Respiratory-type flows facilitate the exchange of fluid through an orifice in many natural and engineered environments. The external flow dynamics for an idealized respiratory-type flow, consisting of periodic inhalation and exhalation of a fixed tidal volume of fluid through a circular orifice at the end of a tube, are investigated. In both numerical and experimental investigations, inertial effects produce asymmetric inhalant and exhalant flow structures, resulting in a dynamic exchange of fluid volume across the orifice. A Lagrangian approach is used to quantify the reinhalation ratio $r_I$, defined as the amount of exhaled fluid that is subsequently reinhaled. Results show that these flow structure asymmetries and hence $r_I$ are strongly sensitive to Reynolds number, and, to a lesser extent, Womersley number or Strouhal number. At low Reynolds number, where viscous effects dominate, we observe flow kinematics similar to an ideal source or sink and the exchange ratio asymptotes to an upper limit. As the inertial effects become more dominant with increasing Reynolds number, we instead observe jetlike flow structures and a rapid decrease in $r_I$. In the context of biological sensory and metabolic processes, these results suggest organisms can optimize the exchange of fluid with surrounding environment by modulating the asymmetries in the flow structures arising during olfactory and respiratory activity.

中文翻译：

---

理想呼吸型流动的动力学：中间雷诺数之间的潮汐交换

在许多自然环境和工程环境中，呼吸型流量有助于通过孔口进行流体交换。研究了理想呼吸型流动的外部流动动力学，包括通过管道末端的圆形孔口定期吸入和呼出固定潮气量的流体。在数值研究和实验研究中，惯性效应都会产生不对称的吸入和呼出气流结构，从而导致整个孔内流体体积的动态交换。拉格朗日方法用于量化再吸入率${\mathrm{[R}}_{\mathrm{一世}}$，定义为随后再吸入的呼出液体量。结果表明，这些流动结构不对称，因此${\mathrm{[R}}_{\mathrm{一世}}$对雷诺数，以及在较小程度上对沃默斯利数或斯特劳哈尔数非常敏感。在低雷诺数下（粘性作用占主导），我们观察到与理想源或汇相似的流运动学，并且交换比渐近达到上限。随着惯性效应随着雷诺数的增加而变得越来越占主导地位，我们改为观察射流状的流动结构并迅速减小${\mathrm{[R}}_{\mathrm{一世}}$。在生物学的感觉和代谢过程中，这些结果表明生物体可以通过调节嗅觉和呼吸活动中产生的流动结构的不对称性来优化与周围环境的流体交换。