مدل عددی برای خازن های کانال های خرد و کولر گازی: قسمت دوم - مطالعات شبیه سازی و مقایسه مدل

For a microchannel heat exchanger (MCHX), given the working conditions, main geometric data of the fin and tubes, heat transfer and face areas, there are multiple choices for the refrigerant circuitry and aspect ratio. Numerical studies using the Fin1Dx3 model, presented in Part I, are undertaken in order to assess the impact on the heat transfer of these design parameters for a microchannel gas cooler. The effect of fin cuts in the gas cooler performance has also been studied numerically as function of the refrigerant circuitry, where it has been found that an optimum circuitry for the use of fin cuts exists. Finally, with the aim of presenting the Fin1Dx3 model as a suitable design tool for MCHX, the model has been compared against the authors’ previous model (Fin2D) and other representative models from the literature in terms of accuracy and computational cost. The Fin1Dx3 model has reduced the simulation time by one order of magnitude with regard to Fin2D, and in terms of accuracy deviates less than 0.3%.

Currently, an increasing interest in microchannel heat exchangers (MCHXs) has arisen in refrigeration and air conditioning applications due to their high compactness and high effectiveness. The high effectiveness is a consequence of large heat transfer coefficients as a result of using small hydraulic diameters. Given an air side heat transfer area, high compactness means a reduced volume, resulting in light heat exchangers with high mechanical strength being able to operate with low refrigerant charges. Natural refrigerants are considered more environmentally friendly than other commonly-used refrigerants with similar or even better performance. However, working with some natural refrigerants has the following chief drawbacks: ammonia is toxic in large quantities; propane is highly flammable, and in fact IEC 60335-1 (2010) restricts the amount of hydrocarbon that can be used in a system to 150 g; carbon dioxide is neither toxic nor flammable but it works at high pressure, requiring of high mechanical strength components. Therefore, the features of MCHXs play an important role in the use of natural refrigerants: reduced volumes for getting low refrigerant charges in the case of flammable refrigerants like propane, and high mechanical strength in the case of transcritical CO2 systems. Additionally, a suitable heat exchanger design for obtaining low refrigerant charges is a serpentine MCHX. This kind of heat exchanger minimises the refrigerant charge because it has no headers, thus saving this volume and the corresponding refrigerant charge. Nowadays, simulation software is an appropriate tool for the design of products in which complex physical phenomena occur. These tools allow the saving of a lot of cost and time in the laboratory. Currently, some models for MCHXs are available in the literature: Asinari et al., 2004, CoilDesigner, 2010, Fronk and Garimella, 2011, García-Cascales et al., 2010, MPower, 2010 and Shao et al., 2009, and Yin et al. (2001). The modelling approaches and assumptions employed by them were extensively discussed in Part I (Martínez-Ballester et al., 2012), where the authors of the current work presented the fundamentals of the new proposed model: Fin1Dx3. This model is based on the previous Fin2D model (Martínez-Ballester et al., 2011) but introduces a new formulation, which allows the same accuracy to be retained with a large reduction in the computational cost. In the Fin1Dx3 model, the main heat transfer processes, which are modelled in a different and novel way with respect to other MCHX models available in the literature, are: - 2D longitudinal heat conduction (LHC) in the tube. - Heat conduction between tubes along the fin in contrast with the usual adiabatic-fin-tip assumption. - Consideration of an air temperature zone close to each tube wall, in addition to the air bulk temperature. In air-to-refrigerant heat exchangers, heat conduction between tubes along the fins appears when a temperature difference exists between the tubes, which always degrades the heat exchanger effectiveness. Several experimental studies indicated that the heat exchanger performance can be significantly degraded by the tube-to-tube heat transfer via connecting fins. Domanski et al. (2007) measured as much as a 23% reduction in the capacity of a finned-tube evaporator when different exit superheats were imposed on individual refrigerant circuits. This heat conduction and its negative effects can be avoided by cutting the fins, what has been studied in the literature. For a finned tube gas cooler, Singh et al. (2010) reported heat load gain of up to 12% and fin material savings of up to 40%, for a target heat load, by cutting the fins. However, not so large improvements have been achieved for MCHXs, namely: Asinari et al. (2004) concluded that the impact of using the adiabatic-fin-tip, which assumes no heat conduction, in predicted results can be considered negligible for a wide range of applications; Park and Hrnjak (2007) reported measurements of capacity improvements of up to 3.9% by cutting the fins in a CO2 serpentine microchannel gas cooler. Application of the fin theory is an assumption widely used and necessary when a model uses fin efficiency to evaluate the heat transfer from fins to air. The fin efficiency is based on the fin theory that assumes uniform air temperature along the fin height, which is not always satisfied, as explained in Part I (Martínez-Ballester et al., 2012) (Sections 1 and 2). In the literature, only a few models discretize the governing equations along the fin height and do not use the fin efficiency theory. The Fin1Dx3 model proposed in Part I (Martínez-Ballester et al., 2012) takes into account all previously explained effects, and it can simulate any refrigerant circuitry regarding the number of refrigerant passes, tubes and tube connections. In addition, the model has the option of working in two different modes: continuous fin or fin cut. The reason for these two modes is to be able to evaluate the improvements by cutting the fins on the heat transfer. Through the design process of an MCHX, the geometric data of tubes and fins are usually imposed by the manufacturer. Fin pitch, heat transfer area and face area of an MCHX is usually obtained by consideration of performance requirements. However, given a working conditions, multiple choices exist for the number of refrigerant passes, refrigerant connections and the aspect ratio (L/H) of the MCHX. In fact, some simulation software like EVAP-COND (2010) has the capability of optimising the heat load, varying the circuitry of a finned tube heat exchanger. Shao et al. (2009) studied the effect of the number of refrigerant passes for a serpentine MCHX working as a condenser, with the same face area and heat transfer area. The authors obtained up to 30% differences on heat load only by changing the number of refrigerant passes. Given that the circuitry has an important influence on the heat exchanger performance, the usefulness of simulation software for this purpose is clearly justified, since optimisation via experimentation would take too long, is difficult and expensive. On the other hand, depending on the model’s assumptions some parameter can be studied or not, e.g. the impact of the aspect ratio (L/H) on the heat transfer of a heat exchanger would be null if it is evaluated with a model which applies the adiabatic-fin-tip efficiency. This design parameter can only be assessed if the model adequately accounts for the heat conduction between tubes. A model that uses the adiabatic-fin-tip without any correction term, to take into account the heat conduction between tubes, is always predicting results as if the heat exchanger had all fins cut, hence these models always overpredict the heat transfer (Domanski et al., 2007). In order to evaluate the effect of cutting fins, the model has to be able to simulate both scenarios; with and without the fin cut. There are few models that can estimate the impact of cutting fins on the prediction results. For finned tubes, Singh et al. (2008) presented a model, referred to as a “resistance model”, to account for heat transfer between tubes through the fins. They included a term for heat conduction along fins between neighbouring tubes while still using the concept of adiabatic-fin-tip efficiency. The drawback of this methodology is the use of a set of multipliers that are dependent on the problem, which have to be determined either experimentally or numerically. Asinari et al. (2004) proposed a three-dimensional model for microchannel gas coolers using CO2 as the refrigerant; the model employs a finite-volume and finite-element hybrid technique. They applied this model to evaluate the effect of heat conduction between tubes for one gas cooler, without any modification, operating in the operating conditions of one test. Martínez-Ballester et al. (2011) presented a model referred to as Fin2D which did not apply fin theory and was able to assess the impact of the fin cuts, but with a large computational cost since it needs to use a large discretization of the fin surface. According to the ideas previously put forward, the authors considered studying some design parameters of an MCHX such as: aspect ratio and number of refrigerant passes. The influence of fin cuts was also studied for different refrigerant circuitry. The impact of all these parameters depends strongly on the heat conduction between tubes, LHC and air-side heat transfer. Hence the need for the use of a model which accurately takes into account all previous phenomena, otherwise it would not be possible to evaluate the effects of some of the aforementioned parameters on the MCHX performance. To this end, the simulation studies were carried out with the new proposed model Fin1Dx3. The more sensitive the case study to LHC and heat conduction between tubes, the larger the impact will be on the performance due to variations in the defined parameters. The impact of LHC and heat conduction between tubes will increase as the temperature gradient on a tube and the temperature difference between tubes increases. That is the reason why a microchannel gas cooler working with CO2 in transcritical pressures has been chosen as the case study. The reasons are based on the temperature glide of CO2 during supercritical gas cooling, in contrast with a condenser where the temperature during condensation remains approximately constant. Representative values can be extracted from the experimental results of Zhao et al. (2001), where CO2 undergoes temperature variations along a single tube from 25 K up to 85 K while the maximum temperature difference between two neighbouring tubes ranges from 30 K to 100 K. These kinds of numerical study on MCHXs are barely available in the literature. The goal of the case studies selected is to contribute to a better understanding of the influence of some of the design parameters on MCHX performance. The goal of Part I (Martínez-Ballester et al., 2012) was to present the Fin1Dx3 model as a tool for the simulation of MCHXs. In Part I (Martínez-Ballester et al., 2012) it was explained that the model discretization is based on the Fin2D model (Martínez-Ballester et al., 2011), which had large computational requirements. However the new discretization of Fin1Dx3 allows, for same accuracy, a considerable reduction in the number of both air and fin cells, so that a large reduction in computational cost is expected. In order to assess the degree of accomplishment achieved regarding these statements, a comparison study between the accuracy and simulation time of the Fin2D and FinDx3 models has been carried out. Part I (Martínez-Ballester et al., 2012) extensively discussed how other authors model the heat conduction between tubes and the air-side heat transfer, thus that Part II presents a comparison between the Fin1Dx3 model and an alternative approach that is representative of others models from the literature, regarding the modelling of these phenomena. This alternative approach is based on the work of Singh et al. (2008) and Lee and Domanski (1997). Although these approaches were originally proposed for finned tube heat exchangers, in this paper they have been adapted to MCHXs.

The present work analyzes the impact of some design parameters of MCHXs on its performance. These parameters were the number of refrigerant passes, aspect ratio and the effect of fin cuts. The success of simulation tools to this end depends on the assumptions of the model, i.e. some parameters produce effects due to phenomena not taken into account by the model. For instance, a model that does not account for heat conduction between tubes cannot study the effect of the aspect ratio; otherwise, the results would be always the same. The numerical studies presented were carried out using a model for the MCHXs that uses the novel approach Fin1Dx3, presented in Part I (Martínez-Ballester et al., 2012), which takes into account: heat conduction between tubes, fin cut or continuous fin, detailed air discretization, 2D longitudinal heat conduction along the tube and the effects of non-mixed air in the Y direction. For a gas cooler working with CO2 under transcritical pressures, the main conclusions of the simulation studies were: • For a gas cooler where no phase change occurs, heat transfer is always increased by increasing the number of refrigerant passes, regardless of the increase in pressure drop. • The fin cuts always increase the heat transfer. In the gas cooler analysed, the improvement with regard to the continuous fin depends on the air velocity and number of refrigerant passes: the lower the velocity the greater the improvement in capacity. There is an optimum value for the number of refrigerant passes, regardless of air velocity, which is 3 passes for the case analysed. The improvement in heat transfer was as much as 3%. • Regarding the aspect ratio of a serpentine heat exchanger, given a heat transfer area and a face area, the best aspect ratio corresponds to a gas cooler with a reduced length (L) and large height (H). The reason is based on the fact that this configuration reduces heat conduction between tubes. Numerical studies on the accuracy and computational cost were presented in order to compare the proposed models of Fin1D and Fin1Dx3 with regard to the authors’ previous models and other representative models from the literature. The main conclusions of these comparisons were the following: • The solution time of Fin1Dx3 has been reduced by one order of magnitude with regard to Fin2D, whereas the differences in the results are less than 0.3%, which are considered negligible for practical applications. The computation time difference between Fin1Dx3 and Fin1D was determined to be double. • Corrected-Fin can lead to accurate results when compared with a model with an equivalent approach that models heat conduction between the tubes in a more fundamental way, such as Fin1Dx3. The difference between the predicted results from both models was between 1% and 2%. The computational costs of the Fin1D and Corrected-Fin models are the same. • Nevertheless, the authors would like to emphasise the fact that the present work shows no computational saving or advantage in accuracy by adding correction terms to an approach that uses adiabatic-fin-tip efficiency rather than a more fundamental approach, regarding the phenomena of heat conduction between tubes, like Fin1D. • By comparison of deviations between the Fin1D, Corrected-Fin and Fin1Dx3 models, it was concluded that the main factor responsible for the differences between them was the effect of non-mixed air along the fin height.