1 Introduction

Today, the high-speed video (HSV) recording has become an almost inalienable part of experimental studies of the process of liquid boiling. Starting from the first papers (Gunter 1951; Lubuntsov et al. 1964; Mamontova 1966; Abdelmessih et al. 1972), the researchers have obtained the video data on the growth dynamics and departure of vapor bubbles, their interaction and the features of crisis phenomena development during boiling of various liquids at different pressures. The obtained information allowed to significantly improve the understanding of nucleation and bubble dynamics and to create new theoretical approaches to describe the bubble growth rate, bubble departure diameter, etc. In addition, the usage of high-speed visualization as a rule allows to analyze and to identify the mechanisms of heat transfer enhancement during boiling using various functional modified surfaces (Zupančič et al. 2017; Surtaev et al. 2018a; Dedov et al. 2019; Sadaghiani et al. 2020).

High-speed video recording of liquid boiling traditionally is performed from the side of heating element. However, as noted by many researchers, such format of visualization has shortcomings. In particular, the activation of numerous nucleation sites at relatively low heat fluxes makes it difficult to identify individual vapor bubbles. More recently, various researchers (Nishio and Tanaka 2004; Garrabos et al. 2010; Gerardi et al. 2010; Surtaev et al. 2018b) have proposed and used the special design of a transparent heating element that allowed to perform the high-speed visualization from the bottom side of the heat exchange surface. Such format of recording makes it possible to study in detail the microlayer region and dry spots evolution and to measure the nucleation site density during boiling over a wide range of heat fluxes. In particular, the analysis of the data obtained from the bottom side visualization during boiling directly on the ultra-smooth sapphire surface allowed the authors (Surtaev et al. 2018b; Surtaev et al. 2020) to show that the dry spots under the bubble grow linearly with time and significantly depend on the pressure and working fluids. At the same time, one of the main problems is processing of a wide array of video data obtained in an unconventional way. For example, to provide a detailed investigation of the vapor bubbles growth and departure, it is necessary to analyze the maximum possible number of bubbles formed in a dynamic process in various nucleation sites over a heating surface. In the case of manual processing of experimental data, such challenge becomes very labor intensive. Moreover, the measurements of void fraction near the heated surface at high heat fluxes by manual data processing become an almost impossible task.

The development of computer and digital technologies can significantly simplify the processing procedures of experimental data, including visual measurements. Automatic HSV images processing using different software algorithms is becoming an increasingly common practice in the research of various two-phase systems (Maurus et al. 2004; Vorob’ev et al. 2012; Strokina et al. 2016; Nguyen et al. 2018; Ronshin and Chinnov 2019; Lobanov et al. 2019). In particular, Maurus et al. (2004) developed an HSV data processing algorithm to study the dynamics of vapor bubbles during water subcooled flow boiling. Using this methodology, a huge number of bubble cycles were analyzed as a result of which the temporal characteristics of bubble evolution were studied in detail. Ronshin and Chinnov (2019) have used the postprocessing of images to characterize two-phase flow in microchannel. The local void fraction, size of characteristic regions of the liquid films on the upper and lower walls of microchannel, frequency of bubble formation, bubble size and other quantitative characteristics have been measured using developed algorithm. Lobanov et al. (2019) used the automated image processing to determine the size of bubbles during bubbly turbulent flow in a pipe with sudden expansion. In addition, one of the tasks in the study of two-phase systems, which is also solved using an automatic image processing, is the measurement of the so-called void fraction (Takenaka et al. 1996; Rana et al. 2014; Gabriel et al. 2018). In recent years for the analysis of high-speed visualization images for various two-phase flows systems, neural networks are also actively developed, one of the stages of which is the processing of input images (Yan et al. 2018; Abdurakipov et al. 2019; Fu and Liu 2019). At the same time, there is no universal automatic algorithm which can be used to analysis of the data obtained by using HSV from the bottom view at boiling on the transparent heating element. Therefore, the aim of the present study was to develop automatic processing algorithm for determination of the basic characteristics of the vapor bubbles evolution and void fraction near a heated wall during liquid boiling. For automatic processing, HSV dataset obtained in experiments from the bottom side of a transparent heating element at water boiling in a range of pressure down to 5.5 kPa was used.

2 Measuring and image processing techniques

2.1 Experimental setup and test section

To study the effect of system pressure on vapor bubbles evolution during pool boiling, the experimental setup described in detail in Surtaev et al. (2020) was used. This setup consists of two sealed vessels inserted one inside another. To maintain a constant temperature of the working liquid, the boiling chamber is mounted in the isothermal bath with two electric preheaters. The setup is vacuumed according to DIN 28400-3:1992-06 standard. The inner chamber was evacuated through a valve and a liquid nitrogen cold trap connected to the vacuum pump «EVP» 2XZ-1C at its top. To eliminate the effect of pressure increasing during boiling, the working volume was equipped with water-cooled condenser. The value of the system pressure was calculated based on the indications of the «Thyracont» VD81 vacuum gauge (p) taking into account the influence of hydrostatic pressure of a liquid column over the heater: ps = p + ρlgH. The experiments were performed for ps value varying in the range from 5.5 to 103 kPa. In the experiments, MilliQ by «Merck» deionized water on the saturation line for a given pressure ps was used as a working fluid.

In the experiments, sapphire substrate of 60 mm in diameter with electro-conductive indium–tin oxide (ITO) film deposited by ion-plasma sputtering on its bottom side was used as the heating element (Fig. 1). The thicknesses of the sapphire substrate and ITO film heater were 3 mm and 1 μm, respectively. As it is noted in a number of researches, the advantage of the usage ITO as heater material in experiments devoted to the investigation of local and integral characteristics of heat transfer at nucleate boiling is its transparency in the visible wavelength range (380–750 nm) and opacity in the IR range (3–5 μm). At the same time, sapphire transmission in the wavelength range of 0.3–5 μm exceeds 80%. The combination of these properties makes it possible to measure non-stationary temperature field of the ITO film surface by infrared camera and to visualize the evolution of vapor bubbles and dry spots by high-speed video camera (Gerardi et al. 2010; Surtaev et al. 2018b; Serdyukov et al. 2018).

Fig. 1
figure 1

The scheme of the transparent heating element used in the experiments

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Samples were resistively heated (Joule heating) by the DC power supply «Elektro Automatik» via thin silver electrodes vacuum deposited onto the ITO film. The heat flux density was calculated as q = V·I/A, where I is the current through the thin film heater and V is the voltage drop on it. The heating area in experiments was A = 28 × 30 mm2.

2.2 Image acquisition and processing

The visualization of water pool boiling was performed using high-speed monochrome digital video camera Phantom by «Vision Research» from the bottom side of transparent heater, as shown in Fig. 1. As it will be shown below, such visualization format made it possible to study in detail the dynamics of growth and departure of vapor bubbles with varying pressure, as well as to investigate the behavior of two-phase flow near a heating surface during sub-atmospheric boiling. The HSV camera used in the experiments has 800 × 600 pixel SR-CMOS monochrome sensor with 4800 ISO/ASA sensitivity. The experiments were conducted with the frame rates of 4000 fps at 800 × 600 and 10000 fps at 512 × 384. To increase the spatial resolution of video recording, Nikon 105 mm f/2.8G macro-lens with 1:1 magnification was used. The maximum field of view during the experiments was 28 × 21 mm2, and the depth of field was about 4 mm, which was enough to simultaneously measure the areas of the dry spots and diameters of the bubble base with sizes less than the dimension of the heating surface during boiling at different pressures. To calculate the spatial resolution of the imaging system used in the study, the measurement of the diameter of a calibrated flat washer placed directly on the surface of sapphire substrate was made. The maximum spatial resolution of video recording in experiments was 35 μm per pixel.

The programs of automatic HSV images processing were developed in the MATLAB environment. The video data processing was performed using two programs based on the use of the functions of the MATLAB Image Processing Toolbox extension package, using various algorithms to determine the diameters of the circles on an image. The first algorithm (hereinafter referred to as Gradient) is based on the areas selection according to the brightness gradient of an image using the Sobel–Feldman operator (Sobel filter). After targeting the borders, a gradient image is binarized. The determination of the circles on an image is realized by calculating the ratio k of the areas of simply connected regions to the square of their perimeter: k = S/P2. Since for a circle this value takes a maximum value of 1/(4π), therefore the regions for which the ratio k is ≥ 0.9·1/(4π) are automatically marked as circles. In turn, their diameter, i.e., the desired size of the vapor bubbles, is determined as Db = 2·(S/π)0.5.

The second method is based on the Hough transform to determine circles (Yuen et al. 1990; Atherton and Kerbyson 1999; Davies 2012). This method is implemented in the imfindcircles MATLAB function, which returns the coordinates of the centers and the radii of circles in an image. The main advantage of this method is its ability to detect not only closed, but also open, incomplete circles on a grayscale image, which increases its robustness compared to the previous method. To track the evolution of each individual vapor bubble in both used programs, automatic matching of bubbles on two subsequent frames was implemented. The essence of this technique is that the circle on the current frame is identified with corresponding circle on the previous one only if the center of the old circle lies within the boundaries of the circle on the new frame.

In addition, the program that allows to estimate the evolution of the void fraction near a heated wall during boiling at sub-atmospheric pressures was developed using the Image Processing Toolbox functions. To do this, the boundaries of the bubbles were determined from the brightness gradient in an input HSV image, after which their inner region was automatically filled up and areas were automatically calculated and summed up. The result of the used image processing algorithm was derived as the ratio of the total area of the filled regions Ao and a heating surface A at a given moment.

2.3 Uncertainty analysis

The error of the measurement of the system pressure ps value in experiments was ± 0.5 kPa. The measurement error of the input heat flux density q is composed of the errors of measure of the current through the heater I, the voltage drop V on it and the area of the heating surface A: q = V∙I/A. Thus, the relative error in measuring the value of q was less than 5%. Furthermore, the estimations of heat losses for heated sapphire sample that did not exceed 8% were carried out. To verify the heat flux density measurements, test experiments were conducted with saturated water under atmospheric pressure at the heat fluxes corresponding to the natural convection mode without nucleate boiling. Comparison with the McAdams' model (McAdams 1954) showed that a discrepancy between experimental and calculated data is within 10%, which means that the heat losses were correctly evaluated. The total error of the heat flux density measurement did not exceed 13%

In the case of manual image processing, the geometry parameters of vapor bubbles were measured by counting pixels in a captured frame of video recording. Therefore, the measurement error is determined by the spatial resolution of the imaging system and by the uncertainty of the definition of bubbles edges. As the result, the total error can reach ± 100 μm. The accuracy analysis of the developed HSV image processing programs was carried out by measurements of the sizes of flat washers of various diameters (5, 10 and 20 mm) placed directly on the sapphire surface. It was shown that the developed algorithms can measure the sizes of specified objects with high accuracy and a maximum error not exceeding 70 µm.

3 Results and discussion

3.1 Bubble dynamics at boiling at various pressures

Figure 2 presents the frames of high-speed visualization of water boiling obtained from the bottom side of a transparent heater at various pressures ps and a given heat flux density of q = 60.5 kW/m2. It can be seen that such high-speed visualization allows to analyze the evolution of vapor bubbles and to obtain the information about such internal boiling characteristics as the growth rate and departure diameter of vapor bubbles, their lifetime and the nucleation site density. In addition, as was noted in introduction, this recording format allows one to study the evolution of dry spots formed at the base of vapor bubbles. A detailed analysis of the evolution and growth rate of dry spot at water boiling with varying pressure is presented in Surtaev et al. (2020).

Fig. 2
figure 2

Frames of high-speed visualization of water pool boiling at various system pressures ps, obtained from the bottom side of a transparent heater

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The analysis of the HSV frames shows that pressure reduction significantly affects the pattern of liquid boiling. First of all, with decreasing pressure, the number of nucleation sites decreases, and the size and lifetime of vapor bubbles, instead, increase. For example, for atmospheric pressure (ps = 103 kPa) at a presented heat flux, about ten bubbles with a diameter of less than 6 mm are observed on the surface. The pressure reduction to ps = 42 kPa leads only one vapor bubble, the size of which can reach 13 mm, to form on the heating surface. At a pressure ps = 8.8 kPa, the growth rate of the vapor bubble increases significantly that led, during short time (less than 8 ms), the diameter of the bubble to become larger than the size of the heater.

Figure 3 shows the original frames of high-speed video recording of boiling water at various pressures and the results of their processing using two different algorithms (Gradient and Hough Transform). The boundaries of vapor bubbles, automatically marked by the subprogram for evolution tracking for each individual vapor bubble, are shown by red dotted lines. As can be seen from the figures, both developed programs quite accurately find and determine the boundaries of bubbles, which allows to trace the evolution of an entire ensemble of vapor bubbles during boiling at various pressures. The main difference of the developed programs consists in the following fact. When the imfindcircles function of the Hough Transform program is used, the desired circles (i.e., vapor bubbles) are immediately marked in the original image, without its binarization, as in the case of the Gradient algorithm. A comparative analysis also shows that the Hough transform-based program detects bubbles, including at the stage of their direct departure, when their shape begins to differ from the circle. In addition, as can be seen from the frames for the case of boiling at atmospheric pressure (Fig. 3b, 2 ms), the Hough Transform program detects individual vapor bubbles even in the case of their boundaries interaction.

Fig. 3
figure 3

The original and processed by the developed image processing programs HSV frames of water pool boiling (q = 60.5 kW/m2) at a ps = 42 kPa and b ps = 103 kPa

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In Fig. 4 the numerical results of the automatic video data processing, as well as the results of manual processing of the size of a vapor bubble at the stage of its growth and departure during water boiling at the pressure ps = 42 kPa are presented. The comparative analysis shows that the dependencies obtained by using automatic processing are in good agreement with the results of manual processing. The slight differences are observed at the initial stage of the bubble growth (up to 2 ms, Fig. 4) and at the stage of its departure, when the diameter of the bubble base remains almost constant (starting from 12 ms, Fig. 4). In particular, it is clear that the Hough transform determines the diameter of the just appeared bubble with higher accuracy, while the Gradient program at this stage does not distinguish bubble boundary and, as a result, is unable to find the bubble. This may be due to the insufficient contrast of an original image for its correct binarization procedure. On the other hand, the Gradient program gives a more accurate result at the stage of bubble departure, on which the bubble loses its spherical shape due to boundary fluctuations. The algorithm based on the Hough transform originally does not have the ability to take into account possible deviations of a vapor bubble boundary from the circle shape and gives an incorrect result, displayed in Fig. 4 as the fluctuations of Db value.

Fig. 4
figure 4

The comparison of the work of developed HSV data processing programs for a bubble growth curve analysis (ps = 42 kPa, q = 60.5 kW/m2)

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Therefore, the selection of image processing algorithm for HSV recording of the nucleate boiling depends on the research task. To determine the values of the bubble departure diameter, it is more advisable to use the binarization procedure of an image with the subsequent areas selection by the brightness gradient. In the case of analysis of the nucleation and growth rates of vapor bubbles at the initial, the so-called inertial growth stage, it is more correct to use the imfindcircles function of the Hough Transform program.

Figure 5a shows the growth curves obtained using automatic image processing based on Hough Transform algorithm for an ensemble of vapor bubbles formed during boiling at atmospheric pressure (ps = 103 kPa, q = 60.5 kW/m2). It can be seen from the figure that the growth rate and the maximum size of vapor bubbles for different nucleation sites, activated at various times, can noticeably differ from each other. As was shown by Surtaev et al. (2018b) based on the analysis of high-speed infrared thermography data, this is due to the difference in the boiling incipience temperature for various nucleation sites.

Fig. 5
figure 5

The results of the automatic HSV images processing for large ensemble of vapor bubbles at atmospheric water boiling (ps = 103 kPa, q = 60.5 kW/m2): a the bubbles growth curves; b the distribution of the bubble departure diameter value

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As follows from Fig. 5a, for a correct description of the bubble departure diameter during nucleate boiling, it is necessary to conduct a detailed statistical analysis for various nucleation sites. In the present study using the Gradient program, such analysis was performed for a large ensemble of vapor bubbles. Figure 5b presents a histogram of the distribution of the Ddep value for an ensemble of 80 bubbles for given ps and q. The value of Ddep was determined at the moment of vapor bubble departure from the surface, which is accompanied by collapse of the triple contact line and complete rewetting of the dry spot under the bubble’s base (Surtaev et al. 2018b). It can be seen that the obtained data distribution is well described by the normal distribution, with the data dispersion up to 100%.

Based on the automatic processing of HSV images using the Hough Transform program, the effect of pressure reduction on the growth dynamics of individual vapor bubbles was analyzed. For this, a statistical analysis of the growth curves for the ensemble of bubbles was carried out for each studied pressure. The obtained typical curves of bubble growth are shown in Fig. 6a. It can be seen from the graph that, with pressure reduction from 103 to 8.8 kPa, the bubble growth rate and its size increase significantly. In addition, using the Gradient program, the average values of the bubble departure diameter for various pressures were obtained (Fig. 6b). For calculation of the bubble departure diameter at system pressure less than 20 kPa, the frames of high-speed visualization from the side view of heating surface were used. Presented graph indicates that the Ddep value also significantly increases with pressure reduction.

Fig. 6
figure 6

The pressure influence on a the vapor bubbles growth curves and b their departure diameters at water pool boiling (q = 60.5 kW/m2)

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The analysis of the presented results shows that the developed automatic images processing programs for HSV from a bottom side of a transparent heater have allowed to significantly simplify and facilitate the process of the video data processing and following their analysis. As a result, a wide range of experimental dependences which described the influence of the pressure on the bubbles growth rate and departure diameters during boiling was obtained. In the future, it is planned to improve the algorithm with the option of measuring an areas of the dry spots and the temporal characteristics of the bubble dynamics, such as the waiting time for the bubble appearance at individual nucleation site and the nucleation frequency in automatic mode.

3.2 Features of boiling at low sub-atmospheric pressure ps = 5.5 kPa

Recently, Giraud et al. (2015) found that during saturated water pool boiling at pressure of ps = 1.2 kPa, the departure of massive vapor bubble from a heating surface is accompanied by the appearance of numerous small bubbles. Over time, the size and frequency of such bubbles decrease until the vaporization is completely stopped. After the waiting period, a large vapor bubble appears again on the surface and the process repeats. The authors called this regime as “cyclic boiling regime” implying that the nucleation cycle can restart as soon as described “bubble crisis” ends. At the same time, the quantitative analysis and underlying mechanisms of this boiling regime remain unresolved problems.

In the present study, similar boiling behavior was observed during pool boiling experiments at the pressure of ps = 5.5 kPa (Fig. 7a). It is necessary to note that in these experimental conditions, the hydrostatic pressure of the liquid column over the heating surface becomes comparable with the external pressure in the system. From the HSV images obtained from the bottom side of the transparent heater and shown in Fig. 7a, it can be seen that after the departure of massive vapor bubbles (1, 2), numerous bubbles with smaller sizes are formed all over the heating surface (3). After a certain time, the bubbles disappear, the nucleation process ends and the heating surface becomes almost free of the vapor (4). After this “respite” the formation of numerous vapor bubbles with the sizes lower than the size of the first massive bubbles starts again (5) and (7). Such regime of extensive periodic boiling is happening over a time significantly exceeding the lifetime of the first large bubbles. After its completion and waiting time, similar to Giraud et al. (2015), activation of new massive bubbles happens, and the described cyclic boiling regime repeats. Apparently, such pulsating character of boiling occurs due to pressure fluctuations in the working volume caused by the rapid growth and departure of massive vapor bubbles which in turn can lead to a change in the saturation conditions near the heated wall. It can be assumed that in the period between the moments with the maximum values of the void fraction, the liquid near the heated wall is subcooled, which leads to the observed deactivation of nucleation sites and a sharp decrease in the relative void fraction, which will be shown below. This assumption is confirmed by the analysis of high-speed visualization from the side view, which showed that after the appearance and growth of vapor bubbles at a certain moment, they begin to intensively condense over the entire surface of the heater. At the same time, for better understanding of the physics of this regime it is necessary to carry out further detailed theoretical analysis, as well as additional experimental studies that would allow to measure the pressure near the heated wall and the unsteady temperature field in the liquid using such methods as two-color LIF (Voulgaropoulos et al. 2019) and rainbow schlieren technique (Narayan et al. 2019). Also in the future experiments, it is necessary to pay the special attention to the influence of the liquid level and hydrostatic pressure of the liquid column on this pulsating boiling mode.

Fig. 7
figure 7

a The original images of HSV and b the results of their automated processing for water pool boiling at ps = 5.5 kPa (q = 80 kW/m2)

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With the use of developed HSV images processing program (Fig. 7b), we have proposed a method to describe the periodical behavior of this pulsating boiling regime using experimental data on the evolution of the void fraction near the heated wall. Since the shape of the bubbles formed during “cycle boiling regime” is far from spherical, in this case the simplified Gradient program without the function of determining circles was used. From Fig. 7b, it can be seen that the used algorithm well distinguishes areas near the heated wall occupied by vapor.

Figure 8 shows the obtained time dependence of the relative void fraction near the heated wall estimated by the measurements of the areas occupied by vapor A0/A. Moments in time marked on the graph corresponding to HSV frames presented in Fig. 7. It can be seen that at the initial stage, two massive bubbles consecutively form, occupying almost the entire heating surface (A0/A > 0.9). After the departure of the second one, the reduction of the maximum value of relative void area up to the A0/A = 0.3—0.5 with alternating peaks of the minimum (A0/A < 0.1) is observed. Thus, a cyclic change in the void fraction near the heated wall occurs. From the presented graph, it becomes possible to determine the period of fluctuations of the A0/A value after the departure of the massive bubble and to estimate the characteristic frequency of observed cyclic boiling behavior. In particular, for the case shown in Fig. 8 it is about 15 Hz.

Fig. 8
figure 8

The evolution of the void fraction close to a heating wall during water pool boiling at ps = 5.5 kPa (q = 80 kW/m2)

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Thus, the results of the present study show that the usage of a transparent heater design and the developed HSV data processing programs allows to analyze the void fraction evolution during boiling in a wide range of operating parameters. In particular, using this approach it becomes possible to study the behavior of a liquid–vapor system at ultra-low pressures, which, as the authors hope, will help to shed light on the mechanisms of pulsating boiling regime in future.

4 Conclusions

With the use of the special designed transparent heating element based on thin ITO film deposited onto a sapphire substrate and high-speed visualization from its bottom side, the evolution of vapor bubbles and void fraction near the heated wall during water boiling in the pressure range from 5.5 to 103 kPa was studied. To analyze the obtained wide set of video data, the algorithms for automatic image processing were proposed and described, which allow to determine the interfacial boundaries and to trace individual vapor bubbles. As a result, a detailed statistical analysis of the growth curves and departure diameters for bubbles formed in different nucleation sites during boiling at various pressures was carried out. In particular, it was shown that with a pressure reduction, the increase in the growth rate of vapor bubbles and their departure diameter occurs. For analysis of bubble growth especially on initial stage, it is better to use the Hough Transform algorithm, while the Gradient program is more preferable when analyzing the bubble departure diameters. In experiments at low sub-atmospheric pressure of 5.5 kPa, the pulsating boiling regime after the departure of massive vapor bubbles has been detected. It is shown that suggested algorithm based on the measurements of evolution of void fraction near the heated wall allows to describe the cyclic boiling regime and to determine the characteristic frequency of this process.

The presented results show the high promise of the high-speed visualization from the bottom side of a transparent heater to determine the main characteristics of bubble dynamic during liquid boiling at various pressures. The automatic study image processing algorithms developed in the study allow to significantly reduce the visual data processing time. We hope that the observed at low sub-atmospheric pressure pulsating boiling regime would draw attention of researchers to clarify this phenomenon.