Proceedings of the ASME 2017 Power Conference Joint With ICOPE-17 POWER2017-ICOPE-17 June 26-30, 2017, Charlotte, North Carolina, USA
POWER-ICOPE2017-3084
VISUALIZED MEASUREMENT ON EVOLUTION OF BUBBLE PATTERNS IN A DIRECT-CONTACT HEAT EXCHANGER
Qingtai Xiao State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization Kunming University of Science and Technology Kunming, Yunnan, 650093 PR China Email:
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Shibo Wang State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization Kunming University of Science and Technology Kunming, Yunnan, 650093 PR China Email:
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Jianxin Xu∗ State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization Kunming University of Science and Technology Kunming, Yunnan, 650093 PR China Email:
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Hua Wang State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization Kunming University of Science and Technology Kunming, Yunnan, 650093 PR China Email:
[email protected]
ABSTRACT Direct-contact heat exchanger involves the exchange of heat between two immiscible fluids at different temperatures. Considering that there is a linear relationship between the flow patterns of a bubble swarm and heat transfer coefficient, it is inevitably to investigate the evolution of flow patterns for heat transfer enhancement in different mixing systems. However, the dynamical complexity and random variability of multiphase flow have put forward a severe challenge to improve the accuracy and realtime performance of visualized measurement of multiphase flow. The entropy of an image shows its quality objectively. Generally speaking, if the value of image entropy is large enough, then the mixing uniformity is good enough. Hence, in this paper, image entropy is used to assess the mixing uniformity and estimate the homogeneous time in the direct-contact boiling heat transfer process. The evolution of bubbles movement is experimentally tracked using an imaging technique. Variations in time of im-
∗ Address
age entropy values bring new insights to study and compare mixing performance of different direct-contact heat transfer process. The results show the evolutions of bubble patterns in a directcontact exchanger have been successfully visualized measured.
INTRODUCTION Mixing is an essential unit operation in the chemical and metallurgical industries. It has a decisive impact on the overall performance of reaction processes. Without good mixing, operation costs can be higher. Hence, the efficient evaluation of mixing effects is required [1]. Direct-contact heat transfer is one of the most efficient kinds of boiling heat transfer processes widely used in water desalination, geothermal heat recovery, ocean thermal energy conversion, thermal energy storage systems and other numerous engineering systems [2, 3]. Homogeneous and heterogeneous are two main bubbling regimes in the direct-contact heat transfer process [4].
all correspondence to this author.
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FIGURE 1.
DIRECT-CONTACT HEAT EXCHANGER
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
FIGURE 2.
Industrially, the regimes are less likely prevail easily. Huang et al. (2014) presented a good description of the characteristics of the entire flow pattern in a direct-contact heat exchanger and contributes to quantify the relationship between bubble swarm patterns and heat transfer performance [5]. In our previous work [6], a image analysis technique was employed to compute the p-values for bubble images comparison, by means of some statistical hypothesis-testing tools including KolmogorovSmirnov test and χ 2 test. In addition, the different experimental cases with the same Betti numbers can be identified by using the hypothesis-testing method [6]. These experimental works have been devoted to investigate the mixing process in a direct-contact heat exchanger. Moreover, the notion of entropy was used to measure the amount of image information [7, 8]. Entropy theory was also used to assess phylogenetic relationships of Lycium samples [9] in the field of mathematical statistics. Image entropy has been applied in the field of engineering geology [10]. Furthermore, the time and spatial heat transfer performance and the transition process to chaos in a uniform and directed flow were also reported [11]. The 0-1 test method [12], which is based on Euclidean extension instead of a phase space reconstruction to investigate the chaotic characteristic of the data, has been successfully and generally applied to theoretical time series or any other types of dynamical systems, as well as real experimental data [13, 14]. Inspired and motivated by these studies in the literature, the key issue to be addressed then is how to measure and compare the space-time uniformity of random bubble swarm. The image entropy method [15] is used to quantify the evolution of boiling bubbles in this article. The rest outline of the article is organized as follows. In the next section, experimental equipment for direct-contact heat transfer and methodology ,i.e. the image entropy method, are presented. The the results and discussion are presented in Section 3 while the summary and conclusions are briefly summarized in Section 4 finally.
TREATMENT FOR THREE BUBBLE IMAGES
Experimental and image entropy Direct-contact Heat Exchanger A general overview of the setup used to perform the directcontact heat transfer experiments is shown in Fig. 1. There are 10 main experimental pieces of equipment, including pressure gauges (2), thermometers (3), inlet (10) and outlet (1) pipelines of dispersed phase, inlet (7) and outlet (9) pipelines of continuous phase, the viewing window (4), nozzles (8), level gauge (6) and K-type thermocouple (5). The bubble images were obtained by high-speed video camera. The heat transfer fluid was used as the continuous phase, and refrigerant R-245fa (1,1,1,3,3 pentafluoropropane) was used as the dispersed phase in all runs. Some more specific details of this experimental setup for direct-contact heat transfer and design parameters with different cases can been seen in references [16, 17]. Image Entropy Method A function of an image is to pass information; thus information theory can be play an important role [18]. The notion of entropy was used to measure the amount of image information [19]. Assuming that levels of a bubble image follow a multinomial distribution [20], the entropy of a P · Q image [19] is defined as
255
IE = −P · Q · ∑ πg · log2 πg
(1)
g=0
In algebraic topology, the first Betti numbers β1 provides a measure of the number of tunnels in the structure [21], which can be applied to quantify the quality of multiphase mixing [22]. However, Betti numbers does not take the position and size of object into consideration [23].
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TABLE 1.
THE PARAMETER AND DATA OF THREE IMAGES
Mixing transient
Initial
Midterm
Final
Betti numbers (i.e. β1 )
93
205
176
Image entropy values
5.1029
5.6796
6.2631
Results and discussion Bubble image processing The sample images chosen from patterns in the mixing process is shown in Fig. 2. These include the original images (i.e. Fig. 2a, Fig. 2b and Fig. 2c) and gray-scale images (i.e. Fig. 2d, Fig. 2e and Fig. 2f). Three color images of bubble swarm came from initial (see Fig. 2a), midterm (see Fig. 2b) and final (see Fig. 2c) mixing process, respectively. The white spots (blobs) are bubble swarm in Fig. 2d, Fig. 2e and Fig. 2f. RGB values C can be converted to gray level values by forming a weighted sum of the red (R), green (G), and blue (B) components:
C = 0.2989 · R + 0.5870 · G + 0.1140 · B
FIGURE 3.
EVOLUTION OF IMAGE ENTROPY VALUES
Chaos detection using 0-1 test Chaos is a common phenomenon in nature [25]. Chaotic characteristics of the image entropy values are analyzed in this section. According to the results of the 0-1 test for chaos detection as applied to our case, the plane of pc (n) versus qc (n) does not show a Brownian motion-like behavior. In addition, Dc (n) is not linearly correlated with n. Quantifying above inference using the correlation coefficient method, Kc ≈ 0 which reflects this system is not chaotic was obtained.
(2)
Hence, the reduction of the original color bubble image to gray level image is such that every bubble image corresponded to one integer matrix. The matrix consists of 921,600 elements within a set of {0, 1, 2, · · ·, 255}. Mixing uniformity evaluation In our work, a new index (IE) has been obtain by Eqn. 1. Experiments confirmed that Betti numbers could result in significant errors in mixing uniformity evaluation. In Tab. 1, the computing results show that the evaluation values of mixing uniformity by image entropy method are much better than the Betti numbers method [24]. The reason why Betti numbers experienced an inverse transition change is mainly because of the coalescence of bubbles. Moreover, quantitative comparisons of the homogenization curve using the image entropy method was conducted with the reported experimental data. As shown in Fig. 3, an interesting tendency occurs in experimental case L8 (i.e. the height of heat transfer fluid H=600 mm, the initial heat transfer temperature difference ∆T =100 K, the refrigerant flow rate Ug = 1 × 104 m3 /s, and the flow rate of the heat transfer fluid U0 =0.3 kg/s). It is clearly observed that the entropy values obtained from images taken regularly from the beginning of mixture to the end increase at the beginning and then rapidly becomes stabilized after fluctuations. Hence, the variation of the image entropy values with time t can be an effective method to determine the critical mixing time and mixing uniformity.
Conclusions In this study, the mixing uniformity in a direct-contact heat exchanger was investigated using an image analysis technique, i.e. the image entropy method. It presents an alternative route to explore bubble regime. Generally speaking, if the value of image entropy is large enough, then the mixing uniformity is good [enough] as well. Variations in time of image entropy values bring new insights to study and compare mixing performance of different direct-contact heat transfer process. In addition, the image entropy dynamics was also characterized.
ACKNOWLEDGMENT Thanks are due to Jianxin Pan and Wuqiang Yang from The University of Manchester for valuable discussion and essential help. The authors are also grateful for financial support from the National Natural Science Foundation of China (Grant Nos.: 51666006 & 51406071), Scientific and Technological Leading Talent Projects in Yunnan Province (No.: 2015HA019) and Foundation of Yunnan Province (No.: E060503). Authors wish to extend special thanks to anonymous reviewers for numerous
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detailed questions and constructive comments that greatly improved the presentation.
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