his work studies the stability properties of a dielectric liquid confined between two indefinite plane electrodes, the so-called electro-hydrodynamic (EHD) electro- convection problem, that presents a full coupling between the electric field and the velocity field. The EHD stability has been already studied in the past, owing to its practical importance and theoretical interest, but several open problems still exist. In fact, very simple analytical and/or numerical models have been employed, with sometimes far-reaching simplifying assumptions like that of neglecting the charge diffusion process altogether. As a matter of fact, discrepancies exist between the critical values of the governing parameters measured in experiments as compared to those educed from theoretical analysis. This work reports on several, substantial improvements of the state-of-the-art in the study of EHD electroconvection. The effect of charge diffusion is taken into account, and a cross-flow is explicitly considered in the form of a laminar Poiseuille flow. Moreover, and perhaps most importantly, we apply to the EHD problem the re- cent theoretical tools of non-modal stability analysis. After a physically sound norm is defined to quantify the disturbance amplitude, the non-modal stability analysis allows us to describe the non-normality of the underlying stability operator, which implies that the EHD system is capable to support transient growth, albeit of mild intensity, in both the hydrostatic case and in the case with shear. The important role of charge diffusion is described, which enhances instability through increased mixing, and is connected to wall-based modes. The EHD-Poiseuille system is found to be unstable to perturbations that at low Re are dominated by the electrical parameters.
In questo lavoro cono state indagate le proprit di stabilit di una delle pi classiche confugrazioni che vede l’accoppiamento di un campo di moto fluido all’effetto di un campo elettrico, ossia la presenza di un liquido dielettrico all’interno di due elettrodi di geometria piana indefinita. Questo tipo di problema meglio noto come proble- ma elettrodinamico o EHD ed il fenomeno d’istabilit che lo caratterizza chiamato elettroconvezione. Data la sua importanza sia dal punto di vista applicativo che dal punto di vista teorico il fenomeno dell’elettroconvezione e dei processi che la innes- cano sono stati oggetto di molte attenzioni. Purtroppo il profondo accoppiamento accoppiamento che esiste tra il fluido e il campo elettrico ha reso di fatto necessario lo sviluppo di modelli matematici molto semplificati. Il trascurare la diffusione di carica e l’effetto di una correte imposta ha difatto accumato tutti i lavori fino ad oggi rivelando serie discrepanze tra i risultati teorici e quelli sperimentali. Questo lavoro ha dunque la pretesa di includere ed indagare tutti i fenomeni fisici trascurati fino ad ora quali la diffusione di carica e l’effeto di una corrente sovraim- posta. Inoltre si voluto indagare anche gli aspetti legati alla non normalit dell’oper- atore EHD. Questo infatti non esclude che il problema qui trattato presenti crescite energetiche a tempo finito. Si dimostrato che la diffusione di carica ha un importanto ruolo instabilizzanze sia sul problema idrostatico che nel caso con flusso di Poisoulle e che sono presenti crescite energetiche a tempo finito attraversomeccanismi sia elettrici che puramente fluidodinamici.
Non modal linear stability analysis of an EHD channel flow
BEZZECCHI, EMANUELE
2009/2010
Abstract
his work studies the stability properties of a dielectric liquid confined between two indefinite plane electrodes, the so-called electro-hydrodynamic (EHD) electro- convection problem, that presents a full coupling between the electric field and the velocity field. The EHD stability has been already studied in the past, owing to its practical importance and theoretical interest, but several open problems still exist. In fact, very simple analytical and/or numerical models have been employed, with sometimes far-reaching simplifying assumptions like that of neglecting the charge diffusion process altogether. As a matter of fact, discrepancies exist between the critical values of the governing parameters measured in experiments as compared to those educed from theoretical analysis. This work reports on several, substantial improvements of the state-of-the-art in the study of EHD electroconvection. The effect of charge diffusion is taken into account, and a cross-flow is explicitly considered in the form of a laminar Poiseuille flow. Moreover, and perhaps most importantly, we apply to the EHD problem the re- cent theoretical tools of non-modal stability analysis. After a physically sound norm is defined to quantify the disturbance amplitude, the non-modal stability analysis allows us to describe the non-normality of the underlying stability operator, which implies that the EHD system is capable to support transient growth, albeit of mild intensity, in both the hydrostatic case and in the case with shear. The important role of charge diffusion is described, which enhances instability through increased mixing, and is connected to wall-based modes. The EHD-Poiseuille system is found to be unstable to perturbations that at low Re are dominated by the electrical parameters.File | Dimensione | Formato | |
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https://hdl.handle.net/10589/13141