Eventos Anais de eventos
ENCIT 2022
19th Brazilian Congress of Thermal Sciences and Engineering
The Effect of Rheological Properties on the Amplification of Roll Waves
Submission Author:
Valdirene Rocho , SC , Brazil
Co-Authors:
Valdirene Rocho, Sergio Viçosa Möller, Guilherme Henrique Fiorot
Presenter: Valdirene Rocho
doi://10.26678/ABCM.ENCIT2022.CIT22-0309
Abstract
Due to their complex nature, fluids of non-Newtonian nature can be present in the most diverse types of flows, whether industrial or natural. The flow behavior of these types of fluids is subject to various dynamic conditions that must be controlled to ensure their smooth evolution, without producing distortions in the flow. Furthermore, these flows themselves can develop instabilities during their time-spatial evolution and, thus, it is necessary to understand how this evolution occurs. In this context, this paper presents a theoretical analysis concerning two types of linear stability analysis for free-surface flows considering a power-law fluid. The analysis is conducted to verify the flow stability and to obtain the wave growth rate from flow parameters. First, a small perturbation linear stability analysis was conducted to obtain the marginal stability curve and the spatial wave growth rate. This analysis was studied as a consequence of the hyperbolic character of the equations that constitute the linearized system of Saint-Venant type equations. From this analysis, it was possible to establish the domain suitable for the generation of roll waves as a function of the Froude number. Next, a stability analysis was performed through a Taylor series expansion on the same system of equations, expanding the solution around the steady and uniform flow, to obtain a general function for the wave growth rate. The spatial growth rate is presented based on the linearized model, neglecting terms of higher orders. This study aims to evaluate the rheological effect of non-Newtonian properties on the amplification rate and to obtain indications about the spatial development of roll waves as a function of such parameters. From the obtained functionals, it was possible to perform comparative analyses, identifying and separating the effect of the flow index on the spatial evolution of instability within the flow. Moreover, through the obtained functionals, it was also possible to estimate the minimum length criterion necessary for the roll waves to travel through the channel until they become stable, with a criterion still dependent on the Froude number.
Keywords
Free-surface flow, stability analysis, power-law fluid, Roll Waves
