Molecular dynamics study on transport properties of supercritical working fluids: Literature review and case study
Introduction
Over past decades, the energy consumption all over the world increases continuously because of the increment of population and economic development. How to utilize energy efficiently is an urgent issue and irreversible historical trend to be addressed. Thermodynamic cycle is considered to be a promising way to deal with the issues because it could utilize the low-grade energy with a high energy conversion efficiency [1]. In order to further improve the thermal performance of thermodynamic cycles, amount of studies focused on thermodynamic cycles in various of applications with large energy demand, including power generation [2], refrigeration [3], heat generation [4] and so on. Particularly, in some current applications, supercritical thermodynamic cycles (STC), including supercritical steam cycle, supercritical organic Rankine cycle (ORC) and supercritical CO2 Brayton cycle are developing gradually because of their advantages over subcritical cycles [5], [6], [7]. Generally, with the same power output, supercritical cycles always have a higher thermal efficiency compared to subcritical cycles [5]. Besides, supercritical CO2 cycles are attractive because they are much more economical and commonly has a lower energy demand for compressing [6], [7]. Dunham and Iverson [8] compared thermal efficiency values of some supercritical CO2 thermodynamic cycles and steam Rankine cycle, and they found that thermal efficiency of a CO2 recompression STC with wet cooling is 5% higher than that of steam Rankine cycles.
Among all of the types of these STCs, the essential and critical problem of studies on STCs is thermophysical properties of working fluids. More exactly, the research framework can be seen in Fig. 1. For one thing, in a real cycle, the highest Carnot efficiency cannot be achieved practically because of the constraint of working fluids [9]. For another, some irreversible loss can also be introduced owing to the working fluids. Therefore, effects of thermophysical properties of working fluids on thermal performance of STCs can be understood from perspectives of thermodynamics and heat/mass transfer.
From the perspective of thermodynamics, pvTx (pressure, specific volume, temperature and composition) is the thermophysical properties of interest. In current studies, plenty of researchers studied the pvTx of working fluids theoretically [10] and experimentally [11] in both subcritical and supercritical regions. Furthermore, effects of pvTx on performance of a thermodynamic cycle are also carefully analyzed [12]. Therefore, pvTx of working fluids has been extensively studied.
From the perspective of heat and mass transfer, transport properties, which include thermal conductivity, viscosity and diffusion, are the thermophysical properties of interest. Such properties could determine the real efficiency and the economy of a thermodynamic cycle. Thermal conductivity is a parameter characterizing the working fluids’ ability of heat transfer. Practically, it is an important parameter in the design of heat exchangers [13] and this further affects the costs of a system. So far, thermal conductivity of some working fluids can be found in databases [14], and there’re also some predictive methods, including empirical models based on experimental regression [15], group contribution methods [16] and so on, developed based on heat conduction mechanism. Nevertheless, there still hasn’t been a complete method to estimate thermal conductivity of liquids yet [17]. For viscosity, it is a parameter to characterize the working fluids’ resistance to shear stress. Practically, in thermodynamic cycles, working fluids with low viscosity are expected, because a low viscosity could result in a low power consumption and a rapid heat and mass transfer [18]. In current studies, some studies proposed experimental studies to obtain the viscosity, like studies proposed by Teja and Rice [19] and Neindre and Garrabos [20]. Furthermore, some predictive models have been developed based on the experimental data as well [21]. However, similar to the prediction of thermal conductivity, there’s also no complete method to estimate the viscosity. Therefore, highly experiments dependent models and the lack of complete method to estimate the transport properties cause the following critical knowledge gaps.
Firstly, Fig. 2 shows one of the knowledge gap of current studies on transport properties of some typical working fluids. In the figure, critical temperatures Tc (the end of the bar colored in red), the maximum applicable temperatures of predictive models Tmax (the end of the bar colored in blue) and the decomposition temperatures Tdec (the end of the bar colored in yellow) are compared. Therein, the decomposition temperatures of HFC245fa, HFC236fa, HFC152a and HFC134a were obtained from the experiments proposed by Dai et al. [22]. The decomposition temperature of HFO1234yf was obtained from the ReaxFF molecular dynamics study proposed by Cao et al. [23]. It can be seen that for most of the working fluids, the applicable maximum temperatures of predictive models are slightly higher than critical temperatures. Nevertheless, the decomposition temperatures are much higher than the maximum applicable temperature of predictive models, and the temperature ranges are filled with diagonal lines. The region filled with diagonal lines can be considered as the knowledge gap of transport properties. If the working conditions of a STC are in this region, it would be difficult to design a system or analyze the performance.
Secondly, transport properties are sometimes inconsistent for some supercritical working fluids when different databases are utilized, especially in the region beyond the fitting conditions of the predictive models. Taking the prediction of the popular working fluids, CO2, utilizing the popular database REFPROP as an example, the viscosity obtained by different versions of REFPROP [24], version 9.1 and 10, are compared in Fig. 3. The figure shows the relative deviation of impure supercritical CO2 (99% CO2, 0.8% N2 and 0.2% O2) to the pure CO2. Particularly, this comparison is important in engineering, because impurities may enter the system in practice and this leads to a deviation from the designed condition, which further decrease the thermal performance. In Fig. 3, the horizontal axis represents the pressure, while the vertical axis represents the relative deviation between pure CO2 and impure CO2. Different colors of curves represents different temperatures and different symbols represents results obtained by different databases. It can be seen that the relative deviations and even their trends obtained by version 9.1 and 10 are not the same. With the increase of the pressure, the relative deviation decreases monotonously for version 10, while behaving as a quadratic curve for version 9.1. Furthermore, the viscosity of the mixture can be lower than the pure for version 10, which is not observed in version 9.1. Though the reducing function parameters concerning the CO2/O2 have a modification in the later version, it’s still not compelling with the limited experiment data, due to the empirical model owns lame physical significance.
Therefore, there’s still a long pathway to a comprehensive understanding on the transport properties of working fluids in the supercritical region. Molecular simulation becomes a promising method to solve the dilemma to some extent.
Molecular simulation (MS), which is flourishing from garden to field since the Nobel Prize in 2013, offers an opportunity to bridge the nano structure and the macro thermodynamic properties. Ungerer et al. [25] reviewed the application of MS in thermophysical properties’ estimation. Particularly, as one branch of MS, molecular dynamics (MD), including equilibrium molecular dynamics (EMD) and non-equilibria molecular dynamics (NEMD), is popular to estimate transport properties of working fluids. With the help of MD, transport properties in both subcritical and supercritical regions can be calculated based on the molecular structure of working fluids. For EMD, transport properties can be calculated through a statistical-based functions, named Green-Kubo relation. For NEMD, momentum and positions of each atom during the transport can be revealed, and transport properties can be calculated through classical relations like Fourier’s law and Newton’s law of viscosity. The two methods have both advantages and disadvantages. However, few studies evaluate the applicability of each MD techniques according to specific transport properties, considering most of research only employed one kind of MD technique without enough comparisons. Thus there’s few screening criterion of MD techniques beyond the scope of research experience.
So far, to the best of the authors’ knowledge, there has been few systemic study focusing on the analyses of supercritical thermodynamic cycles. This study focuses on the knowledge gaps above and endeavors to solve the difficulties in determining transport properties applied in supercritical thermodynamic cycles. This paper is arranged as the following. In Section 2, the state-of-the-art of transport properties calculated utilizing MD are reviewed. Therein, some basic principles of MD and calculation of transport properties are introduced in Section 2.1. Besides, an overview of current studies on thermal conductivity, viscosity and diffusion coefficient can be seen in Section 2.2. What’s more, in order to evaluate the performance of each MD methods in the supercritical region, especially in the region beyond the applicability of existing predictive models, some case studies are proposed in Section 3. Finally, in Section 4, according to the review and case studies, the challenges and the development prospects are put forward. The results of this study would be benefit for analyses and construction of supercritical thermodynamic cycles.
Section snippets
Literature review
In this section, the basic principle of molecular dynamics simulation is introduced firstly, followed by a special introduction and review of transport properties calculation utilizing MD. This section aims to provide a clear understanding on the state-of-the-art of techniques for transport propertied calculation.
Case study
According to the literature review above, several MD techniques have been developed to calculate the transport properties. In this section, in order to evaluate the predictive ability of MD for supercritical working fluids and clarify which technique is more suitable for transport properties calculation of supercritical working fluids, a case study is proposed. This section first covers the methodology of the MD calculation, followed by the results analyses of the thermal conductivity and the
Challenges and opportunities
Nowadays, STCs attract increasingly attention of researchers all over the world. In STCs, the temperature of STC has a better match with that of heat sources, thus the exergy efficiency of STCs is always higher than that of subcritical thermodynamic cycles [104]. As the carrier of energy transfer and conversion, working fluids play an important role in STCs. Particularly, transport properties, like thermal conductivity and viscosity of working fluids significantly affect the actual performance
Conclusions
In this study, the state-of-the-art of molecular dynamics in the calculation of transport properties of working fluids utilized in supercritical thermodynamic cycles is systematically reviewed. Currently, both equilibrium molecular dynamics and non-equilibrium molecular dynamics have achieved good success in the calculation of transport properties, but the selection of both methods is ambiguous and few studies evaluate the performance of the both methods. It brings inconvenience to their
Acknowledgement
The work is supported by Innovation Development and Demonstration Project of Ocean Economy (Grant No. BHSF2017-19), National Natural Science Foundation of China (Grant No. 51776138) and Tianjin Talent Development Special Support Program for High-Level Innovation and Entrepreneurship Team.
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