- Email: [email protected]
Cooling of porous metal surfaces by droplet impact
International Journal of Heat and Mass Transfer 152 (2020) 119494
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt
Cooling of porous metal surfaces by droplet impact N. Lipson∗, S. Chandra Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, Canada
a r t i c l e
i n f o
Article history: Received 8 August 2019 Revised 15 January 2020 Accepted 10 February 2020
Keywords: Droplet impact Porous surfaces Leidenfrost evaporation Spray cooling
a b s t r a c t An experimental study was conducted on the impact of droplets of pure water and n-heptane on impervious and porous (5 μm and 100 μm pore size) stainless steel surfaces. Surface porosity, roughness and thermal conductivity were measured. Droplet diameter (2.5 mm) and impact velocity (0.9 m/s) were kept constant while surface temperature was varied from room temperature to 300 °C. Droplet impact was observed using a high-speed video camera. Droplet evaporation times were measured by recording the change in weight of the surface on which the droplet was deposited and surface temperature variation during droplet impact measured using a fast response surface thermocouple. Droplets spread out on porous surfaces during impact to form a thin film that was then drawn into pores by capillary forces. The rate of droplet spread decreased with greater surface roughness. The Leidenfrost temperature of n-heptane droplets increased with surface porosity while water droplets did not go into film boiling on the porous surfaces. A one-dimensional heat conduction model was used to estimate heat transfer coefficients between the impacting droplets and substrates. Heat transfer coefficients increased with surface temperature until sufficient vapor was generated at the liquid-solid interface to inhibit contact. Heat transfer coefficients then decreased with further increases in temperature. © 2020 Published by Elsevier Ltd.
1. Introduction Liquid droplet impact on hot surfaces has been studied for years since it plays an important role in many industrial applications. As examples, droplet impact occurs in fire suppression by sprinkler systems; spray cooling of hot surfaces; and in spray combustion systems where the evaporation rate of fuel droplets on heated surfaces is of critical importance. A large number of experimental studies have been carried out on the subject of droplet impact on hot, impermeable surfaces (e.g., [1–6]) in which the researchers varied the liquids tested, impact conditions, substrate properties, and environmental conditions. Liang and Mudawar [7] have given an extensive review of this literature. By comparison, far fewer experimental studies have carried out on the impact of droplets on heated porous surfaces, even though porous surfaces are used in many applications. Avedisian and Koplik [8] studied evaporation of methanol droplets on several different alumina surfaces with increasing porosity and found that the Leidenfrost temperature, above which droplets are levitated on a cushion of their own vapor, increased with porosity. Chandra and Avedisian [9] photographed n-heptane droplets impacting on a heated, ceramic porous surface and found
∗
Corresponding author. E-mail address: [email protected] (N. Lipson).
https://doi.org/10.1016/j.ijheatmasstransfer.2020.119494 0017-9310/© 2020 Published by Elsevier Ltd.
that the droplet spreading rate was lower than that on an impervious metal surface and there was no transition to film boiling on the porous surface. Abu-Zaid and Atreya [10] studied the transient cooling of low-thermal-conductivity porous and nonporous ceramic solids by individual water droplets using thermocouples embedded in the surfaces. The evaporation time of droplets on the nonporous solid was found to be larger than that of the porous solid. Abu-Zaid [11,12] extended the study to gasoline and diesel droplets impinging on impermeable and porous plates. Yu et al. [13] experimentally observed water droplets impacting on a substrate with a porosity of 34% and pore size of 76 nm that was maintained at a temperature of 300 °C where droplets were in the film boiling regime. Little difference was observed in the impact dynamics on a porous surface or non-porous surface, which was attributed to the pore size being very small. Singh et al. [14] observed the evaporation of sessile droplets placed on heated, nano-porous alumina surfaces and found that pore size and morphology significantly affects evaporation. Kim and Lee [15] studied water droplet impact on porous surfaces made by sintering glass beads while varying the surface temperature, droplet impact velocity and surface porosity. An infra-red camera was used to record surface temperature variation during droplet evaporation. When a liquid droplet contacts a heated wall, vapor is generated at the liquid solid interface. If the rate of vapor generation
2
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
is sufficiently large the pressure created as it tries to escape may be sufficient to levitate the droplet, leading to a transition to film boiling. However, if the substrate is porous vapor can penetrate into it, relieving the pressure and delaying or entirely preventing the onset of film boiling. The Leidenfrost temperature is therefore a function of substrate porosity. It also depends on liquid properties: water has much higher latent heat than most hydrocarbons so that it requires more energy to produce a given mass of vapor. The high liquid-solid contact angle of water, compared to that of hydrocarbons, means that when it impacts a solid surface it traps air pockets in surface cavities that act as bubble nucleation sites and promote boiling. The transition to film boiling of water droplets is therefore different from that of liquid hydrocarbons. The study of droplets evaporating on a porous surface is made difficult by several factors. The evaporation time of a droplet resting on a porous surface is difficult to determine accurately from photographs since liquid that has penetrated into pores is not visible. Changing the porosity of a surface can also affect other properties such as its density, thermal conductivity and surface roughness; isolating the influence of any one parameter can be difficult. One method to quantify the heat transfer from impacting drops on impervious surfaces has been to measure the substrate temperature change during impact. Pasandideh-Fard et al. [6] measured substrate temperature variations at the point of impact using a commercially available fast response eroding thermocouple and developed an analytical model to determine the cooling effectiveness of a droplet impact on an impermeable heated surface. Wang et al. [16] installed thermocouples 2.5 mm below the top surface to measure substrate temperature variation during droplet impact. However, the response time of such a sub-surface thermocouple will be much longer than the time for droplet impact. Kim and Lee [15] attempted to observe surface temperature variations at the point of impact using an infra-red camera, but these measurements were valid only once the droplet had completely permeated into surface pores and the surface was directly visible to the camera. We undertook an experimental study to determine the rate of heat transfer from impacting droplets to porous metal surfaces. Two porous surfaces were used, made from sintered stainless-steel powders, one with small (5 μm) and the other with large (100 μm) average diameter pores. For comparison an impervious stainlesssteel surface was also used in tests. The porosity, surface roughness and thermal conductivity of each of the surfaces were measured. Experiments were carried out with droplets of pure water and n-heptane (C7 H16 ), which has low surface tension and penetrates much more rapidly into surface pores than water. Droplet diameter (2.5 mm) and impact velocity (0.9 m/s) were kept constant while surface temperature was varied from room temperature to 300 °C. The objective was to investigate how changing porosity affected droplet impact dynamics, droplet evaporation, and surface cooling. 2. Experimental method
the pores were completely filled with liquid and then immediately transferring the liquid-saturated sample to a tray placed on a balance and weighing the mass of liquid. The volume of liquid was divided by the external volume of the plate to calculate porosity. This process was repeated 50 times for each plate and the average value was determined. A Surfometer (Precision Devices Inc., Milan, Michigan, United States) was used to measure the average roughness (Ra ) values for the porous and impermeable substrates by drawing a stylus across the surface. The tip radius of the stylus was 2.5 μm, the stroke length was set to 10.16 mm, and measurements were repeated 10 times at different locations on each surface to get an average roughness. The average porosity and roughness values are listed in Table 1 along with the standard deviation of each measurement in parentheses. To determine the thermal conductivity, k, of the porous samples used in this study, an experimental technique similar to that outlined in ASTM E1225 was employed [17]. The method involves placing the sample to be tested between two specimens of a material with known thermal properties and applying a temperature gradient across the stack. When the system reaches steady state, the measured temperature gradients on the hot and the cold side, along with the thermal properties of the known specimens can be used to determine the thermal conductivity of the sample. The sample to be tested was sandwiched between the ends of two aluminum 6061 alloy cylinders, each 15.24 cm (6 ) long and 5.08 cm (2 ) in diameter with a thermal conductivity of 167.0 W/mK. A copper heater block supplied with 90 W of power was used to heat one end of the stack while the other end was cooled using a water cooled block whose temperature was maintained at 20 °C by a chiller. Thermally conductive silicone paste (OT-201, Omega Engineering, Laval, Quebec, Canada) was applied at the interface between the aluminum bars and the heater block, and heat sink. Two thermal interface graphite sheets (EYGS0909ZLX2, Panasonic Canada Inc., Mississauga, Ontario, Canada) were used between the substrate and the aluminum bars to reduce thermal contact resistance and enhance heat transfer. The heater block was insulated using silicone rubber while the rest of the stack was insulated using Superwool Plus (Morgan Advanced Materials, Windsor, UK). Each aluminum cylinder had 6 holes drilled along its length, spaced 2.54 cm (1 ) apart, into which were inserted type J thermocouples that were used to measure the axial temperature gradient. The six thermocouples in each aluminum rod were used to confirm that steady state had been reached and that the temperature distribution was linear, from which the applied heat flux was calculated. The heat flux was divided by the temperature drop across the test plate to calculate the thermal conductivity listed in Table 1. Lipson [18] has given a detailed description of the experimental procedure. The thermal diffusivity of a material with porosity ɛ is defined as a = ρ (1k−ε )c where ρ is the density of the bulk metal and c its specific heat. Calculated values of thermal diffusivity for the three plates are listed in Table 1.
2.1. Measurement of substrate properties
2.2. Measuring droplet evaporation time
The three metal substrates used in experiments were square, approximately 45 mm x 45 mm in length and width and 2.0 mm thick. One was an impermeable 316 stainless-steel plate while the other two were commercially available (Mott Corporation, Farmington, Connecticut, United States) porous plates made by sintering 316 stainless-steel powders. Fig. 1 shows SEM images of the surfaces of the two porous plates, one with an average pore size of 5 μm and the other with an average pore size of 100 μm, as specified by the manufacturer. The average porosity (ɛ) of each plate was determined by immersing it in a bath of n-heptane until
Fig. 2 shows the experimental setup employed to observe the impact and evaporation of a pure water and n-heptane droplet on the heated substrate. Using a syringe pump (NE-10 0 0, New Era Pump Systems, Inc., Farmingdale, New York, United States), liquid was forced through a 26 gauge blunt hypodermic needle for pure water and a 16 gauge needle for n-heptane, which produced 2.5 mm diameter droplets for both liquids. The droplets formed on the needle tip, and once large enough would detach under their own weight. Droplet size was determined by individually weighing 50 droplets, which revealed a drop-to-drop variation of less than
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
3
Fig. 1. SEM images of the sintered porous stainless-steel samples (5 μm and 100 μm average pore size) used during experimentation. Table 1 Measured porosity, surface roughness and thermal diffusivity of the test surfaces. The standard deviation of each measurement is given in parentheses. Thermal diffusivity values are calculated. Surface
Porosity ɛ %
Roughness Ra (μm)
Thermal Conductivity k (W/mK)
Thermal Diffusivity α (m2 /s)
Solid 316 stainless steel 5 μm average pore size 100 μm average pore size
0 30.6 (1.9) 44.3 (0.7)
0.1 (0.004) 4.7 (0.1) 12.2 (1.6)
13.1 (1.7) 2.7 (0.3) 1.0 (0.1)
3.3 × 10−6 9.7 × 10−7 4.5 × 10−7
Fig. 2. Schematic of experimental setup: (1) Syringe pump coupled with a 10 ml syringe, (2) Vertical height adjustment, (3) Hypodermic needle, (4) Substrate and Thermal Mass, (5) High-speed camera, (6) Wireless thermocouple connector, (7) Light source, (8) Light diffuser, (9) PC logging scale data, and monitoring substrate temperature, (10) Digital scale, (11) Temperature controller, (12) 120 V Variable auto transformer, (13) PC capturing high-speed camera images.
±2%. The nominal diameter of a spherical droplet of equal weight was calculated and found to be 2.5 mm for both liquids. This was confirmed using high speed video images of 50 droplets in flight and measuring their diameters. The impact velocity was controlled by adjusting the vertical distance from the tip of the needle to the top of the substrate and was fixed at 50 mm ± 1 mm for the experiments. The impact velocity was chosen such that no splash would occur on any of the three substrates investigated when the substrate was at room temperature. Room temperature for this study was recorded as 23 °C ± 3 °C. The impact velocities for the pure water and n-heptane droplets at the time of impact, determined from high speed imaging, were 0.9 m/s and varied by ±5% for water and ±9% for n-heptane.
Substrates were heated by placing them on an aluminum block (45 mm × 45 mm × 20 mm thick) that was heated using a single 100 W cartridge heater. The voltage applied to the heater was adjusted with a 120 V variable auto transformer and the substrate surface temperature was regulated using a temperature controller (CN90 0 0A, Omega Engineering, Laval, Quebec, Canada) and could be controlled to ±0.1 °C. A gauge 24, type K thermocouple was fixed using high temperature cement (CC High Temperature Cement, Omega Engineering, Laval, Quebec, Canada) to of each of the substrates. The surface temperatures were monitored using a wireless thermocouple connector (MWTC-D-K-915, Omega Engineering, Laval, Quebec, Canada) transmitting to a computer. At surface temperatures ranging from 60 °C to 120 °C, droplet evaporation was measured by placing the heater block and test
4
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
Fig. 3. Top down view (top) \ profile view (bottom) schematic of the fast response thermocouple used to measure surface temperature variations directly under the droplet.
surface on a digital scale (AG245, Mettler Toledo, Mississauga, Ontario, Canada) with a weighing capacity of 210 mg and resolution of 0.1 mg and recording the weight decrease as a function of time with a sampling frequency of 3 Hz. When surface temperatures reached 150 °C or higher droplet lifetimes became very short, less than 1 s. The response time of the scale was then not fast enough to measure droplet evaporation and a high-speed camera (Fastcam SA5, Photron, Tokyo, Japan) equipped with a bellows and 105 mm lens was used instead. At these temperatures there was very little penetration of liquid into surface pores. A 55 W light emitting diode was used as the light source. To verify the accuracy of using weight measurements to determine droplet lifetime the average evaporation time for 10 droplets placed on a heated, impervious surface was measured using both the weight method and the high-speed camera, and the results found to differ by less than 7%. 2.3. Surface temperature variation Fig. 3 shows a schematic of the thermocouple design employed to measure the surface temperature variations directly under the droplet. A surface thermocouple was created in which the stainless-steel substrate acted as one of the thermocouple materials, a technique that has previously been described by Heichal et al. [19] who determined that it produces microsecond response times. A 600 μm hole was drilled in the center of each of the substrates and a sheathed 250 μm diameter Constantan wire was inserted through it, using high-temperature ceramic cement to secure it in place and electrically isolate it from the substrate. The gap between the substrate and embedded constantan wire was bridged using a thin layer of silver conductive paste (735,825– 25 G, Sigma-Aldrich Chemicals Company, St. Louis, Missouri, United States) that formed the temperature sensing junction. The droplet impacted with its center over this junction, positioned using micrometer stages. The silver film sat on the surface of the metal substrates and measurements from SEM images showed that it was at most 600 μm in diameter. The maximum diameter of the liquid film created by the spreading droplet varied from 8 to 13 times that of the silver layer, so that its surface area represented 1 to 2% of the liquid-solid contact area. High-speed camera images showed
that the thermocouple made no measurable difference to the absorption/evaporation time of the liquid, suggesting it had negligible effect on the substrate porosity in this study. A 316 stainless-steel wire, 500 μm in diameter, was attached to the substrate by inserting it into a 600 μm hole drilled near the edge of the substrate and pinching it close using a hammer and a punch. The other end of the stainless-steel wire was welded to a Constantan wire and the junction placed in a vacuum flask filled with ice and water that was maintained at 0 °C ± 1 °C. The two Constantan wires, one from the substrate and the other from the cold junction were connected to a signal amplifier (Omni-amp III, Omega Engineering, Laval, Quebec, Canada) that amplified the signal by 100X before sending it to a digital oscilloscope. Droplets fell through a 9.53 mm slotted optical switch (OPB910W55Z, TT Electronics, Woking, UK) whose output was monitored by an Arduino Uno microcontroller that triggered the oscilloscope. Surface thermocouples were calibrated by placing each substrate in an oven whose temperature was raised from room temperature up to 300 °C in 50 °C increments, letting it reach steady state at each step determined when the measured temperature did not change for more than 10 min. The voltage generated by the surface thermocouple and the substrate temperature measured by a type-K thermocouple attached to the substrate near the junction being tested were both recorded. The substrate was then allowed to cool in 50 °C decrements with the voltage and temperature being recorded at each step. This process was repeated twice for each substrate and calibration curves were developed by plotting the surface thermocouple output voltage as a function of temperature. 3. Results and discussion Fig. 4 shows photographs of the first 25 ms after water droplets impact on the impermeable (Fig. 3a), 5 μm (Fig. 3b), and 100 μm (Fig. 3c) pore size substrates that were kept at room temperature (~23 °C). Immediately following impact on all three surfaces, a sudden increase in pressure at the point of impact results in a liquid sheet jetting outwards radially from the point of impact (t = 1 ms). The rate of spreading was lower on the porous surfaces which may have been due to both their increasing roughness and also due to penetration of liquid into the surface. A droplet with diameter Do
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
5
Fig. 4. Water droplet impact on the (a) impermeable, (b) 5 μm and (c) 100 μm surfaces. Surface temperature Tw = 23 °C, Vi = 0.9 m/s ± 5%, do = 2.5 mm ±2%, We = 29, Photograph Angle = 30°.
that lands with velocity Vo on a pore of diameter dp will penetrate if the stagnation pressure in the liquid is greater than the capillary pressure so that,
ρVo2 2
>
4σ dp
(1)
Or, using the definition of the Weber number W e = ρVo2 D0 /σ ,
We
dp >8 D0
(2)
The Weber numbers in our experiments were 29 for water and 65 for n-heptane, so that even for the larger pore size (100 μm) the left-hand side of Eq. (2) was always less than 8 where there would have been very little liquid penetration during impact. The reduced spread was therefore largely due to increased surface roughness [20,21]. The water droplets spread until they reach their maximum extent (t = 5 ms) after which surface tension forces begin to pull them back until they lift off the surface. The height of rise was greater on the porous surfaces (see Fig. 4, t = 10 ms) since the maximum spread was less and thus there was greater kinetic energy in the liquid when the droplets started to recoil. A lone bubble can be seen trapped inside the droplet at the center on the impermeable surface (see Fig. 4a at 1 ms) right up
until the droplet settles after impact at 25 ms. This phenomenon was previously observed by Chandra and Avedisian [4] which they attributed to air entrapment at the solid-liquid interface. The bubble is absent in the droplet on the 5 μm, and 100 μm surfaces during the spreading process because the airs able to escape into the porous structure following droplet impact. Fig. 5 shows sequences of photographs of the first 25 ms after n-heptane droplets impact the impermeable (Fig. 5a), 5 μm pore size (Fig. 5b), and 100 μm pore size (Fig. 5c) substrates at room temperature (23 °C). The impact Weber number (65) was too low to satisfy the criteria of Eq. (2) for liquid to penetrate substrate pores during impact, so the droplets spread radially following impact on all the surfaces (t = 1 ms). The rate of spreading was significantly less on the rougher porous surfaces than on the smooth impermeable surface, as was the maximum diameter reached (t = 10 ms). After this time the liquid began to disappear into the porous substrates, drawn in by capillary forces. On the 100 μm pore substrate no liquid could be seen on the surface at t = 10 ms, whereas only a faint outline could be seen on the 5 μm pore surface at t = 15 ms. The spread rate of an impacting droplet can be quantified by measuring the diameter of the liquid film in contact with the substrate (Ds ) and normalizing it by the initial droplet diameter (Do ) to
6
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
Fig. 5. n-Heptane droplet impact on the (a) impermeable, (b) 5 μm and (c) 100 μm surfaces. Surface temperature Tw = 23 °C, Vi = 0.9 m/s ± 9%, do = 2.5 mm ± 2%, We = 65, Photograph Angle = 30°.
define the “spread factor” β = Ds /Do . Fig. 6 shows the variation of the spread factor for water and n-heptane droplets on the impermeable and porous substrates at room temperature as a function of the dimensionless time (t∗ = tVo /Do ). It is clear from Fig. 6 that as the porosity increases, and thus the surface roughness, the maximum spread diameter and rate of spreading decreases for both the water and n-heptane. The n-heptane drops spread much farther than water drops due to their lower surface tension. The maximum extent of spread decreases with surface porosity for both liquids due to the greater roughness of the porous surfaces, and this effect is much more pronounced for the n-heptane drops. Surface porosity does not have much effect on the time at which maximum spread is reached for water drops as there is little penetration into the surface during spreading due to its higher surface tension. However, the n-heptane drops seep into the porous substrates very rapidly and therefore disappear at progressively shorter times as porosity increases. Heating the substrates changes impact dynamics since vapor is generated on the solid surface where the liquid touches it. Fig. 7 shows water droplets impacting on impermeable and porous surfaces initially heated to 150 °C. Heterogeneous nucleation begins in surface cavities immediately after impact (Fig. 7a, t = 0.2 ms) and bubbles rapidly fill the entire droplet (Fig. 7a, t = 1 ms). Increasing
surface roughness is known to promote nucleate boiling and it is likely that a porous surface which is rougher than an impervious surface (see Table 1) has a larger number of nucleation sites so that bubble formation is enhanced, though it is not possible to conclusively show this from the photographs of Fig. 7. The increased vapor generation at the liquid-solid interface aids droplet recoil and the droplet therefore rises higher on the 5 μm pore surface than it did on the same surface at room temperature (compare Fig. 4b, t = 15 ms with Fig. 7b, t = 15 ms). The effect of surface temperature on droplet impact is less evident on the 100 μm pore surface, as seen by comparing Figs. 4c and 7c, which may be because vapor easily penetrates the larger pores and causes less pressure build-up under the liquid than was the case with the 5 μm pore surface. Fig. 8 shows the impact of n-heptane droplets on the three test surfaces at a temperature of 150 °C, which is well above the liquid boiling temperature of 98.4 °C. Bubble nucleation started as soon as the droplets contacted the surface (Fig. 8a, t = 0.2 ms). A large vapor bubble formed inside the droplet on the 5 μm surface, visible as a white region in Fig. 8b at t = 1 ms, which lifted the liquid off the substrate before escaping after which the liquid film settled back on the surface. Bubble nucleation and escape was violent, repeatedly lifting the droplet (Fig. 8b, t = 5 ms) and finally making it fragment (Fig. 8b, t = 10 ms). These small droplets were in
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
7
some cases thrown off the substrate and in others remained on it. Vapor formation prevented liquid from penetrating into the 5 μm pore surface as it had done when the surface was maintained at room temperature (compare Figs. 5b and 8b). Vigorous boiling was also seen in the droplet on the surface with 100 μm pores, with a large bubble breaking through the liquid film and causing fragmentation. No liquid was visible on the surface by t = 10 ms, though it was not entirely clear if this was because it had evaporated or penetrated into the surface. A large number of small, secondary droplets were ejected from the n-heptane film on all three surfaces, as had previously been observed [22–24] during impact of droplets on hot surfaces, where it was attributed to vapor bubble explosions breaking through the liquid film. 3.1. Droplet evaporation time
Fig. 6. Spread factor as a function of the dimensionless time for both water and n-heptane on the impermeable and two porous substrates at room temperature (23 °C).
The rate of heat transfer from the substrate to a droplet deposited on it is reflected in the droplet evaporation time. As the substrate heats up, a plot of droplet lifetime as a function of the initial surface temperature can be used to identify changes in the dynamics of impact and evaporation. Fig. 9 shows the variation of droplet lifetime with initial surface temperature (Tw,o ) for water droplets deposited on the three surfaces for 60 °C < Tw,o < 300 °C.
Fig. 7. Water droplet impact on the (a) impermeable, (b) 5 μm and (c) 100 μm surfaces. Surface temperature Tw = 150 °C (nucleate boiling regime), Vi = 0.9 m/s ± 5%, do = 2.5 mm ±2%, We = 29.
8
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
Fig. 8. n-Heptane droplet impact on the (a) impermeable, (b) 5 μm and (c) 100 μm surfaces. Surface temperature Tw = 150 °C (nucleate boiling regime), Vi = 0.9 m/s ± 9%, do = 2.5 mm ± 2%, We = 65.
For Tw,o > 150 °C, where the lifetimes were too short to be seen clearly, an insert is used to show the data on a logarithmic scale that allows differences between the three surfaces to be identified. Each data point represents the average of 10 measurements and error bars represent the standard deviation. As the surface temperature was raised droplet lifetime decreased on all three surfaces. Droplets placed on the substrate with 5 μm pores had a significantly lower evaporation time than those on the other two surfaces for Tw,o < 110 °C. Droplet lifetime depends on many parameters including: the extent of droplet spread; penetration of liquid into the substrate; rate of bubble nucleation; the rate at which vapor escapes; and substrate thermal diffusivity. Surface porosity can enhance heat transfer since it increases the area of contact between the liquid and substrate, promotes bubble nucleation and allows vapor generated during boiling to escape rapidly. However, too large a porosity can also reduce thermal diffusivity significantly (see Table 1) and prevent heat conduction from the surrounding substrate into the region cooled by the evaporating droplet. Once the surface temperature increased above 200 °C the droplet on the impervious surface began to go into film boiling and the droplet lifetime increased with surface temperature. The Leidenfrost temperature, corresponding to the maximum
droplet lifetime, was 235 °C. Above that temperature droplets were in stable film boiling and evaporation time decreased with surface temperature. Droplets on the porous surfaces were not levitated because vapor below them could escape into the substrate and there was not enough pressure to lift the liquid. Fig. 10 shows the evaporation times of n-heptane droplets on the heated substrates, which were significantly lower than those for water drops due to their much lower latent heat of vaporization (2257 kJ/kg for water, 318 kJ/kg for n-heptane). At temperatures below 90 °C the evaporation time was longer on the porous substrates than on the impermeable surface. n-Heptane rapidly infiltrates surface pores and then takes longer to evaporate from them than it does when it is on the surface of the heated plate. At surface temperatures above 100 °C the evaporation time is similar on all three substrates. Once Tw,o is greater than the boiling point of n-heptane (98.4 °C) rapid vapor generation prevents the liquid from penetrating into pores and droplets evaporate while resting on top of the substrate (see Fig. 8c). Surface porosity then has less effect on evaporation time. Increasing substrate temperature further led to a transition to film boiling. The larger the pore size, the higher the temperature required to produce sufficient vapor to levitate the droplet. The Leidenfrost point was
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
Fig. 9. Evaporation time as a function of the surface temperature for the (a) impermeable, (b) 5 μm pore and (c) 100 μm pore size substrates using pure water as the working fluid. A graph insert is shown at surface temperatures ranging from 150 °C to 300 °C using a log time scale to show evaporation time differences between the surfaces.
9
Fig. 11. Surface temperature as a function of time for the water droplet on the impermeable, 5 μm and 100 μm surfaces at the point of impact at an initial surface temperature of 160 °C. Temperatures are shown up until the droplet reached its maximum spread factor on the impermeable surface.
Fig. 10. Evaporation time as a function of the surface temperature for the (a) impermeable, (b) 5 μm and (c) 100 μm surfaces using n-heptane as the working fluid. A graph insert is shown at surface temperatures ranging from 150 °C to 300 °C using a log time scale to show evaporation time differences between the surfaces.
190 °C on the impermeable surface, 225 °C on the 5 μm pore surface, and 285 °C on the 100 μm pore surface. 3.2. Surface temperature variation
Fig. 12. Comparison between surfaces (a) impermeable, (b) 5 μm and (c) 100 μm with the drop in surface temperature after 4 ms, the maximum time taken for the water droplet (at 23 °C) to spread on surface (a), as a function of the initial surface temperature. The temperature was measured at the point of impact. Standard deviations in ࢞Tw are shown.
The cooling effectiveness of an impacting drop can be measured by recording the surface temperature variation at the point of impact. Fig. 11 shows the temperature recorded by the surface thermocouples under water droplets impacting on the three surfaces maintained at an initial temperature of 160 °C. The temperature variation is shown for the first 4.0 ms following impact, which is the time required for the droplet to spread to its maximum extent on the impermeable surface (see Fig. 4a). After this time droplets recoiled, with some bouncing off the surface, so temperature measurements at a single point were much less repeatable after 4.0 ms. The temperature of the impermeable surface showed the fastest initial decrease and that of the 100 μm pore surface the slowest, reflecting the difference in thermal diffusivities of the three surfaces. However, the 5 μm pore surface showed the largest overall temperature drop after 4 ms. Fig. 12 shows the decrease in substrate temperature (࢞Tw ) under impacting water drops, measured 4.0 ms after impact, as a function of initial substrate temperature from 60 °C to 290 °C for the three test surfaces. Each data point is the average of 5 measurements and the error bars represent the standard deviation. The
5 μm pore surface had the largest temperature drop while that on the impermeable surface was slightly lower. The 100 μm pore surface, which had the lowest thermal conductivity, showed a much lower temperature change than the other surfaces. Droplets went into film boiling when the temperature of the impervious surface was raised above 235 °C, but this change is not evident from the measured temperature change, suggesting that there was liquidsolid contact during the initial stages of impact. Fig. 13 shows the substrate temperature decrease during impact of n-heptane droplets, measured 13.4 ms after impact, which was the time required for maximum droplet spread on the impermeable surface (see Fig. 5a). ࢞Tw increased with initial surface temperature for 60 °C≤Tw ≤160 °C, but this trend reversed for Tw ≥200 °C when droplets placed on the impermeable surface went into film boiling (see Fig. 10). Even though droplets placed on the porous surface did not go into film boiling until higher surface temperatures were reached, because of the lower latent heat of vaporization of n-heptane compared to water, there was enough vapor produced to reduce liquid-solid contact and therefore diminish
10
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
Fig. 13. Comparison between surfaces (a) impermeable, (b) 5 μm and (c) 100 μm with the drop in surface temperature after 13.4 ms, the maximum time taken for the n-heptane droplet (at 23 °C) to spread on surface (a), as a function of the initial surface temperature. The temperature was measured at the point of impact. Standard deviations in ࢞Tw are shown.
Fig. 14. Heat transfer coefficient for the water during droplet spreading on the impermeable, 5 μm and 100 μm surfaces as a function of the initial surface temperature. Heat transfer coefficients are shown on a log scale.
heat transfer. The impermeable surface had the lowest temperature drop, showing that the effect of vapor generation offset the higher thermal diffusivity of the substrate, unlike the case for water. 3.3. Heat transfer coefficient When a droplet impacts on a heated surface the thermal distur√ bance propagates over a thermal diffusion length L ∼ αt , where t is the time from impact. During the time for droplet spreading (~10 ms), L~0.1 mm, which is much smaller than the droplet diameter. We can therefore approximate heat transfer in the substrate by one-dimensional heat conduction and the variation in surface temperature Tw (x,t) can be described using equation:
∂ Tw ∂ 2 Tw =α ∂t ∂ x2
(3)
where x is distance in the substrate, measured from the surface. Assuming that the substrate can be regarded as a semi-infinite solid for the short times considered, the following boundary conditions can be applied:
Tw (∞, t ) = Tw,0
(4)
where Tw, 0 is the initial substrate temperature. Assuming that the droplet temperature Td remains constant and that h is the convective heat transfer coefficient between the liquid and solid at the interface x = 0
−k
Fig. 15. Heat transfer coefficient for the n-heptane during droplet spreading on the impermeable, 5 μm and 100 μm surfaces as a function of the initial surface temperature. Heat transfer coefficients are shown on a log scale.
∂ Tw = h[Td − Tw (0, t )] ∂ x x=0
(5)
The initial condition is that
Tw (x, 0 ) = Tw,0
(6)
Eq. (3) can be solved along with the boundary and initial conditions using a Laplace transform method to find the surface temperature variation [25]:
Tw (0, t ) = Tw,0 + (Td − Tw,0 ) 1 − erfc
h√ at k
· exp
h2 at k2
(7) The heat transfer coefficient was determined by performing a least-squares fit to match Eq. (7) to the measured surface temperature variations, such as those in Fig. 11. The first 4.0 ms after
impact were considered for water droplets and the first 13.4 ms for n-heptane droplets, which was approximately the time for the droplets to reach their maximum spread factor. Fig. 14 shows the calculated heat transfer coefficients for water droplets as a function of initial surface temperature. The value of h reflects the magnitude of heat transfer between the impacting droplet and the substrate at the point of impact and removes the effect of the thermal diffusivity of the surrounding surface, which is considered separately in Eq. (7). The higher the surface porosity, the lower the heat transfer, since pores reduce the actual surface area in contact with the liquid. The higher roughness of the porous substrates also leads to entrapment of air and vapor in surface cavities that may reduce heat transfer. The heat transfer coefficient of the two porous surfaces increases with surface temperature since there is no transition to film boiling and higher temperatures promote nucleate boiling. Water droplets on the impermeable surface went into film boiling at the Leidenfrost temperature of 235 °C, above which the heat transfer coefficient decreases with increasing temperature. Fig. 15 shows the variation of heat transfer coefficients with surface temperature for n-heptane droplets impacting on the three test surfaces. At lower temperatures, Tw ≤ 120 °C, h increased
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
with surface temperature. Above that, as droplets began to boil and vapor was generated at the liquid-solid interface, heat transfer coefficients began to decrease. For temperatures greater than Tw = 200 °C, which is above the Leidenfrost temperature on a solid surface, heat transfer coefficient values were low and decreased gradually with increasing temperature. 4. Conclusions The impact of water and n-heptane droplets on stainless steel substrates of varying porosity was studied. Increasing substrate porosity resulted in lower thermal diffusivity and higher surface roughness. The droplets did not have a high enough velocity to penetrate surface pores during impact but spread out on the surface to form a thin film that was drawn into the porous surfaces by capillary forces. The rate of droplet spread decreased with increasing porosity because surface roughness also increased. Water droplets went into film boiling on the impervious surface when it was heated above 235 °C, but not on the porous surfaces. The Leidenfrost temperature of n-heptane droplets increased with surface porosity. Surface temperature variation during droplet impact was measured and a one-dimensional heat conduction model used to estimate heat transfer coefficients between the droplet and substrate. The heat transfer coefficients increased with surface temperature until sufficient vapor was generated at the liquid-solid interface to inhibit contact. Heat transfer coefficients then decreased with further increases in temperature. Declaration of Competing Interest We wish to draw the attention of the Editor to the following facts which may be considered as potential conflicts of interest and to significant financial contributions to this work. Funding for the project was provided by the Natural Sciences and Engineering Research Council of Canada. CRediT authorship contribution statement N. Lipson: Conceptualization, Writing - review & editing. S. Chandra: Conceptualization, Data curation, Investigation, Validation, Writing - original draft. References [1] B.S. Gottfried, C.J. Lee, K.J. Bell, The Leidenfrost phenomenon: film boiling of liquid droplets on a flat plate, Int. J. Heat Mass Transf. 9 (1966) 1167–1187.
11
[2] L.H.J. Wachters, N.A.J. Westerling, The heat transfer from a hot wall to impinging water drops in the spheroidal state, Chem. Eng. Sci. 21 (1966) 1047–1056. [3] G.S. Emmerson, The effect of pressure and surface material on the Leidenfrost point of discrete drops of water, Int. J. Heat Mass Transf. 18 (1975) 381–386. [4] S. Chandra, C.T. Avedisian, On the collision of a droplet with a solid surface, Proc. R. Soc. A 432 (1991) 13–41. [5] S. Chandra, M. di Marzo, Y.M. Qiao, P. Tartarini, Effect of liquid-solid contact angle on droplet evaporation, Fire Saf. J. 27 (1996) 141–158. [6] M. Pasandideh-Fard, S.D. Aziz, S. Chandra, J. Mostaghimi, Cooling effectiveness of a water drop impinging on a hot surface, Int. J. Heat Fluid Flow 22 (2001) 201–210. [7] G. Liang, I. Mudawar, Review of drop impact on heated walls, Int. J. Heat Mass Transf. 106 (2017) 103–126. [8] C.T. Avedisian, J. Koplik, Leidenfrost boiling of methanol droplets on hot porous/ceramic surfaces, Int. J. Heat Mass Transf. 30 (2) (1987) 379–393. [9] S. Chandra, C.T. Avedisian, Observations of droplet impingement on a ceramic porous surface, Int. J. Heat Mass Transf. 35 (10) (1992) 2377–2388. [10] M. Abu-Zaid, A. Atreya, Transient cooling of hot porous and nonporous ceramic solids by droplet evaporation, ASME. J. Heat Transf. 116 (1994) 694–701. [11] M. Abu-Zaid, An experimental study of the evaporation of gasoline and diesel droplets on hot surfaces, Int. Commun. Heat Mass Transf. 21 (2) (1994) 315–322. [12] M. Abu-Zaid, Droplet evaporation on porous and non-porous ceramic solids heated from top, Heat Mass Transf. 38 (3) (2002) 203–211. [13] Z. Yu, F. Wang, L.-S. Fan, Experimental and numerical studies of water droplet impact on a porous surface in the film-boiling regime, Ind. Eng. Chem. Res. 47 (23) (2008) 9174–9182. [14] S.K. Singh, S. Khanderkar, D. Pratap, S.A. Ramakrishna, Wetting dynamics and evaporation of sessile droplets on nano- porous alumina surfaces, Colloids Surf. A 432 (2013) 71–81. [15] W.S. Kim, S.Y. Lee, Behavior of a water drop impinging on heated porous surfaces, Exp. Therm. Fluid Sci. 55 (2014) 62–70. [16] X.W. Wang, J.Y. Ho, K.C. Leong, An experimental investigation of single droplet impact cooling on hot enhanced surfaces fabricated by selective laser melting, Int. J. Heat Mass Transf. 120 (2018) 652–670. [17] ASTM Standard E1225-04, Standard Test Method For Thermal Conductivity of Solids by Means of the Guarded- Comparative-Longitudinal Heat Flow Technique, ASTM International, West Conshohocken, PA, 2004. [18] N. Lipson, The Collision of Water and n-Heptane Droplets on Heated Sintered Porous Stainless-Steel Surfaces MASc Thesis, University of Toronto, 2018. [19] Y. Heichal, S. Chandra, E. Bordatchev, A fast-response thin filmed thermocouple to measure rapid surface temperature changes, Exp. Therm. Fluid Sci. 30 (2005) 153–159. [20] J. Liu, W. Franco, G. Aguilar, Effect of surface roughness on single cryogen droplet spreading, J. Fluids Eng. 130 (4) (2008) 1–9. [21] C. Tang, M. Qin, X. Weng, X. Zhang, P. Zhang, J. Li, Z. Huang, Dynamics of droplet impact on solid surface with different roughness, Int. J. Multiph. Flow 96 (2017) 56–69. [22] H. Chaves, A.M. Kubitzek, F. Obermeier, Dynamic processes occurring during the spreading of thin liquid films produced by drop impact on hot walls, Int. J. Heat Fluid Flow 20 (5) (1999) 470–476. [23] G.E. Cossali, M. Marengo, M. Santini, Secondary atomization produced by single drop vertical impacts onto heated surfaces, Exp. Therm. Fluid Sci. 29 (8) (2005) 937–946. [24] G.E. Cossali, M. Marengo, M. Santini, Thermally induced secondary drop atomization by single drop impact onto heated surfaces, Int. J. Heat Fluid Flow 29 (2008) 167–177. [25] F.P. Incropera, D.P. DeWitt, T.L. Bergman, A.S. Lavine, in: Fundamentals of Heat and Mass Transfer, 6 th edition, Wiley, New York, 2006, p. 286.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt
Cooling of porous metal surfaces by droplet impact N. Lipson∗, S. Chandra Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, Canada
a r t i c l e
i n f o
Article history: Received 8 August 2019 Revised 15 January 2020 Accepted 10 February 2020
Keywords: Droplet impact Porous surfaces Leidenfrost evaporation Spray cooling
a b s t r a c t An experimental study was conducted on the impact of droplets of pure water and n-heptane on impervious and porous (5 μm and 100 μm pore size) stainless steel surfaces. Surface porosity, roughness and thermal conductivity were measured. Droplet diameter (2.5 mm) and impact velocity (0.9 m/s) were kept constant while surface temperature was varied from room temperature to 300 °C. Droplet impact was observed using a high-speed video camera. Droplet evaporation times were measured by recording the change in weight of the surface on which the droplet was deposited and surface temperature variation during droplet impact measured using a fast response surface thermocouple. Droplets spread out on porous surfaces during impact to form a thin film that was then drawn into pores by capillary forces. The rate of droplet spread decreased with greater surface roughness. The Leidenfrost temperature of n-heptane droplets increased with surface porosity while water droplets did not go into film boiling on the porous surfaces. A one-dimensional heat conduction model was used to estimate heat transfer coefficients between the impacting droplets and substrates. Heat transfer coefficients increased with surface temperature until sufficient vapor was generated at the liquid-solid interface to inhibit contact. Heat transfer coefficients then decreased with further increases in temperature. © 2020 Published by Elsevier Ltd.
1. Introduction Liquid droplet impact on hot surfaces has been studied for years since it plays an important role in many industrial applications. As examples, droplet impact occurs in fire suppression by sprinkler systems; spray cooling of hot surfaces; and in spray combustion systems where the evaporation rate of fuel droplets on heated surfaces is of critical importance. A large number of experimental studies have been carried out on the subject of droplet impact on hot, impermeable surfaces (e.g., [1–6]) in which the researchers varied the liquids tested, impact conditions, substrate properties, and environmental conditions. Liang and Mudawar [7] have given an extensive review of this literature. By comparison, far fewer experimental studies have carried out on the impact of droplets on heated porous surfaces, even though porous surfaces are used in many applications. Avedisian and Koplik [8] studied evaporation of methanol droplets on several different alumina surfaces with increasing porosity and found that the Leidenfrost temperature, above which droplets are levitated on a cushion of their own vapor, increased with porosity. Chandra and Avedisian [9] photographed n-heptane droplets impacting on a heated, ceramic porous surface and found
∗
Corresponding author. E-mail address: [email protected] (N. Lipson).
https://doi.org/10.1016/j.ijheatmasstransfer.2020.119494 0017-9310/© 2020 Published by Elsevier Ltd.
that the droplet spreading rate was lower than that on an impervious metal surface and there was no transition to film boiling on the porous surface. Abu-Zaid and Atreya [10] studied the transient cooling of low-thermal-conductivity porous and nonporous ceramic solids by individual water droplets using thermocouples embedded in the surfaces. The evaporation time of droplets on the nonporous solid was found to be larger than that of the porous solid. Abu-Zaid [11,12] extended the study to gasoline and diesel droplets impinging on impermeable and porous plates. Yu et al. [13] experimentally observed water droplets impacting on a substrate with a porosity of 34% and pore size of 76 nm that was maintained at a temperature of 300 °C where droplets were in the film boiling regime. Little difference was observed in the impact dynamics on a porous surface or non-porous surface, which was attributed to the pore size being very small. Singh et al. [14] observed the evaporation of sessile droplets placed on heated, nano-porous alumina surfaces and found that pore size and morphology significantly affects evaporation. Kim and Lee [15] studied water droplet impact on porous surfaces made by sintering glass beads while varying the surface temperature, droplet impact velocity and surface porosity. An infra-red camera was used to record surface temperature variation during droplet evaporation. When a liquid droplet contacts a heated wall, vapor is generated at the liquid solid interface. If the rate of vapor generation
2
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
is sufficiently large the pressure created as it tries to escape may be sufficient to levitate the droplet, leading to a transition to film boiling. However, if the substrate is porous vapor can penetrate into it, relieving the pressure and delaying or entirely preventing the onset of film boiling. The Leidenfrost temperature is therefore a function of substrate porosity. It also depends on liquid properties: water has much higher latent heat than most hydrocarbons so that it requires more energy to produce a given mass of vapor. The high liquid-solid contact angle of water, compared to that of hydrocarbons, means that when it impacts a solid surface it traps air pockets in surface cavities that act as bubble nucleation sites and promote boiling. The transition to film boiling of water droplets is therefore different from that of liquid hydrocarbons. The study of droplets evaporating on a porous surface is made difficult by several factors. The evaporation time of a droplet resting on a porous surface is difficult to determine accurately from photographs since liquid that has penetrated into pores is not visible. Changing the porosity of a surface can also affect other properties such as its density, thermal conductivity and surface roughness; isolating the influence of any one parameter can be difficult. One method to quantify the heat transfer from impacting drops on impervious surfaces has been to measure the substrate temperature change during impact. Pasandideh-Fard et al. [6] measured substrate temperature variations at the point of impact using a commercially available fast response eroding thermocouple and developed an analytical model to determine the cooling effectiveness of a droplet impact on an impermeable heated surface. Wang et al. [16] installed thermocouples 2.5 mm below the top surface to measure substrate temperature variation during droplet impact. However, the response time of such a sub-surface thermocouple will be much longer than the time for droplet impact. Kim and Lee [15] attempted to observe surface temperature variations at the point of impact using an infra-red camera, but these measurements were valid only once the droplet had completely permeated into surface pores and the surface was directly visible to the camera. We undertook an experimental study to determine the rate of heat transfer from impacting droplets to porous metal surfaces. Two porous surfaces were used, made from sintered stainless-steel powders, one with small (5 μm) and the other with large (100 μm) average diameter pores. For comparison an impervious stainlesssteel surface was also used in tests. The porosity, surface roughness and thermal conductivity of each of the surfaces were measured. Experiments were carried out with droplets of pure water and n-heptane (C7 H16 ), which has low surface tension and penetrates much more rapidly into surface pores than water. Droplet diameter (2.5 mm) and impact velocity (0.9 m/s) were kept constant while surface temperature was varied from room temperature to 300 °C. The objective was to investigate how changing porosity affected droplet impact dynamics, droplet evaporation, and surface cooling. 2. Experimental method
the pores were completely filled with liquid and then immediately transferring the liquid-saturated sample to a tray placed on a balance and weighing the mass of liquid. The volume of liquid was divided by the external volume of the plate to calculate porosity. This process was repeated 50 times for each plate and the average value was determined. A Surfometer (Precision Devices Inc., Milan, Michigan, United States) was used to measure the average roughness (Ra ) values for the porous and impermeable substrates by drawing a stylus across the surface. The tip radius of the stylus was 2.5 μm, the stroke length was set to 10.16 mm, and measurements were repeated 10 times at different locations on each surface to get an average roughness. The average porosity and roughness values are listed in Table 1 along with the standard deviation of each measurement in parentheses. To determine the thermal conductivity, k, of the porous samples used in this study, an experimental technique similar to that outlined in ASTM E1225 was employed [17]. The method involves placing the sample to be tested between two specimens of a material with known thermal properties and applying a temperature gradient across the stack. When the system reaches steady state, the measured temperature gradients on the hot and the cold side, along with the thermal properties of the known specimens can be used to determine the thermal conductivity of the sample. The sample to be tested was sandwiched between the ends of two aluminum 6061 alloy cylinders, each 15.24 cm (6 ) long and 5.08 cm (2 ) in diameter with a thermal conductivity of 167.0 W/mK. A copper heater block supplied with 90 W of power was used to heat one end of the stack while the other end was cooled using a water cooled block whose temperature was maintained at 20 °C by a chiller. Thermally conductive silicone paste (OT-201, Omega Engineering, Laval, Quebec, Canada) was applied at the interface between the aluminum bars and the heater block, and heat sink. Two thermal interface graphite sheets (EYGS0909ZLX2, Panasonic Canada Inc., Mississauga, Ontario, Canada) were used between the substrate and the aluminum bars to reduce thermal contact resistance and enhance heat transfer. The heater block was insulated using silicone rubber while the rest of the stack was insulated using Superwool Plus (Morgan Advanced Materials, Windsor, UK). Each aluminum cylinder had 6 holes drilled along its length, spaced 2.54 cm (1 ) apart, into which were inserted type J thermocouples that were used to measure the axial temperature gradient. The six thermocouples in each aluminum rod were used to confirm that steady state had been reached and that the temperature distribution was linear, from which the applied heat flux was calculated. The heat flux was divided by the temperature drop across the test plate to calculate the thermal conductivity listed in Table 1. Lipson [18] has given a detailed description of the experimental procedure. The thermal diffusivity of a material with porosity ɛ is defined as a = ρ (1k−ε )c where ρ is the density of the bulk metal and c its specific heat. Calculated values of thermal diffusivity for the three plates are listed in Table 1.
2.1. Measurement of substrate properties
2.2. Measuring droplet evaporation time
The three metal substrates used in experiments were square, approximately 45 mm x 45 mm in length and width and 2.0 mm thick. One was an impermeable 316 stainless-steel plate while the other two were commercially available (Mott Corporation, Farmington, Connecticut, United States) porous plates made by sintering 316 stainless-steel powders. Fig. 1 shows SEM images of the surfaces of the two porous plates, one with an average pore size of 5 μm and the other with an average pore size of 100 μm, as specified by the manufacturer. The average porosity (ɛ) of each plate was determined by immersing it in a bath of n-heptane until
Fig. 2 shows the experimental setup employed to observe the impact and evaporation of a pure water and n-heptane droplet on the heated substrate. Using a syringe pump (NE-10 0 0, New Era Pump Systems, Inc., Farmingdale, New York, United States), liquid was forced through a 26 gauge blunt hypodermic needle for pure water and a 16 gauge needle for n-heptane, which produced 2.5 mm diameter droplets for both liquids. The droplets formed on the needle tip, and once large enough would detach under their own weight. Droplet size was determined by individually weighing 50 droplets, which revealed a drop-to-drop variation of less than
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
3
Fig. 1. SEM images of the sintered porous stainless-steel samples (5 μm and 100 μm average pore size) used during experimentation. Table 1 Measured porosity, surface roughness and thermal diffusivity of the test surfaces. The standard deviation of each measurement is given in parentheses. Thermal diffusivity values are calculated. Surface
Porosity ɛ %
Roughness Ra (μm)
Thermal Conductivity k (W/mK)
Thermal Diffusivity α (m2 /s)
Solid 316 stainless steel 5 μm average pore size 100 μm average pore size
0 30.6 (1.9) 44.3 (0.7)
0.1 (0.004) 4.7 (0.1) 12.2 (1.6)
13.1 (1.7) 2.7 (0.3) 1.0 (0.1)
3.3 × 10−6 9.7 × 10−7 4.5 × 10−7
Fig. 2. Schematic of experimental setup: (1) Syringe pump coupled with a 10 ml syringe, (2) Vertical height adjustment, (3) Hypodermic needle, (4) Substrate and Thermal Mass, (5) High-speed camera, (6) Wireless thermocouple connector, (7) Light source, (8) Light diffuser, (9) PC logging scale data, and monitoring substrate temperature, (10) Digital scale, (11) Temperature controller, (12) 120 V Variable auto transformer, (13) PC capturing high-speed camera images.
±2%. The nominal diameter of a spherical droplet of equal weight was calculated and found to be 2.5 mm for both liquids. This was confirmed using high speed video images of 50 droplets in flight and measuring their diameters. The impact velocity was controlled by adjusting the vertical distance from the tip of the needle to the top of the substrate and was fixed at 50 mm ± 1 mm for the experiments. The impact velocity was chosen such that no splash would occur on any of the three substrates investigated when the substrate was at room temperature. Room temperature for this study was recorded as 23 °C ± 3 °C. The impact velocities for the pure water and n-heptane droplets at the time of impact, determined from high speed imaging, were 0.9 m/s and varied by ±5% for water and ±9% for n-heptane.
Substrates were heated by placing them on an aluminum block (45 mm × 45 mm × 20 mm thick) that was heated using a single 100 W cartridge heater. The voltage applied to the heater was adjusted with a 120 V variable auto transformer and the substrate surface temperature was regulated using a temperature controller (CN90 0 0A, Omega Engineering, Laval, Quebec, Canada) and could be controlled to ±0.1 °C. A gauge 24, type K thermocouple was fixed using high temperature cement (CC High Temperature Cement, Omega Engineering, Laval, Quebec, Canada) to of each of the substrates. The surface temperatures were monitored using a wireless thermocouple connector (MWTC-D-K-915, Omega Engineering, Laval, Quebec, Canada) transmitting to a computer. At surface temperatures ranging from 60 °C to 120 °C, droplet evaporation was measured by placing the heater block and test
4
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
Fig. 3. Top down view (top) \ profile view (bottom) schematic of the fast response thermocouple used to measure surface temperature variations directly under the droplet.
surface on a digital scale (AG245, Mettler Toledo, Mississauga, Ontario, Canada) with a weighing capacity of 210 mg and resolution of 0.1 mg and recording the weight decrease as a function of time with a sampling frequency of 3 Hz. When surface temperatures reached 150 °C or higher droplet lifetimes became very short, less than 1 s. The response time of the scale was then not fast enough to measure droplet evaporation and a high-speed camera (Fastcam SA5, Photron, Tokyo, Japan) equipped with a bellows and 105 mm lens was used instead. At these temperatures there was very little penetration of liquid into surface pores. A 55 W light emitting diode was used as the light source. To verify the accuracy of using weight measurements to determine droplet lifetime the average evaporation time for 10 droplets placed on a heated, impervious surface was measured using both the weight method and the high-speed camera, and the results found to differ by less than 7%. 2.3. Surface temperature variation Fig. 3 shows a schematic of the thermocouple design employed to measure the surface temperature variations directly under the droplet. A surface thermocouple was created in which the stainless-steel substrate acted as one of the thermocouple materials, a technique that has previously been described by Heichal et al. [19] who determined that it produces microsecond response times. A 600 μm hole was drilled in the center of each of the substrates and a sheathed 250 μm diameter Constantan wire was inserted through it, using high-temperature ceramic cement to secure it in place and electrically isolate it from the substrate. The gap between the substrate and embedded constantan wire was bridged using a thin layer of silver conductive paste (735,825– 25 G, Sigma-Aldrich Chemicals Company, St. Louis, Missouri, United States) that formed the temperature sensing junction. The droplet impacted with its center over this junction, positioned using micrometer stages. The silver film sat on the surface of the metal substrates and measurements from SEM images showed that it was at most 600 μm in diameter. The maximum diameter of the liquid film created by the spreading droplet varied from 8 to 13 times that of the silver layer, so that its surface area represented 1 to 2% of the liquid-solid contact area. High-speed camera images showed
that the thermocouple made no measurable difference to the absorption/evaporation time of the liquid, suggesting it had negligible effect on the substrate porosity in this study. A 316 stainless-steel wire, 500 μm in diameter, was attached to the substrate by inserting it into a 600 μm hole drilled near the edge of the substrate and pinching it close using a hammer and a punch. The other end of the stainless-steel wire was welded to a Constantan wire and the junction placed in a vacuum flask filled with ice and water that was maintained at 0 °C ± 1 °C. The two Constantan wires, one from the substrate and the other from the cold junction were connected to a signal amplifier (Omni-amp III, Omega Engineering, Laval, Quebec, Canada) that amplified the signal by 100X before sending it to a digital oscilloscope. Droplets fell through a 9.53 mm slotted optical switch (OPB910W55Z, TT Electronics, Woking, UK) whose output was monitored by an Arduino Uno microcontroller that triggered the oscilloscope. Surface thermocouples were calibrated by placing each substrate in an oven whose temperature was raised from room temperature up to 300 °C in 50 °C increments, letting it reach steady state at each step determined when the measured temperature did not change for more than 10 min. The voltage generated by the surface thermocouple and the substrate temperature measured by a type-K thermocouple attached to the substrate near the junction being tested were both recorded. The substrate was then allowed to cool in 50 °C decrements with the voltage and temperature being recorded at each step. This process was repeated twice for each substrate and calibration curves were developed by plotting the surface thermocouple output voltage as a function of temperature. 3. Results and discussion Fig. 4 shows photographs of the first 25 ms after water droplets impact on the impermeable (Fig. 3a), 5 μm (Fig. 3b), and 100 μm (Fig. 3c) pore size substrates that were kept at room temperature (~23 °C). Immediately following impact on all three surfaces, a sudden increase in pressure at the point of impact results in a liquid sheet jetting outwards radially from the point of impact (t = 1 ms). The rate of spreading was lower on the porous surfaces which may have been due to both their increasing roughness and also due to penetration of liquid into the surface. A droplet with diameter Do
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
5
Fig. 4. Water droplet impact on the (a) impermeable, (b) 5 μm and (c) 100 μm surfaces. Surface temperature Tw = 23 °C, Vi = 0.9 m/s ± 5%, do = 2.5 mm ±2%, We = 29, Photograph Angle = 30°.
that lands with velocity Vo on a pore of diameter dp will penetrate if the stagnation pressure in the liquid is greater than the capillary pressure so that,
ρVo2 2
>
4σ dp
(1)
Or, using the definition of the Weber number W e = ρVo2 D0 /σ ,
We
dp >8 D0
(2)
The Weber numbers in our experiments were 29 for water and 65 for n-heptane, so that even for the larger pore size (100 μm) the left-hand side of Eq. (2) was always less than 8 where there would have been very little liquid penetration during impact. The reduced spread was therefore largely due to increased surface roughness [20,21]. The water droplets spread until they reach their maximum extent (t = 5 ms) after which surface tension forces begin to pull them back until they lift off the surface. The height of rise was greater on the porous surfaces (see Fig. 4, t = 10 ms) since the maximum spread was less and thus there was greater kinetic energy in the liquid when the droplets started to recoil. A lone bubble can be seen trapped inside the droplet at the center on the impermeable surface (see Fig. 4a at 1 ms) right up
until the droplet settles after impact at 25 ms. This phenomenon was previously observed by Chandra and Avedisian [4] which they attributed to air entrapment at the solid-liquid interface. The bubble is absent in the droplet on the 5 μm, and 100 μm surfaces during the spreading process because the airs able to escape into the porous structure following droplet impact. Fig. 5 shows sequences of photographs of the first 25 ms after n-heptane droplets impact the impermeable (Fig. 5a), 5 μm pore size (Fig. 5b), and 100 μm pore size (Fig. 5c) substrates at room temperature (23 °C). The impact Weber number (65) was too low to satisfy the criteria of Eq. (2) for liquid to penetrate substrate pores during impact, so the droplets spread radially following impact on all the surfaces (t = 1 ms). The rate of spreading was significantly less on the rougher porous surfaces than on the smooth impermeable surface, as was the maximum diameter reached (t = 10 ms). After this time the liquid began to disappear into the porous substrates, drawn in by capillary forces. On the 100 μm pore substrate no liquid could be seen on the surface at t = 10 ms, whereas only a faint outline could be seen on the 5 μm pore surface at t = 15 ms. The spread rate of an impacting droplet can be quantified by measuring the diameter of the liquid film in contact with the substrate (Ds ) and normalizing it by the initial droplet diameter (Do ) to
6
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
Fig. 5. n-Heptane droplet impact on the (a) impermeable, (b) 5 μm and (c) 100 μm surfaces. Surface temperature Tw = 23 °C, Vi = 0.9 m/s ± 9%, do = 2.5 mm ± 2%, We = 65, Photograph Angle = 30°.
define the “spread factor” β = Ds /Do . Fig. 6 shows the variation of the spread factor for water and n-heptane droplets on the impermeable and porous substrates at room temperature as a function of the dimensionless time (t∗ = tVo /Do ). It is clear from Fig. 6 that as the porosity increases, and thus the surface roughness, the maximum spread diameter and rate of spreading decreases for both the water and n-heptane. The n-heptane drops spread much farther than water drops due to their lower surface tension. The maximum extent of spread decreases with surface porosity for both liquids due to the greater roughness of the porous surfaces, and this effect is much more pronounced for the n-heptane drops. Surface porosity does not have much effect on the time at which maximum spread is reached for water drops as there is little penetration into the surface during spreading due to its higher surface tension. However, the n-heptane drops seep into the porous substrates very rapidly and therefore disappear at progressively shorter times as porosity increases. Heating the substrates changes impact dynamics since vapor is generated on the solid surface where the liquid touches it. Fig. 7 shows water droplets impacting on impermeable and porous surfaces initially heated to 150 °C. Heterogeneous nucleation begins in surface cavities immediately after impact (Fig. 7a, t = 0.2 ms) and bubbles rapidly fill the entire droplet (Fig. 7a, t = 1 ms). Increasing
surface roughness is known to promote nucleate boiling and it is likely that a porous surface which is rougher than an impervious surface (see Table 1) has a larger number of nucleation sites so that bubble formation is enhanced, though it is not possible to conclusively show this from the photographs of Fig. 7. The increased vapor generation at the liquid-solid interface aids droplet recoil and the droplet therefore rises higher on the 5 μm pore surface than it did on the same surface at room temperature (compare Fig. 4b, t = 15 ms with Fig. 7b, t = 15 ms). The effect of surface temperature on droplet impact is less evident on the 100 μm pore surface, as seen by comparing Figs. 4c and 7c, which may be because vapor easily penetrates the larger pores and causes less pressure build-up under the liquid than was the case with the 5 μm pore surface. Fig. 8 shows the impact of n-heptane droplets on the three test surfaces at a temperature of 150 °C, which is well above the liquid boiling temperature of 98.4 °C. Bubble nucleation started as soon as the droplets contacted the surface (Fig. 8a, t = 0.2 ms). A large vapor bubble formed inside the droplet on the 5 μm surface, visible as a white region in Fig. 8b at t = 1 ms, which lifted the liquid off the substrate before escaping after which the liquid film settled back on the surface. Bubble nucleation and escape was violent, repeatedly lifting the droplet (Fig. 8b, t = 5 ms) and finally making it fragment (Fig. 8b, t = 10 ms). These small droplets were in
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
7
some cases thrown off the substrate and in others remained on it. Vapor formation prevented liquid from penetrating into the 5 μm pore surface as it had done when the surface was maintained at room temperature (compare Figs. 5b and 8b). Vigorous boiling was also seen in the droplet on the surface with 100 μm pores, with a large bubble breaking through the liquid film and causing fragmentation. No liquid was visible on the surface by t = 10 ms, though it was not entirely clear if this was because it had evaporated or penetrated into the surface. A large number of small, secondary droplets were ejected from the n-heptane film on all three surfaces, as had previously been observed [22–24] during impact of droplets on hot surfaces, where it was attributed to vapor bubble explosions breaking through the liquid film. 3.1. Droplet evaporation time
Fig. 6. Spread factor as a function of the dimensionless time for both water and n-heptane on the impermeable and two porous substrates at room temperature (23 °C).
The rate of heat transfer from the substrate to a droplet deposited on it is reflected in the droplet evaporation time. As the substrate heats up, a plot of droplet lifetime as a function of the initial surface temperature can be used to identify changes in the dynamics of impact and evaporation. Fig. 9 shows the variation of droplet lifetime with initial surface temperature (Tw,o ) for water droplets deposited on the three surfaces for 60 °C < Tw,o < 300 °C.
Fig. 7. Water droplet impact on the (a) impermeable, (b) 5 μm and (c) 100 μm surfaces. Surface temperature Tw = 150 °C (nucleate boiling regime), Vi = 0.9 m/s ± 5%, do = 2.5 mm ±2%, We = 29.
8
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
Fig. 8. n-Heptane droplet impact on the (a) impermeable, (b) 5 μm and (c) 100 μm surfaces. Surface temperature Tw = 150 °C (nucleate boiling regime), Vi = 0.9 m/s ± 9%, do = 2.5 mm ± 2%, We = 65.
For Tw,o > 150 °C, where the lifetimes were too short to be seen clearly, an insert is used to show the data on a logarithmic scale that allows differences between the three surfaces to be identified. Each data point represents the average of 10 measurements and error bars represent the standard deviation. As the surface temperature was raised droplet lifetime decreased on all three surfaces. Droplets placed on the substrate with 5 μm pores had a significantly lower evaporation time than those on the other two surfaces for Tw,o < 110 °C. Droplet lifetime depends on many parameters including: the extent of droplet spread; penetration of liquid into the substrate; rate of bubble nucleation; the rate at which vapor escapes; and substrate thermal diffusivity. Surface porosity can enhance heat transfer since it increases the area of contact between the liquid and substrate, promotes bubble nucleation and allows vapor generated during boiling to escape rapidly. However, too large a porosity can also reduce thermal diffusivity significantly (see Table 1) and prevent heat conduction from the surrounding substrate into the region cooled by the evaporating droplet. Once the surface temperature increased above 200 °C the droplet on the impervious surface began to go into film boiling and the droplet lifetime increased with surface temperature. The Leidenfrost temperature, corresponding to the maximum
droplet lifetime, was 235 °C. Above that temperature droplets were in stable film boiling and evaporation time decreased with surface temperature. Droplets on the porous surfaces were not levitated because vapor below them could escape into the substrate and there was not enough pressure to lift the liquid. Fig. 10 shows the evaporation times of n-heptane droplets on the heated substrates, which were significantly lower than those for water drops due to their much lower latent heat of vaporization (2257 kJ/kg for water, 318 kJ/kg for n-heptane). At temperatures below 90 °C the evaporation time was longer on the porous substrates than on the impermeable surface. n-Heptane rapidly infiltrates surface pores and then takes longer to evaporate from them than it does when it is on the surface of the heated plate. At surface temperatures above 100 °C the evaporation time is similar on all three substrates. Once Tw,o is greater than the boiling point of n-heptane (98.4 °C) rapid vapor generation prevents the liquid from penetrating into pores and droplets evaporate while resting on top of the substrate (see Fig. 8c). Surface porosity then has less effect on evaporation time. Increasing substrate temperature further led to a transition to film boiling. The larger the pore size, the higher the temperature required to produce sufficient vapor to levitate the droplet. The Leidenfrost point was
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
Fig. 9. Evaporation time as a function of the surface temperature for the (a) impermeable, (b) 5 μm pore and (c) 100 μm pore size substrates using pure water as the working fluid. A graph insert is shown at surface temperatures ranging from 150 °C to 300 °C using a log time scale to show evaporation time differences between the surfaces.
9
Fig. 11. Surface temperature as a function of time for the water droplet on the impermeable, 5 μm and 100 μm surfaces at the point of impact at an initial surface temperature of 160 °C. Temperatures are shown up until the droplet reached its maximum spread factor on the impermeable surface.
Fig. 10. Evaporation time as a function of the surface temperature for the (a) impermeable, (b) 5 μm and (c) 100 μm surfaces using n-heptane as the working fluid. A graph insert is shown at surface temperatures ranging from 150 °C to 300 °C using a log time scale to show evaporation time differences between the surfaces.
190 °C on the impermeable surface, 225 °C on the 5 μm pore surface, and 285 °C on the 100 μm pore surface. 3.2. Surface temperature variation
Fig. 12. Comparison between surfaces (a) impermeable, (b) 5 μm and (c) 100 μm with the drop in surface temperature after 4 ms, the maximum time taken for the water droplet (at 23 °C) to spread on surface (a), as a function of the initial surface temperature. The temperature was measured at the point of impact. Standard deviations in ࢞Tw are shown.
The cooling effectiveness of an impacting drop can be measured by recording the surface temperature variation at the point of impact. Fig. 11 shows the temperature recorded by the surface thermocouples under water droplets impacting on the three surfaces maintained at an initial temperature of 160 °C. The temperature variation is shown for the first 4.0 ms following impact, which is the time required for the droplet to spread to its maximum extent on the impermeable surface (see Fig. 4a). After this time droplets recoiled, with some bouncing off the surface, so temperature measurements at a single point were much less repeatable after 4.0 ms. The temperature of the impermeable surface showed the fastest initial decrease and that of the 100 μm pore surface the slowest, reflecting the difference in thermal diffusivities of the three surfaces. However, the 5 μm pore surface showed the largest overall temperature drop after 4 ms. Fig. 12 shows the decrease in substrate temperature (࢞Tw ) under impacting water drops, measured 4.0 ms after impact, as a function of initial substrate temperature from 60 °C to 290 °C for the three test surfaces. Each data point is the average of 5 measurements and the error bars represent the standard deviation. The
5 μm pore surface had the largest temperature drop while that on the impermeable surface was slightly lower. The 100 μm pore surface, which had the lowest thermal conductivity, showed a much lower temperature change than the other surfaces. Droplets went into film boiling when the temperature of the impervious surface was raised above 235 °C, but this change is not evident from the measured temperature change, suggesting that there was liquidsolid contact during the initial stages of impact. Fig. 13 shows the substrate temperature decrease during impact of n-heptane droplets, measured 13.4 ms after impact, which was the time required for maximum droplet spread on the impermeable surface (see Fig. 5a). ࢞Tw increased with initial surface temperature for 60 °C≤Tw ≤160 °C, but this trend reversed for Tw ≥200 °C when droplets placed on the impermeable surface went into film boiling (see Fig. 10). Even though droplets placed on the porous surface did not go into film boiling until higher surface temperatures were reached, because of the lower latent heat of vaporization of n-heptane compared to water, there was enough vapor produced to reduce liquid-solid contact and therefore diminish
10
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
Fig. 13. Comparison between surfaces (a) impermeable, (b) 5 μm and (c) 100 μm with the drop in surface temperature after 13.4 ms, the maximum time taken for the n-heptane droplet (at 23 °C) to spread on surface (a), as a function of the initial surface temperature. The temperature was measured at the point of impact. Standard deviations in ࢞Tw are shown.
Fig. 14. Heat transfer coefficient for the water during droplet spreading on the impermeable, 5 μm and 100 μm surfaces as a function of the initial surface temperature. Heat transfer coefficients are shown on a log scale.
heat transfer. The impermeable surface had the lowest temperature drop, showing that the effect of vapor generation offset the higher thermal diffusivity of the substrate, unlike the case for water. 3.3. Heat transfer coefficient When a droplet impacts on a heated surface the thermal distur√ bance propagates over a thermal diffusion length L ∼ αt , where t is the time from impact. During the time for droplet spreading (~10 ms), L~0.1 mm, which is much smaller than the droplet diameter. We can therefore approximate heat transfer in the substrate by one-dimensional heat conduction and the variation in surface temperature Tw (x,t) can be described using equation:
∂ Tw ∂ 2 Tw =α ∂t ∂ x2
(3)
where x is distance in the substrate, measured from the surface. Assuming that the substrate can be regarded as a semi-infinite solid for the short times considered, the following boundary conditions can be applied:
Tw (∞, t ) = Tw,0
(4)
where Tw, 0 is the initial substrate temperature. Assuming that the droplet temperature Td remains constant and that h is the convective heat transfer coefficient between the liquid and solid at the interface x = 0
−k
Fig. 15. Heat transfer coefficient for the n-heptane during droplet spreading on the impermeable, 5 μm and 100 μm surfaces as a function of the initial surface temperature. Heat transfer coefficients are shown on a log scale.
∂ Tw = h[Td − Tw (0, t )] ∂ x x=0
(5)
The initial condition is that
Tw (x, 0 ) = Tw,0
(6)
Eq. (3) can be solved along with the boundary and initial conditions using a Laplace transform method to find the surface temperature variation [25]:
Tw (0, t ) = Tw,0 + (Td − Tw,0 ) 1 − erfc
h√ at k
· exp
h2 at k2
(7) The heat transfer coefficient was determined by performing a least-squares fit to match Eq. (7) to the measured surface temperature variations, such as those in Fig. 11. The first 4.0 ms after
impact were considered for water droplets and the first 13.4 ms for n-heptane droplets, which was approximately the time for the droplets to reach their maximum spread factor. Fig. 14 shows the calculated heat transfer coefficients for water droplets as a function of initial surface temperature. The value of h reflects the magnitude of heat transfer between the impacting droplet and the substrate at the point of impact and removes the effect of the thermal diffusivity of the surrounding surface, which is considered separately in Eq. (7). The higher the surface porosity, the lower the heat transfer, since pores reduce the actual surface area in contact with the liquid. The higher roughness of the porous substrates also leads to entrapment of air and vapor in surface cavities that may reduce heat transfer. The heat transfer coefficient of the two porous surfaces increases with surface temperature since there is no transition to film boiling and higher temperatures promote nucleate boiling. Water droplets on the impermeable surface went into film boiling at the Leidenfrost temperature of 235 °C, above which the heat transfer coefficient decreases with increasing temperature. Fig. 15 shows the variation of heat transfer coefficients with surface temperature for n-heptane droplets impacting on the three test surfaces. At lower temperatures, Tw ≤ 120 °C, h increased
N. Lipson and S. Chandra / International Journal of Heat and Mass Transfer 152 (2020) 119494
with surface temperature. Above that, as droplets began to boil and vapor was generated at the liquid-solid interface, heat transfer coefficients began to decrease. For temperatures greater than Tw = 200 °C, which is above the Leidenfrost temperature on a solid surface, heat transfer coefficient values were low and decreased gradually with increasing temperature. 4. Conclusions The impact of water and n-heptane droplets on stainless steel substrates of varying porosity was studied. Increasing substrate porosity resulted in lower thermal diffusivity and higher surface roughness. The droplets did not have a high enough velocity to penetrate surface pores during impact but spread out on the surface to form a thin film that was drawn into the porous surfaces by capillary forces. The rate of droplet spread decreased with increasing porosity because surface roughness also increased. Water droplets went into film boiling on the impervious surface when it was heated above 235 °C, but not on the porous surfaces. The Leidenfrost temperature of n-heptane droplets increased with surface porosity. Surface temperature variation during droplet impact was measured and a one-dimensional heat conduction model used to estimate heat transfer coefficients between the droplet and substrate. The heat transfer coefficients increased with surface temperature until sufficient vapor was generated at the liquid-solid interface to inhibit contact. Heat transfer coefficients then decreased with further increases in temperature. Declaration of Competing Interest We wish to draw the attention of the Editor to the following facts which may be considered as potential conflicts of interest and to significant financial contributions to this work. Funding for the project was provided by the Natural Sciences and Engineering Research Council of Canada. CRediT authorship contribution statement N. Lipson: Conceptualization, Writing - review & editing. S. Chandra: Conceptualization, Data curation, Investigation, Validation, Writing - original draft. References [1] B.S. Gottfried, C.J. Lee, K.J. Bell, The Leidenfrost phenomenon: film boiling of liquid droplets on a flat plate, Int. J. Heat Mass Transf. 9 (1966) 1167–1187.
11
[2] L.H.J. Wachters, N.A.J. Westerling, The heat transfer from a hot wall to impinging water drops in the spheroidal state, Chem. Eng. Sci. 21 (1966) 1047–1056. [3] G.S. Emmerson, The effect of pressure and surface material on the Leidenfrost point of discrete drops of water, Int. J. Heat Mass Transf. 18 (1975) 381–386. [4] S. Chandra, C.T. Avedisian, On the collision of a droplet with a solid surface, Proc. R. Soc. A 432 (1991) 13–41. [5] S. Chandra, M. di Marzo, Y.M. Qiao, P. Tartarini, Effect of liquid-solid contact angle on droplet evaporation, Fire Saf. J. 27 (1996) 141–158. [6] M. Pasandideh-Fard, S.D. Aziz, S. Chandra, J. Mostaghimi, Cooling effectiveness of a water drop impinging on a hot surface, Int. J. Heat Fluid Flow 22 (2001) 201–210. [7] G. Liang, I. Mudawar, Review of drop impact on heated walls, Int. J. Heat Mass Transf. 106 (2017) 103–126. [8] C.T. Avedisian, J. Koplik, Leidenfrost boiling of methanol droplets on hot porous/ceramic surfaces, Int. J. Heat Mass Transf. 30 (2) (1987) 379–393. [9] S. Chandra, C.T. Avedisian, Observations of droplet impingement on a ceramic porous surface, Int. J. Heat Mass Transf. 35 (10) (1992) 2377–2388. [10] M. Abu-Zaid, A. Atreya, Transient cooling of hot porous and nonporous ceramic solids by droplet evaporation, ASME. J. Heat Transf. 116 (1994) 694–701. [11] M. Abu-Zaid, An experimental study of the evaporation of gasoline and diesel droplets on hot surfaces, Int. Commun. Heat Mass Transf. 21 (2) (1994) 315–322. [12] M. Abu-Zaid, Droplet evaporation on porous and non-porous ceramic solids heated from top, Heat Mass Transf. 38 (3) (2002) 203–211. [13] Z. Yu, F. Wang, L.-S. Fan, Experimental and numerical studies of water droplet impact on a porous surface in the film-boiling regime, Ind. Eng. Chem. Res. 47 (23) (2008) 9174–9182. [14] S.K. Singh, S. Khanderkar, D. Pratap, S.A. Ramakrishna, Wetting dynamics and evaporation of sessile droplets on nano- porous alumina surfaces, Colloids Surf. A 432 (2013) 71–81. [15] W.S. Kim, S.Y. Lee, Behavior of a water drop impinging on heated porous surfaces, Exp. Therm. Fluid Sci. 55 (2014) 62–70. [16] X.W. Wang, J.Y. Ho, K.C. Leong, An experimental investigation of single droplet impact cooling on hot enhanced surfaces fabricated by selective laser melting, Int. J. Heat Mass Transf. 120 (2018) 652–670. [17] ASTM Standard E1225-04, Standard Test Method For Thermal Conductivity of Solids by Means of the Guarded- Comparative-Longitudinal Heat Flow Technique, ASTM International, West Conshohocken, PA, 2004. [18] N. Lipson, The Collision of Water and n-Heptane Droplets on Heated Sintered Porous Stainless-Steel Surfaces MASc Thesis, University of Toronto, 2018. [19] Y. Heichal, S. Chandra, E. Bordatchev, A fast-response thin filmed thermocouple to measure rapid surface temperature changes, Exp. Therm. Fluid Sci. 30 (2005) 153–159. [20] J. Liu, W. Franco, G. Aguilar, Effect of surface roughness on single cryogen droplet spreading, J. Fluids Eng. 130 (4) (2008) 1–9. [21] C. Tang, M. Qin, X. Weng, X. Zhang, P. Zhang, J. Li, Z. Huang, Dynamics of droplet impact on solid surface with different roughness, Int. J. Multiph. Flow 96 (2017) 56–69. [22] H. Chaves, A.M. Kubitzek, F. Obermeier, Dynamic processes occurring during the spreading of thin liquid films produced by drop impact on hot walls, Int. J. Heat Fluid Flow 20 (5) (1999) 470–476. [23] G.E. Cossali, M. Marengo, M. Santini, Secondary atomization produced by single drop vertical impacts onto heated surfaces, Exp. Therm. Fluid Sci. 29 (8) (2005) 937–946. [24] G.E. Cossali, M. Marengo, M. Santini, Thermally induced secondary drop atomization by single drop impact onto heated surfaces, Int. J. Heat Fluid Flow 29 (2008) 167–177. [25] F.P. Incropera, D.P. DeWitt, T.L. Bergman, A.S. Lavine, in: Fundamentals of Heat and Mass Transfer, 6 th edition, Wiley, New York, 2006, p. 286.