1.Beijing Key Laboratory of Multiphase Flow and Heat Transfer for Low Grade Energy, North China Electric Power University, Beijing 102206, China 2.Key Laboratory of Power Station Energy Transfer Conversion and System, Ministry of Education, North China Electric Power University, Beijing 102206, China
Abstract:Supercritical fluids (SCF) have been widely utilized in the industrial processes, such as extraction, cleaning, drying, foaming and power generation driven by primary energy. Therefore, SCF have attracted more and more attention in recent years. At supercritical state, liquid, and gas phase are not clearly distinguished, but the thermal-physical properties of fluid show an interesting characteristic, especially near the pseudo-critical temperature. Thus, it is of great significant to study the structure and density time series evolution of SCF.Due to high pressure and temperature for SCF, it can be challenging to collect experimental data of SCF. However, the advantage of molecular dynamics simulation in convenience, safty and cost over experiments. Therefore, in this paper,molecular dynamics simulation was performed to investigate the fluid structure and density series fluctuation curves at supercritical state, and the influence of parameters varitation including pressure and temperature onstructural characteristics was analyzed. In the simulation system, more than 104 atoms and simple Lennard-Jones(LJ) supercritical fluids were contained. The radial distribution function(RDF), coordination number(CN), density time series curve and permutation entropy of fluids at different pressures and temperatures were calculated. At specified pressure, the position of the first peak value of RDF gradually moves to the right with the increase of temperature, and the trend weakens with the increase of pressure. CN shows a downward trend with the increase of pressure and the CN difference at different temperatures gradually decreases. Simultaneously, the CN distribution area becomes narrow with the increase of pressure. The high/low density region calibrated by CN is stable, concentrated and large area distribution at low pressure, and the average density region is small, with the increase of pressure, the area of high/low density region is only a size of a few molecular and fluctuates sharply with time, and the area of average region is constantly expanding. At relatively low pressure, the density time series curve shows the characteristic that both the fluctuation range and quasi-period are large at pseudo-critical temperature. Simultaneously, the permutation entropy obtained from the time series curve shows three cases: (i) at low pressure (P = 1.1Pc), the minimum permutation entropy is obtained under the temperature that is lower than pseudo-critical temperature, and the system has higher orderliness; (ii) at moderate pressure (P = 1.3Pc and 1.5Pc), the state points corresponding to minimum permutation entropy is consistent with that corresponding to the maximum of isothermal compression coefficient and (iii) at high pressure (P = 2.0Pc), the permutation entropy curve fluctuates slightly and remains basically on the horizontal line. The results provide reliable support for revealing the characteristics of SCF from the microscale, and also provide useful inspiration for the practical application of SCF. Keywords:supercritical fluids/ molecular dynamics/ structure characteristics/ permutation entropy
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2.物理模型及模拟细节图1(a)为物理模型示意图. 系统沿着x, y, z三个方向均采用周期性边界条件. 模拟体系尺寸为${L_x} = {L_y} = {L_z} = L$, 模拟系统内充满超临界流体氩, 初始氩原子按照FCC晶格排列方式布置. 有文献[19]研究表明, 超临界流体模拟过程中需要较大的系统尺寸, 得到的计算结果具有较高的可靠性, 因此本文模拟过程中, 各模拟工况均维持系统原子数为104个, 根据不同计算工况的温度和压力, 确定各工况对应的密度, 得到模拟体系的尺寸范围为27.2283$\sigma$—40.8040$\sigma $. 图 1 (a) 物理模型图; (b) 模拟状态点在相图中的分布 Figure1. (a) Physical model of system; (b) simulation points on phase diagram with Widom line, liquid-like and gas-like region.
超临界流体氩的临界点温度(Tc)为150.687 K, 压力(${P_{\rm{c}}}$)为4.863 MPa, 密度(${\rho _{\rm{c}}}$)为535.6 kg/m3, 为揭示不同的超压力、拟临界温度(Tpc)附近超临界流体结构及密度时间序列曲线波动特性, 选择1.1${P_{\rm{c}}}$—2.0${P_{\rm{c}}}$4个超临界压力, 如图1(b)所示, 每个压力下取0.95${T_{{\rm{pc}}}}$—1.05${T_{{\rm{pc}}}}$7个工况进行模拟分析. 根据超临界流体的物性参数和相关研究结果可以得到, 定压比热容(cp)的极值点连成的线即为Widom线, 也是超临界区类液类气的分界曲线, 计算工况在定压比热容的曲线上的分布如图2(a)所示, 计算工况包括了类液和类气区域, 且都集中在拟临界点附近. 相应的等温压缩系数(kT)的变化曲线如图2(b)所示, 从图中可以得到在$P = 1.1{P_{\rm{c}}}$时, 等温压缩系数在拟临界温度下取得极值, 随着压力的增大, 取得极值点的位置发生右偏, 在$P = 1.3{P_{\rm{c}}}$和$1.5{P_{\rm{c}}}$时, 均在$1.01{T_{{\rm{pc}}}}$得到极值点, 当压力增大到$2.0{P_{\rm{c}}}$时, 等温压缩系数在文中选取的计算温度区间内呈现一个平缓的上升趋势, 没有出现极值点. 超临界流体物性突变是流体结构发生变化的具体表现, 也是各工况计算分析中需要重点考虑的因素. 图 2 (a) 定压比热容(cp)变化曲线; (b) 等温压缩系数(kT)变化曲线 Figure2. (a) The curve of cp under different pressures; (b) the curve of kT under different pressures.
计算超临界流体氩的配位数能清楚反映出流体的内部结构. 具体模拟结果如图4所示. 图 4 配位数 (a) P = 1.1Pc; (b) P = 1.3Pc; (c) P = 1.5Pc; (d) P = 2.0Pc Figure4. Coordination number: (a) P = 1.1Pc; (b) P = 1.3Pc; (c) P = 1.5Pc; (d) P = 2.0Pc.
计算中允许的波动量为30%${N_{\rm{e}}}$, 则$\delta $应满足2$\delta $+1=0.3${N_{\rm{e}}}$, 进一步得到不同参数下$\delta $的具体值, 利用划分原则可以判断密度分布趋势, 称该方法为“30%方法”. 采用该方法, 根据配位数得到在$P = 1.1{P_{\rm{c}}}$和$2.0{P_{\rm{c}}}$, $T = {T_{{\rm{pc}}}}$流体在xy平面内高/低及平均密度区分布随时间的演化如图6所示. 图 6 流体在xy平面内高/低密度区分布随时间的演化 (a) P = 1.1Pc, T = Tpc; (b) P = 2.0Pc, T = Tpc Figure6. Liqud atoms evolution over the xy plane with different pressure: (a) P = 1.1Pc, T = Tpc; (b) P = 2.0Pc, T = Tpc.
图6(a)表示在0—5000τ的时间范围内$P = 1.1{P_{\rm{c}}}$, $T = {T_{{\rm{pc}}}}$时的演化过程, 由图可知, 该计算工况产生的均值区面积较小, 低密度区的位置主要集中在模拟系统的中部, 随着时间的演化, 密度在不停地波动, 低密度区呈现分散-聚合-分散的演化规律, 产生的高密度区的面积相对较大且位置集中, 演化过程中波动微弱. 由于在超临界区表面张力的消失, 不存在亚临界工况下的弯曲界面. 形成该现象的原因主要是由于当密度低时, 分子间引力起主导作用, 在温度的影响下分子处于不断的相互碰撞中, 能量的增加, 导致高密度区的形成. 此外, 该工况拟临界点位置出现等温压缩系数的极值点, 形成较高的密度区所付出的代价变小, 超临界流体的关联长度在拟临界处也存在极大值, 因此会出现大面积的, 相对稳定的高密度区. 在确定尺寸和分子数的系统中, 高密度区的形成必然会引起低密度区的产生. 随着高密度区的形成, 分子间的距离缩短, 增大的斥力将部分分子从高密度区向低密度区推, 当分子间距离较大时, 引力起主导作用, 会使得分子再次聚集成高密度区, 但此时作用势效应相对等温压缩系数效应较小, 因此各区域所处位置稳定, 波动微弱. 随着压力的升高, 流体的等温压缩系数仍存在极值点, 但是数值较小, 流体可压缩性减弱, 较难形成高密度区, 仅在分子间短程势作用下, 形成由几个分子组成的且较为分散的高密度区, 形成相对较大的平均值区, 如图6(b)所示. 随时间的演化, 各区域不停波动, 存在明显的嵌套现象, 系统中局部出现类似“花斑”的现象, 这些花斑若隐若现、此起彼伏、互相嵌套的性质和相关教课书[31]中提出的结论保持一致. 从图7可以直观地观察各工况不同密度区所占比例随时间的变化. 不同的压力条件下, 类液和类气区的占比一直处于一个波动的状态, 仅观察曲线, 发现波动过程并没有实际的规律可循, 整体表现为一个混乱的动态变化过程. 从图7(a)和图7(b)分图中发现随着压力增大类液和类气区的占比整体呈现下降的趋势, 进一步说明随压力增大, 形成高密度区较为困难, 计算压力距临界压力越远, 流体的均匀性越强. 在$P = 1.1{P_{\rm{c}}}$, $T = {T_{{\rm{pc}}}}$的工况时, 高密度区占比约为60%, 低密度区的占比约为35%, 此时均匀区域的占比最小, 系统的不均匀性最强. 图 7 不同压力下, 拟临界点温度下高/低密度区占比 (a) 高密度区占比; (b) 低密度区占比 Figure7. The ratio of high/low density region at pseudo-critical point temperature under different pressure: (a) The ratio of high density region; (b) the ratio of low density region.