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Abstract
This paper deals with a mathematical modeling of flow stability of Newtonian and non-Newtonian fluids in the gap between two concentric cylinders, one of which rotates. A typical feature of the flow is the formation of a vortex flow, so-called Taylor vortices. Vortex structures are affected by the speed of the rotating cylinder and the physical properties of the fluids, i.e., viscosity and density. Analogy in terms of viscosity is assumed for non-Newtonian and magnetorheological fluids. Mathematical models of laminar, transient and turbulent flow with constant viscosity and viscosity as a function of the deformation gradient were formulated and numerically solved to analyze the stability of single-phase flow. To verify them, a physical experiment was performed for Newtonian fluids using visualizations of vortex structures—Taylor vortices. Based on the agreement of selected numerical and physical results, the experience was used for numerical simulations of non-Newtonian magnetorheological fluid flow.
Highlights
Immiscible liquids are specified as a system of two components, e.g., liquid–liquid or liquid–solid phase
The solid phase is represented by particles dispersed in the carrier fluid
In case of magnetorheological fluids, we must account for the influence of the magnetic field, which can change the Newtonian viscosity to a non-Newtonian one [1,2,3,4,5,6]
Summary
Immiscible liquids are specified as a system of two (or more) components, e.g., liquid–liquid or liquid–solid phase. The solid phase is represented by particles dispersed in the carrier fluid. Their interaction in the flow depends on their chemical composition and physical properties. In case of magnetorheological fluids, we must account for the influence of the magnetic field, which can change the Newtonian viscosity to a non-Newtonian one [1,2,3,4,5,6]. Viscosity is considered constant for Newtonian fluids. For non-Newtonian and magnetorheological fluids, it depends on the deformation gradient [2,6,7,8,9]. Non-Newtonian fluids are widely used in the industry, especially in the hydraulic gaps of rotary machines
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