Scholarlink

<p>We study the long-wavelength instability of a viscous Newtonian liquid film driven by gravity and flowing along a vertical cylinder. This study includes a control mechanism based on the injection and suction of liquid acting perpendicular to the cylinder wall, as suggested by Thompson Phys Fluids 28(1):012107, (2016) . First, we formulate the approximate boundary layer equations, which are valid up to second order in the gradient expansion. In order to reduce the dimensionality of the system, we use the weighted residual integration method, following the approach of Ruyer-Quil et al J Fluid Mech 603:431–462, (2008). Appropriate weight functions are selected before averaging the boundary layer equations over the film thickness. The resulting model accurately captures the nonlinear dynamics of the axisymmetric flow through two coupled evolution equations for the flow rate <i>q</i> and the film thickness <i>h</i>. A normal mode analysis is performed to determine the instability criterion. In addition, the Riccati transformation method is applied to solve the eigenvalue problem associated with the fully linearized Navier–Stokes equations. This numerical method is then used to validate the weighted residual model.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Modeling of a thin liquid film flowing down a vertical cylinder in the presence of a control mechanism

  • 期刊论文

  • 发表日期：

    2025年9月8日

查看全文
  • Abdelmalek Mehayech,
  • Nadia Mehidi Bouam,
  • Amar Djema,
  • Zakaria Haddad

摘要

We study the long-wavelength instability of a viscous Newtonian liquid film driven by gravity and flowing along a vertical cylinder. This study includes a control mechanism based on the injection and suction of liquid acting perpendicular to the cylinder wall, as suggested by Thompson Phys Fluids 28(1):012107, (2016) . First, we formulate the approximate boundary layer equations, which are valid up to second order in the gradient expansion. In order to reduce the dimensionality of the system, we use the weighted residual integration method, following the approach of Ruyer-Quil et al J Fluid Mech 603:431–462, (2008). Appropriate weight functions are selected before averaging the boundary layer equations over the film thickness. The resulting model accurately captures the nonlinear dynamics of the axisymmetric flow through two coupled evolution equations for the flow rate q and the film thickness h. A normal mode analysis is performed to determine the instability criterion. In addition, the Riccati transformation method is applied to solve the eigenvalue problem associated with the fully linearized Navier–Stokes equations. This numerical method is then used to validate the weighted residual model.