- Email: [email protected]
Water falling film evaporation on a corrugated plate
International Journal of Thermal Sciences 81 (2014) 29e37
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Water falling film evaporation on a corrugated plate Armel Gonda a, b, Philippe Lancereau a, Philippe Bandelier a, Lingai Luo c, *, Yilin Fan c, Sylvain Benezech d a
LITEN/LETH, CEA Grenoble, 17 rue des martyrs, 38054 Grenoble Cedex 9, France LOCIE, CNRS UMR 5271, Université de Savoie, Polytech Annecy-Chambery, Campus Scientifique, Savoie Technolac, 73376 Le Bourget du Lac Cedex, France c Laboratoire de Thermocinétique, CNRS UMR 6607, Université de Nantes, La Chantrerie, Rue Christian Pauc, BP 50609, 44306 Nantes Cedex, France d Alfa Laval Packinox, 71100 Chalon sur Saône, France b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 November 2012 Received in revised form 10 January 2014 Accepted 26 February 2014 Available online 28 March 2014
This paper presents experimental results on the study of falling water film evaporation on a single vertical corrugated plate. The corrugated plate module, made of stainless steel having a total heat transfer area of 0.267 m2, was fabricated and tested in a pilot scale setup. The special geometry of the plate module allows the heat transfer between the liquid flowing in parallel channels inside de module and a film flowing on the two outer faces. Hydrodynamic and thermal tests were carried out. Results of heat transfer for evaporation from the surface of the water film are presented and compared to various correlations found in the literature. It is observed that when the surface is invaded by the film, decreasing film flow-rate provides higher ratio of wetted surface compared to increasing film flow-rate. The enhancement of heat transfer has been observed. Based on our own results, a new correlation has been proposed to predict the evaporative heat transfer by falling film. Ó 2014 Elsevier Masson SAS. All rights reserved.
Keywords: Falling film Evaporation Heat transfer Corrugated plate Wetting
1. Introduction During recent years, research aimed at the development of technologies that make more efficient use of renewable energy such as solar energy and waste heat from industry plants and power stations is attaining a fast growth. Based on absorption/ desorption of water by aqueous solutions, absorption process is now widely considered for solar or waste heat driven refrigeration [1], heat or cooling transportation over long distance [2,3] and long-term solar heat storage [4e6]. In the operating cycle of the absorption system using saline solution (LiBr/H2O; CaCl2/H2O, LiCl/ H2O, etc.), water is the working fluid and evaporates under vacuum condition. Used for the evaporation of fluids under vacuum in desalination [7] and chemical industry [8], falling film technique is well adapted for low pressure applications, due to its low pressure drop characteristic. Compared with flooded-type evaporators, falling film evaporators have the advantages of high evaporatingside heat transfer coefficient, low working fluid charge and small temperature difference between the working fluid and the wall [9]. Experimental researches on falling film evaporation were reviewed by Ribatski and Jacobi [10], by Thome [8] and by
* Corresponding author. Tel.: þ33 240683167; fax: þ33 240683141. E-mail address: [email protected] (L. Luo). http://dx.doi.org/10.1016/j.ijthermalsci.2014.02.010 1290-0729/Ó 2014 Elsevier Masson SAS. All rights reserved.
Gonzalez et al. [11]. Special emphasis was given on falling film evaporation on horizontal tubes and experimentally based correlations were presented to predict heat transfer coefficient in evaporating falling films for water, ammonia and alternative refrigerants. Experimental studies on falling film evaporation on a single vertical tube have also been reported in the literature and correlations were also proposed for water films [12,13] and for highly viscous liquid films [13e15]. Some of the correlations dealing with non-boiling falling water film evaporation are summarized in Table 1. Note that the Nusselt number (Nu) for falling film is usually defined as:
Nu ¼
1=3 hf v2 $ k g
(1)
Where hf is the convective heat transfer coefficient in falling film (W/m2 K), k the thermal conductivity of fluid (W/m K), v the kinematics viscosity of fluid (m2/s) and g the gravitational acceleration (m/s2). The Reynolds number (Re) for characterizing the flow regime of falling film is expressed as:
Re ¼
4$G
m
(2)
30
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
a A A1 A2 A3 B C1 Cp DH e g h k Ka Nu Pr q Q Re T DTLMTD U
constant defined in Eq. (7) () module total heat transfer area (m2) parameter defined in Table 1 parameter defined in Table 1 parameter defined in Table 1 parameter defined in Table 1 parameter defined in Table 1 specific heat (J/kg K) hydraulic diameter of channels (m) plate wall thickness (m) gravitational acceleration (m/s2) heat transfer coefficient (W/m2 K) thermal conductivity of fluid (W/m K) Kapitza number h (g$m4)/(r$s3) Nusselt number defined in Eq. (1) () Prandtl number h m$Cp/k () heat flux density (W/m2) mass flow-rate of heating fluid (kg/s) Reynolds numbers defined in Eqs. (2) and (8) () temperature ( C) logarithmic mean temperature difference ( C) overall heat transfer coefficient (W/m2 K)
Greek symbols constant defined in Eq. (7) () specific mass flow-rate (g/s m) parameter defined in Table 1 plate slope ( ) thermal conductivity of plate wall (W/m K) dynamic viscosity (Pa s) v kinematics viscosity (m2/s) r density (kg/m3) s surface tension (kg/s2)
a G dþ q l m
Subscripts f falling film side h heating fluid side i inlet lam laminar o outlet s saturation tur turbulent
where G is the mass flow-rate per width unit (g/m s) and m the dynamic viscosity (Pa s). Compared to shell-and-tubes configuration, vertical plate-type heat exchangers can be more compact, lighter and cheaper for falling film evaporation [16,17]. However, systematic experimental studies are lacking so that only very few correlations are available to predict the thermal performance on this geometry. The main technological barriers are [18]: -
-
-
velocity of the heating fluid (m/s) constant defined in Eq. (9) () constant defined in Eq. (9) ()
V x y
Nomenclature
It is difficult to obtain thin falling films reliably and reproducibly; Dry zones appear when the flow-rate becomes low or the heat flux becomes high; Distribution header which intends to spread the liquid in the form of a thin and uniform film has to be designed delicately.
Kafi et al. [7] developed one of the few correlations for a vertical plate-type evaporator for seawater desalination. In their study, horizontal wires were placed on the plate surface to improve film spreading and to promote turbulences. The hydrodynamics and thermal performances of falling film evaporation under vacuum condition were investigated. To the best of our knowledge, no other correlations are available for vertical plate under vacuum conditions. In the present study, non-boiling falling water film evaporation on a corrugated plate (called “module” here after) is explored. We shall first investigate the hydrodynamic aspect to evaluate the wettability of the falling film on the plate. Then results of thermal test will also be discussed and compared with several correlations for approaching geometries. Finally, a new correlation based on our results and working conditions will be proposed to predict the heat transfer of water evaporating falling film on a corrugated plate, for
Table 1 Several experimental studies on falling film evaporation. Authors
Material and geometry
Heating method
Pr range
Re range
Correlations for film side heat transfer
Kafi et al. [7]
Hot water
3.5
100e800
Nutur ¼ 0.0033$Re0.4$Pr0,65
Chun and Seban [12]
Stainless steel plate with metallic grids to promote film turbulences; height: 1.8 m; width: 0.4 m. Outside of vertical stainless steel tube; diameter: 0.029 m; heated length: 0.292 m.
Electrical
1.77e5.7
320e21,000
Nulam ¼ 0.821$Re0.22 Nutur ¼ 0.0038$Re0.4$Pr0.65 Transition: Re ¼ 5900/Pr1.06
Alhusseini et al. [13]
Outside of vertical stainless steel tube; diameter: 0.0381 m; length: 2.9 m.
Electrical
1.73e46.6
34e15,600
Nu ¼ ðNu5lam þ Nu5tur Þ1=5 Nulam ¼ 2.65$Re0.158$Ka0.0563 Nutur ¼
Han and Fletcher [19]
Horizontal brass tube: smooth, circumferentially and axially grooved. Diameter: 0.0508 m; length: 0.254 m.
Electrical
1.3e3.6
770e7,000
þ1=3
Pr$d ðA1 $Pr 3=4 þA2 $Pr 1=2 þA3 $Pr 1=4 þC1 ÞþðB$Ka1=2 $Pr1=2 Þ
where: A1 ¼ 9:17 þ þ A2 ¼ 0:328$p$ð130 þ d Þ=d þ þ2 þ2 A3 ¼ 0:0289$ð152100 þ 2340$d þ 7$d Þ=d 0:0675 þ0;333 Þ B ¼ 2:51$106 $d $Ka0:173 =Reð3:49$Ka C1 ¼ 8:82 þ 0:0003$Re dþ ¼ 0:0946$Re0:8 Nutur ¼ 0.025$Re0.2$Pr0.53 (smooth-tube) Nutur ¼ 0.0028$Re0.5$Pr0.85 (grooved-tube)
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
potential application in the design of novel absorption machines for solar or waste energy storage. 2. Experiment 2.1. Experimental apparatus Based on the operating principle of absorption machines, an experimental setup has been built to investigate non-boiling water falling film evaporation on a corrugated plate. Fig. 1 shows a schematic of the experimental setup and a photo view of the whole installation. The setup comprises an evaporator (the module with its film distribution header), a condenser, temperature controlling devices and associated instruments for temperature, pressure and
31
flow-rates measurements. The module and the condenser are each enclosed within a borosilicate glass column of 0.6 m in diameter and 1 m in height. The whole installation occupies a surface of 2.40 m 2 m with a height of 4.20 m. There are three fluid circuits in the setup: the working fluid circuit (blue line in Fig. 1(a)), the heating fluid circuit (red line) and the cooling fluid circuit (green line). In the heating circuit, hot water is pumped from an electric heater (Etirex Incoloy 825; 12 kW) to the inside of module channels where it releases heat to the falling film for evaporation. After that, it returns to the electric heater for recycling. Flow-rate and inlet temperature in the heating circuit are respectively controlled by a pump (Movitec VF04-3 PD) and a power electric heater. Likewise in the cooling circuit, cold water is pumped from a cooler (Ciatcooler RBB 35; 10 kW at 5 C) toward
Fig. 1. Schematic (a) and picture (b) of the experimental setup.
32
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
the condenser which consists of two spiral plate heat exchangers (Spirec G.23.54). Pressure inside the test loop is controlled by the condenser. In the working fluid circuit, distilled water is pumped by a gear pump (Micropump W29412) from a water tank (left side of Fig. 1(a)) to the inlet of the module and then flows down by gravity as falling film. Heated by the hot water of the heating circuit, the liquid film is partially evaporated. Under our tested conditions, nucleate boiling was never observed. While the generated vapor flows against the falling film flow direction, towards the condenser via a connecting tube between two glass columns, the residual liquid is collected at the bottom of the module and returns to water tank. Condensed water is collected by another water tank (right side of Fig. 1(a)). Liquid temperatures in the water tanks are controlled by two refrigerated thermostatic baths (Huber CC-415; 1 kW at 0 C).
Made of polycarbonate, it is composed of two parts: the distributor and the redistributors. Water flows firstly through the distributor, both edges of which are drilled 26 vertical semi-cylindrical holes of 3 mm diameter, 13 on each edge. Then, water flows along the internal walls of the header until it reaches the redistributors. By overflowing, the redistributors uniformly spread the liquid along the width of both sides of the plate module.
2.3. Data reduction Table 2 gives the range of parameters covered experimentally. To perform calculations, the following assumptions were made: -
2.2. Corrugated module and distribution header The core component in the system that interested us is the “module” as a carrier for falling film evaporation. Fig. 2 shows a schematic of the corrugated module and a cutting view of one of its channels. Manufactured by Ziepack (a subsidiary of Alfa Laval Packinox), this corrugated plate is made from two plain stainless steel sheets, which are welded together by horizontal lines. These lines define adjacent and independent channels. Then, the corrugated geometry of the module is obtained by introducing a pressurized liquid between the two sheets; this produces a swelling of the two sheets between the welded lines to form the channels [20]. Hot water of the heating circuit enters the plate from the bottom and flows through the 26 channels one after another in series (single channel, multi-passage configuration), guided by horizontal baffles in two distribution areas at both sides. The heating fluid then exits the plate at the top. As a result, it is locally cross-flow and globally counter-current flow configuration. The external surface area of the channels is 0.267 m2, corresponding to the heat exchange surface area of the module. A fluid distribution header (Fig. 3) is designed and integrated to the module in order to spread the working fluid along the module width in the form of a thin, continuous and uniform liquid film.
-
-
-
-
-
The heat loss from the distribution areas is neglected; All the heat is transferred to the falling film; the heat transfer area is totally wetted; All the evaporation takes place from the surface of the film at saturation temperature; Heat transfer by radiation is negligible; Physical properties of the heating fluid are evaluated at the mean temperature between inlet and outlet; Swelling of the module hasn’t thinned the two stainless steel sheets; heat transfer area equals to sheets areas before swelling; Water falling film is spread on the module at saturation temperature; As fluids are pure and clean, there is no fouling.
The overall heat flux density received by the evaporating film (q) is calculated as follows:
q ¼
Q $Cp$ðTi To Þ A
(3)
where Q is the heating fluid mass flow-rate (kg/s), Cp the specific heat of heating fluid (J/kg K), Ti and To the inlet and outlet temperature of heating fluid, respectively ( C) and A the module total heat transfer area (m2). The logarithmic mean temperature difference (DTLMTD) is calculated between evaporating falling film and heating water:
Fig. 2. Corrugated module schematic and cutting view of a channel (unit: mm). (a) Corrugated module; (b) cutting view of a channel.
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
DTLMTD ¼
ðTi Ts Þ ðTo Ts Þ ðTi Ts Þ ln ðT o Ts Þ
33
(4)
where Ts is the saturation temperature at the surface of the film ( C). Thus overall heat transfer coefficient of the module (U) can be calculated as:
U ¼
q
DTLMTD
(5)
The mean heat transfer coefficient of falling film evaporation (hf) can be expressed as:
hf ¼
1 1 e 1 U hh l
(6)
where hh is the mean convective heat transfer coefficient of heating water inside the module channels, e the plate wall thickness (m) and l the thermal conductivity of plate wall (W/m K). Convective heat transfer coefficient of heating water inside the module channels (hh) is calculated according to a correlation provided by Ziepack, the module manufacturer and inspired by the Dittus Boelter correlation:
hh ¼
k $a$Re0;8 $Pr 0;4 DH
(7)
where DH is the hydraulic diameter of channels (m) and a a parameter to take account of the channels shape which are not circular. DH and a are industrial property of Ziepack. Reynolds number of heating fluid is typically calculated from:
Re ¼
r$V$DH m
(8)
where V is the velocity of the heating fluid (m/s). To give an order of magnitude, the calculated heating side convective thermal resistance is about 23% of the total thermal resistance. Nusselt number of the film (Nu) is calculated from Eq. (1). 2.4. Experimental procedure and uncertainty analysis Before operation a vacuum pump (Vacuubrand MD 1C) was used to put the working fluid circuit under vacuum conditions. Leakages were checked by a helium leak detector (Leybold UL 200) and coated with mastic (Diatex LSM1310). This helped to make the experimental setup airtight under vacuum conditions for several months. Distilled water was charged by siphon into the setup and was then degassed by boiling; the released air was evacuated by the vacuum pump. For each test, it takes three hours to reach the steady state. To reduce the errors, the measurements were repeated and the dispersion to the mean value is taken into account in the calculation of the uncertainty. Each variable used in the calculations is the result of the arithmetic average of approximately 300 readings. According to previous equations, the falling film heat transfer coefficient (hf) is calculated from temperatures and flow-rate measurements. Type K thermocouples were used to measure
Fig. 3. Schematic side view and picture of the module with the distribution header. (a) Picture of the module with the distribution header; (b) side view of the distribution header.
34
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
Table 2 Experimental conditions.
Absolute pressure (kPa) Saturation temperature ( C) Prandtl number Film flow-rate (g/s) Film Reynolds number Heating temperature ( C)
Series 1
Series 2
1 7 10.45 35e80 237e550 9e19
2 17.5 7.4 25e85 230e790 28e30
temperatures. An absolute pressure sensor (Rosemount 3051; 0e 10 kPa) was used to measure the pressure inside the glass column containing the module, so that the corresponding saturation temperature (Ts) can be determined. Coriolis mass flowmeters (Micromotion F025; 0e750 g/s) were used to measure flow-rates. Table 3 shows the measurement uncertainty at various positions. These sensors were calibrated on a small scale of measurements to improve accuracy. A propagation of error analysis [21] was performed to estimate uncertainty for Nu. Errors bars for the calculated falling film Nusselt number are shown in Fig. 8. It should be noted that the uncertainties on geometrical parameters of the module due to fabrication imperfections and irregularities are not considered in this estimation.
Fig. 4. Falling film pictures from high-speed camera (Photron Fastcam SA3) Record Rate (fps) 2000; G ¼ 234 g/s m.
3. Results and discussion Hydrodynamic tests were performed on the module integrated with the distribution header at ambient temperature and pressure (no evaporation) to observe the wetting of the film on the plate surface. Then, low pressure evaporation tests in the whole experimental setup were carried out to investigate the thermal performances of such a module. 3.1. Hydrodynamic results The fluid distribution header was installed to spread the working fluid along the module width in the form of a thin, continuous and uniform liquid film. The horizontality of the distributor and the module plate was well examined during our tests. Thus at the top of the module, the formation of dry zones because of maldistribution is eliminated. Fig. 4 shows that the water film flows with interfacial turbulence. It can be seen a rivulet of water flowing on the first peak and small ripples moving on the film surface. Indeed, on the inclined part of the plate, the film Reynolds number is well above its critical value proposed by Benjamin [22]:
5 Re > $cot q 6
(9)
where q is the angle of the inclined part of the plate ( ). As indicated in Fig. 8, the values of film Reynolds number in this study ranged from about 200 to 800, which are more than a hundred times higher than the critical value.
Table 3 Measurement uncertainty at various positions. Position
Items
Instruments accuracy
Glass column
Temperature Pressure Temperature Flow-rate Temperature Flow-rate
0.08 K 0.03 kPa 0.08 K 0.3 g/s 0.08 K 0.5 g/s
Working fluid circuit Heating circuit
The wetted surface area was evaluated by adding to water a food coloring agent (Blue E133) in negligible concentration to avoid physical properties modification (less than 1% weight). Pictures of the plate were then recorded for different flow-rates, and an analysis of the images by thresholding method was used to calculate the ratio of wetted surface area. This was done to quantify the same phenomenon observed with pure water. Fig. 5 shows the full views of the film with the colored water. Eight extracted thresholded pictures of the falling-film for different flow-rate are provided: four pictures (a, b, c and d) for the increasing flow-rate and four other (a0 , b0 , c0 and d0 ) for the decreasing flow-rate. The image treatment process was carried out using GIMP image software. In GIMP software, color selection tool was used to automatically select all non-wetted surface area by adjusting the threshold option and selecting the area by saturation. These options allow selecting the areas enclosed by dotted lines in the different images, as shown in Fig. 5. Then, the number of pixels selected from the “histogram” option as well as the total size of the image from the “scale of the image” option can be obtained. With this treatment, the ratio of wetted surface area under different working conditions could be obtained and Fig. 6 in the manuscript could be plotted. Shown in Fig. 6 are curves plotted from an observation of the ratio of wetted surface to the total surface area for increasing and decreasing falling film flow-rate. As can be seen in Figs. 5 and 6, the ratio of wetted surface area increases with the increase of falling film flow-rate. Meanwhile, an interesting phenomenon is observed: at same flow-rate, the ratio of wetted surface area for decreasing flow remains higher than that observed during increasing flow. For example for a specific mass flow-rate of 50 g/s m, the ratio of wetted surface area is about 50% for increasing flow-rate, while it is more than 90% for decreasing flow-rate. Same observation was reported by Podgorski [23]. In fact, the stability of the liquid film on a non-wettable surface is a common issue: the surface tension effect tends to maintain dry zones in the falling film. As a result, the falling film flows in form of rivulets. But there exists a critical flowrate above which any dry zones would be swept away [24]. This minimum wetting flow-rate has been investigated by some
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
35
Fig. 5. Extracted thresholded pictures of the falling-film for different flow-rate.
researchers [25e31]. When the increasing flow-rate reaches this critical value, gravity and inertia effects predominate over surface tension effect, so that all dry zones will be covered by the film. Decreasing flow is different with respect to increasing flow, because the surface area is initially totally wetted, as shown in Fig. 5. For film flow-rate larger than 50 g/s m, the module surface area is totally wetted. The film thickness decreases with decreasing flowrate until a dry zone appears, and the dewetting begins for a specific flow-rate at about G ¼ 50 g/s m. Dry zones nucleation requires a very small film thickness. This can occur for very low film flowrates, or because of film surface-wave instabilities. Naturally, the supply of heat to evaporate the film will accentuate this phenomenon. This observation is also important since a good wetting of the module is indispensible for efficient evaporative heat transfer, especially under low flow-rates conditions. To ensure a good
wetting of the module, low pressure evaporation tests were carried out by decreasing the falling film flow-rate. 3.2. Thermal results Following the hydrodynamic results, all the thermal results were obtained with a decreasing flow-rate for a better wetting of the plate surface. Experimental results from thermal tests are shown in Fig. 7 which plots the Nusselt number as a function of film Reynolds number. These results were obtained during water falling film evaporation at Pr ¼ 10.45, for different heating temperatures. Correlations listed in Table 1 are also plotted in Fig. 7 for comparison. It can be observed that the Nusselt number increases with increasing Reynolds number under our tested conditions, implying
36
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
Fig. 6. Comparison on ratio of wetted surface area for increasing and decreasing falling film flow-rate.
that the flow regime of the falling film is turbulent, even when the film Reynolds number is low (Re ¼ 237). The heating temperature effect is chaotic since the points are mixed. In the absence of nucleate boiling, the dispersion of the points explains the variations from one heating temperature to another. By comparing with correlations proposed in the literature, it can also be observed that our experimental results do not correspond well to these predictions. This is unsurprising since those correlations are based on different geometries other than corrugated plate (e.g. horizontal or vertical tubes, smooth or grooved). The most comparable work is that of Kafi et al. [7], whose correlation was based on the evaporation of water on a vertical smooth plate with horizontal metallic wires. The wires promote turbulence so that earlier transition of flow regime was also achieved. Under our tested conditions (250 < Re < 500), the values of Nusselt number obtained are at least 50% higher than these predictions, showing the enhancement of heat transfer by using our innovative corrugated geometry. The work of Chun and Seban [12] predicts the flow regime transition at about Re ¼ 500; this correlation has been developed with water on the outside of a vertical tube. Alhusseini et al. [13] extended the work of Chun and Seban [12] by using two different fluids (water and propylene glycol). The values of Nusselt number of our tests become higher than the wavy laminar prediction from
Fig. 8. Nusselt number versus Reynolds number, experimental results at Pr ¼ 10.45 and Pr ¼ 7.45.
Chun and Seban [12] and from Alhusseini et al. [13] when Re > 350 and Re > 500, respectively. The trend of the experimental results suggests that they will be higher than the two turbulent predictions from these two studies. However, for Re < 350 (resp. Re < 500), low Reynolds number turbulences induced by the corrugated geometry are less efficient for the enhancement of heat transfer than the surface-wave instabilities in wavy laminar regime. Comparing with the correlations proposed by Han and Fletcher [19] for falling film evaporation on horizontal tubes (turbulent regimes), it can be observed that the thermal performance of the corrugated module is better than that of smooth tube, but not as good as that of grooved one. This observation suggests that structuring the module surface may further intensify the heat transfer. It should be noted that the curves shown in Fig. 7 are plotted for Pr ¼ 10.45, which, to some extent are out of the application range for several correlations. Very few correlations were established with water at low pressure, i.e. for high Prandtl numbers. However, this comparison is not meaningless because it helps to get an idea about the performances of the module. Based on the experimental results obtained, a new correlation is proposed using the standard form for the turbulent flow:
Nu ¼ a$Rex $Pr y
Shown in Fig. 8 are the experimental results used to determine the parameters a, x and y by fitting method. Each set of measurements corresponds to a constant Prandtl number: Pr ¼ 10.45 and Pr ¼ 7.4.
Nu ¼ 0:00175$Re0:57 $Pr 0:67
Fig. 7. Nusselt number obtained versus Reynolds number for various heating temperature and comparison with different correlations in the literature (Pr ¼ 10.45).
(10)
(11)
Fig. 9. Comparison of the proposed correlation and the experimental results.
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
The applicable range of this new correlation is: 230 < Re < 790 and 7.4 < Pr < 10.45. As shown in Fig. 9, good agreement has been observed between experimental data and theoretical prediction with error within 10%. 4. Conclusion Based on the operating principle of absorption machines, an experimental setup has been built to study non-boiling water falling film evaporation on a vertical corrugated plate. Study of the falling film hydrodynamics has shown that the decreasing film flow-rate mode could ensure a good wetting of the plate surface area, even at low flow-rates. However, this is not the case for increasing film flow-rate. Thermal performances of the module during the falling film evaporation at low pressure were evaluated and compared with different geometries in the literature, in terms of falling film Nusselt number: -
-
-
Enhanced heat transfer compared to a smooth plate with horizontal wires (Nu at least 50% higher). For Re < 350, more advantageous to use single vertical-tube geometry in the wavy laminar regime. For 350 < Re < 500, comparable thermal performance. For Re > 500, the corrugated geometry becomes more efficient. Better thermal performance than that of a smooth horizontal tube when Re > 350, but worse than that of a grooved one. This observation suggests that structuring the module surface may further intensify the heat transfer.
A new correlation has been developed based on our experimental data to predict the falling film evaporation on a vertical corrugated plate. For 230 < Re < 790 and 7.4 < Pr < 10.45, good agreement has been observed between experimental data and theoretical prediction with error within 10%. This correlation will be used in a numerical simulation, performed with the software EES (Engineering Equation Solver), which will be useful in predesign of an evaporator for long-term solar heat storage with absorption machines. Future experimental work will investigate the coupling of evaporation, condensation, desorption and absorption phenomena. Acknowledgments Financial support was provided by the ANR (French National Research Agency) and by OSEO (French State Agency for Innovation) respectively under the research projects PROSSIS ANR-07Stock-E-08 and ISI Solaire Duo. References [1] Y. Fan, L. Luo, B. Souyri, Review of solar sorption refrigeration technologies: development and applications, Renew. Sustain. Energy Rev. 11 (2007) 1758e 1775. [2] Q. Ma, L. Luo, R. Wang, Z. Xia, L. Pin, B. Souyri, Performance analysis and validation on transportation of heat energy over long distance by ammoniae water absorption cycle, Int. J. Energy Res. 34 (2010) 839e847.
37
[3] Q. Ma, L. Luo, R.Z. Wang, G. Sauce, A review on transportation of heat energy over long distance: exploratory development, Renew. Sustain. Energy Rev. 13 (2009) 1532e1540. [4] R. Weber, V. Dorer, Long-term heat storage with NaOH, Vacuum 82 (2008) 708e716. [5] K.E. N’Tsoukpoe, N. Le Pierres, L. Luo, Numerical dynamic simulation and analysis of a lithium bromide/water long-term solar heat storage system, Energy 37 (2012) 346e358. [6] H. Liu, K.E. N’Tsoukpoe, N. Le Pierres, L. Luo, Evaluation of a seasonal storage system of solar energy for house heating using different absorption couples, Energy Convers. Manag. 52 (2011) 2427e2436. [7] F. Kafi, V. Renaudin, D. Alonso, J.M. Hornut, New med plate desalination process: thermal performances, Desalination 166 (2004) 53e62. [8] J.R. Thome, Falling film evaporation: state-of-the-art review of recent work, J. Enhanc. Heat Transf. 6 (1999) 263e277. [9] W. Li, X.Y. Wu, Z. Luo, R.L. Webb, Falling water film evaporation on newlydesigned enhanced tube bundles, Int. J. Heat Mass Transf. 54 (2011) 2990e 2997. [10] G. Ribatski, A.M. Jacobi, Falling-film evaporation on horizontal tubes e a critical review, Int. J. Refrig. 28 (2005) 635e653. [11] J.M. Gonzalez G, J.M.S. Jabardo, W.F. Stoecker, Falling Film Ammonia Evaporators, 1992. ACRC TR-33. [12] K.R. Chun, R.A. Seban, Heat transfer to evaporating liquid films, ASME J. Heat. Transf. 93 (1971) 391e396. [13] A.A. Alhusseini, K. Tuzla, J.C. Chen, Falling film evaporation of single component liquids, Int. J. Heat Mass Transf. 41 (1998) 1623e1632. [14] F. Weise, Experimentelle Untersuchungen zur Strömung und Wärmeübertragung von Reinstoff-Fallfilmen mit hohen Prandtl-Zahlen, in: Cuvillier (Ed.), ICTV-Schriftenreihe Band 3, Braunschweig, 2007. [15] M. Johansson, L. Vamling, L. Olausson, Heat transfer in evaporating black liquor falling film, Int. J. Heat Mass Transf. 52 (2009) 2759e2768. [16] D.S. Kim, C.A. Infante Ferreira, Flow patterns and heat and mass transfer coefficients of low Reynolds number falling film flows on vertical plates: effects of a wire screen and an additive, Int. J. Refrig. 32 (2009) 138e 149. [17] M. Flamensbeck, F. Summerer, P. Riesch, F. Ziegler, G. Alefeld, A cost effective absorption chiller with plate heat exchangers using water and hydroxides, Appl. Therm. Eng. 18 (1998) 413e425. [18] B.Q. Liu, P. Le Goff, Contacteur gaz-liquide à film ruisselant sur plaque plane pour evaporation, absorption et desorption, Rev. Gen. Therm. 364 (1992). [19] J. Han, L.S. Fletcher, Falling film evaporation and boiling in circumferential and axial grooves on horizontal tubes, Ind. Eng. Chem. Proc. Des. Dev. 24 (1985) 570e575. [20] S. Benezech, P.X. Bussonnet, M. Claudel, F. Noel, Heat Exchanger and a Corresponding Exchange Module, International Patent WO 2005/073657A1, 2005. [21] B.N. Taylor, C.E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, National Institute of Standards and Technology Technical Note 1297, 1994. [22] T. Brooke Benjamin, Wave formation in laminar flow down an inclined plane, J. Fluid Mech. 9 (1957) 554e573. [23] T. Podgorski, Ruissellement en conditions de mouillage partiel (PhD thesis), Université de Paris 6, France, 2000. [24] T. Podgorski, J.M. Flesselles, L. Limat, Dry arches within flowing films, Phys. Fluids 11 (1999) 845e852. [25] T. Podgorski, J.-M. Flesselles, L. Limat, Courbure de la frontière d’une zone sèche dans un film en écoulement, C.R. Acad. Sci. Paris 9 (2001) 1361e 1367. [26] D.E. Hartley, W. Murgatroyd, Criteria for the break-up of thin liquid layers flowing isothermally over solid surfaces, Int. J. Heat Mass Transf. 7 (1964) 1003e1015. [27] E. Rio, L. Limat, Wetting hysteresis of a dry patch left inside a flowing film, Phys. Fluids 18 (2006) 032102. [28] J. Sebilleau, L. Lebon, L. Limat, Stability of a dry patch in a viscous flowing film, Eur. Phys. J. Spec. Top. 166 (2009) 139e142. [29] K.R. Morison, Q.A.G. Worth, N.P. O’dea, Minimum wetting and distribution rates in falling film evaporators, Food Bioprod. Process. 84 (2006) 302e310. [30] B.C. Hoke, J.C. Chen, Thermocapillary breakdown of subcooled falling liquid films, Ind. Eng. Chem. Res. 31 (1992) 688e694. [31] Q. Wang, X. Ma, Z. Lan, J. Chen, T. Bai, Heat transfer characteristics of falling film process on coated division tubes: effect of the surface configurations, Ind. Eng. Chem. Res. 49 (2010) 6622e6629.
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Water falling film evaporation on a corrugated plate Armel Gonda a, b, Philippe Lancereau a, Philippe Bandelier a, Lingai Luo c, *, Yilin Fan c, Sylvain Benezech d a
LITEN/LETH, CEA Grenoble, 17 rue des martyrs, 38054 Grenoble Cedex 9, France LOCIE, CNRS UMR 5271, Université de Savoie, Polytech Annecy-Chambery, Campus Scientifique, Savoie Technolac, 73376 Le Bourget du Lac Cedex, France c Laboratoire de Thermocinétique, CNRS UMR 6607, Université de Nantes, La Chantrerie, Rue Christian Pauc, BP 50609, 44306 Nantes Cedex, France d Alfa Laval Packinox, 71100 Chalon sur Saône, France b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 November 2012 Received in revised form 10 January 2014 Accepted 26 February 2014 Available online 28 March 2014
This paper presents experimental results on the study of falling water film evaporation on a single vertical corrugated plate. The corrugated plate module, made of stainless steel having a total heat transfer area of 0.267 m2, was fabricated and tested in a pilot scale setup. The special geometry of the plate module allows the heat transfer between the liquid flowing in parallel channels inside de module and a film flowing on the two outer faces. Hydrodynamic and thermal tests were carried out. Results of heat transfer for evaporation from the surface of the water film are presented and compared to various correlations found in the literature. It is observed that when the surface is invaded by the film, decreasing film flow-rate provides higher ratio of wetted surface compared to increasing film flow-rate. The enhancement of heat transfer has been observed. Based on our own results, a new correlation has been proposed to predict the evaporative heat transfer by falling film. Ó 2014 Elsevier Masson SAS. All rights reserved.
Keywords: Falling film Evaporation Heat transfer Corrugated plate Wetting
1. Introduction During recent years, research aimed at the development of technologies that make more efficient use of renewable energy such as solar energy and waste heat from industry plants and power stations is attaining a fast growth. Based on absorption/ desorption of water by aqueous solutions, absorption process is now widely considered for solar or waste heat driven refrigeration [1], heat or cooling transportation over long distance [2,3] and long-term solar heat storage [4e6]. In the operating cycle of the absorption system using saline solution (LiBr/H2O; CaCl2/H2O, LiCl/ H2O, etc.), water is the working fluid and evaporates under vacuum condition. Used for the evaporation of fluids under vacuum in desalination [7] and chemical industry [8], falling film technique is well adapted for low pressure applications, due to its low pressure drop characteristic. Compared with flooded-type evaporators, falling film evaporators have the advantages of high evaporatingside heat transfer coefficient, low working fluid charge and small temperature difference between the working fluid and the wall [9]. Experimental researches on falling film evaporation were reviewed by Ribatski and Jacobi [10], by Thome [8] and by
* Corresponding author. Tel.: þ33 240683167; fax: þ33 240683141. E-mail address: [email protected] (L. Luo). http://dx.doi.org/10.1016/j.ijthermalsci.2014.02.010 1290-0729/Ó 2014 Elsevier Masson SAS. All rights reserved.
Gonzalez et al. [11]. Special emphasis was given on falling film evaporation on horizontal tubes and experimentally based correlations were presented to predict heat transfer coefficient in evaporating falling films for water, ammonia and alternative refrigerants. Experimental studies on falling film evaporation on a single vertical tube have also been reported in the literature and correlations were also proposed for water films [12,13] and for highly viscous liquid films [13e15]. Some of the correlations dealing with non-boiling falling water film evaporation are summarized in Table 1. Note that the Nusselt number (Nu) for falling film is usually defined as:
Nu ¼
1=3 hf v2 $ k g
(1)
Where hf is the convective heat transfer coefficient in falling film (W/m2 K), k the thermal conductivity of fluid (W/m K), v the kinematics viscosity of fluid (m2/s) and g the gravitational acceleration (m/s2). The Reynolds number (Re) for characterizing the flow regime of falling film is expressed as:
Re ¼
4$G
m
(2)
30
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
a A A1 A2 A3 B C1 Cp DH e g h k Ka Nu Pr q Q Re T DTLMTD U
constant defined in Eq. (7) () module total heat transfer area (m2) parameter defined in Table 1 parameter defined in Table 1 parameter defined in Table 1 parameter defined in Table 1 parameter defined in Table 1 specific heat (J/kg K) hydraulic diameter of channels (m) plate wall thickness (m) gravitational acceleration (m/s2) heat transfer coefficient (W/m2 K) thermal conductivity of fluid (W/m K) Kapitza number h (g$m4)/(r$s3) Nusselt number defined in Eq. (1) () Prandtl number h m$Cp/k () heat flux density (W/m2) mass flow-rate of heating fluid (kg/s) Reynolds numbers defined in Eqs. (2) and (8) () temperature ( C) logarithmic mean temperature difference ( C) overall heat transfer coefficient (W/m2 K)
Greek symbols constant defined in Eq. (7) () specific mass flow-rate (g/s m) parameter defined in Table 1 plate slope ( ) thermal conductivity of plate wall (W/m K) dynamic viscosity (Pa s) v kinematics viscosity (m2/s) r density (kg/m3) s surface tension (kg/s2)
a G dþ q l m
Subscripts f falling film side h heating fluid side i inlet lam laminar o outlet s saturation tur turbulent
where G is the mass flow-rate per width unit (g/m s) and m the dynamic viscosity (Pa s). Compared to shell-and-tubes configuration, vertical plate-type heat exchangers can be more compact, lighter and cheaper for falling film evaporation [16,17]. However, systematic experimental studies are lacking so that only very few correlations are available to predict the thermal performance on this geometry. The main technological barriers are [18]: -
-
-
velocity of the heating fluid (m/s) constant defined in Eq. (9) () constant defined in Eq. (9) ()
V x y
Nomenclature
It is difficult to obtain thin falling films reliably and reproducibly; Dry zones appear when the flow-rate becomes low or the heat flux becomes high; Distribution header which intends to spread the liquid in the form of a thin and uniform film has to be designed delicately.
Kafi et al. [7] developed one of the few correlations for a vertical plate-type evaporator for seawater desalination. In their study, horizontal wires were placed on the plate surface to improve film spreading and to promote turbulences. The hydrodynamics and thermal performances of falling film evaporation under vacuum condition were investigated. To the best of our knowledge, no other correlations are available for vertical plate under vacuum conditions. In the present study, non-boiling falling water film evaporation on a corrugated plate (called “module” here after) is explored. We shall first investigate the hydrodynamic aspect to evaluate the wettability of the falling film on the plate. Then results of thermal test will also be discussed and compared with several correlations for approaching geometries. Finally, a new correlation based on our results and working conditions will be proposed to predict the heat transfer of water evaporating falling film on a corrugated plate, for
Table 1 Several experimental studies on falling film evaporation. Authors
Material and geometry
Heating method
Pr range
Re range
Correlations for film side heat transfer
Kafi et al. [7]
Hot water
3.5
100e800
Nutur ¼ 0.0033$Re0.4$Pr0,65
Chun and Seban [12]
Stainless steel plate with metallic grids to promote film turbulences; height: 1.8 m; width: 0.4 m. Outside of vertical stainless steel tube; diameter: 0.029 m; heated length: 0.292 m.
Electrical
1.77e5.7
320e21,000
Nulam ¼ 0.821$Re0.22 Nutur ¼ 0.0038$Re0.4$Pr0.65 Transition: Re ¼ 5900/Pr1.06
Alhusseini et al. [13]
Outside of vertical stainless steel tube; diameter: 0.0381 m; length: 2.9 m.
Electrical
1.73e46.6
34e15,600
Nu ¼ ðNu5lam þ Nu5tur Þ1=5 Nulam ¼ 2.65$Re0.158$Ka0.0563 Nutur ¼
Han and Fletcher [19]
Horizontal brass tube: smooth, circumferentially and axially grooved. Diameter: 0.0508 m; length: 0.254 m.
Electrical
1.3e3.6
770e7,000
þ1=3
Pr$d ðA1 $Pr 3=4 þA2 $Pr 1=2 þA3 $Pr 1=4 þC1 ÞþðB$Ka1=2 $Pr1=2 Þ
where: A1 ¼ 9:17 þ þ A2 ¼ 0:328$p$ð130 þ d Þ=d þ þ2 þ2 A3 ¼ 0:0289$ð152100 þ 2340$d þ 7$d Þ=d 0:0675 þ0;333 Þ B ¼ 2:51$106 $d $Ka0:173 =Reð3:49$Ka C1 ¼ 8:82 þ 0:0003$Re dþ ¼ 0:0946$Re0:8 Nutur ¼ 0.025$Re0.2$Pr0.53 (smooth-tube) Nutur ¼ 0.0028$Re0.5$Pr0.85 (grooved-tube)
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
potential application in the design of novel absorption machines for solar or waste energy storage. 2. Experiment 2.1. Experimental apparatus Based on the operating principle of absorption machines, an experimental setup has been built to investigate non-boiling water falling film evaporation on a corrugated plate. Fig. 1 shows a schematic of the experimental setup and a photo view of the whole installation. The setup comprises an evaporator (the module with its film distribution header), a condenser, temperature controlling devices and associated instruments for temperature, pressure and
31
flow-rates measurements. The module and the condenser are each enclosed within a borosilicate glass column of 0.6 m in diameter and 1 m in height. The whole installation occupies a surface of 2.40 m 2 m with a height of 4.20 m. There are three fluid circuits in the setup: the working fluid circuit (blue line in Fig. 1(a)), the heating fluid circuit (red line) and the cooling fluid circuit (green line). In the heating circuit, hot water is pumped from an electric heater (Etirex Incoloy 825; 12 kW) to the inside of module channels where it releases heat to the falling film for evaporation. After that, it returns to the electric heater for recycling. Flow-rate and inlet temperature in the heating circuit are respectively controlled by a pump (Movitec VF04-3 PD) and a power electric heater. Likewise in the cooling circuit, cold water is pumped from a cooler (Ciatcooler RBB 35; 10 kW at 5 C) toward
Fig. 1. Schematic (a) and picture (b) of the experimental setup.
32
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
the condenser which consists of two spiral plate heat exchangers (Spirec G.23.54). Pressure inside the test loop is controlled by the condenser. In the working fluid circuit, distilled water is pumped by a gear pump (Micropump W29412) from a water tank (left side of Fig. 1(a)) to the inlet of the module and then flows down by gravity as falling film. Heated by the hot water of the heating circuit, the liquid film is partially evaporated. Under our tested conditions, nucleate boiling was never observed. While the generated vapor flows against the falling film flow direction, towards the condenser via a connecting tube between two glass columns, the residual liquid is collected at the bottom of the module and returns to water tank. Condensed water is collected by another water tank (right side of Fig. 1(a)). Liquid temperatures in the water tanks are controlled by two refrigerated thermostatic baths (Huber CC-415; 1 kW at 0 C).
Made of polycarbonate, it is composed of two parts: the distributor and the redistributors. Water flows firstly through the distributor, both edges of which are drilled 26 vertical semi-cylindrical holes of 3 mm diameter, 13 on each edge. Then, water flows along the internal walls of the header until it reaches the redistributors. By overflowing, the redistributors uniformly spread the liquid along the width of both sides of the plate module.
2.3. Data reduction Table 2 gives the range of parameters covered experimentally. To perform calculations, the following assumptions were made: -
2.2. Corrugated module and distribution header The core component in the system that interested us is the “module” as a carrier for falling film evaporation. Fig. 2 shows a schematic of the corrugated module and a cutting view of one of its channels. Manufactured by Ziepack (a subsidiary of Alfa Laval Packinox), this corrugated plate is made from two plain stainless steel sheets, which are welded together by horizontal lines. These lines define adjacent and independent channels. Then, the corrugated geometry of the module is obtained by introducing a pressurized liquid between the two sheets; this produces a swelling of the two sheets between the welded lines to form the channels [20]. Hot water of the heating circuit enters the plate from the bottom and flows through the 26 channels one after another in series (single channel, multi-passage configuration), guided by horizontal baffles in two distribution areas at both sides. The heating fluid then exits the plate at the top. As a result, it is locally cross-flow and globally counter-current flow configuration. The external surface area of the channels is 0.267 m2, corresponding to the heat exchange surface area of the module. A fluid distribution header (Fig. 3) is designed and integrated to the module in order to spread the working fluid along the module width in the form of a thin, continuous and uniform liquid film.
-
-
-
-
-
The heat loss from the distribution areas is neglected; All the heat is transferred to the falling film; the heat transfer area is totally wetted; All the evaporation takes place from the surface of the film at saturation temperature; Heat transfer by radiation is negligible; Physical properties of the heating fluid are evaluated at the mean temperature between inlet and outlet; Swelling of the module hasn’t thinned the two stainless steel sheets; heat transfer area equals to sheets areas before swelling; Water falling film is spread on the module at saturation temperature; As fluids are pure and clean, there is no fouling.
The overall heat flux density received by the evaporating film (q) is calculated as follows:
q ¼
Q $Cp$ðTi To Þ A
(3)
where Q is the heating fluid mass flow-rate (kg/s), Cp the specific heat of heating fluid (J/kg K), Ti and To the inlet and outlet temperature of heating fluid, respectively ( C) and A the module total heat transfer area (m2). The logarithmic mean temperature difference (DTLMTD) is calculated between evaporating falling film and heating water:
Fig. 2. Corrugated module schematic and cutting view of a channel (unit: mm). (a) Corrugated module; (b) cutting view of a channel.
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
DTLMTD ¼
ðTi Ts Þ ðTo Ts Þ ðTi Ts Þ ln ðT o Ts Þ
33
(4)
where Ts is the saturation temperature at the surface of the film ( C). Thus overall heat transfer coefficient of the module (U) can be calculated as:
U ¼
q
DTLMTD
(5)
The mean heat transfer coefficient of falling film evaporation (hf) can be expressed as:
hf ¼
1 1 e 1 U hh l
(6)
where hh is the mean convective heat transfer coefficient of heating water inside the module channels, e the plate wall thickness (m) and l the thermal conductivity of plate wall (W/m K). Convective heat transfer coefficient of heating water inside the module channels (hh) is calculated according to a correlation provided by Ziepack, the module manufacturer and inspired by the Dittus Boelter correlation:
hh ¼
k $a$Re0;8 $Pr 0;4 DH
(7)
where DH is the hydraulic diameter of channels (m) and a a parameter to take account of the channels shape which are not circular. DH and a are industrial property of Ziepack. Reynolds number of heating fluid is typically calculated from:
Re ¼
r$V$DH m
(8)
where V is the velocity of the heating fluid (m/s). To give an order of magnitude, the calculated heating side convective thermal resistance is about 23% of the total thermal resistance. Nusselt number of the film (Nu) is calculated from Eq. (1). 2.4. Experimental procedure and uncertainty analysis Before operation a vacuum pump (Vacuubrand MD 1C) was used to put the working fluid circuit under vacuum conditions. Leakages were checked by a helium leak detector (Leybold UL 200) and coated with mastic (Diatex LSM1310). This helped to make the experimental setup airtight under vacuum conditions for several months. Distilled water was charged by siphon into the setup and was then degassed by boiling; the released air was evacuated by the vacuum pump. For each test, it takes three hours to reach the steady state. To reduce the errors, the measurements were repeated and the dispersion to the mean value is taken into account in the calculation of the uncertainty. Each variable used in the calculations is the result of the arithmetic average of approximately 300 readings. According to previous equations, the falling film heat transfer coefficient (hf) is calculated from temperatures and flow-rate measurements. Type K thermocouples were used to measure
Fig. 3. Schematic side view and picture of the module with the distribution header. (a) Picture of the module with the distribution header; (b) side view of the distribution header.
34
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
Table 2 Experimental conditions.
Absolute pressure (kPa) Saturation temperature ( C) Prandtl number Film flow-rate (g/s) Film Reynolds number Heating temperature ( C)
Series 1
Series 2
1 7 10.45 35e80 237e550 9e19
2 17.5 7.4 25e85 230e790 28e30
temperatures. An absolute pressure sensor (Rosemount 3051; 0e 10 kPa) was used to measure the pressure inside the glass column containing the module, so that the corresponding saturation temperature (Ts) can be determined. Coriolis mass flowmeters (Micromotion F025; 0e750 g/s) were used to measure flow-rates. Table 3 shows the measurement uncertainty at various positions. These sensors were calibrated on a small scale of measurements to improve accuracy. A propagation of error analysis [21] was performed to estimate uncertainty for Nu. Errors bars for the calculated falling film Nusselt number are shown in Fig. 8. It should be noted that the uncertainties on geometrical parameters of the module due to fabrication imperfections and irregularities are not considered in this estimation.
Fig. 4. Falling film pictures from high-speed camera (Photron Fastcam SA3) Record Rate (fps) 2000; G ¼ 234 g/s m.
3. Results and discussion Hydrodynamic tests were performed on the module integrated with the distribution header at ambient temperature and pressure (no evaporation) to observe the wetting of the film on the plate surface. Then, low pressure evaporation tests in the whole experimental setup were carried out to investigate the thermal performances of such a module. 3.1. Hydrodynamic results The fluid distribution header was installed to spread the working fluid along the module width in the form of a thin, continuous and uniform liquid film. The horizontality of the distributor and the module plate was well examined during our tests. Thus at the top of the module, the formation of dry zones because of maldistribution is eliminated. Fig. 4 shows that the water film flows with interfacial turbulence. It can be seen a rivulet of water flowing on the first peak and small ripples moving on the film surface. Indeed, on the inclined part of the plate, the film Reynolds number is well above its critical value proposed by Benjamin [22]:
5 Re > $cot q 6
(9)
where q is the angle of the inclined part of the plate ( ). As indicated in Fig. 8, the values of film Reynolds number in this study ranged from about 200 to 800, which are more than a hundred times higher than the critical value.
Table 3 Measurement uncertainty at various positions. Position
Items
Instruments accuracy
Glass column
Temperature Pressure Temperature Flow-rate Temperature Flow-rate
0.08 K 0.03 kPa 0.08 K 0.3 g/s 0.08 K 0.5 g/s
Working fluid circuit Heating circuit
The wetted surface area was evaluated by adding to water a food coloring agent (Blue E133) in negligible concentration to avoid physical properties modification (less than 1% weight). Pictures of the plate were then recorded for different flow-rates, and an analysis of the images by thresholding method was used to calculate the ratio of wetted surface area. This was done to quantify the same phenomenon observed with pure water. Fig. 5 shows the full views of the film with the colored water. Eight extracted thresholded pictures of the falling-film for different flow-rate are provided: four pictures (a, b, c and d) for the increasing flow-rate and four other (a0 , b0 , c0 and d0 ) for the decreasing flow-rate. The image treatment process was carried out using GIMP image software. In GIMP software, color selection tool was used to automatically select all non-wetted surface area by adjusting the threshold option and selecting the area by saturation. These options allow selecting the areas enclosed by dotted lines in the different images, as shown in Fig. 5. Then, the number of pixels selected from the “histogram” option as well as the total size of the image from the “scale of the image” option can be obtained. With this treatment, the ratio of wetted surface area under different working conditions could be obtained and Fig. 6 in the manuscript could be plotted. Shown in Fig. 6 are curves plotted from an observation of the ratio of wetted surface to the total surface area for increasing and decreasing falling film flow-rate. As can be seen in Figs. 5 and 6, the ratio of wetted surface area increases with the increase of falling film flow-rate. Meanwhile, an interesting phenomenon is observed: at same flow-rate, the ratio of wetted surface area for decreasing flow remains higher than that observed during increasing flow. For example for a specific mass flow-rate of 50 g/s m, the ratio of wetted surface area is about 50% for increasing flow-rate, while it is more than 90% for decreasing flow-rate. Same observation was reported by Podgorski [23]. In fact, the stability of the liquid film on a non-wettable surface is a common issue: the surface tension effect tends to maintain dry zones in the falling film. As a result, the falling film flows in form of rivulets. But there exists a critical flowrate above which any dry zones would be swept away [24]. This minimum wetting flow-rate has been investigated by some
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
35
Fig. 5. Extracted thresholded pictures of the falling-film for different flow-rate.
researchers [25e31]. When the increasing flow-rate reaches this critical value, gravity and inertia effects predominate over surface tension effect, so that all dry zones will be covered by the film. Decreasing flow is different with respect to increasing flow, because the surface area is initially totally wetted, as shown in Fig. 5. For film flow-rate larger than 50 g/s m, the module surface area is totally wetted. The film thickness decreases with decreasing flowrate until a dry zone appears, and the dewetting begins for a specific flow-rate at about G ¼ 50 g/s m. Dry zones nucleation requires a very small film thickness. This can occur for very low film flowrates, or because of film surface-wave instabilities. Naturally, the supply of heat to evaporate the film will accentuate this phenomenon. This observation is also important since a good wetting of the module is indispensible for efficient evaporative heat transfer, especially under low flow-rates conditions. To ensure a good
wetting of the module, low pressure evaporation tests were carried out by decreasing the falling film flow-rate. 3.2. Thermal results Following the hydrodynamic results, all the thermal results were obtained with a decreasing flow-rate for a better wetting of the plate surface. Experimental results from thermal tests are shown in Fig. 7 which plots the Nusselt number as a function of film Reynolds number. These results were obtained during water falling film evaporation at Pr ¼ 10.45, for different heating temperatures. Correlations listed in Table 1 are also plotted in Fig. 7 for comparison. It can be observed that the Nusselt number increases with increasing Reynolds number under our tested conditions, implying
36
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
Fig. 6. Comparison on ratio of wetted surface area for increasing and decreasing falling film flow-rate.
that the flow regime of the falling film is turbulent, even when the film Reynolds number is low (Re ¼ 237). The heating temperature effect is chaotic since the points are mixed. In the absence of nucleate boiling, the dispersion of the points explains the variations from one heating temperature to another. By comparing with correlations proposed in the literature, it can also be observed that our experimental results do not correspond well to these predictions. This is unsurprising since those correlations are based on different geometries other than corrugated plate (e.g. horizontal or vertical tubes, smooth or grooved). The most comparable work is that of Kafi et al. [7], whose correlation was based on the evaporation of water on a vertical smooth plate with horizontal metallic wires. The wires promote turbulence so that earlier transition of flow regime was also achieved. Under our tested conditions (250 < Re < 500), the values of Nusselt number obtained are at least 50% higher than these predictions, showing the enhancement of heat transfer by using our innovative corrugated geometry. The work of Chun and Seban [12] predicts the flow regime transition at about Re ¼ 500; this correlation has been developed with water on the outside of a vertical tube. Alhusseini et al. [13] extended the work of Chun and Seban [12] by using two different fluids (water and propylene glycol). The values of Nusselt number of our tests become higher than the wavy laminar prediction from
Fig. 8. Nusselt number versus Reynolds number, experimental results at Pr ¼ 10.45 and Pr ¼ 7.45.
Chun and Seban [12] and from Alhusseini et al. [13] when Re > 350 and Re > 500, respectively. The trend of the experimental results suggests that they will be higher than the two turbulent predictions from these two studies. However, for Re < 350 (resp. Re < 500), low Reynolds number turbulences induced by the corrugated geometry are less efficient for the enhancement of heat transfer than the surface-wave instabilities in wavy laminar regime. Comparing with the correlations proposed by Han and Fletcher [19] for falling film evaporation on horizontal tubes (turbulent regimes), it can be observed that the thermal performance of the corrugated module is better than that of smooth tube, but not as good as that of grooved one. This observation suggests that structuring the module surface may further intensify the heat transfer. It should be noted that the curves shown in Fig. 7 are plotted for Pr ¼ 10.45, which, to some extent are out of the application range for several correlations. Very few correlations were established with water at low pressure, i.e. for high Prandtl numbers. However, this comparison is not meaningless because it helps to get an idea about the performances of the module. Based on the experimental results obtained, a new correlation is proposed using the standard form for the turbulent flow:
Nu ¼ a$Rex $Pr y
Shown in Fig. 8 are the experimental results used to determine the parameters a, x and y by fitting method. Each set of measurements corresponds to a constant Prandtl number: Pr ¼ 10.45 and Pr ¼ 7.4.
Nu ¼ 0:00175$Re0:57 $Pr 0:67
Fig. 7. Nusselt number obtained versus Reynolds number for various heating temperature and comparison with different correlations in the literature (Pr ¼ 10.45).
(10)
(11)
Fig. 9. Comparison of the proposed correlation and the experimental results.
A. Gonda et al. / International Journal of Thermal Sciences 81 (2014) 29e37
The applicable range of this new correlation is: 230 < Re < 790 and 7.4 < Pr < 10.45. As shown in Fig. 9, good agreement has been observed between experimental data and theoretical prediction with error within 10%. 4. Conclusion Based on the operating principle of absorption machines, an experimental setup has been built to study non-boiling water falling film evaporation on a vertical corrugated plate. Study of the falling film hydrodynamics has shown that the decreasing film flow-rate mode could ensure a good wetting of the plate surface area, even at low flow-rates. However, this is not the case for increasing film flow-rate. Thermal performances of the module during the falling film evaporation at low pressure were evaluated and compared with different geometries in the literature, in terms of falling film Nusselt number: -
-
-
Enhanced heat transfer compared to a smooth plate with horizontal wires (Nu at least 50% higher). For Re < 350, more advantageous to use single vertical-tube geometry in the wavy laminar regime. For 350 < Re < 500, comparable thermal performance. For Re > 500, the corrugated geometry becomes more efficient. Better thermal performance than that of a smooth horizontal tube when Re > 350, but worse than that of a grooved one. This observation suggests that structuring the module surface may further intensify the heat transfer.
A new correlation has been developed based on our experimental data to predict the falling film evaporation on a vertical corrugated plate. For 230 < Re < 790 and 7.4 < Pr < 10.45, good agreement has been observed between experimental data and theoretical prediction with error within 10%. This correlation will be used in a numerical simulation, performed with the software EES (Engineering Equation Solver), which will be useful in predesign of an evaporator for long-term solar heat storage with absorption machines. Future experimental work will investigate the coupling of evaporation, condensation, desorption and absorption phenomena. Acknowledgments Financial support was provided by the ANR (French National Research Agency) and by OSEO (French State Agency for Innovation) respectively under the research projects PROSSIS ANR-07Stock-E-08 and ISI Solaire Duo. References [1] Y. Fan, L. Luo, B. Souyri, Review of solar sorption refrigeration technologies: development and applications, Renew. Sustain. Energy Rev. 11 (2007) 1758e 1775. [2] Q. Ma, L. Luo, R. Wang, Z. Xia, L. Pin, B. Souyri, Performance analysis and validation on transportation of heat energy over long distance by ammoniae water absorption cycle, Int. J. Energy Res. 34 (2010) 839e847.
37
[3] Q. Ma, L. Luo, R.Z. Wang, G. Sauce, A review on transportation of heat energy over long distance: exploratory development, Renew. Sustain. Energy Rev. 13 (2009) 1532e1540. [4] R. Weber, V. Dorer, Long-term heat storage with NaOH, Vacuum 82 (2008) 708e716. [5] K.E. N’Tsoukpoe, N. Le Pierres, L. Luo, Numerical dynamic simulation and analysis of a lithium bromide/water long-term solar heat storage system, Energy 37 (2012) 346e358. [6] H. Liu, K.E. N’Tsoukpoe, N. Le Pierres, L. Luo, Evaluation of a seasonal storage system of solar energy for house heating using different absorption couples, Energy Convers. Manag. 52 (2011) 2427e2436. [7] F. Kafi, V. Renaudin, D. Alonso, J.M. Hornut, New med plate desalination process: thermal performances, Desalination 166 (2004) 53e62. [8] J.R. Thome, Falling film evaporation: state-of-the-art review of recent work, J. Enhanc. Heat Transf. 6 (1999) 263e277. [9] W. Li, X.Y. Wu, Z. Luo, R.L. Webb, Falling water film evaporation on newlydesigned enhanced tube bundles, Int. J. Heat Mass Transf. 54 (2011) 2990e 2997. [10] G. Ribatski, A.M. Jacobi, Falling-film evaporation on horizontal tubes e a critical review, Int. J. Refrig. 28 (2005) 635e653. [11] J.M. Gonzalez G, J.M.S. Jabardo, W.F. Stoecker, Falling Film Ammonia Evaporators, 1992. ACRC TR-33. [12] K.R. Chun, R.A. Seban, Heat transfer to evaporating liquid films, ASME J. Heat. Transf. 93 (1971) 391e396. [13] A.A. Alhusseini, K. Tuzla, J.C. Chen, Falling film evaporation of single component liquids, Int. J. Heat Mass Transf. 41 (1998) 1623e1632. [14] F. Weise, Experimentelle Untersuchungen zur Strömung und Wärmeübertragung von Reinstoff-Fallfilmen mit hohen Prandtl-Zahlen, in: Cuvillier (Ed.), ICTV-Schriftenreihe Band 3, Braunschweig, 2007. [15] M. Johansson, L. Vamling, L. Olausson, Heat transfer in evaporating black liquor falling film, Int. J. Heat Mass Transf. 52 (2009) 2759e2768. [16] D.S. Kim, C.A. Infante Ferreira, Flow patterns and heat and mass transfer coefficients of low Reynolds number falling film flows on vertical plates: effects of a wire screen and an additive, Int. J. Refrig. 32 (2009) 138e 149. [17] M. Flamensbeck, F. Summerer, P. Riesch, F. Ziegler, G. Alefeld, A cost effective absorption chiller with plate heat exchangers using water and hydroxides, Appl. Therm. Eng. 18 (1998) 413e425. [18] B.Q. Liu, P. Le Goff, Contacteur gaz-liquide à film ruisselant sur plaque plane pour evaporation, absorption et desorption, Rev. Gen. Therm. 364 (1992). [19] J. Han, L.S. Fletcher, Falling film evaporation and boiling in circumferential and axial grooves on horizontal tubes, Ind. Eng. Chem. Proc. Des. Dev. 24 (1985) 570e575. [20] S. Benezech, P.X. Bussonnet, M. Claudel, F. Noel, Heat Exchanger and a Corresponding Exchange Module, International Patent WO 2005/073657A1, 2005. [21] B.N. Taylor, C.E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, National Institute of Standards and Technology Technical Note 1297, 1994. [22] T. Brooke Benjamin, Wave formation in laminar flow down an inclined plane, J. Fluid Mech. 9 (1957) 554e573. [23] T. Podgorski, Ruissellement en conditions de mouillage partiel (PhD thesis), Université de Paris 6, France, 2000. [24] T. Podgorski, J.M. Flesselles, L. Limat, Dry arches within flowing films, Phys. Fluids 11 (1999) 845e852. [25] T. Podgorski, J.-M. Flesselles, L. Limat, Courbure de la frontière d’une zone sèche dans un film en écoulement, C.R. Acad. Sci. Paris 9 (2001) 1361e 1367. [26] D.E. Hartley, W. Murgatroyd, Criteria for the break-up of thin liquid layers flowing isothermally over solid surfaces, Int. J. Heat Mass Transf. 7 (1964) 1003e1015. [27] E. Rio, L. Limat, Wetting hysteresis of a dry patch left inside a flowing film, Phys. Fluids 18 (2006) 032102. [28] J. Sebilleau, L. Lebon, L. Limat, Stability of a dry patch in a viscous flowing film, Eur. Phys. J. Spec. Top. 166 (2009) 139e142. [29] K.R. Morison, Q.A.G. Worth, N.P. O’dea, Minimum wetting and distribution rates in falling film evaporators, Food Bioprod. Process. 84 (2006) 302e310. [30] B.C. Hoke, J.C. Chen, Thermocapillary breakdown of subcooled falling liquid films, Ind. Eng. Chem. Res. 31 (1992) 688e694. [31] Q. Wang, X. Ma, Z. Lan, J. Chen, T. Bai, Heat transfer characteristics of falling film process on coated division tubes: effect of the surface configurations, Ind. Eng. Chem. Res. 49 (2010) 6622e6629.