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ENCIT 2020
18th Brazilian Congress of Thermal Sciences and Engineering
Linear Stability Analysis of Non-Newtonian Free Surface Flows a Mathematical Study on the Temporal and Spatial Branches.
Submission Author:
Valdirene Rocho , SC , Brazil
Co-Authors:
Valdirene Rocho, Guilherme Henrique Fiorot, Sergio Viçosa Möller
Presenter: Valdirene Rocho
doi://10.26678/ABCM.ENCIT2020.CIT20-0197
Abstract
Free surface fluid flow may eventually present itself in sufficient conditions for certain hydrodynamic instabilities to appear. These instabilities are called roll waves and are hydrodynamic structures that propagate along with the flow, with constant velocity and amplitude. In this scenario, it is necessary to understand how the roll waves evolution occurs in order to control and predict the flow behavior. In this work, a theoretical approach was conducted using stability analysis to the mathematical model. The flow modeling was based on the Cauchy equations, with the Herschel-Bulkley rheological model inserted in the viscous part of the tension tensor. The objective of this work was to perform linear stability analysis and obtain information on the temporal and spatial branches of the solution obtained for the dispersion equation D(w, k)=0 of the problem. It was mathematically demonstrated that the instability criteria can be defined through the minimum Froude number (F_{min}) and Froude number on the singularity point (F_s), which retrieves solutions from the literature. In addition, this work explored the results for a Herschel-Bulkley type of fluid and evidenced asymptotic characteristics of the growth rates and wave propagation velocity of instabilities for long waves (k \rightarrow 0) and short waves ( k \rightarrow +\infty).
Keywords
Free-surface flow, Roll Waves, Herschel-Bulkley, stability analysis
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