Simulations for the flow of viscoplastic fluids in a cavity driven by the movement of walls by Lattice Boltzmann Method
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Simulations for the flow of viscoplastic fluids in a cavity driven by the movement of walls by Lattice Boltzmann Method Siva Subrahmanyam Mendu1,2,* and Prasanta Kumar Das2 Department of Mechanical Engineering, MVGR College of Engineering(A), Vizianagaram-535005, India 2 Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, 721302, India (Received April 16, 2020; accepted June 27, 2020)
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The current paper is focused on analyzing the flow of viscoplastic fluid in a cavity that is driven by the two walls. The Lattice Boltzmann method (LBM) is used to solve the discrete Boltzmann equation. To represent the stress-strain rate relationship of viscoplastic fluids, the Bingham Papanastasiou constitutive model is considered. Cavity flow filled with Bingham fluids is considered for validating the present LBM code. After successful validation of the code, the analysis is extended for three dissimilar wall motions- simultaneous and opposed movement of the parallel facing walls, and the simultaneous motion of non-facing walls. The flow dynamics of Bingham fluid is influenced by Reynolds and Bingham numbers which can be studied using velocity and streamline plots. Subsequently, the yielded and un-yielded zones in a cavity have been effectively tracked using the limiting condition of yield stress. Further, the effect of wall motion on the variation of those zones inside a cavity has been studied. Finally, the drag coefficient for considered wall motions is presented. Keywords: LBGK model, Viscoplastic fluid, cavity flow, dissimilar wall motion
1. Introduction Viscoplastic fluids such as paints, slurries, gels, and food products are received significant importance in various industrial applications due to their generous usage among the non-Newtonian fluid community. As the name suggests, viscoplastic fluids exhibit combined features of plastic solids and viscous fluids. In this regard, the magnitude of the local stress is of utmost importance. If the local stress of the fluid body exceeds a typical value, denoted as yield stress, it starts flowing. Several idealized models (Chhabra, 2007) are available to characterize the rheology of viscoplastic fluids. Bingham model is one among them to represent the behavior of such fluids. Balmforth et al. (2014) presented a brief review of different models to describe the rheological behavior of viscoplastic fluids and computational techniques used for analyzing the dynamics of such liquids. Several numerical techniques were proposed for flow analysis of Bingham fluids in various complex bounded domains. The square cavity flow is considered by many researchers for testing computational fluid dynamics (CFD) codes since a wide range of fluid flow phenomena can be observed in this simple confinement. Significant progress has been observed in the development of conventional CFD techniques for simulating Bingham fluid flow in moving wall square cavities. Mitsoulis and Zisis (2001) studied the cavity flow filled with Bingham using finite eleme
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