Flame inhibition/suppression by water mist:

Droplet size/surface area, flame structure,

and flow residence time effects

H.K. Chelliah *

Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville VA 22904-4746, USA

Abstract

The variation of optimal water droplet size on flame inhibition/suppression is investigated numerically

by exploiting the distinct flow residence time of laminar methane–air premixed flames and counterflow nonpremixed flames. For a gas inflow stream saturated with water vapor, it is shown that the relevant flow

residence time of a premixed flame is governed by the droplet trajectory through the preheat region, while

for a non-premixed flame, the relevant time scale is governed by the convective-diffusive layer relative to

the saturated air-stream. Assuming no velocity lag between the gas and droplets at the inflow, a factor

of four difference in droplet residence time is related to the predicted optimal droplet sizes of 6.5 lm for

premixed flames and 20 lm for non-premixed flames. For droplets larger than the optimal size, the flame

strength (defined as the square of the normalized burning velocity for premixed flames or normalized

extinction strain rate for non-premixed flames) is shown to decrease linearly with increasing specific droplet

surface area. As the water droplets approach the optimal size, the linear correlation stated above fails for

both premixed and non-premixed flames; this failure can have major implications for the design of watermist fire suppression systems. A comparison of present predictions and previously reported experimental

data is also presented.

2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Water-mist; Inhibition/suppression; Laminar flames; Residence time

1. Introduction

Condensed-phase agents, such as fine-water

droplets or water mist, are widely used in many

fire suppression/inhibition applications. Unlike

gaseous-phase agents, the fine-water droplets promote fire suppression/inhibition primarily

through thermal effects associated with the relatively large latent heat of vaporization. Full realization of thermal effects of fine-water droplets,

however, is primarily determined by the droplet

size, the flame structure, and the two-phase flow

field. This paper reports a detailed numerical analysis relating the above parameters to droplet residence time of two commonly used laboratory flow

configurations, namely (i) freely-propagating premixed flames and (ii) non-premixed counterflow

flames.

In an early investigation by Rosser et al. [1],

the heating rate of condensed-phase fire suppressants (e.g. sodium bicarbonate particles) in the

preheat region of a premixed flame was analyzed.

1540-7489/$ - see front matter 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

doi:10.1016/j.proci.2006.08.065

* Fax: +1 434 982 2037.

E-mail address: harsha@virginia.edu

Proceedings of the Combustion Institute 31 (2007) 2711–2719

www.elsevier.com/locate/proci

Proceedings

of the

Combustion

Institute
Their results indicated a strong correlation

between the flame inhibition effectiveness and

the specific surface area of the particles, with particles below 5 lm showing no further change in

their effectiveness. About two decades later, using

finite-rate kinetics and large-activation energy

asymptotics, Mitani [2] reinvestigated the interaction of sodium bicarbonate particles with a premixed flame structure, as well as water sprays

containing alkali salts [3]. The detailed counterflow

flame analysis in the presence of condensed-phase

droplets was first considered by Continillo and

Sirignano [4], where the general formulation for

flame-droplet interactions was presented subjected

to the self-similar approximation. While numerous analytical/numerical investigations followed

[5–8], Lentati and Chelliah [9] reported a detailed

numerical investigation on counterflow flame suppression with fine-water droplets as illustrated in

Fig. 1. Analysis of the flame structure and critical

flame extinction results have yielded quantitative

information about the physical, thermal, and

chemical mechanisms contributing to flame suppression [10].

In the present work, the inhibition of a onedimensional, freely propagating premixed flame

with fine-water droplets, as illustrated in Fig. 2,

is investigated using a two-phase reacting flow

model, similar to that used in non-premixed

flames [9]. Although previous analyses of gaseous

premixed and non-premixed flames have indicated

a one-to-one correlation between the square of the

burning velocity of a premixed flame, ðS0

LÞ

2

, and

the extinction condition of a non-premixed flame,

aext [11], such correlations are shown to break

down with the addition of water droplets, consistent with the recently reported flame suppression/

inhibition experiments [12]. By varying the water

droplet size at the inflow boundary, it is shown

that differences in flow residence times between

the premixed and counterflow non-premixed

flames lead to different optimal droplet sizes, the

underlying reason for the breakdown in the correlation mentioned above. The differences on flame

suppression effectiveness observed based on the

two laboratory flow configurations imply that

extension of flame suppression results to largescale fires with complex flow fields must carefully

consider the residence time and droplet size

effects.

The predicted flame suppression/inhibition

data are also analyzed on the basis of droplet surface area per unit mass, yielding considerable

insight into the non-linear effects associated with

the optimal droplet size. Specifically, the present

results indicate that only droplets much larger

than the optimal drop size satisfy the specific droplet surface area concepts proposed in 1960’s [1],

with major implications for the design of watermist systems.

2. Formulation of two-phase premixed and

non-premixed flames

A hybrid Eulerian–Lagrangian approach is

used to numerically solve for the two-phase reacting flow equations describing steady, laminar premixed and non-premixed counterflow flames in

the presence of fine-water droplets. In the counterflow field, under the assumption of self-similarity

near the axis of symmetry, i.e. v = v(x),

u = rU(x), Yi = Yi(x), T = T(x), where x is the

axial distance, r the radial distance, v the axial

velocity, u the radial velocity, U(x) the x-dependent component of u, Yi the mass fraction of species i (i = 1,...,N) and T the temperature of the

gas-phase, the Eulerian formulations for gasphase species and energy equations are exactly

the same as a one-dimensional premixed flame,

and are given by

Methane

Air/Droplets

Non-premixed

Flame

Gas stagnation

plane

Mixing layer

Droplet

stagnation

plane

Fig. 1. Schematic of the counterflow non-premixed

flame configuration with fine-water droplets introduced

with the saturated air-stream.

Inflow Outflow

Pre-heat region Post-flame region 

Reaction layer x=-∞ x x=+∞

Fig. 2. Schematic of the premixed flame configuration

with fine-water droplets introduced with the saturated

inflow stream.

2712 H.K. Chelliah / Proceedings of the Combustion Institute 31 (2007) 2711–2719
qv

dY i

dx þ

d

dx

ðqY iV iÞ 1⁄4 W ix_ i þ ðdia Y iÞSm ð1Þ

q

XN

i1⁄41

ðv þ V iÞY icpi

dT

dx 1⁄4 ddx k

dT

dx



XN

i1⁄41

W ix_ ihi þ Sh haSm:

ð2Þ

Here, Vi, x_ i, Wi, hi, and cpi are the diffusion velocity, molar production rate, molecular weight,

enthalpy, and specific heat at constant pressure

of species i, respectively, while q and k are the

gas-mixture density and thermal conductivity,

respectively. The terms on RHS, Sm and Sh are

the mass and enthalpy source terms associated

with evaporating droplets and dia is the Kronecker

delta function, where subscript a identifies the

evaporating species (in this case water). The influence of radiative transport on droplet evaporation

and subsequent interaction with flames were

investigated by Kee and co-workers [13,14], however, for flow residence times of the order of several msec as considered here, the radiation

effects are negligible.

The main difference between the two flow fields

is manifested in the mass continuity equation

because of the non-uniform flow associated with

the counterflow field (i.e. radial flow effect). In

the presence of evaporating droplets, the mass

continuity for the counterflow field is given by,

d

dx

ðqvÞ þ 2qU 1⁄4 Sm; ð3Þ

while for one-dimensional premixed flames, with

U = 0, the relevant mass continuity equation

reduces to d(qv)/dx = Sm. For counterflow flames,

the solution for U(x) can be obtained by solving

the radial momentum equation,

qv

dU

dx þ qU2 1⁄4 ddx l

dU

dx

 J þ SU USm; ð4Þ

where l is the coefficient of viscosity, SU is the

radial momentum source term associated with

droplets, and J is the radial pressure gradient defined by J = (1/r)(op/or). For the steady, incompressible flow considered here the leading order

pressure term is set to atmospheric pressure and

q is determined via the equation of state.

The above coupled equations must be solved

subject to the appropriate boundary conditions

of the two flow fields, i.e. for premixed flames,

x 1⁄41 : v 1⁄4 v1; T 1⁄4 T 1; Y i 1⁄4 Y i;1;

x 1⁄4þ1 :

dT 1

dx 1⁄4 0; dY i;1dx 1⁄4 0; ð5Þ

and for non-premixed flames (subscript F and O

identifying the fuel and air streams),

x 1⁄4 l

2 : v 1⁄4 vF; U 1⁄4 UF; T 1⁄4 T F; Y i 1⁄4 Y i;F;

x 1⁄4 þ

l

2 : v 1⁄4 vO; U 1⁄4 U O; T 1⁄4 T O; Y i 1⁄4 Y i;O:

ð6Þ

Unless otherwise mentioned, the following boundary conditions for stoichiometric premixed methane–air flame with saturated water vapor are

imposed, T1 = 300 K and species Y CH4;1 1⁄4

0:054, Y O2;1 1⁄4 0:215, Y N2;1 1⁄4 0:708,

Y H2O;1 1⁄4 0:023. For counterflow flames with nozzle separation distance of l = 1 cm, the inflow conditions used are TF = TO = 300 K, UF = UO = 0

(plug flow boundary conditions), composition of

fuel boundary Y CH4;F 1⁄4 1, while that of air with saturated water vapor Y O2;O 1⁄4 0:228, Y N2;O 1⁄4 0:749,

Y H2O;O 1⁄4 0:023. The values of vF and vO are varied

with momenta balanced to obtain any desired flow

strain rates. The imposition of vF and vO for the

first-order mass continuity equation yields a unique value for J, the pressure eigen value [15,16].

Once the droplet source terms Sm, Sh, and SU,

are evaluated based on the Lagrangian equations

described below, finite-rate chemistry effects can

be resolved accurately to analyze the thermal

effects associated with the droplets.

2.1. Droplet source terms

The droplet source terms Sm, Sh, and SU must

be described based on their trajectory through the

flame structure. The Lagrangian description of

droplet transport is used for small droplet number

density (or dilute droplet loadings) because of the

concerns about the validity of continuum approximation for the condensed phase. The relevant

droplet conservation equations for mass, x-momentum, and energy can be written as [9],

dmd

dt 1⁄4 m_ d; ð7Þ

d

dt

ðmdvdÞ1⁄4m_ dvd þ 3pdlðv vdÞ: ð8Þ

d

dt

ðmdhdÞ1⁄4m_ dðhd þ LÞ þ H; ð9Þ

where the subscript d refers to droplet properties.

Here, d is the droplet diameter, md = (p/6)qdd3 the

droplet mass, m_ d the mass evaporation rate of the

droplet, hd 1⁄4 h0

d þ cp;dðT T 0Þ the specific enthalpy of the droplet, L the specific latent heat of

vaporization, and H the heat flux to the droplet

from the gas. Both m_ d and H are estimated using

an analytical formula derived assuming d2

-law

[17], which is applicable for isolated evaporating

droplets under quasi-steady evaporation conditions. In Eq. (8), the viscous drag force due to

droplet motion relative to the gas-phase is based

H.K. Chelliah / Proceedings of the Combustion Institute 31 (2007) 2711–2719 2713
on Stokes drag coefficient of CD = 24/Red. This

assumption is valid for droplet Reynolds number

Red 6 1, which is generally satisfied for cases

where the initial droplet velocity is assumed to

be the same as the gas velocity at the inflow

boundary. Furthermore, the droplet evaporation

in the cold inflow region, i.e. outside the thermal

mixing layer, is avoided by saturating the gas

stream with water vapor [18]. Consequently, the

droplet size remains constant until the droplets

enter the preheat (convective-diffusive) layer.

For counterflow flames, in addition to Eqs.

(7)–(9), an equation for radial momentum of the

droplets, given by

d

dt

ðmdUdÞ þ mdU2

d 1⁄4 m_ dUd þ 3pddlðU UdÞ;

ð10Þ

coupled with the local droplet number density, nd,

must be integrated to obtain the mass source

terms Sm, Sh, and SU that appear in Eqs. (1)–

(4). For counterflow flames, nd will vary with axial

location and its variation can be obtained by integrating the following equation for droplet flux

fraction, FðtÞ [9]

dF

dt

þ 2FUd 1⁄4 0: ð11Þ

Here, F 1⁄4 1 at the droplet inflow boundary, but

F will decrease rapidly as the droplets approach

the stagnation plane because of the flow straining

effect. In one-dimensional premixed flames,

assuming negligible droplet coalescence or

break-up, nd remains constant across flame structure (i.e. F 1⁄4 1 everywhere).

To outline the approach used to evaluate the

droplet source terms, let / denote the right-hand

side terms of Eqs. (7)–(10) (i.e. m_ d, m_ dvdþ

3pdlðv vdÞ, m_ dðhd þ LÞ þ H, and m_ dUdþ

3pdlðU UdÞ). In terms of /, the droplet source

terms in Eqs. (1)–(4) contributing to an arbitrary

grid point j with a grid size of dxj, can be written

as

S/j 1⁄4 ð1=dxjÞnd0 vd0

XKj

k1⁄41

Z tkþdtk

tk

FðtÞ/dt; ð12Þ

where at each cell j the integration of Lagrangian

equations are performed in Kj time steps with step

size of dtk. Here nd0 is the droplet number density

at the inflow boundary and vd0 is the velocity of

droplets, assumed to be same as the gas-velocity.

For one-dimensional premixed flames, Eq. (12)

is still applicable with the constraint that U and

Ud are identically zero.

2.2. Numerical method

In the absence of droplet source terms, numerical integration of Eqs. (1)–(4) describing non-premixed and premixed flame propagation using a

modified-Newton approach is well established

[16,19]. In the presence of evaporating water droplets, a similar modified-Newton approach coupled

with the source terms arising from the integrated

Lagrangian equations of droplet motion has been

previously adopted by [6,9,13]. In particular, the

Lagrangian equations describing the droplet

motion are integrated via a mixed explicit–implicit

scheme, as described in [9]. The approach selected

is based on numerical stability in the limit the

time-step size dtn fi 0 in Eq. 12. Provided the

droplet does not travel more than a fraction of

the local grid size, the source terms determined

by integration of Lagrangian equations yield stable consistent results.

The thermochemical and transport properties

in the conservation equations are calculated using

the Sandia Chemkin and transport libraries

[20,21]. The detailed chemical reaction model for

methane–air system used consists of 17 species in

39 elementary reactions [22].

3. Results and discussion

Based on phenomenological concepts and

more rigorous large-activation energy asymptotic

solution approaches, it can be shown that the

burning velocity of a premixed flame is proportional to the square-root of the chemical reaction

rate. The overall burning rate, however, can be

inhibited by several mechanisms, namely chemical

mechanisms via scavenging of radical species,

thermal mechanisms via decrease of flame temperature, and physical mechanisms via dilution or

flow field modifications. In general, flame inhibitors may include one or several of the above

mechanisms, however, the focus here is to understand the dominant thermal suppression mechanism of fine-water droplets.

In experiments, the fuel–air mixture is expected

to be saturated with water vapor if water droplets

are introduced sufficiently upstream of the premixed flame [12,18]. For a typical inflow pressure

and temperature of 1 atm and 300 K, the saturation mass fraction of water vapor is 0.023 (or

0.035 in mole fraction). The resulting dilution or

displacement of the fuel-air mixture by water

vapor can reduce the burning velocity of the premixed flame. For example, the predicted burning

velocity of a dry stoichiometric, methane–air

flame of S0

L 1⁄4 40:8 cm s1 reduces to

SL,vap = 34.9 cm s1 with addition of saturated

water vapor, about 14% reduction. Since the focus

here is on condensed phase mass addition, the

flame burning velocity results with addition of

fine-water droplets are normalized by SL,vap. An

important implication of imposing saturated

water vapor condition is that the droplets entering

the computational domain (i.e. x = 1) do not

2714 H.K. Chelliah / Proceedings of the Combustion Institute 31 (2007) 2711–2719
evaporate until they reach the preheat (convective-diffusive) region of the premixed flame, as

illustrated in Fig. 2. Therefore, the droplet residence time in the cold upstream region of the

flame structure is of no consequence in terms of

mass evaporation.

3.1. Droplet transport and source terms

When a significant mass fraction of water

droplets is introduced, the flame burning velocity

decreases significantly with changes in the flame

structure. For the purpose of analyzing droplet

history and dynamics, (e.g. droplet size, temperature, and velocity) and the distribution of source

terms contributing to the flame inhibition, the

coupling source terms are initially turned ‘‘off’’

in the gas-phase equations, i.e. Sm = SU = Sh ” 0.

Under such uncoupled conditions with the flame

structure unaffected, Fig. 3 shows the variation

of normalized droplet size (d/d0 where d0 is the initial droplet size at the inflow boundary) for several

initial monodispersed droplet sizes of 10, 20, and

30 lm. It is seen that the small droplets evaporate

rapidly upon entering the preheat region of the

premixed flame, while the larger droplets continue

to evaporate downstream of the flame, in the postflame region. The observed variation in evaporation rate with decreasing droplet size can be

directly related to the increased surface area to

volume ratio of the droplet. For dilute droplet

loading and low shear flows, it is reasonable to

assume negligible droplet coalescence or breakup, hence the droplet distribution will remain

monodispersed at any given cross-section while

their size will decrease across the flame structure.

The gas velocity increases rapidly (because of

the gas expansion) across the steady premixed

flame structure. Consequently, the motion of relatively large droplets, introduced with the same initial velocity as the gas, may show a velocity lag

compared to the gas, as seen in Fig. 4. The droplet

response to such sudden velocity variation can be

characterized by Stokes number, defined as

St = td/tf, where td is the droplet response time

given by td 1⁄4 qdd2

d=ð18lÞ and tf is the flow

response time given by tf  d/SL. Here d is the

characteristic flame thickness, essentially the

thickness of the preheat zone. For droplets of

10 lm, the estimated values for St = 0.04 and

for 30 lm it is St = 0.34. As seen from Fig. 4, with

increasing St, the velocity lag between the droplets

and the gas increases. Besides the velocity lag

effect, the droplet temperature (Td and uniform

inside the droplet) may lag from the thermal equilibrium temperature (Td,equil) as the droplet size

increases, i.e. when the heat flux to the droplet is

equal to the latent heat of evaporation. Figure 5

shows a comparison of the predicted droplet temperature with the equilibrium droplet temperature

indicating that small droplets follow Td,equil closely while the larger droplets lag Td,equil slightly

(note: Td,10lm ” Td,equil). Because of the relatively

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

Distance, x (cm)

Normalized Diameter

0 0.2 0.4 0.6 0.8 1

0

750

1500

2250

Gas Temperature, T (K)

Gas Temperature 

10 μm

20 μm

30 μm

Fig. 3. Variation of normalized droplet diameter across

the premixed flame structure, for different initial droplet

sizes. Also shown is the gas-phase temperature vs.

distance.

0 0.2 0.4 0.6 0.8 1

0

100

200

Distance, x (cm)

Velocity (cm/s)

0 0.2 0.4 0.6 0.8 1

0

750

1500

2250

Gas Temperature, T (K)

Gas Temperature 

Gas Velocity 

10 μm

20 μm

30 μm

Fig. 4. Comparison of the gas and droplet velocity

across the premixed flame structure, for different initial

droplet sizes. Also shown is the gas-phase temperature

vs. distance.

0 0.1 0.2 0.3 0.4 0.5

300

350

400

Distance, x (cm)

Droplet Temperature, Td (K)

0.1

0

750

1500

2250

Gas Temperature, T (K)

Gas Temperature 

10 μm

20 μm

30 μm

Fig. 5. Comparison of gas and droplet equilibrium

temperature (Tequil) across the premixed flame structure,

for different initial drop sizes.

H.K. Chelliah / Proceedings of the Combustion Institute 31 (2007) 2711–2719 2715
low evaporation temperature of water, this subtle

difference has no significant effect on the predicted

results.

With gas-droplet coupling turned ‘‘off,’’ Figs. 6

and 7 show the mass source term (Sm) and the

enthalpy source term (Sh haSm), respectively,

for selected droplet sizes. The magnitude of the

source terms depends on the droplet loading,

which can be characterized by the initial droplet

mass fraction (Y0) defined as Y0 = md0nd0vd0/

(md0nd0vd0 + q1v1), where md0 is the initial

mass of the droplet. For Y0 = 0.02, Fig. 6 shows

that 10 lm droplets have a rapid mass evaporation rate at the flame front, hence the maximum

thermal cooling effect near the peak heat release

region associated with the enthalpy source terms

as shown in Fig. 7, while 30 lm droplets show a

broad evaporation region with significant mass

and energy transfer in the post-flame region. The

enthalpy source terms in the post-flame region

seen for large droplets can affect the flame via

modification of the downstream boundary condition due to heat loss, however with a secondary

impact on the flame inhibition.

3.2. Premixed flame inhibition and comparisons

with non-premixed flames

When the droplet interaction with homogeneous kinetics is turned ‘‘on’’ (i.e. Sm „ 0, etc.), a

significant inhibition of the flame burning velocity

is expected, depending on the droplet loading and

size. For the purpose of comparison of premixed

flame inhibition results with counterflow non-premixed flame extinction results, the square of the

normalized burning velocity of a premixed flame

is defined here as the flame strength,

S 1⁄4 ðSL=SL;vapÞ:

2 Figure 8 shows the variation of

the predicted flame strength vs. droplet mass fraction (Y0) for several initial droplet sizes. The previously reported experimental data [12] with a

median droplet size of 13 lm is also shown in

Fig. 8 indicating a reasonable agreement with

the present predictions. The existence of an optimal droplet size can be clearly demonstrated by

plotting S vs. d0 as shown in Fig. 9, with Y0 as

a parameter. For Y0 = 0.03 and a range of droplet

sizes considered, flame strength S is seen to

asymptote as d0 approaches 6.5 lm. Our previous

numerical work [9,10], however, has shown that a

different optimal droplet size (15–20 lm) exists

for counterflow non-premixed flames, as shown

in Fig. 10. The distinct optimal droplet size for

the two flame configurations considered can be

explained by considering the flow residence times

of the two flames, as discussed below.

For droplet water mass fraction Y0 = 0.01 and

optimal drop size of 6.5 lm (see Fig. 9), the premixed burning velocity is 29 cm s1

. Based on

the droplet trajectory through the preheat layer

of this flame, the integrated droplet residence time

0 0.1 0.2 0.3 0.4 0.5

0

0.005

0.01

0.015

Distance, x (cm)

Mass Source Term, Sm (gm/cm3)

0.1

0

750

1500

2250

Gas Temperature, T (K)

Gas Temperature 

10 μm

20 μm

30 μm

Fig. 6. The mass source term (Sm) across the premixed

flame structure, for different initial droplet sizes and

Y0 = 0.02. Also shown is the gas-phase temperature

profile.

0 0.1 0.2 0.3 0.4

0

2

4

x 1010

Distance, x (cm)

Q and (Sh Si m)× 50 (erg/cm3/s)

0.1

0

1000

2000

Gas Temperature, T (K)

Gas Temperature 

Heat Release Rate (Q)

(Sh iSm) for 20 μm

(Sh i

Sm) for 30 μm

(Sh i

Sm) for 10 μm

Fig. 7. The enthalpy source term (Sh hiSm) across the

premixed flame structure, for different initial droplet

sizes and Y0 = 0.02. Also shown is the gas-phase

temperature and heat release rate profiles.

0 0.01 0.02 0.03

0

0.2

0.4

0.6

0.8

1

Droplet Mass Fraction, Y0

(SL/SL,vap)

2

6.5 μm

10 μm

30 μm

20 μm

Experimental data (Ref. [12])

Fig. 8. Variation of the flame strength of a premixed

flame vs. droplet mass fraction, for different initial drop

sizes.

2716 H.K. Chelliah / Proceedings of the Combustion Institute 31 (2007) 2711–2719
is 4.1 ms. In contrast, for a non-premixed flame

with the same Y0 = 0.01 and drop size of 20 lm,

the flame extinction strain rate is 287 s1

. The corresponding integrated residence time of a droplet

entering the convective-diffusive layer on the airside of the non-premixed flame is 16.2 ms. Besides

the subtle difference in temperature profile and

water vapor pressure, this factor of 4 difference

in the residence time is the primary reason for variation of optimal droplet size between the two laboratory flames considered. While such variation in

residence time on the effectiveness of droplet/particle size has been previously understood qualitatively [23], this is the first time quantitative

optimal drop size data has been presented based

on two commonly used laboratory flames.

3.3. Droplet surface area effect

In early studies on condensed-phase fire suppressants, a significant emphasis was placed on

the specific particle surface area [1]. Further analysis of the present numerical results in the context

of such surface area concepts highlights interesting limitations of this important hypothesis.

Assuming that the fine-water droplets always

remain spherical, the surface area of monodispersed droplets per unit mass is proportional to

Y 0=d0  As. An identical value for the specific

surface area parameter As can be realized by various combinations of inflow droplet mass loading

Y0 and droplet size d0. Following this definition of

As, all the flame strength results shown in Fig. 9

for premixed flames are presented in Fig. 11 as a

function of As. Several intriguing conclusions

can be drawn from Fig. 11, namely for droplets

greater than 6.5 lm, the premixed flame strength

ðSL=S0

LÞ

2 decreases linearly with increasing As.

But, for optimal droplet size of 6.5 lm or smaller,

a significant departure from the linear behavior is

observed.

Furthermore, based on the flame extinction

data shown on Fig. 10, a similar plot for non-premixed flame strength aext/aext,vap as a function of

As can be constructed as shown in Fig. 12. Once

again, for droplets greater than the optimal size

of 20 lm, the flame strength varies linearly with

As. The optimal droplets or smaller (i.e.

d0 6 20 lm) clearly deviate from this linear trend.

The new results presented in Figs. 11 and 12

can have a significant impact on design of optimal

fine-water (or mist) fire-suppression systems. Specifically, if the water mist used is well above the

optimal droplet size based on the characteristic

residence time of the relevant flame structure

(i.e. premixed or non-premixed, laminar or turbulent, etc.), then simple surface area per unit mass

analysis is sufficient to determine the water-mist

loading, or the size. On the other hand, if the

water droplet employed is of the optimal size or

smaller, then a simple linear correlation between

0 10 20 30 40

0

0.2

0.4

0.6

0.8

1

Droplet Diameter, d0 (μm)

(SL/SL,vap)

2

Y0=0.01

Y0

=0.02

Y0

=0.03

Fig. 9. Variation of the flame strength of a premixed

flame vs. droplet diameter, for selected water mass

fractions Y0.

0 10 20 30 40 50

0

0.2

0.4

0.6

0.8

1

Droplet Diameter, d0 (μm)

(aext/aext,vap)

Y0=0.01

Y0

=0.02

Y0

=0.03

Fig. 10. Variation of the flame strength of a nonpremixed flame vs. droplet diameter, for selected water

mass fractions Y0.

0 1 2 3

x 10

0

0.2

0.4

0.6

0.8

1

Y0/d0 (1/μm)

(SL/SL,vap)

2

6.5 μm

10 μm

20 μm

30 μm

Fig. 11. Variation of the flame strength of a premixed

flame vs. droplet surface area parameter ðAs 1⁄4 Y 0=d0Þ.

The line is a linear fit through predicted data for

d0 P 10 lm.

H.K. Chelliah / Proceedings of the Combustion Institute 31 (2007) 2711–2719 2717
flame strength and surface area parameter shown

in Figs. 11 and 12 will yield an inaccurate estimate

for Y0. Consequently, any future design of watermist systems with optimal droplet size distributions must carefully consider the nonlinear

interactions between thermal and finite-rate effects

to determine the true mass loading.

4. Conclusions

The purpose of this paper is to present quantitative information about the coupling between

optimal water droplet (or mist) size and the flow

residence time in suppression/inhibition of gaseous flames. For a case where the water droplets

were introduced with the same velocity as the

gas velocity, by considering two distinct flame

structures with a factor of four difference in flow

residence times, it was shown that the optimal

monodispersed water droplet size can vary from

20 to 6.5 lm.

Another important finding of the present work

is that the commonly assumed hypothesis about

droplet surface area per unit mass is only applicable for droplet sizes greater than the optimal drop

size that inhibits or extinguishes the flame. By

considering both premixed and non-premixed

flames with distinct optimal drop sizes, it has

been conclusively shown that as the optimal drop

size is approached, the non-linear coupling

between thermal effects and finite-rate chemistry

leads to the break down of the linear correlation

between flame strength and surface area parameter. This new finding can have a significant

impact on design of optimal water mist systems

where the water supply is limited, for example

water-mist fire suppression systems in space

applications.

Acknowledgments

This work was supported by the DoD SERDPSs Next Generation Fire Suppression Technology Program and by NIST internal funding.

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0 1 2 3 4

x 10

0

0.2

0.4

0.6

0.8

1

Y0/d0 (1/μm)

(aext/aext,vap)

10 μm

20 μm

30 μm

50 μm

40 μm

Fig. 12. Variation of the flame strength of a nonpremixed flame vs. droplet surface area parameter

ðAs 1⁄4 Y 0=d0Þ. The line is a linear fit through predicted

data for d0 P 30 lm.

2718 H.K. Chelliah / Proceedings of the Combustion Institute 31 (2007) 2711–2719
Comments

Yuji Nakamura, Hokkaido University, Japan. Could

you comment on the possible reason for breaking the

classical surface area correlation in small mist? Is this because the mist is not in a liquid phase (rather gas phase)

in the flame zone?

In the experiment, it could be possible that droplets

would gather together (increase in diameter) before moving into the flame sheet. Is there any chance this may cause

the discrepancy between your single diameter prediction?

Reply. Effectiveness of large droplets (>optimal size)

is clearly governed by the thermal diffusion across the

boundary layer, hence the observed linear correlation

with specific surface area. As correctly pointed out, for

optimal or smaller droplets, the effectiveness is not

directly related to the surface area, but is a function of

the location where the maximum cooling due to latent

heat of vaporization occurs, i.e., reaction layer or preheat layer.

The maximum condensed water mass fraction considered is Y0 = 0.03 and corresponding ratio of droplet–droplet separation distance to droplet diameter is

greater than 20. Under these conditions, the probability

of droplet coalescence is negligible hence the droplet size

distribution is expected to remain monodispersed. It

should be pointed out that premixed flame inhibition

predictions shown in Fig. 8 indicate reasonable agreement with experiments; however, I have no explanation

for the differences observed in non-premixed flame suppression comparisons.

d

Michael Delichatsios, University of Ulster, UK. Can

you comment on the effect of flame radiation (dominant

in fires) on the determination of any ‘‘optimal’’ size?

Reply. In the present laboratory flames with short

flow residence times, the radiation effects are not important. However, in large-scale fires, the radiation field can

clearly influence the optimal droplet size. Furthermore,

the departure of the droplet inflow velocity from the inflow gas velocity (assumed to be identical here) can also

affect the optimal droplet size.

d

James W. Fleming, Naval Research Laboratory,

USA. Was gravity included in your counter-flow calculations? An estimation of the location of the aerosol

oscillatory plan suggests that drops might reside longer

in the flame region if delivered with the air from the

lower tube. Could this be a reason for the disagreement

you report?

Reply. In numerical simulation of counterflow flames

under high-strain rates, the gravity effects are not important. However, in experiments with large cross-sectional

feed tubes where the gas-velocity approaches the settling

velocity of droplets, a shift in the droplet size distribution may be experienced depending on whether droplets

are introduced from the top or the bottom nozzle. We

have accounted for such shift in droplet size distribution

at the nozzle exit, so it is unlikely that gravity is the cause

for the observed differences in counterflow flames.

H.K. Chelliah / Proceedings of the Combustion Institute 31 (2007) 2711–2719 2719