physics behind water mist

Proc. IWMA conference 2004, 6-8 October 2004, Rome, Italy

The physics behind water mist systems Bjarne Paulsen Husted, Danish Institute of Fire and Security Technologyi, Denmark Göran Holmstedt, Lund University, Department of Fire Safe Engineering, Sweden Tommy Hertzberg, SP Swedish National Testing and Research Institute, Sweden 1 Introduction The use of water mist for fire extinguishment has increased rapidly in recent years. The main reason is the abandonment of halon-based extinguishing system in favour of environmentally friendlier systems. With increased use of water mist, the evolution of existing techniques for producing relevant droplets for a chosen enclosure and probable fire scenario has occurred. This has called for a more detailed and thorough understanding of the interaction between water and the fire environment. One tool to enhance the knowledge of water mist is to use numerical models. However there is a big discrepancy between the results from current available models for calculation of water mist as Fluent, FDS and Branzfire and results from experiments1. In this paper, physical and theoretical descriptions of water droplet dynamics in a fire environment are gathered to form a basis for more accurate numerical models. Phenomena that will be discussed are:

• Spray formation • Droplet size distribution • Spray throw-length • Spray-gas momentum transfer • Heat absorption • Gas- and surface- cooling

Different types of nozzles will be discussed and spray droplet velocity maps based on PIV, (Particle Induced Velocimetry) will be shown. 1.1 Formation of droplet from different types of nozzles There are three different mechanisms for forming a spray:

o By creating a rotation in the spray (swirl), o By colliding water jets o By direct droplet creation from a turbulent water jet, on leaving the nozzle.

The most common type in water mist systems is by direct droplet formation from a turbulent water jet. How the break-up of the jet takes place depends on the jet speed and diameter. There are four different ways droplets can be formed from a water jet:

A �Rayleigh break-up� regime. The droplet is formed far away from the nozzle. The diameter of the droplets is bigger than the hole in the nozzle.

i Email: [email protected], Danish Institute of Fire and Security Technology, Jernholmen 12, 2650 Hvidovre, Denmark, ph. +4536349000. Fax. +4536349001

1

mailto:[email protected]


B �First wind-induced break-up�. Droplet formation occurs several nozzle diameters downstream of the nozzle outlet. The diameter of the droplets is about the same size as the hole in the nozzle.

C �Second wind-induced break-up�. Droplet formation takes place a short distance

downstream of the nozzle. The diameter of the droplets is smaller than the diameter of the hole in nozzle.

D �Atomization�. Droplet formation takes place at the exit from the nozzle. The diameter of the droplets is much smaller than the diameter of the hole in the nozzle.

Figure 1 shows a picture of the four different ways droplets can be formed.

Figure 1. Different kinds of droplet formation2

The dominating factors that control the droplet formation mechanism are the Reynolds number and the Ohnesorge number. The Ohnesorge number, Oh, is the ratio between the viscous forces and the surface tension.

dOh

ρσµ

= (1)

where µ is the dynamic viscosity of the fluid (Ns/m2), σ is the surface tension (Ν/m), ρ is the density and d is the diameter of the nozzle. For a typical high pressure nozzle with a internal diameter of 0.8 mm the Ohnesorge number is 0.004.

2


Figure 2. Droplet formation at different Reynolds- and Ohnesorge numbers /Schneider/2

1.2 Droplet size distribution after droplet formation The creation of a spray results in droplets of different sizes. Small droplets (<2mm) are more or less spherical and can be accurately described by a diameter. To describe the droplet distribution of the entire spray, statistical methods are normally used. One way to characterize a spray by a single parameter is to use the Sauter mean diameter, often written d32. Sauter mean diameter is a number used to express the average droplet size in terms of the average ratio of volume to surface area of the droplets. Sauter mean diameter therefore is the diameter of a hypothetical droplet whose ratio of volume to surface area is equal to that of the entire spray. The droplet size also depends on the pressure in the nozzle. The droplet size is reduced considerately up to a pressure of 7 bars. At higher pressures, the situation becomes more complex and droplet size is reduced at a much lower rate. Figure 3 shows the measured droplet size distribution at different pressures.

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300

Diameter (10^-6 m)

% D

ropl

ets

15 bar80 bar100 bar

Figure 3. Droplet size distribution at 3 different pressures1

3


Table 1 shows d32 (Sauter mean diameter) variation at the 3 different pressures in Figure 3. It can be seen that the diameter is only reduced by 50%, when increasing the pressure from 15 to 100 bar. Table 1 d32 variation with pressure1 15 bar 80 bar 100 bar Sauter mean Diameter 41.30 µm 33.07 µm 23.70 µm

1.3 Deceleration of droplets � aerodynamic properties of the

spray 1.3.1 Forces on a single droplet A number of forces act on a droplet that is moving in air e.g. the �Magnus�, Saffman and Faxen forces. However, many of them can be neglected compared to gravity and frictional forces. The remaining forces that acts on the droplet can be derived from Newton's second law:

( ) ( ) lll

D vvvvdCgmvmdtdF −⋅−⋅

⋅⋅⋅−⋅⋅=

8

= 2 ρπ

(2)

In the equation:

F = The total force which acts on the droplet, m = mass of droplet = 6

3dw

πρ ⋅

ρw = density of water, d = droplet diameter, v = droplet velocity vector, g = gravity, lv = velocity vector of the surrounding air,

CD = drag coefficient related to the Reynolds number of the droplet ) v

( l

µρ⋅⋅ d

Due to the frictional force, the droplet will slow down. Setting the force F = 0 in equation 2 gives the terminal velocity of the droplet. For droplet Reynolds number less than 1, the drag coefficient (CD) can be calculated on the basis of Stokes law, CD = 24/Re. This means that equation 2 can be solved analytically for droplets up to 80 µm. For droplets bigger than 80 µm (Re>1), the equation must be solved by numerical methods. 1.3.2 Deceleration of single water droplets with high initial speed Water droplets that leave a spray nozzle at higher speed than the terminal velocity are quickly slowed down. Deceleration and throw length can be calculated by equation 2, but in this high-speed case, calculation of the drag coefficient is more complex and the equation must be solved numerically. Figure 5 and figure 6 show examples of deceleration of single droplets in cold air (i.e. no mass loss) with an initial speed of 100 m/s. The surrounding air is considered to be still.

4


0 0.002 0.004 0.006 0.008 0.010

10

20

30

40

50

60

70

80

90

100

Time [s]

m/s

0.005 mm0.01 mm0.05 mm0.1 mm0.5 mm

Figure 5 Vertical deceleration of different droplet sizes. Initial speed is 100 m/s.

0 0.002 0.004 0.006 0.008 0.010

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time [s]

m

0.005 mm0.01 mm0.05 mm0.1 mm0.5 mm

Figure 6 Vertical distance vs. time for various droplet sizes. Initial speed 100 m/s.

As can been seen from the calculations in figure 5 and figure 6, small droplets decelerate very fast. A droplet size of 100 µm, typical for water mist systems, deaccelerates in 0.01 second from 100 till 10 m/s in a distance of 0.3 m. During deceleration, the droplet evaporates, depending on the moisture content and temperature of the air. This influences the drag force and the droplet size, but according to 3 it has only a minor influence on the drag force in equation (2). As can be seen from the calculation, the throw length for single water droplets with diameters < 100-200 µm is very short, even if they have a initial speed created by a water pressure of 100-200 bar in the nozzle. The only way to increase throw length is to reduce the relative velocity between the droplet and the surrounding air.

5


1.3.3 Retardation of water droplets in a spray The momentum lost by the droplet during deceleration is transferred to the surrounding air, which will therefore move in the same direction as the droplet. In a spray with many droplets, this implies that air will be sucked into the spray. The acceleration of air means that the relative velocity between the droplets and the surrounding air is reduced, which will increase the throw length of the droplets. How this will occur depends on how the nozzle distributes the droplets. The most common spray patterns are full cone and hollow cone. In a full cone spray, the droplets are distributed evenly across the entire spray angle, whereas in a hollow cone, the droplets are mostly in the perimeter of the cone. By analysing two pictures of droplets illuminated with a laser sheet and taken with a short time interval, the velocity field can be defined experimentally. This type of measuring equipment is called PIV, �Particle Induced Velocimetry�, figure 7.

Figure 7 Velocity field in a spray (Hollow cone, 80 bar, nozzle diameter = 0.8 mm).

From figure 7, it can be seen that the droplets in the spray are decelerated from 90-100 m/s to10-30 m/s in a distance of 0.3 m and that the velocity field inside the hollow cone is very complex.

ϑ

φ

νl

s

r Nozzle

Figure 8. Entrainment of air in a full cone spray

6


For nozzles that form a full cone spray the air velocity, νl, in the spray can be calculated from4:

r

pmvl

0.5

w

⋅

≈∗

where is mass flow rate of water, p is the nozzle pressure and r is the spray

radius, calculated from

∗

mw

o

o

45, tan

45,21 ) + 2/( tan

>/4)( ⋅ =

≤

⋅⋅≈

ϑϑ

ϑφϑ

sr

sr

where ϑ is the cone angle, s is the distance from the nozzle and φ is defined in the entrainment picture above.

Velocity of air in a full cone spray (spray angle 60 degrees)

0102030405060

0 0,2 0,4 0,6 0,8 1 1,2

Distance from nozzle, m

m/s

1 l/min2 l/min5 l/min10 l/min

Figure 9 Calculated mean air flow speed in a full cone at various water mass flows

From figure 9, it can be seen that the air velocity is less than 5 m/s 1 m downstream of the full cone nozzles, at flows up to 10 l/min. This means that the droplet will have lost most of the initial momentum and also the additional momentum obtained from air entrainment close to the nozzle. 1.4 Evaporation of water droplets Evaporation of water droplets depends on the temperature and moisture content in the surrounding air. In the following, only temperatures above 100° C are considered. The heating of the droplet from the start temperature to 100° C is ignored, as the energy required is much smaller than the energy required to evaporate the droplet. The dynamic change of droplet volume is given by

dtdd

dtd

dtd

dtdV dddd 22

3

23

61

61 Π

=⋅Π=Π= (3)

7


The convective heat transfer to a droplet in hot air is proportional to the temperature difference ∆T between the air and the droplet, heat transfer coefficient h and the square of the droplet diameter, which gives

ThTAhdtdQ

∆⋅

⋅Π⋅⋅=∆⋅⋅=

2

24 d

(4)

where Q is the energy. If the heating of the droplet to 100° C is ignored, the received energy leads only to evaporation of the droplet, which can be described as:

dtdH

dtdVH

dtdQ

wvwvdd 2 ⋅⋅

Π⋅⋅−=⋅⋅−=

2ρρ (5)

where Hv is the heat of evaporation for water. The change in droplet diameter over time can then be written as

TH

hdtd

v

∆⋅⋅

−=ρ

2d (6)

Water droplets < 0.1 mm For small water droplets the heat transfer coefficient h is given by the dimensionless Nusselt number, Nu:

5.033.0 RePr6.02 ⋅⋅+=⋅

=k

hNu d (7)

This equation can be solved analytically for some simple cases. For droplets smaller than 0.1 mm, the droplet is decelerated very rapidly and reaches terminal velocity quickly. At that velocity, natural convection will dominate and the Nusselt number will be equal to 2. Combining equations 6 and 7 gives:

dd

⋅⋅∆⋅⋅

−=ρvH

Tkdtd 4 (8)

If the temperature difference between the droplet and the air is constant over time, an integration of (8) leads to

t⋅−= β20

2 dd (9) where

ρβ

⋅∆⋅⋅

=vH

Tk8

Table 2 shows the lifetime for droplets with different diameters and different gas temperatures.

8


Table 2. Lifetime for droplets in hot air, free falling. Temperature 150°C 200°C 300°C 400°C 600°C

D [10-6 m] Life time [10-3 s] 5 3,9 1,8 0,8 0,5 0,2

10 15,6 7,2 3,1 1,8 0,9 50 391,2 178,9 76,9 45,4 22,2

100 1564,8 715,8 307,5 181,4 88,9 However, during deceleration the convective heat transfer dominates, which will reduce droplet lifetime even further. Using equations (2), (6) and (7), a system of partial differential equations are obtained that can be solved numerically Table 3. Initial speed 100 m/s, temperature in fire room 150 °C. Droplet diameter (10-6 m) Distance Life time, Initial sp. 100 m/s 5 0.239 mm 3.9 ms 10 7.87 mm 15.5 ms 50 111 mm 372.0 ms 100 387 mm 1400.0 ms Table 3 shows how far a droplet is transported and the estimated droplet lifetime. In table 4, the lifetime for droplets with and without initial speed is shown. It can be seen from table 4 that the lifetime of the droplet is not greatly influenced by the initial droplet speed. Table 4. Comparison of lifetime for free falling droplets with droplets with an initial speed of 100 m/s, at a gas temperature of 150 °C. Droplet diameter (10-6 m) Life time, free falling Life time, Initial sp. 100 m/s 5 3.9 ms 3.9 ms 10 15.6 ms 15.5 ms 50 391.2 ms 372.0 ms 100 1564.8 ms 1400.0 ms The reason for the small difference in lifetimes is due to the fast deceleration of the droplet, as seen in figure 10. Note that the droplet has a high speed for only a short period. The conclusion is that a high initial speed (high nozzle pressure) does not substantially increase the evaporation rate.

9


0 0.2 0.4 0.6 0.8 1 1.2 1.40

20

40

60

80

100

Time [s]

m/s

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.2

0.4

0.6

0.8

1x 10-4

m

Figure 10. Evaporation of a droplet of 0.1 mm with an initial speed of 100 m/s against time. Left axis is speed of droplet; right axis is diameter of droplet. Temperature of gas is 150 °C.

1.5 Extinguishing performance of water

Water can enhance extinguishment of fire in different ways: • Flame extinguishing. Droplets enter the flames. The flames are cooled to such low

temperatures that they can no longer exist. Flames are extinguished. Hot surfaces will for a time continue to produce pyrolysis product that can be reignited.

• Surface cooling. The droplets hit the burning surface, which is cooled down to a temperature that no longer can produce enough pyrolysis products to sustain a fire.

• The droplets blocks or reduces re-radiation from flames and thereby lowers the heating rate and pyrolysis rate from surfaces.

1.5.1 Flame extinguishing Flame extinguishment can in principle be explained by the chemical reaction that takes place in the flames. An extinguishing media can either participate actively in the flame reactions or it can work as a collision partner and heat absorber (temperature is lowered). Water and water droplets mostly work as heat absorbers and to a lesser degree by depletion of oxygen and fuel. The basic idea behind this kind of extinguishment, �fire point theory�, is to make a energy balance for the flames. This theory was originaly introduced by Rasbash and has been further developed by Ewing5, 6, 7, 8, 9 . The thermal quenching concept is based on energy balance at stochiometry in the flame:

∑∑ ∫∫∫∫ ∆−−−∆=++ didiT

gNNT

gppcfgwT

lww HXdTCXdTCXHXdTCdTCLX155015501550

373

373

0

22

00

)( (10)

where Xw represent the mole fraction of water, Xf = mole fraction of fuel, Xp= mole fraction of combustion products, XN2 = mole fraction of nitrogen, Xdi= mole fraction of dissociated molecules. C represent the molar heat capacity of lw = liquid water, gw = water vapour, gp =

10


combustion products and gN2 = nitrogen. L is the latent heat of vaporisation of water, cH∆ = heat of combustion, = heat of dissociation. diH∆ Experimentally, it has been found that a hydrocarbon flame will extinguish at an adiabatic flame of about 1550°K. It can be shown using equation (10) that for a premixed stoichiometric propane-air flame a concentration of 280 g water per cubic metre can extinguish the flame (assuming that all water will be evaporated). For a diffusion flame, an extinguishing concentration of 140-190 g water mist per cubic meter would be required, as a diffusion flame has higher heat loss than a premixed flame. Experimental measurements on diffusion flames9 gives values which vary between 150 to 200 g water per cubic meter air. This is very close to the theoretical calculation. If water vapour at 100°C is used instead of water droplets, about double the amount of water is required. 1.5.2 Surface cooling Water that reaches a burning surface is heated up and evaporates, thereby cooling the surface. The pyrolysis rate from the surface decreases and when it gets sufficiently small, about a heat release of 50-75 kW per square meter8, flames on the surface can no longer exist. This case can also be described by the thermal extinguishing theory. Theory and experiments8 show that the amount of water required to extinguish a wood based fire (pyrolysis rate < about 5 g/(s*m2)) is 2 g/(s*m ≈ 2) water. If the surface is also subjected to radiation, the demand for water to extinguish the flame is increased dramatically. For example, at a radiation level on the surface of 25 kW/ m2, the demand for water goes up to 10 g/(s*m2). When water is sprayed at a hot wall, it will absorb heat. Water has a high latent heat of vaporisation, 2260 kJ/kg. By using water the right way, high cooling effects can be obtained. After the water has hit the wall, it will be warmed up while running down the wall. Some of the water will be evaporated. But the heat transfer from a hot wall to a water droplet is a very complex process, which depends on the collision speed of the droplet at the wall, the diameter of the droplet and the temperature of the wall. Here the dimensionless parameter, Weber number (We), is used to describe what happens at the collision. 1.6 Absorption of radiation in water mist Attenuation of radiation in a volume S of an absorbing gas is described by the Lambert-Beers law, written in differential form as:

)(),(),( λλλ iSKds

Sdia−=

where i is the radiation intensity, λ the radiation wave length and Ka the absorption coefficient. The solution to this equation is the well-known expression:

[ ]SKaeiSi )()0,(),( λλλ −= If the gas is also emitting radiation due to high temperatures, the following differential expression is used:

)(),()(),(),( λλλλλbaa iSKiSK

dsSdi

+−=

11


where ib is the black-body radiation from the particle based on its temperature. The emission and absorption coefficients are assumed equal, based on Kirchoff's law that states that the emissivity and the absorbtivity of a gas are equal. If the volume S contains particulate material (e.g. water droplets) that scatter radiation, the intensity attenuation obtained in S can be described by similar simple expressions as long as the physics of in-scattering (i.e. the radiation intensity increase due to scattering in surrounding particles) can be neglected. This simplification leads to a Lambert-Beer type of attenuation description:

)(),(),( λλλ iSKds

Sdis−=

where λ is the radiation wave length and Ks is the scatter coefficient. i(S�) ds i(S) i(S+ds)

Schematic picture of in-scattering

For a monodisperse particle cloud, Ks can be calculated from

0NCK ss = where Cs is the scattering area of a particle and N0 is the number of particles. Since the particle area is proportional to the square of the diameter

2dCs ∝ and the number of particles for a given mass fraction f depends on the particle diameter as

30dfN ∝

it can be stated that

dfKs ∝

i.e. that the scattering coefficient increases with diminishing diameter for a given mass fraction. The differential equation describing radiation attenuation based on absorption, emission and scattering is then obtained as:

( ) )(),()(),(),(),( λλλλλλbasa iSKiSKSK

dSSdi

++−=

If the coefficients are assumed constant, the following solution is obtained:

[ ] [ ]( )SKb

SK aeieiSi )()( 1)0,(),( λλλλ −− −+= where K=Ka+Ks .

12


If in-scattering is included in the model and spherical coordinates (θ, φ) used, an integro-differential equation, the Radiation Transfer Equation (RTE) is obtained:

( ) '''sin)'()',',(4

)(),,(),,( 2

0 0∫ ∫ →+++−=π

λ

π

λλλ φθθφθ

πφθ

φθddSSPSi

KSiKSiKK

dSSdi s

basa

where index λ is used to indicate wave-length dependence and P is the phase function, defined by

−=→ → scatteringisotropicinStoscatteredEnergy

directionSthetoSthefromscatteredEnergySSP ds'lim)'( 0

i.e. P=1 when the scattering is isotropic (direction-independent) . The phase function can be derived from Maxwell�s fundamental equations on electricity and magnetism. When particle size is much lessii than the electromagnetic wave length (λ), a more simple, Rayleigh scattering model can be used, giving as phase functioniii

( ))(cos143)( 2 Θ+=ΘP

where θ is the angle between the plane of the incident ray and the reflected ray. For a �large�iv opaque particle having a diffuse reflecting surface the phase function

( ))cos()sin(38)( ΘΘ−Θ=Θπ

P

is obtained. The phase functions given are depicted in figure 12. Phase function P

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0 20 40 60 80 100 120 140 160 180

Angle, θ

P( θ

)

Rayleigh

isotropic

Diffuse

Figure 12 Phase functions

As can be seen from the figure, Rayleigh scattering has a minimum in a plane orthogonal to the incident plane but diffusive scattering is dominated by backward scattering.

ii Basically when

λπξ d

= <0.3

iii Since the phase function is general for all incident angles P=P(x) is written instead of P=P(x�->x). iv Basically when ξ > 5. For 0.3 < ξ < 5, Mie scattering theory is used.

13


1.7 Simulating radiation The Radiation Transfer Equation is the general model used for calculating heat flux. The solution requires an initial value and values for various coefficients that might be obtained from Maxwell�s equations or a more simplified approach. The main difference between different simulation tools is the treatment of in-scattering. In figure 13 is shown a comparison between a well-known simplified model for the full RTE, the �Two-flux model� and a model without the scattering contribution, i.e. only based on the Lambert-Beers law10. As can be seen, the estimated transmission is markedly different when

scattering is included.

igure 13 Simulation results for water mist attenuation of a black-body radiation source (1923ºC). The

Figure 14 t oplet sizes. Gas phase

10

Simulated attenuation comparison

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300 350 400 450 500

Distance from radiation source (cm)

Tran

smis

sion

(%) Lambert-Beers law

"two-flux model"

Famount of water is 5% by weight and the droplet diameter 15 µm.10

demonstrates simulated irradiation attenuation for differen drabsorption has been neglected. Values are obtained from Yang et. al10.

Simulated attenuation as a function of droplet size and amount of water

Figure 14 Simulated attenuation 3 meters away from a 1000°C black-body radiation source

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9

Amount of water (weight%)

Tran

smis

sion

(%) 500 µm

100 µm

10 µm

10

14


15

1.8 Conclusion

• Heat transfer during deceleration of high-speed droplets can be ignored.

• Modelling of water mist systems can be divided into two, deceleration can be treated separately from evaporation of the droplet.

• Fast water droplets quickly loose their momentum to the surrounding air

• The water concentration to reduce radiation from a fire is about 30-40 g/m3, whereas

the concentration required to extinguish the fire is 5 times higher, about 180 g/m3. I.e. it requires much less water to prevent flame spread than to extinguish a fire.

• Small droplets are better than larger droplets in reducing radiation

• Small droplets will evaporate very fast and the main radiation absorption will take

place in the gas phase of water rather than the liquid phase 1.9 Acknowledgement Contribution from the Swedish Fire Research Board (BRANDFORSK) is gratefully acknowledged.

1 Hertzberg T., Hahne A., Josefsson C., Holmstedt G., Husted B., Vattendimma: Teori, fysik och simulering.

BRANDFORSK projekt 514-021, SP Rapport 2004:15, Brandteknik, Borås 2004, Sweden. 2 Schneider B. M., Experimentelle Untersuchungen zur Spraystruktur in transienten, verdampfenden und nicht

verdampfenden Brennstoffstrahlen unter Hochdruck., Phd. thesis, Diss. ETH Nr. 15004, ETH, Zürich 2003 3 Gardiner, A.J. The mathematical modelling of the interaction between sprinkler sprays and the thermally

buoyant layers of gases in fires. England 1988. 4 Rasbash. Lecture notes, University of Edinburgh 5 Ewing, C.T., Hughes, JT and Carhart HW, The extinction of hydrocarbon flames based on the heat-absorption

process which occur in them, Fire and Materials, 8, pp. 148-156, 1984 6 Ewing, C.T., Faith, F.R, Hughes, JT and Carhart HW, Evidence for flame extinguishment by thermal

mechanism, Fire Technology, 25, pp 195-212, 1989 7 Beyler C, A unified model of fire suppression, Journal of Fire Protection Eng. vol 4, no 1 pp 5-16, 1992 8 S. Särdqvist and G. Holmstedt, Water for manual Fire Suppression, J. of Fire Protection Eng. 11, 209-231

(2001) 9 P. Andersson and G. Holmstedt, Limitations of Water Mist as a Total Flooding Agent, J. of Fire Protection

Eng., 9(4) 1999, pp 31-50 10 Yang W., Parker T., Ladouceur H.D., Kee J.K., The interaction of thermal radiation and water mist in fire

suppression, Fire Safety Journal, 39, 41-66, 2004

physics behind water mist

Documents