Forchheimer型非Darcy渗流系统的滞后分岔  

Hysteretic Bifurcation in Systems of Forchheimer's Non-Darcy Flow

作　　者：四旭飞[1] 唐平[2] 李天珍[3] 黄先伍[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221116 [2]湘潭大学职业技术学院,湖南湘潭411105 [3]徐州工程学院土木建筑工程系,江苏徐州221008

出　　处：《采矿与安全工程学报》2007年第2期203-207,共5页Journal of Mining & Safety Engineering

基　　金：国家自然科学基金重大项目(50490270);江苏省自然科学基金项目(BK2002114);人事部博士后专项基金项目(2004035676);江苏省博士生科研资助计划项目;中国矿业大学科研基金项目(A200412)

摘　　要：在对Forchheimer型非Darcy渗流系统的控制方程进行简化的基础上,分析了系统平衡态的存在性、稳定性及其跳跃,详细讨论了系统的滞后分岔.研究表明:当非Darcy流β因子由负变为正时,平衡态的一支可能失去稳定性,或者跳到另一支,系统发生滞后分岔;当系统的空参量和边界压力发生变化时,稳定的平衡态和不稳定的平衡态合为一个鞍结点,系统发生切分岔.Based on the simplification about the control equations of systems of Forchheimer;s non-Darcy flow, a set of dimensionless partial-differential equation is obtained, and analysis on the existence, stability and jump of the steady states of the system is carried out, and hysteretic bifurcation in the system is discussed in details. This study shows that a branch of steady state may be unstable, or jumps to the other branch of steady state if the non-Darcy flow β factor changes from positive to negative in value, and so hysteretic bifurcation exists in the system. When both the control parameters and pressure on the boundary be content with a certain relation, two branch of steady states, in which a branch is stable and the other is unstable, may coincide, and so tangential bifurcation exists in the system.

关 键 词：滞后分岔 Forchheimer型非Darcy渗流 非Darcy流β因子 切分岔 

分 类 号：TD313.5[矿业工程—矿井建设]