**Direct-Contact Heat Exchanger Direct-Contact Heat Exchanger**

Hua Wang, Qingtai Xiao and Jianxin Xu Hua Wang, Qingtai Xiao and Jianxin Xu

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/66630

#### **Abstract**

Direct-contact heat transfer involves the exchange of heat between two immiscible fluids by bringing them into contact at different temperatures. There are two basic bubbling regimes in direct-contact heat exchanger: homogeneous and heterogeneous. Industrially, however, the homogeneous bubbling regime is less likely to prevail, owing to the high gas flow rates employed. The mixture homogeneity and the non-homogeneity of the mixture can be characterized by the Betti numbers and the mixing time can be estimated relying on image analysis and statistics in a direct-contact heat exchanger. To accurately investigate the space-time features of the mixing process in a direct contact heat exchanger, the uniformity coefficient method based on discrepancy theory for assessing the mixing time of bubbles behind the viewing windows is effective. Hence, the complexity of the bubble swarm patterns can be reduced and their mechanisms clarified, and the heat transfer performance in a direct-contact heat exchanger can be elucidated.

**Keywords:** direct-contact heat transfer, flow pattern, Betti numbers, discrepancy, mixing uniformity

### **1. Introduction**

#### **1.1. Direct-contact heat exchanger**

Direct transfer involves two immiscible fluids under different temperatures in contact for heat exchange [1]. Compared with the traditional direct-contact heat exchanger, heat transfer means has more advantages due to a more simple design, low temperature driving force and higher heat transfer efficiency [2, 3]. Direct-contact heat exchangers (DCHEs) make use of gas-liquid phase change heat exchanger within the working fluid. That is to say, DCHEs put to use heat transfer between two kinds of fluid in the absence of a partition. A direct contact heat exchanger can be used for seawater desalination, heat recovery, ocean thermal energy conversion, thermal energy storage systems, etc.[4, 5]. In addition, DCHEs have been applied

to give a good solution in harnessing the solar energy [6] and provide a better understanding of ice formation, growth and detachment from the droplets producing ice slurry [7].

#### **1.2. Mixing efficiency assessment**

Mixing plays a fundamental role in many industrial applications, such as chemical engineering, metallurgical process, printing process, medical and bio-medical industries, and has a decisive impact on the overall performance of reaction processes. The purpose of mixing is to obtain a homogeneous mixture; however, many researchers have pointed out that the local mixing and the flow pattern has significant effects on the properties of the final products [8]. There is an increased want for measuring and comparing mixing performance. An efficient evaluation of mixing effects is required in those various fields, but as a result of its intricacy, theoretical methods are very limited. Monitoring or measuring the mixing appropriately is of much concern from the practical point of view and for the confirmation of theoretical models as much [9]. The existence of a second phase that makes the continuous phase flow and mixing process more complicated, especially for a direct contact with the boiling heat transfer process. The boiling heat transfer process, in which mixing efficiency assessment is common, is one of the most efficient kinds of heat transfer processes widely used in numerous engineering systems. Hence, the work of characterizing the homogeneous bubbling regimes in a DCHE is one of the most useful and instructive topics in DCHE.

#### **1.3. Bubbling regimes**

There are two basic types of bubbling regimes in DCHE: homogeneous and heterogeneous. In the homogeneous bubbling regime, there are few diversifications in the size of the bubbles, and breakage and coalescence phenomena are inappreciable [10–12]. Industrially, nevertheless, the homogeneous bubbling regime is not likely to prevail, thanks to the high gas flow rates used. This is good for the heterogeneous bubbling regime, characterized by a widespread of bubble sizes and crucial frequencies of breakage and coalescence [13]. For an air-water system, Ribeiro and Lage [13] employed transient experimental measuring of the temperature of the liquid, bubbling height, evaporation rate, gas volume fraction and bubble size distributions in a direct-contact evaporator for four surface gas velocities including operation in both homogeneous and heterogeneous bubbling regimes. Ribeiro et al. [14] also analysed the photographs of homogeneous and heterogeneous bubbling regimes using different liquids in a DCHE handling with a perforated-plate sparger. Le Coënt et al. [15] studied the compounding of two staves and a viscous liquid in a classical reactor. He found that there was an alleged "pseudohomogeneous" state before it was mixed completely homogeneously. In reality, a pseudohomogeneity was achieved much more quickly (<40 s), but subsequent images revealed that polymers still remained in the reactor. The time of the pseudo-homogeneous state begins is called the pseudo-homogeneous time. In our DCHE, we found that there was a comparatively stable state in the completely heterogeneous bubbling regimes also. Consequently, we defined this completely stable state as pseudo-homogeneous. Peyghambarzadeh et al. [16] found that bubble growth was a considerably complicated process, and detecting distinguishable bubbles was scarcely possible at high heat fluxes, while in this experiment, we have captured the rough sketch of bubbles.

#### **1.4. Image analysis**

to give a good solution in harnessing the solar energy [6] and provide a better understanding

Mixing plays a fundamental role in many industrial applications, such as chemical engineering, metallurgical process, printing process, medical and bio-medical industries, and has a decisive impact on the overall performance of reaction processes. The purpose of mixing is to obtain a homogeneous mixture; however, many researchers have pointed out that the local mixing and the flow pattern has significant effects on the properties of the final products [8]. There is an increased want for measuring and comparing mixing performance. An efficient evaluation of mixing effects is required in those various fields, but as a result of its intricacy, theoretical methods are very limited. Monitoring or measuring the mixing appropriately is of much concern from the practical point of view and for the confirmation of theoretical models as much [9]. The existence of a second phase that makes the continuous phase flow and mixing process more complicated, especially for a direct contact with the boiling heat transfer process. The boiling heat transfer process, in which mixing efficiency assessment is common, is one of the most efficient kinds of heat transfer processes widely used in numerous engineering systems. Hence, the work of characterizing the homogeneous bubbling regimes in a DCHE is one of the most useful

There are two basic types of bubbling regimes in DCHE: homogeneous and heterogeneous. In the homogeneous bubbling regime, there are few diversifications in the size of the bubbles, and breakage and coalescence phenomena are inappreciable [10–12]. Industrially, nevertheless, the homogeneous bubbling regime is not likely to prevail, thanks to the high gas flow rates used. This is good for the heterogeneous bubbling regime, characterized by a widespread of bubble sizes and crucial frequencies of breakage and coalescence [13]. For an air-water system, Ribeiro and Lage [13] employed transient experimental measuring of the temperature of the liquid, bubbling height, evaporation rate, gas volume fraction and bubble size distributions in a direct-contact evaporator for four surface gas velocities including operation in both homogeneous and heterogeneous bubbling regimes. Ribeiro et al. [14] also analysed the photographs of homogeneous and heterogeneous bubbling regimes using different liquids in a DCHE handling with a perforated-plate sparger. Le Coënt et al. [15] studied the compounding of two staves and a viscous liquid in a classical reactor. He found that there was an alleged "pseudohomogeneous" state before it was mixed completely homogeneously. In reality, a pseudohomogeneity was achieved much more quickly (<40 s), but subsequent images revealed that polymers still remained in the reactor. The time of the pseudo-homogeneous state begins is called the pseudo-homogeneous time. In our DCHE, we found that there was a comparatively stable state in the completely heterogeneous bubbling regimes also. Consequently, we defined this completely stable state as pseudo-homogeneous. Peyghambarzadeh et al. [16] found that bubble growth was a considerably complicated process, and detecting distinguishable bubbles was scarcely possible at high heat fluxes, while in this experiment, we have captured the rough

of ice formation, growth and detachment from the droplets producing ice slurry [7].

**1.2. Mixing efficiency assessment**

146 Heat Exchangers– Design, Experiment and Simulation

and instructive topics in DCHE.

**1.3. Bubbling regimes**

sketch of bubbles.

A literature survey showed that image analysis has been used in transparent laboratory vessels to circumvent the drawback of subjectivity of measurement interpretation. Fortunately, the image processing technology has been widely used for feature extraction in medical and chemical industries. Thus, just that technology of image intensification, these bubble images can be computed with the following methods. Bubble growth is severely a function of flow of heat and liquid flow rate [16]. If the flow rate is lower, larger bubbles are observed at constant heat fluxes. This may be due to the fact that the growth of bubbles weakens with the time which is necessary at the velocity of flow is higher. Hence, the bubbles are smaller than those observed at higher high velocity. Similarly, according to the results of Ref. [16], the effect of heat flux is more meaningful than that of flow velocity. Many small bubbles are created on the heat transfer surface, inventing high turbulence flow at high heat fluxes. Consequently, heterogeneous and pseudo-homogeneous bubbling regimes are necessary and worth learning in a DCHE. At the meantime, it is one of the most challenging tasks of direct-contact heat transfer. The current commonly used method is to do with image processing techniques to acquire the features of bubbling regimes.

#### **1.5. Betti numbers**

In 1995, Hyde et al. [17] recommended the topological invariant features the topology penetration structure complexity, in the number of micro-structure processing is one of the two material phases. From the perspective of theory, Betti numbers are the number of handles a special case of a topological invariants in a micro-structure [18]. Algebraic topology provides measurable information on complex objects, and Betti numbers are rough measures of this information. Gameiro et al. [18] came up with a method using the Betti numbers to describe the geometry of the fine-grained and snake-like micro-structures created in the process of spinodal decomposition. The zeroth Betti numbers *β*<sup>0</sup> figure the number of connected components (pieces) in the space Ω. More accurately, if *β*<sup>0</sup> = *k*, then Ω has exactly *k* components. The first Betti numbers *β*<sup>1</sup> state a measure of the number of tunnel structure. In a two-dimensional field, tunnels are decreased to loops. It is a remarkable fact that the size and the shape of the component and the loops and do not affect the number of Betti numbers. Friedrich [19] proposed the same chemical group which used the structure descriptors to distinguish un-related chemical group of chondrite and the application of Betti numbers to research the difference in rock chondrite meteorites. A multiphase mixture usually shows a macroscopic homogeneity consisting scattered fine pieces. With an increase in dispersity of the pieces, the homogeneity of the mixture was increased. In the cracks of the pieces are the blowholes, and a polymerization of blowholes gets an aggregation. The more frequently the pores appear, the more likely agglomeration is to occur at the surface. Moreover, increase in the number of pores showed that the heterogeneity of the mixture was mixed more evenly.

In our previous work, using the Betti numbers for gas-liquid-solid three-phase mixing effects of molten salt system based on the reaction of CH<sup>4</sup> + ZnO were characterized. Nitrogen was used to imitate the gas phase (CH<sup>4</sup> ) and mainly mixing effect in the sink. The zeroth Betti numbers were used to measure the number of pieces in the patterns, bring about beneficial parameter to describe the mixture homogeneity, which was the number of masters in the micro-structure occupied by one of the two phases. The first Betti numbers were introduced to describe the mixing heterogeneity of mixture. Because we only quantified the solid-liquid mixed flow pattern, the mixture of nitrogen bubble will disappear after image binarization.

#### **1.6. Heat transfer performance**

It must be pointed out that Gulawani et al. [20] studied and founded that the turbulent flow pattern in a gas-liquid interface heat transfer coefficient and the immersed surface has a significant impact. Under Gulawani et al. [20, 21] inspiration and guidance, our work is mainly described the flow pattern characteristics of bubbles under the effect of heat transfer in the DCHE. Dahikar et al. [22] and Tayler et al. [23] used the Betti numbers to represent the heterogeneous and pseudo-homogeneous of bubbles. In addition, the relationship between the Betti numbers and the heat transfer coefficient has been obtained in a DCHE.

#### **1.7. Mixing time.**

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. But, we found that the Betti number method to be used for mixing time and the different evaluation indexes for mixing time have a similar trend, such as the slope *p* [15], pH, tracer concentration *ct*, the percentage of mixed pixels, *M*(%) [31], and the standard deviation (σG) [26]. 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. 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. The 3σ principle is that if the sample data come from a normal distribution *N*(μ, σ<sup>2</sup> ), most of the data (99.73%) will lie within the range [μ-3σ, μ+3σ]. It is imposed to detect outliers in the quality control of samples. If the result is normal, the process of the product specification will lie within the scope μ±3σ of the standard value. 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.

#### **1.8. L2 -star discrepancy**

parameter to describe the mixture homogeneity, which was the number of masters in the micro-structure occupied by one of the two phases. The first Betti numbers were introduced to describe the mixing heterogeneity of mixture. Because we only quantified the solid-liquid mixed flow pattern, the mixture of nitrogen bubble will disappear after image binarization.

It must be pointed out that Gulawani et al. [20] studied and founded that the turbulent flow pattern in a gas-liquid interface heat transfer coefficient and the immersed surface has a significant impact. Under Gulawani et al. [20, 21] inspiration and guidance, our work is mainly described the flow pattern characteristics of bubbles under the effect of heat transfer in the DCHE. Dahikar et al. [22] and Tayler et al. [23] used the Betti numbers to represent the heterogeneous and pseudo-homogeneous of bubbles. In addition, the relationship between the Betti

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. But, we found that the Betti number method to be used for mixing time and the different evaluation indexes for mixing time have a similar trend, such as the slope *p* [15], pH, tracer concentration *ct*, the percentage of mixed pixels, *M*(%) [31], and the standard deviation (σG) [26]. 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. 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

numbers and the heat transfer coefficient has been obtained in a DCHE.

**1.6. Heat transfer performance**

148 Heat Exchangers– Design, Experiment and Simulation

**1.7. Mixing time.**

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 abovementioned 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 1980 [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.

#### **1.9. Modified L<sup>2</sup> -star discrepancy**

Recently, we were vitalized and motivated by Xu et al. [39], by the literature that introduces the relatively not complicated and accurately uniformity coefficient (UC) technology, which is based on image processing technology and the theory of uniform design to determine the mixing time and uniformity in a DCHE. The space-time characteristics can be quantified by means of the uniformity coefficient method, which based on *L*<sup>2</sup> -star discrepancy (UC-LD) and provides a method of direct measurement about the macro-mixing evolution. 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*<sup>2</sup> -star discrepancy is much easier to calculate numerically according to Heinrich [41]. Unfortunately, the *L*<sup>2</sup> -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*<sup>2</sup> norm, namely, the centred discrepancy (CD) and the wrap-around discrepancy (WD). The centred discrepancy (CD) and the wrap-around discrepancy (WD) satisfy a Koksma-Hlawka type inequality according to Xu et al. [39]. According to the theory of UC-LD, if the image shows a low CD or WD that can be called homogeneous mixing of a set or bubble swarm pattern, and the use of UC-CD and UC-WD provides at least likely to get a good approximation of mixing bubble swarm of spatial distribution. Additionally, UC-CD and UC-WD exhibit some advantages including rotation invariance, reflection invariance and projection uniformity [39].

#### **1.10. Chapter structure**

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.
