Modal decomposition analysis of unsteady viscous liquid sheet flows

Abstract

The unsteady dynamics of a gravitational liquid sheet, driven by a continuous harmonic perturbation in the lateral velocity component applied at the inlet section, is analyzed. The topology and the dynamics of the relevant flow structures are characterized by applying POD (Proper Orthogonal Decomposition) and spectral POD (SPOD) modal decompositions on two-dimensional two-phase numerical simulation data obtained with the volume-of-fluid approach. The investigation is carried out by varying the Weber number, the forcing frequency (Strouhal number), and the Reynolds number. The supercritical regime (We > 1) features a traveling perturbation, exhibiting a spatial structure with leading sinuous modes. SPOD spectra confirm the occurrence of a discontinuity in frequency response between the supercritical and subcritical regimes. In the subcritical regime (We < 1), the investigation highlights the excitation of a combined sinuous–varicose motion when the system is driven at resonance frequency for a relatively high Reynolds number (approaching the inviscid limit). The emergence of varicose modes is favored by low Weber numbers. The excitation of these modes occurs when the Weber number is decreased from We = 0.90 down to 0.75, with a progressive shift of the varicose mode from higher harmonics toward the main frequency; it can be considered as a possible mechanism of breakup observed in experiments when the inlet flow rate is progressively reduced. The flow reconstruction based on both POD and SPOD confirms the good capability of SPOD modes to capture dynamically relevant features of the fluid motion in subcritical conditions.

Natural frequency discontinuity of vertical liquid sheet flows at transcritical threshold

“…In the subcritical regime, instead, an agreement within 5 % was found between the natural frequency arising from the model and the resonance frequency of the VOF simulated sheet subjected to a time continuous sinusoidal transverse velocity forcing v f applied at the inlet section (Della Pia et al 2021). In the latter case, the curtain shape was found to be influenced by a nonlinear interaction between a dominant sinuous mode and secondary varicose ones, which were identified through the spectral proper orthogonal decomposition of the two-phase flow field (Colanera et al 2021).…”

“…In the latter case, the curtain shape was found to be influenced by a nonlinear interaction between a dominant sinuous mode and secondary varicose ones, which were identified through the spectral proper orthogonal decomposition of the two-phase flow field (Colanera et al. 2021).…”

Extended cluster-based network modeling for coherent structures in turbulent flows

“…These modes can be used to construct reduced-order models and control the flow (Rowley and Dawson [10]). Spectral Proper Orthogonal Decomposition (SPOD) (Sieber et al [11]) can extract phenomena occurring at different frequencies and energy levels and is successfully employed in different flow configurations (Ribeiro and Wolf [12], Chu et al [13], Colanera et al [14], Karami and Soria [15]). Recently, the integration of Machine Learning has opened new perspectives for understanding and modeling complex behaviors.…”

Modal analysis of a 3D gravitational liquid sheet

“…By means of these methodologies, we explore the effect of two main governing parameters on the flow dynamics, namely the liquid sheet aspect ratio, AR = W/H, where H and W are the sheet inlet thickness and width, and the Weber number, W e = ρ l U H/(2σ), in which U is the inlet liquid velocity, ρ l the liquid density, and σ the surface tension coefficient. Finally, for the highest aspect ratio value considered (AR = 40), we investigate the forced dynamics of the system excited by a harmonic perturbation in transverse velocity component applied at the inlet section, comparing results with ones arising from a purely two-dimensional analysis of the flow [3]. The obtained results highlight the low rank behavior exhibited by the flow, suggesting that reduced order modeling could be particularly appealing to reduce complexity and computational effort in numerical simulation of this class of flows.…”