Modelling gravity-driven film flow on inclined corrugated substrate using a high fidelity weighted residual integral boundary-layer method
Modelling gravity-driven film flow on inclined corrugated substrate using a high fidelity weighted residual integral boundary-layer method
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DOI：
10.1063/1.5063013
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发表时间：
2019-02
影响因子：
4.6
通讯作者：
S. Veremieiev;D. Wacks
中科院分区：
文献类型：
--
作者：
S. Veremieiev;D. Wacks
本文对周期性波纹基底上自由表面重力驱动液膜流动的稳定性进行了计算研究。基础数学公式构成了Ruyer-Quil和Manneville提出的加权剩余积分边界层（WIBL）方法的扩展[“改进的倾斜平面流动建模”，Eur. Phys.J. B 15（2），357 - 369（2000）]和D'Alessio等人["Instability in gravity-driven flow over uneven surfaces，" Phys.Fluids 21（6），062105（2009）]，以在长波长展开中包括三阶和四阶项。采用Floquet理论得到了自由表面的稳态解和相应的中性扰动曲线，并与相应的实验数据和完整的Navier-Stokes（N-S）解进行了验证。正弦和平滑的矩形波纹变陡度被认为是。结果表明，该模型是能够预测的稳定性特征图案，包括短波的鼻子和稳定/不稳定的岛屿实验报告的粘性薄膜流在倾斜的地形，提供了一个有吸引力的权衡之间的完整的N-S计算的准确性和效率的积分方法。研究表明，WIBL模型的计算精度随雷诺数和振幅的增大而减小，随陡度参数和波长与毛细管长度之比的增大而增大。基础数学公式构成了Ruyer-Quil和Manneville提出的加权剩余积分边界层（WIBL）方法的扩展[“改进的倾斜平面流动建模”，Eur. Phys.J. B 15（2），357 - 369（2000）]和D'Alessio等人["Instability in gravity-driven flow over uneven surfaces，" Phys.Fluids 21（6），062105（2009）]，以在长波长展开中包括三阶和四阶项。采用Floquet理论得到了自由表面的稳态解和相应的中性扰动曲线，并与相应的实验数据和完整的Navier-Stokes（N-S）解进行了验证。正弦和平滑的矩形波纹变陡度被认为是。结果表明，该模型是能够预测的特征模式的稳定性，包括短期的水和天然气。
A computational investigation is conducted concerning the stability of free-surface gravity-driven liquid film flow over periodic corrugated substrate. The underpinning mathematical formulation constitutes an extension of the weighted residual integral boundary-layer (WIBL) method proposed by Ruyer-Quil and Manneville [“Improved modeling of flows down inclined planes,” Eur. Phys. J. B 15(2), 357–369 (2000)] and D’Alessio et al. [“Instability in gravity-driven flow over uneven surfaces,” Phys. Fluids 21(6), 062105 (2009)] to include third- and fourth-order terms in the long-wavelength expansion. Steady-state solutions for the free-surface and corresponding curves of neutral disturbances are obtained using Floquet theory and validated against corresponding experimental data and full Navier-Stokes (N-S) solutions. Sinusoidal and smoothed rectangular corrugations with variable steepness are considered. It is shown that the model is capable of predicting characteristic patterns of stability, including short-wave nose and isles of stability/instability as reported experimentally for viscous film flow over inclined topography, providing an attractive trade-off between the accuracy of a full N-S computation and the efficiency of an integral method. The range of parameter values for which the WIBL model remains valid is established; in particular, it is shown that its accuracy decreases with the Reynolds number and corrugation amplitude, but increases with the steepness parameter and ratio of wavelength to capillary length.A computational investigation is conducted concerning the stability of free-surface gravity-driven liquid film flow over periodic corrugated substrate. The underpinning mathematical formulation constitutes an extension of the weighted residual integral boundary-layer (WIBL) method proposed by Ruyer-Quil and Manneville [“Improved modeling of flows down inclined planes,” Eur. Phys. J. B 15(2), 357–369 (2000)] and D’Alessio et al. [“Instability in gravity-driven flow over uneven surfaces,” Phys. Fluids 21(6), 062105 (2009)] to include third- and fourth-order terms in the long-wavelength expansion. Steady-state solutions for the free-surface and corresponding curves of neutral disturbances are obtained using Floquet theory and validated against corresponding experimental data and full Navier-Stokes (N-S) solutions. Sinusoidal and smoothed rectangular corrugations with variable steepness are considered. It is shown that the model is capable of predicting characteristic patterns of stability, including short-wa...