颗粒气体多室盒装化系统的动力学行为研究
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摘要
本文从实验和数值模拟两个方面研究了垂直激励作用下多室盒装化颗粒系统的动力学行为。
在实验方面,首次将两室盒装化系统研究扩展到多室系统,主要探讨了二元颗粒混合物在两种排列形式的系统中(非循环系统和循环系统)受外加正弦激励作用时的动力学行为。实验观测到颗粒混合物在这两类系统内有着不同的振荡聚集规律,即:对于非循环系统,二元颗粒混合气体在线性排列的小室中依次振荡聚集,其顺序是固定不变的,每次从某一固定小室向另一固定小室聚集转换所需的时间基本是恒定的,而从位于两端小室向中间小室转换所需时间大约是从中间向两端的两倍;对于循环系统,二元颗粒混合气体振荡没有一个固定的聚集顺序,颗粒在小室中随机循环,聚集转换的平均时间随聚集次数呈指数函数衰减,并趋于常值。此外,在振荡态向均匀态转换的过渡区域,首次观测到振荡聚集态和对称均匀态共存的间歇性聚集现象。
在数值模拟方面,采用事件驱动法模拟两室、三室和四室盒装化系统中颗粒气体的演化过程,重现了颗粒混合物的三种动力学形态----非对称聚集态、振荡聚集态和对称均匀态,详细讨论了两种颗粒的质量比、直径比、颗粒个数比、恢复系数和盒子宽度等参数对振荡区间范围和聚集幅值的影响,给出了盒装化系统动力学演化特征随这些参数变化的一般规律,第一次指出系统的聚集幅值随激振强度的增加按照玻尔兹曼函数关系变化。与实验不同的是,模拟得到的振荡周期是随机的,在三(四)个小室中的聚集顺序是无序的,颗粒在每个小室中的平均驻留时间与(f-f_0)~(-a)成正比(这里f为外加激振频率,f_0为出现振荡现象的临界激振频率)。特别值得注意的是,同种颗粒盒装化系统的模拟中,首次得到了稳定的振荡聚集现象。
In this thesis,we use experiments and numerical simulation to research the dynamic behavior of a vibrofluidized granular gas in N connected compartments.
In experiment,we firstly extend two-connected compartmentalized system to N-compartment system,and discuss the dynamic behavior of a binary granular mixture in two kinds of systems respectively(one system is cyclic and the other is non-cyclic).The rules of cyclic oscillation in these systems are found to be different in experiment.For a non-cyclic system,the order and interval of the clustering in a linear configuration are invariable.The particles always cluster periodically in one of the N compartments in a tactic order.The mean interval time of the clustering transition from the aside to the middle is two times of the one with opposite clustering direction.But for a cyclic system,the binary gas clusters cyclically into one of the compartments in a random order and the interval of the clustering transition has a tendency to decrease with evolution of time and tends to a constant value.In addition,in a certain transition range a remarkable intermittent clustering behavior is observed at first in our experiment,i.e.the granular gas undergoing a cyclic oscillation shows a sudden uniform state and keeps it for a long time until the new cyclic cluster state emerges.
In numerical simulation,we apply the event driven method to simulate evolution of granular gas in N connected compartmentalized systems(N=2,3,4),and make three dynamic behaviors found in experiments recur.Three dynamic behaviors are stationary asymmetric segregated state、periodic one and stationary homogeneous one.The effect of granular parameters such as mass radios of two kinds of granulars、diameter ratios、granular number、restitution coeffictients and the length of compartment on oscillation regime and clustering amplitude are investigated in detailed.The rules of dynamic characteristics of system associated with these parameters are presented.The clustering amplitude varies with the increase of applied intensity in Boltzmann function,which is found firstly.It is different from experiments results that the oscillation cyclic periods obtained in numerical simulation are random and the order of clustering in three or four compartments system is variable.The mean interval time in each compartment is proportional to (f-f_0)~(-a),where f denotes the applied frequency and f_0 is a transitional value between periodic state and stationary asymmetric segregated state.Especially, stationary cyclic oscillation phenomenon is firstly found in a compartalized granular system only composed with one kind of particles.
在实验方面,首次将两室盒装化系统研究扩展到多室系统,主要探讨了二元颗粒混合物在两种排列形式的系统中(非循环系统和循环系统)受外加正弦激励作用时的动力学行为。实验观测到颗粒混合物在这两类系统内有着不同的振荡聚集规律,即:对于非循环系统,二元颗粒混合气体在线性排列的小室中依次振荡聚集,其顺序是固定不变的,每次从某一固定小室向另一固定小室聚集转换所需的时间基本是恒定的,而从位于两端小室向中间小室转换所需时间大约是从中间向两端的两倍;对于循环系统,二元颗粒混合气体振荡没有一个固定的聚集顺序,颗粒在小室中随机循环,聚集转换的平均时间随聚集次数呈指数函数衰减,并趋于常值。此外,在振荡态向均匀态转换的过渡区域,首次观测到振荡聚集态和对称均匀态共存的间歇性聚集现象。
在数值模拟方面,采用事件驱动法模拟两室、三室和四室盒装化系统中颗粒气体的演化过程,重现了颗粒混合物的三种动力学形态----非对称聚集态、振荡聚集态和对称均匀态,详细讨论了两种颗粒的质量比、直径比、颗粒个数比、恢复系数和盒子宽度等参数对振荡区间范围和聚集幅值的影响,给出了盒装化系统动力学演化特征随这些参数变化的一般规律,第一次指出系统的聚集幅值随激振强度的增加按照玻尔兹曼函数关系变化。与实验不同的是,模拟得到的振荡周期是随机的,在三(四)个小室中的聚集顺序是无序的,颗粒在每个小室中的平均驻留时间与(f-f_0)~(-a)成正比(这里f为外加激振频率,f_0为出现振荡现象的临界激振频率)。特别值得注意的是,同种颗粒盒装化系统的模拟中,首次得到了稳定的振荡聚集现象。
In this thesis,we use experiments and numerical simulation to research the dynamic behavior of a vibrofluidized granular gas in N connected compartments.
In experiment,we firstly extend two-connected compartmentalized system to N-compartment system,and discuss the dynamic behavior of a binary granular mixture in two kinds of systems respectively(one system is cyclic and the other is non-cyclic).The rules of cyclic oscillation in these systems are found to be different in experiment.For a non-cyclic system,the order and interval of the clustering in a linear configuration are invariable.The particles always cluster periodically in one of the N compartments in a tactic order.The mean interval time of the clustering transition from the aside to the middle is two times of the one with opposite clustering direction.But for a cyclic system,the binary gas clusters cyclically into one of the compartments in a random order and the interval of the clustering transition has a tendency to decrease with evolution of time and tends to a constant value.In addition,in a certain transition range a remarkable intermittent clustering behavior is observed at first in our experiment,i.e.the granular gas undergoing a cyclic oscillation shows a sudden uniform state and keeps it for a long time until the new cyclic cluster state emerges.
In numerical simulation,we apply the event driven method to simulate evolution of granular gas in N connected compartmentalized systems(N=2,3,4),and make three dynamic behaviors found in experiments recur.Three dynamic behaviors are stationary asymmetric segregated state、periodic one and stationary homogeneous one.The effect of granular parameters such as mass radios of two kinds of granulars、diameter ratios、granular number、restitution coeffictients and the length of compartment on oscillation regime and clustering amplitude are investigated in detailed.The rules of dynamic characteristics of system associated with these parameters are presented.The clustering amplitude varies with the increase of applied intensity in Boltzmann function,which is found firstly.It is different from experiments results that the oscillation cyclic periods obtained in numerical simulation are random and the order of clustering in three or four compartments system is variable.The mean interval time in each compartment is proportional to (f-f_0)~(-a),where f denotes the applied frequency and f_0 is a transitional value between periodic state and stationary asymmetric segregated state.Especially, stationary cyclic oscillation phenomenon is firstly found in a compartalized granular system only composed with one kind of particles.
引文
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