充液超弹性气球的膨胀和收缩动力学
On the inflation and deflation dynamics of liquid-filled, hyperelastic balloons
摘要：
我们推导了一个降阶模型，描述了充液超弹性气球的膨胀和放气动力学，着重于无粘层流和气球的伸展运动。我们初步研究了固体的支配运动的流场和压力场，这在整个放气是通过解决潜在的问题。然而，在充气期间，流动分离在球囊内产生射流，需要不同的方法。这两种流态的分析导致一个简单的分段模型，描述的流体压力在充气和放气，然后通过有限元计算进行验证。然后，我们使用变分方法推导出方程的气球的动力学，产生一个非线性的混合振荡器方程，描述之间的相互作用的伸缩模式的气球，和截留的流体。分析和图形调查建议的模型，在不同的操作条件下，其静态和动态行为的光。我们建议的模型和它的基本假设进行了验证，利用一个完全耦合的有限元方案，表现出良好的协议。
英文摘要：
We derive a reduced-order model describing the inflation and deflation dynamics of a liquid-filled hyperelastic balloon, focusing on inviscid laminar flow and the extensional motion of the balloon. We initially study the flow and pressure fields for dictated motion of the solid, which throughout deflation are obtained by solving the potential problem. However, during inflation, flow separation creates a jet within the balloon, requiring a different approach. The analyses of both flow regimes lead to a simple piecewise model, describing the fluidic pressure during inflation and deflation, which is then verified by finite element computations. We then use a variational approach to derive the equation governing the balloon's dynamics, yielding a nonlinear hybrid oscillator equation, describing the interaction between the extensional mode of the balloon, and the entrapped fluid. Analytical and graphical investigations of the suggested model are presented, shedding light on its static and dynamic behaviour under different operating conditions. Our suggested model and its underlying assumptions are verified utilizing a fully coupled finite element scheme, showing excellent agreement.
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