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Influences of confinement on subatmospheric water vaporization phenomena in a vertical rectangular channel
International Journal of Heat and Mass Transfer 145 (2019) 118725
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Influences of confinement on subatmospheric water vaporization phenomena in a vertical rectangular channel Florine Giraud, Brice Tremeac Laboratoire du Froid, des Systèmes Energétiques et Thermiques (Lafset), Cnam, HESAM Université, 292 Rue Saint-Martin, 75003 Paris, France
a r t i c l e
i n f o
Article history: Received 13 June 2019 Received in revised form 2 August 2019 Accepted 11 September 2019 Available online 18 September 2019 Keywords: Water vaporization Subatmospherique pressure Low saturation temperature Confinement Two-phase flow
a b s t r a c t The influence of confinement on water vaporization phenomena occurring close to the triple point in a vertical rectangular channel of 0.2 m 0.5 m is investigated. The influence of the driving pressure, the operating pressure and the filling ratio on flow boiling and on time-averaged overall heat transfer depending on the channel thickness is introduced and discussed. It is shown that three main different phenomena at the top of the bubbles occurred depending on the confinement number and on water vaporization production rate: dendrites, evaporation waves and curved interface. Entrainment of droplets by the vapour flow was also observed for the highest confinement number investigated (Co = 0.69). These different phenomena observed impact the heat transfer leading to higher performances for a confinement number of 0.69 compared to confinement number of 0.35 and 0.23 for rate of vapour production obtained at high driving pressures and low filling ratio but also for operating conditions obtained at low driving pressure and high filing ratio. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Due to environmental regulations, most polluting refrigerant used in thermal systems must be phase down. In this context, water is a lasting replacement for refrigerants currently used in heat pumps and chillers. It is an environmentally friendly fluid and, thermodynamically, it is one of the best refrigerants to use since the latent heat of vaporization and the heat capacity are high. However, currently, only few technologies rely on this refrigerant due to scientific and technical challenges. One of this issue lies in the evaporator. Indeed, using water as refrigerant requires working at operating pressure close to the triple point (0.66 kPa). At these low pressures, the hydrostatic pressure is of the same order of magnitude of the operating pressure. Thus, the boiling environment could be highly subcooled at the bottom of the evaporator if a liquid pool is created while it is superheated close to the free surface. In this case, i.e. when a liquid pool is created, the evolution of the thermodynamic properties inside the liquid pool cannot be neglected. This leads to unusual boiling environment. In addition to this unusual boiling environment, due to the low vapour density, explosive bubbles of centimetre size are observed [1–3]. Despite the apparent complexity of vaporization phenomena occurring in this range of pressure and the need to develop compact evaporators for thermal systems using water as refrigerant,
E-mail address: [email protected] (F. Giraud) https://doi.org/10.1016/j.ijheatmasstransfer.2019.118725 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
only few studies focus on this component [4–6]. Knowledge on heat transfer phenomena occurring at these operating pressures is insufficient and the design of evaporators remains empirical leading to a not optimized design that affects both the performance and the compactness of the systems. In addition to complex phenomena described there before, in compact evaporator like platetype heat exchanger, effect of the confinement must be taken into account. It is indeed known, at higher pressure, that heat transfer could be enhanced in confined space due to a change of several mechanisms (flattened of bubbles which foster site-seeding, increased of the velocity of the feeding fluid at the channel entrance, etc.). However, this trend is observed only at low heat fluxes and for a thickness of the narrow channel lower than a given thickness [7–9]. This given thickness is commonly accepted to be qffiffiffiffiffiffiffiffiffiffiffiffiffiffi given by the capillary length (Lc = gðq rq Þ) which could be associl
v
ated, as an image, to the departure diameter of the bubble: if the thickness of the narrow space is higher than the capillary length, bubbles are not affected by the confinement; if the thickness of the narrow space is lower than the capillary length, bubbles are flattened and heat transfer phenomena are affected by the confinement [10]. Moreover, several studies show the existence of an optimal thickness of the narrow channel [7–9] which is given, according to Ait Ameur [9], at 0.25 time the capillary length: below this point, the viscous effects limit the increase of the velocity for very narrow channels thicknesses. However, at operating pressure of few kilopascal, the capillary length is of a few millimetres
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Nomenclature u We
Latin letters a variable (–) A section area (m2) Bo Bond number Co confinement number Dh hydraulic diameter (m) e channel thickness (m) FA enhancement factor (%) FR filling ratio (%) G mass flux (kg m2 s1) g gravitational acceleration (m s2) Dhlv latent heat of vaporization (J kg1) * jv vapour production rate
K Lc P DP S T t
standard uncertainty (–) Weber number
Greek letters d instrumental error (–) k thermal conductivity (W m1 K1) u heat flux (W) l dynamic viscosity (N s m2) q density (kg m3) r surface tension (N m1)
modified overall heat transfer coefficient (W m2 K1) capillary length (m) pressure (Pa) driving pressure (Pa) exchange area temperature (K) time (s)
(2.7 mm at 2 kPa) whereas bubbles size is of few centimetres. There is thus a factor 100 between the capillary length and the bubbles departure diameter observed in [1]. At these low pressures, it is thus expected different trends since, due to the size of bubbles, the effect of the confined space should be observed even for channel thicknesses higher than the capillary length. The given thickness of the channel might also be already too narrow compared to the size of the bubble so that a degraded heat transfer may then be observed whichever the confined space and the heat flux given. Thus, in order to increase knowledge on water vaporization phenomena occurring close to the triple, experiments were conducted in a rectangular channel of 0.5 m high and 0.2 m width. The influence of the thickness of the channel, and thus, of the confinement number, on vaporization phenomena and on heat transfer was investigated for various operating conditions. After introducing the experimental test facility used, vaporization phenomena observed by mean of a high speed and high resolution camera are introduced and discussed. Boiling phenomena observed are classified depending on the Weber vapour number and the vapour production rate. Then, influence of these observed phenomena and various parameters like the filling ratio, the operating pressure and the driving pressure on the overall heat transfer obtained experimentally and then, predicted by mean of mathematical models, are discussed.
Sub/Superscripts acq relative to sf relative to sc relative to in relative to instr relative to l relative to sat saturation v relative to
the the the the the the
acquisition system cold sink hot sink inlet instrument liquid phase
the vapour phase
In order to heat up the working fluid flowing upward inside this channel a third plate of stainless steel is used to create a second channel in which a secondary fluid flows in a parallel manner (Fig. 1). The channel thus created is integrated in a pumpassisted closed loop thermosiphon. The pump is used to overcome the pressure losses due to the measurements devices such as the flow meter. The saturation temperatures of the thermosiphon are set by means of two heating/cooling devices (named B1 and B2 in Fig. 2). A third heating device (named B3 in Fig. 2) is used to set the fluid temperature at the expander inlet to generate a two-phase flow before feeding the channel. All of this constituted the experimental set-up which was already used in in [11]. T-type thermocouples (named T + a number in Fig. 2) and pressure transducers (named P + a number in Fig. 2) are inserted at different points of the test facility. They allow measuring the temperatures with an accuracy of ±0.1 K at the inlet and outlet of each component for the two fluids (primary and secondary) and the absolute pressure at different points of the test rig with an accuracy of ±0.075% of the reading. The coolant mass flow rate is measured using an electromagnetic flow meter (named F2 in Fig. 2) in a range of 0.017– 0.034 kg s1 with an accuracy of ±0.5% of the measured flow rate.
2. Experimental test facility 2.1. Experimental set-up
Visualization
PMMA plate
stainless steel plates
The rectangular channel is made of one stainless steel plate of 6 mm and one transparent polymethyl methacrylate (PMMA) plate of 500 mm height and 200 mm width. The spacing between these two plates can be set at 2 mm, 4 mm and 6 mm which correspond to Confinement number of respectively 0.69, 0.35 and 0.23 (Eq. (1) – thermophysical properties calculated using Refprop 9).
Co ¼
1 Dh
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r
gðql qv Þ
¼
LC Dh
refrigerant
ð1Þ
secondary fluid
Fig. 1. Schematic of the channel (named evaporator in Fig. 2) [11].
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Fig. 2. Drawing of the pump-assisted thermosiphon loop used [11].
Specifications of each measuring devices with associated accuracy as well as the range of each devices and the standard data uncertainties are gathered in Table 1. All the devices are connected to the National Instruments acquisition system. The maximal error of the acquisition system is 0.02% [12]. Data uncertainties are estimated assuming the instrumental error was uniformly distributed and could be estimated by Eq. (2) like in [12].
uðaÞ ¼
dinstr þ dacq pffiffiffi 3
Table 2 Domain covered by the experimental test. Parameters
Field
Filling ratio (FR)
[10–50] % (equivalent in [5–25] cm) [2–15] °C (equivalent in an operating pressure of [0.7–1.7] kPa) [30–45] °C (equivalent in a mass vapor quality inlet of [1.7–3.8] %) [10–25] °C (equivalent in a driving pressure of [0.3–2.1] kPa) 2 mm, 4 mm, 6 mm
Temperature set point at the condenser (bath B2 – Tsf,in) Temperature set point at the thermostatic bath B3
ð2Þ
Temperature set point at the channel (bath B1 – Tsc,in)
2.2. Experimental procedure
Channel thickness (refrigerant side – e)
For each set of operating condition, testing consisted of maintaining constant fluid temperature at the outlet of the three thermostatic baths. This result of maintaining constant the pressure at the condenser (maximal fluctuation of 80 Pa and scatter of 10 Pa for operating conditions leading to the maximal vapour generation), constant the temperature of the secondary fluid at the entrance of the channel (the mass flux being also set at a constant value), constant the temperature before the expansion of the feeding fluid and constant the filling ratio. To maintain the desired filling ratio, the feeding mass flow controller is automatically controlled by a PID controller for which the control parameter is the heat flux. Indeed, the heat flux is estimated by a balance at the secondary fluid and on the refrigerant side assuming that the heat flux is only due to phase-change. This balance thus allows to estimate the feeding mass flow rate to maintain the filling ratio. Once a steady-state is obtained, data are recorded each second for at least 20 min.
this experimental domain, i.e. each set of operating conditions are located at equal distance of each other if one considers a chart of four dimensions, one dimension for each centered parameter (ranging from 1 for the lowest level of the parameter to 1 for the highest level of the same parameter). 3. Influence of the channel thickness on vaporization phenomena For the three channel thicknesses tested (2, 4 and 6 mm – Confinement number of 0.69, 0.35 and 0.23), the two mains flow regime described in [11] for a confinement number of 0.35 (e = 4 mm) were observed, i.e.: – A flow regime (Fig. 3) during which bubbles, at the inlet of the channel, collapsed. These bubbles were due to the fact the evaporator is fed by a two phase flow. About 5 cm below the free surface, bubbles of several centimeters appeared time to time. This bubble pushed the free surface up until the double vapour-liquid-vapour interface breaks. Droplets were projected
2.3. Experimental domain covered The experimental domain covered during these studies is given in Table 2. Experimental data are homogeneously distributed in
Table 1 Specification of the different measuring devices and standard data uncertainties associated. Devices
Type
Accuracy of the device
Range
Data uncertainties
Thermometer Refrigerant flow meter Coolant flow meter Pressure measurement
T-type thermocouple Thermal mass flow meter Electromagnetic flow meter Pressure transmitter with ceramic sensor
0.1 K ±1% of full scale ±0.5% of reading ±0.075% of reading
10 to 85 °C 0.04–2 kg h1 0.017–0.034 kg s1 0–5 kPa
0.06 K 0.01 kg h1 0.00006 kg s1 0.0009 kPa
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5 cm
5 cm
5 cm
5 cm
Falling film
Falling film
t = 0 ms
t = 160 ms
t = 210 ms
t = 520 ms
Fig. 3. Video sequence of phenomena observed inside the channel of the evaporator for Co = 0.35 (FR = 30%, Tsf,in = 8.5 °C, Tsc,in = 17.5 °C) [11].
on the surface creating a falling liquid film which then evaporates. The departure of the large bubble could be followed by the departure of several other bubbles with a diameter smaller than that of the first large bubble. – A flow regime during which the bubbles feeding the channel grown and splashed liquid over the surface without collapsing like it was the case in the previous regime. This flow regime was observed for low filling ratio. For a confinement number of 0.69, two other mains phenomena, different than those observed for Co = 0.35 and Co = 0.23 were observed. Indeed, as a bubble grows and splashes liquid on the wall like observed for Co = 0.35 and Co = 0.23 (Fig. 3), for operating conditions leading to driving pressure higher than 1.50 kPa, for Co = 0.69, the liquid was dragged by the vapour flow and evacuated forming an upward liquid flow (Fig. 4). The central plate was wetted up to a higher location than for the two other thicknesses. Dry paths and local accumulation of water were created and liquid was evacuated from the evaporator following a preferential path. The accumulation of water trapped between the two walls could
t = 480 ms
t = 640 ms
remain trapped during several minutes before flowing down, being dragged by the vapour flow or being evaporated. The presence of this liquid water in the vapour part was probably due to the predominance of the capillary forces as the thickness of the channel was narrower than the capillary length calculated for water at the same operating conditions (around 2.7 mm). It worth noting, for Co = 0.35, droplets observed in the vapour part like in Fig. 3 were attached to the adiabatic wall only. The occurrence of the phenomena describes in Fig. 4 has to be linked to the high rate of vaporization obtained in these conditions. Indeed, Fig. 5 shows the evolution of the rate of vaporization for all the data conducted depending on the confinement number Co (Eq. (1)). The rate of vapour production j*v (Eq. (3)) was calculated like proposed by [13], i.e.:
G jv ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gDh qv ðql qv Þ With
t = 920 ms
G¼
ð3Þ
u
ð4Þ
Dhlv :A
t =1860 ms
t = 2330 ms
Fig. 4. Video sequence of the upward flow observed (Co = 0.69, FR = 40%, Tsf,in = 10.4 °C, Tsc,in = 19.4 °C; t = 0 is given at the beginning of the bubble growth).
F. Giraud, B. Tremeac / International Journal of Heat and Mass Transfer 145 (2019) 118725
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Fig. 5. Confinement number and rate of vapour production for data obtained.
As the Confinement number increases (and thus the thickness of the channel decreases), the rate of vapour production increases. For Co = 0.69 the rate of vaporization increases up to reach the entrainment limit leading to phenomena like phenomena described in Fig. 4. This limit was obtained in this study for a j*v superior to 0.69, which also correspond to data for which the Weber number exceeds the unity. The Weber number was calculated as followed (Eq. (5)):
We ¼
G 2 Dh
qv rl
ð5Þ
The second main difference observed occurred during the growth of the large bubble. When the large bubble grown, three main different phenomena were observed at the top of this one: – No disturbance of the vapour/liquid interface of the bubble at all. The interface of the bubble was curved and smooth whatever the time growth considered (Fig. 6a). – Disturbance of the vapour/liquid interface on the top of the bubble looking like the occurrence of boiling (Fig. 6b). This phenomenon is similar to the one observed in [14] in their study of the evaporation waves. It thus will be referred thereafter as ‘‘evaporation waves”. – Appearance of disturbances at the top of the bubbles as the bubble grown forming dendrites at the top of the bubbles (Fig. 6c). This phenomenon will be referred thereafter as ‘‘dendrites”. Fig. 7 shows the occurrence of these different phenomena depending on the rate of vapour production. These data are based on videos sequences obtained. For each operating conditions around three large bubbles were recorded and proceeded. Data located on the top of Fig. 7 are data for which smooth interfaces were observed and on contrary, data located at the bottom of Fig. 7 are data for which dendrites were observed. The mention ‘‘Both” means that during test conducted, for a given operating conditions both phenomena were observed from one bubble to another. Like illustrated in Fig. 7, the occurrence of the dendrites was observed for almost all test conducted for Co = 0.69. This was especially observed for operating conditions leading to a rate of vapour
production higher than 0.36. For rate of vapour production lower than 0.36 and Co = 0.35 and 0.23, no clear trend was observed. It seems nevertheless that for Co = 0.35, evaporation waves were most often observed than for Co = 0.23. In an attempt to better characterize the occurrence of this three phenomena, Fig. 8 shows the predominance of the phenomena observed depending on the rate of the vapour production and on the Weber number. The occurrence of liquid entrainment is also mentioned in this figure in order to be as wide as possible. The part named in Fig. 8 ‘‘Curved interface and evaporation waves” refers to experimental domain for those evaporation waves (ew), curved interface (ci) of both (ci/ew) could be observed for a given operating conditions (Fig. 7). Like shown in Fig. 7, for one operating conditions for Co = 0.35 and one operating conditions for Co = 0.23, both evaporation waves and dendrites were observed (ew/d). For the sake of simplicity these data are contained in the ‘‘Curved interface and evaporation waves” part although, strickly speaking, another area should be created. These two data are obtained for j*v = 0.16/We = 0.22 and j*v = 0.15/We = 0.42 for respectively Co = 0.35 and Co = 0.23. Three main parts could be observed in Fig. 8 depending on the rate of vapour production and the Weber number. By looking on the graph from the right side to the left side, one might observe that for a rate of vapour production higher than 0.29 (conditions obtained solely with a thickness of the channel of 2 mm which correspond to Co = 0.69), except for one data for those j*v = 0.32 (Fig. 7), dendrites were observed. It worth noting that, although this is not represented in Fig. 8 or Fig. 7, for a rate of vapour production higher than 0.36, dendrites were observed during the major part of the growth whereas for rate of vapour production ranging between 0.29 and 0.36 (still solely obtained for Co = 0.69), dendrites were solely observed at the end of the bubble growth. Then, for rate of the vapour flow ranging between 1.56 and 0.29, phenomena observed depend on the Weber number: for Weber number lower than 0.2 (conditions obtained for Co = 0.69), curved interfaces were observed; on contrary, for Weber number higher than 0.2 (conditions obtained for Co = 0.35), evaporation waves were observed except for three operating conditions for those curved interfaces were observed. These three data are gathered almost on the same spot in Fig. 7. Then
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20 cm
20 cm
20 cm
20 cm
t = 178 ms
a) t = 139 ms
t = 166 ms
t = 171 ms
20 cm
20 cm
20 cm
20 cm
Evaporation waves
b) t = 98 ms
t = 154 ms
20 cm
20 cm
t = 160 ms
t = 176 ms
dendrites
dendrites
Liquid rivulet c) t = 123 ms
t = 152 ms
t = 178 ms
t = 213 ms
Fig. 6. Example of video sequence of bubble with (a) a curved interface (Co = 0.23, DP = 1.18 kPa, FR = 20%, Psat = 1.46 kPa) (b) disturbance looking like evaporation waves (Co = 0.35, DP = 1.10 kPa, FR = 30%, Psat = 0.88 kPa) (c) disturbance forming dendrites (Co = 0.69, DP = 1.18 kPa, FR = 20%, Psat = 1.46 kPa) – t = 0 is given at the beginning of the bubble growth).
for rate of vapour production lower than 0.18, for Co = 0.35 and 0.23, whichever the Weber number, evaporation waves or curved interface or both could be observed. No significant trend regarding the occurrence preferably of the evaporation waves or curved interfaces was observed. In this part of the graph, for Co = 0.69, the formation of dendrites was observed again. The occurrence of the dendrites was thus most likely linked to the predominance of the capillary forces and inertial forces which tend to defragment the bubble. Indeed, these phenomenon was observed only for Co = 0.69. Moreover, according to data obtained, the occurrence of this dendrites seemed all the more pronounced as the bubble growth velocity was high. Finally, following the methodology developed by [15] and recently used in [13], by plotting data on the We-Bo graph (Fig. 9), it is clearly seen that,
although all the data were obtained within the gravity dominated regime, as the thickness of the channel decreases, and thus the confinement number increase, data are spread in the surface tension and inertia area. This figure thus highlights that inertia force and surface tension played a major role in phenomena observed. In this figure, Bond number was calculated as followed:
Bo ¼
Dh 2 gðql qv Þ
rl
ð6Þ
Thermophysical properties of the vapour were calculated considering the saturation conditions obtained at the vapour pressure (i.e. at the inlet of the evaporator – pressure drops were thus neglected in the vapour part of the evaporator) and thermophysical
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Curved interface (ci) Both (ci/ew) Evaporation waves (ew) Both (ew/d) Dentrites (d)
Fig. 7. Occurrence of the ‘‘curved interface” (ci), the ‘‘evaporation waves” (ew) and the ‘‘dendrites” (d) depending on the confinement number Co and the rate of vapour production j*v.
Fig. 8. Occurrence of the ‘‘curved interface” (named also ‘‘ci”), the ‘‘evapourative waves” and the ‘‘dendrites” (named also ‘‘d”), depending on the confinement number, the rate of vapour production j*v and the Weber (We) number.
properties of the liquid were calculated considering that in the liquid pool, temperature was set by the secondary fluid as shown in [11]. It worth noting that although the experimental setup worked as a pump assisted thermosiphon, the mass flow measured by F1 (Fig. 2) ranges between 0 and 4.2 104 kg s1, which leads to maximum mass flux of 0.2 kg m2 s1. It also worth noting that Weber number exceeds unity in Fig. 9 for data obtained at high driving pressure and filling ratio of around 20%. As mentioned there-before, it was during these particular operating conditions that liquid dragged by the vapour flow was observed. The occurrence of the ‘‘evaporation waves” was most likely linked to the super-heat of liquid pool and to the liquid temperature since it impacts the liquid viscosity. It also seems that it was linked to the significance of inertia forces since the higher the Weber number, the higher the occurrence of the phenomena according to data recorded. However, no significant trend was observed regarding the occurrence of this phenomenon. Further study will be conducted in near future in order to study more in detail the occurrence of this phenomenon.
Gravity forces dominate
Inertia forces dominate Surface tension forces dominate
Fig. 9. Relative dominance of forces for data obtained.
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The occurrence of the ‘‘evaporation waves” and ‘‘dendrites” impacts the liquid film created above the newly form free interface and thus the time-averaged heat flux obtained since it impacts the way of bubbles grow and then splash liquid above the newly form interface. For example, in the case of the occurrence of dendrites at the top of the bubble, the liquid was not more relatively homogeneously distributed on the wall: liquid rivulet created during the bubble growth still existed as it broke (Fig. 6c – t = 213 ms). Similarly, the occurrence of ‘‘evaporation waves” seemed to lead to a lower height up to which the liquid was splashed. 4. Influence of the channel thickness on the heat transfer Time-averaged heat flux obtained during this experimental campaign depending on the given driving pressure are shown in Fig. 10. They were calculated as the mean value of heat fluxes obtained by a heat balance at the secondary fluid every one second during at least 20 min once steady state is set on. The driving pressure (Eq. (7)) was calculated as the difference of pressure between the pressure recorded at the outlet of the evaporator (imposed by the condenser) and the saturation pressure one will obtained if the
evaporator is closed and thermal equilibrium with the secondary fluid is reached. In other word, the driving pressure is calculated as the difference of pressure between the pressure imposed by condenser ðPsat;v Þand the evaporator assuming that this component is isolated and in thermal equilibrium with the heat sink (Psat(Tsc,in)).
DP ¼ Psat;v Psat ðTsc;in Þ
ð7Þ
The spreading of data observed in Fig. 10 is due to the fact that for a given driving pressure and a given confinement number, the filling ratio and the operating pressure were not necessary the same leading to different time-averaged heat fluxes. For example, for Co = 0.69, at a maximal driving pressure of 0.58 kPa, timeaveraged heat fluxes ranging between 62 W and 90 W were recorded. A time-averaged heat flux of 62 W was obtained at a saturation pressure of 1.00 kPa and a filling ratio of 20% whereas a time-averaged heat flux of 90 W was obtained at a saturation pressure of 1.45 kPa and a filling ratio of 35%. The influence of the filling ratio and of the operating pressure will be discussed in Sections 4.2 and 4.3.
Fig. 10. Time-averaged heat flux for a confinement number of 0.69, 0.35 and 0.23 depending on the maximal driving pressure.
Experimental uncertainties area
Fig. 11. Evolution of an enhancement factor with the driving pressure for Co = 0.69 and Co = 0.23 by comparison with Co = 0.35.
F. Giraud, B. Tremeac / International Journal of Heat and Mass Transfer 145 (2019) 118725
4.1. General trend Taking into account that the experimental uncertainties vary from 6 to 20% (calculated from the logarithm method) and correspond to a variation of around ±20 W for each data, there was not a significant influence of the confinement number between Co = 0.35 and Co = 0.23 on the experimental time-averaged obtained heat flux. However, even with an overestimation of the uncertainties, it could be seen in Fig. 10 that a confinement number of 0.69 lead to the best, but also to the worst time-averaged heat flux in the experimental domain covered. Indeed, the lowest and the highest heat flux were recorded for Co = 0.69. Moreover, for driving pressure higher than 1.50 kPa, obtained heat fluxes were higher for Co = 0.69 than for a confinement number of 0.35 and 0.23. Thus, in Fig. 10, the overall trend is: for a maximal driving pressure lower than 1.00 kPa, heat transfer was poorer for Co = 0.69 than for the two other confinement numbers (0.35 and 0.23) and for a maximal driving pressure higher than 1.50 kPa, heat transfer was foster for Co = 0.69 than for Co = 0.35 and 0.23. To significantly observed this trend, Fig. 11 shows the evolution of an enhancement factor (inspired by the one used in [16]) with the driving pressure. The enhancement factor (FA), was calculated as follow (Eq. (8)):
FA ¼
K2mm=6mm K4mm
ð8Þ
K4mm
With K (Eq. (9)) an overall heat transfer coefficient [17] calculated by considering the entire heat exchanger surface (liquid area
9
+ vaporization area + vapour area) and the logarithmic mean temperature difference in the vaporization area (called falling film area in [11]):
K ¼
u
ð9Þ
SDTLM
With:
DTLM ¼
Tsc;in Tsc;out T
ð10Þ
T
sat;v sc;in lnðTsc;out Þ Tsat;v
where Tsat,v is the saturation temperature of the fluid at the free interface. The difference observed between in one hand a confinement number of 0.69 and in other hand confinement numbers of 0.35 and 0.23 was probably mainly due to the significance of the capillary forces and, for high driving pressure, to the high rate of vapour production reached for Co = 0.69. Indeed, data for those obtained heat fluxes were significantly higher for Co = 0.69 than for Co = 0.35 and Co = 0.23 for a same set of operating conditions correspond to operating conditions leading to a j*v superior to 0.69 (Fig. 12). It also corresponded to operating conditions for those the Weber number was higher than 1. Although operating conditions were similar for each thicknesses in terms of heat sources, operating pressure and filling ratio, only a confinement number of 0.69 lead to such j*v and We. Phenomena like the ones described in Fig. 4 were thus observed for these operating conditions: liquid was dragged up by the vapour flow. Since an upward liquid flow was created thank to the vapour flow, even if dry patches were created, almost all the surface area of the channel was wetted.
a)
Liquid entrainment
b)
Liquid entrainment
Fig. 12. Obtained time-averaged heat fluxes depending on (a) the rate of vapour production (j*v), (b) the Weber number (We).
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It thus corresponds to data for those performances were higher than performances obtained for Co = 0.35 and Co = 0.23. The poorer performances for Co = 0.69 than for Co = 0.35 or Co = 0.23 were obtained for operating conditions for those similar We and j*v could be reached (Fig. 12). In these conditions, for Co 0.69, surface tension and buoyancy force were predominant. For these data, like for all the major part of data recorded for Co = 69, disturbances on the top of the bubbles were observed but, in contrast to what happen for higher Weber number, no upward liquid flow was observed. Moreover, most likely due to the surface tension, bubbles size seemed to be smaller and bubble growth slower than for the two other thicknesses. It thus lead to a thicker liquid film thickness and thus to lower local heat transfer coefficient. 4.2. Influence of the filling ratio depending on the channel thickness As mentioned previously, the operating conditions and the filling ratio impacted the time-averaged heat flux recorded. The influence of these parameters depends on the confinement number. Fig. 13 shows the influence of the filling ratio for different maximal driving pressure and for confinement numbers. Plots show on this figure are theoretical trend according to mathematical models developed following a Design Of Experiments methodology based
on experimental data obtained. Half of the experimental data show in Fig. 10 were indeed set at operating conditions given by a Design Of Experiments of Doelhert type. The other half of the experimental data were used to validate models obtained. A model was developed for each confinement number using as factor of influence the liquid height (linked to the filling ratio), the temperature set-point at the condenser (linked to the saturation pressure), the temperature set-point at the thermostatic bath B3 (linked to the vapour quality) and the temperature difference between the temperature set-point at the condenser and the temperature set-point et the evaporator (linked, in part, to the driving pressure). These models were then obtained by means of a Taylor series of the relationship between the response (here the heat flux) and the factor of influence. These models allow to predict the cooling capacities at ±15% [18]. Since for Psat = 0.70 kPa, a driving pressure of 1.76 kPa leads to operating conditions for which models are not defined, theoretical heat fluxes were not plotted in Fig. 13a for this driving pressure. Generally, for each confinement number tested (0.69, 0.35 and 0.23), the obtained heat flux increases with the increase of the filling ratio. However, this trend is not significant for Co = 0.69 at a driving pressure of 1.76 kPa (especially for Psat = 1.10 kPa where an increase of +12% is predicted). In addition, for Co = 0.35 and
Psat = 0.7 kPa
Psat = 1.1 kPa
a)
b) Psat = 1.4 kPa
c)
Fig. 13. Theoretical influence of the filling ratio depending on the confinement number and on the maximal driving pressure for an operating pressure of (a) Psat = 0.70 kPa, (b) Psat = 1.10 kPa and (c) Psat = 1.40 kPa.
11
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Co = 0.23 at low driving pressure, an optimal filling ratio in the experimental domain is even observed. The observation of an optimal filling ratio was already observed in [19] for Co = 0.35. This trend was assumed to be due to two aspects: the importance of the amount of liquid located above the growing bubble and the subcooled condition which permits to store the energy then release during the bubble growth. Even if it seems that indeed the subcooled conditions, and more likely, the gradient of subcooled conditions, plays an important role, these leads will be further investigated in near future. It worth noting that, the difference of theoretical performances obtained for Co = 0.23 and Co = 0.35 ranges between ±20% whichever the operating pressure. This difference may be included inside the experimental and theoretical uncertainties. However, this difference is more significant between Co = 0.69 and Co = 0.35 which allow to draw some conclusions: like mentioned previously, a confinement number of 0.69 will theoretically conduct to higher heat fluxes than for Co = 0.23 and Co = 0.35 at high driving pressure and low filling ratio. The given filling ratio up to which this trend is observed depend on the operating pressure: the higher the operat-
ing pressure, the higher the given filling ratio up to which this trend is observed. This trend will be discussed thereafter. 4.3. Influence of the operating pressure depending on the channel thickness Still based on the theoretical models, the evolution of the timeaveraged obtained heat flux with the operating pressure for the three confinement numbers and a filling ratio of 10%, 30% and 50% are shown in Fig. 14. For a driving pressure of 1.76 kPa, for FR = 10% and FR = 30%, since low operating pressure leads to operating conditions for which models are not defined, curves were not plotted up to 0.70 kPa. For Co = 0.23 and Co = 0.35, except for Co = 0.23 at a FR of 10% and an operating pressure of 0.58 kPa, the predicted timeaveraged heat flux decreases with the operating pressure. A similar trend is observed for Co = 0.69 at low filling ratio but at FR = 30% and FR = 50% an optimal operating pressure is observed in the experimental domain. This general trend, i.e. a decrease of the theoretical heat flux with the operating pressure, is probably due to
FR=30%
FR=10%
a)
b)
FR=50%
c)
Fig. 14. Theoretical influence of the working pressure depending on the confinement number and on the maximal driving pressure for a filling ratio of (a) 10%, (b) 30% and (c) 50%.
F. Giraud, B. Tremeac / International Journal of Heat and Mass Transfer 145 (2019) 118725
the decrease of the wall superheat with the operating pressure at a given driving pressure. Indeed, since the saturation pressure is a logarithmic function of the temperature, to set a given driving pressure, the temperature difference between the secondary fluid and the refrigerant must be higher when the operating pressure is close to the triple point. The existence of an optimal operating pressure for Co = 0.69 must be due to the evolution of the thermophysical properties close to the triple point. Indeed, as the pressure increases, the liquid viscosity decreases and the vapour density increases. Thus, inertial forces play a less significant role when the pressure increase. However, since the vapour density strongly increases in these ranges of pressure with the pressure, the rate of vapour production strongly decreases as well, delaying the occurrence of liquid entrainment. As mentioned previously, for a driving pressure of 1.76 kPa, performances obtained for Co = 0.69 are higher than performances obtained for Co = 0.23 and Co = 0.35. However, this trend was observed from a given operating pressure which increases with the increase of the filling ratio. This observation is most likely due to the difference of falling film area created. Indeed, probably due to the amount of water comprise between the free interface and the bubbles, the height up to which the liquid is splashed when bubbles break is smaller at low filling ratio than at high filling ratio leading to a lower exchange area at low filling ratio than at high filling ratio. Moreover, the liquid surface area created is, without the occurrence of liquid dragged by the vapour flow, smaller at Co = 0.69 than at Co = 0.23 or Co = 0.35, due to the predominance of the surface tension (explaining the lower performances obtained for Co = 0.69 for DP = 0.58 kPa and DP = 1.00 kPa). However, at DP = 1.76 kPa, the entrainment of droplet at Co = 0.69 by the vapour flow allows to expand the initially formed liquid film area. Thus, the liquid film area finally obtained is wider for Co = 0.69 than for Co = 0.23 or Co = 0.35. However, as the filling ratio increases, the liquid film area formed by the breaking of the droplets at Co = 0.23 and Co = 0.35 increase. Thus, at Co = 0.69, the vapour flow should carry from a longer distance droplet to create a liquid film wider than for the two other thicknesses. To successfully obtain this condition, the liquid viscosity should be as low as possible. This condition is obtained when the operating pressure increase since the liquid viscosity decrease with the increase of the operating pressure.
4.4. Closing remarks In order to sum up, still based on models, the experimental domain which lead to higher heat transfer processes for Co = 0.69 than for Co = 0.35 and Co = 0.23 is shown in Fig. 15. To take into account uncertainties, a margin of +15% of the heat flux was taken, i.e. solely operating conditions leading to u0:69 > 1:15 u0:35 are represented in this figure. Like shown in Fig. 15, a confinement number of 0.69 lead to higher heat transfer processes than a confinement number of 0.35 and 0.23 for operating conditions represented on the bottom right and on the top left of Fig. 15, i.e. at high driving pressure and low filling ratio and at low driving pressure and high filling ratio. This trend at high driving pressure and low filling ratio was already discussed all along the paper and is due to the evolution of the thermophysical properties of water close to the triple point and on the significance of surface tension forces and inertial forces. At low driving pressure, the poorer performances are theoretically obtained for a confinement number of 0.69. However, as the pressure decreases and firstly for high filling ratio and then for all filling ratio, the trend starts to be reversed. This trend is probably due to the fact that, due to the confinement, the fluid is warmer for Co = 0.69 than for Co = 0.35 at given operating conditions. Thus,
P (kPa)
12
Psat (kPa)
Fig. 15. Theoretical experimental domain leading to higher performances with a confinement number of 0.69.
although the driving pressure is low, conditions are favourable to maintain the occurrence of boiling which allows regenerating the liquid film before it is completely evaporated. It worth noting that conditions given in Fig. 15, especially the driving pressure, are specific to the channel tested in this study. Indeed, since the central plate is made of 6 mm stainless steel, the overall thermal resistance of the evaporator is high. Thus, driving pressure calculated in this study are much higher than driving pressure required to observe these phenomena in a less capacitive thermal channel. 5. Conclusion At Co = 0.69 (e = 2 mm), during the bubble growth, apparition of dendrites at the top of the bubble were observed for almost all the test conducted. For some operating conditions, disturbances on the liquid/vapour interface of the bubble were also observed for Co = 0.23 (e = 6 mm) and Co = 0.35 (e = 4 mm) but these disturbances rather look like the evaporation waves described in [14]. Moreover, at high driving pressure and low filling ratio, for a confinement number of 0.69, entrainment of droplets by the vapour flow was observed. It was shown that this phenomenon occurred for Weber number close to the unity and higher and for rate of vapour flow j*v higher than 0.69. The occurrence of these various phenomena were gathered in a j*v-We diagram. In this diagram, three main parts are highlighted: for j*v higher than 0.29 (solely obtained for Co = 0.69) dendrites were observed; for j*v ranging between 1.56 and 0.29, phenomena observed depend on the Weber number: for Weber number lower than 0.2 (conditions obtained for Co = 0.69), curved interfaces were observed; on contrary, for Weber number higher than 0.2 (conditions obtained for Co = 0.35), evaporation waves were mostly observed; then for j*v lower than 0.18, for Co = 0.35 and 0.23, whichever the Weber number, evaporation waves or curved interface or the occurrence of both could be observed. The occurrence of these various phenomena impacted the way of bubbles break and thus, the heat transfer. It is thus shown that a Confinement number of 0.35 and 0.23 (e = 4 and e = 6 mm) lead to similar trend and similar time-averaged obtained heat fluxes. Trends observed for Co = 0.69 (e = 2 mm) were, on the contrary, different and heat transfer were generally lower. This trend is assumed to be due to the significance of the surface tension forces which tended to defragment bubbles and slowed down their growth which lead to a lower height up to which the liquid was
F. Giraud, B. Tremeac / International Journal of Heat and Mass Transfer 145 (2019) 118725
splashed and to a thicker film with the generation of liquid rivulet. It is however shown that a confinement number of 0.69 should theoretically leads to higher heat transfer than Co = 0.35 and Co = 0.23 at high driving pressure and low filling ratio and at low driving pressure and high filling ratio. The higher performances for Co = 0.69 at high driving pressure were confirmed experimentally and visualization shows that these performances were obtained for data for those the entrainment of liquid by the vapour flow was observed. The generation of this upward liquid film allowed a wider exchange area and thus a higher overall heat transfer. Declaration of Competing Interest
[6]
[7]
[8] [9]
[10] [11]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
[12]
Acknowledgement
[14]
The authors want to thank Lisa Fluro, a former intern at the Lafset Laboratory, who conducted the experiments under the supervision of the authors.
[13]
[15]
[16]
References [17] [1] S.J.D. Van Stralen, R. Cole, W.M. Sluyter, M.S. Sohal, Bubble growth rates in nucleate boiling of water at subatmospheric pressures, Int. J. Heat Mass Transf. 18 (1975) 655–669. [2] S. Michaie, R. Rullière, J. Bonjour, Experimental study of bubble dynamics of isolated bubbles in water pool boiling at subatmospheric pressures, Exp. Therm Fluid Sci. 87 (2017) 117–128. [3] K. Wojtasik, B. Zajaczkowski, R. Rullière, J. Bonjour, Novel sensor for local analysis of bubble dynamics at low pressure, Exp. Therm Fluid Sci. 104 (2019) 175–185. [4] F. Lanzerath, J. Seiler, M. Erdogan, H. Schreiber, M. Steinhilber, A. Bardow, The impact of filling level resolved: capillary-assisted evaporation of water for adsorption heat pumps, Appl. Therm. Eng. 102 (2016) 513–519. [5] R. Volmer, J. Eckert, G. Füldner, L. Schnabel, Evaporator development for adsorption heat transformation devices–influencing factors on non-stationary
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evaporation with tube-fin heat exchangers at sub-atmospheric pressure, Renew. Energy 110 (2017) 141–153. P.C. Thimmaiah, A. Sharafian, M. Rouhani, W. Huttema, M. Bahrami, Evaluation of low-pressure flooded evaporator performance for adsorption chillers, Energy 122 (2017) 144–158. Y. Katto, S. Yokoya, Experimental study of nucleate pool boiling in case of making interference-plate approach to the heating surface, in: 3rd International Heat Transfer Conference, Chicago, 1966, pp. 219–227. J. Bonjour, Amélioration des transferts thermiques en ébullition naturelle convective par effet de confinement, Ph.D. Thesis, Insa de Lyon, France, 1996. Ameur M. Ait, Etude experimentale de l’ébulltion naturelle confinée: analyse des instabilités et des transferts thermiques, Ph.D. Thesis, Insa de Lyon, France, 2006. B. Stutz, M. Lallemand, F. Raimbault, J. Passos, Nucleate and transition boiling in narrow horizontal spaces, Heat Mass Transfer. 45 (2009) 929–935. F. Giraud, R. Rullière, C. Toublanc, J. Bonjour, M. Clausse, Experimental study of water vaporization occurring inside a channel of a smooth plate-type heat exchanger at subatmospheric pressure, Appl. Therm. Eng. 106 (2016) 180–191. K. Zhang, Y.D. Hou, W.X. Tian, Y.Q. Fan, G.H. Su, S.Z. Qiu, Experimental investigations on single-phase convection and steam-water two-phase flow boiling in a vertical rod bundle, Exp. Therm Fluid Sci. 80 (2017) 147–154. K. Smith, R. Kempers, A.J. Robinson, Confinement and vapour production rate influences in closed two-phase reflux thermosyphons Part A: flow regimes, Int. J. Heat Mass Transf. 119 (2018) 907–921. B. Stutz, J.R. Simões-Moreira, Onset of boiling and propagating mechanisms in a highly superheated liquid-the role of evaporation waves, Int. J. Heat Mass Transf. 56 (1–2) (2013) 683–693. S. Baba, N. Ohtani, O. Kawanami, K. Inoue, H. Ohta, Experiments on dominant force regimes in flow boiling using mini-tubes, Front. Heat Mass Transf. (FHMT) 3 (4) (2013). J. Bonjour, F. Boulanger, D. Gentile, M. Lallemand, Etude phénoménologique de l’ébullition en espace confiné à partir d’un site de nucléation isolé, Rev. Gén. Therm. 36 (1997) 562–572. F. Giraud, P. Vallon, B. Tremeac, Experimental study of water vaporization occurring inside the channel of a smooth-plate type heat exchanger connected to an adsorber and comparison with trends observed in absorption configuration, Int. J. Refrig. 77 (2017) 60–74. F. Giraud, L. Fluro, B. Tremeac, Water vaporization inside a smooth plate-type heat exchanger at subatmospheric pressure: impact of the channel thickness, ICR2019. Montreal. Paper 413 (2019), https://doi.org/10.18462/iir. icr.2019.413. F. Giraud, C. Toublanc, R. Rullière, J. Bonjour, M. Clausse, Establishment of an experimental design in the context of water vaporization occuring on a plate cross section, International Congress of Refrigeration 2015, Yokohama, Japan, Paper 0542, 2015.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Influences of confinement on subatmospheric water vaporization phenomena in a vertical rectangular channel Florine Giraud, Brice Tremeac Laboratoire du Froid, des Systèmes Energétiques et Thermiques (Lafset), Cnam, HESAM Université, 292 Rue Saint-Martin, 75003 Paris, France
a r t i c l e
i n f o
Article history: Received 13 June 2019 Received in revised form 2 August 2019 Accepted 11 September 2019 Available online 18 September 2019 Keywords: Water vaporization Subatmospherique pressure Low saturation temperature Confinement Two-phase flow
a b s t r a c t The influence of confinement on water vaporization phenomena occurring close to the triple point in a vertical rectangular channel of 0.2 m 0.5 m is investigated. The influence of the driving pressure, the operating pressure and the filling ratio on flow boiling and on time-averaged overall heat transfer depending on the channel thickness is introduced and discussed. It is shown that three main different phenomena at the top of the bubbles occurred depending on the confinement number and on water vaporization production rate: dendrites, evaporation waves and curved interface. Entrainment of droplets by the vapour flow was also observed for the highest confinement number investigated (Co = 0.69). These different phenomena observed impact the heat transfer leading to higher performances for a confinement number of 0.69 compared to confinement number of 0.35 and 0.23 for rate of vapour production obtained at high driving pressures and low filling ratio but also for operating conditions obtained at low driving pressure and high filing ratio. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Due to environmental regulations, most polluting refrigerant used in thermal systems must be phase down. In this context, water is a lasting replacement for refrigerants currently used in heat pumps and chillers. It is an environmentally friendly fluid and, thermodynamically, it is one of the best refrigerants to use since the latent heat of vaporization and the heat capacity are high. However, currently, only few technologies rely on this refrigerant due to scientific and technical challenges. One of this issue lies in the evaporator. Indeed, using water as refrigerant requires working at operating pressure close to the triple point (0.66 kPa). At these low pressures, the hydrostatic pressure is of the same order of magnitude of the operating pressure. Thus, the boiling environment could be highly subcooled at the bottom of the evaporator if a liquid pool is created while it is superheated close to the free surface. In this case, i.e. when a liquid pool is created, the evolution of the thermodynamic properties inside the liquid pool cannot be neglected. This leads to unusual boiling environment. In addition to this unusual boiling environment, due to the low vapour density, explosive bubbles of centimetre size are observed [1–3]. Despite the apparent complexity of vaporization phenomena occurring in this range of pressure and the need to develop compact evaporators for thermal systems using water as refrigerant,
E-mail address: [email protected] (F. Giraud) https://doi.org/10.1016/j.ijheatmasstransfer.2019.118725 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
only few studies focus on this component [4–6]. Knowledge on heat transfer phenomena occurring at these operating pressures is insufficient and the design of evaporators remains empirical leading to a not optimized design that affects both the performance and the compactness of the systems. In addition to complex phenomena described there before, in compact evaporator like platetype heat exchanger, effect of the confinement must be taken into account. It is indeed known, at higher pressure, that heat transfer could be enhanced in confined space due to a change of several mechanisms (flattened of bubbles which foster site-seeding, increased of the velocity of the feeding fluid at the channel entrance, etc.). However, this trend is observed only at low heat fluxes and for a thickness of the narrow channel lower than a given thickness [7–9]. This given thickness is commonly accepted to be qffiffiffiffiffiffiffiffiffiffiffiffiffiffi given by the capillary length (Lc = gðq rq Þ) which could be associl
v
ated, as an image, to the departure diameter of the bubble: if the thickness of the narrow space is higher than the capillary length, bubbles are not affected by the confinement; if the thickness of the narrow space is lower than the capillary length, bubbles are flattened and heat transfer phenomena are affected by the confinement [10]. Moreover, several studies show the existence of an optimal thickness of the narrow channel [7–9] which is given, according to Ait Ameur [9], at 0.25 time the capillary length: below this point, the viscous effects limit the increase of the velocity for very narrow channels thicknesses. However, at operating pressure of few kilopascal, the capillary length is of a few millimetres
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Nomenclature u We
Latin letters a variable (–) A section area (m2) Bo Bond number Co confinement number Dh hydraulic diameter (m) e channel thickness (m) FA enhancement factor (%) FR filling ratio (%) G mass flux (kg m2 s1) g gravitational acceleration (m s2) Dhlv latent heat of vaporization (J kg1) * jv vapour production rate
K Lc P DP S T t
standard uncertainty (–) Weber number
Greek letters d instrumental error (–) k thermal conductivity (W m1 K1) u heat flux (W) l dynamic viscosity (N s m2) q density (kg m3) r surface tension (N m1)
modified overall heat transfer coefficient (W m2 K1) capillary length (m) pressure (Pa) driving pressure (Pa) exchange area temperature (K) time (s)
(2.7 mm at 2 kPa) whereas bubbles size is of few centimetres. There is thus a factor 100 between the capillary length and the bubbles departure diameter observed in [1]. At these low pressures, it is thus expected different trends since, due to the size of bubbles, the effect of the confined space should be observed even for channel thicknesses higher than the capillary length. The given thickness of the channel might also be already too narrow compared to the size of the bubble so that a degraded heat transfer may then be observed whichever the confined space and the heat flux given. Thus, in order to increase knowledge on water vaporization phenomena occurring close to the triple, experiments were conducted in a rectangular channel of 0.5 m high and 0.2 m width. The influence of the thickness of the channel, and thus, of the confinement number, on vaporization phenomena and on heat transfer was investigated for various operating conditions. After introducing the experimental test facility used, vaporization phenomena observed by mean of a high speed and high resolution camera are introduced and discussed. Boiling phenomena observed are classified depending on the Weber vapour number and the vapour production rate. Then, influence of these observed phenomena and various parameters like the filling ratio, the operating pressure and the driving pressure on the overall heat transfer obtained experimentally and then, predicted by mean of mathematical models, are discussed.
Sub/Superscripts acq relative to sf relative to sc relative to in relative to instr relative to l relative to sat saturation v relative to
the the the the the the
acquisition system cold sink hot sink inlet instrument liquid phase
the vapour phase
In order to heat up the working fluid flowing upward inside this channel a third plate of stainless steel is used to create a second channel in which a secondary fluid flows in a parallel manner (Fig. 1). The channel thus created is integrated in a pumpassisted closed loop thermosiphon. The pump is used to overcome the pressure losses due to the measurements devices such as the flow meter. The saturation temperatures of the thermosiphon are set by means of two heating/cooling devices (named B1 and B2 in Fig. 2). A third heating device (named B3 in Fig. 2) is used to set the fluid temperature at the expander inlet to generate a two-phase flow before feeding the channel. All of this constituted the experimental set-up which was already used in in [11]. T-type thermocouples (named T + a number in Fig. 2) and pressure transducers (named P + a number in Fig. 2) are inserted at different points of the test facility. They allow measuring the temperatures with an accuracy of ±0.1 K at the inlet and outlet of each component for the two fluids (primary and secondary) and the absolute pressure at different points of the test rig with an accuracy of ±0.075% of the reading. The coolant mass flow rate is measured using an electromagnetic flow meter (named F2 in Fig. 2) in a range of 0.017– 0.034 kg s1 with an accuracy of ±0.5% of the measured flow rate.
2. Experimental test facility 2.1. Experimental set-up
Visualization
PMMA plate
stainless steel plates
The rectangular channel is made of one stainless steel plate of 6 mm and one transparent polymethyl methacrylate (PMMA) plate of 500 mm height and 200 mm width. The spacing between these two plates can be set at 2 mm, 4 mm and 6 mm which correspond to Confinement number of respectively 0.69, 0.35 and 0.23 (Eq. (1) – thermophysical properties calculated using Refprop 9).
Co ¼
1 Dh
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r
gðql qv Þ
¼
LC Dh
refrigerant
ð1Þ
secondary fluid
Fig. 1. Schematic of the channel (named evaporator in Fig. 2) [11].
3
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Fig. 2. Drawing of the pump-assisted thermosiphon loop used [11].
Specifications of each measuring devices with associated accuracy as well as the range of each devices and the standard data uncertainties are gathered in Table 1. All the devices are connected to the National Instruments acquisition system. The maximal error of the acquisition system is 0.02% [12]. Data uncertainties are estimated assuming the instrumental error was uniformly distributed and could be estimated by Eq. (2) like in [12].
uðaÞ ¼
dinstr þ dacq pffiffiffi 3
Table 2 Domain covered by the experimental test. Parameters
Field
Filling ratio (FR)
[10–50] % (equivalent in [5–25] cm) [2–15] °C (equivalent in an operating pressure of [0.7–1.7] kPa) [30–45] °C (equivalent in a mass vapor quality inlet of [1.7–3.8] %) [10–25] °C (equivalent in a driving pressure of [0.3–2.1] kPa) 2 mm, 4 mm, 6 mm
Temperature set point at the condenser (bath B2 – Tsf,in) Temperature set point at the thermostatic bath B3
ð2Þ
Temperature set point at the channel (bath B1 – Tsc,in)
2.2. Experimental procedure
Channel thickness (refrigerant side – e)
For each set of operating condition, testing consisted of maintaining constant fluid temperature at the outlet of the three thermostatic baths. This result of maintaining constant the pressure at the condenser (maximal fluctuation of 80 Pa and scatter of 10 Pa for operating conditions leading to the maximal vapour generation), constant the temperature of the secondary fluid at the entrance of the channel (the mass flux being also set at a constant value), constant the temperature before the expansion of the feeding fluid and constant the filling ratio. To maintain the desired filling ratio, the feeding mass flow controller is automatically controlled by a PID controller for which the control parameter is the heat flux. Indeed, the heat flux is estimated by a balance at the secondary fluid and on the refrigerant side assuming that the heat flux is only due to phase-change. This balance thus allows to estimate the feeding mass flow rate to maintain the filling ratio. Once a steady-state is obtained, data are recorded each second for at least 20 min.
this experimental domain, i.e. each set of operating conditions are located at equal distance of each other if one considers a chart of four dimensions, one dimension for each centered parameter (ranging from 1 for the lowest level of the parameter to 1 for the highest level of the same parameter). 3. Influence of the channel thickness on vaporization phenomena For the three channel thicknesses tested (2, 4 and 6 mm – Confinement number of 0.69, 0.35 and 0.23), the two mains flow regime described in [11] for a confinement number of 0.35 (e = 4 mm) were observed, i.e.: – A flow regime (Fig. 3) during which bubbles, at the inlet of the channel, collapsed. These bubbles were due to the fact the evaporator is fed by a two phase flow. About 5 cm below the free surface, bubbles of several centimeters appeared time to time. This bubble pushed the free surface up until the double vapour-liquid-vapour interface breaks. Droplets were projected
2.3. Experimental domain covered The experimental domain covered during these studies is given in Table 2. Experimental data are homogeneously distributed in
Table 1 Specification of the different measuring devices and standard data uncertainties associated. Devices
Type
Accuracy of the device
Range
Data uncertainties
Thermometer Refrigerant flow meter Coolant flow meter Pressure measurement
T-type thermocouple Thermal mass flow meter Electromagnetic flow meter Pressure transmitter with ceramic sensor
0.1 K ±1% of full scale ±0.5% of reading ±0.075% of reading
10 to 85 °C 0.04–2 kg h1 0.017–0.034 kg s1 0–5 kPa
0.06 K 0.01 kg h1 0.00006 kg s1 0.0009 kPa
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5 cm
5 cm
5 cm
5 cm
Falling film
Falling film
t = 0 ms
t = 160 ms
t = 210 ms
t = 520 ms
Fig. 3. Video sequence of phenomena observed inside the channel of the evaporator for Co = 0.35 (FR = 30%, Tsf,in = 8.5 °C, Tsc,in = 17.5 °C) [11].
on the surface creating a falling liquid film which then evaporates. The departure of the large bubble could be followed by the departure of several other bubbles with a diameter smaller than that of the first large bubble. – A flow regime during which the bubbles feeding the channel grown and splashed liquid over the surface without collapsing like it was the case in the previous regime. This flow regime was observed for low filling ratio. For a confinement number of 0.69, two other mains phenomena, different than those observed for Co = 0.35 and Co = 0.23 were observed. Indeed, as a bubble grows and splashes liquid on the wall like observed for Co = 0.35 and Co = 0.23 (Fig. 3), for operating conditions leading to driving pressure higher than 1.50 kPa, for Co = 0.69, the liquid was dragged by the vapour flow and evacuated forming an upward liquid flow (Fig. 4). The central plate was wetted up to a higher location than for the two other thicknesses. Dry paths and local accumulation of water were created and liquid was evacuated from the evaporator following a preferential path. The accumulation of water trapped between the two walls could
t = 480 ms
t = 640 ms
remain trapped during several minutes before flowing down, being dragged by the vapour flow or being evaporated. The presence of this liquid water in the vapour part was probably due to the predominance of the capillary forces as the thickness of the channel was narrower than the capillary length calculated for water at the same operating conditions (around 2.7 mm). It worth noting, for Co = 0.35, droplets observed in the vapour part like in Fig. 3 were attached to the adiabatic wall only. The occurrence of the phenomena describes in Fig. 4 has to be linked to the high rate of vaporization obtained in these conditions. Indeed, Fig. 5 shows the evolution of the rate of vaporization for all the data conducted depending on the confinement number Co (Eq. (1)). The rate of vapour production j*v (Eq. (3)) was calculated like proposed by [13], i.e.:
G jv ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gDh qv ðql qv Þ With
t = 920 ms
G¼
ð3Þ
u
ð4Þ
Dhlv :A
t =1860 ms
t = 2330 ms
Fig. 4. Video sequence of the upward flow observed (Co = 0.69, FR = 40%, Tsf,in = 10.4 °C, Tsc,in = 19.4 °C; t = 0 is given at the beginning of the bubble growth).
F. Giraud, B. Tremeac / International Journal of Heat and Mass Transfer 145 (2019) 118725
5
Fig. 5. Confinement number and rate of vapour production for data obtained.
As the Confinement number increases (and thus the thickness of the channel decreases), the rate of vapour production increases. For Co = 0.69 the rate of vaporization increases up to reach the entrainment limit leading to phenomena like phenomena described in Fig. 4. This limit was obtained in this study for a j*v superior to 0.69, which also correspond to data for which the Weber number exceeds the unity. The Weber number was calculated as followed (Eq. (5)):
We ¼
G 2 Dh
qv rl
ð5Þ
The second main difference observed occurred during the growth of the large bubble. When the large bubble grown, three main different phenomena were observed at the top of this one: – No disturbance of the vapour/liquid interface of the bubble at all. The interface of the bubble was curved and smooth whatever the time growth considered (Fig. 6a). – Disturbance of the vapour/liquid interface on the top of the bubble looking like the occurrence of boiling (Fig. 6b). This phenomenon is similar to the one observed in [14] in their study of the evaporation waves. It thus will be referred thereafter as ‘‘evaporation waves”. – Appearance of disturbances at the top of the bubbles as the bubble grown forming dendrites at the top of the bubbles (Fig. 6c). This phenomenon will be referred thereafter as ‘‘dendrites”. Fig. 7 shows the occurrence of these different phenomena depending on the rate of vapour production. These data are based on videos sequences obtained. For each operating conditions around three large bubbles were recorded and proceeded. Data located on the top of Fig. 7 are data for which smooth interfaces were observed and on contrary, data located at the bottom of Fig. 7 are data for which dendrites were observed. The mention ‘‘Both” means that during test conducted, for a given operating conditions both phenomena were observed from one bubble to another. Like illustrated in Fig. 7, the occurrence of the dendrites was observed for almost all test conducted for Co = 0.69. This was especially observed for operating conditions leading to a rate of vapour
production higher than 0.36. For rate of vapour production lower than 0.36 and Co = 0.35 and 0.23, no clear trend was observed. It seems nevertheless that for Co = 0.35, evaporation waves were most often observed than for Co = 0.23. In an attempt to better characterize the occurrence of this three phenomena, Fig. 8 shows the predominance of the phenomena observed depending on the rate of the vapour production and on the Weber number. The occurrence of liquid entrainment is also mentioned in this figure in order to be as wide as possible. The part named in Fig. 8 ‘‘Curved interface and evaporation waves” refers to experimental domain for those evaporation waves (ew), curved interface (ci) of both (ci/ew) could be observed for a given operating conditions (Fig. 7). Like shown in Fig. 7, for one operating conditions for Co = 0.35 and one operating conditions for Co = 0.23, both evaporation waves and dendrites were observed (ew/d). For the sake of simplicity these data are contained in the ‘‘Curved interface and evaporation waves” part although, strickly speaking, another area should be created. These two data are obtained for j*v = 0.16/We = 0.22 and j*v = 0.15/We = 0.42 for respectively Co = 0.35 and Co = 0.23. Three main parts could be observed in Fig. 8 depending on the rate of vapour production and the Weber number. By looking on the graph from the right side to the left side, one might observe that for a rate of vapour production higher than 0.29 (conditions obtained solely with a thickness of the channel of 2 mm which correspond to Co = 0.69), except for one data for those j*v = 0.32 (Fig. 7), dendrites were observed. It worth noting that, although this is not represented in Fig. 8 or Fig. 7, for a rate of vapour production higher than 0.36, dendrites were observed during the major part of the growth whereas for rate of vapour production ranging between 0.29 and 0.36 (still solely obtained for Co = 0.69), dendrites were solely observed at the end of the bubble growth. Then, for rate of the vapour flow ranging between 1.56 and 0.29, phenomena observed depend on the Weber number: for Weber number lower than 0.2 (conditions obtained for Co = 0.69), curved interfaces were observed; on contrary, for Weber number higher than 0.2 (conditions obtained for Co = 0.35), evaporation waves were observed except for three operating conditions for those curved interfaces were observed. These three data are gathered almost on the same spot in Fig. 7. Then
6
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20 cm
20 cm
20 cm
20 cm
t = 178 ms
a) t = 139 ms
t = 166 ms
t = 171 ms
20 cm
20 cm
20 cm
20 cm
Evaporation waves
b) t = 98 ms
t = 154 ms
20 cm
20 cm
t = 160 ms
t = 176 ms
dendrites
dendrites
Liquid rivulet c) t = 123 ms
t = 152 ms
t = 178 ms
t = 213 ms
Fig. 6. Example of video sequence of bubble with (a) a curved interface (Co = 0.23, DP = 1.18 kPa, FR = 20%, Psat = 1.46 kPa) (b) disturbance looking like evaporation waves (Co = 0.35, DP = 1.10 kPa, FR = 30%, Psat = 0.88 kPa) (c) disturbance forming dendrites (Co = 0.69, DP = 1.18 kPa, FR = 20%, Psat = 1.46 kPa) – t = 0 is given at the beginning of the bubble growth).
for rate of vapour production lower than 0.18, for Co = 0.35 and 0.23, whichever the Weber number, evaporation waves or curved interface or both could be observed. No significant trend regarding the occurrence preferably of the evaporation waves or curved interfaces was observed. In this part of the graph, for Co = 0.69, the formation of dendrites was observed again. The occurrence of the dendrites was thus most likely linked to the predominance of the capillary forces and inertial forces which tend to defragment the bubble. Indeed, these phenomenon was observed only for Co = 0.69. Moreover, according to data obtained, the occurrence of this dendrites seemed all the more pronounced as the bubble growth velocity was high. Finally, following the methodology developed by [15] and recently used in [13], by plotting data on the We-Bo graph (Fig. 9), it is clearly seen that,
although all the data were obtained within the gravity dominated regime, as the thickness of the channel decreases, and thus the confinement number increase, data are spread in the surface tension and inertia area. This figure thus highlights that inertia force and surface tension played a major role in phenomena observed. In this figure, Bond number was calculated as followed:
Bo ¼
Dh 2 gðql qv Þ
rl
ð6Þ
Thermophysical properties of the vapour were calculated considering the saturation conditions obtained at the vapour pressure (i.e. at the inlet of the evaporator – pressure drops were thus neglected in the vapour part of the evaporator) and thermophysical
7
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Curved interface (ci) Both (ci/ew) Evaporation waves (ew) Both (ew/d) Dentrites (d)
Fig. 7. Occurrence of the ‘‘curved interface” (ci), the ‘‘evaporation waves” (ew) and the ‘‘dendrites” (d) depending on the confinement number Co and the rate of vapour production j*v.
Fig. 8. Occurrence of the ‘‘curved interface” (named also ‘‘ci”), the ‘‘evapourative waves” and the ‘‘dendrites” (named also ‘‘d”), depending on the confinement number, the rate of vapour production j*v and the Weber (We) number.
properties of the liquid were calculated considering that in the liquid pool, temperature was set by the secondary fluid as shown in [11]. It worth noting that although the experimental setup worked as a pump assisted thermosiphon, the mass flow measured by F1 (Fig. 2) ranges between 0 and 4.2 104 kg s1, which leads to maximum mass flux of 0.2 kg m2 s1. It also worth noting that Weber number exceeds unity in Fig. 9 for data obtained at high driving pressure and filling ratio of around 20%. As mentioned there-before, it was during these particular operating conditions that liquid dragged by the vapour flow was observed. The occurrence of the ‘‘evaporation waves” was most likely linked to the super-heat of liquid pool and to the liquid temperature since it impacts the liquid viscosity. It also seems that it was linked to the significance of inertia forces since the higher the Weber number, the higher the occurrence of the phenomena according to data recorded. However, no significant trend was observed regarding the occurrence of this phenomenon. Further study will be conducted in near future in order to study more in detail the occurrence of this phenomenon.
Gravity forces dominate
Inertia forces dominate Surface tension forces dominate
Fig. 9. Relative dominance of forces for data obtained.
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The occurrence of the ‘‘evaporation waves” and ‘‘dendrites” impacts the liquid film created above the newly form free interface and thus the time-averaged heat flux obtained since it impacts the way of bubbles grow and then splash liquid above the newly form interface. For example, in the case of the occurrence of dendrites at the top of the bubble, the liquid was not more relatively homogeneously distributed on the wall: liquid rivulet created during the bubble growth still existed as it broke (Fig. 6c – t = 213 ms). Similarly, the occurrence of ‘‘evaporation waves” seemed to lead to a lower height up to which the liquid was splashed. 4. Influence of the channel thickness on the heat transfer Time-averaged heat flux obtained during this experimental campaign depending on the given driving pressure are shown in Fig. 10. They were calculated as the mean value of heat fluxes obtained by a heat balance at the secondary fluid every one second during at least 20 min once steady state is set on. The driving pressure (Eq. (7)) was calculated as the difference of pressure between the pressure recorded at the outlet of the evaporator (imposed by the condenser) and the saturation pressure one will obtained if the
evaporator is closed and thermal equilibrium with the secondary fluid is reached. In other word, the driving pressure is calculated as the difference of pressure between the pressure imposed by condenser ðPsat;v Þand the evaporator assuming that this component is isolated and in thermal equilibrium with the heat sink (Psat(Tsc,in)).
DP ¼ Psat;v Psat ðTsc;in Þ
ð7Þ
The spreading of data observed in Fig. 10 is due to the fact that for a given driving pressure and a given confinement number, the filling ratio and the operating pressure were not necessary the same leading to different time-averaged heat fluxes. For example, for Co = 0.69, at a maximal driving pressure of 0.58 kPa, timeaveraged heat fluxes ranging between 62 W and 90 W were recorded. A time-averaged heat flux of 62 W was obtained at a saturation pressure of 1.00 kPa and a filling ratio of 20% whereas a time-averaged heat flux of 90 W was obtained at a saturation pressure of 1.45 kPa and a filling ratio of 35%. The influence of the filling ratio and of the operating pressure will be discussed in Sections 4.2 and 4.3.
Fig. 10. Time-averaged heat flux for a confinement number of 0.69, 0.35 and 0.23 depending on the maximal driving pressure.
Experimental uncertainties area
Fig. 11. Evolution of an enhancement factor with the driving pressure for Co = 0.69 and Co = 0.23 by comparison with Co = 0.35.
F. Giraud, B. Tremeac / International Journal of Heat and Mass Transfer 145 (2019) 118725
4.1. General trend Taking into account that the experimental uncertainties vary from 6 to 20% (calculated from the logarithm method) and correspond to a variation of around ±20 W for each data, there was not a significant influence of the confinement number between Co = 0.35 and Co = 0.23 on the experimental time-averaged obtained heat flux. However, even with an overestimation of the uncertainties, it could be seen in Fig. 10 that a confinement number of 0.69 lead to the best, but also to the worst time-averaged heat flux in the experimental domain covered. Indeed, the lowest and the highest heat flux were recorded for Co = 0.69. Moreover, for driving pressure higher than 1.50 kPa, obtained heat fluxes were higher for Co = 0.69 than for a confinement number of 0.35 and 0.23. Thus, in Fig. 10, the overall trend is: for a maximal driving pressure lower than 1.00 kPa, heat transfer was poorer for Co = 0.69 than for the two other confinement numbers (0.35 and 0.23) and for a maximal driving pressure higher than 1.50 kPa, heat transfer was foster for Co = 0.69 than for Co = 0.35 and 0.23. To significantly observed this trend, Fig. 11 shows the evolution of an enhancement factor (inspired by the one used in [16]) with the driving pressure. The enhancement factor (FA), was calculated as follow (Eq. (8)):
FA ¼
K2mm=6mm K4mm
ð8Þ
K4mm
With K (Eq. (9)) an overall heat transfer coefficient [17] calculated by considering the entire heat exchanger surface (liquid area
9
+ vaporization area + vapour area) and the logarithmic mean temperature difference in the vaporization area (called falling film area in [11]):
K ¼
u
ð9Þ
SDTLM
With:
DTLM ¼
Tsc;in Tsc;out T
ð10Þ
T
sat;v sc;in lnðTsc;out Þ Tsat;v
where Tsat,v is the saturation temperature of the fluid at the free interface. The difference observed between in one hand a confinement number of 0.69 and in other hand confinement numbers of 0.35 and 0.23 was probably mainly due to the significance of the capillary forces and, for high driving pressure, to the high rate of vapour production reached for Co = 0.69. Indeed, data for those obtained heat fluxes were significantly higher for Co = 0.69 than for Co = 0.35 and Co = 0.23 for a same set of operating conditions correspond to operating conditions leading to a j*v superior to 0.69 (Fig. 12). It also corresponded to operating conditions for those the Weber number was higher than 1. Although operating conditions were similar for each thicknesses in terms of heat sources, operating pressure and filling ratio, only a confinement number of 0.69 lead to such j*v and We. Phenomena like the ones described in Fig. 4 were thus observed for these operating conditions: liquid was dragged up by the vapour flow. Since an upward liquid flow was created thank to the vapour flow, even if dry patches were created, almost all the surface area of the channel was wetted.
a)
Liquid entrainment
b)
Liquid entrainment
Fig. 12. Obtained time-averaged heat fluxes depending on (a) the rate of vapour production (j*v), (b) the Weber number (We).
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It thus corresponds to data for those performances were higher than performances obtained for Co = 0.35 and Co = 0.23. The poorer performances for Co = 0.69 than for Co = 0.35 or Co = 0.23 were obtained for operating conditions for those similar We and j*v could be reached (Fig. 12). In these conditions, for Co 0.69, surface tension and buoyancy force were predominant. For these data, like for all the major part of data recorded for Co = 69, disturbances on the top of the bubbles were observed but, in contrast to what happen for higher Weber number, no upward liquid flow was observed. Moreover, most likely due to the surface tension, bubbles size seemed to be smaller and bubble growth slower than for the two other thicknesses. It thus lead to a thicker liquid film thickness and thus to lower local heat transfer coefficient. 4.2. Influence of the filling ratio depending on the channel thickness As mentioned previously, the operating conditions and the filling ratio impacted the time-averaged heat flux recorded. The influence of these parameters depends on the confinement number. Fig. 13 shows the influence of the filling ratio for different maximal driving pressure and for confinement numbers. Plots show on this figure are theoretical trend according to mathematical models developed following a Design Of Experiments methodology based
on experimental data obtained. Half of the experimental data show in Fig. 10 were indeed set at operating conditions given by a Design Of Experiments of Doelhert type. The other half of the experimental data were used to validate models obtained. A model was developed for each confinement number using as factor of influence the liquid height (linked to the filling ratio), the temperature set-point at the condenser (linked to the saturation pressure), the temperature set-point at the thermostatic bath B3 (linked to the vapour quality) and the temperature difference between the temperature set-point at the condenser and the temperature set-point et the evaporator (linked, in part, to the driving pressure). These models were then obtained by means of a Taylor series of the relationship between the response (here the heat flux) and the factor of influence. These models allow to predict the cooling capacities at ±15% [18]. Since for Psat = 0.70 kPa, a driving pressure of 1.76 kPa leads to operating conditions for which models are not defined, theoretical heat fluxes were not plotted in Fig. 13a for this driving pressure. Generally, for each confinement number tested (0.69, 0.35 and 0.23), the obtained heat flux increases with the increase of the filling ratio. However, this trend is not significant for Co = 0.69 at a driving pressure of 1.76 kPa (especially for Psat = 1.10 kPa where an increase of +12% is predicted). In addition, for Co = 0.35 and
Psat = 0.7 kPa
Psat = 1.1 kPa
a)
b) Psat = 1.4 kPa
c)
Fig. 13. Theoretical influence of the filling ratio depending on the confinement number and on the maximal driving pressure for an operating pressure of (a) Psat = 0.70 kPa, (b) Psat = 1.10 kPa and (c) Psat = 1.40 kPa.
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Co = 0.23 at low driving pressure, an optimal filling ratio in the experimental domain is even observed. The observation of an optimal filling ratio was already observed in [19] for Co = 0.35. This trend was assumed to be due to two aspects: the importance of the amount of liquid located above the growing bubble and the subcooled condition which permits to store the energy then release during the bubble growth. Even if it seems that indeed the subcooled conditions, and more likely, the gradient of subcooled conditions, plays an important role, these leads will be further investigated in near future. It worth noting that, the difference of theoretical performances obtained for Co = 0.23 and Co = 0.35 ranges between ±20% whichever the operating pressure. This difference may be included inside the experimental and theoretical uncertainties. However, this difference is more significant between Co = 0.69 and Co = 0.35 which allow to draw some conclusions: like mentioned previously, a confinement number of 0.69 will theoretically conduct to higher heat fluxes than for Co = 0.23 and Co = 0.35 at high driving pressure and low filling ratio. The given filling ratio up to which this trend is observed depend on the operating pressure: the higher the operat-
ing pressure, the higher the given filling ratio up to which this trend is observed. This trend will be discussed thereafter. 4.3. Influence of the operating pressure depending on the channel thickness Still based on the theoretical models, the evolution of the timeaveraged obtained heat flux with the operating pressure for the three confinement numbers and a filling ratio of 10%, 30% and 50% are shown in Fig. 14. For a driving pressure of 1.76 kPa, for FR = 10% and FR = 30%, since low operating pressure leads to operating conditions for which models are not defined, curves were not plotted up to 0.70 kPa. For Co = 0.23 and Co = 0.35, except for Co = 0.23 at a FR of 10% and an operating pressure of 0.58 kPa, the predicted timeaveraged heat flux decreases with the operating pressure. A similar trend is observed for Co = 0.69 at low filling ratio but at FR = 30% and FR = 50% an optimal operating pressure is observed in the experimental domain. This general trend, i.e. a decrease of the theoretical heat flux with the operating pressure, is probably due to
FR=30%
FR=10%
a)
b)
FR=50%
c)
Fig. 14. Theoretical influence of the working pressure depending on the confinement number and on the maximal driving pressure for a filling ratio of (a) 10%, (b) 30% and (c) 50%.
F. Giraud, B. Tremeac / International Journal of Heat and Mass Transfer 145 (2019) 118725
the decrease of the wall superheat with the operating pressure at a given driving pressure. Indeed, since the saturation pressure is a logarithmic function of the temperature, to set a given driving pressure, the temperature difference between the secondary fluid and the refrigerant must be higher when the operating pressure is close to the triple point. The existence of an optimal operating pressure for Co = 0.69 must be due to the evolution of the thermophysical properties close to the triple point. Indeed, as the pressure increases, the liquid viscosity decreases and the vapour density increases. Thus, inertial forces play a less significant role when the pressure increase. However, since the vapour density strongly increases in these ranges of pressure with the pressure, the rate of vapour production strongly decreases as well, delaying the occurrence of liquid entrainment. As mentioned previously, for a driving pressure of 1.76 kPa, performances obtained for Co = 0.69 are higher than performances obtained for Co = 0.23 and Co = 0.35. However, this trend was observed from a given operating pressure which increases with the increase of the filling ratio. This observation is most likely due to the difference of falling film area created. Indeed, probably due to the amount of water comprise between the free interface and the bubbles, the height up to which the liquid is splashed when bubbles break is smaller at low filling ratio than at high filling ratio leading to a lower exchange area at low filling ratio than at high filling ratio. Moreover, the liquid surface area created is, without the occurrence of liquid dragged by the vapour flow, smaller at Co = 0.69 than at Co = 0.23 or Co = 0.35, due to the predominance of the surface tension (explaining the lower performances obtained for Co = 0.69 for DP = 0.58 kPa and DP = 1.00 kPa). However, at DP = 1.76 kPa, the entrainment of droplet at Co = 0.69 by the vapour flow allows to expand the initially formed liquid film area. Thus, the liquid film area finally obtained is wider for Co = 0.69 than for Co = 0.23 or Co = 0.35. However, as the filling ratio increases, the liquid film area formed by the breaking of the droplets at Co = 0.23 and Co = 0.35 increase. Thus, at Co = 0.69, the vapour flow should carry from a longer distance droplet to create a liquid film wider than for the two other thicknesses. To successfully obtain this condition, the liquid viscosity should be as low as possible. This condition is obtained when the operating pressure increase since the liquid viscosity decrease with the increase of the operating pressure.
4.4. Closing remarks In order to sum up, still based on models, the experimental domain which lead to higher heat transfer processes for Co = 0.69 than for Co = 0.35 and Co = 0.23 is shown in Fig. 15. To take into account uncertainties, a margin of +15% of the heat flux was taken, i.e. solely operating conditions leading to u0:69 > 1:15 u0:35 are represented in this figure. Like shown in Fig. 15, a confinement number of 0.69 lead to higher heat transfer processes than a confinement number of 0.35 and 0.23 for operating conditions represented on the bottom right and on the top left of Fig. 15, i.e. at high driving pressure and low filling ratio and at low driving pressure and high filling ratio. This trend at high driving pressure and low filling ratio was already discussed all along the paper and is due to the evolution of the thermophysical properties of water close to the triple point and on the significance of surface tension forces and inertial forces. At low driving pressure, the poorer performances are theoretically obtained for a confinement number of 0.69. However, as the pressure decreases and firstly for high filling ratio and then for all filling ratio, the trend starts to be reversed. This trend is probably due to the fact that, due to the confinement, the fluid is warmer for Co = 0.69 than for Co = 0.35 at given operating conditions. Thus,
P (kPa)
12
Psat (kPa)
Fig. 15. Theoretical experimental domain leading to higher performances with a confinement number of 0.69.
although the driving pressure is low, conditions are favourable to maintain the occurrence of boiling which allows regenerating the liquid film before it is completely evaporated. It worth noting that conditions given in Fig. 15, especially the driving pressure, are specific to the channel tested in this study. Indeed, since the central plate is made of 6 mm stainless steel, the overall thermal resistance of the evaporator is high. Thus, driving pressure calculated in this study are much higher than driving pressure required to observe these phenomena in a less capacitive thermal channel. 5. Conclusion At Co = 0.69 (e = 2 mm), during the bubble growth, apparition of dendrites at the top of the bubble were observed for almost all the test conducted. For some operating conditions, disturbances on the liquid/vapour interface of the bubble were also observed for Co = 0.23 (e = 6 mm) and Co = 0.35 (e = 4 mm) but these disturbances rather look like the evaporation waves described in [14]. Moreover, at high driving pressure and low filling ratio, for a confinement number of 0.69, entrainment of droplets by the vapour flow was observed. It was shown that this phenomenon occurred for Weber number close to the unity and higher and for rate of vapour flow j*v higher than 0.69. The occurrence of these various phenomena were gathered in a j*v-We diagram. In this diagram, three main parts are highlighted: for j*v higher than 0.29 (solely obtained for Co = 0.69) dendrites were observed; for j*v ranging between 1.56 and 0.29, phenomena observed depend on the Weber number: for Weber number lower than 0.2 (conditions obtained for Co = 0.69), curved interfaces were observed; on contrary, for Weber number higher than 0.2 (conditions obtained for Co = 0.35), evaporation waves were mostly observed; then for j*v lower than 0.18, for Co = 0.35 and 0.23, whichever the Weber number, evaporation waves or curved interface or the occurrence of both could be observed. The occurrence of these various phenomena impacted the way of bubbles break and thus, the heat transfer. It is thus shown that a Confinement number of 0.35 and 0.23 (e = 4 and e = 6 mm) lead to similar trend and similar time-averaged obtained heat fluxes. Trends observed for Co = 0.69 (e = 2 mm) were, on the contrary, different and heat transfer were generally lower. This trend is assumed to be due to the significance of the surface tension forces which tended to defragment bubbles and slowed down their growth which lead to a lower height up to which the liquid was
F. Giraud, B. Tremeac / International Journal of Heat and Mass Transfer 145 (2019) 118725
splashed and to a thicker film with the generation of liquid rivulet. It is however shown that a confinement number of 0.69 should theoretically leads to higher heat transfer than Co = 0.35 and Co = 0.23 at high driving pressure and low filling ratio and at low driving pressure and high filling ratio. The higher performances for Co = 0.69 at high driving pressure were confirmed experimentally and visualization shows that these performances were obtained for data for those the entrainment of liquid by the vapour flow was observed. The generation of this upward liquid film allowed a wider exchange area and thus a higher overall heat transfer. Declaration of Competing Interest
[6]
[7]
[8] [9]
[10] [11]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
[12]
Acknowledgement
[14]
The authors want to thank Lisa Fluro, a former intern at the Lafset Laboratory, who conducted the experiments under the supervision of the authors.
[13]
[15]
[16]
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