The chromatic confocal measurement technique is used to investigate the dynamics of radially expanding free liquid sheets generated by liquid jet impingement onto the flat end of a harmonically excited cylinder. Measurements of the sinuous-mode capillary waves are compared to experimental results reported by Bremond et al. (2007) and analytical solutions from two inviscid linear theories: The "aerodynamic (wave-growth)" theory by Bremond et al. (2007), which considers the interaction between the liquid film and the surrounding gas phase, and the linear theory by Tirumkudulu and Paramati (2013) which neglects the gas phase surrounding the liquid sheet but predicts growth of forced sinuous disturbances due to higher-order inertia terms associated with the thinning of the radially expanding sheet (“thinning” theory). For liquid Weber numbers Wed based on impinging jet velocity and jet diameter which are larger than 800 and aerodynamically stable forcing conditions, agreement with "thinning" theory is found in terms of radial positions of nodes and anti-nodes of the sheet disturbance envelope as well as growth of envelope maxima and minima. However, absolute amplitude values are significantly overpredicted in this case. For all other investigated operating conditions where instability due to film thinning is expected to dominate film dynamics (according to "thinning theory"), no such instability was observed experimentally. For most investigated cases, "aerodynamic wave-growth" theory agreed better with the experimentally observed film behavior. The importance of the naturally most-amplified aerodynamic mode was considered but could not be quantified as part of the present investigation.

中文翻译：

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使用彩色共焦测量的机械强制径向膨胀自由平面液体片上的正弦波测量

彩色共焦测量技术用于研究由液体射流撞击谐波激发圆柱体的平端产生的径向膨胀自由液体片的动力学。将正弦模式毛细管波的测量结果与 Bremond 等人报告的实验结果进行了比较。(2007) 和两个无粘性线性理论的解析解：Bremond 等人的“空气动力学（波浪增长）”理论。(2007)，考虑了液膜与周围气相之间的相互作用，以及 Tirumkudulu 和 Paramati (2013) 的线性理论，该理论忽略了液膜周围的气相，但预测由于高阶引起的强制正弦扰动的增长与径向膨胀板变薄相关的惯性项（“变薄”理论）。对于基于大于 800 的撞击射流速度和射流直径以及空气动力学稳定的强迫条件的液体韦伯数 Wed，在薄片扰动包络线的节点和波腹的径向位置方面也符合“减薄”理论作为信封最大值和最小值的增长。然而，在这种情况下，绝对振幅值被显着高估了。对于所有其他研究的操作条件，由于薄膜变薄导致的不稳定性预计将主导薄膜动力学（根据“变薄理论”），实验上没有观察到这种不稳定性。对于大多数调查案例，“气动波增长”理论与实验观察到的薄膜行为更吻合。