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Experimental analysis of the drop film boiling at ambient pressure
Energy Conversion and Management 76 (2013) 918–924
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Experimental analysis of the drop film boiling at ambient pressure Tadeusz Orzechowski, Sylwia Wcis´lik ⇑ ´ stwa Polskiego 7, 25-314 Kielce, Poland Kielce University of Technology, Department of Environmental Engineering, Aleja Tysia˛clecia Pan
a r t i c l e
i n f o
Article history: Received 31 December 2012 Accepted 30 August 2013
Keywords: Water droplet evaporation Leidenfrost phenomenon Mass flux Heat transfer coefficient Infrared mapping
a b s t r a c t The paper deals with the evaporation of large liquid drops having a mass of 1 g under stable film boiling conditions at ambient pressure. Water drop evaporation was expressed by the heat balance, which provides basis for determining instantaneous values of the heat transfer coefficient. The measurement stand, comprising three independent measurement paths, namely mass registration, temperature measurement and thermal visualisation, was described in detail. The system maintaining a constant temperature of the heating surface was located on the scales, the recordings of which were taken at constant frequency of 2 Hz. The measurement results come in the form of mass change versus time. On this basis, together with the measured area of the perpendicular drop projection onto the heating surface, it was possible to compute instantaneous values of the heat transfer coefficient. Those values decrease with a change in the area and the drop mass. At the beginning of measurements, at the constant temperature of the heating surface 337.5 °C, the heat transfer coefficient equalled 0.32 kW/m2 K, and it was over twice higher for a drop with the mass of 0.2 g. The thermal (infrared) mapping of the drop upper surface was performed using a thermovision camera (THV). The mapping indicates a complex interaction of heat and mass transfer processes, which result in intensive convection movements in the near-surface zone. That is manifested in the form of a highly diversified thermal field of the drop upper surface. The difference between the maximum and minimum temperatures can be as much as 10 K. For the adopted method of heat transfer coefficient computation, an analysis of uncertainties was also performed. The scales accuracy and the camera resolution were found to have the greatest impact on uncertainty in the heat transfer coefficient measurements. Uncertainty in measurement is inversely proportional to the drop size. As a result, measurements and later analysis of results were limited to the bottom of the range determined by the drop mass of 0.2 g. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Droplet vaporization on solid horizontal plate with high overheating has been a subject matter investigated in many technical papers (e.g. [1–3]). Baumeister, who was one of the first researchers thoroughly analysing the problem, presented a solution based on the energy balance. His results concern the formulas for the surface heat transfer coefficient, droplet evaporation time, surface temperature and volume of specified liquid. Further studies dealt with dependencies between the heat transfer coefficient components [4,5], dimensionless ratio of evaporation time, dependence on the universal curve for total evaporation time of water, benzene and carbon tetrachloride droplets [6] and the Leidenfrost point [7,8]. Parallel studies were carried out for spray evaporation [9– 11]. Due to strong interaction between droplets, this phenomenon cannot directly be transferred to that of a single droplet evaporation, especially for larger ones. ⇑ Corresponding author. E-mail addresses: [email protected] (T. Orzechowski), [email protected] (S. Wcis´lik). 0196-8904/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2013.08.057
A series of experimental tests on the single- and multi-droplet boiling systems were described and the results were discussed in paper [12], where interaction of different materials was observed with an infrared camera. Influence of the solid surface thermal conductivity on evaporation cooling process was investigated for a number of different materials: macor, steel and aluminium. The conclusion was that the boiling onset strongly depends on solid–liquid interfacial temperature, and the process is more efficient for materials of higher conductivity. The analysis of liquid droplets evaporation from the macor surface is also found in [13]. Thermal behaviour of two bodies during the evaporation process was discussed on the basis of the proposed model of solid cooling with liquid droplets, and a good congruence between theoretical analysis and measurements was observed. The system was heated by an external radiant panel. Similar interactions occur inside the engine combustion chambers [14,15]. Paper [16] examined whether it is possible to predict the evaporation processes of micro-sized droplets of infinite conductivity in an increasing temperature environment using the droplet evaporation model. Similar to a steady state evaporation process, experimental evaporation rates were found as almost linearly dependent on gas temperature.
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Nomenclature A cp m hfg t Tw Td Ts u
area of drop projection on hot surface (m2) specific heat (kJ/kg K) mass (g) enthalpy of vaporization (kJ/kg) time (s) heating surface temperature (°C) drop mean temperature (°C) saturation temperature (°C) standard uncertainty
Greek symbols a heat transfer coefficient (kW/m2 K)
An experimental method used to measure heat transfer between a hot surface and a non-wetting droplet was discussed in paper [2]. On the basis of infrared camera surface temperature measurements, a solution to the unsteady thermal conduction equation was obtained, which permits to evaluate the heat flux removal. The heat transferred by a droplet 1.5 mm in diameter typically equals 0.19 J, but during a very short time, heat flux may reach even 3.5 MW/m2 with subsequent temperature reduction by 47 °C. Heat transfer associated with a hot surface quenching by a jet of oil-in-water emulsion was investigated in [17]. Axisymmetric jet impingement on a hot metal disc at the temperature of 500– 600 °C was observed and registered by the THV camera. Based on a semi-analytical inverse heat conduction model, heat fluxes were calculated. It was also shown that the amount of the oil components change the rate of heat transfer significantly, especially in the film boiling regime. Experimental measurements of heat transfer due to droplet of low Weber numbers impact on the surface at the temperature above Leidenfrost were presented in paper [18]. An inverse conduction method was used to estimate the heat transfer coefficient as a function of the incoming droplet characteristics and dynamics. Heat transfer coefficients for a single droplet of small size were given. It was concluded that heat transfer coefficient depends, to a large extent, on the wall temperature, but it does not depend on the Weber number. The collision of single water droplets with a hot surface was investigated in [19]. Different boiling regimes were discussed for droplets diameters from 0.53 to 0.60 mm, impact velocities from 1.7 m/s to 4.1 m/s, and the solid surface temperatures ranging from 170 °C to 500 °C. The turbulent film boiling from a horizontal cylinder was theoretically investigated with respect to temperature-dependent vapour properties. Additionally, the effect of the thermal radiation from the surface on the boiling heat flux was studied. It was demonstrated that nonlinear effect would alter the magnitude of the average heat transfer coefficient from the surface [20]. Authors of study [21] made an attempt to prove that convection is the dominant phenomenon responsible for water droplet evaporation. Their assumptions were based on the hypothesis that only steam, due to its very low density, is much lighter than air, which makes a droplet levitate over the surface; for other liquids under consideration that seems to be the opposite. Rayleigh number, which compares buoyancy forces causing convection to diffusion and viscosity forces, was employed. A high value that was obtained Ra = 10 confirms the dominant influence of convection. At the same time, due to difficulties in the analytical description of a liquid droplet evaporation, and because of using many simplifica-
ac, ar Da
ew ri
convection and radiation components of the heat transfer coefficient (kW/m2 K) uncertainty of the heat transfer coefficient (kW/m2 K) heating surface emissivity standard deviation
Abbreviations AC acquisition system DC digital camera Ra Rayleigh number SD standard deviation THV infrared/thermovision camera
tions, the problem is still open, which indicates it is necessary to conduct further research into the phenomenon. In investigations discussed in paper [22], 1.1 g droplet of water with aqueous solutions of KCl and NaCl was deposited on a horizontal aluminium heating surface. The evaporation time was recorded for various temperatures and plotted as evaporation curves. The results show that the dissolved salt increases the Leidenfrost temperature by 20–40 °C. The solvent evaporation from the bottom of the levitating drop increases the salt concentration near the interface, which alters some liquid properties and causes a faster collapse of the vapour film. Takata et al. [23] found that the critical heat flux of TiO2-coated surface is about two times larger than that of a non-coated one, and that Leidenfrost temperature increases as the contact angle decreases. The superhydrophilic surface can be an ideal heat transfer surface. The effect of dissolving gas (CO2) or solid salts (Na2CO3 and NaHCO3) in water droplets boiling on a hot surface was analyzed in [24]. At surface temperatures from 100 °C to 300 °C, dissolved salts were found to reduce the evaporation rate, which is probably caused by the fact that they lower the vapour pressure of water and prevent the nucleate boiling regime. Dissolved carbon dioxide slightly enhances heat transfer in the nucleate boiling regime. Significant heat transfer enhancement and reducing the droplet lifetime to approximately half that of a pure water drop was observed in the case of sodium carbonate. The largest enhancement of heat transfer is produced by the sodium bicarbonate. As regards semi-transparency in infrared fluids, observations of the thermal motion inside the drop were reported in [25]. This visualization method allowed specifying three stages during the evaporating process: a warm-up phase, evaporation with thermal-convective instabilities, and finally evaporation without thermal patterns. All the instabilities depend on the fluid. Surface roughness is another factor discussed in liquid droplet evaporation studies. Those show that roughness conditions of the surface have a great impact on nucleate boiling regime but no such influence was observed for film boiling regime. The conclusion from [26] is that the Leidenfrost temperature on an extremely smooth surface is the same as that on metal plates of standard roughness. The Leidenfrost temperature basically refers to the wettability and thermal properties of the plate, but no relation to the shape, size and distribution of surface roughness can be noted. Additionally, in study [27], it is stated that a decrease in surface roughness extends the droplet evaporation time, which according to the authors, is caused by the droplet faster departure from the surface. Despite of the fact that the problem has been thoroughly analysed, the mechanisms of evaporation are still not fully clear. The
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object of the present study is the levitation of a single drop of water. It floats on a thin layer of vapour, which prevents a direct contact with the hot surface. The aim of the present study is to characterise heat transfer due to droplet evaporation as a function of its size and the heating wall temperature. The weight measurement method makes it possible to directly determine droplet mass under unsteady evaporation conditions. The methodology used in the study allows calculating the instantaneous heat transfer coefficient. 2. Test facility The measuring system is shown in Figs. 1 and 2. It consisted of the following elements: a copper cylinder with heating surface, a wrapped heater, a thermocouple, an electronic scale, a mirror, the acquisition system (AC), a computer, a digital camera (DC), and an infrared camera. The main part of the test stand was a massive copper cylinder with bowl-shaped upper surface having a very large radius of curvature. Such a setup facilitated drop positioning in the cylinder geometrical centre. Additionally, to assure the thermal uniformity of the cylinder, it was coated in heat-resistant (up to 600 °C) black paint with the emissivity of ew 0.85. This coefficient was checked after each application of the paint in order to eliminate possible errors related to painting accuracy. Wrapped heater provided electrical power of 300 W by means of an autotransformer. The heater adjustable output power made it possible to obtain desirable, constant temperature conditions on the surface throughout the experiment. Every time the autotransformer was set, and after any change in parameters, the experimental setup was conditioned for approx. one hour to obtain the best possible stability and uniformity of the system. Additionally, a K-type thermocouple was mounted underneath the heating surface and connected to the data acquisition system, which sent a signal to the computer disc. Due to high copper thermal conductivity, the thermocouple readings were assumed to be the same for the entire surface. Additionally, the uniformity of surface temperature was tested with an infrared camera. Under such measurement conditions, a large drop of water was placed on the heated surface at 20 °C. The initial mass of the drop was slightly more than 1 g, and its diameter was 1 cm (for heating surface temperature Tw = 337.5 °C). The shape, size and the temperature of the investigated drops were observed with both digital and infrared cameras. The cameras recorded images reflected from a specially prepared mirror of known, high reflectivity. The optical system of cameras and mirror was set in such a way so
Fig. 2. The experimental set-up (markings of the elements as shown in Fig. 1).
that an accurate shape of drop projection on the surface could be maintained. In an additional calibration measurement, a K-type thermocouple was located in the geometric centre of the drop to check the results obtained with the THV camera (see Fig. 2). In this way, correct emissivity that needed to be preset in the camera was found. The entire heating system was located on the electronic scales having 0.001 g sensitivity and 0.01 g accuracy. The scales were equipped with RS232 port to transmit results to the computer. A computer program was developed to collect data on the drop weight. The minimum registration frequency was determined by the internal inertia of the scales and by the software processing of analogue signals to the digital ones. The maximum frequency of recording and processing was 10 Hz. The test device consisted of three independent measuring units, namely camera, scales and temperature measurement unit. The first unit mapped the sequential behaviour of drops located on the non-isothermal surface, the second registered a drop weight
Fig. 1. Schematic of the test apparatus: 1 – droplet of water, 2 – copper cylinder, 3 – wrapped heater, 4 – thermocouple, 5 – electronic scale, 6 – infrared camera, 7 – digital camera, 8 – mirror, 9 – tripod, 10 – AC signal processing system, 11 – autotransformer, 12 – computer, and 13 – voltmeter.
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loss over time, and the third controlled the drop surface temperature. An infrared camera recorded temperature of the visible, external surface of the drop, and additionally the temperature of the heating surface. The drop area could be evaluated from the upper surface temperature distribution (thermogram). That required calculating the number of pixels with the individual size calibration of a single element.
3. Experimental investigation The main outcome of the experiment was determining drop mass change as a function of time. Measurement recording started at the weight of a single drop of 1 g evaporating at ambient pressure (which corresponded to zero time in measurement results presented in Fig. 3). The weight registration frequency was set to 2 Hz. One of the problems that needed to be solved was the impact of the weight of the elastic cables on the measured weight. The problem was solved successfully by carefully prepared cable suspension (see Fig. 1). After balancing and conditioning for a few hours, the wires got arranged properly and did no longer affect the scales readings, so it was possible to take a single series of measurements. The behaviour of a drop was studied in several series of measurements at different values of the heating power. The total drop evaporation time was a few minutes for the assumed surface temperature of 337.5 °C and the initial mass of 1 g. Usually, more than 30 measurements for each of the analyzed surface temperatures were taken. Such number of measurements was necessary to prevent errors, check repeatability, and to make a statistical evaluation. Exemplary results are presented in Fig. 3 showing 33 curves at constant surface temperature. It should be noted that such accuracy of the Tw temperature was obtained due to the high heat capacity of the heating cylinder and continuous electrical power supply for the entire duration of the experiment. Drop mass (1 g) was less than 0.5% of the total copper cylinder mass 360 g. Consequently, the heat dissipated from the cylinder surface did not significantly change its temperature. The calculated standard deviation from the reference value Tw during the first 200 s of evaporation was about SD = 2.56 °C. From 33 curves, after statistical analysis and assessing the quality of measurements, an average curve was determined (bold, dashed line in Fig. 3) With respect to this average value, the instantaneous standard deviation was computed as a function of drop mass loss, which is shown in Fig. 4. Drop evaporation leads to a gradual increase in the mass standard deviation. In Fig. 4, a progressive growth is seen until stan-
Fig. 4. Standard deviation from drop mass (at first 200 s of evaporation) for exemplary surface temperature, Tw = 337.5 °C.
dard deviation reaches 0.02 g. That corresponds to approximately half of the initial mass of the drop, after which standard deviation has pretty much a constant value. The surface temperature (Tw) was measured with a K-type thermocouple. The drop temperature (Tk) was calculated from thermograms taken with a THV camera. It was the temperature averaged over 80% of the drop projection area (see Fig. 5a). For the exemplary heating surface temperature (Tw = 337.5 °C), the average drop temperature was Td = 90.58 °C, so it was almost 10 °C lower than the water saturation temperature at ambient pressure. The value was estimated for the first 200 s of the measurement (0–200 s). It should be noted that the drop surface temperature was highly variable. The maximum value in this case was 95.42 °C, while the minimum was 84.77 °C. The temperature of the drop upper surface changed over time. At the heating surface temperature Tw = 337.5 °C, its maximum standard deviation computed from the mean drop temperature was 2.57 °C and it was later used to assess the measurement uncertainty (90.58 °C ± 2.57 °C). The result obtained indicates very strong convective processes inside the drops, which can be seen in exemplary thermograms presented in Fig. 5 and in Table 1 corresponding to Fig. 5. In Table 1, corresponding to thermograms in Fig. 5, basic statistical descriptors, such as standard deviation, mean, minimum and maximum temperatures from the visible drop area, are provided. These values were estimated on the basis of 75% of that area (as indicated in the first thermogram), so the drop diameter is reduced by about 10%. In this way the directional reflectance and emissivity were eliminated. Additionally, the image reconstruction techniques for visualization of the flow inside the strongly curved surface, i.e. evaporating drops, have been found in the literature [28]. It is suggested that convection inside evaporating liquid drops is distributed symmetrically, and therefore the problem must be considered as an axially symmetric one, but presented investigations clearly contradict this theory. Drop, during the evaporation, produces a local cooling of the surface, which affects its behaviour and changes the nature of the process. 4. Methodology The following energy balance can be written for a drop located on the heating surface:
Fig. 3. The drop mass versus time for exemplary surface temperature, Tw = 337.5 °C.
ðar þ ac ÞðT w T d ÞA ¼ hfg
dm dm cp ðT s T d Þ dt dt
ð1Þ
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Fig. 5. Exemplary thermograms of the drop upper surface.
Table 1 Descriptive statistics from drop upper surface related to Fig. 5. Item
t (s)
Mean (°C)
Min (°C)
Max (°C)
SD (°C)
a b c d e f g h i
0 7 17 21.5 25 44 60 71.5 80
91.80 91.81 89.28 90.95 91.47 88.55 90.07 89.99 89.52
89.81 88.96 87.24 88.65 89.36 86.11 87.12 86.16 87.22
95.31 95.76 95.49 97.10 96.20 98.78 95.63 97.23 96.96
0.99 1.38 1.41 1.35 1.14 1.62 1.50 1.72 1.38
In the energy balance (1), it is assumed that heat transfer on the upper drop surface is negligibly small [29]. Mass transfer from the drop upper surface occurs due to diffusion. It is a small-scale process compared with the production of mass at the drop bottom. The left hand-side of the equation above represents heat transfer from the drop bottom surface by convection and radiation, while the right hand-side is a sum of the heat required to heat up the drop from the current to the saturation temperature, and the heat needed to vaporize the mass flux. The instantaneous heat transfer coefficient from the heating surface a = ar + ac (as a sum of radiation and convection heat transfer coefficients) can be calculated after determining all the necessary components in Eq. (1). The parameters hfg and cp are taken from the thermodynamic properties tables. A large number of points registered allow applying their numerical differentiation with smoothing with the use of procedures available in commercial software. Fig. 6 shows the measurement results (see Fig. 3) after differentiation and smoothing, which in this case is a polynomial approximation of the fourth order.
Fig. 6. Polynomial approximation of the average drop mass as a function of time.
The unknown heat transfer coefficient (i.e. the sum of convective ac and radiant ar) can be calculated from Eq. (1). The needed drop area A(t) was estimated from the film registered by the thermovision camera (Fig. 5) according to [30]. Final calculation results are shown in Fig. 7.
5. Measurement uncertainties It seems to be essential to estimate the measurement uncertainties resulting from the accuracy of laboratory instruments. To determine the maximum combined standard uncertainty (Da) of the heat transfer coefficient, on the basis of other quantities related
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Fig. 7. The overall heat transfer coefficient for exemplary heating surface temperature, Tw = 337.5 °C.
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Fig. 9. Experimental results and numerical calculations of the drop mass change versus time.
6. Conclusions
Fig. 8. Heat transfer coefficient as a function of drop mass and its absolute combined standard uncertainty for exemplary heating surface temperature, Tw = 337.5 °C.
to the energy balance (Eq. (1)), the following dependence (Eq. (2)) is proposed:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi !2 u 2 2 2 @ a 2 u @a @ a @ a 2 2 t Da ¼ u2A þ dm udm þ ðuT w Þ þ ðuT d Þ dt @A @T w @T d @ dt ð2Þ Eq. (2) is written in accordance with Type A evaluation of standard uncertainty [31]. The result of estimation is shown in Fig. 8. The average values of the combined standard uncertainty fractions are: uA = 10.7%, udm/dt = 89.0%, uTw = 0.2% and uTd = 0.1%. The differential Eq. (1) was solved numerically using measured heat transfer coefficients and the area of the drop projection. That resulted in obtaining drop mass change versus time. Fig. 9 presents the computational results for the case discussed. A thin dashed line in this figure represents selected extreme measurement series for recorded drop mass loss versus time, whereas a dotted line denotes the average from all measurement series. As can be seen in Fig. 9, a very good congruence between measurement data and numerical computations was obtained. In Fig. 9 both dashed lines indicate experimental limits.
It is extremely difficult to provide a theoretical description for the evaporation of a liquid drop floating over a hot surface, the temperature of which is higher than Leidenfrost point. The complex character of interrelated processes of heat and mass transfer results from vapour outflow, unstable in time, from under the drop bottom surface. That leads to intensive convection movements in the sub-surface zone. The phenomenon is reflected in the diversified thermal zone of the droplet upper surface, an example of which is illustrated in Fig. 5a. It can be seen that at the drop average temperature of 89 °C, the difference between the maximum and minimum temperature values can amount to as much as 10 °C. Similar values were also obtained in the initial calibration tests, in which temperature was measured with a thermocouple located inside the drop (see Fig. 2). Water drop evaporation was described using the heat balance (1). The equation serves as the basis to determine instantaneous values of the heat transfer coefficient. To do that, the system for stabilising the heating surface temperature was placed on the scales, the readings of which were recorded at the frequency of 2 Hz. The measurement results come in the form of mass change versus time. The drops that were investigated had the initial mass of 1 g. The measurement range, and consequently later analysis, were limited by the bottom value determined by drop mass of 0.2 g. It can be explained by the fast growth in the measurement uncertainties accompanying the decrease in drop mass and size. According to the uncertainty analysis performed in the study, the uncertainty was approx 4.8% at the beginning of the measurements, and it increased to approx 11% for drops that had a mass five times smaller. It should be added that measurement uncertainty was affected to the greatest extent by the scales accuracy and the camera resolution. On the basis of recorded drop mass versus time, and also of the computed drop contact area with the heating surface, instantaneous values of the heat transfer coefficient were calculated. Those increased with mass loss and the contact area reduction. The change can be seen in Fig. 8. At the heating surface temperature of 337.5 °C, the coefficient equals 0.32 kW/m2 K for a drop mass of 1 g, and it increases by 100% for drop mass of 0.2 g. The results obtained in the study demonstrate that under film boiling conditions the amount of heat removed by a liquid drop from the surface heated above Leidenfrosta point, varies with the drop mass and the contact area. The methodology for computing instantaneous values of the heat transfer coefficient proposed in the study provides a tool that is precise enough to accurately represent the drop evaporation process (see Fig. 9).
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Experimental analysis of the drop film boiling at ambient pressure Tadeusz Orzechowski, Sylwia Wcis´lik ⇑ ´ stwa Polskiego 7, 25-314 Kielce, Poland Kielce University of Technology, Department of Environmental Engineering, Aleja Tysia˛clecia Pan
a r t i c l e
i n f o
Article history: Received 31 December 2012 Accepted 30 August 2013
Keywords: Water droplet evaporation Leidenfrost phenomenon Mass flux Heat transfer coefficient Infrared mapping
a b s t r a c t The paper deals with the evaporation of large liquid drops having a mass of 1 g under stable film boiling conditions at ambient pressure. Water drop evaporation was expressed by the heat balance, which provides basis for determining instantaneous values of the heat transfer coefficient. The measurement stand, comprising three independent measurement paths, namely mass registration, temperature measurement and thermal visualisation, was described in detail. The system maintaining a constant temperature of the heating surface was located on the scales, the recordings of which were taken at constant frequency of 2 Hz. The measurement results come in the form of mass change versus time. On this basis, together with the measured area of the perpendicular drop projection onto the heating surface, it was possible to compute instantaneous values of the heat transfer coefficient. Those values decrease with a change in the area and the drop mass. At the beginning of measurements, at the constant temperature of the heating surface 337.5 °C, the heat transfer coefficient equalled 0.32 kW/m2 K, and it was over twice higher for a drop with the mass of 0.2 g. The thermal (infrared) mapping of the drop upper surface was performed using a thermovision camera (THV). The mapping indicates a complex interaction of heat and mass transfer processes, which result in intensive convection movements in the near-surface zone. That is manifested in the form of a highly diversified thermal field of the drop upper surface. The difference between the maximum and minimum temperatures can be as much as 10 K. For the adopted method of heat transfer coefficient computation, an analysis of uncertainties was also performed. The scales accuracy and the camera resolution were found to have the greatest impact on uncertainty in the heat transfer coefficient measurements. Uncertainty in measurement is inversely proportional to the drop size. As a result, measurements and later analysis of results were limited to the bottom of the range determined by the drop mass of 0.2 g. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Droplet vaporization on solid horizontal plate with high overheating has been a subject matter investigated in many technical papers (e.g. [1–3]). Baumeister, who was one of the first researchers thoroughly analysing the problem, presented a solution based on the energy balance. His results concern the formulas for the surface heat transfer coefficient, droplet evaporation time, surface temperature and volume of specified liquid. Further studies dealt with dependencies between the heat transfer coefficient components [4,5], dimensionless ratio of evaporation time, dependence on the universal curve for total evaporation time of water, benzene and carbon tetrachloride droplets [6] and the Leidenfrost point [7,8]. Parallel studies were carried out for spray evaporation [9– 11]. Due to strong interaction between droplets, this phenomenon cannot directly be transferred to that of a single droplet evaporation, especially for larger ones. ⇑ Corresponding author. E-mail addresses: [email protected] (T. Orzechowski), [email protected] (S. Wcis´lik). 0196-8904/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2013.08.057
A series of experimental tests on the single- and multi-droplet boiling systems were described and the results were discussed in paper [12], where interaction of different materials was observed with an infrared camera. Influence of the solid surface thermal conductivity on evaporation cooling process was investigated for a number of different materials: macor, steel and aluminium. The conclusion was that the boiling onset strongly depends on solid–liquid interfacial temperature, and the process is more efficient for materials of higher conductivity. The analysis of liquid droplets evaporation from the macor surface is also found in [13]. Thermal behaviour of two bodies during the evaporation process was discussed on the basis of the proposed model of solid cooling with liquid droplets, and a good congruence between theoretical analysis and measurements was observed. The system was heated by an external radiant panel. Similar interactions occur inside the engine combustion chambers [14,15]. Paper [16] examined whether it is possible to predict the evaporation processes of micro-sized droplets of infinite conductivity in an increasing temperature environment using the droplet evaporation model. Similar to a steady state evaporation process, experimental evaporation rates were found as almost linearly dependent on gas temperature.
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Nomenclature A cp m hfg t Tw Td Ts u
area of drop projection on hot surface (m2) specific heat (kJ/kg K) mass (g) enthalpy of vaporization (kJ/kg) time (s) heating surface temperature (°C) drop mean temperature (°C) saturation temperature (°C) standard uncertainty
Greek symbols a heat transfer coefficient (kW/m2 K)
An experimental method used to measure heat transfer between a hot surface and a non-wetting droplet was discussed in paper [2]. On the basis of infrared camera surface temperature measurements, a solution to the unsteady thermal conduction equation was obtained, which permits to evaluate the heat flux removal. The heat transferred by a droplet 1.5 mm in diameter typically equals 0.19 J, but during a very short time, heat flux may reach even 3.5 MW/m2 with subsequent temperature reduction by 47 °C. Heat transfer associated with a hot surface quenching by a jet of oil-in-water emulsion was investigated in [17]. Axisymmetric jet impingement on a hot metal disc at the temperature of 500– 600 °C was observed and registered by the THV camera. Based on a semi-analytical inverse heat conduction model, heat fluxes were calculated. It was also shown that the amount of the oil components change the rate of heat transfer significantly, especially in the film boiling regime. Experimental measurements of heat transfer due to droplet of low Weber numbers impact on the surface at the temperature above Leidenfrost were presented in paper [18]. An inverse conduction method was used to estimate the heat transfer coefficient as a function of the incoming droplet characteristics and dynamics. Heat transfer coefficients for a single droplet of small size were given. It was concluded that heat transfer coefficient depends, to a large extent, on the wall temperature, but it does not depend on the Weber number. The collision of single water droplets with a hot surface was investigated in [19]. Different boiling regimes were discussed for droplets diameters from 0.53 to 0.60 mm, impact velocities from 1.7 m/s to 4.1 m/s, and the solid surface temperatures ranging from 170 °C to 500 °C. The turbulent film boiling from a horizontal cylinder was theoretically investigated with respect to temperature-dependent vapour properties. Additionally, the effect of the thermal radiation from the surface on the boiling heat flux was studied. It was demonstrated that nonlinear effect would alter the magnitude of the average heat transfer coefficient from the surface [20]. Authors of study [21] made an attempt to prove that convection is the dominant phenomenon responsible for water droplet evaporation. Their assumptions were based on the hypothesis that only steam, due to its very low density, is much lighter than air, which makes a droplet levitate over the surface; for other liquids under consideration that seems to be the opposite. Rayleigh number, which compares buoyancy forces causing convection to diffusion and viscosity forces, was employed. A high value that was obtained Ra = 10 confirms the dominant influence of convection. At the same time, due to difficulties in the analytical description of a liquid droplet evaporation, and because of using many simplifica-
ac, ar Da
ew ri
convection and radiation components of the heat transfer coefficient (kW/m2 K) uncertainty of the heat transfer coefficient (kW/m2 K) heating surface emissivity standard deviation
Abbreviations AC acquisition system DC digital camera Ra Rayleigh number SD standard deviation THV infrared/thermovision camera
tions, the problem is still open, which indicates it is necessary to conduct further research into the phenomenon. In investigations discussed in paper [22], 1.1 g droplet of water with aqueous solutions of KCl and NaCl was deposited on a horizontal aluminium heating surface. The evaporation time was recorded for various temperatures and plotted as evaporation curves. The results show that the dissolved salt increases the Leidenfrost temperature by 20–40 °C. The solvent evaporation from the bottom of the levitating drop increases the salt concentration near the interface, which alters some liquid properties and causes a faster collapse of the vapour film. Takata et al. [23] found that the critical heat flux of TiO2-coated surface is about two times larger than that of a non-coated one, and that Leidenfrost temperature increases as the contact angle decreases. The superhydrophilic surface can be an ideal heat transfer surface. The effect of dissolving gas (CO2) or solid salts (Na2CO3 and NaHCO3) in water droplets boiling on a hot surface was analyzed in [24]. At surface temperatures from 100 °C to 300 °C, dissolved salts were found to reduce the evaporation rate, which is probably caused by the fact that they lower the vapour pressure of water and prevent the nucleate boiling regime. Dissolved carbon dioxide slightly enhances heat transfer in the nucleate boiling regime. Significant heat transfer enhancement and reducing the droplet lifetime to approximately half that of a pure water drop was observed in the case of sodium carbonate. The largest enhancement of heat transfer is produced by the sodium bicarbonate. As regards semi-transparency in infrared fluids, observations of the thermal motion inside the drop were reported in [25]. This visualization method allowed specifying three stages during the evaporating process: a warm-up phase, evaporation with thermal-convective instabilities, and finally evaporation without thermal patterns. All the instabilities depend on the fluid. Surface roughness is another factor discussed in liquid droplet evaporation studies. Those show that roughness conditions of the surface have a great impact on nucleate boiling regime but no such influence was observed for film boiling regime. The conclusion from [26] is that the Leidenfrost temperature on an extremely smooth surface is the same as that on metal plates of standard roughness. The Leidenfrost temperature basically refers to the wettability and thermal properties of the plate, but no relation to the shape, size and distribution of surface roughness can be noted. Additionally, in study [27], it is stated that a decrease in surface roughness extends the droplet evaporation time, which according to the authors, is caused by the droplet faster departure from the surface. Despite of the fact that the problem has been thoroughly analysed, the mechanisms of evaporation are still not fully clear. The
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object of the present study is the levitation of a single drop of water. It floats on a thin layer of vapour, which prevents a direct contact with the hot surface. The aim of the present study is to characterise heat transfer due to droplet evaporation as a function of its size and the heating wall temperature. The weight measurement method makes it possible to directly determine droplet mass under unsteady evaporation conditions. The methodology used in the study allows calculating the instantaneous heat transfer coefficient. 2. Test facility The measuring system is shown in Figs. 1 and 2. It consisted of the following elements: a copper cylinder with heating surface, a wrapped heater, a thermocouple, an electronic scale, a mirror, the acquisition system (AC), a computer, a digital camera (DC), and an infrared camera. The main part of the test stand was a massive copper cylinder with bowl-shaped upper surface having a very large radius of curvature. Such a setup facilitated drop positioning in the cylinder geometrical centre. Additionally, to assure the thermal uniformity of the cylinder, it was coated in heat-resistant (up to 600 °C) black paint with the emissivity of ew 0.85. This coefficient was checked after each application of the paint in order to eliminate possible errors related to painting accuracy. Wrapped heater provided electrical power of 300 W by means of an autotransformer. The heater adjustable output power made it possible to obtain desirable, constant temperature conditions on the surface throughout the experiment. Every time the autotransformer was set, and after any change in parameters, the experimental setup was conditioned for approx. one hour to obtain the best possible stability and uniformity of the system. Additionally, a K-type thermocouple was mounted underneath the heating surface and connected to the data acquisition system, which sent a signal to the computer disc. Due to high copper thermal conductivity, the thermocouple readings were assumed to be the same for the entire surface. Additionally, the uniformity of surface temperature was tested with an infrared camera. Under such measurement conditions, a large drop of water was placed on the heated surface at 20 °C. The initial mass of the drop was slightly more than 1 g, and its diameter was 1 cm (for heating surface temperature Tw = 337.5 °C). The shape, size and the temperature of the investigated drops were observed with both digital and infrared cameras. The cameras recorded images reflected from a specially prepared mirror of known, high reflectivity. The optical system of cameras and mirror was set in such a way so
Fig. 2. The experimental set-up (markings of the elements as shown in Fig. 1).
that an accurate shape of drop projection on the surface could be maintained. In an additional calibration measurement, a K-type thermocouple was located in the geometric centre of the drop to check the results obtained with the THV camera (see Fig. 2). In this way, correct emissivity that needed to be preset in the camera was found. The entire heating system was located on the electronic scales having 0.001 g sensitivity and 0.01 g accuracy. The scales were equipped with RS232 port to transmit results to the computer. A computer program was developed to collect data on the drop weight. The minimum registration frequency was determined by the internal inertia of the scales and by the software processing of analogue signals to the digital ones. The maximum frequency of recording and processing was 10 Hz. The test device consisted of three independent measuring units, namely camera, scales and temperature measurement unit. The first unit mapped the sequential behaviour of drops located on the non-isothermal surface, the second registered a drop weight
Fig. 1. Schematic of the test apparatus: 1 – droplet of water, 2 – copper cylinder, 3 – wrapped heater, 4 – thermocouple, 5 – electronic scale, 6 – infrared camera, 7 – digital camera, 8 – mirror, 9 – tripod, 10 – AC signal processing system, 11 – autotransformer, 12 – computer, and 13 – voltmeter.
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loss over time, and the third controlled the drop surface temperature. An infrared camera recorded temperature of the visible, external surface of the drop, and additionally the temperature of the heating surface. The drop area could be evaluated from the upper surface temperature distribution (thermogram). That required calculating the number of pixels with the individual size calibration of a single element.
3. Experimental investigation The main outcome of the experiment was determining drop mass change as a function of time. Measurement recording started at the weight of a single drop of 1 g evaporating at ambient pressure (which corresponded to zero time in measurement results presented in Fig. 3). The weight registration frequency was set to 2 Hz. One of the problems that needed to be solved was the impact of the weight of the elastic cables on the measured weight. The problem was solved successfully by carefully prepared cable suspension (see Fig. 1). After balancing and conditioning for a few hours, the wires got arranged properly and did no longer affect the scales readings, so it was possible to take a single series of measurements. The behaviour of a drop was studied in several series of measurements at different values of the heating power. The total drop evaporation time was a few minutes for the assumed surface temperature of 337.5 °C and the initial mass of 1 g. Usually, more than 30 measurements for each of the analyzed surface temperatures were taken. Such number of measurements was necessary to prevent errors, check repeatability, and to make a statistical evaluation. Exemplary results are presented in Fig. 3 showing 33 curves at constant surface temperature. It should be noted that such accuracy of the Tw temperature was obtained due to the high heat capacity of the heating cylinder and continuous electrical power supply for the entire duration of the experiment. Drop mass (1 g) was less than 0.5% of the total copper cylinder mass 360 g. Consequently, the heat dissipated from the cylinder surface did not significantly change its temperature. The calculated standard deviation from the reference value Tw during the first 200 s of evaporation was about SD = 2.56 °C. From 33 curves, after statistical analysis and assessing the quality of measurements, an average curve was determined (bold, dashed line in Fig. 3) With respect to this average value, the instantaneous standard deviation was computed as a function of drop mass loss, which is shown in Fig. 4. Drop evaporation leads to a gradual increase in the mass standard deviation. In Fig. 4, a progressive growth is seen until stan-
Fig. 4. Standard deviation from drop mass (at first 200 s of evaporation) for exemplary surface temperature, Tw = 337.5 °C.
dard deviation reaches 0.02 g. That corresponds to approximately half of the initial mass of the drop, after which standard deviation has pretty much a constant value. The surface temperature (Tw) was measured with a K-type thermocouple. The drop temperature (Tk) was calculated from thermograms taken with a THV camera. It was the temperature averaged over 80% of the drop projection area (see Fig. 5a). For the exemplary heating surface temperature (Tw = 337.5 °C), the average drop temperature was Td = 90.58 °C, so it was almost 10 °C lower than the water saturation temperature at ambient pressure. The value was estimated for the first 200 s of the measurement (0–200 s). It should be noted that the drop surface temperature was highly variable. The maximum value in this case was 95.42 °C, while the minimum was 84.77 °C. The temperature of the drop upper surface changed over time. At the heating surface temperature Tw = 337.5 °C, its maximum standard deviation computed from the mean drop temperature was 2.57 °C and it was later used to assess the measurement uncertainty (90.58 °C ± 2.57 °C). The result obtained indicates very strong convective processes inside the drops, which can be seen in exemplary thermograms presented in Fig. 5 and in Table 1 corresponding to Fig. 5. In Table 1, corresponding to thermograms in Fig. 5, basic statistical descriptors, such as standard deviation, mean, minimum and maximum temperatures from the visible drop area, are provided. These values were estimated on the basis of 75% of that area (as indicated in the first thermogram), so the drop diameter is reduced by about 10%. In this way the directional reflectance and emissivity were eliminated. Additionally, the image reconstruction techniques for visualization of the flow inside the strongly curved surface, i.e. evaporating drops, have been found in the literature [28]. It is suggested that convection inside evaporating liquid drops is distributed symmetrically, and therefore the problem must be considered as an axially symmetric one, but presented investigations clearly contradict this theory. Drop, during the evaporation, produces a local cooling of the surface, which affects its behaviour and changes the nature of the process. 4. Methodology The following energy balance can be written for a drop located on the heating surface:
Fig. 3. The drop mass versus time for exemplary surface temperature, Tw = 337.5 °C.
ðar þ ac ÞðT w T d ÞA ¼ hfg
dm dm cp ðT s T d Þ dt dt
ð1Þ
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Fig. 5. Exemplary thermograms of the drop upper surface.
Table 1 Descriptive statistics from drop upper surface related to Fig. 5. Item
t (s)
Mean (°C)
Min (°C)
Max (°C)
SD (°C)
a b c d e f g h i
0 7 17 21.5 25 44 60 71.5 80
91.80 91.81 89.28 90.95 91.47 88.55 90.07 89.99 89.52
89.81 88.96 87.24 88.65 89.36 86.11 87.12 86.16 87.22
95.31 95.76 95.49 97.10 96.20 98.78 95.63 97.23 96.96
0.99 1.38 1.41 1.35 1.14 1.62 1.50 1.72 1.38
In the energy balance (1), it is assumed that heat transfer on the upper drop surface is negligibly small [29]. Mass transfer from the drop upper surface occurs due to diffusion. It is a small-scale process compared with the production of mass at the drop bottom. The left hand-side of the equation above represents heat transfer from the drop bottom surface by convection and radiation, while the right hand-side is a sum of the heat required to heat up the drop from the current to the saturation temperature, and the heat needed to vaporize the mass flux. The instantaneous heat transfer coefficient from the heating surface a = ar + ac (as a sum of radiation and convection heat transfer coefficients) can be calculated after determining all the necessary components in Eq. (1). The parameters hfg and cp are taken from the thermodynamic properties tables. A large number of points registered allow applying their numerical differentiation with smoothing with the use of procedures available in commercial software. Fig. 6 shows the measurement results (see Fig. 3) after differentiation and smoothing, which in this case is a polynomial approximation of the fourth order.
Fig. 6. Polynomial approximation of the average drop mass as a function of time.
The unknown heat transfer coefficient (i.e. the sum of convective ac and radiant ar) can be calculated from Eq. (1). The needed drop area A(t) was estimated from the film registered by the thermovision camera (Fig. 5) according to [30]. Final calculation results are shown in Fig. 7.
5. Measurement uncertainties It seems to be essential to estimate the measurement uncertainties resulting from the accuracy of laboratory instruments. To determine the maximum combined standard uncertainty (Da) of the heat transfer coefficient, on the basis of other quantities related
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Fig. 7. The overall heat transfer coefficient for exemplary heating surface temperature, Tw = 337.5 °C.
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Fig. 9. Experimental results and numerical calculations of the drop mass change versus time.
6. Conclusions
Fig. 8. Heat transfer coefficient as a function of drop mass and its absolute combined standard uncertainty for exemplary heating surface temperature, Tw = 337.5 °C.
to the energy balance (Eq. (1)), the following dependence (Eq. (2)) is proposed:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi !2 u 2 2 2 @ a 2 u @a @ a @ a 2 2 t Da ¼ u2A þ dm udm þ ðuT w Þ þ ðuT d Þ dt @A @T w @T d @ dt ð2Þ Eq. (2) is written in accordance with Type A evaluation of standard uncertainty [31]. The result of estimation is shown in Fig. 8. The average values of the combined standard uncertainty fractions are: uA = 10.7%, udm/dt = 89.0%, uTw = 0.2% and uTd = 0.1%. The differential Eq. (1) was solved numerically using measured heat transfer coefficients and the area of the drop projection. That resulted in obtaining drop mass change versus time. Fig. 9 presents the computational results for the case discussed. A thin dashed line in this figure represents selected extreme measurement series for recorded drop mass loss versus time, whereas a dotted line denotes the average from all measurement series. As can be seen in Fig. 9, a very good congruence between measurement data and numerical computations was obtained. In Fig. 9 both dashed lines indicate experimental limits.
It is extremely difficult to provide a theoretical description for the evaporation of a liquid drop floating over a hot surface, the temperature of which is higher than Leidenfrost point. The complex character of interrelated processes of heat and mass transfer results from vapour outflow, unstable in time, from under the drop bottom surface. That leads to intensive convection movements in the sub-surface zone. The phenomenon is reflected in the diversified thermal zone of the droplet upper surface, an example of which is illustrated in Fig. 5a. It can be seen that at the drop average temperature of 89 °C, the difference between the maximum and minimum temperature values can amount to as much as 10 °C. Similar values were also obtained in the initial calibration tests, in which temperature was measured with a thermocouple located inside the drop (see Fig. 2). Water drop evaporation was described using the heat balance (1). The equation serves as the basis to determine instantaneous values of the heat transfer coefficient. To do that, the system for stabilising the heating surface temperature was placed on the scales, the readings of which were recorded at the frequency of 2 Hz. The measurement results come in the form of mass change versus time. The drops that were investigated had the initial mass of 1 g. The measurement range, and consequently later analysis, were limited by the bottom value determined by drop mass of 0.2 g. It can be explained by the fast growth in the measurement uncertainties accompanying the decrease in drop mass and size. According to the uncertainty analysis performed in the study, the uncertainty was approx 4.8% at the beginning of the measurements, and it increased to approx 11% for drops that had a mass five times smaller. It should be added that measurement uncertainty was affected to the greatest extent by the scales accuracy and the camera resolution. On the basis of recorded drop mass versus time, and also of the computed drop contact area with the heating surface, instantaneous values of the heat transfer coefficient were calculated. Those increased with mass loss and the contact area reduction. The change can be seen in Fig. 8. At the heating surface temperature of 337.5 °C, the coefficient equals 0.32 kW/m2 K for a drop mass of 1 g, and it increases by 100% for drop mass of 0.2 g. The results obtained in the study demonstrate that under film boiling conditions the amount of heat removed by a liquid drop from the surface heated above Leidenfrosta point, varies with the drop mass and the contact area. The methodology for computing instantaneous values of the heat transfer coefficient proposed in the study provides a tool that is precise enough to accurately represent the drop evaporation process (see Fig. 9).
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