NBSIR 77-1287

Analytical and Experimental

Study of Evaporative Cooling

and Room Fire Suppression by

Corridor Sprinkler System

Stanley T. Liu

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D C. 20234

October 1977

Final Report

Supported in Part by:

Office of Policy Development and Research

Department of Housing and Urban Development

Washington, D.C. 20410

NBSIR 77-1287

ANALYTICAL AND EXPERIMENTAL

STUDY OF EVAPORATIVE COOLING

AND ROOM FIRE SUPPRESSION BY

CORRIDOR SPRINKLER SYSTEM

Stanley T. Liu

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

October 1977

Final Report

Supported in Part by

Office of Policy Development and Research

Department of Housing and Urban Development

Washington, D.C. 20410

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

CONTENTS

Page

LIST OF FIGURES . iv

SI CONVERSION UNITS vi

Abstract 1

1. INTRODUCTION 2

2. MATHEMATICAL ANALYSIS 3 2.1. Evaporative Cooling of a Hot Gas Flow by Water Spray 3 2.1.1. Analysis 3 2.1.2. Numerical Results and Discussion 6 2.2. Trajectory of a Liquid Droplet with Evaporation 3 2.2.1. Analysis 8 2.2.2. Numerical Results and Discussion H

2.2.3. Scaling Criteria for Reduced Scale Model Test .... 12

3. EXPERIMENTAL STUDY 13

3.1. Preliminary Full-Scale Corridor Sprinkler Test I 3 3.1.1. Test Setup and Instrumentation I 3 3.1.2. Test Results and Discussion 14

3.1.3. Comparison of Theoretical and Experimental Results. . 1®

3.2. One-Quarter Scale Model Experiment 19

3.2.1. Experimental Apparatus and Instrumentation 19

3.2.2. Test Procedure

3.2.3. Comparison of Full-Scale to One-Quarter Scale Results

3.2.4. Test Results Using Solid Fuel 21

4. CONCLUSIONS 23

5. REFERENCES 2 5

APPENDIX - HEAT TRANSFER BY SPRAY EVAPORATION IN A CROSS FLOW 49

iii
LIST OF FIGURES

Page

Figure 1. Schematic of One-Dimensional Model for Spray Evaporation

Analysis 26

Figure 2. Dimensionless Temperature Drop Due to Droplet

Evaporation 27

Figure 3. Variation in Vapor Concentration Due to Droplet

Evaporation 28

Figure 4. Similarity of Temperature Variation Due to Droplet

Evaporation 29

Figure 5. Schematic of a Droplet in a Cross Wind 29

Figure 6. Trajectory of a Droplet Injected Against a Cross Flow. ... 30

Figure 7. Time History of the Variations of a Droplet in High

Temperature Cross Flow 31

Figure 8. Comparison of Droplet Trajectory Based on Scaling Criteria . 32

Figure 9. Schematic of Full-Scale Corridor Sprinkler Test Setup. ... 33

Figure 10. Location of Thermocouples, Gas Sampling Port, and Burner

(Full-Scale Test) 34

Figure 11. Time History of Exit Gas Temperature at Burn-room Doorway

(No Spray) 35

Figure 12. Variations of Ceiling Gas Temperature Along the Corridor

(No Spray) 36

Figure 13. Time History of Corridor Ceiling Gas Temperature (0.05 m

below Ceiling) 37

Figure 14. Time History of Corridor Exit Gas Temperature Outside

Spray Zone (0.31 m below Ceiling) 38

Figure 15. Burner Room 0 2 and C0 2 Concentration (Floor Level) Just

Before the End of Each Run 39

Figure 16. Comparison of Net Corridor Exit Gas Temperature Reduction by

Water Spray (Theoretical vs Experimental) . 40

Figure 17. Schematic of One-Quarter Scale Model Experiment Setup. ... 41

Figure 18. Location of Burners, Thermocouples, Gas Sampling Port,

and Fuel Pad (One-Quarter Scale Model) 42

Figure 19. Time History of Corridor Temperature Drop 4 3

Figure 20. Corridor Exit Temperature Reduction, Full-Scale vs One-Quarter Scale Tests 44

IV
LIST OF FIGURES, cont '

d

Figure 21. Burn-room Floor Level Oxygen Content, Full-Scale vs OneQuarter Scale Tests 4 5 Figure 22. Burn-room Doorway Exit Gas Temperature Variation

(Plexiglass Fuel) 46

Figure 23. 0 2 Content at Burn-room Floor Level (Plexiglass Fuel) ... 47

Figure 24 . 0 2 Content and Gas Temperature Variations (Wood Crib

Fuel) 48

v
SI CONVERSION UNITS

In view of present accepted practice in this technological area, U.S.

customary units of measurement have been used in this report. It should be

noted that the U.S. is a signatory to the General Conference on Weights and

Measures which gave official status to the metric SI system of units in

1960. Readers interested in making use of the coherent system of SI units

will find conversion factors in ASTM Standard Metric Practice Guide, ASTM

Designation E 380-72 (available from American Society for Testing and

Materials, 1916 Race Street, Philadelphia, Pa. 19103). Conversion factors

for units used in this paper are:

Length

1 in = 0.0254 meter

1 ft = 0.3048 meter

Area

1 in 2 = 6.4516 x 10 ** meter 2

1 ft 2 = 9.2903 x 10

2 meter2

Pressure

1 psi = 6895 pascal

Volume

1 gal = 3.785 dm 3

Density of Water Application

1 gal/min/ft 2 = 40.746 mm/min

vi
ANALYTICAL AND EXPERIMENTAL STUDY OF EVAPORATIVE

COOLING AND ROOM FIRE SUPPRESSION BY CORRIDOR SPRINKLER SYSTEM

Stanley T. Liu

Abstract

Investigations, both theoretical and experimental, are

conducted to evaluate the effects of a corridor sprinkler system

on the cooling and suppression of a fire in an adjacent compartment connected by an open doorway. A simplified one dimensional

mathematical model is presented to predict the net reduction of

the corridor ceiling hot gas temperature by evaporative cooling.

Scaling criteria based on the analysis of the motion of an evaporating droplet were developed for the correlation of full-scale

and small-scale experimental results and the design requirements

of a small-scale experiment. Representative test results from a full-scale and a one-quarter scale model experiments are presented.

These tests demonstrate the effectiveness of water spray in

reducing the corridor hot gas temperature to a level low enough

for safe passage, and in causing a strong recirculating flow at

the room doorway. This flow reduces the oxygen content around

the fire significantly, and results in a much reduced burning

rate of the fuel. The effect of the spray droplet size on the

cooling and on fire suppression is discussed.

Key words: Automatic sprinklers; compartment fire; corridor

sprinkler systems; droplet size; droplet trajectory; evaporative

cooling; fire suppression; full-scale test; gas temperature;

oxygen content; recirculating flow; reduced scale model test;

scaling criteria; spray water flow rate; water spray.

1
1 . INTRODUCTION

In October 1973, the U.S. Department of Housing and Urban Development

(Hl'D) issued changes to fire protection requirements in the Minimum Property

Standards (MPS) for multi-family [l]

1 and Care Type [2] Housing. These

changes pertained to the installation of automatic sprinklers in these

occupancy types. Of particular interest was the requirement for installation

of automatic sprinklers in corridors in all multi-family structures four

stories or more in height and in care-type housing of fire resistive or noncombustible construction regardless of height. In March 1974, a research

project, sponsored by the Office of Policy Development and Research of HUD,

was initiated at the National Bureau of Standards (NBS) to evaluate the

current criteria [3] and to improve design for corridor sprinkler systems.

This report, as part of the overall project, is a study on the function and

effectiveness of using water spray in the corridor when there is a fire in an adjacent compartment with the door left open. The objectives are to study

(1) the cooling of the hot combustion products issuing out of the doorway by

the evaporation of the spray droplets and, (2) the containment and possible

extinguishment of the fire in its room of origin.

In general, the water spray from a sprinkler works to contain and

suppress a fire underneath it by direct wetting and cooling of the combustibles, by evaporative cooling of the hot combustion products above the combustibles, and by returning the oxygen deficient upper atmosphere down to the

region around the burning fuel. This is discussed in some detail in reference [4]. For the spray to be effective, a network of sprinklers is

generally installed directly above the combustibles to be protected. For the

present study where the water spray is outside the burn-room, direct wetting

of the burning combustibles is insignificant. However, another mechanism,

the transfer of momentum between the spray and the hot gas flow exiting from

the doorway and along the corridor ceiling, comes into play. This transfer

of momentum from the spray droplets to the hot gas flow caused by aerodynamic

drag on the droplets creates a downward motion of the gas flow toward the

corridor floor. This flow has a very low oxygen concentration because it

contains the original products of combustion, vapor from the droplets, and

partly evaporated droplets. When this flow comes into contact, mixes with,

and is carried by the floor level fresh air inflow back into the burn-room,

oxygen supply to the room is reduced. The amount of reduction in oxygen

Numbers in brackets refer to the literature references listed at the end

of this paper.

2
concentration determines the decrease in the burning rate of the fuel and the

possible extinguishment of the fire. This complex process depends on the

effectiveness of droplet evaporation and momentum transfer, which in turn are

dependent on the water spray flux-density and droplet diameter, and is the

subject of the study here.

In this report, both a mathematical analysis and some experimental

results will be presented. The mathematical analysis will be presented in

two parts. The first part will be a study on the effects of spray droplet

diameter on the cooling of a hot gas flow as it travels down the length of

the corridor under a simplified one dimensional geometry. The second part

will study the momentum transfer and change in the trajectory of a droplet as

it is injected into a hot gas flow. A scaling criteria for relating fullscale and small-scale experiments based on the analyses will be presented.

The experimental study involves both full-scale and one-quarter scale model

tests. Results and observations of these tests including the fire behavior,

the corridor ceiling gas temperature variations, and the burn-room floor

level oxygen and carbon dioxide concentrations, all under the action of the

water spray from sprinklers and spray nozzles, will be shown.

2. MATHEMATICAL ANALYSIS

2.1. Evaporative Cooling of a Hot Gas Flow by Water Spray

2.1.1. Analysis

Previous investigations on the heat and mass transfer of fine liquid

droplets in a gaseous medium were conducted mostly by researchers in the combustion research field and in the spray-drying industry. A summary of their

works are given together with a comprehensive list of references in a review

paper by Bahn [5] and more recently by Masters [6] and Ahmadzadeh and Harker

[7]

.

Both theoretical and experimental works were reported. Part of their

findings, which has a direct bearing upon the present study, are summarized

as following:

(1) During evaporation, the droplet temperature remains constant

and is equal to the adiabatic saturation temperature of the

surrounding hot gas at temperature T and humidity w . For

an air-water-vapor system, the adiabatic saturation temperature

is the same as the wet-bulb temperature

.

3
( 2 ) For droplets with diameter less than 1.5 mm, the effects

of surface circulation and volume distortion can be neglected

and the droplets can be treated as solid spheres.

(3) For air-water-vapor system at 1 atm pressure, the Lewis Number

(ratio of Prandtl Number and Schmidt Number) is close to 1. An

analogy between heat transfer and mass transfer exists, and the

Nusselt Number for heat transfer can be estimated by using the

Ranz-Marshall correlation [8]

:

i/ 2 1/3

Nun = hD/k = 2 (1 + 0.3 Re Pr ) (1)

L) 3. U

where

Nu_ = Nusselt Number based on droplet diameter = hD/k

D 3

h = Convection heat transfer coefficient

D = Droplet diameter

k^ = thermal conductivity of air

Re

D

= Reynolds Number based on droplet diameter = UD/v

Pr = Prandtl Number of air = v/ot v = Kinematic viscosity of air

a = Thermal diffusivity of air

The analysis described here deals with the case of hot combustion products

flowing out of a compartment door into a corridor where a water spray directed

normal to the gas flow acts to continuously reduce the gas temperature along

the length of the corridor by evaporation. To simplify the analysis, a onedimensional model is used, and air is assumed to be the gas.

The simplified model is shown in figure 1. Hot dry air at temperature

T and mass flow rate iti is assumed to exit from a door and rise immediately

o a

J up to the ceiling. The hot air moves down the corridor with a flow area of

WxH where W is the width of the corridor and H the depth below the ceiling.

Water spray with a uniform droplet diameter D at a given height and uniform

droplet flux density N flows vertically down from the ceiling through the hot

air layer at a constant terminal velocity V and temperature T^ . Cold air at

temperature T^ is assumed to be underneath the hot air layer and flows in the

opposite direction. Stable stratification, hence no mixing, is assumed for

this analysis.

The following additional assumptions are made:

(1) Airflow is turbulent with uniform velocity and temperature at

any location x.

4
( 2 ) All the corridor surfaces are adiabatic and the only heat

transfer is between the hot air and the water droplets.

Radiation is neglected, and no mixing occurs between the hot

and cold air layers. Preheating of the droplets from their

initial temperature to the wet-bulb temperature T

g is also

neglected when compared with the heat of evaporation.

(3) Mixing of the hot air and the vapor generated by evaporation

is instantaneous. Vapor assumes the same velocity and

temperature as the airflow.

By writing down the mass balance and energy balance equations for a differential control element dx at x, and applying equation (1) , the change

in the hot air temperature and the water vapor mass flow rate along the

length of the corridor due to the evaporation of the spray is shown to be

(details of the derivation are shown in the appendix) in dimensionless form:

B(6 - 1) 0 (1+B)

(1 + B) In ES ( 2 ) 1 + Be 1 + B0

u>(S) = B (cp /cp ) (1 - 0)

a. V

(3)

where

0 (T-T

g

)/(T

o

- T

g

) = Dimensionless temperature

ihv/ih = humidity ratio

S = X/W = Dimensionless distance along the corridor

B

E (TrD 2 NW2 Hh)/ (A cp o V.)

a. a. u Total heat transferred to droplets

Energy input

N = Droplet flux density (No. of droplets/sec/unit area normal

to spray flow)

m

v Mass flow rate of vapor

h,. = Latent heat of evaporation at T

fg s

5
cp ,cp ' ca. Specific heat of vapor and air, respectively

h = heat transfer coefficient to a droplet, from eq . (1)

In obtaining eqs . (2) and (3), the heat transfer coefficient h was

assumed to remain constant. This is not actually true since the droplet

diameter and the terminal velocity are continuously decreasing when falling

through the hot air layer, and h is a function of the diameter and velocity

(Reynolds Number) . To estimate the variation of h as a function of temperature and droplet diameter, a calculation was made for h at three temperature

levels and three droplet sizes covering the ranges normally encountered in

actual conditions, and is shown in the following table:

T

o

°C

T

s

°C

Values

h in

of Heat Transfer Coeff.

J/s*m2, K for Droplet

Diameter of

1 mm 1/2 mm 1/4 mm

600 85 329 414 607

280 60 283 346 482

120 35 272 323 443

where T

q

is the hot air inlet temperature and T

g is the adiabatic saturation

temperature of the water droplets. Values of T

s for the values of T

q

shown

are experimental data given in reference [9]

.

Physical property values of

air (c , k , v,a) were evaluated at the arithmatic mean of T and T . Since

pa a os

the fraction change in droplet diameter is proportional to 1/3 power of the

change in mass, the decrease in droplet diameter is much smaller than the

decrease in mass. For example, a reduction of the droplet mass by evaporation

to one-half of its original value will reduce the droplet diameter by only

20%. For a 1 mm diameter droplet at constant T

q

, this will result in a change in the value of h by less than 6% as computed from equation 1. Since

a normal sprinkler produces droplets with diameter mostly in the range of 0.5

mm to 1.2 mm where evaporation is not very efficient [10] , the assumption of

a constant value for h is a reasonable assumption for estimation purpose.

2.1.2. Numerical Results and Discussion

Numerical examples of eqs. (2) and (3) are computed for the values of

T

q

, T

g

, and D listed in the above table for h. Computations were based on

the following data:

6
.545 kg/s

= . 0339 dm 3 /s-m 2 (.05 gal/mirrft 2

)

= 1.22 m

= 2.44 m

The value of is equivalent to the hot gas mass flow rate of a fullydeveloped room fire. The spray flux density is approximately equal to a flow

rate of 1.262 dm 3 /s (20 gal/min) from a sprinkler head with a coverage of

37.16 m 2 (400 ft 2

) at a distance of 1.22 m (4 ft) underneath the sprinkler

head [10]. The results are shown in figures 2 and 3.

Figure 2 shows the effect of droplet diameter on the variation of the

dimensionless mixture temperature due to droplet evaporation versus the

dimensionless corridor distance S. It is seen that for droplets with diameter

larger than 0.5 mm, a long length of corridor is required to reduce the

mixture temperature to a low level. Since the droplet diameter varies in

some fashion directly with the nozzle diameter of a sprinkler for the same

water flow rate, the installation or design using a small orifice sprinkler

is indicated. Figure 3 shows the variations of the mixture humidity ratio as an indication of the total amount of evaporation. It is seen that, for the

purpose of cooling, spray with a large droplet diameter (larger than 0.5 mm)

is not very efficient. This is in agreement with the conclusion presented in

reference [10]

.

It should be pointed out that in obtaining the above results, heat loss

through the walls and the mixing of hot and cold air layers were neglected.

Both of these act to decrease the temperature along the corridor in addition

to the decrease caused by evaporation. Therefore, in an actual situation, a sprinkler which gives a spray with mean droplet diameter as large as 1 mm

might be satisfactory as far as cooling of the combustion products down the

corridor is concerned. However, for the purpose of vapor generation and

recirculation as a means of fire suppression, droplets with smaller diameter

are preferred. This will be shown later in the results from the full-scale

tests

.

Examination of eq. (2) shows that if the temperature variation 6 is

plotted versus the product ES , all the curves in figures 2 and 3 will approximately merge into a single curve for all expected values of B (or gas inlet

Spray water volume flux density

H

W

7
temperature). This is shown in figure 4. Therefore, the parameter E acts as

a stretching factor and can be used as a scaling factor for scale model

experiments

.

2.2. Trajectory of a Liquid Droplet with Evaporation

2.2.1. Analysis

The motion of a droplet in a high temperature gas medium has been studied

in reference [10] in determining the distance of penetration of the droplet

into a rising hot gas plume. There the ability of the droplet in penetrating

the rising plume is the main criterion, and the motion of the droplet was

assumed to be one-dimensional and in the vertical gravitational plane. The

present study deals with the motion of an evaporating droplet injected at an arbitrary angle into a horizontal high temperature gas stream. The objective

is to obtain information on:

(1) the maximum distance of throw of a droplet in a spray as a function of the droplet diameter when injected opposing to a hot

ceiling gas flow,

(2) the change in the trajectory of the droplet so as to quantify the

momentum transfer between the droplet and the hot gas flow, and

(3) the scaling criteria needed in correlating reduced scale experimental results with full-scale tests.

The study is restricted to the two-dimensional case, that is, the motion

of the droplet is in a vertical plane parallel with the streamline of the hot

gas flow.

A schematic of the problem is shown in figure 5. A droplet with initial

diameter D

q

and velocity U

q

at temperature T

g is injected at at angle 9 q

into

a horizontal hot air stream at velocity V and temperature T . The wet-bulb

d 3. temperature of the air stream is equal to the droplet temperature T .

Applying Newton's second law of motion to the droplet in the horizontal

and vertical directions, results in,

du

Horizontal : m = F

Q

sin<|> (5)

8
Vertical

( 6 ) du

Vertical : m

^ = dt

= -Fd cos <p + mg (1 - P a/P w

) ( 6 )

where 4

> =: tan

- 1 (ux-V

a )/u

y ( 7 )

f

d

=: Drag force = C

D (| AjP

a U

2

) ( 8 )

u = relative velocity of droplet to airstream

u

2 = (u -V ) 2 + u

2

(

g

) x a y

u =

l /2

(u 2 +u 2

) = droplet velocity ( 10 )

C

D

= drag coefficient = C Re

D

' (li)

m = I

"Pw

D ( 12 )

> II 1 2 4

- ttD = Projected area of droplet (13)

P„ P = = w , a density of water and air, respectively .

The evaporation rate of the droplet in flight is.

dm = dthA (Ta-T

g

)/h

f (14)

where A =

2

ttD = surface area of the droplet,

h^fg latent heat of evaporation of water

h heat transfer coefficient from eq. (1)

.

The initial conditions for equations (5), (6), and (14) are, at t = 0;

u =

X

U sin 6 0 0

c

II U cos 0 0 0

D Do

9
The relationship of C

D versus Re

Q

, eq. (11), with the constant C=12 , fits

well with the experimental correlation of a sphere [11] for Reynolds Number

from 10 to 200 which is the range of interest in the present study. The

effects of acceleration and evaporation on C

D

are neglected (which was also

the assumption used in references 6 to 8)

.

After re-arrangement of equations (5) to (15) , and assuming (1-p /p ) =

d. W

1, the equations can be written as, in dimensionless form,

du

x dt

* 3 /9 * * * it -(3/4) Cn HD /2

(p /p ) f (u , U ) (u -V ) D a w x' y x a

(16)

du

dt

-(3/4) C h*D*

_ 3/2

(p /p ) f (u* , u*) u* + D0

a' w x' y y Fr (17)

dD

dt

-2G (H*/D* ) (Re°

pr) "‘ [2 + 0.6 Pr

1/3 Re d*

1 / 2 f (u • u

y>]

(18)

Initial conditions:

where

at t = 0

;

u = sin e x (

* u = cos e y <

* D = 1 (19)

* * f (ux

, u

y

) [

* * 2 * 2

”1 (UX-V + uy J

V

u

X

u /u

x' o

u u /U

y o

V va /u

a ^o

10
* t — tU /H

o

* H = H/D

o

* D = D/Dq

C

°o

= 12/Re 1/2 o \

= p U D /y a o o' a

Fr = UQ/gH = Froude Number

G = P C (T -T )/(p h, ) a pa as w tg

2.2.2. Numerical Results and Discussion

The system of the three first order non-linear differential equations

(16) to (18) has no known closed form solutions, thus numerical solutions

using the Runge-Kutta method were obtained for the following conditions:

U

q

= 12.2 m/s

V°o “ O' 1

0 = -90°

o

H = 1.22 m

T = room temperature (no evaporation) , and 600 °C (T = 85 °C) a s

D

q

= 1/4, 1/2, 3/4, and 1 mm.

The results of the numerical solution are shown in figures 6 to 8.

Figure 6 shows the difference in the trajectory of a droplet with and without

evaporation in a high temperature environment. The change in the horizontal

distance travelled and the longer time required to travel a certain vertical

distance due to the changing diameter by evaporation is clearly shown. For

the case D

q

= 1/4 mm, the droplet is completely evaporated in less than

11
0.5 second over a very short distance of vertical fall. For droplet injected

at less than 90° angle, the influence of evaporation will be less in a finite thickness hot air layer because of a shorter residence time. Note

that the curving trajectory of the droplet in the cross airflow gives an indication of the blocking effect of a large group of droplets on the airflow

caused by the transfer of momentum from the decelerating droplets to the

airflow. The circles in the figure indicate the position of the droplet at

each 0.1 second interval.

Figure 7 shows the percent change in droplet diameter, mass, and magnitude

of velocity as a function of time. It is seen that the smaller the diameter

the faster the rate of change.

2.2.3. Scaling Criteria for Reduced Scale Model Test

Examination of equations (16) and (17) shows that if the droplet diameter

is assumed to remain constant, similarity in droplet trajectory will result

under the same temperature environment if the following four parameters are

kept constant:

* V

a = VUo

- constant

Fr = Uo /gH = constant

h*cd -

o constant

* t = t U /H = o constant (21)

Equations (21) can be used as the scaling criteria when conducting a reduced

scale model study. If the length scale ratio of full size to the model is L,

eq. (21) will give, for the model,

H ~ 1/L

U ~ V ~ D ~t~ 1/L 1/2

(22) o a o

'

The mass flow rate of the combustion products is proportional to area

times velocity, which gives the scaling of mass flow rate as:

ih ~ H

2 V ~ 1/L

5 /

2 (23) d d

12
For the flow field of the full-scale and the model to be similar, the

initial momentum ratio of the water spray to the combustion products should

be kept constant. Therefore, iti U /ill V = constant, which gives the scalinq

of the mass flow rate of the spray as:

^ *

a

(Va/U

o

} ^ *

a

^ 1/L 5/2

(24)

From previous analysis on the temperature variation of the combustion

products flowing through a spray of water droplets, the parameter E = it (ND 2 HW2 h)/(Cp *

aUo^

f°un<^ to be useful for scaling. Assuming the heat

transfer coefficient, h, is constant, the scaling factor for the droplet flux

density is by equations ( 23 ) and ( 24 ),

N 'v (m U )/(D 2 H

3

) ^ L (25) a o

The above relationship for scaling spray droplets was also obtained by

G. Heskestad [ 12 ]

.

When the droplet diameter changes due to evaporation, similarity in

trajectory no longer holds. However, it still holds in an approximate sense

where L is equal to 4. Thus, it is seen from figure 8 that when plotted

* /

against the dimensionless time t , and scaled droplet diameter D

q

/VL, the

deviations in trajectory are close enough to be acceptable. Equations (22)

to (25) therefore can be used as a criterion for reduced scale model study

with the scale factor L equal to 4.

3 . EXPERIMENTAL STUDY

3.1. Preliminary Full-Scale Corridor Sprinkler Test

3.1.1. Test Setup and Instrumentation

In order to determine qualitatively on an experimental basis the effect

of the interaction of the water spray and the hot gas flow on the fire inside

the burn-room, a short series of tests was conducted under a simplified burnroom and corridor arrangement. In this arrangement, hexane fuel injected

through a nozzle at the floor level was used to simulate the fire in a compartment with door open to a corridor. The burn-room was located at the end

of the corridor and in line with the corridor vertical center plane. This is

13
to provide a simpler flow path for the hot gas of the burn-room in order to

avoid the complication of the normal room-corridor situation with a sharp 90°

turn and its accompanying complex flow pattern. A schematic of the arrangement is shown in figure 9.

Instrumentation for this special test involved a gas sampling setup with

the sampling port located at 0.15 m above the burn-room floor midway between

the burner and the burn-room doorway. Two Chromel-Alumel (30 gage) thermocouples were installed inside the burn-room near the ceiling and thirty were

installed outside in the corridor along the vertical center-plane at various

heights from the floor level. The locations of the burner, gas sampling

port, and thermocouples are shown in figure 10. Samples of gas from the

burn-room were fed to an electrolytic oxygen detection cell and an infrared

carbon dioxide analyzer which continuously monitored the 0 2 and C0 2 concentration levels in the air stream going to the burn-room. The thermocouples

in the corridor were shielded from direct contact with the spray droplets by

shallow cups (24 mm diameter) with the thermocouple bead just clear of the

bottom of the cup. This arrangement proved to be fairly successful except

for several thermocouples near the centerline of the sprinkler head where

droplets carried by strong local circulation wetted the thermocouple bead.

These thermocouples then measured the water temperature rather than the gas

temperature

.

Tests were conducted for a series of different sprinkler sizes, heat

release rates, and sprinkler water flow rates. The test conditions are

listed in table 1. Each test was run for 150 seconds except for 5 of these

tests which lasted only 60 to 75 seconds because the flame was starved out

which automatically triggered a safety mechanism and shut off the fuel supply.

The sprinkler was turned on manually 25 to 30 seconds after the fire was

started in all the tests. A check out run with the automatic release mechanism in place showed that 20 seconds is required for the 74 °C (165 °F)

rated sprinklers to open under the fire sizes tested.

3.1.2. Test Results and Discussion

The results of the full-scale tests are shown in table 1, and figures 11

to 15. Table 1 gives the time averaged burn-room hot gas temperature measured

0.31 m below the ceiling. It is interesting to note that the time-averaged

burn-room hot gas temperature in some cases is higher than the calibration

run with no water spray. This is probably caused by the observed lifting up

of the flame and the consequent burning of the fuel at a height closer to the

14
Table 1. Test Conditions of Full-Scale Corridor Sprinkler Experiment

Test

No.

* Heat Release

Rate , Qh

(kW)

Sprinkler

Size

(nominal

,

inch)

Water

Flow Rate

Q

(gal/min)

Burn-Room Gas

Temperature**

,

Time Averaged

(°C)

Observations

and

Comments

1 738 Calibration run 610 No water spray

2 738 1/2 24.5 587 Fog fill-in corridor

and burn-room

3 738 1/2 20 572 Little fog present

4 738 3/8 20 608 Fog fill-in

corridor and

burn-room

5 738 3/8 15 602 Some fog

6 738 3/8 10 630 Little fog.

Droplets very

large

7 738 1/4 15 616 Flame-out in 40 s. Thick fog obscure

flame

.

8 738 1/4 15 600 Flame-out in 40 s. Thick fog obscure

flame

9 738 1/4 10 608 Little fog.

Droplets very large

10 350 Calibration run 456 No water spray

11 350 1/2 35 486 Flame-out in 40 s. Thick fog obscure

flame

12 350 1/2 30 517 Flame-out in 50 s. Thick fog

13 350 1/2 30 505 Flame lift up.

Thick fog.

14 350 1/2 25 502 Some fog.

15 350 3/8 24 512 Flame lift up.

Thick fog.

16 350 3/8 20 510 Fog fill-in

corridor and

burn-room

17 350 3/8 15 490 Some fog.

18 350 1/4 10 488 Little fog.

19 1050 1/4 15 670 Flame-out in 30 s. Thick fog

* * 20 350 1/4 15 514 Large amount of

fog

.

* * * 21 738 1/4 15 629 Large amount of

fog

Heat release rates are only approximate values due to inaccuracy in fuel flow rate

measurement.

Measured 0.31 m below ceiling and 0.61 from doorway.

***Sprinkler located 2.75 m from burn-room doorway.

15
ceiling than the one with no water spray. The heat release rates in table 1 are only a qualitative indication of the fire size due to the inaccuracy in

fuel flow measurement. Table 1 also gives a description of visual observation

during the tests. In general, whenever the flame was put out, thick fog

(condensing vapor) was also present and obscured the view of the flame. This

is caused by the large amount of evaporation of the water spray.

Figures 11 and 12 are the results of the two calibration runs without

water spray. Figure 11 shows the time history of the burn-room doorway exit

gas temperature measured 0.46 m below the doorway soffit. This temperature

is a measure of the average initial gas temperature the water spray will

contact, and it is seen that it reaches a fairly steady-state after 30 seconds

for both fire sizes (indicated by the burn-room gas temperature near the

ceiling) . The much lower gas temperature at the doorway as compared to the

burn-room gas temperature is caused by the large entrainment of incoming cold

air into the exit gas layer at the doorway. Figure 12 shows the decrease in

the ceiling hot gas temperature measured at 0.05 m below the ceiling as it

flows down the corridor due to heat loss through the wall and entrainment of

incoming cold air below the hot gas layer, as discussed in section 2.1.2.

Figure 13, 14, and 15 are examples of the results of the tests with the

sprinkler turned on. Figure 13 shows a typical case on the temperature variation of the ceiling gas flow before and after the sprinkler operation. It

is seen that the temperature was significantly reduced when the sprinkler was turned on. The temperature at 4.5 m from the doorway was reduced to such a low level (60 °C) that heat from the combustion products no longer poses a problem if the corridor is used for evacuation purpose. However, this does

not take into account the effect of poisonous smoke in the flow. Since this

particular burner used produced very little smoke, the effect of the water

spray on the bulk movement of smoke in a fire could not be determined during

this series of tests.

Figure 14 shows the effect of the sprinkler size, and hence the spray

weight mean droplet diameter, on the corridor ceiling exit gas temperature

just outside of the spray zone. The temperature measured was at 0.31 m below

the ceiling which is a measure of the average ceiling flow gas temperature.

It is seen that for approximately the same water flow rate through the sprinkler head, and at approximately the same temperature level at the time the

spray was turned on, the smaller sized sprinkler which produces a spray with

a smaller weight mean droplet diameter [10] achieved a larger temperature

reduction. This confirms the conclusion of section 2.1.

16
Figure 15 gives the oxygen and carbon dioxide concentration of the

incoming airflow at the floor level (0.15 m above) of the burn-room just

before the end of each run. Data from both fire sizes (test Nos. 2-9 and 11-

18) are plotted on the graph since, from figure 11 it can be seen that the

doorway exit gas temperatures are fairly close for both fire sizes. The

normal concentration levels near the burn-room floor are 20.9% for 0 2 and

0.1% or less for C0 2 , both by volume. An increase in C0 2 level and a decrease in 0 2 level indicate the presence of the combustion products and vapor

mixture carried down from the ceiling level by the water spray and mixed with

the incoming fresh airflow, and the amounts changed give an indication of the

strength of the recirculation. It is seen that for the same water flow rate,

the smaller orifices which produced smaller weight mean diameter droplets

created a stronger recirculation flow. For the four cases where the fire was put out, the concentration level changed drastically, which showed the effectiveness of the blockage of the fresh air inflow by the recirculation

flow. It is also seen that the smaller orifice sprinklers required a much

smaller water flow rate to produce the required recirculation flow. Therefore, if a sprinkler is to be used for this special type of fire control, it

should be designed to give a mean droplet diameter in the 0.5 mm to 1.0 mm range

.

The effect of the location of the sprinkler with respect to the burnroom doorway is obtained by comparing the results of test Nos. 7, 20 and

21 (table 1). In test No. 7, the sprinkler was located 1.22 m from the

doorway while in tests 20 and 21 it was 2.75 m from the doorway. The com- parison is shown in the following table. The data were the results at the

end of each test.

Test 7 Test 20 Test 21

Burn-room % 0 2 Concentration (floor

level) 17.0 19 .

3

19.1

Burn-room % Co 2 Concentration (floor

level) 2.9 1 . 10 1.35

Corridor exit gas temperature

(4.5 m from doorway) 40 °C 0 CJ (T\ O 110 °C

Fire at end of test (observation) out not out not out

17
It is seen from the above table that the spray is more effective in

creating recirculation flow at the doorway and in reducing the temperature

downstream of the corridor when placed closer to the doorway. This is because

the spray that covers the doorway encounters the exiting hot gas flow at a higher temperature since there is less chance of heat loss to the walls and

mixing of hot and cold gas layers. The higher temperature gradient between

the hot gas and the water droplets results in a better evaporation effect.

Therefore, it is better to locate the sprinkler closer to the doorway than

farther away from it.

3.1.3. Comparison of Theoretical and Experimental Results

An examination of figure 4 shows that, for all expected values of B, the

dimensionless temperature 0 can be written as, approximately,

6 = (T-T

g )/(To-Tg

) = f (ES) .

Re-arranging terms of the above equation gives

AT = T

q

- T = (T

q

-T

s

) [1-f (ES) ] (26)

where AT is the net reduction in the hot gas temperature due to spray evaporation.

Figure 16 shows a comparison of the theoretical results from equation

(26) and the experimental results on the reduction of the corridor exit gas

temperature. The experimental values are the differences of measured temperatures just before the spray was turned on and just before it was turned off.

The values are from the thermocouple located at 0.31 m below the ceiling and

just outside of the spray zone. The value T

q

in equation (26) was assumed to

be 350 °C because an examination of figure 11 and also the data from the runs with the spray on showed that the burn-rooin doorway exit gas temperature

measured at 0.46 m below the soffit were in the range of 325 °C to 360 °C.

The weight mean droplet diameters for the three sprinkler sizes, at a flow

rate of 0.945 to 1.26 dm 3 /s (15 to 20 gpm) and a spray flux density of 0.034

liter/s*m 2 (0.05 gpm/ft 2 ), were estimated to have a value of between 0.9 mm

to 1.2 mm based on experimental results reported in reference [10]. It is seen from figure 16 that the agreement between the theoretical value based on

a uniform droplet size, and the experimental results, are fairly good.

However, this agreement should be tempered with the fact that the theoretical

18

1
model can only be used to predict the net reduction in the hot gas temperature

due to spray evaporation. It cannot be used to predict the actual temperature

variation of the hot ceiling gas flow without the incorporation into the

formulation of the heat loss through the wall and the complex mixing effect

of the hot gas and cold air layers.

3.2. One-Quarter Scale Model Experiment

In section 2 of this report, it is seen that it is possible to use a reduced scale model in conducting the experiment discussed in section 3.1.

Since a reduced scale model experiment is less costly and less time consuming

to conduct and more versatile in varying the parameters associated with a problem in determining their effects on the results, a one-quarter scale

(L = 4) burn-room corridor apparatus was constructed. The purpose was to

determine whether the scaling criteria developed in section 2 are applicable

by comparing the results obtained with the previous full-scale test, and to

conduct experiments with different sources of fuel to determine the effects

of the water spray on the burning characteristics of the fuels.

3.2.1. Experimental Apparatus and Instrumentation

A schematic of the experimental apparatus is shown in figure 17. A 0.61-m

cube burn-room made of 1.27 cm thickness asbestos millboard is connected

to a 0.61-m by 0.61-m cross sectional area corridor, 2.14-m long and made of

1/16-inch stainless steel plate. The burn-room and the corridor are separated

by a 0.23-m by 0.51-m doorway centered at the centerline of the corridor.

Instrumentation involved the measurement of oxygen concentration near the

burn-room floor, three thermocouples (gage 30, chromel-alumel) located at the

burn-room doorway exit, burn-room floor level, and corridor ceiling exit

(outside of spray zone), respectively, and the natural gas and water flow

rates to the meeker burners and spray nozzle, respectively. The locations of

the burners, gas sampling port, and thermocouples are shown in figure 18.

The output from the electrolytic 0 2 detector cell and the thermocouples were

recorded on strip-chart recorders.

3.2.2. Test Procedure

Tests were conducted using three small industrial spray nozzles of

different design to simulate a sprinkler. The three nozzles are, from data

obtained from the manufacturers:

19
1. Pin nozzle where the spray is generated by a solid jet impact on

a pin opposing the jet. The weight mean droplet size is in the

range of 0.25 to 0.20 mm at a flow rate of 1.01 dm 3 /min (0.267 gpm)

and at a nozzle pressure of 2.76 x 10 5 pascal, (or 40 psig) . The

spray included angle is 90°.

2. Spiral nozzle with an included angle of 90° and a flow rate of

1.38 dm 3 /min (0.366 gpm) at a nozzle pressure of 2.76 x 10 5 pascal. The weight mean droplet size is approximately 0.3 to

0.4 mm.

3. Whirl nozzle with an included angle of 120° and a flow rate of

1.07 dm 3 /min (0.283 gpm) at a nozzle pressure of 2.76 x 10 5 pascal. The weight mean droplet size is approximately 0.4 to

0 . 5 mm.

Three types of fuel were used during the test. They are:

1. Methane gas through four meeker burners at a total heat release

rate of 21 kW,

2. Plexiglass plate 0.635 cm thick and a surface area of 465 cm2 and 697 cm2

,

3. Small wood cribs with a total mass of 1.75 kg made of 0.65 cm by

0.65 cm wood sticks with a spacing of 0.65 cm.

The tests with methane gas as fuel were run with all three nozzles under

steady-state conditions to check the validity of the scaling criteria discussed previously. Steady-state run with meeker burner is possible because

the air supply to the burner is through the burner itself by virtue of the

design of the meeker burner. The tests with the solid fuel were run with the

pin nozzle due to its closer resemblence with a regular sprinkler. The

results of the test are discussed in the following paragraphs.

3.2.3. Comparison of Full-Scale to One-Quarter Scale Results

To check the validity of the scaling criteria (eqs. (21) to (25)

)

described previously, a series of steady-state tests using the meeker burner

with methane gas as fuel were conducted. The results of those tests, as compared with the full-scale tests, are given in figures 19 to 21.

20
Figure 19 shows an example of the time history of the corridor temperature drop when the spray was turned on. With the scale factor L = 4, the

scaled water flow rate through the nozzle was Q L

' = 0.775 dm 3 /s (12.3

gpm) (eq. (24)) as compared with the full-scale rate of 0.945 dm 3 /s (15

gpm) . It is seen that under similar doorway exit gas temperatures, the rate

and magnitude of the corridor temperature drop outside the spray zone are very similar for the full-scale and one-quarter scale tests.

Figure 20 shows the net reduction in the corridor exit gas temperature

as a function of the scaled water flow rate, and figure 21 shows the change

in the oxygen concentration at the burn-room floor level due to the action

of the spray. Based on a weight mean droplet diameter of 0.9 mm for the

1/4-in sprinkler for the full-scale, the mean droplet diameter for the small

— 1/2 nozzles should be 0.9 L =0.45 mm which is fairly close to two of the

three nozzles tested. It is seen from figure 20 and 21 that the results for

the full-scale and one-quarter scale tests agree reasonably well. The

smaller net reduction in the corridor exit temperature and the larger decrease

in the 0 2 content for the one-quarter scale tests are probably caused by the

difference in the spray included angle of the nozzles which is 180° for the

three sprinklers and 90° to 120° for the small nozzles. Since the hot gas

layer is near the ceiling a larger included angle of the spray covers more

of the hotter gas layer and gives longer residence time for the spray droplets

in the layer. Both tend to improve the effect of evaporation. On the other

hand, a smaller angle gives a larger downward momentum transfer from the

droplets to the hot gas and hence creates a better recirculation flow.

From the above discussion, it is seen that the one-quarter scale model

design based on the scaling criteria of equations (21) to (25) can be used

to simulate and predict results of a full-scale test, provided some care is

exercised in choosing spray nozzles to simulate the full-scale flow patterns.

3.2.4. Test Results Using Solid Fuel

In the previous test using meeker burners with methane gas as fuel

under steady-state conditions, the burning rate of the fuel is independent

of the fresh air inflow through the doorway to the burn-room. In an actual

room fire, the oxygen content of the burn-room determines the burning rate

of the combustibles in the room. To investigate the effect of a corridor

water spray on the burning rate and possible extinguishment of a solid fuel,

tests were conducted using plexiglass plates and wood cribs located in the

back half of the burn-room on a piece of 1.2 cm thickness asbestos millboard

21
as shown in figure 18. The fuel was ignited with a small amount of alcohol

and steady burning over the entire plexiglass surface or the wood cribs was established before the spray was turned on. The pin nozzle was used as the

spray nozzle since the pin acts as a deflector and gives a closer resemblance

to the deflector in a regular sprinkler. The results of the tests are illustrated in figures 22, 23 and 24.

Figures 22 and 23 show the burn-room doorway exit gas temperature and

the burn-room floor level oxygen content variations as a function of time

after the spray is turned on. The fuel was plexiglass plate with surface

areas of 465 cm2 and 697 cm 3

, respectively. Observation during the tests

showed that the flame over the burning surface of the plexiglass was extinguished within 30 seconds for the 697 cm 2 case. For the smaller fuel surface

area (465 cm 2

) case, the burning area was reduced to less than one-quarter

of the original area and restricted to the back edge of the plate, but the

burning remained thereafter in a near steady-state. These observations are

shown clearly in figures 22 and 23. The burning rate is represented by the

doorway exit hot gas temperature and it is seen that in both cases the

temperature starts to decrease after the spray is turned on. This decrease

in burning rate is caused by a decrease in the oxygen supply to the burning

fuel as shown in figure 23. Figures 22 and 23 also show that for the flame

to be put out, the initial fire size and hence the exit temperature should

be high enough so that enough vapor can be generated and circulated back

into the burn-room to reduce the oxygen content around the fuel rapidly

enough to a level low enough to starve out the flame. It is interesting to

note that even though the flame was not completely extinguished for the

smaller fire size, the burning rate remained at a reduced rate even with the

oxygen content going back to a near normal level. This is probably because

some very small water droplets were carried into the burn-room together with

the recirculating flow and either physically wet the fuel surface or absorb

enough heat by evaporating around the fuel to keep the burning rate from

returning to its original level.

Figure 24 shows the case when wood crib was used as the fire source. Observation during the test again showed that the flame was reduced to only

flickering near the back edge of the crib. However, the fire over the whole

crib was not extinguished but stayed in a glowing state, even though the

burning rate stayed at a much reduced rate. When the spray was turned off,

flaming burning returned to the whole crib rapidly as can be seen from

figure 24 on the rise of the doorway exit temperature and the burn-room

floor level oxygen content in front of the fire. Figure 24 also shows a

22
typical change of the corridor ceiling gas temperature outside of the spray

zone and the temperature near the burn-room floor level in front of the

fire. It is seen that the spray actually reduced the corridor exit temperature below that of the incoming air temperature to the burn-room. The

increased burn-room floor level air temperature is caused by the mixing of

part of the doorway exit hot gas entrained into the spray with the fresh air

inflow. This also serves as an indication of the creation of recirculation

flow by the spray.

It should be pointed out that the extinguishment of a flaming plexiglass

fire is dependent on the size of the burn-room. If the room is much larger

than the present one, steady-state burning might be achieved sooner and the room oxygen content will not be decreased to the level required for flame

out to occur. However, reduced burning rate will still be achieved as shown

in figures 22 to 24. Comparison of the behavior of the fire using the two

different types of solid fuel also shows that complete extinguishment of a fire with the corridor spray depends on the type of combustibles in the

room. For a fire in an advanced stage like a fully developed deep burning

crib fire, smoldering fire will continue even with a much reduced oxygen

content in the room. This is similar to the problem in firefighting en- countered sometimes when C0 2 is used as an extinguishing agent. Unless the

temperature of the entire burning fuel is reduced to a low level, there is

the chance of returning to flaming combustion once the application of the

extinguishing agent is stopped.

4. CONCLUSIONS

Based on the analysis and experiments described in the previous section,

the following conclusions are obtained:

1. It is possible to predict the net reduction in corridor exit gas

temperature, when a sprinkler in the corridor is turned on, by a simplified one-dimensional analysis. The analysis shows that

spray with a smaller weight mean droplet diameter is more effective

in cooling down the hot combustion products.

2. Scaling criteria based on the motion of a single evaporating

droplet are developed and shown to be applicable in the design of

a reduced scale model experiment and in correlation of the results

between the model and full-scale tests.

23
3. Full-scale and reduced scale model tests show that when a fire is

burning in an adjacent room with open doorway, the application of

a water spray in the corridor is effective in reducing the corridor

exit gas temperature outside of the spray zone to a level low

enough for safe passage.

4. It is possible for the spray to create a recirculating flow at the

doorway so that vapor, fine droplets, and the combustion products

will flow back into the burn-room. This back flow can reduce the

burning rate of the fuel to a much lower level , and may even be

able to extinguish the fire if the initial fire size is large

enough so that sufficient vapor is generated to sufficiently

reduce the oxygen content around the fire.

5. A smaller sprinkler that produces a smaller mean droplet size

under the same water flow rate is more effective than a larger

sprinkler in both the cooling of the combustion products and

reducing the burning rate of a fuel.

6. The sprinkler is more effective when placed closer to the doorway

than farther away from the doorway.

Finally, it should be pointed out that due to the limited number of

test runs and limitation of the nozzle design, the results are only a qualitative indication of the effects of the spray on the hot gas flow and on the

fire. Further tests on a more comprehensive plan and with a better design

and knowledge of the nozzle characteristics (exact droplet size, spray flux

density and larger spray angle) are needed to fully ascertain the optimum

droplet size, spray angle, spray flow rate, and the effects of the spray and

the limitation on a quantitative basis.

24
5. REFERENCES

[1] Minimum Property Standards for Multi-family Housing, HUD 4910.1,

Department of Housing and Urban Development, Washington, D.C. (1973

Edition)

.

[2] Minimum Property Standards for Care-Type Housing, HUD 4920.1, Department

of Housing and Urban Development, Washington, D.C. (1973 Edition).

[3] Installation of Automatic Sprinkler Systems, NFPA No. 13, National Fire

Protection Association, Boston, Mass (1975 Revision)

.

[4] Thompson, N. J. , Fire Behavior and Sprinklers, Chapter 7, National

Fire Protection Association, Boston, Mass. (1964).

[5] Bahn, G. S. , Role of Vaporization Rate in Combustion of Liquid Fuels,

Literature of the Combustion of Petroleum, Advances in Chemistry Series

20, American Chemical Society, Washington, D.C. (1958).

[6] Masters, G., Spray Drying, Chapter 8, CRC Press, The Chemical Rubber

Company (1972)

.

[7] Ahmadzadeh, J. and Harker, J. H. , Evaporation from Liquid Droplets in

Free Fall, Trans. Inst. Chern. Engrs. , Vol . 52 (1974).

[8] Ranz, W. E. and Marshall, W. R. , Jr., Evaporation from Drops, Chemical

Engineering Progress, Vol. 48, Nos. 3 & 4 (1952).

[9] Nishiwaki, N. , Kinetics of Liquid Combustion Processes: Evaporation and

Ignition Lag of Fuel Droplets, Fifth Symposium (International) on Combustion, The Combustion Institute (1955)

.

[10] Yao, C. and Kalelkar, A. S., Effect of Drop Size on Sprinkler Performance,

FMRC Series No. 18792 (May 1970).

[11] Schlichting, H. , Boundary Layer Theory, 4th Ed., McGraw-Hill Book Co.,

New York (1960 )

.

[12] Heskestad, G. , Physical Modeling of Fire, Journal oi Fire and Flammability, Vol. 6 (July 1975).

25
s///////; - ///v//////////////////////////////

26

Figure

1.

Schematic

of

One-Dimensional

Model

for

Spray

Evaporation

Analysis
8=0.513

(T0

=600°C,

T,=85 #

C)

8=0.068

(T

ft *

I20*C,

T«=35°C)

27

Figure

2.

Dimensionless

Temperature

Drop

Due

to

Droplet

Evaporation
r

£

sX

M

(/)

28

Figurr

3.

Variation

in

Vapor

Concentration

Due

to

Droplet

Evaporation
(T-TS

)/(T0

-TS)

ES

Figure 4. Similarity of Temperature Variation

Due to Droplet Evaporation

Figure 5. Schematic of a Droplet in a Cross Wind

29
DROPLET

TRAJECTORY

(WATER)

X/H

-25

-20

-15

-IQ

-05

J

'ceiling '"”T"1

30 -

Figure

6.

Trajectory

ofa

Droplet

Injected

Against a

Cross

Flow
U/U0

or

D/D0

or

Va /Uo=O.IO

Uo s 12.2 m/s

0O

S -90°

Ta

= 600°C, Ts

= 8 5°C

FRACTION MASS EVAPORATED

DIAMETER

VELOCITY (Magnitude)

OTIME WHEN VERTICAL DISTANCE TRAVELED

EQUALS 1.22 m

Figure 7. Time History of the Variations of a Droplet

in High Temperature Cross Flow

(O* Evaporated Prior to 1.22 m)

31
X

s>-

32

l

Figure

8.

Comparison

of

Droplet

Trajectory

Based

on

Scaling

Criteria
HEXANE

FUEL

PUMP

.91x

2.13

DOORWAY

O <

_i

Ol

<t>

UJ

_lUl

33

Figure

9.

Schematic

of

Full-Scale

Corridor

Sprinkler

Test

Setup
SPRINKLER !

ocoQ

OCocooowz<

_Ja> a:uj

»-z

uio

_l<o

oc

111 <oo

cl3Ooo2K

HIX

ilx <Oooa<m

V)<

e>n©

m

p;w

EhWSsHm&oH

Ui8a

-api<

-p

tn

0)

E-I

CD i—l

nJU

UiIP

faP

CDGPP

pa*0g

fO

-ppo

fa0g

*r-| r—I

a.e

nJ

t/i

010O

01

a) i—i apooonp

<d AEh

fal OGO

•r\ -P

ccl ao

PIo

a)pP

•H

fa

34
NO

SPRAY

o

35

Figure

11.

Time

History

of

Exit

Gas

Temperature

at

Burn-Room

Doorway

(No

Spray)
500r

NO

SPRAY

36

DISTANCE

FROM

BURN

ROOM
2

CLO

|C'— c

CL 6 -

35 -on

LJ (0

C

37

Figure

13.

Time

History

of

Corridor

Ceiling

Gas

Temperature

(0.05 m

below

Ceiling)
3o‘3anivH3di/\i3i sv9 iix3 aoamaoo

38

Figure

14.

Time

History

of

Corridor

Exit

Gas

Temperature

Outside

Spray

Zone

(0.31

m

below

Ceiling)
C0

2

CONCENTRATION

~%

BY

VOL.

0

2

CONCENTRATION

~%

BY

VOL

Figure 15. Burner Room 0 2 and C0 2 Concentration (Floor Level)

Just Before the End of Each Run

i 39
QCUJ

_l

z

m

CL

tc

UJ

a

:

a.

CO

a:UJ

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z

(£a.co

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£

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p a

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p

-p d) d> -p is <d IS O >1 Xi cO G

w O

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(d u

CU G £ ^

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4iv‘NOiiona3a 3 an±va3diN 3 i svo

40
or, u.

«

>

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•o *

o> o

41

Figure

17.

Schematic

of

One-Quarter

Scale

Model

Experiment

Setup
DOORWAY,

0.23" x

0.51

CENTERED zo

tnC

*HE >-H (C (L) Ui T)O

W) S3

(0 O Q) i—I - rd (A O

<D Cfl a u

U)

a) (d a Cm 3 .H m a)3

MM &M o

<U

l-l 3

tn *H

Cm

42
cc, UJ

_J

CUoua

a)

5-1 p

-P

(0u

a)

a\

i—

I

a)up

tr> -H

En

43

TIME

AFTER

SPRAY

ON,

s
O

1/2

in.

STANDARD

SPRINKLER

U! -PW

<u

<U i—I

fdu

cou

cu -pu

fd3OI<Dco

-3

•r4upooo

CM

QJP3

Cn H

Cm

44 -

SCALED

WATER

FLOW

RATE, QWL5'2 ,

6PM
O

1/2

in.

STANDARD

SPRINKLER

~

3/8

in.

SPRINKLER

FULL-SCALE,

L=I

O

1/4

in.

SPRINKLER

_

•

SPRAY

NOZZLE,

120°

WHIRL

JET

e

SPRAY

NOZZLE,

90°

SPIRAL

1/4

SCALE

MODEL

in

“lro

CSi

I I J I I -I I —Jo

c* ® Ef $2 *£> ^ jo oj

“10A AS %‘NOIlVdlNaONOO *0

33A31 UOOU INOOdNdnQ

CN

QJ3

-H

fa

45

SCALED

WATER

FLOW

RATE,

QwL 5

'

2

,

GPM
PLEXIGLASS

PLATE

AS

FUEL

(0.635

cm

thick)

PIN

IMPACTOR

NOZZLE

WATER

FLOW

RATE

Q

w

*1.01

dm 3

/min.

(0.267

GPM)

0o'3Uni\/U3d\N31 SV9

46
JJO AVddS

(A

r-I

CL) Pw

W

(0

I—

I

tT'

t

rH

<u>

a;

a

ou

CM o

ro

CM

<UP

tn

•rH P4

47

TIME

AFTER

SPRAY

ON
GAS

TEMPERATURE,

°C

0

2

CONCENTRATION,

%

VOL

WOOD CRIB (1.75 kg) FIRE

PIN IMPACTOR NOZZLE

WATER FLOW RATE Gw

= 1.32 dm3/min. (0.35 GPM)

Figure 24. 0 2 Content and Gas Temperature Variations (Wood Crib Fuel)

48
APPENDIX HEAT TRANSFER BY SPRAY EVAPORATION IN A CROSS FLOW

Referring to figure 1, for a differential control volume dx at mass balance and energy balance equations are, with the assumptions

in section 2 . 1 :

Mass balance:

j * . dm

3- (m + m ) = j dx a v dx

where m^ = mass flow rate of dry air

m

v

= mass flow rate of vapor

m NW

w

constant

m^ = mass evaporated per droplet

N = Droplet flux density, (No. of drops/sec-unit area)

W = Width of corridor

Energy balance :

3— (me T) + 3— (m h ) - m Nh c W = 0 dx a p

' dx v v w f

where h = Enthalpy of vapor at temperature T v

h- = Enthalpy of water at temperature T

c ,c Pa Pv

= Specific heat capacity of air and vapor, respectively

Using h (T) = h (T) - h (T ) + h (T ) = c (T-T ) + h (T ) ^ v v v s v s pv

s v s

and by definition, the heat of evaporation at temperature T

g is

hfg<V * W - W

eq. (A-2) can be written as:

me 3

-^- + m c **+ c (T-T ) + a pa dx v pv dx I pv

s hf

g] m NW w

= 0

x , the

specified

(A-l)

(A- 2 )

(A- 3

)

( A- 4

49
The boundary conditions for eqs. (A-l) and (A-4) are

at x = 0

;

t = T

m

v =0

Substituting eq. (A-l) into eq . (A-2) and using eq. (A-3)

me T + m C (T-T ) + m h dx a pa v pv

v fg

= 0

(A- 5)

Integrating with respect to x and using the boundary condition eq. (A-5)

,

m = m c (T v a pa

or, w(x) = c (T -T)

Pa °

-T) / [c (T-T ) + h, 1 ° / L Pv

S fg

J

]

(A- 6

)

c (T-T ) + hjPv

s fg

where o-i (x) = m /m

v' a

The total heat transferred from hot air to droplets over distance H at

droplets velocity V is:

q

= hA(NWdx) (T-T

s

) (H/V

fc

) = (m^NWdx) h

f

which gives

m = hA (H/V.) (T-T ) /h^ w

/ t s ' fg (A- 7)

where A = nD = surface area of a droplet

h = heat transfer coefficient from eq . (1), Section 2.1

Substituting eq. (A-7) and (A-6) into eq . (A-4) gives the differential

equation for the temperature of the air-vapor mixture:

m c

a P.

C (T -T) C (T-T ) "] P o

1 _1_ v HT * i-i- = - NWhA (H/V ) (T-T ) dx t s

P s

1 + V

C (T-T ) + h_

L pv

s fg

Kfg

(A- 8

)

50

i
Assuming that h, H, V

t

, are constant, and defining

0 = (T-T

s )/ (TQ-Ts

) , S = x/W

B = c (T -T )/h , E = TrD 2 NhW2 H/(m c V ) (A-9)

Py ^ ^ ^“9 ^ P^

The solution to eq. (A-8) can be written, after simplification, as:

B(e-l)

1 + B0 (1+B) fcn

9 ( 1+B)

1+B0 ES (A-10

)

Also, eq. (A-6 ) can be written as:

to = (c /c ) (B) (1-0) (A- 11

)

Eqs . (A-10) and (A-ll) give the solution for the air-vapor mixture temperature

T and humidity ratio to as a function of x.

51

NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 77-1287

2. Gov’t Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Analytical and Experimental Study of Evaporative

Cooling and Room Fire Suppression by Corridor Sprinkler

System

5. Publication Date October 1977

6. Performing Organization Code

7. AUTHOR(S)

Stanley T. Liu 8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4915679

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as No. 9

13. Type of Report & Period Covered Final Report

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less [actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) Investigations, both theoretical and experimental, are conducted to evaluate

the effects of a corridor sprinkler system on the cooling and suppression of a fire in an adjacent compartment connected by an open doorway. A simplified one dimensional mathematical model is presented to predict the net reduction of the

corridor ceiling hot gas temperature by evaporative cooling. Scaling criteria

based on the analysis of the motion of an evaporating droplet were developed for

the correlation of full-scale and small-scale experimental results and the design

requirements of a small-scale experiment. Representative test results from a fullscale and a one-quarter scale model experiments are presented. These tests demonstrate the effectiveness of water spray in reducing the corridor hot gas temperature to a level low enough for safe passage, and in causing a strong recirculating

flow at the room doorway. This flow reduces the oxygen content around the fire

significantly, and results in a much reduced burning rate of the fuel. The effect

of the spray droplet size on the cooling and on fire suppression is discussed.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Automatic sprinklers; compartment fire; corridor sprinkler

systems; droplet size; droplet trajectory; evaporative cooling; fire suppression;

full-scale test; gas temperature; oxygen content; recirculating flow; reduced scale

model test; scaling criteria; spray water flow rate; water spray.

18. AVAILABILITY Unlimited

For Official Distribution. Do Not Release to NTIS

I Order From Sup. of Doc., U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. Cl 3

1 Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCL ASS1FIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

56

22. Price

$ 5.25

USCOMM-DC 29042-P74