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The effect of bubble nucleation on the performance of a wickless heat pipe in microgravity

The effect of bubble nucleation on the performance of a wickless heat pipe in microgravity www.nature.com/npjmgrav ARTICLE OPEN The effect of bubble nucleation on the performance of a wickless heat pipe in microgravity 1 1 1✉ 2 Jiaheng Yu , Anisha Pawar , Joel L. Plawsky and David F. Chao Bubble nucleation was investigated in a 20-mm-long, wickless heat pipe on the International Space Station. Over 20 h of running experiments using pentane as the working fluid, more than 100 nucleation events were observed. Bubble nucleation at the heater end temporarily boosted peak pressures and vapor temperatures in the device. At the moment of nucleation, the heater wall temperature significantly decreased due to increased evaporation and the original vapor bubble collapsed due to increased pressure. A thermal model was developed and using the measured temperatures and pressures, heat transfer coefficients near the heater end of the system were extracted. Peak heat transfer coefficients during the nucleation event were over a factor of three higher than at steady-state. The heat transfer coefficient data were all collapsed in the form of a single, linear correlation relating the Nusselt number to the Ohnesorge number. npj Microgravity (2022) 8:12 ; https://doi.org/10.1038/s41526-022-00197-5 INTRODUCTION induced by the bubble growth are all found to be the related factors that affect the heat transfer behavior of boiling systems. A heat pipe is an efficient heat transfer device that operates by Rapid heating of a liquid leads to instabilities which can be recirculation of a fluid through liquid-vapor phase change and 29–32 observed in the form of abrupt boiling . Orrit et al. performed capillary forces. Heat pipes have found extensive application in experiments on a single 80 nm gold nanoparticle to investigate space research where high heat flux rates are required for cooling the boiling regime at a nanoscale level . They observed how the over long distances. With no moving parts and a low need for behavior of a nanobubble changes on varying the heater power maintenance, heat pipes are an attractive alternative to traditional and found that 120 µW is the boiling threshold above which vapor 1–5 heat exchangers . nanobubbles form and disappear. Monde et al. applied a The Constrained Vapor Bubble (CVB) experiment studied the theoretical model to study the homogenous nucleate boiling heat transfer behavior of a transparent, wickless heat pipe aboard regime in ethanol at atmospheric pressure . They calculated the the International Space Station to understand the influence of time to boiling explosion and the liquid temperature inside a interfacial and intermolecular forces on the vapor-liquid distribu- liquid control volume and found their results were in close 6,7 tion in the absence of gravity . The CVB consisted of a square agreement with the literature. Hasan et al. observed explosive fused silica cuvette, so the interface between the vapor and liquid nucleation of bubbles in microgravity as part of NASA’s Zero Boil- inside the heat pipe could be observed and the liquid film Off Tank experiment. They reported that at relatively low heat thickness on the walls of the device measured using interfero- fluxes, high values of superheat could be sustained punctuated metry. The high temperature at the heater end caused the periodically by rapid nucleation and growth of a vapor bubble. working fluid to evaporate, and the vapor condensed at the cold Reza and Zhang carried out molecular dynamics simulations of end, which was kept at a temperature well below the saturation argon on a copper surface . The aim was to study the effect of temperature of the vapor. Capillary forces arising from the sharp nanostructures on heat transfer. They found that the nanostruc- 8–11 corners of the cuvette returned the liquid back to the hot end . tured surface provides an advantage in heat transfer over a flat In one incarnation of the experiment, bubble nucleation, akin to surface due to the increased interaction between the liquid and nucleate boiling, was observed and is the subject of this paper. the structured surface. The temperature at which explosive boiling Boiling is a ubiquitous phase change phenomenon occurring in occurs was found to depend on the size of the nanostructures. 12–19 superheated fluids . Many researchers have studied the A rapid drop in the surface temperature was observed in many growth and departure of bubbles on a heated surface under 37,38 nucleate boiling experiments . A significant amount of heat various temperature and pressure conditions to understand the was absorbed during evaporation creating a bubble in a short 20–23 process of nucleate boiling in detail . Most experiments have time period. Meanwhile, the bubble formation process agitated been conducted under constant pressure conditions in Earth’s the flow in the liquid phase, which also enhanced the heat transfer gravity, though over the years, there have been quite a few process. However, in wick-structured heat pipe systems, nucleate 20,24 experiments in low gravity and microgravity conditions . boiling is generally considered to be a detrimental factor for heat Numerical models were also developed to predict and evaluate pipe performance . At high heat fluxes, bubbles generated by 25–27 the heat transfer mechanisms during nucleate boiling . The nucleate boiling occur within the wick and block the cooled liquid curvature of the meniscus underneath a bubble, the effect of from returning to the heated end. This circumstance is referred to interfacial forces, the thermal resistance at the liquid-vapor as the boiling limit of the heat pipe, which restricts the maximum 28 40 interface, the role of Marangoni convection , and the turbulence operating temperature . In contrast, experiments using wickless 1 2 The Howard P. Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA. NASA Glenn Research Center, Cleveland, OH 44135, USA. email: plawsky@rpi.edu Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; J. Yu et al. Box 1 Nomenclature Roman symbols A cross sectional area of the cuvette wall (m ) h average internal heat transfer coefficient (W/m K) in k thermal conductivity (W/m K) L characteristic length (m) Nu Nusselt number n the number of pressure data in a nucleation cycle n the number of temperature data in a nucleation cycle Oh Ohnesorge number P system pressure (Pa) P inside perimeter of the cuvette (m) in Fig. 1 Surveillance Image of the CVB system. A snapshot by the P initial stage system pressure of the nucleation cycles (Pa) initial surveillance camera of the partially filled 20 mm CVB module at the P outside perimeter of the cuvette (m) out steady state. 19 thermocouples, TC#01 to TC#19, were installed on q conduction heat transfer rate (W) cond the sidewall of the cuvette. The spacing of the thermocouples is 1.5 mm except for the first thermocouple, TC#01, which was q thermal radiation heat transfer rate (W) out,rad embedded in the wall between the heater and the working liquid. q internal heat transfer rate (W) in q’ conduction heat flow per unit length (W/m) cond q’ outside radiation heat flow per unit length (W/m) METHODS out,rad q’ internal heat transfer flow per unit length (W/m) Hardware configuration and sampling rate settings in −1 s sampling rate of the pressure data (s ) In the CVB experiment, a fused silica cuvette was used as a −1 transparent wickless heat pipe. The cuvette had a cross-sectional s sampling rate of the temperature data (s ) dimension of 5.5 × 5.5 mm outside and 3.0 × 3.0 mm inside the T temperature (K) cavity space. The working fluid of the heat pipe was pure pentane. t time (s) The constrained bubble in the cuvette section was generated by th TC#n the n thermocouple evacuating the system and then partially filling the liquid into the T saturation vapor temperature (K) CVB module. Videos and images of the experiments were T temperature of the external environment (K) recorded by a wide-angle surveillance camera to observe the ΔT superheat (K) migration of the bubble inside the cuvette. The temperature x distance (m) profile along the main axis of the heat pipe was measured by 19 thermocouples installed on one side of the cuvette (Fig. 1). Fig. S.4 Greek symbols 2 shows the wells that were drilled on the cuvette surface. The α thermal diffusivity of the liquid (m /s) beads of the type-E thermocouple junctions were embedded in ε emissivity of the cuvette material the corresponding wells to ensure good contact for temperature μ dynamic viscosity of the liquid (N s/m ) measurements. The temperature of the heater wall was measured ρ density (kg/m ) by the first thermocouple, TC#01, at 0.63 mm. The last thermo- 2 4 σ Stefan–Boltzmann constant (W/m K ) couple, TC#19 at 27.5 mm, detected and recorded the tempera- σ surface tension of the liquid (N/m) l ture of the cold finger. From TC#01 to TC#19, the effective length of the cuvette for the investigation is bounded in this region. The −1 sampling rate of the temperature readings was 0.5 s ≤ s ≤ −1 1.0 s , and the accuracy of the thermocouples was less than heat pipes/thermosyphons showed an increase in the heat flux 41,42 ±0.5 °C. During the entire nucleation experiment was achieved due to boiling in the bulk liquid phase . (00:00:00–20:21:17 Oct 17, 2010), the power input to the heater This paper extends the previous research on nucleate boiling in was set at 1.535 W and this maintained the steady-state the CVB system in microgravity to seven experimental “bins” temperature of the heater wall at ~117 °C. Meanwhile, the covering the range of nucleation events that occurred. The work temperature at the cold end was controlled by the cold finger emphasizes the analysis of the effect of nucleation on heat pipe and was held at 20 ± 0.1 °C. The internal pressure of the CVB performance . A one-dimensional heat transfer analytical model system was measured by a pressure transducer that was attached was developed based on the work by Bowman and Maynes, which downstream of the cuvette section. The specified accuracy of the allowed us to evaluate an average heat transfer coefficient in the sensor is ± 0.69 kPa. The sampling rate of the system pressure evaporation region and to compare that with the strength of the −1 readings is s = 1.0 s . The experiment was conducted onboard nucleation event . We found nucleation reduced the heater wall the International Space Station in the Fluids Integrated Rack (FIR) temperature and boosted the heat transfer coefficient significantly to minimize the influence of gravitational force and focus on though temporarily. Stronger nucleation events in the CVB system analyzing the effect of interfacial forces and nucleate boiling. The led to higher heat transfer coefficients and more effective heat Light Microscopy Module in the FIR was used for the optical pipe performance. Meanwhile, stronger nucleation also minimized observations. A more detailed description of the apparatus and the difference between the heater wall temperature and operation of the explosive nucleation CVB experiment can be saturation vapor temperature. Box 1 presents the nomenclature found in the previous publication . table for all variables used in this article. npj Microgravity (2022) 12 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; J. Yu et al. RESULTS more recently developed thermal analyses to quantify how the internal heat flow and heat transfer coefficient changed during the Overview of the microgravity CVB experiment course of these events. The CVB experiment was performed aboard the International Space Figure 1 shows the apparatus used in the experiment. The 20 mm Station to understand how microgravity affects the performance of a module, made of fused silica, was evacuated and then partially filled self-contained, evaporating and condensing system, like a heat pipe. with pure liquid pentane as the working fluid. Power inputs to the The microgravity conditions minimized the effects of body forces on heater (1.535 W) and the temperature of the condenser (19 °C) were the system and allowed interfacial forces to dominate the behavior. held constant. The power input was chosen as the best compromise The gravitational acceleration was ~0.19 µg over the experimental between the frequency of nucleation events and not exceeding the period and so the Bond number was effectively zero. More pressure limits that would automatically shut down the experiment. information on the microgravity environment can be found in Temperature profiles along the main axis of the heat pipe were 43,45,46 references . In the CVB experiments, several different lengths of measured by 19 thermocouples attached within one sidewall, the heat pipe were explored. Following bubble disruption during launch, temperature of the external environment was also recorded, and the getting all the vapor back into a single bubble and coaxing that system pressure was monitored and recorded by a pressure sensor bubble to adhere to the heater wall involved first turning on the located downstream of the condenser end. Video of a number of condenser to cool the back end of the system and condense any these events were obtained using a surveillance camera and can be vapor that remained there, and then turning on the heater to force found in the Supplementary Information section. The experimental the bubble to migrate toward it. This procedure worked for longer system was not designed to study nucleation and so pressure, versions of the heat pipe but failed in the shortest, 20 mm-long, temperature, and video were not fast enough to record all the details version due to strong interfacial forces that created flows in the of the nucleation event. Still, sufficient measurements were made corners of the device and prevented the bubble from attaching to throughout each event to provide some level of understanding. 8–11,45–50 the heater wall . Instead, bubbles would randomly nucleate at the heater wall, merge with the original vapor bubble, and Bubble nucleation in the CVB system eventually the new, single bubble would migrate back to the center of the device. In a previous paper, we analyzed a single such event . Figure 2a shows the pressure profile across 20 h of the nucleation In this paper, we were interested in analyzing many more and using experiment. The square dots represent the times associated with Fig. 2 Pressure data from the nucleation CVB experiment. a Pressure profile across the entire experiment duration (00:00:00–20:21:17 Oct 17, 2010). Peak pressure in each cycle is labeled using square dots. b Histogram of all the 119 cycles observed during the entire experiment. 5 5 5 5 5 With a bin size of 0.1 × 10 Pa, there are 7 bins in the diagram. The 7 intervals are (2.6 × 10 Pa–2.7 × 10 Pa), (2.7 × 10 Pa–2.8 × 10 Pa), (2.8 × 5 5 5 5 5 5 5 5 5 5 10 Pa–2.9 × 10 Pa), (2.9 × 10 Pa–3.0 × 10 Pa), (3.0 × 10 Pa–3.1 × 10 Pa), (3.1 × 10 Pa–3.2 × 10 Pa), and (3.2 × 10 Pa–3.3 × 10 Pa). c Superheat (ΔT) during the nucleation events. Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 12 J. Yu et al. Fig. 3 Nucleation event milestones .a Initial state with bubble near the middle of the device. b Moment of the nucleation event. A new bubble was generated at the hot end by evaporation of the liquid phase. The original bubble in (a) collapsed with the sudden increase in the system pressure. c The start of the bubble merging process for the new and the original bubble. d The end of the merging process for the two bubbles. At this moment, the combined bubble was still attached to the heater wall. e Progression of the bubble back toward its initial location. f Return of the bubble to its initial location. the local peak pressures, in each nucleation cycle. These peak pressures were not the pressure at the actual nucleation event itself but the point where the newly nucleated bubble and original bubble merged. The nucleation event and growth of the new bubble were too fast for us to record. 119 cycles were observed over the course of 20 h. In Fig. 2b, the data shows that peak 5 5 pressures ranged from 2.6 × 10 Pa to 3.3 × 10 Pa which we now bin into seven wells separated by 0.1 × 10 Pa. 60% of the cycles exhibited peak pressures between 3.1–3.3 × 10 Pa with only four cycles between 2.6–2.8 × 10 Pa. Figure 2c shows the superheat, ΔT, associated with each of these scenarios. The superheat was defined as the temperature difference between the heater wall, T , and the saturation temperature, T , associated with the TC#01 v measured pressure. This latter temperature was determined using Fig. 4 Pressure and temperature profiles for the nucleation event the Antoine equation for pentane. Notice that the superheat shown in Fig. 3. Profiles of the system pressure and the heater wall increased between each nucleation event. The experiment was temperature for the nucleation cycle (09:34:57–09:39:02) illustrated eventually stopped to insure we could revisit the module and in Fig. 3. attempt to run it later as a heat pipe. The details of a single nucleation event were discussed in as showninFig. 3b. The pressure increase associated with the detail in a previous publication ,soonlyabriefreviewis nucleation of the new bubble collapsed the original bubble so provided here. Figure 3 consists of images illustrating the key features of a typical nucleation cycle, and Fig. 4 depicts the that we observed two bubbles simultaneously inside the changes in pressure and heater wall temperature that occurred cuvette (Fig. 3b). In Fig. 4, the new bubble near the heater wall significantly boosted the internal pressure due to strong during this nucleation event. The low thermal conductivity of evaporation. At the same time, it dramatically cooled down the the glass walls coupled with radiation losses from the cell to the surroundings established a large temperature gradient heater wall temperature. The vapor in the original bubble between the hot and cold ends. Strong capillary return flow condensed to accommodate the sudden increase in pressure prevented the vapor bubble from attaching to the heater wall due to nucleation. The decrease in the pressure profile (Fig. 4) (Fig. 3a). The flow at the tail of the bubble is best observed in right after nucleation corresponded to a relaxation following the single nucleation event video in Supplementary Informa- thecollapseofthe original bubble. Theremnant of theoriginal tion. The superheated liquid at the heater wall would bubble then moved towards the new bubble, and the two occasionally promote the nucleation of a vapor bubble there bubbles merged into one (Fig. 3c, d). At the stage of Fig. 3d, the npj Microgravity (2022) 12 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA J. Yu et al. Fig. 5 System pressures and heater wall temperatures. a Pressure profiles for the 7 peak pressure groups at the sampling times of the pressure transducer. The time at the peak pressure is used to align the profiles. b Change of the heater wall temperatures with time for the 7 peak pressure groups. c The minimum heater wall temperatures for the 20 cycles in the 7 peak pressure groups. CVB system behaved similarly to a conventional heat pipe but nucleation. This pressure was very close to the safety cutoff of then the bubble detached from the heater wall (Fig. 3e) and the the system and luckily occurred too fast for the software to pressure began to decrease due to a decrease in the rate of register. Outside of the nucleation event, the rest of the cycle evaporation as the bubble moved toward the condenser end. was slow enough to record and so we characterize the events Thecurvatureofthe corner liquid on theleft-hand side of the using the second peak pressure which occurs when the two bubble is higher than that on the right in Fig. 3dand this bubbles coalesce. established a capillary flow that brought liquid from the Figure 5a, b align the 7 pressure profiles and the heater wall condenser end. This replenished liquid to the hot end and temperature profiles at the peak pressure times (dashed line). From helped separate the bubble from the heater wall. The bubble the different pressures at the coalescence stage, we can infer that migrated back to its starting position (Fig. 3f). Thus, Fig. 3fwas nucleation boosted the system pressure to different levels driven the final state of one nucleation cycle and the initial state of the by an increase in the amount of vapor generated. As mentioned next nucleation cycle. The process is most easily seen in the earlier, the temperature of the heater wall decreased significantly videos that can be found in the Supplementary Information. during the nucleation event because a new bubble was generated We selected 20 out of 119 cycles representing every bin in at the heater end. It is important to notice that the minimum Fig. 2b. We only picked those events where there were clear heater wall temperature in each group generally precedes the peak initial and final stages though in some instances, nucleation pressure at bubble coalescence. This indicates that this peak events, appeared in bursts (see Supplementary Information for pressure was due not only to the initial nucleation event but also a video). Fig. S.1 highlights the 20 cycles we selected for the analysis, and Table S.1 summarizes the basic information of due to evaporation that occurred while the new, single bubble was each cycle. Since there are only 7 peak pressure groups in the attached to the heater wall. The lower minimum value of the histogram of Fig. 2b, we again picked 7 representative cycles to heater wall temperature is found in the higher peak pressure show in the figures. group. In Fig. 5c, the summary of all the 20 cycles shows that the The duration of the nucleation phenomenon in the experi- decrease in the minimum heater wall temperature due to more ment was much faster than any of the experiment’s instruments severe nucleation events (higher peak pressures) prevailed could detect. The sampling rate for the pressure readings throughout the entire experiment. To help quantify this observa- −1 −1 (≈1s ) and temperature readings (≈0.5 s )was nothigh tion, we use a one-dimensional (1-D) heat transfer model to enough to catch the moments of nucleation for all events and determine the heat flow rates to and from the internal walls of the nucleation and bubble merging in the video occurred within device and to calculate a heat transfer coefficient at the evaporator one video frame. It would be difficult to identify,eveninFig. 4, throughout each nucleation event. if the 3.23 × 10 Pa first peak was the real internal pressure at Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 12 J. Yu et al. DISCUSSION surrounding environment (q ); phase change and convective out,rad flow of the working fluid (q ) internally. in The basic structure of the thermal model is similar to a standard fin A differential equation presented in Eq. (1) was derived based with the addition of convection and phase change inside the heat on the control volume in Fig. 6. pipe. The model is inspired by the one originally developed by Bowman and Maynes . Natural convection outside the cuvette is d T 4 4 kA  P hðÞ T  T  σεP T  T ¼ 0 c in in v out neglected due to the microgravity environment. Therefore, three 2 dx |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} (1) |fflfflfflffl{zfflfflfflffl} heat transfer mechanisms are included as shown in Fig. 6: q q in out;rad cond conduction of heat through the glass wall from the hot end to the cold end (q ); thermal radiation from the external surface to the cond Fig. 6 One dimensional heat transfer model geometry. Schematic of the CVB heat pipe with various heat transfer mechanisms. Heat was absorbed by the internal fluid near the hot end but was released near the cold end. Fig. 7 q’ profile and saturation vapor temperature. Two regions with different heat transfer behaviors are identified in the CVB module in based on the position where q’ = 0. a Internal heat transfer profile, q’ , at the initial stage of the nucleation cycle shown in Fig. 3a. in in b Surveillance image showing the physical location where the first q’ = 0 occurs and identifying the absorption and release regions. in c Saturation vapor temperature calculated using the q’ profile and the Antoine equation for the 7 peak pressure groups. in npj Microgravity (2022) 12 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA J. Yu et al. Fig. 8 Average internal heat transfer coefficient, h , and q’ profile at the nucleation stage. a Change of the average internal heat transfer in in coefficient with time in the heat absorption region for the 7 peak pressure groups. The maximum error of the average heat transfer coefficients for the 7 cycles in (a) is 1.34 W/m K. b Internal heat flow rate profile, q’ , at the moment of nucleation, Fig. 3b, in the cycle. c The in maximum average internal heat transfer coefficients for the entire 20 nucleation events in the analysis. Errors are smaller than 0.58 W/m K. In Eq. (1), T represents the saturation vapor temperature, and Figure 7c compares the calculation of T from the two methods for v v h is an average heat transfer coefficient that is used to evaluate the 7 groups. The sampling rate of the temperature data was in the performance of the heat pipe, primarily in the region near the slower than that of the pressure data and so saturation vapor heater end. Although T changed with time as the system temperatures estimated from the q’ profiles may not exactly v in pressured varied, it is assumed to be relatively constant within the mirror the rapid changes in pressure that occur at the time of heat pipe at any moment. The saturation vapor temperature was nucleation or bubble coalescence. Thus, using the q’ profiles, the in estimated from the pressure profile using the Antoine equation, measurements during the time interval between the initial stage Eq. (2), when changes to the operating parameters of the CVB and nucleation stage deviate from the bulk data, and these points system are changing relatively slowly. The parameters for the are located at the higher-pressure regions in the cycle. However, Antoine equation are listed in Table S.2 in the Supplementary the majority of the data points where changes are relatively slow 49,50 Information . are highly matched with the saturation vapor temperatures calculated by the Antoine equation, so the thermal model can T ¼  C still predict and describe the dynamic changes in the CVB system (2) A  log P over most of the event. 0 0 0 A second method was also used to obtain a value for T from v q ¼ q þ q (3) in cond out;rad the q’ profile. By rearranging Eq. (1), we can calculate q’ from in in the other two heat transfer components as shown in Eq. (3). Figure With T determined, h can be calculated from Eq. (1)byan 7a demonstrates the q’ profile at the time of Fig. 3b. The region in v in iterative numerical method using h as the adjustable parameter of the heat pipe where q’ < 0 means heat was gained by the in in to fit the model to the temperature profile. Figure 8a shows these internal fluid from the glass wall and the region where q’ >0 in heat transfer coefficients for the 7 groups as a function of time. means heat was lost by the internal fluid to the glass wall. Thus, the heat pipe, such as it is, can be segmented into two primary The average heat transfer coefficients increased significantly at the sections: a heat absorption region and a heat release region, as peak pressure times and decreased rapidly after the new and illustrated in Fig. 7b. The second point where q’ = 0 corresponds original bubbles merged. Figure 8b presents the q’ profile at the in in to the end of the vapor bubble. The transition point between the peak pressure time corresponding to Fig. 3b. Comparing Fig. 7a two, colored sections, where q’ = 0, provides a value for T within and Fig. 8b, the heat absorbed by the internal fluid is much higher in v the vapor bubble and we use the distance between the location of at the peak pressure times, which verifies the new bubble T and the heater wall as the characteristic length of our device. generated at the hot end by nucleation removed the heat from Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 12 J. Yu et al. Fig. 9 The effect of the temperature gradient and length of the heat absorption region on the average internal heat transfer coefficient. a Average internal heat transfer coefficients as a function of temperature gradients in the heat absorption region. The maximum h values in 7 in group are marked as (▢) representing the nucleation and merge stages (Fig. 3b–d), the h values at t =−50 s are marked as (◁) representing in the initial stage prior to bubble nucleation (Fig. 3a), and the h values at t = 150 s are marked as (▷) representing the final stage once the in bubble returns to the center (Fig. 3f). The three special marker types represent the nucleation and merge stage, initial stage, and final stage of the cycle respectively. b Change of the temperature gradient in the heat absorption region with time. c Average internal heat transfer coefficients versus the length of the heat absorption region. Special markers share the same definition as in (a). the glass wall via evaporation. Meanwhile, in Fig. 8a, the maximum Figure 9a presents the heat transfer coefficients as a function of heat transfer coefficient in each group is shown to occur at the the superheat in the heat absorption region. The maximum heat time of peak pressure for each group. Figure 8c summarizes the transfer coefficient in every group decayed with the superheat but relationship between the maximum heat transfer coefficients and the characteristics of the decay depended on the peak pressure peak pressures for all the 20 cycles analyzed. achieved. At the peak pressure times (t = 0 s), in Fig. 9b, the It is important to notice that the highest heat transfer difference in ΔT for the lowest and highest peak pressure groups is coefficient occurs slightly ahead of the peak pressure time in around 11 K. However, at t = 150 s, the difference in ΔT is around each group because the peak pressure represents the stage of 2 K. Therefore, ΔT for the higher peak pressure group decayed bubble coalescence and not the moment of nucleation which faster with time. After the two bubbles merged, both the pressure absorbs much more heat. Due to the low sampling rate of the and the heater wall temperature began returning to their initial temperature data, there was a lag in time for the maximum heat values in the cycle. Due to the constant heat input and condenser transfer coefficient, reflecting the heat pipe performance at the temperature throughout the entire experiment, the difference in nucleation stage in the heat absorption region. ΔT decreased and the tails of all the 7 profiles converged. The trend in the average heat transfer coefficient for the 7 The heat transfer coefficient is also related to the length of the groups is related to the temperature gradient in the heat heat absorption region, or what we define as the characteristic absorption region for the internal fluid. Fig. S.2 shows the full length for the system. In Fig. 9c, the maximum heat transfer temperature profiles for the 7 groups at the peak pressure times coefficient in each group occurred when the length of the heat near the heater end. Stronger nucleation resulted in higher peak absorption region was the shortest. This coincided with the pressure. Therefore, the saturation vapor temperature was higher longest heat release region for the internal fluid. Following bubble at the peak pressure time for stronger nucleation cycles, and a coalescence, as the system pressure decreased, the saturation longer heat release region was available for heat removal. vapor temperature decreased, the length of the heat absorption Meanwhile, the dramatic evaporation at the hot end significantly region became longer and so the average heat transfer coefficient cooled down the heater wall temperature. In Fig. S.2, the heater decreased with time. wall temperature was lower in the higher peak pressure group The agreement between h and the characteristic length, in (stronger nucleation cycle). Therefore, nucleation in this version of shown in Fig. 9c, suggested that it might be useful to evaluate the the CVB heat pipe was beneficial to its performance, as long as the behavior using dimensionless physical quantities. Inspired by the 51,52 bubble remained attached to the heater wall. analyses in , we found the Ohnesorge number, Oh, seems to npj Microgravity (2022) 12 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA J. Yu et al. and overcame some of the limitations that arose due to the poor thermal conductivity of the working fluid and the glass walls of the system. During nucleation, the heater wall temperature significantly decreased due to increased evaporation, and the more severe nucleation events cooled the heater wall by 20 degrees or more. The heat transfer coefficient was found to be directly related to the characteristic length of the system, defined as the difference in locations between the heater wall and the point in the heat pipe where the wall temperature coincided with the saturation temperature of the vapor. All the heat transfer data were collapsed into a single, linear Nu vs. Oh correlation indicating that viscous, surface, and inertial forces dominated the observed behavior. Reporting summary Further information on research design is available in the Nature Research Reporting Summary linked to this article. Fig. 10 Nusselt number correlation. A universal correlation DATA AVAILABILITY between the Nusselt number and Ohnesorge number. Special The datasets generated and analyzed during the current study are available from the markers share the same definition as in Fig. 9a. corresponding author on reasonable request. The raw data is available through NASA’s Physical Science Informatics (PSI) Database under the CVB experiment. [URL: https://www.nasa.gov/PSI]. describe the competition between viscous forces, surface forces and inertial forces driven by the nucleation event (Eq. (4)). In CODE AVAILABILITY addition, the average heat transfer coefficients and characteristic MATLAB (MathWorks, Inc., Natick, United States) is used to process the data length can be used to define a Nusselt number (Eq. (5)) in the heat presented in this study. A custom script is available from the corresponding author absorption region. upon reasonable request. Oh ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi (4) ðÞ ρσ L Received: 14 July 2021; Accepted: 21 March 2022; h L in (5) Nu ¼ μ, ρ, σ , and k are the dynamic viscosity, density, surface tension, REFERENCES and thermal conductivity of the liquid. Based on data from NIST, 1. Faghri, A. Review and advances in heat pipe science and technology. J. 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ACKNOWLEDGEMENTS 26. Stephan, P. & Hammer, J. A new model for nucleate boiling heat transfer. Heat This material is based on the work supported by the National Aeronautics and Space Mass Transf. 30, 119–125 (1994). Administration (NASA) under grant number 80NSSC20K0120 and the National 27. Kolev, N. I. How accurately can we predict nucleate boiling? Exp. Therm. Fluid Sci. Science Foundation (NSF) under grant number CBET-1637816. Any opinions, findings, 10, 370–378 (1995). and conclusions or recommendations expressed in this publication are those of the 28. Petrovic, S., Robinson, T. & Judd, R. L. Marangoni heat transfer in subcooled authors and do not necessarily reflect the view of NASA or NSF. nucleate pool boiling. Int. J. Heat Mass Transf. 47, 5115–5128 (2004). 29. Wang, G. & Cheng, P. An experimental study of flow boiling instability in a single microchannel. Int. Commun. Heat Mass Transf. 35, 1229–1234 (2008). AUTHOR CONTRIBUTIONS 30. Barber, J., Sefiane, K., Brutin, D. & Tadrist, L. Hydrodynamics and heat transfer J.Y. analyzed the bulk of the data, produced all the figures and tables, and prepared during flow boiling instabilities in a single microchannel. Appl. Therm. Eng. 29, the initial manuscript. He is supported by NSF. A.P. worked on the introduction and 1299–1308 (2009). literature search and helped write the introduction section. She is supported by 31. Barber, J., Brutin, D., Sefiane, K., Gardarein, J. L. & Tadrist, L. Unsteady-state NASA. J.P. is the project director, was present during the recording of all the original fluctuations analysis during bubble growth in a “rectangular” microchannel. Int. J. data, and finalized the paper and data analysis. D.C. was the NASA project scientist Heat Mass Transf. 54, 4784–4795 (2011). who was in charge of the CVB experiment and was instrumental in getting more time 32. Kandlikar, S. G. Nucleation characteristics and stability considerations during flow aboard the ISS for us to run the nucleation experiments. boiling in microchannels. Exp. Therm. Fluid Sci. 30, 441–447 (2006). 33. Jollans, T. & Orrit, M. Explosive, oscillatory, and Leidenfrost boiling at the nanoscale. Phys. Rev. E 99, 063110 (2019). COMPETING INTERESTS 34. Hasan, M. N., Hasan, A., Ilias, S., Mitsutake, Y. & Monde, M. Characteristics of Homogeneous Nucleation Boiling in Ethanol during Rapid Linear Boundary The authors declare no competing interests. Heating. Procedia Eng. 90, 624–630 (2014). 35. Hasan, M. M., Lin, C. S., Knoll, R. H. & Bentz, M. D. Explosive boiling at very low heat fluxes: a. microgravity phenomenon. ASME Appl. Mech. Div. 174,125–125 (1993). ADDITIONAL INFORMATION 36. Reza Seyf, H. & Zhang, Y. Molecular dynamics simulation of normal and explosive Supplementary information The online version contains supplementary material boiling on nanostructured surface. J. Heat Transfer 135, 121503 (2013). available at https://doi.org/10.1038/s41526-022-00197-5. 37. Moore, F. D. & Mesler, R. B. The measurement of rapid surface temperature fluctuations during nucleate boiling of water. AIChE J. 7, 620–624 (1961). Correspondence and requests for materials should be addressed to Joel L. Plawsky. 38. Chi-Liang, Y. & Mesler, R. B. A study of nucleate boiling near the peak heat flux through measurement of transient surface temperature. Int. J. Heat Mass Transf. Reprints and permission information is available at http://www.nature.com/ 20, 827–840 (1977). reprints 39. Nemec, P., Čaja, A. & Malcho, M. Mathematical model for heat transfer limitations of heat pipe. Math. Comput. Model. 57, 126–136 (2013). Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims 40. Stephan, P. & Brandt, C. Advanced capillary structures for high performance heat in published maps and institutional affiliations. pipes. Heat Transf. Eng. 25,78–85 (2010). 41. Guichet, V., Almahmoud, S. & Jouhara, H. Nucleate pool boiling heat transfer in wickless heat pipes (two-phase closed thermosyphons): a critical review of cor- relations. Therm. Sci. Eng. Prog. 13, 100384 (2019). Open Access This article is licensed under a Creative Commons 42. Andrzejczyk, R. Experimental investigation of the thermal performance of a Attribution 4.0 International License, which permits use, sharing, wickless heat pipe operating with different fluids: water, ethanol, and ses36. adaptation, distribution and reproduction in any medium or format, as long as you give analysis of influences of instability processes at working operation parameters. appropriate credit to the original author(s) and the source, provide a link to the Creative Energies 12, 80 (2018). Commons license, and indicate if changes were made. The images or other third party 43. Plawsky, J. L., Wayner, P. C. & Isermann, H. P. Explosive nucleation in microgravity: material in this article are included in the article’s Creative Commons license, unless The Constrained Vapor Bubble experiment. Int. J. Heat Mass Transf. 55, indicated otherwise in a credit line to the material. If material is not included in the 6473–6484 (2012). article’s Creative Commons license and your intended use is not permitted by statutory 44. Bowman, W. J. & Maynes, D. Comparison of standard and heat-pipe fins with spe- regulation or exceeds the permitted use, you will need to obtain permission directly cified tip temperature condition. J. Thermophys. Heat Transf. 15,421–426 (2001). from the copyright holder. To view a copy of this license, visit http://creativecommons. 45. Kundan, A. et al. Thermocapillary phenomena and performance limitations of a org/licenses/by/4.0/. wickless heat pipe in microgravity. Phys. Rev. Lett. 114, 146105 (2015). 46. Kundan, A., Plawsky, J. L. & Wayner, P. C. Effect of capillary and marangoni forces on transport phenomena in microgravity. Langmuir 31, 5377–5386 (2015). © The Author(s) 2022 npj Microgravity (2022) 12 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png npj Microgravity Springer Journals

The effect of bubble nucleation on the performance of a wickless heat pipe in microgravity

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www.nature.com/npjmgrav ARTICLE OPEN The effect of bubble nucleation on the performance of a wickless heat pipe in microgravity 1 1 1✉ 2 Jiaheng Yu , Anisha Pawar , Joel L. Plawsky and David F. Chao Bubble nucleation was investigated in a 20-mm-long, wickless heat pipe on the International Space Station. Over 20 h of running experiments using pentane as the working fluid, more than 100 nucleation events were observed. Bubble nucleation at the heater end temporarily boosted peak pressures and vapor temperatures in the device. At the moment of nucleation, the heater wall temperature significantly decreased due to increased evaporation and the original vapor bubble collapsed due to increased pressure. A thermal model was developed and using the measured temperatures and pressures, heat transfer coefficients near the heater end of the system were extracted. Peak heat transfer coefficients during the nucleation event were over a factor of three higher than at steady-state. The heat transfer coefficient data were all collapsed in the form of a single, linear correlation relating the Nusselt number to the Ohnesorge number. npj Microgravity (2022) 8:12 ; https://doi.org/10.1038/s41526-022-00197-5 INTRODUCTION induced by the bubble growth are all found to be the related factors that affect the heat transfer behavior of boiling systems. A heat pipe is an efficient heat transfer device that operates by Rapid heating of a liquid leads to instabilities which can be recirculation of a fluid through liquid-vapor phase change and 29–32 observed in the form of abrupt boiling . Orrit et al. performed capillary forces. Heat pipes have found extensive application in experiments on a single 80 nm gold nanoparticle to investigate space research where high heat flux rates are required for cooling the boiling regime at a nanoscale level . They observed how the over long distances. With no moving parts and a low need for behavior of a nanobubble changes on varying the heater power maintenance, heat pipes are an attractive alternative to traditional and found that 120 µW is the boiling threshold above which vapor 1–5 heat exchangers . nanobubbles form and disappear. Monde et al. applied a The Constrained Vapor Bubble (CVB) experiment studied the theoretical model to study the homogenous nucleate boiling heat transfer behavior of a transparent, wickless heat pipe aboard regime in ethanol at atmospheric pressure . They calculated the the International Space Station to understand the influence of time to boiling explosion and the liquid temperature inside a interfacial and intermolecular forces on the vapor-liquid distribu- liquid control volume and found their results were in close 6,7 tion in the absence of gravity . The CVB consisted of a square agreement with the literature. Hasan et al. observed explosive fused silica cuvette, so the interface between the vapor and liquid nucleation of bubbles in microgravity as part of NASA’s Zero Boil- inside the heat pipe could be observed and the liquid film Off Tank experiment. They reported that at relatively low heat thickness on the walls of the device measured using interfero- fluxes, high values of superheat could be sustained punctuated metry. The high temperature at the heater end caused the periodically by rapid nucleation and growth of a vapor bubble. working fluid to evaporate, and the vapor condensed at the cold Reza and Zhang carried out molecular dynamics simulations of end, which was kept at a temperature well below the saturation argon on a copper surface . The aim was to study the effect of temperature of the vapor. Capillary forces arising from the sharp nanostructures on heat transfer. They found that the nanostruc- 8–11 corners of the cuvette returned the liquid back to the hot end . tured surface provides an advantage in heat transfer over a flat In one incarnation of the experiment, bubble nucleation, akin to surface due to the increased interaction between the liquid and nucleate boiling, was observed and is the subject of this paper. the structured surface. The temperature at which explosive boiling Boiling is a ubiquitous phase change phenomenon occurring in occurs was found to depend on the size of the nanostructures. 12–19 superheated fluids . Many researchers have studied the A rapid drop in the surface temperature was observed in many growth and departure of bubbles on a heated surface under 37,38 nucleate boiling experiments . A significant amount of heat various temperature and pressure conditions to understand the was absorbed during evaporation creating a bubble in a short 20–23 process of nucleate boiling in detail . Most experiments have time period. Meanwhile, the bubble formation process agitated been conducted under constant pressure conditions in Earth’s the flow in the liquid phase, which also enhanced the heat transfer gravity, though over the years, there have been quite a few process. However, in wick-structured heat pipe systems, nucleate 20,24 experiments in low gravity and microgravity conditions . boiling is generally considered to be a detrimental factor for heat Numerical models were also developed to predict and evaluate pipe performance . At high heat fluxes, bubbles generated by 25–27 the heat transfer mechanisms during nucleate boiling . The nucleate boiling occur within the wick and block the cooled liquid curvature of the meniscus underneath a bubble, the effect of from returning to the heated end. This circumstance is referred to interfacial forces, the thermal resistance at the liquid-vapor as the boiling limit of the heat pipe, which restricts the maximum 28 40 interface, the role of Marangoni convection , and the turbulence operating temperature . In contrast, experiments using wickless 1 2 The Howard P. Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA. NASA Glenn Research Center, Cleveland, OH 44135, USA. email: plawsky@rpi.edu Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; J. Yu et al. Box 1 Nomenclature Roman symbols A cross sectional area of the cuvette wall (m ) h average internal heat transfer coefficient (W/m K) in k thermal conductivity (W/m K) L characteristic length (m) Nu Nusselt number n the number of pressure data in a nucleation cycle n the number of temperature data in a nucleation cycle Oh Ohnesorge number P system pressure (Pa) P inside perimeter of the cuvette (m) in Fig. 1 Surveillance Image of the CVB system. A snapshot by the P initial stage system pressure of the nucleation cycles (Pa) initial surveillance camera of the partially filled 20 mm CVB module at the P outside perimeter of the cuvette (m) out steady state. 19 thermocouples, TC#01 to TC#19, were installed on q conduction heat transfer rate (W) cond the sidewall of the cuvette. The spacing of the thermocouples is 1.5 mm except for the first thermocouple, TC#01, which was q thermal radiation heat transfer rate (W) out,rad embedded in the wall between the heater and the working liquid. q internal heat transfer rate (W) in q’ conduction heat flow per unit length (W/m) cond q’ outside radiation heat flow per unit length (W/m) METHODS out,rad q’ internal heat transfer flow per unit length (W/m) Hardware configuration and sampling rate settings in −1 s sampling rate of the pressure data (s ) In the CVB experiment, a fused silica cuvette was used as a −1 transparent wickless heat pipe. The cuvette had a cross-sectional s sampling rate of the temperature data (s ) dimension of 5.5 × 5.5 mm outside and 3.0 × 3.0 mm inside the T temperature (K) cavity space. The working fluid of the heat pipe was pure pentane. t time (s) The constrained bubble in the cuvette section was generated by th TC#n the n thermocouple evacuating the system and then partially filling the liquid into the T saturation vapor temperature (K) CVB module. Videos and images of the experiments were T temperature of the external environment (K) recorded by a wide-angle surveillance camera to observe the ΔT superheat (K) migration of the bubble inside the cuvette. The temperature x distance (m) profile along the main axis of the heat pipe was measured by 19 thermocouples installed on one side of the cuvette (Fig. 1). Fig. S.4 Greek symbols 2 shows the wells that were drilled on the cuvette surface. The α thermal diffusivity of the liquid (m /s) beads of the type-E thermocouple junctions were embedded in ε emissivity of the cuvette material the corresponding wells to ensure good contact for temperature μ dynamic viscosity of the liquid (N s/m ) measurements. The temperature of the heater wall was measured ρ density (kg/m ) by the first thermocouple, TC#01, at 0.63 mm. The last thermo- 2 4 σ Stefan–Boltzmann constant (W/m K ) couple, TC#19 at 27.5 mm, detected and recorded the tempera- σ surface tension of the liquid (N/m) l ture of the cold finger. From TC#01 to TC#19, the effective length of the cuvette for the investigation is bounded in this region. The −1 sampling rate of the temperature readings was 0.5 s ≤ s ≤ −1 1.0 s , and the accuracy of the thermocouples was less than heat pipes/thermosyphons showed an increase in the heat flux 41,42 ±0.5 °C. During the entire nucleation experiment was achieved due to boiling in the bulk liquid phase . (00:00:00–20:21:17 Oct 17, 2010), the power input to the heater This paper extends the previous research on nucleate boiling in was set at 1.535 W and this maintained the steady-state the CVB system in microgravity to seven experimental “bins” temperature of the heater wall at ~117 °C. Meanwhile, the covering the range of nucleation events that occurred. The work temperature at the cold end was controlled by the cold finger emphasizes the analysis of the effect of nucleation on heat pipe and was held at 20 ± 0.1 °C. The internal pressure of the CVB performance . A one-dimensional heat transfer analytical model system was measured by a pressure transducer that was attached was developed based on the work by Bowman and Maynes, which downstream of the cuvette section. The specified accuracy of the allowed us to evaluate an average heat transfer coefficient in the sensor is ± 0.69 kPa. The sampling rate of the system pressure evaporation region and to compare that with the strength of the −1 readings is s = 1.0 s . The experiment was conducted onboard nucleation event . We found nucleation reduced the heater wall the International Space Station in the Fluids Integrated Rack (FIR) temperature and boosted the heat transfer coefficient significantly to minimize the influence of gravitational force and focus on though temporarily. Stronger nucleation events in the CVB system analyzing the effect of interfacial forces and nucleate boiling. The led to higher heat transfer coefficients and more effective heat Light Microscopy Module in the FIR was used for the optical pipe performance. Meanwhile, stronger nucleation also minimized observations. A more detailed description of the apparatus and the difference between the heater wall temperature and operation of the explosive nucleation CVB experiment can be saturation vapor temperature. Box 1 presents the nomenclature found in the previous publication . table for all variables used in this article. npj Microgravity (2022) 12 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; J. Yu et al. RESULTS more recently developed thermal analyses to quantify how the internal heat flow and heat transfer coefficient changed during the Overview of the microgravity CVB experiment course of these events. The CVB experiment was performed aboard the International Space Figure 1 shows the apparatus used in the experiment. The 20 mm Station to understand how microgravity affects the performance of a module, made of fused silica, was evacuated and then partially filled self-contained, evaporating and condensing system, like a heat pipe. with pure liquid pentane as the working fluid. Power inputs to the The microgravity conditions minimized the effects of body forces on heater (1.535 W) and the temperature of the condenser (19 °C) were the system and allowed interfacial forces to dominate the behavior. held constant. The power input was chosen as the best compromise The gravitational acceleration was ~0.19 µg over the experimental between the frequency of nucleation events and not exceeding the period and so the Bond number was effectively zero. More pressure limits that would automatically shut down the experiment. information on the microgravity environment can be found in Temperature profiles along the main axis of the heat pipe were 43,45,46 references . In the CVB experiments, several different lengths of measured by 19 thermocouples attached within one sidewall, the heat pipe were explored. Following bubble disruption during launch, temperature of the external environment was also recorded, and the getting all the vapor back into a single bubble and coaxing that system pressure was monitored and recorded by a pressure sensor bubble to adhere to the heater wall involved first turning on the located downstream of the condenser end. Video of a number of condenser to cool the back end of the system and condense any these events were obtained using a surveillance camera and can be vapor that remained there, and then turning on the heater to force found in the Supplementary Information section. The experimental the bubble to migrate toward it. This procedure worked for longer system was not designed to study nucleation and so pressure, versions of the heat pipe but failed in the shortest, 20 mm-long, temperature, and video were not fast enough to record all the details version due to strong interfacial forces that created flows in the of the nucleation event. Still, sufficient measurements were made corners of the device and prevented the bubble from attaching to throughout each event to provide some level of understanding. 8–11,45–50 the heater wall . Instead, bubbles would randomly nucleate at the heater wall, merge with the original vapor bubble, and Bubble nucleation in the CVB system eventually the new, single bubble would migrate back to the center of the device. In a previous paper, we analyzed a single such event . Figure 2a shows the pressure profile across 20 h of the nucleation In this paper, we were interested in analyzing many more and using experiment. The square dots represent the times associated with Fig. 2 Pressure data from the nucleation CVB experiment. a Pressure profile across the entire experiment duration (00:00:00–20:21:17 Oct 17, 2010). Peak pressure in each cycle is labeled using square dots. b Histogram of all the 119 cycles observed during the entire experiment. 5 5 5 5 5 With a bin size of 0.1 × 10 Pa, there are 7 bins in the diagram. The 7 intervals are (2.6 × 10 Pa–2.7 × 10 Pa), (2.7 × 10 Pa–2.8 × 10 Pa), (2.8 × 5 5 5 5 5 5 5 5 5 5 10 Pa–2.9 × 10 Pa), (2.9 × 10 Pa–3.0 × 10 Pa), (3.0 × 10 Pa–3.1 × 10 Pa), (3.1 × 10 Pa–3.2 × 10 Pa), and (3.2 × 10 Pa–3.3 × 10 Pa). c Superheat (ΔT) during the nucleation events. Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 12 J. Yu et al. Fig. 3 Nucleation event milestones .a Initial state with bubble near the middle of the device. b Moment of the nucleation event. A new bubble was generated at the hot end by evaporation of the liquid phase. The original bubble in (a) collapsed with the sudden increase in the system pressure. c The start of the bubble merging process for the new and the original bubble. d The end of the merging process for the two bubbles. At this moment, the combined bubble was still attached to the heater wall. e Progression of the bubble back toward its initial location. f Return of the bubble to its initial location. the local peak pressures, in each nucleation cycle. These peak pressures were not the pressure at the actual nucleation event itself but the point where the newly nucleated bubble and original bubble merged. The nucleation event and growth of the new bubble were too fast for us to record. 119 cycles were observed over the course of 20 h. In Fig. 2b, the data shows that peak 5 5 pressures ranged from 2.6 × 10 Pa to 3.3 × 10 Pa which we now bin into seven wells separated by 0.1 × 10 Pa. 60% of the cycles exhibited peak pressures between 3.1–3.3 × 10 Pa with only four cycles between 2.6–2.8 × 10 Pa. Figure 2c shows the superheat, ΔT, associated with each of these scenarios. The superheat was defined as the temperature difference between the heater wall, T , and the saturation temperature, T , associated with the TC#01 v measured pressure. This latter temperature was determined using Fig. 4 Pressure and temperature profiles for the nucleation event the Antoine equation for pentane. Notice that the superheat shown in Fig. 3. Profiles of the system pressure and the heater wall increased between each nucleation event. The experiment was temperature for the nucleation cycle (09:34:57–09:39:02) illustrated eventually stopped to insure we could revisit the module and in Fig. 3. attempt to run it later as a heat pipe. The details of a single nucleation event were discussed in as showninFig. 3b. The pressure increase associated with the detail in a previous publication ,soonlyabriefreviewis nucleation of the new bubble collapsed the original bubble so provided here. Figure 3 consists of images illustrating the key features of a typical nucleation cycle, and Fig. 4 depicts the that we observed two bubbles simultaneously inside the changes in pressure and heater wall temperature that occurred cuvette (Fig. 3b). In Fig. 4, the new bubble near the heater wall significantly boosted the internal pressure due to strong during this nucleation event. The low thermal conductivity of evaporation. At the same time, it dramatically cooled down the the glass walls coupled with radiation losses from the cell to the surroundings established a large temperature gradient heater wall temperature. The vapor in the original bubble between the hot and cold ends. Strong capillary return flow condensed to accommodate the sudden increase in pressure prevented the vapor bubble from attaching to the heater wall due to nucleation. The decrease in the pressure profile (Fig. 4) (Fig. 3a). The flow at the tail of the bubble is best observed in right after nucleation corresponded to a relaxation following the single nucleation event video in Supplementary Informa- thecollapseofthe original bubble. Theremnant of theoriginal tion. The superheated liquid at the heater wall would bubble then moved towards the new bubble, and the two occasionally promote the nucleation of a vapor bubble there bubbles merged into one (Fig. 3c, d). At the stage of Fig. 3d, the npj Microgravity (2022) 12 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA J. Yu et al. Fig. 5 System pressures and heater wall temperatures. a Pressure profiles for the 7 peak pressure groups at the sampling times of the pressure transducer. The time at the peak pressure is used to align the profiles. b Change of the heater wall temperatures with time for the 7 peak pressure groups. c The minimum heater wall temperatures for the 20 cycles in the 7 peak pressure groups. CVB system behaved similarly to a conventional heat pipe but nucleation. This pressure was very close to the safety cutoff of then the bubble detached from the heater wall (Fig. 3e) and the the system and luckily occurred too fast for the software to pressure began to decrease due to a decrease in the rate of register. Outside of the nucleation event, the rest of the cycle evaporation as the bubble moved toward the condenser end. was slow enough to record and so we characterize the events Thecurvatureofthe corner liquid on theleft-hand side of the using the second peak pressure which occurs when the two bubble is higher than that on the right in Fig. 3dand this bubbles coalesce. established a capillary flow that brought liquid from the Figure 5a, b align the 7 pressure profiles and the heater wall condenser end. This replenished liquid to the hot end and temperature profiles at the peak pressure times (dashed line). From helped separate the bubble from the heater wall. The bubble the different pressures at the coalescence stage, we can infer that migrated back to its starting position (Fig. 3f). Thus, Fig. 3fwas nucleation boosted the system pressure to different levels driven the final state of one nucleation cycle and the initial state of the by an increase in the amount of vapor generated. As mentioned next nucleation cycle. The process is most easily seen in the earlier, the temperature of the heater wall decreased significantly videos that can be found in the Supplementary Information. during the nucleation event because a new bubble was generated We selected 20 out of 119 cycles representing every bin in at the heater end. It is important to notice that the minimum Fig. 2b. We only picked those events where there were clear heater wall temperature in each group generally precedes the peak initial and final stages though in some instances, nucleation pressure at bubble coalescence. This indicates that this peak events, appeared in bursts (see Supplementary Information for pressure was due not only to the initial nucleation event but also a video). Fig. S.1 highlights the 20 cycles we selected for the analysis, and Table S.1 summarizes the basic information of due to evaporation that occurred while the new, single bubble was each cycle. Since there are only 7 peak pressure groups in the attached to the heater wall. The lower minimum value of the histogram of Fig. 2b, we again picked 7 representative cycles to heater wall temperature is found in the higher peak pressure show in the figures. group. In Fig. 5c, the summary of all the 20 cycles shows that the The duration of the nucleation phenomenon in the experi- decrease in the minimum heater wall temperature due to more ment was much faster than any of the experiment’s instruments severe nucleation events (higher peak pressures) prevailed could detect. The sampling rate for the pressure readings throughout the entire experiment. To help quantify this observa- −1 −1 (≈1s ) and temperature readings (≈0.5 s )was nothigh tion, we use a one-dimensional (1-D) heat transfer model to enough to catch the moments of nucleation for all events and determine the heat flow rates to and from the internal walls of the nucleation and bubble merging in the video occurred within device and to calculate a heat transfer coefficient at the evaporator one video frame. It would be difficult to identify,eveninFig. 4, throughout each nucleation event. if the 3.23 × 10 Pa first peak was the real internal pressure at Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 12 J. Yu et al. DISCUSSION surrounding environment (q ); phase change and convective out,rad flow of the working fluid (q ) internally. in The basic structure of the thermal model is similar to a standard fin A differential equation presented in Eq. (1) was derived based with the addition of convection and phase change inside the heat on the control volume in Fig. 6. pipe. The model is inspired by the one originally developed by Bowman and Maynes . Natural convection outside the cuvette is d T 4 4 kA  P hðÞ T  T  σεP T  T ¼ 0 c in in v out neglected due to the microgravity environment. Therefore, three 2 dx |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} (1) |fflfflfflffl{zfflfflfflffl} heat transfer mechanisms are included as shown in Fig. 6: q q in out;rad cond conduction of heat through the glass wall from the hot end to the cold end (q ); thermal radiation from the external surface to the cond Fig. 6 One dimensional heat transfer model geometry. Schematic of the CVB heat pipe with various heat transfer mechanisms. Heat was absorbed by the internal fluid near the hot end but was released near the cold end. Fig. 7 q’ profile and saturation vapor temperature. Two regions with different heat transfer behaviors are identified in the CVB module in based on the position where q’ = 0. a Internal heat transfer profile, q’ , at the initial stage of the nucleation cycle shown in Fig. 3a. in in b Surveillance image showing the physical location where the first q’ = 0 occurs and identifying the absorption and release regions. in c Saturation vapor temperature calculated using the q’ profile and the Antoine equation for the 7 peak pressure groups. in npj Microgravity (2022) 12 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA J. Yu et al. Fig. 8 Average internal heat transfer coefficient, h , and q’ profile at the nucleation stage. a Change of the average internal heat transfer in in coefficient with time in the heat absorption region for the 7 peak pressure groups. The maximum error of the average heat transfer coefficients for the 7 cycles in (a) is 1.34 W/m K. b Internal heat flow rate profile, q’ , at the moment of nucleation, Fig. 3b, in the cycle. c The in maximum average internal heat transfer coefficients for the entire 20 nucleation events in the analysis. Errors are smaller than 0.58 W/m K. In Eq. (1), T represents the saturation vapor temperature, and Figure 7c compares the calculation of T from the two methods for v v h is an average heat transfer coefficient that is used to evaluate the 7 groups. The sampling rate of the temperature data was in the performance of the heat pipe, primarily in the region near the slower than that of the pressure data and so saturation vapor heater end. Although T changed with time as the system temperatures estimated from the q’ profiles may not exactly v in pressured varied, it is assumed to be relatively constant within the mirror the rapid changes in pressure that occur at the time of heat pipe at any moment. The saturation vapor temperature was nucleation or bubble coalescence. Thus, using the q’ profiles, the in estimated from the pressure profile using the Antoine equation, measurements during the time interval between the initial stage Eq. (2), when changes to the operating parameters of the CVB and nucleation stage deviate from the bulk data, and these points system are changing relatively slowly. The parameters for the are located at the higher-pressure regions in the cycle. However, Antoine equation are listed in Table S.2 in the Supplementary the majority of the data points where changes are relatively slow 49,50 Information . are highly matched with the saturation vapor temperatures calculated by the Antoine equation, so the thermal model can T ¼  C still predict and describe the dynamic changes in the CVB system (2) A  log P over most of the event. 0 0 0 A second method was also used to obtain a value for T from v q ¼ q þ q (3) in cond out;rad the q’ profile. By rearranging Eq. (1), we can calculate q’ from in in the other two heat transfer components as shown in Eq. (3). Figure With T determined, h can be calculated from Eq. (1)byan 7a demonstrates the q’ profile at the time of Fig. 3b. The region in v in iterative numerical method using h as the adjustable parameter of the heat pipe where q’ < 0 means heat was gained by the in in to fit the model to the temperature profile. Figure 8a shows these internal fluid from the glass wall and the region where q’ >0 in heat transfer coefficients for the 7 groups as a function of time. means heat was lost by the internal fluid to the glass wall. Thus, the heat pipe, such as it is, can be segmented into two primary The average heat transfer coefficients increased significantly at the sections: a heat absorption region and a heat release region, as peak pressure times and decreased rapidly after the new and illustrated in Fig. 7b. The second point where q’ = 0 corresponds original bubbles merged. Figure 8b presents the q’ profile at the in in to the end of the vapor bubble. The transition point between the peak pressure time corresponding to Fig. 3b. Comparing Fig. 7a two, colored sections, where q’ = 0, provides a value for T within and Fig. 8b, the heat absorbed by the internal fluid is much higher in v the vapor bubble and we use the distance between the location of at the peak pressure times, which verifies the new bubble T and the heater wall as the characteristic length of our device. generated at the hot end by nucleation removed the heat from Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 12 J. Yu et al. Fig. 9 The effect of the temperature gradient and length of the heat absorption region on the average internal heat transfer coefficient. a Average internal heat transfer coefficients as a function of temperature gradients in the heat absorption region. The maximum h values in 7 in group are marked as (▢) representing the nucleation and merge stages (Fig. 3b–d), the h values at t =−50 s are marked as (◁) representing in the initial stage prior to bubble nucleation (Fig. 3a), and the h values at t = 150 s are marked as (▷) representing the final stage once the in bubble returns to the center (Fig. 3f). The three special marker types represent the nucleation and merge stage, initial stage, and final stage of the cycle respectively. b Change of the temperature gradient in the heat absorption region with time. c Average internal heat transfer coefficients versus the length of the heat absorption region. Special markers share the same definition as in (a). the glass wall via evaporation. Meanwhile, in Fig. 8a, the maximum Figure 9a presents the heat transfer coefficients as a function of heat transfer coefficient in each group is shown to occur at the the superheat in the heat absorption region. The maximum heat time of peak pressure for each group. Figure 8c summarizes the transfer coefficient in every group decayed with the superheat but relationship between the maximum heat transfer coefficients and the characteristics of the decay depended on the peak pressure peak pressures for all the 20 cycles analyzed. achieved. At the peak pressure times (t = 0 s), in Fig. 9b, the It is important to notice that the highest heat transfer difference in ΔT for the lowest and highest peak pressure groups is coefficient occurs slightly ahead of the peak pressure time in around 11 K. However, at t = 150 s, the difference in ΔT is around each group because the peak pressure represents the stage of 2 K. Therefore, ΔT for the higher peak pressure group decayed bubble coalescence and not the moment of nucleation which faster with time. After the two bubbles merged, both the pressure absorbs much more heat. Due to the low sampling rate of the and the heater wall temperature began returning to their initial temperature data, there was a lag in time for the maximum heat values in the cycle. Due to the constant heat input and condenser transfer coefficient, reflecting the heat pipe performance at the temperature throughout the entire experiment, the difference in nucleation stage in the heat absorption region. ΔT decreased and the tails of all the 7 profiles converged. The trend in the average heat transfer coefficient for the 7 The heat transfer coefficient is also related to the length of the groups is related to the temperature gradient in the heat heat absorption region, or what we define as the characteristic absorption region for the internal fluid. Fig. S.2 shows the full length for the system. In Fig. 9c, the maximum heat transfer temperature profiles for the 7 groups at the peak pressure times coefficient in each group occurred when the length of the heat near the heater end. Stronger nucleation resulted in higher peak absorption region was the shortest. This coincided with the pressure. Therefore, the saturation vapor temperature was higher longest heat release region for the internal fluid. Following bubble at the peak pressure time for stronger nucleation cycles, and a coalescence, as the system pressure decreased, the saturation longer heat release region was available for heat removal. vapor temperature decreased, the length of the heat absorption Meanwhile, the dramatic evaporation at the hot end significantly region became longer and so the average heat transfer coefficient cooled down the heater wall temperature. In Fig. S.2, the heater decreased with time. wall temperature was lower in the higher peak pressure group The agreement between h and the characteristic length, in (stronger nucleation cycle). Therefore, nucleation in this version of shown in Fig. 9c, suggested that it might be useful to evaluate the the CVB heat pipe was beneficial to its performance, as long as the behavior using dimensionless physical quantities. Inspired by the 51,52 bubble remained attached to the heater wall. analyses in , we found the Ohnesorge number, Oh, seems to npj Microgravity (2022) 12 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA J. Yu et al. and overcame some of the limitations that arose due to the poor thermal conductivity of the working fluid and the glass walls of the system. During nucleation, the heater wall temperature significantly decreased due to increased evaporation, and the more severe nucleation events cooled the heater wall by 20 degrees or more. The heat transfer coefficient was found to be directly related to the characteristic length of the system, defined as the difference in locations between the heater wall and the point in the heat pipe where the wall temperature coincided with the saturation temperature of the vapor. All the heat transfer data were collapsed into a single, linear Nu vs. Oh correlation indicating that viscous, surface, and inertial forces dominated the observed behavior. Reporting summary Further information on research design is available in the Nature Research Reporting Summary linked to this article. Fig. 10 Nusselt number correlation. A universal correlation DATA AVAILABILITY between the Nusselt number and Ohnesorge number. Special The datasets generated and analyzed during the current study are available from the markers share the same definition as in Fig. 9a. corresponding author on reasonable request. The raw data is available through NASA’s Physical Science Informatics (PSI) Database under the CVB experiment. [URL: https://www.nasa.gov/PSI]. describe the competition between viscous forces, surface forces and inertial forces driven by the nucleation event (Eq. (4)). In CODE AVAILABILITY addition, the average heat transfer coefficients and characteristic MATLAB (MathWorks, Inc., Natick, United States) is used to process the data length can be used to define a Nusselt number (Eq. (5)) in the heat presented in this study. A custom script is available from the corresponding author absorption region. upon reasonable request. Oh ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi (4) ðÞ ρσ L Received: 14 July 2021; Accepted: 21 March 2022; h L in (5) Nu ¼ μ, ρ, σ , and k are the dynamic viscosity, density, surface tension, REFERENCES and thermal conductivity of the liquid. Based on data from NIST, 1. Faghri, A. Review and advances in heat pipe science and technology. J. 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Explosive nucleation in microgravity: material in this article are included in the article’s Creative Commons license, unless The Constrained Vapor Bubble experiment. Int. J. Heat Mass Transf. 55, indicated otherwise in a credit line to the material. If material is not included in the 6473–6484 (2012). article’s Creative Commons license and your intended use is not permitted by statutory 44. Bowman, W. J. & Maynes, D. Comparison of standard and heat-pipe fins with spe- regulation or exceeds the permitted use, you will need to obtain permission directly cified tip temperature condition. J. Thermophys. Heat Transf. 15,421–426 (2001). from the copyright holder. To view a copy of this license, visit http://creativecommons. 45. Kundan, A. et al. Thermocapillary phenomena and performance limitations of a org/licenses/by/4.0/. wickless heat pipe in microgravity. Phys. Rev. Lett. 114, 146105 (2015). 46. Kundan, A., Plawsky, J. L. & Wayner, P. C. Effect of capillary and marangoni forces on transport phenomena in microgravity. Langmuir 31, 5377–5386 (2015). © The Author(s) 2022 npj Microgravity (2022) 12 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA

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