黏弹性材料本构方程的广义分数阶单元

提出广义分数阶单元网络, 取消了Schiessel等人所提出的分数阶单元法对参数的限制, 增加了“协调方程”, 将模型解的构造扩充到广义函数空间, 使其包含更多的具有明显物理意义的解. 应用并发展了离散求逆Laplace变换的方法, 给出了模型方程的广义解. 讨论了广义分数阶单元网络Zener, Poyinting-Thomson模型. 结果表明, 有关黏弹性材料本构方程经典的和前人所得的经典整数阶和分数阶单参数模型的所有结果均可作为本文的特例而被包括.     

广义Maxwell黏弹性流体在两平板间的非定常流动

将分数阶微积分运算引入Maxwell黏弹性流体的本构方程，研究了黏弹性流体在两平板问的非定常流动．对于广义Maxwell黏弹性流体的分数阶导数模型，导出了对时间具有分数阶导数的特殊运动方程，利用分数阶微积分的Laplace变换理论，得到了流动的解析解．     

Bifurcation of flow and mass transport in a curved blood vessel

A numerical analysis of flow and concentration fields of macromolecules in a, slightly curved blood vessel was carried out. Based on these results, the effect of the bifurcation of a flow on the mass transport in a curved blood vessel was discussed. The macromolecules turned out to be easier to deposit in the inner part of the curved blood vessel near the critical Dean number. Once the Dean number is higher than the critical number, the bifurcation of the flow appears. This bifurcation can prevent macromolecules from concentrating in the inner part of the curved blood vessel. This result is helpful for understanding the possible correlations between the blood dynamics and atherosclerosis. The project supported by National Natural Science Foundation of China (10002003), JSPS Postdoctoral Fellowship for Foreign Researcher and Foundation for University Teachers, the Ministry of Education     

Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion

The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively in its own plane is investigated and the anomalous diffusion problems of the stress field and vortex sheet caused by this process are studied. Many previous and classical results can be considered as particular cases of this paper, such as the solutions of the fractional diffusion equations obtained by Wyss; the classical Rayleigh’s time-space similarity solution; the relationship between stress field and velocity field obtained by Bagley and co-worker and Podlubny’s results on the fractional motion equation of a plate. In addition, a lot of significant results also are obtained. For example, the necessary condition for causing the vortex sheet is that the time fractional diffusion index β must be greater than that of generalized second order fluid α; the establiihment of the vorticity distribution function depends on the time history of the velocity profile at a given point, and the time history can be described by the fractional calculus.     

弯曲圆管内漩涡结构分叉现象的理论研究

利用拓扑结构分析方法,分析了弯曲圆管内定常流在横截面上流线的奇点个数及分布规律,给出了二次流的漩涡数目由2个变为4个,流态结构发生分叉现象的理论判据。进而,利用Galerkin方法,得到了弯曲圆管内定常流的流函数和轴向速度的半解析表达式,给出了流态结构发生分叉现象的临界Dean数,所得结果与理论判则一致。     

Velocity overshoot of start-up flow for a Maxwellfluid in a porous half-space

Stokes' first problem has been investigated for a Maxwell fluid in a porous half-space for gaining insight into the effect of viscoelasticity on the start-up flow in a porous medium. An exact solution was obtained by using the Fourier sine transform. It was found that at large values of the relaxation time the velocity overshoot occurs obviously and the system exhibits viscoelastic behaviours. On the other hand, for short relaxation time the velocity overshoot disappears and the system exhibits viscous behaviours. A critical value of the relaxation time was obtained for the emergence of the velocity overshoot. Furthermore, it was found that the velocity overshoot is caused by both the viscoelasticity of the Maxwell fluid and the Darcy resistance resulting from the structure of the micropore in the porous medium.     

广义二阶流体涡流速度的衰减和温度扩散

将分数阶微积分运算引入到二阶流体的本构关系中,建立了带分数阶导数的广义二阶流体模型．研究了广义二阶流体涡流速度的衰减和温度扩散,利用分数阶导数的Laplace变换和广义Mittag-Leffler函数,得到了涡流速度场和温度场的精确解,分析了分数阶指数对涡流速度的衰减和温度扩散的影响．     

Relaxation Oscillation of Thermal Convection in Rotating Cylindrical Annulus

Chaotic thermal convection in a rapidly rotating cylindrical annulus is investigated numerically and the relaxation oscillation state is obtained under the no-slip boundary condition. The dominant frequency of the oscillation is inherited directly from a vacillating mode, whose nonlinear interaction with another high-frequency vacillating mode leads to the chaotic state at high Rayleigh numbers through an RTN-type route. Furthermore, the effects of Coriolis parameter and Rayleigh number on the quasi-periodic burst of kinetic energy are discussed as well.     

弯曲血管中的血液流动和大分子传质

采用数值模拟的方法,研究主动脉弯曲血管中的定常/脉动流动及低密度脂肪蛋白(LDL)和血清白蛋白(Albumin)传质．计算结果表明,对于主动脉弓模型,二次流漩涡的位置随时间变化．在弯曲变化比较剧烈的区域大分子浓度较高,壁面浓度外壁高于内壁．这些流动变化比较剧烈的区域可能是动脉硬化或血栓形成的危险区域．     

BLOOD FLOW AND MACROMOLECULAR TRANSPORT IN CURVED BLOOD VESSELS

A numerical analysis of the steady/pulsatile flow and macromolecular (such as LDL and Albumin) transport in curved blood vessels was carried out. The computational results predict that the vortex of the secondary flow is time-dependent in the aortic arch. The concentration of macromolecule concentrates at the region of sharp curve, and the wall concentration at the outer part is higher than that at the inner part. Atherosclerosis and thrombosis are prone to develop in such regions with sharp flow.