柔性粘弹性管中的瞬态可压缩流动
Transient compressible flow in a compliant viscoelastic tube
AI总结：
针对MEMS等领域的相关问题，研究低雷诺数下粘弹性管内可压缩流动的瞬态流固耦合，通过摄动展开解析求解，分析三类问题并揭示流固耦合对流量及频率响应的影响。
摘要：
受微机电系统（MEMS）控制器气动驱动、芯片实验室或仿生软机器人相关问题，以及气体与软固体微流变学研究的启发，我们分析了低雷诺数下可压缩流动在粘弹性管内传输时的瞬态流固耦合（FSI）问题。我们将流体密度表示为压力的线性函数，并采用润滑近似进一步简化流体动力学问题；另一方面，结构力学由修正的Donnell壳理论描述，该理论考虑了Kelvin-Voigt型线性粘弹性力学响应。流体与结构力学问题通过管的径向变形和流体动力压力耦合。对于小可压缩数和弱耦合情况，通过摄动展开解析求解方程。我们分析了三个示例问题：第一，获得了稳态流动条件下压力的精确（隐式）解；第二，求解了管入口脉冲增压的瞬态问题；第三，分析了入口压力振荡的瞬态响应。我们表明，入口压力振荡会在管内产生声流，这归因于流固耦合与可压缩性相互作用诱导的非线性压力梯度；此外，我们证明流固耦合会使体积流量提升。流体动力压力振荡表现出低通频率响应（对振荡周期取平均时），而管变形的频率响应类似带通滤波器。
英文摘要：
Motivated by problems arising in the pneumatic actuation of controllers for micro-electromechanical systems (MEMS), labs-on-a-chip or biomimetic soft robots, and the study of microrheology of both gases and soft solids, we analyze the transient fluid--structure interaction (FSIs) between a viscoelastic tube conveying compressible flow at low Reynolds number. We express the density of the fluid as a linear function of the pressure, and we use the lubrication approximation to further simplify the fluid dynamics problem. On the other hand, the structural mechanics is governed by a modified Donnell shell theory accounting for Kelvin--Voigt-type linearly viscoelastic mechanical response. The fluid and structural mechanics problems are coupled through the tube's radial deformation and the hydrodynamic pressure. For small compressibility numbers and weak coupling, the equations are solved analytically via a perturbation expansion. Three illustrative problems are analyzed. First, we obtain exact (but implicit) solutions for the pressure for steady flow conditions. Second, we solve the transient problem of impulsive pressurization of the tube's inlet. Third, we analyze the transient response to an oscillatory inlet pressure. We show that an oscillatory inlet pressure leads to acoustic streaming in the tube, attributed to the nonlinear pressure gradient induced by the interplay of FSI and compressibility. Furthermore, we demonstrate an enhancement in the volumetric flow rate due to FSI coupling. The hydrodynamic pressure oscillations are shown to exhibit a low-pass frequency response (when averaging over the period of oscillations), while the frequency response of the tube deformation is similar to that of a band-pass filter.
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