Direct-Contact Heat Transfer
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Dahikar et al. In addition, the relationship between the Betti numbers and the heat transfer coefficient has been obtained in a DCHE. Both mixing speed and phase transition time in the direct contact boiling heat transfer process are fast. An accurate mixing time is critical to appropriately evaluate computational fluid dynamics models and then enhances equipment understanding and develops scale down models for process characterization and design space definition during late stage process development.
In the past few years, many researchers have studied the mixing time and many methods were proposed to measure mixing time. But at present, there is no generally accepted method of measuring mixing time, mainly because of each method is not universal, that is each method has its own limitations, such as conductivity [ 24 ], pH [ 25 ], the dual indicator system method [ 26 ], tracer concentration [ 27 — 30 ], electrical resistance tomography [ 9 ], coloration decolouration methods [ 31 ], the box counting with erosions method [ 15 ] and Betti numbers with image analysis [ 32 ].
The limitation of each method has been described in details [ 31 ]. In all of the above-mentioned technologies, the Betti numbers are one of the most worthy methods to measure the mixing time and get further information of the mixing process. The Betti numbers can be effectively quantitative mixing time, the development process of mixing and degree of homogeneity.
It has been used to characterize the evolution of the bubble group in direct contact with the boiling heat transfer process. These indicators change at the beginning of the mixing and quickly tend to be stable after fluctuations. The mixture of non-uniformity caused these fluctuations.
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This is the inevitable process of pseudo-homogeneous critical point to determine the influence accurate estimates of mixing time, which has often been overlooked. A literature survey shows that it is mainly used for determining the critical point of mixing time, including the mean value of Betti number mean method [ 32 ], slope p slope method [ 31 ], and standard deviation SD and the selected threshold [ 33 ]. Accurate estimation about the mixing time of work was published less than others, especially the critical point determination impact.
The idea of a three-sigma method is inspired and motivated by statistical process control SPC. According to Woodall [ 34 ], SPC can commonly be divided into two phases. The data of phase I are clean gathered under stable operating conditions, whereas the major of phase II is to detect any changes. It is imposed to detect outliers in the quality control of samples. Otherwise, the production process is considered to be abnormal.
Homoplastically, a changed three-sigma edit test has been successfully used in distributed self-fault diagnosis algorithm for large-scale wireless sensor networks [ 35 ]. Our research confirmed that the critical point of the response time ignored may result in significant error in mixing time estimation. The mixing process in DCHE has been studied by many experiments.
Similarly, at present, there is no generally accepted way to measure mixing homogeneity, mainly because each method has its own deficiencies, such as thermal method, conduct metric method, pH method, decolourization methods, Schlieren method, Betti numbers method [ 36 ], etc. In all of the above-mentioned technologies, the Betti numbers have been used to characterize the evolution of the heterogeneous and pseudo-homogeneous bubbling regimes.
But, with the Betti numbers for characterization of mixing uniformity have a space-time limitation; it may lead to significant errors in the evaluation of mixing uniformity. The key question is how to measure the random bubble swarm of minimum difference of space-time consistency bubble swarm of domain. Fang and Wang putted forward the concept of UD uniform design that dispersed experimental points uniformly scattered on the domain. One should choose a set of given all possible designs with amount of minimum difference of laboratories under the design of all possible factors and experimental runs.
The above is the basic idea of UD [ 37 ]. UD has been widely used since [ 38 ]. Inspired and motivated by Fang [ 37 — 39 ], our main research objects are the study of characteristics of time-space features and analyse the mixing process of numerical simulation and experimental analysis. Uniform design theory and image analysis have been applied to quantitative uniformity of time and space in a DCHE.
Recently, we were vitalized and motivated by Xu et al. The space-time characteristics can be quantified by means of the uniformity coefficient method, which based on L 2 -star discrepancy UC-LD and provides a method of direct measurement about the macro-mixing evolution.
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With the same Betti number just is aimed to separate the local and global uniform [ 40 ]. Whereas, the nature of the UC such as rotation invariance has not been explored and it has a lot dependence of calculating the initial conditions of UC, namely UC-LD. Clearly, the L 2 -star discrepancy is much easier to calculate numerically according to Heinrich [ 41 ]. Unfortunately, the L 2 -star discrepancy shows some shortcomings, as pointed out by Hickernell [ 42 ]. For instance, it is influenced by all the sub-dimensions of the projection uniformity.
In order to overcome these shortcomings, Hickernell studied uniformity of some new measure methods, which are also associated with the L 2 norm, namely, the centred discrepancy CD and the wrap-around discrepancy WD. The chapter is organized as follows. In the next section, experiments and methodology are presented; the results and discussion are presented subsequently; the conclusion is briefly summarized in this section finally.
Then the acknowledgements and references are presented in the end. The schematic of the experiment employed in the present research is sketched in Figure 1 [ 32 ]. There are two circulation loops in the test device for this experiment. The first loop, which consists of the DCHE 1 , electric heater 2 , heat transfer fluid HTF , pump 7 and connecting inlet and outlet pipelines, is a continuous-phase circulation loop for fluid flow, and the other, which consists of the DCHE 1 , centrifugal pump 4 , plate condenser 5 , centrifugal pump 6 and connecting inlet and outlet pipelines, is a dispersed-phase circulation loop for working medium flow.
The temperature control device, gear oil pump 3 , regulates the initial temperature difference arising from heat exchange. The frequency control cabinet, gas mass flow-meter 8 , regulates the rates of flow of the HTF and working medium. The patterns were imaged by a high-speed shutter video camera, which was placed at the second viewing window. In the bubble evaporation process, we could observe the most active stage of the bubbling regime. HTF and the refrigerant Rfa 1, 1, 1, 3, 3 pentafluoropropane were used as the continuous phase and the dispersed phase in all runs, respectively.
The settings of the experimental plan affecting the heat transfer capacity of the tested DCHE are determined through the orthogonal array OA experimental design method. As listed in Table 1 , design parameters with four factors and three levels were selected to investigate the influence of heat transfer capacity. The L 9 3 4 orthogonal array table was chosen for designing the experiment. The interaction between the design parameters was neglected in the present study. As shown in Table 2 , the numbers E 1 —E 9 denote different experimental levels according to the orthogonal array table.
The images, which were blurred in photographing, can be improved using some image processing techniques. It takes 8 minutes to shoot in each occasion of the orthogonal experiment. Because of difficulties in storing and calculating these images, we choose equal interval sampling from images, in total, 12, images are collected. Figure 2 is randomly obtained in the present image-processing process. In order to suppress the background of the original image, eliminate noise and enhance the image, gray-scale transformation, top-hat transform is used here.
The binaruzation operation was used to calculate the Betti numbers. With a dilation process, an erosion process named as an opening was executed. This process, aiming at removing tiny or isolate points at the finer locations, and smoothing the boundaries of larger points, could not change the size of the image significantly. In contrast, with a dilation erosion process, a dilation process named as an opening was executed.
This operation, aiming at filling up tiny pores within the points, connecting nearby points, and smoothing the borders, could not alter the size of the image significantly. The opening is used here to remove small holes representing sile bubbles or small bubble swarms of the binarization images. Since the behavioural characteristics of bubble swarms could not be accurately portrayed by binarized images with noise, an opening operation must be executed to eliminate image noise by the appropriate thresholds selected.
Thus, the white area indicates the bubble swarm, and the black area refers to the continuous phase. As the experimental conditions, the captured image is relatively fuzzy; however, its quality can be improved by using the digital image processing techniques. The resultant image that could be used for the following analysis was identifiable.
Owing to the complexity of the DCHE multiphase structure, heat exchange performance has often been expressed in terms of the volumetric heat transfer coefficient, h V , which is given by [ 43 ]:. In all the equations, the subscript c refers to the continuous phase, d refers to the dispersed phase, i refers to the inlet, and o refers to the outlet.
As shown in the experiment, some agglomerates still exist in the vessel after stirring for quite a long time. With computational homology, an original analysis method aiming at getting the quantification of the mixture homogeneity and non-homogeneity was proposed.
In a two-dimensional domain, tunnels are reduced to loops. In other words, the mixing effect will vary with the number of pieces in the glass vessel. The time T can be employed to obtain the minimum mixing time. One can easily count these white regions. The calculation of Betti number is difficult, and the methods are only in their early stages [ 44 ]. The free software package CHomP was used to calculate Betti numbers [ 44 , 45 ]. The bubble sizes were found to be almost the same by inspecting many test images. With the pseudo-homogeneous time, the entire visible area was covered by the bubbles [ 36 ].
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Just as we all known, combining the evolution of Betti numbers, we can distinguish whether the distribution is uniform or not. In the beginning, the Betti number increases and then rapidly stabilizes after fluctuations. As Figure 3 shows, a conversion operation of open operation images was performed.