6.1 kW (small scale), it was observed that the length
629
of the flame was slightly shortened, compared to the case of ‘free burning’, by the downward flow
630
induced by water sprays. Under the above-mentioned spray and burning conditions, the chemical
631
heat release rates, Qchem, were not affected in the period of water spray activation.
632
633
In the case of Q = 26.0 kW (medium scale), the flame was completely cracked and the burning
634
surface of the fire source was exposed by the downward flow induced by water sprays. These
635
cracking and exposing phenomena were periodically observed, but the flame could continue to burn.
636
In the case of Q = 4.6 kW (small scale), the length of the flame was shortened by the downward flow
637
induced by water sprays to about half of the case of ‘free burning’.
638
639
In the case of Q = 26.0 kW (medium scale), the flames cracked by the downward flow induced by
640
the water sprays continued burning while adhering to the rim of the gas burner. Part of the cracked
641
flame was occasionally extinguished at the rim, in which case unburned gaseous fuel might leak
44
642
slightly from the unburned rim of the gas burner. Moreover, it is likely that some combustion
643
products might escape from the exhaust collection system since the 26 kW fire was a weak fire
644
condition subjected to water spray. Therefore, Qchem might slightly decrease during the water spray
645
activation. The proof of this phenomenon can be a subject of future works as the attention of this
646
study was focused on scaling, rather than performing highly accurate calorimetry measurements.
647
Furthermore, the decrease in Qchem due to cooling was small and remained within the range of
648
uncertainty. Considering the findings of White [17, 20], which showed no significant reduction in O2
649
consumption or CO2 generation for gaseous fuel flames exposed to extinguishment by either
650
nitrogen dilution of the oxidizer or water mist spray, we can assume that Qchem for a gaseous fuel fire
651
in the case of 26 kW was not affected by water sprays. In the case of Q = 4.6 kW (small scale), Qchem
652
decreased slightly after water spray activation, but gradually recovered from the decrease, therefore,
653
Qchem in time averaging was almost the same as the value during ‘free burning’. Taken together,
654
under these conditions in the medium and small scales (26.0 and 4.6 kW), the chemical heat release
655
rates, Qchem, were not affected in the period of the water spray activation.
656
657
During Q = 17.4 (medium scale) and 3.1 kW (small scale) cases, the flame was immediately and
45
658
completely cracked and extinguished within 30 seconds by the downward flow induced by water
659
sprays. In the case of 17.4 kW (medium scale) as shown in Fig. 9(d), we performed re-ignition with
660
an igniter several times immediately after the flame had been extinguished (while water was
661
discharging from the nozzle), but the flame was extinguished within 30 seconds each time. In cases
662
of the flame being extinguished, Qchem, Qconv, Qrad, and Qcool could not be estimated due to no steady
663
period in Table 3.
664
665
Different qualitative flame burning characteristics were observed as effects of water spray mass flux
666
in the medium and small scales. As the water spray mass flux around the center of the fire source in
667
the small scale was smaller than that in the medium scale, the flame cracking in the small scale was
668
observed only at the lowest heat release rate of 3.1 kW.
669
46
Heat release rate Q (kW)
60 Qchem Qconv Qrad Qcool Qgas
W.S.
50 40 30 20 10 0 0
240
670 671
480 720 Time t (s)
960
1200
(a) Q = 42.9 kW.
Heat release rate Q (kW)
60
40 30 20 10 0 0
672 673
Qchem Qconv Qrad Qcool Qgas
W.S.
50
240
480 720 Time t (s) (b) Q = 34.7 kW.
47
960
1200
Heat release rate Q (kW)
60 Qchem Qconv Qrad Qcool Qgas
W.S.
50 40 30 20 10 0 0
240
674 675
480 720 Time t (s)
960
1200
(c) Q = 26.0 kW.
Heat release rate Q (kW)
60
40 30 20 10 0 0
676 677
678
Qchem Qconv Qrad Qcool Qgas
W.S.
50
240
480 720 Time t (s)
960
1200
(d) Q = 17.4 kW.
Fig. 9. Heat release rates in the medium scale: Vw = 0.91 L/min, Dv,0.5 = 0.418 mm, Lm = 1.33 m.
48
Heat release rate Q (kW)
10 W.S.
8 6
Qchem Qconv Qrad Qcool Qgas
4 2 0 0
240 480 720 960 1200 1440 1680 Time t (s)
679 680
(a) Q = 7.6 kW.
Heat release rate Q (kW)
10 W.S.
8 6 4 2 0 0
240 480 720 960 1200 1440 1680 Time t (s)
681 682
Qchem Qconv Qrad Qcool Qgas
(b) Q = 6.1 kW.
49
Heat release rate Q (kW)
10 W.S.
8 6
Qchem Qconv Qrad Qcool Qgas
4 2 0 0
240 480 720 960 1200 1440 1680 Time t (s)
683 684
(c) Q = 4.6 kW.
Heat release rate Q (kW)
10 W.S.
8 6
Qchem Qconv Qrad Qcool Qgas
4 2 0 0
240 480 720 960 1200 1440 1680 Time t (s)
685 686
687
(d) Q = 3.1 kW.
Fig. 10. Heat release rates in the small scale: Vw = 0.16 L/min, Dv,0.5 = 0.295 mm, Ls = 0.67 m.
688
50
689
Table 3 Primary data and conditions during ‘free burning’ and water spray activation.
Scale
690
Time range (s) m s (kg/s) Q gas (kW) 300 – 420 0.15 42.94 300 – 420 0.16 34.70 Medium 300 – 420 0.17 26.02 300 – 420 0.18 17.35 Average 0.17 300 – 600 0.11 7.59 300 – 600 0.12 6.14 Small 300 – 600 0.11 4.59 300 – 600 0.11 3.06 Average 0.11
Scale
691
Time range (s) m s (kg/s) Q gas (kW) 480 – 600 0.16 42.94 480 – 720 0.17 34.70 Medium 480 – 720 0.18 26.02 – 0.19 17.35 Average 0.18 720 – 960 0.11 7.59 720 – 960 0.13 6.14 Small 720 – 960 0.11 4.59 – 0.12 3.06 Average 0.11
Q chem (kW) 39.04 ± 1.80 32.61 ± 1.87 23.80 ± 1.95 14.47 ± 2.04 6.31 5.68 3.98 3.00
± ± ± ±
1.22 1.41 1.22 1.29
Q chem (kW) 39.56 ± 1.91 32.15 ± 1.96 22.68 ± 2.05 – 6.28 ± 1.23 5.51 ± 1.41 4.01 ± 1.25 –
r e (m) 0.198 0.203 0.210 0.219
m we (kg/s) 0.006724 0.006938 0.007287 0.007738
Water spray Q cool /m we (kJ/kg) 2338 ± 527 1919 ± 430 1321 ± 340 –
Water spray (s) 430-608 428-727 428-720 420-720
0.102 0.103 0.107 0.109
0.000808 0.000826 0.000882 0.000920
1853 ± 1651 1925 ± 1814 1311 ± 1473 –
673-960 673-970 670-960 660-960
Free burning η 0.91 0.94 0.91 0.83 0.90 0.83 0.93 0.87 0.98 0.90
(–) ± 0.04 ± 0.05 ± 0.07 ± 0.12 ± ± ± ±
0.16 0.23 0.27 0.42
Water spray η (–) 0.92 ± 0.04 0.93 ± 0.06 0.87 ± 0.08 – 0.91 0.83 ± 0.16 0.90 ± 0.23 0.87 ± 0.27 – 0.87
692 693
51
Q conv (kW) 23.43 ± 0.48 20.67 ± 0.41 15.84 ± 0.35 11.29 ± 0.27 4.28 3.53 2.69 1.88
± ± ± ±
0.22 0.17 0.16 0.14
Q rad (kW) 11.32 ± 3.90 9.46 ± 3.26 6.90 ± 2.38 4.20 ± 1.45 1.84 1.68 1.17 0.89
± ± ± ±
0.63 0.58 0.40 0.31
k rad (–) 1.06 1.01 1.02 0.91 1.00 0.87 1.01 0.93 1.02 0.96
Q conv (kW) 15.22 ± 0.32 12.37 ± 0.28 9.09 ± 0.25 –
Q rad (kW) 8.62 ± 2.97 6.46 ± 2.23 3.96 ± 1.37 –
Q cool (kW) 15.72 ± 3.54 13.31 ± 2.98 9.62 ± 2.48 –
3.37 ± 0.19 2.52 ± 0.15 1.92 ± 0.14 –
1.41 ± 0.49 1.41 ± 0.49 0.93 ± 0.32 –
1.50 ± 1.33 1.59 ± 1.50 1.16 ± 1.30 –
694
4.3 Fire cooling performance
695
Figure 11 shows a comparison of the fire cooling performance in the medium and small scales. The
696
circles and triangles indicate Qcool in the medium and small scales, respectively. The value of Qcool at
697
the small scale was converted into that at the medium scale with the scaling relationships shown in
698
Table 1. The error bar indicates measurement uncertainty with 95% confidence. Since the
699
measurement uncertainties of Qcool in both scales were of the same order of magnitude, after
700
converting the values at the small scale into those at the medium scale, the ranges of uncertainties at
701
the small scale became larger than those at the medium scale. Figure 11 indicates that the fire
702
cooling performance at the small scale was obviously smaller than that at the medium scale. This is
703
due to the fact that the water spray mass flux distributions in both scales were different, as shown in
704
Figs. 7 and 8. Especially, the water spray mass flux around the center position on the fire source at
705
the small scale was half the value of that at the medium scale. Therefore, at the small scale, the
706
interaction of water sprays with the fire plume and flame on the fire source decreased.
707
52
20
5/2
S Qcool [kW]
15 10 5 0 -5 10
Medium Small S = 2
20
30
40
50
5/2
S Qchem [kW] 708 709
Fig. 11. Relationship between Qcool and Qchem in the medium and small scales with water sprays.
710
Medium: Vw = 0.91 L/min, Dv,0.5 = 0.418 mm, Lm = 1.33 m. Small: Vw = 0.16 L/min, Dv,0.5 = 0.295
711
mm, Ls = 0.67 m.
712
53
713
4.4 Evaluation of cooling performance using effective interaction area
714
In order to reproduce the fire cooling performance in the medium-scale experiment from the
715
small-scale fire experiment, several experimental conditions in both scales (geometry, heat release
716
rate, working pressure, droplet diameter, and water spray mass flux distribution) must sufficiently
717
satisfy the scaling relationships. As shown in Fig. 11, we could not reproduce the fire cooling
718
performance in the medium scale when the result from the small-scale experiment was scaled up.
719
This was due to the insufficient scaling of the water spray mass flux distribution.
720
721
It is obvious that not all the droplets discharged from a water spray nozzle contribute to fire cooling.
722
Especially, in case of the small-scale experiment, it is likely that many droplets with no interaction
723
with the flame fell into the water receiving tank, since the water spray mass flux distribution in the
724
small scale was more uniform than that in the medium scale. Therefore, we introduced the effective
725
interaction area between the water spray and fire plume to take into consideration only the water
726
mass flux that effectively interacted with the fire [27].
727
728
Figure 12 shows a schematic representation of the model of the effective interaction area and the
54
729
physical parameters in the interaction between the water sprays and plume. First, we considered the
730
effective interaction area, Se, formed by the collision of an upward fire plume produced by a fire
731
source and a downward flow induced by water sprays, based on the spray and plume angles, θ and α,
732
as shown in Fig. 12. The radially distributed velocity and temperature profiles were assumed to be of
733
Gaussian distributions [28]. Generally, the relationship between the half-width of a Gaussian
734
distribution, b, and the height of a plume, z, is given by [29]:
735
b = 0.13z
736
In this study, we selected twice the half-width, 2b (95% of the integrated value of the
737
two-dimensional Gaussian distribution), as the radius of the plume that interacted with the water
738
sprays. As a result, it could be assumed that almost all of the upward plume interacted with water
739
sprays when estimating the radius of the effective interaction area:
740
α = 2 tan −1 ( 2b / z ) = 30°
741
As a result, the plume angle was estimated as α = 30°. Then, we estimated the water flow rate
742
formed by the group of water droplets passing through the effective interaction area from the water
743
spray mass flux distribution as shown in Fig. 8. Finally, we defined the water spray mass flow rate as
744
the actual delivery mass flow rate directly contributing to fire cooling. The radius of the effective
(30)
(31)
55
745
interaction area was estimated by:
rw = Lw tan
θ
746
747
2
(32)
rp = ( Lp − Z f 0 ) tan
α 2
(33)
748
where the spray angle, θ, in Table 2 was used for estimating the effective interaction area, and Zf0
749
indicates the virtual origin using the following formula recommended by Heskestad [30]:
750
2/5 Z f 0 = −1.02 D + 0.083Qchem
(34)
751
Taking the condition rw = rp into account, the distance from the nozzle to the effective interaction
752
area and the radius of the effective interaction area are derived as follows:
Lw = 753
( L − Z ) tan α2 f0
θ
re = Lw tan 754
α
tan + tan 2 2
(35)
θ 2
(36)
755
The actual delivery water spray mass flow rate, mwe, on the fire source was estimated by integrating
756
the water spray mass flux distribution as shown in Fig. 8 from the center to the radius of the effective
757
interaction area, re:
758
mwe = 2π ∫ mw′′ rdr
759
When deriving Eq. (37), the spray profile along the distance from the nozzle exit was assumed to be
re
(37)
0
56
760
a cone shape as shown in Fig. 12. In this study, as the effective interaction areas in the medium and
761
small scales were located at about 0.2 and 0.1 m from the nozzle exit, respectively, a cone shape
762
could be expected.
763
764
It was difficult to accurately estimate the effective amount of water that contributed to flame cooling,
765
as the water droplets interact with the flame. In this study, therefore, it was assumed that only water
766
droplets falling in the cylindrical space formed by the space from the effective interaction area to the
767
burning surface of the fire interacted with the flame and plume, and as a result, they evaporated and
768
performed flame cooling. However, some of the water droplets sprayed from the nozzle might pass
769
through the cylindrical space. Although the water droplets interacted with the flame while passing
770
through the cylindrical space, the water droplets fell on the floor in the outer region of the cylindrical
771
space. As a result, the actual delivery water spray mass flow rate estimated from the effective
772
interaction area tends to be underestimated. This error will be high when the spray angle is much
773
larger than the fire plume angle.
774
775
Since the distributions of the water spray mass flux in Fig. 7 were measured under flameless
57
776
conditions, it is likely that the distribution of the water spray mass flux actually changed due to the
777
interaction of sprays with the fire plume. In particular, the falling trajectory of small-diameter
778
droplets (e.g. diameter < 100 µm) is affected by the interaction of sprays with the fire plume.
779
However, as water droplets with small diameters evaporate immediately in the plume region, they
780
contribute to flame cooling although their falling trajectories change. On the other hand, the falling
781
trajectory of the large-diameter droplets is not significantly affected by the interaction. Although the
782
distribution of the water spray mass flux measured under flameless conditions includes the
783
contribution of both small and large diameter droplets, it can be used effectively for estimating the
784
actual delivery water spray mass flow rate contributing to flame cooling under the conditions with
785
flames.
786
787
Figure 13 shows the relationship between Qcool normalized by the actual delivery water spray mass
788
flow rate, mwe, on the effective interaction area and Qchem in the medium and small scales with water
789
sprays. By normalizing the fire cooling rate by the actual delivery water spray mass flow rate, we
790
succeeded in obtaining well-correlated fire cooling performance in both the medium and small scales.
791
It was difficult to completely satisfy the scaling relationships of the water spray and fire conditions
58
792
in both scales; however, introducing the actual delivery water spray mass flow rate could relax the
793
scaling relationship on the water spray mass flux distribution.
794
795
In this study, although the spray working pressure, total water spray flow rate and droplet diameter
796
were scaled correctly, the water spray mass flux distribution near the fire could not be scaled
797
correctly. Therefore, normalizing the fire cooling rate by the actual delivery water spray mass flow
798
rate was introduced for scaling relaxation. On the other hand, if the water spray mass flux
799
distribution near the fire was scaled correctly in addition to the spray working pressure and droplet
800
diameter, the fire cooling rate would have been scaled correctly without normalizing by the actual
801
delivery water spray mass flow rate. In this case, the scaling of the water spray mass flux distribution
802
in areas away from the fire can be relaxed. In the scaling relaxation based on this new perspective,
803
although the spray working pressure, droplet diameter and the water spray mass flux distribution
804
near the fire will be scaled correctly, the total water spray mass flow rate will not be scaled correctly.
805
Scaling relaxation focusing on the scaling of the water spray mass flux distribution near the fire
806
would be also worth investigating as a future research.
807
59
z
Nozzle
2b
Water sprays
Vel. and temp. b profiles
Lw
θ
Se
L α Lp
z
Cylindrical space
D Q r Fire
Zf0
qw’’ Water flux distribution 0
808 809
r
re
Fig. 12. Schematic representation of the model of the effective interaction area.
Qcool /mwe [kJ/kg]
4000 3000
Medium Small S = 2
2000 1000 0
-1000 10
20
30
40
50
5/2
S Qchem [kW] 810 811
Fig. 13. Relationship between Qcool normalized by the actual delivery water spray mass flow rate,
812
mwe, on the effective interaction area and Qchem in the medium and small scales with water sprays.
813 60
814
5. Conclusions
815
Even if the scaling of the water spray flow rate, the droplet diameter, the working pressure, and the
816
heat release rate was satisfactory, when the geometrical scaling of the nozzles was not sufficient, the
817
scaling of the water spray mass flux distributions on the fire sources for both scales was not satisfied.
818
In the scaling of a fire experiment with water sprays, normally, it is quite challenging to sufficiently
819
establish the experimental conditions, especially when nozzles are not geometrically similar. In this
820
study, we conducted a series of medium and small-scale fire cooling experiments and established a
821
new scaling relaxation for scaling of the water spray mass flux distribution. The main conclusions
822
are as follows:
823
(1) The fire cooling performance obtained from the medium-scale experiment could not be
824
reproduced using the small-scale experiment with insufficient scaling of the water spray mass flux
825
distribution.
826
(2) By normalizing the fire cooling rate by the actual delivery water spray mass flow rate, we
827
succeeded in obtaining well-correlated fire cooling performance for both the medium and small
828
scales.
829
(3) Introducing the actual delivery water spray mass flow rate can relax its scaling relationship on
61
830
the water spray mass flux distribution.
831
(4) The actual delivery water spray mass flow rate estimated from the effective interaction area tends
832
to be underestimated when the spray angle is much larger than the fire plume angle.
833
834
The global measurements data with uncertainty described in this paper constitute a useful database
835
for CFD code development and validation for scenarios of fire cooling by water sprays before
836
conducting any parametric or complex study. A number of future experimental studies are also
837
identified.
838
839
Acknowledgments
840
Part of this work was conducted with the support of the JSPS KAKENHI under Grant Number
841
JP16KK0125.
842
62
843
Appendix A. Measurement uncertainty
844
Normally, measurement uncertainty at a 95% confidence level, U, comprises the bias limit, B, the
845
precision index of average, Sx , and Student t value as follows [31]:
846
U = B2 + ( tSx )
847
The bias limit, B, is the estimated value of the upper limit of bias error. The product of the precision
848
index of average and Student t value is the estimated value of the precision error limit. The precision
849
index of average is evaluated as follows:
2
(A.1)
N
x=
∑x
i
i =1
850
N
(A.2) N
Sx = 851
∑( x − x ) i =1
2
i
N ( N − 1)
(A.3)
852
where N is the number of sampling data and x is the sampling data. In the fire experiments, we
853
measured data at 1-s intervals and evaluated the data as the value averaged for 180, 240, and 300
854
seconds. As the number of sampling data was larger than 30, Student t value was evaluated as two.
855
The bias limits were evaluated as half of the measuring precision for each instrument. Table A.1 lists
856
the bias limits for all the instruments, the precision indexes of average for all the measurement
857
values and sensitivity for all the measurements during ‘free burning’ at the heat release rate of 42.9
63
858
kW in the medium scale.
859
860
A1. Convective component of the chemical heat release rate
861
The convective component of the chemical heat release rate was calculated as follows:
862
Qconv = ms Cp _ gas ∆Tgas
863
where ms, Cp_gas, and ∆Tgas are the mass flow rate of the smoke flowing through the smoke duct, the
864
specific heat of mixed exhaust gas at constant pressure, and the rise in temperature of the smoke
865
flow in the duct close to the hood, respectively. The mass flow rate, ms, was estimated from the
866
pressure difference of the Pitot tube installed in the duct and the rise in temperature, ∆Td, in the duct
867
at the installed position of the Pitot tube. The convective component of the chemical heat release rate
868
depended on the input parameters, ∆Tgas, ∆Td, and pressure difference, ∆P, of the Pitot tube as
869
follows:
870
Qconv = Qconv ( ∆Tgas , ∆Td , ∆P)
871
The absolute sensitivity and the relative sensitivity of the convective component to its input
872
quantities are as follows:
θ ∆T = gas
873
(A.4)
(A.5)
∂Qconv ∂∆Tgas
(A.6)
64
∂Qconv ∂∆Td
(A.7)
∂Qconv ∂∆P
(A.8)
θ∆T = d
874
875
θ∆P =
Rθ∆Tgas = 876
Rθ∆Td = 877
Rθ∆P = 878
∂Qconv ∆Tgas ∂∆Tgas Qconv
ave
(A.9)
∂Qconv ∆Td ∂∆Td Qconv
ave
(A.10)
∂Qconv ∆P ∂∆P Qconv
ave
(A.11)
879
Estimating the convective component of the chemical heat release rate based on three parameters,
880
we can represent the bias limit, B, and the precision index of average, Sx , as follows:
881
B = θ ∆Tgas B∆Tgas
882
Sx = θ ∆Tgas Sx ∆Tgas
883
The measurement uncertainty at a 95% confidence level of the convective component of the
884
chemical heat release rate was estimated by using Eq. (A.1).
(
(
) + (θ 2
∆Td
) + (θ
B∆Td
) + (θ
2
∆Td
1/ 2
2
Sx ∆Td
∆P
2 B∆P )
) + (θ
(A.12) 1/ 2
2
∆P
2 Sx ∆P )
(A.13)
885
886
A2. Radiative component of the chemical heat release rate
887
The radiative component of the chemical heat release rate was calculated as follows.
888
2 ′ Qrad = 4πrrad krad ( χrad ) qrad
889
where krad is the correction factor obtained from Eq. (20), and q’rad is the radiative heat flux
(A.14)
65
890
measured by the water-cooled radiometer. Furthermore, the correction factor, krad, depended on the
891
radiative fraction of the chemical heat release rate, χrad. The radiative component of the chemical
892
heat release rate depended on the input parameters χrad and q’rad as follows:
893
′ ) Qrad = Qrad ( χrad , qrad
894
The sensitivity of the radiative component to its input quantities can be estimated based on Equation
895
(A.15). The bias limit, B, and the precision index of average, Sx , can be represented as follows:
896
(
(
B = (θχ Bχ ) + θqrad ′ Bqrad ′ 2
(A.15)
))
2 1/2
(A.16)
897
Sx = θqrad ′ Sxqrad ′
898
The measurement uncertainty at a 95% confidence level of the radiative component was estimated
899
by using Eq. (A.1).
(A.17)
900
901
A3. Chemical heat release rate
902
The chemical heat release rate depended on many input parameters, the volume fractions of gases,
903
XO2, XCO2, XCO, XH2O, the rise in temperature of smoke, ∆Td, and the pressure difference of the Pitot
904
tube in the smoke duct, ∆P, as follows:
905
Qchem = Qchem X O2 , X CO2 , X CO , X H2O , ∆Td , ∆P
(
)
(A.18)
66
906
The sensitivity of the chemical heat release rate to its input quantities can be estimated based on
907
Equation (A.18). The bias limit and the precision index of average can be represented as follows:
908
909
((
B = θO2 BO2
((
) ( 2
Sx = θO2 SxO2
+ θCO2 BCO2
) + (θ 2
CO2
)
2
SxCO2
(
+ (θCO BCO ) + θ H2O BH2O 2
) + (θ 2
CO
(
) ( 2
+ θ∆Td B∆Td
SxCO ) + θH2O SxH2O 2
) + (θ 2
∆Td
)
2
+ (θ∆P B∆P )
Sx∆Td
)
2
2
)
1/2
+ (θ∆P Sx∆P )
(A.19) 2
)
1/2
(A.20)
910
The measurement uncertainty at a 95% confidence level of the chemical heat release rate was
911
estimated by using Eq. (A.1).
912
913
Through the fire experiments, we obtained many measurement values: gas concentrations (oxygen,
914
carbon dioxide, carbon monoxide and water vapor), rise in temperature, and pressure difference
915
measured by the Pitot tube in the smoke duct. As the values of the precision index of average of the
916
data measured by instruments were significantly less than the values of the bias limit of the
917
instruments, the measurement uncertainty of the data measured was dominated by the bias limits of
918
the instruments. The chemical heat release rate estimated by the oxygen consumption method was
919
dominated by the bias limit of the oxygen analyzer (POT8000). The effect of other measurement
920
values except for this parameter on the chemical heat release rate was small.
921
67
922
A4. Fire cooling rate
923
The fire cooling rate with uncertainty was estimated from the chemical and radiative heat release
924
rates, the convective heat flow rate, and these uncertainties as follows:
925
Qcool ± UQcool = ( Qchem − Qconv − Qrad ) ± UQ2chem + UQ2conv + UQ2rad
(A.21)
926
927
A5. Water spray mass flux
928
The water spray mass flux, m''w, was estimated as follows:
mw'' = 929
M cup Acup ∆tcup
(A.22)
930
As the contribution of Acup and ∆tcup to uncertainty of water spray mass flux was small compared to
931
Mcup, we only considered the effect of Mcup on the water spray mass flux in the uncertainty analysis.
932
The precision index of average was estimated from 32 data (4×8) except for the center position (4
933
data at the center position), obtained from experiments repeated 4 times and water spray mass flux
934
distributions obtained from cups arranged every 45 degrees as shown in Fig. 6. As the number of
935
data was larger than 30, we could evaluate Student t value as two (Student t value of 3.182 at the
936
center position). The water spray mass flux was dominated by the precision index of average of the
937
mass of water received by the cup, Mcup. The effect of the bias limit of instruments on the water
68
938
spray mass flux was small. The measurement uncertainty at a 95% confidence level of the water
939
spray mass flux was estimated by using Eq. (A.1).
940
941
Table A.1 Uncertainty analysis under the condition of ‘free burning’ (Q = 42.9 kW); parameters,
942
values, absolute sensitivity, relative sensitivity, bias limit, and precision index of average. Note that
943
the values of absolute and relative sensitivities are unique to the specific measurement conditions.
Q
Q conv
Q rad
Parameter
Value
Absolute sensitivity, θ
∆T gas
166 °C
1.6×10
142 °C
−2.8×10
∆P
7.62 Pa
1.5×10
χ q' rad ∆P X X
944
-2
∆T d
∆T d
Q chem
-1
A O2
A
CO2 A X CO S X H2O
0
3.9×10 2
0.85 kW/m 142 °C 7.62 Pa 19.39% 1.15%
Bias limit, B
Precision index of average, ̅ Sx
0
1K
6.79×10 K
-1
1K
4.74×10 K
-1
0.25 Pa
0
0.1
3.24×10 Pa 0
1.1×10
−1.7×10 5.0×10
1
0.29
Relative sensitivity, Rθ
1.0×10
1
0
1.3×10
1.0×10
-2
-1
−4.7×10
−1.7×10
0
-1
2.6×10
5.0×10 3
−2.6×10
2
−5.7×10
1
−1.3×10
-1
−1.7×10
2
−3.1×10
1
−1.1×10
13 ppm
−9.5×10
1.33%
−3.2×10
-4 -2
-1 -1
-4
-2
2
-4
6.25×10
-4
5.0×10
-6
5.0×10
-3
2.0×10
945
946
Appendix B. The model of a primary delay system in the preconditioning process
947
69
-3
2
4.32×10 kW/m 1.25×10 kW/m -1 1K 4.74×10 K -2 0.25 Pa 3.24×10 Pa -5
1.00×10
-6
7.83×10
-6
0.12×10
-5
1.97×10
948
It was assumed that the gas concentration in the air tanks used in the preconditioning process has
949
always spatially uniform distribution. The uniform gas concentration changes over time as an
950
exponential process. The estimation model equation is shown as follows.
951
w w w X out = 1 − exp − t 1 − exp − t 1 − exp − t X in V1 V2 V3
952
where, Xout and Xin are the volume fractions of input and output gases, V1, V2, and V3 are the internal
953
volume of the first air tank, the air space of the water cooling tank, and the internal volume of the
954
second air tank, w and t are the volume flow rate of gases drawn by the pump and elapsed time,
955
respectively. This equation shows a generic primary delay system [32].
956
70
(B.1)
957
References
958
[1] G. Heskestad, Physical modeling of fire. J. Fire Flammability 6 (1975) 254–273.
959
[2] G. Heskestad, Scaling the interaction of water sprays and flames, Fire Safety Journal 37 (2002)
960
535–548.
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75
Highlights
1. Fire cooling performance by sprays was examined using model scale experiments.
2. Scaling relaxation was developed for the scaling of the spray mass flux distribution.
3. Scaling relaxation could account for cooling performance under incomplete scaling.
4. Global measurements can be used for CFD validation on the fire cooling by sprays.
Conflict of Interest
There is no conflict of interest in this study.
S0379-7112(19)30079-7
DOI:
https://doi.org/10.1016/j.firesaf.2020.102965
Reference:
FISJ 102965
To appear in:
Fire Safety Journal
Received Date: 11 February 2019 Revised Date:
5 February 2020
Accepted Date: 5 February 2020
Please cite this article as: F. Tanaka, W. Mizukami, K.A.M. Moinuddin, Fire cooling performance by water sprays using medium and small-scale model experiments with scaling relaxation, Fire Safety Journal (2020), doi: https://doi.org/10.1016/j.firesaf.2020.102965. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Futoshi Tanaka: Conceptualization, Methodology, Software, Formal analysis, Data curation, Writing - Original draft, Supervision. Wataru Mizukami: Validation, Investigation, Data curation, Visualization. Khalid A.M. Moinuddin: Conceptualization, Methodology, Writing- Reviewing and Editing.
1
Fire cooling performance by water sprays using medium and
2
small-scale model experiments with scaling relaxation
3
Futoshi Tanakaa*, Wataru Mizukamib, and Khalid A.M. Moinuddinc
4 5 6
a
7
3-9-1 Bunkyo, Fukui-shi, Fukui 910-8507, Japan
Mechanical Engineering, Faculty of Engineering, University of Fukui
8 9 10
b
Mechanical Engineering, Graduate School of Engineering, University of Fukui
3-9-1 Bunkyo, Fukui-shi, Fukui 910-8507, Japan
11 12
c
13
P.O. Box 14428, Melbourne, Victoria 8001, Australia
Center for Environmental Safety and Risk Engineering, Victoria University
14 15
*
16
Tel: +81-776-27-9817, Fax: +81-776-27-8748
17
Email: [email protected]
18
Postal address: Mechanical Engineering, Faculty of Engineering, University of Fukui,
19
3-9-1 Bunkyo, Fukui-shi, Fukui 910-8507, Japan
Corresponding author:
20 21
1
22
Abstract
23
The fire cooling performance by water sprays is investigated in medium and small-scale fire cooling
24
experiments. The scaling relationships considered are the fire diameter, spray height, heat release
25
rate, spray angle, flow rate, working pressure, and droplet diameter. Full-cone-type spray nozzles of
26
different sizes are used in both scale experiments. Although spray conditions (spray angle, flow rate,
27
pressure, and droplet diameter) satisfying the scaling relationships are used, when the geometrical
28
scaling of the nozzles is not sufficient, the water spray mass flux distributions generated by the
29
nozzles do not fulfill the scaling relationship. To resolve this problem, we propose a new scaling
30
relaxation for scaling the fire cooling effect of water sprays even under incomplete scaling
31
conditions in the water spray mass flux distributions. In the scaling relaxation, we propose an
32
effective plane in which the group of water droplets collides with the fire plume, and assume that
33
only the water droplets passing through the effective plane contribute to fire cooling. Based on the
34
experimental data, we show that scaling with sufficient accuracy is possible by normalizing with the
35
spray flow rate directly contributing to the fire cooling. The scaling accuracy tends to decrease with
36
the increasing spray angle.
2
37
Keywords:
38
Fire cooling
39
Water sprays
40
Scaling relaxation
41
Model experiments
42
3
43
Nomenclature
44
Acup
opening area of the cup (m2)
45
b
half-width of Gaussian distribution (m)
46
Cpi
specific heat of each gas component species (kJ/(kg·K))
47
Cp_gas
specific heat of mixed exhaust gas (kJ/(kg·K))
48
D
fire source diameter (m)
49
Dd
diameter of the smoke duct (m)
50
Dv
volumetric diameter of droplet (mm)
51
Dv,0.5
median volumetric diameter of droplet (mm)
52
E'
net heat of combustion per unit volume of oxygen (MJ/m3)
53
E"
net heat of combustion per unit volume of oxygen consumed in the burning of carbon
54
monoxide (MJ/m3)
55
g
gravitational acceleration (m/s2)
56
H
relative humidity in percent (%)
57
∆H
heat of combustion (MJ/kg)
58
krad
correction factor for a radiative heat release rate (–)
59
L
length from burning surface of a fire to a spray head, characteristic length (m)
60
Lp
length from burning surface to effective interaction area (m)
61
Lw
length from spray head to effective interaction area (m)
62
Mcup
mass of water received by the cup (kg)
63
Me
molecular weight of the exhaust gas mixture (kg/kmol)
64
ms
mass flow rate of smoke in the smoke duct (kg/s)
65
mwe
actual delivery water spray mass flow rate (kg/s)
66
m″w
water spray mass flux (kg/(m2·s))
67
P
pressure (kPa)
68
PH2O
water vapor pressure (kPa)
69
Pw
working pressure of water spray (MPa)
70
Q
desired heat release rate (kW)
71
Qchem
chemical heat release rate measured by the oxygen consumption method (kW)
72
Qconv
convective heat flow rate (kW)
73
Qcool
rate of fire cooling by water sprays (kW)
74
Qgas
theoretical heat release rate estimated from mass flow rate of fuel (kW)
4
75
Qloss
rate of heat loss (kW)
76
Qrad
radiative heat release rate (kW)
77
qrad
radiative heat flux (kW/m2)
78
R0
universal gas constant (kJ/(kmol·K))
79
Re
gas constant of the exhaust gas mixture (kJ/(kg·K))
80
Red
droplet Reynolds number (–)
81
r
radius coordinate for water mass flux distribution (m)
82
re
radius of effective interaction area (m)
83
rrad
distance from fire center to the face of a radiometer (m)
84
S
scale ratio (–)
85
Se
effective interaction area (m2)
86
T
temperature (K)
87
∆T
rise in temperature (K)
88
t
time (s)
89
∆tcup
discharging time (s)
90
us
velocity in the smoke duct (m/s)
91
Va
volume flow rate of ambient air drawn from the hood (m3/s)
92
Vs
volume flow rate in the smoke duct (m3/s)
93
Vw
spray flow rate (L/min)
94
X
mole (volume) fraction (–)
95
Y
mass fraction (–)
96
Zf0
virtual origin (m)
97
x, y, z
the axes of coordinates (m)
98 99
Greek letters
100
Ω
spatial distribution function (–)
101
α
plume angle (°)
102
β
correction factor in the smoke duct (–)
103
γ
empirical constant for drop size distribution (–)
104
η
combustion efficiency (–)
105
θ
spray angle (°)
106
ρs
density of smoke (kg/m3)
5
107
σ
empirical constant for drop size distribution (–)
108
oxygen depletion (–)
109
χrad
radiative fraction (–)
110 111
Superscripts
112
A
gas components without water vapor in the gas analyzer
113
AW
gas components with water vapor in the gas analyzer
114
DT
dew point temperature
115
S
gas components in the smoke duct
116
°
gas components in the ambient air
117 118
Subscripts
119
CO
carbon monoxide
120
CO2
carbon dioxide
121
H 2O
water vapor
122
N2
nitrogen
123
O2
oxygen
124
amb
ambient condition
125
m
medium scale
126
s
small scale
127
6
128
1. Introduction
129
130
In the 1970s, Heskestad derived a set of scaling relationships for the thermo-fluid dynamic
131
interaction of water sprays with fires in geometrically similar spaces based on the Froude modeling
132
concept [1]. Subsequently, the scaling relationships proposed were used to evaluate fire extinction
133
similarity on 1:10, 1:3 and 1:1 scale fire experiments with water sprays in a large space, and the
134
effectiveness of the scaling theory was validated [2–3].
135
136
Yu investigated the effect of droplet size on the scaling relationships derived by Heskestad for
137
applying the scaling relationships to the extinguishment phenomenon by water mist with a low
138
Reynolds number based on the droplet diameter (Red ≤ 1) [4]. The finding from this investigation
139
indicated that droplet size for low Reynolds number conditions should be scaled with the 1/4-power
140
of length scale, instead of the 1/2-power found for high Reynolds number conditions. Later,
141
Jayaweera and Yu confirmed the droplet size scaling requirement for low Reynolds number
142
conditions with a series of fire cooling experiments [5, 6]. This improvement was warranted as the
143
scaling relationships derived by Heskestad were developed for sprinklers with significant inertia
7
144
compared to gas flow (Red > 1). Furthermore, Yu derived a general rule for the scaling of the
145
diameter of a droplet under a wide range of droplet Reynolds numbers, and validated this general
146
rule [7]. After improving the scaling relationships, Yu et al. conducted a series of fire suppression
147
experiments to evaluate the efficacy of physical scaling of water mist suppression of a gas fire, pool
148
fire and solid combustible fire in enclosures [8-10]. These experiments were conducted using full
149
and 1:3 scale enclosures. The results showed that water mist cooling and fire development could be
150
reasonably reproduced during enclosure fires by physical scaling based on Froude modeling.
151
Furthermore, Yu et al. presented an evaluation of the scaling of fire extinguishment by water mist in
152
a large industrial machinery enclosure [11]. Four fire scenarios were selected using full and 1:2 scale
153
enclosures. Based on the obtained results, they concluded that the scaling relationships for water
154
mist fire suppression could be used to determine the fire extinguishing performance of full-scale
155
water mist protection.
156
157
In addition to Yu’s research to evaluate the efficacy of physical scaling of water mist, many model
158
scale experiments have been conducted for fires in large structures with water sprays where
159
full-scale fire experiments were difficult. For example, many model-scale studies have been
8
160
conducted on the influence of water sprays installed in tunnels on fires. Ingason carried out 1:23
161
model scale tunnel fire tests with a water spray system in order to capture the basic behavior of water
162
sprays in a longitudinal tunnel flow [12]. Li and Ingason conducted 1:15 model scale tunnel fire tests
163
to clarify the effectiveness of an automatic sprinkler system in a tunnel with longitudinal ventilation
164
[13]. Furthermore, Li and Ingason examined how the combustion products were released while a
165
water sprinkler system was active, using a 1:4 scale model tunnel [14].
166
167
Heskestad proposed the use of geometrically similar nozzles in order to preserve the spray
168
trajectories [2, 3]. Many model scale experiments with water sprays have been conducted using
169
geometrically similar nozzles following the suggestion of Heskestad in addition to satisfying scaling
170
relationships for the working pressure, spray flow rate, and average diameter of droplets. In principle,
171
when the spray trajectory is preserved, the scaling of the water spray mass flux distribution on a
172
floor is automatically satisfied.
173
174
In model scale fire experiments with water sprays, it is necessary to satisfy the scaling relationships
175
concerning geometric similarity including the nozzle, heat release rate of the fire, working pressure
9
176
of the water spray nozzle (determining the initial speed of water droplets), spray flow rate, average
177
diameter of droplets, and water spray mass flux distribution on a floor, and it is quite challenging to
178
fulfill all scaling relationships. In order to prepare a particularly geometrically accurate scaled-down
179
nozzle, a special nozzle must be developed or selected from a number of existing nozzles. As a result,
180
it is quite challenging, or the geometrical similarity of the nozzles must be compromised.
181
182
If geometrically similar nozzles following the suggestion of Heskestad can’t be used, inconsistency
183
in the scaled water spray mass flux distribution on a floor may occur. In this study, we propose a
184
new scaling relaxation to estimate the fire cooling performance in the medium scale from that in the
185
small scale under the condition of inconsistency in the scaled water spray mass flux distribution in
186
medium and small-scale models. In the new scaling relaxation, the actual delivery water spray mass
187
flow rate is used for evaluating the fire cooling performance at medium and small scales.
188
10
189
2. Experimental method
190
In this study, a series of medium and small-scale fire experiments with water sprays were conducted
191
to evaluate the fire cooling performance by water sprays, and Froude’s scaling relationships were
192
applied to the experiments on both scales to evaluate the performance of similarity. Table 1 shows
193
the scaling relationships based on the Froude modeling [1–7]. As the Reynolds number of the flow
194
around a droplet was greater than unity under our experimental conditions, we chose the 1/2 power
195
of scale ratio as per the scaling of droplets [7].
196
Table 1 Scaling relationships for characteristic parameters [1–7].
Unit
197
Scaling (S = scale ratio)
Heat release rate (HRR)
Q [kW]
Q full
=
S
Velocity
u [m/s]
u
=
S
3
full
5/2
Q model
1/2
u
5/2
model
=
S
t full
=
S
T [K]
T full
=
S T model
Pressure
P [kPa]
P
=
S P
Spray flow rate
V w [L/min]
V w full
=
S
Mass flux
m'' [kg/(m s)]
2
m'' full
=
S
Median diameter
D v,0.5 [mm]
D v,0.5 full =
S
Volume flow rate
V [m /s]
V
Time
t [s]
Temperature
full
full
V
model
1/2
t model
0 1
5/2 1/2 1/2
model
V w model m'' model D v,0.5 model
198
199
2.1. Overview of the experimental apparatus
200
Figure 1 shows the experimental apparatus used for this study. The apparatus was constructed as a 11
201
semi-open space, which was 1.6 m wide, 1.6 m deep, and 2.3 m high, and comprised of a hood, a
202
smoke duct and a suction fan for collecting and exhausting the gas including combustion products, a
203
water tank for receiving water spray droplets, a fire source, a water spray equipment, and a gas
204
analyzer system. The size of the hood was 1.6 m in width, 1.6 m in depth, and 1.1 m in height. The
205
upper part of the hood was made of stainless-steel plate of 1.0 mm in thickness and 0.2 m in height,
206
and the lower part of the hood was made of a calcium silicate board of 5 mm in thickness and 0.9 m
207
in height. The smoke duct connecting the hood with the fan was 0.25 m in diameter and made of
208
galvanized steel plates of 0.5 mm in thickness. The size of the water tank for receiving and
209
collecting water spray droplets was 1.5 m in width, 1.5 m in depth, and 0.6 m in height, and was
210
made of stainless-steel plate of 2.0 mm in thickness.
211
212
In the medium and small-scale experiments, two sizes of propane gas burners with inner diameters
213
of 0.155 and 0.08 m, respectively, were used as the fire source, and the rims of the gas burners were
214
made of steel pipe with thicknesses of 5 and 4.2 mm, respectively. The propane gas burners were
215
filled with many ceramic balls of 5 mm in diameter. The burning surfaces of the fire sources were
216
placed directly below a water spray head. During the experiments, the mass flow rate of propane gas
12
217
was regulated by a mass flow controller (model 3660, KOFLOC) to ensure a constant value.
218
219
The length from the spray head to the burning surface of the fire sources was used as the
220
characteristic length, L, in the scaling theory. Equation (1) is the definition of scale ratio, S. S =
221
Lm Ls
(1)
222
The parameters Lm and Ls indicate the characteristic lengths of medium and small scales measured as
223
Lm = 1.33 m and Ls = 0.67 m, respectively. The scale ratio between the medium and small scales was
224
2:1.
225
226
We used the oxygen consumption method developed by Parker [15] and Janssens [16] to measure
227
the heat release rate (HRR) of a fire during ‘free burning’ and water spray activation. In the
228
preconditioning process, the sampling gas drawn from the smoke duct was passed through the first
229
air tank, a cooling bottle filled with water for removing large soot and dust, a hand-made
230
dehumidifier for reducing the relative humidity of the sampling gas, and a filter for completely
231
removing soot, and then collected in the second air tank. Sensors were installed in the first and
232
second air tanks for measuring the relative humidity and gas temperature in the tanks. Furthermore, a
13
233
sensor was also placed in ambient air for measuring the relative humidity and temperature in the air.
234
The water cooling during the pretreatment process has the problem of CO and CO2 dissolution, so if
235
the smoke includes no large soot and dust, water cooling should not have been used in the
236
pretreatment process. In fact, for the clean-burning propane gas in our study there was no need for
237
the water cooling.
238
239
The hand-made dehumidifier consisted of a gas flow section with many fins cooled with ice water.
240
The gas with high humidity was cooled, and its humidity was reduced by condensation. The dew
241
point temperature of the hand-made dehumidifier incorporated in the preconditioning system was
242
about 5 °C. The O2 gas analyzer (POT8000, Shimadzu Corporation, gas analyzer based on the
243
paramagnetic principle) and CO/CO2 gas analyzer with a built-in thermo-electric dehumidifier
244
having the gas dew point temperature of 3.5 °C (CGT7000, Shimadzu Corporation, gas analyzer
245
based on the infra-red (IR) absorption method and Beer-Lambert law) drew the preconditioned gas
246
from the second air tank and measured the concentration of the sampling gas. The dew point of the
247
sample gas entering the O2 and CO/CO2 analyzers was 5 °C and 3.5 °C, respectively.
248
14
249
The oxygen consumption method developed by Parker [15] assumes that the sampling gas is
250
completely dehumidified before being introduced into a gas analyzer. Unfortunately, our hand-made
251
dehumidifier in the preconditioning process could not completely remove all the water vapor from
252
the sampling gas; the dew point temperature was 5 °C for the O2 gas analyzer and 3.5 °C for the CO2
253
and CO analyzer, so we estimated the volume fractions of the completely dehumidified sampling
254
gases assuming that slight water vapor remained in the sampling gases in the second gas tank after
255
the dehumidifier as follows:
X
Ao O2
=
256
X
Ao CO2
X OAW 2
(1 − X ) DT 5 H 2O
=
257
X = A O2
258
A X CO =
AW X CO 2
(1 − X
(2)
o
DT 3.5 H2O
)
(3)
XOAW 2
(1− X ) DT 5 H2O
A XCO = 2
259
o
AW XCO 2
(1− X
DT 3.5 H2O
AW X CO
(4)
)
(5)
260
(1 − X
261
where
XHDT2O5
262
and 3.5 °C, respectively, and
DT 3.5 H 2O
)
and
(6)
XHDT2O3.5
are the volume fractions of water vapor at dew point temperatures of 5
XkAW is the volume fraction of sampling gases with slight water vapor 15
263
measured by the gas analyzers.
264
265
The transport delay time from the flame location through the exhaust collection and sampling probe
266
to the preconditioning system was several seconds (about 5 seconds or less). In the preconditioning
267
process, as the first and second air tanks with the internal volume of 1.5 L and the water cooling tank
268
with air space of about 0.7–0.8 L were used under the sampling gas flow rate of 5 L/min, a large
269
time delay occurred. The preconditioning process with several air tanks can be modeled as a primary
270
delay system under the assumption that the gas concentration in the air tanks is always uniform.
271
Figure 2 indicates the estimated time lag of the preconditioning system and the estimated time lag of
272
the combined preconditioning system and O2 gas analyzer (POT8000). For instance, when gas with a
273
concentration of 100% is introduced to the preconditioning system, the time delay is about 61
274
seconds for reaching a 90% concentration at the output of the preconditioning system. The time
275
delays of the CO2 and CO gas analyzer and the O2 gas analyzer are 30 seconds (CGT7000; 90%
276
response time) and 45 seconds (POT8000; 90% response time), respectively. When we combined the
277
O2 gas analyzer (POT8000) with the preconditioning system during O2 measurement, we found that
278
the time delay for obtaining a 90% response is about 108 seconds. The time delay for obtaining a
16
279
99% response is about 208 seconds. The non-response time from the ignition to the response of the
280
gas analyzers to the gases concentration has been corrected by shifting the time curve of the gas
281
concentration for estimating the chemical heat release rate of fire.
282
283
The mass flow rate of the exhaust gas in the smoke duct was estimated from the rise in temperature
284
in the smoke duct and velocity measured by a thermocouple and a Pitot tube, respectively, installed
285
in the smoke duct as shown in Fig. 1. Leakage or escape of combustion products from the exhaust
286
collection system was not reliably investigated in our system and might have occurred, particularly
287
for the weak fire conditions subjected to spray. Radiative heat flux from the fire was measured by a
288
water-cooled radiometer (RE-4, Tokyo Seiko Co., Ltd.) which was installed 1 m away from the fire.
289
17
290 291
Fig. 1. Schematic of the experimental apparatus: the water spray, fire source, and gas analyzer
292
systems (unit: m).
18
Gas concentration [%]
100 Preconditioning 90% response 61 s
Precon. + O 2 Analyzer 90% response 108 s
50 Input Preconditioning Precon. + O 2 Analyzer
0 0
60
120
180
Time [s] 293 294
Fig. 2. Time delay during gas concentration measurement estimated by the model of a primary delay
295
system.
296
297
2.2. Chemical heat release rate measured by the oxygen consumption method
298
The oxygen consumption method requires the mole (volume) fractions of oxygen, carbon dioxide,
299
carbon monoxide and water vapor to calculate the heat release rate. The mole fractions of the
300
incoming ambient gases and the gases drawn into the analyzers are defined in the same way as those
301
by Parker and Janssen [15, 16]. In Eqs. (7)-(11), the superscripts °, S, and A of the mole fractions
302
indicate the gas components in the ambient air, the smoke duct, and the gas analyzers, respectively.
303 19
304
The chemical heat release rate, Qchem, of the fire source is calculated using Parker’s method as
305
follows [15]:
306
A E "− E ' 1 − φ X CO Qchem = φ − A E ' 2 X O2
307
1 − φ A X Hs 2O o o A Va = Vs 1 − X O2 φ + X O2 A X CO2 + X CO + X O 1 − X Hs 2O 2
308
where E' is the net heat of combustion per unit volume of oxygen (propane: 16.7 MJ/m3, derived
309
from ∆HO2 = 12.77 MJ/kg referred to 25 °C), and E" is the net heat of combustion per unit volume of
310
oxygen consumed in the burning of carbon monoxide (23.1 MJ/m3, derived from ∆HO2,CO = 17.69
311
MJ/kg referred to 25 °C) [17, 18]. The volumetric flow rate of the ambient air drawn from the hood
312
is estimated by Eq. (8). Va and Vs are the volume flow rate referred to standard conditions (25°C, 1
313
atm). The volume fraction of water vapor,
314
immediately after being sampled from the smoke duct in this study. No condensation was observed
315
in the first gas tank or sampling hose even during water spray activation. Oxygen depletion, , is
316
defined as:
317
o 1 − X CO − X Ho 2O 2 X Oo2 − X OA2 A A 1 − X CO − X CO 2 φ= X OA2 X Oo2 1 − A A 1 − X CO − X CO 2
o E ' X O2 Va
(7)
XHs 2O
−1
(8)
, in Eq. (8) was measured in the first gas tank
(9)
20
X Oo2
o XCO 2
318
The initial volume fractions of oxygen,
319
These were measured as the gas concentration of dehumidified air through the preconditioning o
process. Here,
321
X Oo2
322
X Oo2 = X OA2 1 − X Ho 2O
323
o A X CO = X CO 1 − X Ho 2O 2 2
o XCO 2
o
(
o
(
, refer to the incoming air.
o
X OA2
320
and
, and carbon dioxide,
and
A XCO 2
are defined as the initial concentrations of dehumidified air. Then,
are given by:
)
(10)
)
(11)
324
Equations (10) and (11) are substituted into Eq. (9) for and into Eqs. (7) and (8) for the heat
325
release rate of a fire when water vapor is trapped in the preconditioning process.
326
327
In this study, the temperature and relative humidity were measured to estimate the volume fraction
328
of water vapor at three locations. The first location was in the ambient air, the second location was in
329
the first gas tank immediately after being sampled from the smoke duct, and the final location was in
330
the second gas tank after dehumidification. The measurements of the temperature and relative
331
humidity were made every minute. A commercially available thermo-hygrometer was used for the
332
measurements. The temperature and relative humidity were measured by a thermistor element and a
333
ceramic resistor, respectively. From the temperature and relative humidity in the ambient air and
21
334
inside the first gas tank, the volume fractions of water vapor in the ambient air,
335
smoke duct,
X H2O = 336
XHs 2O
, and in the
, were estimated using the following equation:
PH2O H Pamb 100
PH2O
XHo2O
(12)
337
where,
338
relative humidity in percent. The saturated vapor pressure of water was estimated by the equation of
339
the vapor pressure-temperature relationship for saturated water vapor developed by Wagner and
340
Pruß as follows [19]:
341
PH O T ln 2 = c ( a1Θ + a2 Θ1.5 + a3Θ3 + a4 Θ3.5 + a5Θ4 + a6 Θ7.5 ) Pc T ,
342
with Θ = 1-T/Tc, Tc = 647.096 K, Pc = 22.064×103 kPa, a1 = -7.85951783, a2 = 1.84408259, a3 =
343
-11.7866497, a4 = 22.6807411, a5 = -15.9618719, a6 = 1.80122502.
is the saturated vapor pressure of water, Pamb is the ambient pressure, and H is the
(13)
344
345
In the steady-state combustion state, both the temperature and the relative humidity in the first gas
346
tank became almost constant in the averaging period, therefore, the precision index of average
347
became small. On the other hand, the bias limits of the thermo-hygrometer were expected to be in
348
the range of B∆T = ±1 K for the thermistor thermometers and B∆H = ±7% for the ceramic resistance
349
hygrometers. Since the precision index of average was small and negligible, uncertainty of the
22
350
volume fraction of water vapor can be estimated from the bias limit only, and it was about
351
±0.2% estimated from Eq. (14):
∂X H2O ∂X H2O = B∆H + B∆T ∂H ∂T 2
U X H O = BXH O 2
2
352
U XH O 2
=
2
(14)
353
354
355
The volume flow rate in the smoke duct, Vs, was defined as follows:
Vs = β
π 4
Dd2us
(15)
356
where us and Dd are the smoke velocity measured by the Pitot tube at the center of the smoke duct
357
and the diameter of the smoke duct, respectively. The volume flow rate in the smoke duct, Vs, was
358
converted to the volume flow rate referred to standard conditions (25°C, 1 atm) and substituted into
359
Eq. (8). A correction factor, β, was used for estimating average velocity in the smoke duct from the
360
center velocity measured by the Pitot tube. The correction factor was estimated from the velocity
361
distribution in the smoke duct as β = 0.852 by separate calibration experiments.
362
363
In the calibration experiments, the velocity distribution consisting of 13 measurement points in the
364
duct was measured under the same ventilation condition of the hood in the medium scale without the
365
fire source. The correction factor was estimated as the ratio of the volume flow rate obtained from
23
366
the velocity profile in the duct and the volume flow rate obtained from the velocity at the center of
367
the duct. In the fire experiments, the flow velocities at the center of the duct were about 4.0 and 2.3
368
m/s in the medium and small scales, respectively. The Reynolds number of the flow in the duct was
369
6.7×104 in the medium scale and 3.8×104 in the small scale, and both Reynolds numbers were of the
370
same order of magnitude and in a sufficiently turbulent state. When the Reynolds number of the flow
371
was in the same order, it could be expected that there was no significant change in the velocity
372
profile in the duct, so the correction factor measured in the medium scale was also used in the small
373
scale. Furthermore, the effect of buoyancy inside the duct under the fire condition on the correction
374
factor was neglected as the flow was in a sufficiently turbulent state.
375
376
2.3. Radiative heat release rate
377
Radiative heat release rate is the radiative component of Qchem. Figure 3 shows a schematic
378
representation of the distribution of radiative heat flux for estimating the radiative heat release rate.
379
If it is assumed that spatial and temporal variations of radiation from a fire can be separated, the
380
distribution of radiative heat flux, qrad (θ, φ, t), measured rrad away from the fire is given by Eq. (16):
381
′ ( t) qrad (θ,ϕ,t) =Ω(θ,ϕ) qrad
(16)
24
382
where, q’rad (t) is the radiative heat flux measured by the water-cooled radiometer installed rrad away
383
from the fire, Ω (θ, φ) indicates the spatial distribution function, and θ and φ are elevation and
384
azimuth angles, respectively. If the fire is assumed to radiate as a point source, the radiative heat
385
release rate can be estimated by Eq. (17), based on the time curve of the radiative heat flux, q’rad (t): 2 2 ′ ( t ) ∫∫ Ω (θ ,ϕ ) rrad Qrad ( t ) = ∫∫ qrad (θ ,ϕ, t ) rrad sinθ dθ dϕ = qrad sinθ dθ dϕ
ϕ ,θ
386
ϕ ,θ
(17)
387
The value of the surface integral of the spatial distribution function Ω (θ, φ) of the radiation can be
388
expressed as follows using a correction factor, krad: 2 2 4π rrad krad = ∫∫ Ω (θ ,ϕ ) rrad sin θ dθ dϕ
ϕ ,θ
389
(18)
390
When the correction factor, the radiative heat flux measured by the water-cooled radiometer, and the
391
distance from the fire to the radiometer were used, the time variation of the radiative heat release rate
392
was estimated as follows:
393
2 ′ ( t) Qrad ( t ) = 4πrrad krad qrad
394
The correction factor, krad, was derived under the assumption that the time integral of the radiative
395
fraction of Qchem over the average period in ‘free burning’ agrees with the time integral of the
396
radiative heat release rate based on the point source assumption over the same period as shown in Eq.
397
(20):
(19)
25
krad = 398
χ rad ∫ Qchem ( t ) dt ave 2 rad ave
4π r
∫
′ ( t ) dt qrad
(20)
399
where, the value of the global radiative fraction of a propane fire was selected as χrad = 0.29 [18].
400
The distance from the fire to the radiometer was set as rrad = 1.0 m in all fire experiments.
401
402
The correction factor obtained during ‘free burning’ was used to estimate the radiative heat release
403
rate during water spray activation. For the estimation of the correction factor, it was assumed that the
404
spatial distribution function Ω (θ, φ) of the radiation and the global radiative fraction of fire, χrad, did
405
not change during the water spray activation. However, in reality, the latter assumption was not
406
sufficiently valid during the water spray activation. For example, work by White et al. [20] has
407
suggested that the radiative fraction of fire is not constant and reduces when fires are suppressed
408
with water spray owing to the reduction in flame temperature. Furthermore, they confirmed this by
409
direct measurements of the radiative fraction of fire suppressed by nitrogen dilution of the oxidizer.
410
When the oxygen volume fraction in the ambient air with nitrogen dilution was in the range of 0.155
411
to 0.21, the color of the propane flame was yellow indicating soot incandescence. The radiative
412
fraction corresponding to the yellow flame ranged from 0.19 to 0.32 [21]. In our fire experiments,
413
except for the extinguishing condition, since the flame color was observed to be yellow during the
26
414
water spray activation, it can be assumed that the radiative fraction ranged from 0.19 to 0.32. The
415
measurement system used in our study was unable to sense the changes in the radiative fraction
416
during the water spray activation. Therefore, in the estimation of the radiative component of Qchem
417
during the water spray activation, the decrease in prediction accuracy was considered by widening
418
the range of the bias limit B of the global radiative fraction of a propane fire in the uncertainty
419
analysis. Based on work by White et al. [21], the bias limit Bχ of the global radiative fraction of a
420
propane fire was assumed to be Bχ = 0.10. In other words, the radiative fraction was assumed as χrad
421
= 0.29±0.10. As a result, the range of uncertainty has been significantly broadened in the radiative
422
component of Qchem.
423
424
2.4. Convective heat flow rate and heat loss by heat transfer
425
Convective heat flow rate is the convective component of Qchem. The convective heat flow rate of the
426
fire, Qconv, was measured during the fire experiment with and without water sprays. The convective
427
heat flow rate was estimated by the following equation:
428
Qconv = ms Cp _ gas ∆Tgas
429
where, ms, Cp_gas, and ∆Tgas are the mass flow rate of the smoke flowing through the smoke duct, the
(21)
27
430
specific heat of the mixed exhaust gas at constant pressure, and the rise in temperature of the smoke
431
flow in the smoke duct adjacent to the hood, respectively. The specific heat of the mixed exhaust gas
432
was evaluated by a simple mass weighted average of the specific heat of each gas component species
433
(N2, O2, CO2, CO, H2O) dependent on the temperature of the smoke based on the data in
434
NIST-JANAF Thermochemical Tables [22]:
Cp _ gas = ∑YC i pi i
435 436
(22)
The mass flow rate in the smoke duct was defined as follows:
ms = ρsVs = 437
Pamb Vs Re (Tamb + ∆Td )
(23)
438
The mass flow rate was calculated from the smoke density, ρs, and the smoke volume flow rate, Vs.
439
The molecular weight of the exhaust gas mixture, Me, in the smoke duct can be estimated by the
440
following equation derived by Janssens [16]:
441
M e = 18 + 4 1 − X HS 2O
442
where
443
relative humidity and temperature in the first gas tank immediately after being sampled from the
444
smoke duct. The gas constant of the exhaust gas mixture was calculated from the universal gas
445
constant and the molecular weight of the exhaust gas mixture as:
(
X Hs 2O
)( X
A O2
A + 4 X CO + 2.5 2
)
(24)
is the volume fraction of water vapor in the smoke duct, which is estimated from the
28
Re =
446
R0 Me
(25)
447
448
In this study, we installed three thermocouples on the surface of the hood. The approximate value of
449
the rate of heat loss, Qloss, through the hood could be roughly estimated based on the surface
450
temperature by the classical theory for natural convection. When we estimated the rate of heat loss,
451
Qloss, we found that it was 2% or less of Qchem during water spray activation (Qloss ≤ 5% of Qchem
452
during ‘free burning’), therefore, we ignored the rate of heat loss through the surface of the hood.
453
454
2.5. Size distribution of water spray droplets and estimation of droplet diameter
455
In this study, we measured the size distribution of water spray droplets and evaluated the median
456
volumetric diameter, Dv,0.5, from their size distribution. The diameters of spray droplets were
457
measured by using an immersion method [23, 24]. The spray droplets were captured in a small dish
458
containing castor oil and photographed with a microscope and a digital camera, and the diameters of
459
the spray droplets were measured from the photograph. Figure 4 shows an example of the droplets
460
photographed and the measurement of the radius of the droplets. The location where the spray
461
droplets were captured was the same as the burning surface of the fire source. The number of spray
29
462
droplets measured for spray nozzles TG1 and TG03 (refer to Table 2) were 662 and 622 droplets,
463
respectively, to estimate the size distribution and the median volumetric diameter of the spray
464
droplets.
465
466
Figure 5 shows the size distributions of the water spray droplets in the medium and small-scale
467
experiments. The black and red solid lines show the droplet size distributions by cumulative volume
468
fraction (CVF) as measured and prescribed, respectively. The cumulative volume fraction
469
distribution can be prescribed for a water spray as a combination of log-normal and Rosin-Rammler
470
distributions [25]:
471
ln Dv′ 2 Dv 1 Dv ,0.5 1 dD′ exp − v 2π ∫0 σ Dv′ 2σ 2 CVF(Dv ) = γ D 1 − exp −0.693 v D v,0.5
σ= 472
2 2π ( ln 2) γ
=
(D ≤ D ) v
v,0.5
(D > D ) v
v,0.5
(26)
1.15
γ
(27)
473
where Dv,0.5 is the median volumetric droplet diameter and γ and σ are empirical constants.
474
Rosin-Rammler and log-normal distributions are smoothly joined if the relationship between
475
empirical constants γ and σ fulfills the relational expression as shown in Eq. (27). In this study, the
476
parameters γ = 2.6 and σ = 0.442 were determined from the comparison in Fig. 5.
30
Spatial distribution function Ω
qrad (θ, φ, t)
z
y
x Point source χQchem
rrad
q’rad (t) Radiometer
477 478
Fig. 3. Schematic representation of the distribution of radiative heat flux for estimating the radiative
479
component of the chemical heat release rate.
480 481
Fig. 4. Example of the droplets photographed and measured.
482 31
1
CVF [-]
0.8 0.6 0.4 Measured Prescribed γ = 2.6
0.2 0 0
200
400 600 Diameter [µm]
800
1000
483 484
(a) Medium scale: Dv,0.5 = 418 µm
1
CVF [-]
0.8 0.6 0.4 Measured Prescribed γ = 2.6
0.2 0 0
200
400 600 Diameter [µm]
800
485 486
(b) Small scale: Dv,0.5 = 295 µm
487
Fig. 5. Droplet size distributions.
488
489
32
1000
490
3. Experimental conditions
491
Table 2 presents the experimental conditions in the fire cooling experiments. The parameters listed
492
in Table 2 are the fire diameter, D, the desired heat release rate, Q, the water spray conditions in both
493
the medium and small scales, and the nozzle height from the burning surface of a fire source, L,
494
defined as the characteristic length. The heat release rates listed in Table 2 were calculated from the
495
heat of combustion of propane gas (∆H = 46 MJ/kg) [18] and the mass flow rate of propane gas
496
assuming 100% combustion efficiency. However, practically, since the values of the heat release rate
497
measured by the oxygen consumption method were smaller than the values listed in Table 2, the
498
combustion efficiency varied in a range from 83 to 98% in the fire cooling experiments. Water spray
499
nozzles UniJet TG1 and TG03 made by Spraying Systems Co., which can satisfy the scaling
500
relationships of the spray angle, flow rate, working pressure, and droplet diameter, were selected
501
under the medium and small scales. However, it is to be noted that TG1 and TG03 are not
502
geometrically similar and as mentioned earlier, it is challenging to commercially source
503
geometrically similar nozzles. The values in parentheses in Table 2 are ideal values derived from the
504
scaling relationships as shown in Table 1. The ranges of the mass flow rate of the exhaust gas in the
505
smoke duct during ‘free burning’ and water spray activation were from 0.15 to 0.19 kg/s in the
33
506
medium scale and from 0.11 to 0.13 kg/s in the small scale. The mass flow rate of the exhaust gas
507
was determined considering the sensitivities of the gas analyzers and differential pressure gauge for
508
the Pitot tube installed in the smoke duct. Furthermore, the mass flow rate of the exhaust gas was set
509
in a way that the average mass flux of the exhaust gas on the suction area (1.6×1.6 m2) in the hood
510
fulfilled the scaling relationship in the medium and small scales. The lowest possible mass flow rate
511
was chosen so as not to affect the spray transport and fire entrainment behaviors.
512
513
In this study, a full-scale (large-scale) fire was postulated as a fire in a tunnel with the ceiling height
514
of 8 m. It was assumed that a water spray was installed under the ceiling (spray height, L = 8 m) and
515
the heat release rate of a fire ranged from about 1.5 to 3.5 MW (corresponding to a small vehicle fire
516
in the tunnel). The flow rate and the droplet median volumetric diameter of the water spray were
517
assumed to be 80 L/min and about 1 mm, respectively. Based on these conditions in full scale, the
518
experimental conditions in the medium and small scales were determined as shown in Table 2. The
519
scale ratio of the medium and small scales to full scale corresponds to 1:6 and 1:12, respectively.
520
The scale ratio between the medium and small scales was 2:1.
521
34
522
Table 2 Experimental conditions in medium and small-scale fire cooling experiments. Scale
M edium
Small S = 2
Fire diameter, D (m)
0.155
0.08 (0.078)
42.9
7.6 (7.6)
34.7
6.1 (6.2)
26.0
4.6 (4.6)
17.4
3.1 (3.0)
Nozzle type
TG1
TG03
Orifice diameter (mm)
0.94
0.51
Spray angle, θ (°)
54
54 (54)
Spray flow rate, V w (L/min)
0.91
0.16 (0.16)
Working pressure, P w (M Pa)
0.36
0.19 (0.18)
Droplet diameter, D v,0.5 (mm)
0.418
0.295 (0.296)
Spray height, L (m)
1.33
0.67 (0.67)
Heat release rate, Q (kW)
523 524
35
525
4. Results and Discussion
526
527
4.1. Distributions of water spray mass flux
528
To identify the distribution characteristics of the water spray nozzles, the distributions of the water
529
spray mass flux discharged from the nozzles TG1 and TG03 were measured. The conditions of the
530
water sprays are listed in Table 2.
531
532
Figure 6 shows the arrangement of the cups measuring the water spray mass flux distribution.
533
Circular plastic cups with inner and outer diameters of 0.056 and 0.062 m were used in the medium
534
scale. On the other hand, square aluminum cups with outer and inner sides of 0.015 and 0.0126 m
535
were used in the small scale. The cups were arranged on a board set up under the nozzle at intervals
536
of every 0.062 and 0.031 m in the medium and small scales, respectively. The heights between the
537
top surface of the cups and the discharging hole on the nozzle face were set to the same heights from
538
the fire source surface, that is, 1.33 and 0.67 m, respectively. A similar technique was used by
539
Mahmud et al. [26] for the water flux measurements.
540
36
541
In the measurement of the water spray mass flux distribution, the activation periods of water spray
542
discharging were continued for 4 and 10 mins for nozzles TG1 and TG03, respectively. The water
543
spray mass flux, m''w, was estimated from the mass of water received by the cup, Mcup, the opening
544
area of the top surface of the cup, Acup, and discharging time, ∆tcup. Equation (28) defines the water
545
spray mass flux:
mw'' = 546
M cup Acup ∆tcup
(28)
547
The orientation of the nozzle tip incorporated in the spray head was changed 90 degrees clockwise
548
every time and measurements were made four times (0, 90, 180, and 270 degrees, with the x axis as
549
0 degrees). The distributions of the water spray mass flux were evaluated as the average distributions
550
of these four measurements. Figure 7 shows the averaging distributions of the water spray mass flux
551
in the medium and small scales. The intersection of the x and y axes in Fig. 7 indicates the position
552
directly below the spray nozzle and the origin of the coordinates in Fig. 1. The averaging
553
distributions of the water spray mass flux showed concentric distributions in both scales, though the
554
pattern was not fully circular. More non-circular patterns were also observed by Mahmud et al. [26].
555
556
Figure 8 shows a comparison of the curves of the water spray mass flux in the medium and small
37
557
scales. These curves were depicted as the average distribution in the circumferential direction of the
558
water spray mass flux distributions obtained from cups arranged every 45 degrees shown in Fig. 6.
559
The measurement uncertainty at a 95% confidence level of the water spray mass flux at each
560
measurement location was estimated and included as error bars in Fig. 8. In an appendix section, we
561
discuss the details of the uncertainty analysis. The water spray mass flux in the small scale was
562
scaled up to match the medium scale using the scaling relationship shown in Table 1. Even though
563
the water flow rate, working pressure, and droplet diameter were selected to scale satisfactorily, as
564
shown in Table 2, the scaled-up water spray mass flux around the center for the small scale was
565
smaller compared to the medium scale. In model experiments of fire phenomena interacting with
566
water sprays, in addition to the scaling of the nozzle operating conditions, simultaneously satisfying
567
scaling of the water spray mass flux distribution is challenging.
568
38
y
x Cup interval
569 570
Fig. 6. Arrangement of the cups for measuring the water spray mass flux distribution.
571 572
(a) Medium scale (0.91 L/min)
39
573 (b) Small scale (0.16 L/min)
575
Fig. 7. Averaging distributions of the water spray mass flux in the medium and small scales.
Spray mass flux S1/2m''w [kg/m2s]
574
Medium (TG1) Small (TG03) S = 2
0.1
0.05
0
0
0.2
0.4 r-axis Sr [m]
0.6
0.8
576 577
Fig. 8. Averaged water spray mass flux distributions scaled on the radius axis.
40
578
4.2 Time history of heat release rate in fire cooling experiments
579
Figures 9 and 10 show the time curves of the heat release rate in the medium and small scales in the
580
fire cooling experiments. In the case of Q = 7.6 kW, since the water flow rate of the spray nozzle of
581
TG03 was gradually increased after 960 s to examine the water flow rate needed for fire extinction,
582
the time history of data after 960 s is omitted in Fig. 10(a). The omitted data is not required for our
583
further analysis. In these figures, Qchem, Qconv, and Qrad are the chemical heat release rate estimated
584
by the oxygen consumption method, the convective heat flow rate calculated from the rise in
585
temperature and the mass flow rate of smoke flowing in the duct, and the radiative heat release rate
586
estimated from the heat flux measured by the radiometer, respectively. The fire cooling rate by water
587
sprays, Qcool, was defined as follows based on the energy balance:
588
Qcool = Qchem − Qconv − Qrad − Qloss
589
where Qloss denotes the rate of heat loss which was transferred from the smoke flow to the hood and
590
lost to the ambient air. In this study, the rate of heat loss, Qloss, was neglected since its value was
591
small, especially during water spray activation. Qgas, shown by the chain line, indicates the
592
theoretical heat release rate estimated from the mass flow rate of propane gas and its heat of
593
combustion assuming 100% combustion efficiency. In other words, Qgas indicates the desired heat
(29)
41
594
release rate defined as experimental conditions, such as the gas flow rate.
595
596
Table 3 shows multiple respective primary data during ‘free burning’ and water spray activation.
597
The combustion efficiency was defined as η = Qchem/Qgas. Since these values were evaluated as
598
average values, a time range of averaging is also shown in Table 3. The value of η in the case of the
599
heat release rate of 17.4 kW in the medium-scale experiment was measured to be about 4–11%
600
lower than the value of η in the other larger fire cases in the medium scale. Similarly, the value of η
601
in the case of the heat release rate of 7.6 kW in the small-scale experiment was measured to be about
602
4–15% lower than the value of η in the other smaller fire cases in the small scale. As the value of η
603
of 7.6 kW in the period of water spray activation was the same as that of ‘free burning’, we can be
604
confident that it was not due to the influence of water spray. When we considered the range of
605
uncertainty in Qchem, we found that the range in Qchem of 17.4 and 7.6 kW overlaps with Qchem in the
606
other fire cases. Furthermore, since the measurement accuracy of the oxygen consumption method
607
itself is about 10% [16], Qchem in the 17.4- and 7.6-kW cases was judged to be appropriate data.
608
609
In the literature, the value of η in the case of propane gas burning is 0.95 [18]. The average values of
42
610
η in all Qchem during ‘free burning’ were 0.90 and 0.90 in the medium and small scales, respectively,
611
and were close to that in the literature. The uncertainty range of η in the small scale was larger than
612
that in the medium scale. The average values of η in all Qchem cases during the water spray activation
613
were 0.91 and 0.87 in the medium and small scales, respectively, and were close to those during
614
‘free burning’. The convective heat flow rate and radiative heat release rate, Qconv and Qrad,
615
decreased in the period of water spray activation. The convective component, Qconv, decreased
616
because the droplets behaved as a heat sink through heat absorption and evaporation. The radiative
617
component, Qrad, decreased because the small droplets attenuated thermal radiation through a
618
combination of scattering and absorption.
619
620
In the cases of Q = 42.9 and 7.6 kW in the medium and small scales, respectively, the flame on the
621
fire source during the water spray activation continued to burn stably like ‘free burning’. Since the
622
flow rates of water spray were small, the buoyancy produced by the flame was sufficiently stronger
623
than the momentum of the downward flow induced by the droplets discharged during the water
624
spray activation.
625
43
626
In the case of Q = 34.7 kW (medium scale), the tip of the flame was occasionally cracked by the
627
downward flow induced by water sprays. However, after cracking the flame immediately returned to
628
the stable burning condition. In the case of Q = 6.1 kW (small scale), it was observed that the length
629
of the flame was slightly shortened, compared to the case of ‘free burning’, by the downward flow
630
induced by water sprays. Under the above-mentioned spray and burning conditions, the chemical
631
heat release rates, Qchem, were not affected in the period of water spray activation.
632
633
In the case of Q = 26.0 kW (medium scale), the flame was completely cracked and the burning
634
surface of the fire source was exposed by the downward flow induced by water sprays. These
635
cracking and exposing phenomena were periodically observed, but the flame could continue to burn.
636
In the case of Q = 4.6 kW (small scale), the length of the flame was shortened by the downward flow
637
induced by water sprays to about half of the case of ‘free burning’.
638
639
In the case of Q = 26.0 kW (medium scale), the flames cracked by the downward flow induced by
640
the water sprays continued burning while adhering to the rim of the gas burner. Part of the cracked
641
flame was occasionally extinguished at the rim, in which case unburned gaseous fuel might leak
44
642
slightly from the unburned rim of the gas burner. Moreover, it is likely that some combustion
643
products might escape from the exhaust collection system since the 26 kW fire was a weak fire
644
condition subjected to water spray. Therefore, Qchem might slightly decrease during the water spray
645
activation. The proof of this phenomenon can be a subject of future works as the attention of this
646
study was focused on scaling, rather than performing highly accurate calorimetry measurements.
647
Furthermore, the decrease in Qchem due to cooling was small and remained within the range of
648
uncertainty. Considering the findings of White [17, 20], which showed no significant reduction in O2
649
consumption or CO2 generation for gaseous fuel flames exposed to extinguishment by either
650
nitrogen dilution of the oxidizer or water mist spray, we can assume that Qchem for a gaseous fuel fire
651
in the case of 26 kW was not affected by water sprays. In the case of Q = 4.6 kW (small scale), Qchem
652
decreased slightly after water spray activation, but gradually recovered from the decrease, therefore,
653
Qchem in time averaging was almost the same as the value during ‘free burning’. Taken together,
654
under these conditions in the medium and small scales (26.0 and 4.6 kW), the chemical heat release
655
rates, Qchem, were not affected in the period of the water spray activation.
656
657
During Q = 17.4 (medium scale) and 3.1 kW (small scale) cases, the flame was immediately and
45
658
completely cracked and extinguished within 30 seconds by the downward flow induced by water
659
sprays. In the case of 17.4 kW (medium scale) as shown in Fig. 9(d), we performed re-ignition with
660
an igniter several times immediately after the flame had been extinguished (while water was
661
discharging from the nozzle), but the flame was extinguished within 30 seconds each time. In cases
662
of the flame being extinguished, Qchem, Qconv, Qrad, and Qcool could not be estimated due to no steady
663
period in Table 3.
664
665
Different qualitative flame burning characteristics were observed as effects of water spray mass flux
666
in the medium and small scales. As the water spray mass flux around the center of the fire source in
667
the small scale was smaller than that in the medium scale, the flame cracking in the small scale was
668
observed only at the lowest heat release rate of 3.1 kW.
669
46
Heat release rate Q (kW)
60 Qchem Qconv Qrad Qcool Qgas
W.S.
50 40 30 20 10 0 0
240
670 671
480 720 Time t (s)
960
1200
(a) Q = 42.9 kW.
Heat release rate Q (kW)
60
40 30 20 10 0 0
672 673
Qchem Qconv Qrad Qcool Qgas
W.S.
50
240
480 720 Time t (s) (b) Q = 34.7 kW.
47
960
1200
Heat release rate Q (kW)
60 Qchem Qconv Qrad Qcool Qgas
W.S.
50 40 30 20 10 0 0
240
674 675
480 720 Time t (s)
960
1200
(c) Q = 26.0 kW.
Heat release rate Q (kW)
60
40 30 20 10 0 0
676 677
678
Qchem Qconv Qrad Qcool Qgas
W.S.
50
240
480 720 Time t (s)
960
1200
(d) Q = 17.4 kW.
Fig. 9. Heat release rates in the medium scale: Vw = 0.91 L/min, Dv,0.5 = 0.418 mm, Lm = 1.33 m.
48
Heat release rate Q (kW)
10 W.S.
8 6
Qchem Qconv Qrad Qcool Qgas
4 2 0 0
240 480 720 960 1200 1440 1680 Time t (s)
679 680
(a) Q = 7.6 kW.
Heat release rate Q (kW)
10 W.S.
8 6 4 2 0 0
240 480 720 960 1200 1440 1680 Time t (s)
681 682
Qchem Qconv Qrad Qcool Qgas
(b) Q = 6.1 kW.
49
Heat release rate Q (kW)
10 W.S.
8 6
Qchem Qconv Qrad Qcool Qgas
4 2 0 0
240 480 720 960 1200 1440 1680 Time t (s)
683 684
(c) Q = 4.6 kW.
Heat release rate Q (kW)
10 W.S.
8 6
Qchem Qconv Qrad Qcool Qgas
4 2 0 0
240 480 720 960 1200 1440 1680 Time t (s)
685 686
687
(d) Q = 3.1 kW.
Fig. 10. Heat release rates in the small scale: Vw = 0.16 L/min, Dv,0.5 = 0.295 mm, Ls = 0.67 m.
688
50
689
Table 3 Primary data and conditions during ‘free burning’ and water spray activation.
Scale
690
Time range (s) m s (kg/s) Q gas (kW) 300 – 420 0.15 42.94 300 – 420 0.16 34.70 Medium 300 – 420 0.17 26.02 300 – 420 0.18 17.35 Average 0.17 300 – 600 0.11 7.59 300 – 600 0.12 6.14 Small 300 – 600 0.11 4.59 300 – 600 0.11 3.06 Average 0.11
Scale
691
Time range (s) m s (kg/s) Q gas (kW) 480 – 600 0.16 42.94 480 – 720 0.17 34.70 Medium 480 – 720 0.18 26.02 – 0.19 17.35 Average 0.18 720 – 960 0.11 7.59 720 – 960 0.13 6.14 Small 720 – 960 0.11 4.59 – 0.12 3.06 Average 0.11
Q chem (kW) 39.04 ± 1.80 32.61 ± 1.87 23.80 ± 1.95 14.47 ± 2.04 6.31 5.68 3.98 3.00
± ± ± ±
1.22 1.41 1.22 1.29
Q chem (kW) 39.56 ± 1.91 32.15 ± 1.96 22.68 ± 2.05 – 6.28 ± 1.23 5.51 ± 1.41 4.01 ± 1.25 –
r e (m) 0.198 0.203 0.210 0.219
m we (kg/s) 0.006724 0.006938 0.007287 0.007738
Water spray Q cool /m we (kJ/kg) 2338 ± 527 1919 ± 430 1321 ± 340 –
Water spray (s) 430-608 428-727 428-720 420-720
0.102 0.103 0.107 0.109
0.000808 0.000826 0.000882 0.000920
1853 ± 1651 1925 ± 1814 1311 ± 1473 –
673-960 673-970 670-960 660-960
Free burning η 0.91 0.94 0.91 0.83 0.90 0.83 0.93 0.87 0.98 0.90
(–) ± 0.04 ± 0.05 ± 0.07 ± 0.12 ± ± ± ±
0.16 0.23 0.27 0.42
Water spray η (–) 0.92 ± 0.04 0.93 ± 0.06 0.87 ± 0.08 – 0.91 0.83 ± 0.16 0.90 ± 0.23 0.87 ± 0.27 – 0.87
692 693
51
Q conv (kW) 23.43 ± 0.48 20.67 ± 0.41 15.84 ± 0.35 11.29 ± 0.27 4.28 3.53 2.69 1.88
± ± ± ±
0.22 0.17 0.16 0.14
Q rad (kW) 11.32 ± 3.90 9.46 ± 3.26 6.90 ± 2.38 4.20 ± 1.45 1.84 1.68 1.17 0.89
± ± ± ±
0.63 0.58 0.40 0.31
k rad (–) 1.06 1.01 1.02 0.91 1.00 0.87 1.01 0.93 1.02 0.96
Q conv (kW) 15.22 ± 0.32 12.37 ± 0.28 9.09 ± 0.25 –
Q rad (kW) 8.62 ± 2.97 6.46 ± 2.23 3.96 ± 1.37 –
Q cool (kW) 15.72 ± 3.54 13.31 ± 2.98 9.62 ± 2.48 –
3.37 ± 0.19 2.52 ± 0.15 1.92 ± 0.14 –
1.41 ± 0.49 1.41 ± 0.49 0.93 ± 0.32 –
1.50 ± 1.33 1.59 ± 1.50 1.16 ± 1.30 –
694
4.3 Fire cooling performance
695
Figure 11 shows a comparison of the fire cooling performance in the medium and small scales. The
696
circles and triangles indicate Qcool in the medium and small scales, respectively. The value of Qcool at
697
the small scale was converted into that at the medium scale with the scaling relationships shown in
698
Table 1. The error bar indicates measurement uncertainty with 95% confidence. Since the
699
measurement uncertainties of Qcool in both scales were of the same order of magnitude, after
700
converting the values at the small scale into those at the medium scale, the ranges of uncertainties at
701
the small scale became larger than those at the medium scale. Figure 11 indicates that the fire
702
cooling performance at the small scale was obviously smaller than that at the medium scale. This is
703
due to the fact that the water spray mass flux distributions in both scales were different, as shown in
704
Figs. 7 and 8. Especially, the water spray mass flux around the center position on the fire source at
705
the small scale was half the value of that at the medium scale. Therefore, at the small scale, the
706
interaction of water sprays with the fire plume and flame on the fire source decreased.
707
52
20
5/2
S Qcool [kW]
15 10 5 0 -5 10
Medium Small S = 2
20
30
40
50
5/2
S Qchem [kW] 708 709
Fig. 11. Relationship between Qcool and Qchem in the medium and small scales with water sprays.
710
Medium: Vw = 0.91 L/min, Dv,0.5 = 0.418 mm, Lm = 1.33 m. Small: Vw = 0.16 L/min, Dv,0.5 = 0.295
711
mm, Ls = 0.67 m.
712
53
713
4.4 Evaluation of cooling performance using effective interaction area
714
In order to reproduce the fire cooling performance in the medium-scale experiment from the
715
small-scale fire experiment, several experimental conditions in both scales (geometry, heat release
716
rate, working pressure, droplet diameter, and water spray mass flux distribution) must sufficiently
717
satisfy the scaling relationships. As shown in Fig. 11, we could not reproduce the fire cooling
718
performance in the medium scale when the result from the small-scale experiment was scaled up.
719
This was due to the insufficient scaling of the water spray mass flux distribution.
720
721
It is obvious that not all the droplets discharged from a water spray nozzle contribute to fire cooling.
722
Especially, in case of the small-scale experiment, it is likely that many droplets with no interaction
723
with the flame fell into the water receiving tank, since the water spray mass flux distribution in the
724
small scale was more uniform than that in the medium scale. Therefore, we introduced the effective
725
interaction area between the water spray and fire plume to take into consideration only the water
726
mass flux that effectively interacted with the fire [27].
727
728
Figure 12 shows a schematic representation of the model of the effective interaction area and the
54
729
physical parameters in the interaction between the water sprays and plume. First, we considered the
730
effective interaction area, Se, formed by the collision of an upward fire plume produced by a fire
731
source and a downward flow induced by water sprays, based on the spray and plume angles, θ and α,
732
as shown in Fig. 12. The radially distributed velocity and temperature profiles were assumed to be of
733
Gaussian distributions [28]. Generally, the relationship between the half-width of a Gaussian
734
distribution, b, and the height of a plume, z, is given by [29]:
735
b = 0.13z
736
In this study, we selected twice the half-width, 2b (95% of the integrated value of the
737
two-dimensional Gaussian distribution), as the radius of the plume that interacted with the water
738
sprays. As a result, it could be assumed that almost all of the upward plume interacted with water
739
sprays when estimating the radius of the effective interaction area:
740
α = 2 tan −1 ( 2b / z ) = 30°
741
As a result, the plume angle was estimated as α = 30°. Then, we estimated the water flow rate
742
formed by the group of water droplets passing through the effective interaction area from the water
743
spray mass flux distribution as shown in Fig. 8. Finally, we defined the water spray mass flow rate as
744
the actual delivery mass flow rate directly contributing to fire cooling. The radius of the effective
(30)
(31)
55
745
interaction area was estimated by:
rw = Lw tan
θ
746
747
2
(32)
rp = ( Lp − Z f 0 ) tan
α 2
(33)
748
where the spray angle, θ, in Table 2 was used for estimating the effective interaction area, and Zf0
749
indicates the virtual origin using the following formula recommended by Heskestad [30]:
750
2/5 Z f 0 = −1.02 D + 0.083Qchem
(34)
751
Taking the condition rw = rp into account, the distance from the nozzle to the effective interaction
752
area and the radius of the effective interaction area are derived as follows:
Lw = 753
( L − Z ) tan α2 f0
θ
re = Lw tan 754
α
tan + tan 2 2
(35)
θ 2
(36)
755
The actual delivery water spray mass flow rate, mwe, on the fire source was estimated by integrating
756
the water spray mass flux distribution as shown in Fig. 8 from the center to the radius of the effective
757
interaction area, re:
758
mwe = 2π ∫ mw′′ rdr
759
When deriving Eq. (37), the spray profile along the distance from the nozzle exit was assumed to be
re
(37)
0
56
760
a cone shape as shown in Fig. 12. In this study, as the effective interaction areas in the medium and
761
small scales were located at about 0.2 and 0.1 m from the nozzle exit, respectively, a cone shape
762
could be expected.
763
764
It was difficult to accurately estimate the effective amount of water that contributed to flame cooling,
765
as the water droplets interact with the flame. In this study, therefore, it was assumed that only water
766
droplets falling in the cylindrical space formed by the space from the effective interaction area to the
767
burning surface of the fire interacted with the flame and plume, and as a result, they evaporated and
768
performed flame cooling. However, some of the water droplets sprayed from the nozzle might pass
769
through the cylindrical space. Although the water droplets interacted with the flame while passing
770
through the cylindrical space, the water droplets fell on the floor in the outer region of the cylindrical
771
space. As a result, the actual delivery water spray mass flow rate estimated from the effective
772
interaction area tends to be underestimated. This error will be high when the spray angle is much
773
larger than the fire plume angle.
774
775
Since the distributions of the water spray mass flux in Fig. 7 were measured under flameless
57
776
conditions, it is likely that the distribution of the water spray mass flux actually changed due to the
777
interaction of sprays with the fire plume. In particular, the falling trajectory of small-diameter
778
droplets (e.g. diameter < 100 µm) is affected by the interaction of sprays with the fire plume.
779
However, as water droplets with small diameters evaporate immediately in the plume region, they
780
contribute to flame cooling although their falling trajectories change. On the other hand, the falling
781
trajectory of the large-diameter droplets is not significantly affected by the interaction. Although the
782
distribution of the water spray mass flux measured under flameless conditions includes the
783
contribution of both small and large diameter droplets, it can be used effectively for estimating the
784
actual delivery water spray mass flow rate contributing to flame cooling under the conditions with
785
flames.
786
787
Figure 13 shows the relationship between Qcool normalized by the actual delivery water spray mass
788
flow rate, mwe, on the effective interaction area and Qchem in the medium and small scales with water
789
sprays. By normalizing the fire cooling rate by the actual delivery water spray mass flow rate, we
790
succeeded in obtaining well-correlated fire cooling performance in both the medium and small scales.
791
It was difficult to completely satisfy the scaling relationships of the water spray and fire conditions
58
792
in both scales; however, introducing the actual delivery water spray mass flow rate could relax the
793
scaling relationship on the water spray mass flux distribution.
794
795
In this study, although the spray working pressure, total water spray flow rate and droplet diameter
796
were scaled correctly, the water spray mass flux distribution near the fire could not be scaled
797
correctly. Therefore, normalizing the fire cooling rate by the actual delivery water spray mass flow
798
rate was introduced for scaling relaxation. On the other hand, if the water spray mass flux
799
distribution near the fire was scaled correctly in addition to the spray working pressure and droplet
800
diameter, the fire cooling rate would have been scaled correctly without normalizing by the actual
801
delivery water spray mass flow rate. In this case, the scaling of the water spray mass flux distribution
802
in areas away from the fire can be relaxed. In the scaling relaxation based on this new perspective,
803
although the spray working pressure, droplet diameter and the water spray mass flux distribution
804
near the fire will be scaled correctly, the total water spray mass flow rate will not be scaled correctly.
805
Scaling relaxation focusing on the scaling of the water spray mass flux distribution near the fire
806
would be also worth investigating as a future research.
807
59
z
Nozzle
2b
Water sprays
Vel. and temp. b profiles
Lw
θ
Se
L α Lp
z
Cylindrical space
D Q r Fire
Zf0
qw’’ Water flux distribution 0
808 809
r
re
Fig. 12. Schematic representation of the model of the effective interaction area.
Qcool /mwe [kJ/kg]
4000 3000
Medium Small S = 2
2000 1000 0
-1000 10
20
30
40
50
5/2
S Qchem [kW] 810 811
Fig. 13. Relationship between Qcool normalized by the actual delivery water spray mass flow rate,
812
mwe, on the effective interaction area and Qchem in the medium and small scales with water sprays.
813 60
814
5. Conclusions
815
Even if the scaling of the water spray flow rate, the droplet diameter, the working pressure, and the
816
heat release rate was satisfactory, when the geometrical scaling of the nozzles was not sufficient, the
817
scaling of the water spray mass flux distributions on the fire sources for both scales was not satisfied.
818
In the scaling of a fire experiment with water sprays, normally, it is quite challenging to sufficiently
819
establish the experimental conditions, especially when nozzles are not geometrically similar. In this
820
study, we conducted a series of medium and small-scale fire cooling experiments and established a
821
new scaling relaxation for scaling of the water spray mass flux distribution. The main conclusions
822
are as follows:
823
(1) The fire cooling performance obtained from the medium-scale experiment could not be
824
reproduced using the small-scale experiment with insufficient scaling of the water spray mass flux
825
distribution.
826
(2) By normalizing the fire cooling rate by the actual delivery water spray mass flow rate, we
827
succeeded in obtaining well-correlated fire cooling performance for both the medium and small
828
scales.
829
(3) Introducing the actual delivery water spray mass flow rate can relax its scaling relationship on
61
830
the water spray mass flux distribution.
831
(4) The actual delivery water spray mass flow rate estimated from the effective interaction area tends
832
to be underestimated when the spray angle is much larger than the fire plume angle.
833
834
The global measurements data with uncertainty described in this paper constitute a useful database
835
for CFD code development and validation for scenarios of fire cooling by water sprays before
836
conducting any parametric or complex study. A number of future experimental studies are also
837
identified.
838
839
Acknowledgments
840
Part of this work was conducted with the support of the JSPS KAKENHI under Grant Number
841
JP16KK0125.
842
62
843
Appendix A. Measurement uncertainty
844
Normally, measurement uncertainty at a 95% confidence level, U, comprises the bias limit, B, the
845
precision index of average, Sx , and Student t value as follows [31]:
846
U = B2 + ( tSx )
847
The bias limit, B, is the estimated value of the upper limit of bias error. The product of the precision
848
index of average and Student t value is the estimated value of the precision error limit. The precision
849
index of average is evaluated as follows:
2
(A.1)
N
x=
∑x
i
i =1
850
N
(A.2) N
Sx = 851
∑( x − x ) i =1
2
i
N ( N − 1)
(A.3)
852
where N is the number of sampling data and x is the sampling data. In the fire experiments, we
853
measured data at 1-s intervals and evaluated the data as the value averaged for 180, 240, and 300
854
seconds. As the number of sampling data was larger than 30, Student t value was evaluated as two.
855
The bias limits were evaluated as half of the measuring precision for each instrument. Table A.1 lists
856
the bias limits for all the instruments, the precision indexes of average for all the measurement
857
values and sensitivity for all the measurements during ‘free burning’ at the heat release rate of 42.9
63
858
kW in the medium scale.
859
860
A1. Convective component of the chemical heat release rate
861
The convective component of the chemical heat release rate was calculated as follows:
862
Qconv = ms Cp _ gas ∆Tgas
863
where ms, Cp_gas, and ∆Tgas are the mass flow rate of the smoke flowing through the smoke duct, the
864
specific heat of mixed exhaust gas at constant pressure, and the rise in temperature of the smoke
865
flow in the duct close to the hood, respectively. The mass flow rate, ms, was estimated from the
866
pressure difference of the Pitot tube installed in the duct and the rise in temperature, ∆Td, in the duct
867
at the installed position of the Pitot tube. The convective component of the chemical heat release rate
868
depended on the input parameters, ∆Tgas, ∆Td, and pressure difference, ∆P, of the Pitot tube as
869
follows:
870
Qconv = Qconv ( ∆Tgas , ∆Td , ∆P)
871
The absolute sensitivity and the relative sensitivity of the convective component to its input
872
quantities are as follows:
θ ∆T = gas
873
(A.4)
(A.5)
∂Qconv ∂∆Tgas
(A.6)
64
∂Qconv ∂∆Td
(A.7)
∂Qconv ∂∆P
(A.8)
θ∆T = d
874
875
θ∆P =
Rθ∆Tgas = 876
Rθ∆Td = 877
Rθ∆P = 878
∂Qconv ∆Tgas ∂∆Tgas Qconv
ave
(A.9)
∂Qconv ∆Td ∂∆Td Qconv
ave
(A.10)
∂Qconv ∆P ∂∆P Qconv
ave
(A.11)
879
Estimating the convective component of the chemical heat release rate based on three parameters,
880
we can represent the bias limit, B, and the precision index of average, Sx , as follows:
881
B = θ ∆Tgas B∆Tgas
882
Sx = θ ∆Tgas Sx ∆Tgas
883
The measurement uncertainty at a 95% confidence level of the convective component of the
884
chemical heat release rate was estimated by using Eq. (A.1).
(
(
) + (θ 2
∆Td
) + (θ
B∆Td
) + (θ
2
∆Td
1/ 2
2
Sx ∆Td
∆P
2 B∆P )
) + (θ
(A.12) 1/ 2
2
∆P
2 Sx ∆P )
(A.13)
885
886
A2. Radiative component of the chemical heat release rate
887
The radiative component of the chemical heat release rate was calculated as follows.
888
2 ′ Qrad = 4πrrad krad ( χrad ) qrad
889
where krad is the correction factor obtained from Eq. (20), and q’rad is the radiative heat flux
(A.14)
65
890
measured by the water-cooled radiometer. Furthermore, the correction factor, krad, depended on the
891
radiative fraction of the chemical heat release rate, χrad. The radiative component of the chemical
892
heat release rate depended on the input parameters χrad and q’rad as follows:
893
′ ) Qrad = Qrad ( χrad , qrad
894
The sensitivity of the radiative component to its input quantities can be estimated based on Equation
895
(A.15). The bias limit, B, and the precision index of average, Sx , can be represented as follows:
896
(
(
B = (θχ Bχ ) + θqrad ′ Bqrad ′ 2
(A.15)
))
2 1/2
(A.16)
897
Sx = θqrad ′ Sxqrad ′
898
The measurement uncertainty at a 95% confidence level of the radiative component was estimated
899
by using Eq. (A.1).
(A.17)
900
901
A3. Chemical heat release rate
902
The chemical heat release rate depended on many input parameters, the volume fractions of gases,
903
XO2, XCO2, XCO, XH2O, the rise in temperature of smoke, ∆Td, and the pressure difference of the Pitot
904
tube in the smoke duct, ∆P, as follows:
905
Qchem = Qchem X O2 , X CO2 , X CO , X H2O , ∆Td , ∆P
(
)
(A.18)
66
906
The sensitivity of the chemical heat release rate to its input quantities can be estimated based on
907
Equation (A.18). The bias limit and the precision index of average can be represented as follows:
908
909
((
B = θO2 BO2
((
) ( 2
Sx = θO2 SxO2
+ θCO2 BCO2
) + (θ 2
CO2
)
2
SxCO2
(
+ (θCO BCO ) + θ H2O BH2O 2
) + (θ 2
CO
(
) ( 2
+ θ∆Td B∆Td
SxCO ) + θH2O SxH2O 2
) + (θ 2
∆Td
)
2
+ (θ∆P B∆P )
Sx∆Td
)
2
2
)
1/2
+ (θ∆P Sx∆P )
(A.19) 2
)
1/2
(A.20)
910
The measurement uncertainty at a 95% confidence level of the chemical heat release rate was
911
estimated by using Eq. (A.1).
912
913
Through the fire experiments, we obtained many measurement values: gas concentrations (oxygen,
914
carbon dioxide, carbon monoxide and water vapor), rise in temperature, and pressure difference
915
measured by the Pitot tube in the smoke duct. As the values of the precision index of average of the
916
data measured by instruments were significantly less than the values of the bias limit of the
917
instruments, the measurement uncertainty of the data measured was dominated by the bias limits of
918
the instruments. The chemical heat release rate estimated by the oxygen consumption method was
919
dominated by the bias limit of the oxygen analyzer (POT8000). The effect of other measurement
920
values except for this parameter on the chemical heat release rate was small.
921
67
922
A4. Fire cooling rate
923
The fire cooling rate with uncertainty was estimated from the chemical and radiative heat release
924
rates, the convective heat flow rate, and these uncertainties as follows:
925
Qcool ± UQcool = ( Qchem − Qconv − Qrad ) ± UQ2chem + UQ2conv + UQ2rad
(A.21)
926
927
A5. Water spray mass flux
928
The water spray mass flux, m''w, was estimated as follows:
mw'' = 929
M cup Acup ∆tcup
(A.22)
930
As the contribution of Acup and ∆tcup to uncertainty of water spray mass flux was small compared to
931
Mcup, we only considered the effect of Mcup on the water spray mass flux in the uncertainty analysis.
932
The precision index of average was estimated from 32 data (4×8) except for the center position (4
933
data at the center position), obtained from experiments repeated 4 times and water spray mass flux
934
distributions obtained from cups arranged every 45 degrees as shown in Fig. 6. As the number of
935
data was larger than 30, we could evaluate Student t value as two (Student t value of 3.182 at the
936
center position). The water spray mass flux was dominated by the precision index of average of the
937
mass of water received by the cup, Mcup. The effect of the bias limit of instruments on the water
68
938
spray mass flux was small. The measurement uncertainty at a 95% confidence level of the water
939
spray mass flux was estimated by using Eq. (A.1).
940
941
Table A.1 Uncertainty analysis under the condition of ‘free burning’ (Q = 42.9 kW); parameters,
942
values, absolute sensitivity, relative sensitivity, bias limit, and precision index of average. Note that
943
the values of absolute and relative sensitivities are unique to the specific measurement conditions.
Q
Q conv
Q rad
Parameter
Value
Absolute sensitivity, θ
∆T gas
166 °C
1.6×10
142 °C
−2.8×10
∆P
7.62 Pa
1.5×10
χ q' rad ∆P X X
944
-2
∆T d
∆T d
Q chem
-1
A O2
A
CO2 A X CO S X H2O
0
3.9×10 2
0.85 kW/m 142 °C 7.62 Pa 19.39% 1.15%
Bias limit, B
Precision index of average, ̅ Sx
0
1K
6.79×10 K
-1
1K
4.74×10 K
-1
0.25 Pa
0
0.1
3.24×10 Pa 0
1.1×10
−1.7×10 5.0×10
1
0.29
Relative sensitivity, Rθ
1.0×10
1
0
1.3×10
1.0×10
-2
-1
−4.7×10
−1.7×10
0
-1
2.6×10
5.0×10 3
−2.6×10
2
−5.7×10
1
−1.3×10
-1
−1.7×10
2
−3.1×10
1
−1.1×10
13 ppm
−9.5×10
1.33%
−3.2×10
-4 -2
-1 -1
-4
-2
2
-4
6.25×10
-4
5.0×10
-6
5.0×10
-3
2.0×10
945
946
Appendix B. The model of a primary delay system in the preconditioning process
947
69
-3
2
4.32×10 kW/m 1.25×10 kW/m -1 1K 4.74×10 K -2 0.25 Pa 3.24×10 Pa -5
1.00×10
-6
7.83×10
-6
0.12×10
-5
1.97×10
948
It was assumed that the gas concentration in the air tanks used in the preconditioning process has
949
always spatially uniform distribution. The uniform gas concentration changes over time as an
950
exponential process. The estimation model equation is shown as follows.
951
w w w X out = 1 − exp − t 1 − exp − t 1 − exp − t X in V1 V2 V3
952
where, Xout and Xin are the volume fractions of input and output gases, V1, V2, and V3 are the internal
953
volume of the first air tank, the air space of the water cooling tank, and the internal volume of the
954
second air tank, w and t are the volume flow rate of gases drawn by the pump and elapsed time,
955
respectively. This equation shows a generic primary delay system [32].
956
70
(B.1)
957
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958
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75
Highlights
1. Fire cooling performance by sprays was examined using model scale experiments.
2. Scaling relaxation was developed for the scaling of the spray mass flux distribution.
3. Scaling relaxation could account for cooling performance under incomplete scaling.
4. Global measurements can be used for CFD validation on the fire cooling by sprays.
Conflict of Interest
There is no conflict of interest in this study.