学術論文

日本ヒートアイランド学会論文集 Vol.10 (2015)
Journal of Heat Island Institute International Vol.10 (2015)

EFFECT OF WATER TEMPERATURE ON
EVAPORATION OF MIST SPRAYED FROM A NOZZLE
Craig FARNHAM*1 Masaki NAKAO*1 Masatoshi NISHIOKA*1
1
2
Minako NABESHIMA* Takeo MIZUNO**1 Osaka City University, Dept. of Urban Engineering, Osaka, Japan*2 H. Ikeuchi & Co., Ltd., Osaka, Japan
Corresponding author: Craig FARNHAM, craig.farnham@gmail.com

ABSTRACT
Water mist of average droplet diameter near 20μm can be used to create pedestrian “cool spots” or help improvecycle efficiency of outdoor air conditioner units. Pump waste heat, sunlight and other factors may cause the supply
water temperature to become warm. The effect of water temperature over the range from 8°C to 92°C on mist mass
flow rate, droplet diameter, mist evaporation rate and cooling effect were measured. The temperature of air in themist cone was also measured. It was found that an increase of water temperature from 27°C to 60°C yields 7%
lower spray mass flow, 5% smaller Sauter mean diameter, and 6% faster evaporation. Temperatures inside the mist
cone dropped below ambient within 20-40cm of the nozzle even when 92°C water is sprayed. Increasing
temperature of mist spray supply water could have use to speed evaporation in tight spaces, as a heat sink, or as alegionella countermeasure.
Key Words : Mist, Evaporation, Cooling, Temperature, Droplet

1.

yielded a decrease in Sauter mean diameter from 27μm to 20μm.

INTRODUCTION

When water temperatures differ from the environment air,
Evaporative mist cooling is increasingly being used in Japanthe effect on heat and mass transfer is likely to take place very

to decrease outdoor air temperatures. Applications include

close to the nozzle. Holterman(4) and Chaker et al.(5) performed

creating “cool spots” for pedestrians, and reducing intake air

detailed iterative calculations on mist droplet speed and droplet

temperatures of air conditioning outdoor units or gas turbines totemperature respectively. As mist system droplets are very small,boost cycle efficiency. Small water droplets will naturally reacheven relatively large mist droplets of 100μm diameter will

the wet bulb temperature during evaporation as confirmed bydecelerate to near zero relative velocity with air and cool to the

Pruppacher and Klett(1) and cool the entrained air.

wet bulb temperature within about 0.1 second of formation at theGenerally, tap water is used for such cases. A difference
between the mist water temperature and the air temperature will

nozzle. This suggests that any warming effect from hot supply
water would remain localized near the nozzle.

cause a transfer of sensible heat to the air. However, the latentHigh pressure pumps used to drive misting systems canheat transfer is typically much larger than the sensible heat. Yet

become warm when pumping for a long time. Piping and nozzle

if the supply water temperature is hot, the warming effect mayheaders may be exposed to direct sunlight or waste heat. Mistbe significant or the spray itself may be affected.

spray flow rates can be quite low, such that the supply water(2)

examined the effect of water temperature of

speed inside the piping can be as low as 1cm/s for a single

up to 20˚C higher than ambient air on fertilizer solution sprays

Hoffman et al.

nozzle system. It is possible that the water can become quitewith around 200μm average droplet diameter. They found either

warm before reaching the nozzles.

no significant change or a trend to slightly smaller average(3)

diameter in some cases. Moon et al.

Further, it may be desired in some applications to

examined the effect ofdeliberately pump hot water through the system, such as if it

temperature on the atomization in a fuel injector. They foundincreases the speed of evaporation to reduce wetting of thethat increasing the temperature of gasoline from 25˚C to 85˚C

cooling target, or is used as a legionella countermeasure. This

- 35 -

research examines the effect of increased water temperatures on

which mist droplets would evaporate. However, as mist

a mist spray and its cooling effect.

evaporates the air cools, thus the wet bulb depression becomes
smaller and evaporation slows.

2.

THEORY
2.3

Temperature dependent water properties

An increase in an evaporative mist cooling system water

Water properties important to spray and evaporation

supply temperature above the ambient air temperature isprocesses are temperature dependent. Here, properties are

expected to have two major effects;

calculated for ordinary water using the IAPWS95 formulations-

Loss of some of the net cooling due to sensible heatfor density(6) and for surface tension(7). Dynamic viscosity istransfer from the warm water to the air.

calculated using the approximation of Kestin et al.(8) Fig. 1

Change in the nature of the mist spray due toshows the change in water properties relative to their values attemperature-dependency of water properties

20°C.
An example of the effect of water properties on droplet

2.1

formation is the basic case of the dripping faucet, where theThermal balance of evaporating mist as a whole
The cooling effect of mist sprays comes from the latent heatgrowing droplet reaches a diameter such that the surface tensionof evaporation. As the mist droplets evaporate, they take heatis no longer sufficient to support the weight of the drop and it

from the surrounding air. Latent heat is exchanged for sensible

falls. This critical drop diameter D for a faucet with an orificeheat. The amount of latent heat transferred, QL depends on the

diameter of d0 is given by,mass of mist evaporated, as shown in Eq. (1). However, some

6𝑑0 𝜎 1 3
𝐷= (
)
𝜌𝐿 𝑔

⁄

sensible heat, QS is exchanged with the air, depending on the(5)initial droplet temperature, T0 and air temperature, TA as shown

The change in physical properties due to an increase ofin Eq. (2). A water supply above the air temperature will transfer

water temperature from 20°C to 90°C would yield 5% smallersome sensible heat to the air. The heat capacity of water, CP isdrops in such a case. This decrease in drop size is mainly due to4184J/kgK, while the latent heat of evaporation, L is about

the decreased surface tension.

2.45x106J/kg. This means the sensible heat transfer from a mist

In the process of atomization, the behavior of the liquidwith a water supply 30°C warmer than the air will cancel about

stream suddenly interacting with air at high speeds at the nozzle

5% of the cooling effect of the mist mass evaporating.

outlet is far more complex than the faucet case.

𝑄L = 𝐿𝑚ev(1)

𝑄s = 𝐶P 𝑚m (𝑇0 − 𝑇A )

(2)

140%
120%

Dyn. Viscosity

Surf. Tension

LeFebvre's d32

Mist evaporation
Percent of value at 20˚C

2.2

Density

Droplet evaporation rates depend on the air conditions. One
form of a single droplet evaporation equation, Eq.(3) derived
from Pruppacher and Klett(1)

for use in typical air conditions

calculates the change in radius, a over time as a function of thewet bulb depression, ΔTWB. The wet bulb depression is also

60%
40%

0%

various air conditions. It is the maximum possible temperature10

drop due to evaporative cooling. Further, if air conditions can be
droplet in a relatively large parcel of air or a similarly fine mist,

80%

20%

useful as an index to compare the evaporative potential ofassumed as unchanging due to the evaporation, such as a single

100%

20

30

40

50

60

70

80

90

100

Water Temperature ( C)

Fig. 1. Change in water properties and LeFebvre’s d32 equation
as a function of temperature relative to their values at 20°C.

an integration of Eq. (3) to zero radius shows that droplet
evaporation time, tev is directly proportional to the square of theradius, Eq. (4), or diameter. This fact is often termed theatomizers. For this type of nozzle, Lefebvre(9 ) proposed anempirical equation for Sauter mean diameter, d32 as a function of“diameter-square law”.

sprayed liquid density, surface tension, viscosity and other𝑑𝑎∆𝑇WB 𝑘A𝑎( ) ≈ −
𝑑𝑡
𝐿𝜌w

(3)

𝐿𝜌w
) 𝑎2
∆𝑇WB 𝑘A(4)

𝑡𝑒𝑣 ≈ (The nozzles used in this research are high-pressure swirl

parameters, as shown in Eq. (6). Here, the atomization process isthought of as divided into 2 stages. The first stage is thegeneration of instabilities in the liquid sheet which forms at theThese equations yield a rough estimate of the fastest time innozzle outlet, and is accounted for in the first term of the- 36 -

equation. The second stage is the conversion of the instabilities

Holterman’s calculations showed that a 100μm diameter

into ligaments which break up into droplets further away frommist droplet with an initial horizontal speed of 10m/s would

the nozzle outlet, and is represented by the second term of thehave a relaxation time of about 13ms with a stopping distance ofequation.

about 120mm. Doubling the initial speed to 20m/s only
0.25

𝜎𝜇2
𝑑32 = 4.52 ()
𝜌𝐴 ∆𝑃2(t cosθ)0.25 + 0.39 (𝜎𝜌𝐿 0.25(t cosθ)0.75)
𝜌𝐴 ∆𝑃

increases stopping distance to about 200mm. A 20μm droplet has(6)

a relaxation time of 0.8ms and stopping distance of 8mm.

Lefebvre found that liquid density changes had a relatively
small influence on d32 compared to viscosity and surface
tension.(10) A plot of the relative change in d32 with the values at
20°C for the nozzle used here as the basis is included in Fig. 1.
As temperature increases from 20°C to 90°C, predicted d32
decreases by 13%, largely due to the change the first term.
2.4

Continuing travel of the droplets is due to being carried along by
the flow of air and the influence of gravity.
Chaker et al.(5) outlined a complete set of equations forcalculating the evaporation and temperature change in water
droplets in an evaluation of gas turbine inlet mist coolingsystems.
The temperature change is determined by iteration, from theconvection heat transfer with air and the loss of energy to the

Droplet evaporation and temperature change
A more detailed evaluation of mist droplet evaporation is

evaporated mass in each time step.
𝑇d(𝑡+∆𝑡) = 𝑇d(𝑡) +needed to predict the droplet temperature change. This involves
calculating the change in speed of the sprayed drops, their rates∆𝑡𝑆d[ℎ (𝑇 − 𝑇d ) − 𝐿𝑚̇d ]𝑚d 𝐶P 𝑐 A

(9)where the evaporating droplet mass flux ṁd is found by,of heat and mass transfer with the air, and the resulting change indroplet size and temperature, through iteration.

𝑚̇d =The high-pressure swirl atomizing nozzles used here spray

𝑆ℎ𝑀𝐷f 𝑃v,d 𝑃v,a
(
−
)
𝑅𝐷d
𝑇d
𝑇a

(10)

and the convective heat transfer coefficient is found by,

mist droplets from the nozzle orifice at initial speeds on the0.25

order of tens of meters per second. Surrounding air is entrainedhc =into the mist spray and the droplets transfer their momentum toka
ρ2a g(Ta − Td )D3d
[2 + 0.6 ()
Dd
μ2a Taμa 0.33
(
) ]
ρa Df

(11)

it. The droplets decelerate rapidly due to air resistance and their
We calculate the evaporation rate and temperature change

relatively small mass.
The drag force Fd is expressed as a function of the dragfor an 80μm droplet sprayed horizontally with an initial velocity
of 20m/s by following the procedures outlined by Chaker for

coefficient Cd,

mass flux and temperature, combined with those outlined by

1
𝐹d = 𝐶d 𝜌A 𝐴𝑣 22

(7)

Holterman for droplet speed and distance. Water and air

The mist droplets studied here are all under 100μm in
diameter. The average droplet velocity as measured by a PDPA
(Phased Doppler Particle Analyzer) at 2 cm from the nozzle
outlet ranged from 10-15m/s. Attempts to measure velocity evencloser to the nozzle were even more unreliable, due to thedensity of the mist. The Reynolds numbers of all droplets are(11)less than 100. Lapple and Shepherd’s empirical relationshipproperties are calculated as temperature dependent. Allinteractions at the droplet surface are taken to be at the film
temperature24
1  0.125 Re0.72
Reofdropletandsurrounding

airtemperature). The droplet internal temperature is assumed to beuniform, which is reasonable as the Biot number is less than 0.2.
The iteration time step was 0.1ms. Smaller time steps yielded nosignificant change in the result. Results are shown in Fig. 2.
Here, the droplet temperature rapidly falls from the initial

for Cd is valid for Re<1000.

Cd (average

92˚C to below the ambient air temperature within 35ms, no(8)

longer warming the surrounding air through sensible heat flux.

Holterman(4) analyzed the deceleration of droplets in ahorizontal spray. Initially droplets travel too fast to be treated as
Stokes flow. As the drag force is higher than Stokes, thedeceleration rate is initially faster than the Stokes flow case as
calculated by an empirical relation. The drops slow to the Stokes
flow regime and eventually reach a relative velocity of zero.
Holterman made iterative calculations for “relaxation time”, thetime for a drop to lose 95% of its initial speed, and for “stopping

The deceleration is also rapid, with a relaxation time of 16ms,
and a stopping distance of about 136mm. This example of alarge, hot droplet was chosen as a “worst case” for use in mist
evaporative cooling.
Cooler and smaller droplets in hot and dry air at 35˚C and
40%RH will have much faster reactions. A 40μm diameter drop
will fall below ambient air temperature within 5ms with astopping distance of 43mm.

distance”, the distance the drop travels until its horizontal
motion stops in still air.
- 37 -

Diameter
Rel. velocity

Distance traveled
Ambient Temperature

Technologies Inc. (Model# PDI-200), which uses interference

Temperature

150

100

120

80

90

60

60

40

30

20

0

0

patterns in intersecting laser beams to sense droplet diameter andDroplet temperature (˚C)
Velocity relative to air (m/s)

Droplet diameter (μm)
Distance traveled (mm)speed without affecting the spray. The baseline droplet diameter
distribution for the nozzle used in these experiments is theaverage of 8 measurements taken 10cm from the nozzle along
the centerline. Each measurement collected data on 10,000
droplets to form a distribution. The supply water temperature
was 27°C. The average Sauter mean diameter, d32 was 21μm.
The diameter distribution is shown in Fig. 4, grouping the
0

20

40

60

80

droplets into bins of 2μm each, such that the mean diameters are

100

1μm, 3μm, 5μm and so on. The cumulative volume fraction is

Elapsed time from droplet formation (ms)Fig. 2 Temperature, velocity, diameter and distance traveled for a
80mm droplet with initial velocity of 20m/s and initial
temperature of 92˚C.

also shown.
To find the effect of water temperature, diametermeasurements were taken with the PDPA at 10cm from theThus, the effect of hot supply water on the speed of thenozzle as the water temperature was slowly cycled from room

single droplet evaporation process itself can be ignored for our

temperature to 92°C and back to room temperature again.

purposes. Calculations and simulations of mist evaporation can

Measurements of 10,000 droplets were taken about every 2

be done with water properties set as constants.

degrees.

However, the effect on the air temperature and net coolingThisprocesswasrepeated,takingdiametermeasurements at 30cm from the nozzle.

cannot be ignored. Nor can we ignore the possibility that thetemperature-dependency of the water properties has an influence

3.2

Control of water supply temperature
Nozzle supply water was heated inside the nozzle header,on the process of droplet formation and initial droplet size.
The above calculations assume that ambient air temperature

immediately before reaching the nozzle. A 400W electric wireis constant. Calculating the change in air conditions and theirheater of 1900mm length with automatic temperature controller,

effect to slow evaporation within a mist spray of millions ofmade by Nippon Heater Co., Ltd. (Model# MC2-104-05) was

droplets is beyond the scope of a simple calculation. Modelingwrapped around the U-shaped header pipe with the nozzle fittingof air and mist through CFD (Computational Fluid Dynamics)

at one end. Flexible metal hose connected this header to thecan show if the rapid deceleration and cooling of hot mist

high-pressure water pump. The hose length was 10m. Part of thedroplets is maintained even inside a mist spray.

hose was coiled and immersed in a bucket of room temperaturewater to counter any heating of the water by the pump. This

2.5

setup is shown in Fig. 3.

CFD model of mist spray
If a CFD model accurately represents reality, there is value

in the software ability to output properties of the air and mistthat would be difficult or impossible to measure in reality; suchas droplet size distributions at any and all points in the mist,
droplet temperatures, and air temperatures inside the mist.
A 3D model of the mist spray in a 400cm x 45cm x 45cm
duct was made using Ansys® FLUENT 13.0 to help confirm theeffects of supply water temperature on evaporation and cooling.

3.

APPARATUS AND PROCEDURES
Fig. 3. Mist water temperature control and PDPA setup
The nozzles used to produce the mist are hollow-cone,high-pressure swirl atomizers made by H. Ikeuchi Co., Ltd.
(Model# KBN80031). A high pressure water pump supplies tap
water at 5.5MPa, which yields a nozzle flow rate of 2.1L/hr.
3.1

Nozzle water spray temperature was measured in 2 ways.
First, a T-type thermocouple was mounted on the nozzle header
surface 5cm upstream of the nozzle and wrapped in 2 layers of
1cm-thick pipe insulation of 15cm length. Second, a T-type

Measurement of droplet diameters
The droplet diameter distribution was measured with a

PDPA (Phased Doppler Particle Analyzer) made by Artium

thermocouple was embedded in sponge and placed into themouth of a bottle which fit closely over the nozzle. The bottle
and sponge interior almost instantly reach a saturation state, such

- 38 -

that there is no evaporation, and thus no evaporative cooling ofapproximately 99% of the particle distribution from the nozzles

the spray water. Repeated trials confirmed that the sponge

used here.

temperature and the pipe surface temperature were within 1°C

20%

100%

18%

90%

16%

80%

14%

70%

12%

60%

10%

50%

8%

40%

6%

30%

4%

20%

2%

10%

0%

Cumulative volume fraction（％）

Frequency（％）

when the water temperature was steady.

Fig. 5 Setup for simultaneous spray of warm mist and room
temperature mist for measurement of difference in mass flow
rate.

0%
0

20

40
Droplet diameter（μm）

60

80

Fig. 4. Droplet diameter distribution and cumulative volume
fraction measured at 10cm from nozzle. Average of 8
measurements with supply water at 27°C.
3.3

Measurement of mass flow rate
Nozzle flow rate was measured as mass flow. A plastic bottlewith a sponge near the opening fits around the nozzle. The
sponge is slightly separated from the nozzle tip, allowing droplet

Fig. 6. Diagram of duct evaporation measurement apparatus andsensors.

formation, but almost no evaporation. The bottle is weighed
before and after a set period and the flow rate calculated. The
electric heater was set to various temperatures. When the sensor
at the nozzle header reached a steady state, the flow rate wasmeasured by collecting mist for 2, 3 or 4 minutes.
To show that the change in flow rate is due to the watertemperature only, a second nozzle of the same model was added
upstream of the electric heater and header, separated by 5m of
hose. The second nozzle is downstream of the room temperature

A single nozzle was placed on the duct centerline from 0.5m
- 2m from the measurement filter, spraying towards it for 2
minute periods. The filter is weighed before and after spraying tofind the weight of mist captured, and thus the evaporation rate asa ratio with the total amount of mist sprayed as in Eq. (12). The
amount of mist sprayed is taken as a function of the supply watertemperature for the nozzles used, given in Eq. (14), as discussed
in the results Section 4.1.
Y  1

water bath of the flexible high-pressure hose coming from thepump (see Fig. 5), to eliminate temperature increases due topump warming. Flow rates from the second, cool nozzle, and theoriginal warmed nozzle were taken simultaneously overtemperatures ranging from 22°C to 90°C. The nozzles were thenexchanged and the procedure repeated.
3.4

Δmfilterm m T (12)

Two temperature and humidity sensors are located justupwind of the nozzle, their average is used as the inlet air
condition.
A grid of 25 uncoated T-type thermocouples with solder
beads under 1mm was mounted behind the filter for 3 cases.
They were arranged in an evenly spaced 5x5 grid across the

Measurement of mist evaporation rate and cooling
Evaporation rate and evaporative cooling measurements

were done in a forced-draft air duct shown in Fig. 6. The ductcross-section is 45cm x 45cm. An air blower is connected byflexible ducting at the duct outlet such that the suction drives air
through the duct. Combined with damper control, the average air
speed in the duct can be set at 2 - 3m/s. At the end of the duct is
an air filter made by Japan Vilene Co., Ltd. (Model# Viledon
VG-40-56F). The filter particle size capture rate will trap

45cm x 45cm outlet. Readings were recorded every 2 seconds
and the average of all thermocouple data was taken for 30
seconds before misting, and 15 seconds at the middle of the
2-minute misting period. The difference between the initial andthe middle average was taken as the net cooling effect. However,there is a possibility that some sensors may have become wet, as
the filter does not perfectly capture all droplets.
Evaporation rates were measured for 7 different cases of
distance from nozzle to filter, z and inlet air temperature and- 39 -

humidity. All cases had the duct air speed at 3m/s. In each case,two distributions were combined, one for smaller diameters, andthe water temperature was varied from the room temperature to

the other for the larger diameters. Input parameters for the “Setabout 60°C, and 4 to 7 trials were done. Experiment conditions

Injection Properties” window in FLUENT are given in Table 2.

are listed in Table 1.
Table 1. Evaporation test conditions
Case
z(m)
Temp(°C)
R. Hum(%)
A
1.25
23
38
B
0.75
19
45
C
0.5
20
69
D
1.0
19
64
E
2.0
18
68
F
1.5
7
48
G
2.0
5
56
3.5

Table 2 CFD input parameters for mist droplet distributions
Parameter
Hot
Hot
Cool
Cool
ΔTWB(K)
8.6
6.7
3.7
4.2
3.6
2.9
3.2

Direct measurement of temperature in mist cone
A set of 6 uncoated T-type thermocouples with solder beads

less than 1mm diameter were spaced at 3cm intervals in a row

water 1water 2water 1water 2Temperature

363K

363K

300K

300K

Cone angle

40°

40°

40°

40°

Max. diameter

25μm

100μm

25μm

100μm

Min. diameter

1μm

25μm

1μm

25μm

Mean diameter24.8μm

23.4μm

25.5μm

25μm

Spread parameter

3.0

1.75

3.53

2.3

# diameters

20

20

20

20

# particle streams

30

30

30

30

Initial velocity

15m/s

15m/s

15m/s

15m/s

and placed along the nozzle spray centerline, starting 1.5cm
from the nozzle. The water temperature was raised from 27°C to

Change in the droplet evaporation processes due to water

92°C and temperatures of the wet thermocouples recorded at 2

temperature effects in FLUENT was handled by defining thesecond intervals and the 30-second time average was used. The

saturation vapor pressure and binary diffusivity of the air-waterset was then moved closer, to 5mm from the nozzle, and theinterface as linear interpolations from manually-input tables

procedure repeated.

rather than their default constant values. The binary diffusivity
equation(13) used to build a table was,

3.6

CFD model settings

T 
Dv  0.211 105   T0 

The model has 1cm tetrahedral mesh near the nozzle,

1.94

 P0 
 
P

(13)

ranging up to 4cm mesh at the duct inlet and outlet, yielding awith units of m2/s, where the reference temperature T0 is

total of 1.2 million elements, shown in cross-section in Fig. 7.

273.15K and P0 is standard atmospheric pressure. The pressure

The model was run on a Windows7® based 64-bit PC with aterm was assumed as unity for this case. A saturation vapor®

quad-core Intel

Xeon processor and 12GB of RAM. A

pressure table was built from the approximation used in
HASP/ACSS/8502 air conditioning simulator.(14)steady-state calculation converged to a solution in 4 hours.

Water density, thermal conductivity and latent heat ofevaporation were set constant at their values for 27°C.
Duct air speed was set at 0.3m/s to allow for a steady flowthat can yield convergence in the steady-state calculation, yet notdiffer significantly from the air speed arising from a mist sprayin open air. Droplet drag was set to be handled as spheres.
Fig. 7 CFD model mesh of duct

Effects of gravity were included, yielding a mist cone that bends
downward. The air flow was handled as turbulent with the

An injection point representing the nozzle used in therealizable k-ε model in FLUENT.

experiments was set along the centerline of the duct, spraying
along its length. Two simulations were done to evaluate theeffect of the water temperature change. The nozzle flow rate was
not changed (though the mass flow rate was later found to beaffected by water temperature, see Fig. 8). The droplet diameter
distributions were changed to a best-fit with the PDPA droplet
diameter distribution measurement results discussed in Section
4.2 and shown in Fig. 10. Fluent can generate a Rosin-Rammler

The only difference between the two simulations input
parameters was water temperature; one with the spray water
source at room temperature (27˚C) and one with the spray water
source at high temperature (92˚C). The mass flow rate was not
adjusted (in experiment, mass flow dropped with higher
temperature) to avoid confounding the results. The duct inlet air
was set at 27˚C and 75% humidity, which was the ambient in theexperiments to measure temperature inside the mist.

distribution, but such distributions defined by a single medianand standard deviation tend to not match real mist droplet
distributions very well.(12) To make a more realistic distribution,

The simulation was repeated for air conditions morefavorable to evaporation which might be encountered as a “bestcase”, a very hot, dry summer mid-day for Japan, 35˚C and 30%- 40 -

humidity, in which a mist cooling system would likely be used.

during the duct evaporation trials over the range of temperatures.

The droplet distributions were kept the same as above. The
unheated droplet temperature was set at 35˚C (ambient).

4.2

Effect of water temperature on droplet diameter

Abbreviation labels used in the rest of this report for the

There was a trend to smaller d32 at higher temperatures asabove cases are given in Table 3. Here “C” is cool, “H” is hot, “a”

shown in Fig. 9. The best fit trend line has a R2 value of about

is air and “w” is water. Thus the first case “CaCw” is “Cool air,

0.11, with an average decrease of 10% from 20°C to 90°C,

Cool water” and so on. The wet bulb depression ΔTWB is alsosimilar to the trend predicted by Lefebvre. There is a similar

given, which is the maximum possible temperature drop due todecrease, with a stronger correlation (R2=0.30) for the simple

mist evaporative cooling.

(arithmetic) diameter, d10. Both trends are shown in Fig. 9. A
plot of the droplet diameter distributions for low temperature

Table 3. CFD mist-in-duct model conditions
Inlet air conditions
Case
Temp
R.Hum
ΔTWB
(°C)
(%)
(K)
CaCw
27
75
3.4
CaHw
27
75
3.4
HaCw
35
30
13.4
HaHw
35
30
13.4

water (average of 9 measurements at 20-30°C) and highWater temp.
(°C)

temperature water (average of 11 measurements at 75-90°C) is

27
92
35
92

of droplets under 15μm, which is about the arithmetic averageshown in Fig. 10. The hot water tends to have a higher fraction
diameter, while the cooler water has more of the larger droplets.
This trend is similar to that found by Moon et al. (3) with gasoline
at similar temperatures.

4.

RESULTS

+ d10

● d32

26
24

aspects considered in these experiments.

22

4.1

Mean diamter (μm)

Raising the mist supply water temperature had an effect in all

Effect of water temperature effect on mass flow rate
The nozzle mass flow rates decreased with higher

temperatures. Simple linear curve fits have high R2 values of

d32 = 22.9 - 0.0324T
R² = 0.112018
d10 = 15.4 - 0.0328T
R² = 0.30

16
14
12

0.98 for each nozzle. The slope of the best fits are 0.20% and10

0.23% mass flow decrease per °C increase for Nozzle A and B

10

20

30

about a 7% smaller mass flow rate from this nozzle than atypical summer tap water temperature of 27°C. The flow rate

40

50

60

70

80

90

100

Water Temperature ( C)respectively. A supply water temperature of 60°C will yieldFig. 9. Effect of temperature on average droplet diameters d10
and d32

data are shown in Fig. 8.
16%
14%

102%
12%

Frequency (%)

Percent of base flow rate

100%
98%
96%
F = -0.0020T + 1.049
R² = 0.98

94%
92%

88%
86%

20-30degC
75-90degC

8%
6%
4%

Nozzle A
Nozzle B
線形 (Nozzle A)
線形 (Nozzle B)

90%

10%

2%

F = -0.0023T + 1.061
R² = 0.98

0%

84%

0

10

20

30

40

50

60

Droplet diameter（μm）

82%
20

30

40

50

60

70

80

90

100

Fig. 10 Averaged droplet diameter distributions for low and hightemperature water

Water Temperature (˚C)

Fig. 8. Effect of water temperature on mass flow rate from thenozzle.

An increase of water temperature from 28 to 60°C will yieldan average 5% drop in d32 for these nozzles. Because droplet

The best-fit curve for all data, which has a R2 of 0.97, is
mm T   m0 1.054  0.0021T 

evaporation time is proportional to the square of the diameter, a(14)5% smaller droplet will have nearly a 10% faster evaporation

Where m0 is the base mist mass flow rate at 27°C and T is intime, as (95%)2 = 90.25%.

degrees C. This is used to calculate the sprayed mass flow rate
- 41 -

However, these smaller measured diameters themselves may

in part be the result of faster evaporation. As the droplets

results. Also, the duct is far too short to allow for complete

traveled from the orifice to the measurement point 10cm away,

evaporation with these nozzles. At duct lengths where the mist

the higher air temperature in the mist (see below) resulting fromcan completely evaporate, there should be little effect on the net

sensible heat transfer from the hot droplets may have increased

cooling, due to the relatively small amount of sensible heatevaporation speeds during transit.

compared to the latent heat of evaporation.

4.3

Effect of water temperature on evaporation and100%

cooling90%80%

Evaporation rate (%)

The evaporation rates as measured by mist collecting at themeasurement filter increased with higher water temperatures.
This includes considering the lower mass flow rates due toincreased temperature as noted above. Among the data there are
11 pairs in which the duct conditions were the same and thewater temperature was similar (within 2 degrees). The average
difference between measured evaporation rates among these

70%

60%
50%
40%
30%
20%

Case A

Case B

Case C

10%

Case E

Case F

Case G0%pairs was 2.4%, which can be taken as an indication of themeasurement error.
There were 7 sets of evaporation rate measurements. Among

Case D

0

10

20

30
40
50
Water Temperature (˚C)

60

70

Fig. 11 Plot of results for evaporation rates in a duct as afunction of the supply water temperature.

these, there were 3 measurements of the cooling effect with the
5x5 thermocouple grid, results are shown in Table 4. In 6 of 7

2.5
Δ Tc= -0.0219T + 2.622
R² = 0.91

Average Temperature Drop (˚C)

cases there was a clear trend to increased evaporation. The
slopes of the 7 trend lines as determined by least-squares
regression are used to calculate the expected change inevaporation rate when increasing the water supply temperaturefrom 20°C to 60°C.
The average of all cases is a 7.3% increase in evaporation
rate when increasing water supply temperature from 20°C to

1.5
Δ Tc = -0.0011T + 1.343
R² = 0.02

1.0

0.5

Δ Tc = 0.0032T + 0.500
R² = 0.85

0.0Using the same trendline analysis as above for the average

10change in measured cooling (Fig. 12) shows that cooling was

20

30

40

50

60

70

Water Temperature (˚C)

cooling measured by the thermocouple grid behind the filter,
the water supply temperature from 20°C to 60°C. A plot of theCase B
Case C

60°C.

there was an average loss of 0.26K of cooling when increasing

Case A

2.0

Fig. 12. Plot of average temperature drop measured by thethermocouple grid as a function of supply water temperature.
4.4

Temperature inside the mist conesignificantly affected in only one case, which was also the case

The temperature measured inside the spray in the very densewith the highest evaporation rate and longest distance fromsprayed mist near the nozzle drops to near-ambient air

nozzle to filter among the three.

temperature within only 20mm of the nozzle as shown in theplot of results for case CaHw and CaCw in Fig. 13. Even with

Table 4. Effects of water temperature on evaporation rate andcooling
Evaporation
Avg.
Cooling change
Casetrend for 20°C Evap. Ratefor 20°C to 60°C
to 60°C
(%)
A
-2.1%
82
-0.88 KB
+5.8%
63
-0.04 KC
+10.2%
37+0.13 K
D
+8.6%
50
E
+6.6%
95
No dataF+12.9%
49
G
+8.9%
50
Avg
+7.3%
-0.26 K

the supply water temperature at 92°C inside the nozzle, themeasured temperature (plotted with X) only reached 47°C at
5mm from the nozzle. The temperature was less than 1 degree
above the initial ambient within 20mm of the nozzle. Measured
temperatures when supply water was near ambient (plotted as +)were all below the air temperature and within 15mm fell toabout the wet bulb temperature of the initial air condition.
In the CFD simulation runs, virtual sensors were set along
the axis of the spray direction at the 1cm, 5cm, 10cm, 20cm and50cm from the outlet. Unlike the experiment, the air temperature

Further experiments are needed to determine if there iswetting of some sensors, which would affect these averaged

and the temperature of the mist droplets can be evaluatedseparately. The results are included Fig. 13, with air temperature(triangles) and droplet temperature (circles) for the case of hot- 42 -

supply water (red filled) and ambient supply water temperature

headers such that they can be directly touched could be a safety(not filled).

hazard to operators and curious pedestrians.

In case CaHw, the measured temperatures all fall between
the air and droplet temperatures as predicted by the CFD
simulation. It is likely the sensors were measuring a combinationof the air temperature and the water which adhered to thesensors. In case CaCw, the CFD simulation predicts a quick drop
to the wet bulb temperature, while the measured temperatures
were about 0.5K higher.
Profiles of air temperature results from the CFD model
along a section of the middle of the duct and mist cone for coolwater and hot water are shown in Fig. 14 for Case CaCw and
CaHw. For CaCw, air temperature quickly drops to the wet bulb
temperature (the darker shade of blue). For CaHw, there is aregion of air temperature slightly higher than ambient, extending
to about 40cm from the nozzle. Beyond 50cm the temperaturestarts to drop below ambient. The temperature drops below

Fig. 14 CFD results. Profile of air temperature for Case CaCw
(top) and Case CaHw (bottom). Note: Temperatures given in
Kelvin.

ambient sooner at the edges of the mist cone.
A plot of pathlines of droplets for Case CaCw and CaHw isshown in Fig. 15, with the droplet temperature indicated by thecolor. Beyond the immediate region of the nozzle there is little
difference in droplet temperature.
Yet these are “worst cases” with relatively cool, damp air
and a water supply temperature at 92°C. Mist evaporative
cooling would likely not be used. In a “best case” where misting
would be used in Japan, the temperature profiles for cases HaCw
and HaHw are given in Fig. 16. Here the case of cool water
yields temperature drops approaching the wet bulb temperature
as expected. The case of hot water shows no region of air
temperature increasing above ambient, the temperature drop is
about 1-2K smaller than for cold water in the region plotted andapproaches the wet bulb temperature about 1m from the nozzle.

Fig. 15. CFD results. Profile of water droplet temperature along
pathlines for Case CaCw (top) and Case CaHw (bottom). Note:
Temperatures given in Kelvin.

70
CFD, CAHW air
65

CFD, CACW air
CFD, CAHW drops

60

CFD, CACW drops

Temperature (˚C)

55

Experiment, CAHW

50

Experiment, CACW
Initial Air Temp

45

Initial Wet Bulb Temp
40
35
30
25
20
0

5

10

15

20

Distance from nozzle along centerline (mm)Fig. 13 Temperature inside mist at centerline for Case CaCw andCase CaHw.

Fig. 16. CFD results. Profile of air temperature for Case HaCw
(top) and Case HaHw (bottom). Note: Temperatures given in
Kelvin.

A pedestrian in an evaporative mist cool spot would likely
not know that hot water is being sprayed unless they touch thenozzles or headers. If hot water is used, installing nozzles and- 43 -5.

DISCUSSION AND CONCLUSIONSt

spray sheet thicknessmtev

droplet evaporation timesTA

temperature of air°Cthis nozzle lead to:T0

initial temperature of supply water°C-

Smaller mass flow rates

Y

mist evaporation rate--

Smaller mean droplet diameterz

distance from nozzle to filterm-

Faster evaporationμdynamic viscosity

N･s/m2-

Possible increase in temperature close to the nozzle

ρA

density of air

kg/m3

-

Slight reductions in net coolingρwdensity of water

kg/m3

Increasing water temperature may be a useful measure toθspray angle°

increase evaporation rates of mist sprays. This may be useful asσsurface tension of water in air

N/mIncreased supply water temperatures for mist spraying witha measure to reduce wetting in tight spaces, such as applications
to air conditioning units or in inlet air cooling for gas turbines,

Referencespossibly reducing scaling. Further, there seems to be little
reduction in cooling effect nor danger of scalding from the sprayeven at near-boiling supply water temperatures. However,precautions to prevent people touching the hot nozzles andheaders themselves would be needed. Further, the effect of longterm spraying of hot water on the nozzles themselves (perhaps
degrading components or adhesives in the structure, or reducing
lifespan) was not examined here.
Mist water supply lines could be used as a heat sink forsome other relatively small waste heat source in the area of
application, on the order of 5-10% of the net cooling effect, suchas using the mist supply water to cool the high pressure water
pump. The equivalent amount of sensible air cooling from
evaporation would be lost, but if a waste heat source could be
used to heat the mist supply water to 60°C, it could have theadded value of keeping the spray clear of bacteria. Spraying at
60°C for long periods during operation as a preventative
measure against legionella would have little adverse affect on
cooling.
Further research is needed to confirm temperature trends
over a range of conditions and with other nozzles. The effect ofspraying hot water on the lifespan of these nozzles will requirelong-duration testing. Also, the effect of spraying hot water frommultiple nozzles together in the same space will be investigated.

H. Pruppacher and J. Klett: Microphysics of Clouds andPrecipitation. Kluwer Academic Publishers. (1997), pp.
490.
(2) W. Hoffman, B. Fritz, W. Bagley and Y. Lan: J. ASTM
Int’l., 8-4(2011), PaperID JAI103461.
(3) S. Moon, E. Abo-Serie and J. Choi: Atomization andSprays. 8-17 (2007), pp.529-550.
(4) H. Holterman: Kinetics and evaporation of water drops inair. IMAG, Report 2003-12/Wageningen UR.
(2003)Wageningen, The Netherlands.
(5) M. Chaker, C. Meher-Homji and T. Mee III: Inlet Fogging
of Gas Turbine Engines – Part A, Proc. Of ASME Turbo
Expo, Amsterdam, (2002) Report #2002-GT-30562.
(6) W. Wagner and A. Pruss: J. Phys. Chem. Ref. Data, 31-2
(2002), pp.387-534.
(7) IAWPS: “IAPWS Release on Surface Tension of Ordinary
Water Substance”, http://www.iapws.org/relguide/surf.pdf,(1994).
(8) J. Kestin, M. Sokolov and W. Wakeham: J. Phys. Chem.
Ref. Data, 7-3 (1978), pp.941-948.
(9) Lefebvre, Atomization and Sprays. Hemisphere Publishing,(1989) pp. 220.
(10) Lefebvre, Ibid, pp. 220.
(11) K. Asano: Butsuri Idou no Kiso to Ouyou (Fundamentals
and Applications of Transport Physics) Maruzen (2004),[in Japanese].
(12) R. Mugele and H.Evans: Industrial and Engineering
Chemistry, 43-6 (1951), pp.1317-1324.
(13) Pruppacher. Ibid, pp.505.
(14) Japan Building Mechanical and Electrical Engineers
Association, HASP/ACSS/8502 Manual, (1986), [inJapanese].
(Received Oct 30, 2012, Accepted Dec 20, 2012)

NOMENCLATURE

Symbol Meaning

(1)

Units

a

droplet diameterμm

cp

specific heat at constant pressure

J/kg･K

d32

Sauter mean diameterμm

kA

thermal conductivity of air

W/m･K

L

latent heat of evaporation

J/kg

mev

mass of evaporating mist spray

kg/s

ΔP

pressure loss at orificePa

QL

latent heat transferedW

Qs

sensible heat transferedW- 44 -