Molecular dynamics study on viscosity coefficient of working fluid in supercritical CO2 Brayton cycle: Effect of trace gas
Introduction
With compact structure, high cycle efficiency and wide range of application, supercritical CO2 (S−CO2) Brayton cycle has been emerging as a promising power cycle for energy conversion systems [1,2]. In an S−CO2 Brayton cycle, the operating conditions of the compressor are just located above the critical point of the working fluid, which brings an extremely low compressor work, and hence a relatively high cycle efficiency could be obtained. It has been reported that the cycle efficiency could reach 47 % when the maximum and minimum temperature of cycle are 873 K and 293 K, respectively [3].
To improve the performance of the cycle, rather than pure CO2, the working fluid used in the supercritical Brayton cycle (SBC) is often mixed with trace gases in theoretical studies [4,5]. The trace gases could be admixtures of substance or impurities presented in the cycle. The properties of working fluid, including thermodynamics properties and transport properties, would be altered by these trace gases. Intensive researches of effect of trace gases on the performance of SBC have been carried out over the past years. Most of them focus on the effect of shifted critical points on the cycle performance [[6], [7], [8]]. The specific properties of CO2 near critical point are one of key reasons why the S-CO2 Brayton cycle is so charming. Near the critical point, the density of S-CO2 is extremely high, which leads to a significant reduction of compression work. Consequently, the critical point of working fluid generally determines the minimum operating parameters of the cycle, by which the lower minimum temperature would lead to a higher theoretical cycle efficiency. When the trace gas presented in the system, the critical point could be shifted away from the inherent characteristics of pure CO2. From this idea, due to lower critical temperature compared to pure CO2, Xenon (Xe) is recommended as an additive in a number of publications [6,9,10].
However, limited attention was paid to the effect of transport properties like viscosity on the cycle performance. In fact, the trace gas introduced in CO2 not only affect the critical parameter but also the transport properties like viscosity coefficient. The recuperator, which is in great request for SBC, is inevitably influenced by the changed viscosity coefficient [11]. It has been studied that though the mixture of CO2-cyclohexane, CO2-butane, and CO2-isobutane would lead to a higher cycle performance compared to the pure CO2 for a recompression cycle, however, the pressure drop of these mixtures is higher than that of CO2 in the recuperator [12]. The changed performance of the recuperator largely determines the design and optimization of cycle performance further. And for pure Xe, the viscosity coefficient and density are much higher than those of CO2. As a result, the pressure drop would be definetly affected with the mixing of Xe.
The accurate viscosity coefficient of the supercritical CO2-based mixture is the foundation of the above research. But few experimental data is available for most mixture over such an extreme condition [6,13,14]. An alternative is to use the equation of state (EoS) [15]. To author’s knowledge, nearly all the related analyses of exiting researches about the effect of additive on the performance of SBC are performed using an in-house cycle analysis code based on the thermophysical properties from EoSs in REFPROP program [16]. The accuracy of REFPROP properties database plays a decisive role in the feasibility of the research on the additives. The question is that the data from REFPROP program are not always reliable. The EoSs, which own lame physical significance, may not work well in the prediction of thermophysical properties beyond the scope of fitting conditions.
As pointed in our previous work [17], completely opposite results may be derived from different versions of REPROP in the prediction on viscosity coefficient of CO2-based mixture. In Fig. 1, the viscosity of CO2-air obtained from different versions of REFPROP is compared. 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. What’s worse, using REFPROP on the calculation of thermophysical properties of CO2-Xe binary mixture generated severe warning. Binary interaction parameters are not presently available for this mixture. It will be a common case when conducting the calculation of the multi-component mixture. All these calls for a reliable physical properties calculation tool.
Molecular simulation (MS), bridging the nanostructure and the macro thermophysical properties, has been emerging as an important tool to make up for the lack in thermophysical property data of supercritical working fluid [[17], [18], [19]]. Differing from EoSs, MS has a solid physical foundation and can be extended to a wider range. As one of the branches of molecular simulation, molecular dynamics (MD) simulation has been wildly utilized to calculate the viscosity of the supercritical fluid. Using seven different potential models, Aimoli et al. [20] calculate the viscosity of pure CO2 for temperatures between 273.15 and 573.15 K and pressures up to 800 MPa. The result indicates that, with EPM2 model, the predicted viscosity could perfectly agree with the reference (overall average absolute relative deviation is below 5 %). However, when it comes to the calculation of viscosity of S-CO2 mixtures, a few pieces of research are performed using molecular dynamics simulation over the supercritical condition of CO2.
To address the effect of the Xe with a diverse amount on the performance of the S-CO2 Brayton cycle, the viscosity coefficient is calculated through a serial of MD simulations. A proper MD simulation strategy is concluded in the first step. Then, the viscosity of CO2-Xe mixtures was determined. The calculation was conducted at pressure between 8 and 20 MPa and temperature up to 873 K. Based on the simulated viscosity data, the influence of Xe on the pressure drop of recuperator in SBC was discussed further.
Section snippets
The layout of S-CO2 Brayton cycle
Fig. 2 gives a simple recuperated S-CO2 Brayton cycle studied in this paper. Five components are included in the cycle: a turbine, a recuperator, a heat source, a compressor, and a precooler. The operating conditions of each components were also shown in the picture. The system in Fig. 2 was treated as a reference to deduce the possible working conditions of the working fluid. In recuperator, the heat of working fluid exiting the turbine was recovered, while the high-pressure stream exiting the
Force field
The molecular models of CO2, and Xe were taken from Harris et al. [21], and Rappe et al. [22], respectively. All models owning the same number of LJ centers as corresponding molecule nucleus have been considered in this study. And they are rigid with fixed bond length and fixed angle for there is limited even no improvement of accuracy with flexible models for the calculation of viscosity coefficient [20]. As a result, only the intermolecular potentials including Lennard-Jones 12-6 potential
Validation of pure CO2
The viscosity coefficient of pure CO2, as well as the standard deviation, at different working conditions, is given in Fig. 6. On the whole, a growth of the viscosity coefficient of pure CO2 with the increase of pressure and temperature could be observed except for the cases under 20 MPa. A few exceptions may be the joint effect of the limited inherent difference and relatively high simulated uncertainty due to measuring repeatability which is given in the Fig. S1.
To demonstrate the quality of
The effect of the addition of Xe on the viscosity of working fluid
As emphasized in Section. 1, the addition of Xe in the S-CO2 Brayton cycle is likely to influence the pressure drop characteristics, and the extent of change on the viscosity coefficient of working fluid is the foundation of that research. Thus the relative change of viscosity coefficient between binary mixtures CO2-Xe and pure CO2 was summarized in Fig. 10 according to the simulated viscosity coefficient listed in Section. 4.
Clearly, when the temperature is relatively low at 373 K, the change
Conclusion
The viscosity coefficient of CO2 mixtures is a necessity for the design and optimization of the S-CO2 Brayton cycle when trace gas is introduced in the system. In this work, the viscosity coefficient of CO2-Xe in the supercritical region of CO2 is calculated using MD simulations. A reliable simulation strategy is constructed. CO2 mixtures containing different mol fractions of Xe are considered. Based on the simulated thermophysical properties, the effect of the addition of Xe on the viscosity
CRediT authorship contribution statement
Zhenyu Du: Methodology, Writing - original draft, Formal analysis. Shuai Deng: Supervision, Project administration. Li Zhao: Supervision, Funding acquisition. Xianhua Nie: Methodology, Software. Shuangjun Li: Methodology, Validation. Yue Zhang: Investigation. Jie Zhao: Investigation. Nan Zheng: Funding acquisition.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The authors are grateful for the support provided by the National Key Research and Development Program of China under Grant No. 2018YFB1501004, China's Post-doctoral Science Fund under Grant No. 2018M631155.
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