低雷诺数下多物体非定常复杂流动问题

The project focuses on the theoretical investigation for unsteady complex flows related to many bodies submerged in a low Reynolds number flow so as to explore the full coupling of boundaries of bodies with the flow field. Based on such a system with linear dissipation under hydrodynamic interactions, we hope to reveal the importance of fully coupled accelerations of bodies, investigate the characteristics of the acceleraions not in the directions of exerted hydrodynamic interactions due to spatial nonuniformity of added masses, explore spatial features of the immersed 'non-sphere' bodies translating coupled with rotating, explain the effects of physical parameters at body surfaces on their subsequent nonlinear dynamic behaviors, and futhermore, have a much better understanding of nonlinear migrations of the bodies and their diffusions as a coherent whole in order to disclose nature of full body-fluid hydrodynamic coupling and demonstrate phenomena of aggregation and separation. To do this, we shall adopt the Basset method associated with a technique of successive offset functions combined with a 'generalized cyclic permutation' to derive the velocity of the flow around N simple moving bodies, establish the dynamical equations of motion of these bodies with fully coupled accelerations, and then numerically solve these equations and discuss the solutions. We expect that the investigation will present the theoretical fundament to such engineering applications as transportation of particles and drops in chemical engineering, suspension and flocculation of micro-particles in hydraulic engineering, aggregation and sedimentation of PM 2.5 colloids in ecological environment and drug delivery in biomedical engineering.

本项目对线性耗散多物体流固系统（非定常Stokes方程）的非定常复杂流动问题进行理论研究，探索多物体边界和流场完全耦合的本质。通过对水动力相互作用的研究，揭示线性耗散下所有物体加速度全息耦合的重要性，以及由附加质量分布不均匀所导致的物体加速度不沿着水动力方向的相互作用机制；探讨非圆物体平动和转动耦合的空间特性，以及界面参数对物体非线性运动的影响。从而加深对流场中多物体非线性迁移和扩散现象的认识；寻找完全流固耦合对多物体运动的制约机理；研究物体间的水动力强相互作用对流固系统整体输运特性的影响，以及由物体局部非均匀分布和扰动造成的物体群表观上呈现的局部聚集和稀疏等宏观结构现象及相应的动力学过程。为此，我们将采用Basset的分离式解法结合连续补函数和广义循环排序方法以得出含有N个简单运动物体的流体速度场，建立加速度耦合的物体动力学方程组，进而数值求解方程、分析结果，为深入研究提供理论基础。

项目针对多个刚体或变形体在流场中的动力学问题进行了理论上的探讨，加深了对运动边界和物理场耦合问题的认识。就非定常描述水动力相互作用下多个物体的非线性迁移和扩散现象问题而言，找到了一些物体运动的制约机制。成果如下：.1．证明了多个刚体或变形体的Hamilton流-固系统中，描述每个物体载荷的动量框架和以能量作为指标参数的描述整个物体系统速度、加速度对某单一物体影响的Lagrange框架在动力学意义上是等价的。论证了Galilei相对性原理不适宜描述多物体的水动力相互作用问题，特别是变形体的游动问题，进而揭示了背景流场对多物体系统运动学演化的重要意义。此外，论证了所有物体平动、转动、变形加速度会对单一物体施加载荷，从而表明了这些作用成分对该物体非定常运动的刻画是不可或缺的。.2．推导了流体中简单二维细长变形体在保长度、等曲率变形下产生平动、转动运动的速度势。此速度势用来揭示变形体由静止到运动及转向机动等自推进游动机制。探讨重心移动、曲率半径改变对变形体非定常运动特性的影响。.3．理论上讨论了刚性板在具有Stokes流动特性的流场中解的完备性，以便建立其相应的基本解基函数，为精确地确定板状物体在重力场中的沉降运动奠定基础。.4．统计上探讨了微血管Stokes剪切流中肿瘤细胞在白细胞介导下准定常黏附和分离机制，揭示了血液流动对肿瘤细胞的迁移的影响。