模拟生物运动的流固耦合数值研究
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摘要
生物运动中的流固祸合广泛存在于自然界中,其数值模拟方法和相关的物理机理对于人们认识生物运动规律具有重要的作用。此外,此类研究有助于仿生技术的发展,为国民经济建设和国防事业提供技术储备。本文发展了一种新型的罚内置边界-格子玻尔兹曼方法,并围绕柔性丝线/柔性板和流体的相互作用进行了若干研究。主要工作和研究成果如下
(1)发展了适合于具有质量的弹性丝线与周围粘性流体相互作用的罚内置边界玻尔兹曼方法。在这种方法中,丝线上的速度边界条件是通过将其对流体的应力分布到周围流体点上来实现的。为了计算丝线的惯性效应,假定物理丝线仪含有弹性特性,并与流体直接作用；引入只有惯性特性的虚拟(ghost)丝线,它携带丝线的所有质量,但不与流体直接相互作用。物理丝线和虚拟丝线之间通过虚拟弹簧相连,使得物理丝线和虚拟丝线的综合行为与具有惯性特性和弹性特性的丝线相当。这样处理能增加数值稳定性,突破了格子玻尔兹曼方法难以模拟具有质量的弹性丝线与周围流体相互作用的局限性。
(2)研究了弹性丝线和下游刚体的相互干扰。通过改变Reynolds数和丝线与刚体的间距,发现了五种耦合模态,分别为静止状态、涡脱落模态、摆动抑制模态、摆动解耦模态和摆动增益模态。进一步分析发现丝线摆动加剧是由于两物体上脱落涡的同步与合并引起的,尽管在动增益模态中丝线摆动振幅很大,但丝线仍然获得良好的减阻效果,这是圆柱阻塞效应导致丝线有效来流速度的减小和丝线背风面压力的提升引起的。丝线长度和质量比对丝线和刚体相互作用的定性结果影响不大,此外,处于尾迹区的刚体总是获得减阻。
(3)研究了三根并行排列丝线的耦合摆动问题。通过系统地改变丝线间的侧向距离,发现了七种不同的丝线耦合摆动模态,包括单丝模态、对称模态、反相摆动模态、半频摆动模态、无理频率摆动模态、同相摆动模态和不规则摆动模态。通过对流场结构演化的分析,在丝线尾迹中发现了四种典型涡结构,包括合并涡结构、对称涡结构、不规则涡结构和独立涡街结构。通过对比分析发现,涡结构与丝线耦合模态和动力学特征密切相关。此外.在不同的模态中丝线的机械能不同,低机械能的模态更容易被激发。(4)研究了均匀来流中三维柔性板摆动的流固耦合问题。在数值模拟中观察到无质量柔性板的整体稳定性现象,即无论其他参数或者扰动有多大,柔性板总会恢复到静止伸展状态。在一定的参数范围内,系统存在双稳定性现象,即在不同的初始扰动之下,柔性板可能恢复到静止伸长状态(扰动较小时),也可能会失稳进入持续摆动状态(扰动较大时)。将Squire定理加以推广来解释三维柔性板的稳定性和二维丝线情况的区别和联系。此外,通过对柔性板流体小扰动系统能量特性和柔性板周围压力场分布情况的分析,发现系统在正能量波与负能量波的交汇处失稳,要维持持续摆动状态,柔性板必须和周围流体交换能量。
Flow-structure interaction problems inspired from bio-locomotion are ubiquitous in nature. The relevant numerical methods and the basic mechanism of flow-structure interaction are important for understanding the biobehavior. In addition, this issue has the potential to revolutionize our sensing and information gathering capabilities in arcas such as environmental monitoring and homeland security. In this thesis, a new version of penalty immersed boundary method (IBM) based on multi-block lattice Boltzmann method (LBM) is developed, and several topics on interaction be-tween flexible filament(s)/plate and the ambient viscous fluid are studicd. The main conclusions are given as follows:
(1) A modified penalty IBM based on a multi-block LBM is developed to solve the flow-structure interaction problems involving the massive filaments. The effect of the filament is handled by the IBM in which the stress exerted by the filament on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the filament is incorporated by connecting this filament through virtual springs to a ghost filament with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problem.
(2) A filament flapping in the bow wake of a rigid body is considered numerically in order to study the hydrodynamic interaction between flexible and rigid bodies in tandem arrangement. It is shown that the results largely depend on the gap between the two bodies and the Reynolds number. The flexible filament may have larger vibration amplitude but meanwhile experience a reduced drag force. On the other hand, the trailing rigid body enjoys a drag reduction. The qualitative behavior of the filament is independent of the filament's length and mass ratio, and the shape of the rigid body for the parameter regime considered. The result is in contrast with the interaction between two rigid or two flexible objects in tandem arrangement.
(3) A viscous flow past three filaments in side-by-side arrangement at low Reynolds number is studied by numerical simulations and is accolnpanied by a linear sta-bility analysis for inviscid flow. The dynamic characteristics of the filaments are studied while varying the separation distance between the filaments, Reynolds number, and bending rigidity. Seven distinct coupling modes of the filaments including the single-filament mode, symmetrical mode, out-el-phase mode, half-frequency mode, irrational-frequency mode, in-phase synchronized mode, and an erratic flapping state are identified as the separation distance is varied. Four typical vortex structures are observed in the wake of the filaments and are de-scribed as the coalesced vortices, symmetrical vortices, erratic vortices and inde-pendent vortex streets. The vortex structures are highly related to the coupling modes and dynamic characteristics of the filaments. As the Reynolds number is increased or as the bending rigidity is reduced, the filaments gain more energy and may transition from one coupling mode to another.
(4) A three dimensional flexible plate in a uniform flow is numerically and analyt-ically studied. The globally stable motion is observed for the massless plate. The sustained flapping of the plate only occurs when plate mass is involved. Within a certain range of parameters, the system is bistable, which means that the plate can settle into either rest state or sustained flapping depending on the initial conditions. The Squire's theorem is developed to explain the stability and the transformation is obtained using the incoming flow velocity or flutter speed and wave numbers as the transform variables. The analysis of the energy prop-erties in the plate-fluid system and the pressure distribution around the plate reveals that the onset of instability occurs when positive and negative energy waves coalesce and the energy exchange between the plate and the ambient fluid is necessary for the plate to perform sustained flapping.
(1)发展了适合于具有质量的弹性丝线与周围粘性流体相互作用的罚内置边界玻尔兹曼方法。在这种方法中,丝线上的速度边界条件是通过将其对流体的应力分布到周围流体点上来实现的。为了计算丝线的惯性效应,假定物理丝线仪含有弹性特性,并与流体直接作用；引入只有惯性特性的虚拟(ghost)丝线,它携带丝线的所有质量,但不与流体直接相互作用。物理丝线和虚拟丝线之间通过虚拟弹簧相连,使得物理丝线和虚拟丝线的综合行为与具有惯性特性和弹性特性的丝线相当。这样处理能增加数值稳定性,突破了格子玻尔兹曼方法难以模拟具有质量的弹性丝线与周围流体相互作用的局限性。
(2)研究了弹性丝线和下游刚体的相互干扰。通过改变Reynolds数和丝线与刚体的间距,发现了五种耦合模态,分别为静止状态、涡脱落模态、摆动抑制模态、摆动解耦模态和摆动增益模态。进一步分析发现丝线摆动加剧是由于两物体上脱落涡的同步与合并引起的,尽管在动增益模态中丝线摆动振幅很大,但丝线仍然获得良好的减阻效果,这是圆柱阻塞效应导致丝线有效来流速度的减小和丝线背风面压力的提升引起的。丝线长度和质量比对丝线和刚体相互作用的定性结果影响不大,此外,处于尾迹区的刚体总是获得减阻。
(3)研究了三根并行排列丝线的耦合摆动问题。通过系统地改变丝线间的侧向距离,发现了七种不同的丝线耦合摆动模态,包括单丝模态、对称模态、反相摆动模态、半频摆动模态、无理频率摆动模态、同相摆动模态和不规则摆动模态。通过对流场结构演化的分析,在丝线尾迹中发现了四种典型涡结构,包括合并涡结构、对称涡结构、不规则涡结构和独立涡街结构。通过对比分析发现,涡结构与丝线耦合模态和动力学特征密切相关。此外.在不同的模态中丝线的机械能不同,低机械能的模态更容易被激发。(4)研究了均匀来流中三维柔性板摆动的流固耦合问题。在数值模拟中观察到无质量柔性板的整体稳定性现象,即无论其他参数或者扰动有多大,柔性板总会恢复到静止伸展状态。在一定的参数范围内,系统存在双稳定性现象,即在不同的初始扰动之下,柔性板可能恢复到静止伸长状态(扰动较小时),也可能会失稳进入持续摆动状态(扰动较大时)。将Squire定理加以推广来解释三维柔性板的稳定性和二维丝线情况的区别和联系。此外,通过对柔性板流体小扰动系统能量特性和柔性板周围压力场分布情况的分析,发现系统在正能量波与负能量波的交汇处失稳,要维持持续摆动状态,柔性板必须和周围流体交换能量。
Flow-structure interaction problems inspired from bio-locomotion are ubiquitous in nature. The relevant numerical methods and the basic mechanism of flow-structure interaction are important for understanding the biobehavior. In addition, this issue has the potential to revolutionize our sensing and information gathering capabilities in arcas such as environmental monitoring and homeland security. In this thesis, a new version of penalty immersed boundary method (IBM) based on multi-block lattice Boltzmann method (LBM) is developed, and several topics on interaction be-tween flexible filament(s)/plate and the ambient viscous fluid are studicd. The main conclusions are given as follows:
(1) A modified penalty IBM based on a multi-block LBM is developed to solve the flow-structure interaction problems involving the massive filaments. The effect of the filament is handled by the IBM in which the stress exerted by the filament on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the filament is incorporated by connecting this filament through virtual springs to a ghost filament with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problem.
(2) A filament flapping in the bow wake of a rigid body is considered numerically in order to study the hydrodynamic interaction between flexible and rigid bodies in tandem arrangement. It is shown that the results largely depend on the gap between the two bodies and the Reynolds number. The flexible filament may have larger vibration amplitude but meanwhile experience a reduced drag force. On the other hand, the trailing rigid body enjoys a drag reduction. The qualitative behavior of the filament is independent of the filament's length and mass ratio, and the shape of the rigid body for the parameter regime considered. The result is in contrast with the interaction between two rigid or two flexible objects in tandem arrangement.
(3) A viscous flow past three filaments in side-by-side arrangement at low Reynolds number is studied by numerical simulations and is accolnpanied by a linear sta-bility analysis for inviscid flow. The dynamic characteristics of the filaments are studied while varying the separation distance between the filaments, Reynolds number, and bending rigidity. Seven distinct coupling modes of the filaments including the single-filament mode, symmetrical mode, out-el-phase mode, half-frequency mode, irrational-frequency mode, in-phase synchronized mode, and an erratic flapping state are identified as the separation distance is varied. Four typical vortex structures are observed in the wake of the filaments and are de-scribed as the coalesced vortices, symmetrical vortices, erratic vortices and inde-pendent vortex streets. The vortex structures are highly related to the coupling modes and dynamic characteristics of the filaments. As the Reynolds number is increased or as the bending rigidity is reduced, the filaments gain more energy and may transition from one coupling mode to another.
(4) A three dimensional flexible plate in a uniform flow is numerically and analyt-ically studied. The globally stable motion is observed for the massless plate. The sustained flapping of the plate only occurs when plate mass is involved. Within a certain range of parameters, the system is bistable, which means that the plate can settle into either rest state or sustained flapping depending on the initial conditions. The Squire's theorem is developed to explain the stability and the transformation is obtained using the incoming flow velocity or flutter speed and wave numbers as the transform variables. The analysis of the energy prop-erties in the plate-fluid system and the pressure distribution around the plate reveals that the onset of instability occurs when positive and negative energy waves coalesce and the energy exchange between the plate and the ambient fluid is necessary for the plate to perform sustained flapping.
引文
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