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The spray boiling curves obtained in the tests are shown in
Figure 3. It can be seen that the lower the volumetric spray
flux, the higher the dimensionless heat flux at any given
temperature difference. In order to analyze the repeatability
of the measurements two of the tests have been carried out
twice, one at 2 bar (Q”=0.021 m 3 /m 2·s) and the other one at 3
bar (Q”=0.025-0.026 m 3 /m 2·s). This result is in concordance
with the results presented in [2] and [3] concluding that a
spray with a lower density is more efficient, in the sense
defined by equation (1), that is, the ratio of heat flux
removed by the spray to the maximum latent heat flux.
Dimensionless Heat Flux
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
Q"=0.018 (m3/(m2s))
3 /m 2·s)
Q"=0.021 (m3/(m2s))
3 /m 2·s)
Q"=0.021 (m3/(m2s))
3 /m 2·s)
Q"=0.026 (m3/(m2s))
3 /m 2·s)
Q"=0.025 (m3/(m2s))
3 /m 2·s)
0 5 10 15 20 25 30 35 40 45
Temperature difference (ºC)
Figure 3. Spray boiling curves.
Although in Figure 3, the spray boiling curves at a high
volumetric spray flux seems to be worse than at low
volumetric flux, a higher CHF is achieved with a higher
volumetric flow, as can be seen in Figure 4 and Table I.
Critical Heat Flux (W/cm 2 )
800
700
600
500
400
300
200
Q"=0.026 (m3/(m2s))
3 /m 2·s)
Q"=0.025 (m3/(m2s))
3 /m 2·s)
Q"=0.021 (m3/(m2s))
3 /m 2·s)
Q"=0.021 (m3/(m2s))
3 /m 2·s)
Q"=0.018 (m3/(m2s))
3 /m 2·s)
Maximum heat flux
7-9 October 2009, Leuven, Belgium
linear tendency but its slope is lower than the slope of the
maximum heat flux.
Figure 5 shows the efficiency as a function of the Weber
number and the comparison of the present results with those
obtained by Visaria and Mudawar [8]. Equations (3) and (4)
have been used to calculate the efficiency and the Weber
number, respectively:
η = CHF /( ρ
f
Q"
λ + ρ
f
Q"
C
p, f
ΔTsub
)·100 (3)
where C p,f is the liquid specific heat at constant pressure and
ΔT sub is the temperature difference between the saturation
temperature and the spray temperature. As in our
experiments there is no sub-cooling, ΔT sub = 0 and equation
(1) and (3) are equal.
We = ρ Q" 2
d /σ
(4)
f 32
where Q " is the average volumetric spray flux over the
impact area [8], d 32 is the Sauter mean diameter and σ is the
surface tension.
Estes and Mudawar [3] suggested a correlation based on
Reynolds and Weber numbers to obtain d 32 , in order to
employ it in equation (4). This correlation is shown in
equation (5):
1/ 2 −0.259
d / d = 3.67( We )
32 0
d
Re
(5)
0 d0
where d 0 is the nozzle orifice diameter and We and are
d 0
Re d 0
defined as:
Wed
= ρ ( 2 P / ρ ) d
0
/ σ
0 g
Δ
(6)
f
where ρ g is the gas density and ΔP is the pressure drop
across the spray nozzle.
2
Re = ( 2ΔP
/ ρ )
1/
d / υ
(7)
d0 f 0 f
where υ is the kinematic viscosity of the liquid.
f
The equation (5) has been used to make a comparison
between our results and the Estes and Mudawar results [8].
1000
100
0
0.0020 0.0025 0.0030 0.0035 0.0040 0.0045 0.0050 0.0055 0.0060
Mass Flow (kg/s)
Figure 4. CHF vs. maximum heat flux at different spray mass flows.
TABLE I
VALUES OF THE CHF AT DIFFERENT SPRAY MASS FLOWS
AND THE CHF UNCERTAINTY.
Mass flow (g/s) CHF (W/cm 2 ) U CHF (%)
3.60 161.01 ± 2.25
4.13 174.22 ± 2.18
4.25 174.22 ± 2.18
4.97 181.02 ± 2.1
5.16 192.23 ± 2.15
In Figure 4 is also shown the maximum heat flux
calculated considering the ideal situation in which all the
refrigerant evaporates, that is, the heat transfer is only due to
the latent heat as in equation (1). In this figure, as in Figure
3, it is shown that for a low mass flow the difference
between the CHF and the maximum heat flux is lower than
for a high mass flow. Figure 4 also shows that the CHF has a
Efficiency (%)
100
10
Q"=0.026 (m3/(m2s))
3 /m 2·s)
Q"=0.025 (m3/(m2s))
3 /m 2·s)
Q"=0.021 (m3/(m2s))
3 /m 2·s)
Q"=0.021 (m3/(m2s))
3 /m 2·s)
Q"=0.018 (m3/(m2s))
3 /m 2·s)
Visaria and Mudawar [8]
1
0.000001 0.00001 0.0001 0.001 0.01 0.1 1 10
Weber number
Figure 5. Efficiency as a function of the Weber number.
The efficiency of our results shows the same trend as
those obtained by Visa and Mudawar [8].
The Nusselt number has been used to obtain the
dimensionless form of the heat transfer coefficient. This has
been calculated with equation (8).
Nu L
= hL / κ
(8)
where L is the heater length, κ is the thermal conductivity of
the liquid coolant and h is the heat transfer coefficient which
is defined as:
h = q" / ΔT
(9)
©EDA Publishing/THERMINIC 2009 182
ISBN: 978-2-35500-010-2