Receptivity to forcing disturbances in subcritical liquid sheet flows

Abstract

The receptivity to forcing harmonic disturbances of transverse velocity in subcritical liquid sheet flows subjected to gravity is studied. The investigation is carried out both by employing the linear stability theory applied to a simplified one-dimensional inviscid model and by performing fully two-dimensional numerical simulations based on the Volume-of-Fluid technique. The computation of global sinuous eigenmodes and eigenvalues has required the removal of the singularity of the governing equation, for the first time carried out in the case of unconfined gaseous ambient. Direct numerical simulations of the unsteady sheet when continuously forced by a perturbation in lateral velocity are reported. The harmonic forcing, applied at the inlet section, basically excites sinuous modes of the system, related to the natural impulse response. The results of receptivity have been treated by employing a proper one-dimensional reduction technique to compare numerical data with the corresponding findings of the stability theory. Depending on the Reynolds number, two different behaviors are observed: at low Re the large viscous effect makes the system overdamped; as Re increases and the inviscid conditions are approaching, the frequency response exhibits a peak frequency (resonance) which closely agrees with the frequency of the least stable eigenvalue. The various stations synchronize with the critical station as Re increases, and therefore it forces the global oscillations of the flow field. This behavior of the critical station retrieves the role of wavemaker, which fails for high-frequency forcing. The resonance characteristics of the sheet have been further analyzed by inspecting the fully two-dimensional velocity fields. A major finding at low forcing frequency is the nonlinear varicose distortion of the sheet thickness that progressively envelops the basic sinuous shape when the inviscid conditions are approaching.