Modeling of Molecular Diffusion in Non-Homogeneous Media
Background. Due to combined effects of medium inhomogeneity and action of external forces, i.e. Earth’s gravitation, electro-magnetic forces, global rotation, etc., a number of specific fluid motions appear in the environmental and life systems even in absence of pure mechanical reasons. Among them are so called diffusion-induced flows which always exist around obstacles with arbitrary geometry due to breaking of natural molecular flux of a stratifying agent on an impermeable surface.
Objective. The aim of the paper is to analyze numerically a diffusion induced flow structure and dynamics around motionless obstacles immersed into a stably stratified medium, including a sloping plate, a wedge-shaped obstacle, a disc, and a circular cylinder. The numerical results obtained are compared with the available analytical and experimental data.
Methods. The problem is solved numerically using two different algorithms based on the finite difference and finite volume methods. The first approach is implemented in the specially developed Fortran program codes, and the second one is based on the open source package OpenFOAM with the use of C++ programming language for developing special own solvers, libraries, and utilities, which enable solving the problems under consideration.
Results. The numerical simulation reveals a complex multi-level vortex system of compensatory circulating flows around a motionless obstacle, which structure is strongly dependent on its position relative to the horizon. The most intensive and extended high-gradient horizontal interfaces attached to sharp edges or poles of obstacles are clearly observed in the numerical computations and laboratory experiments. Diffusion-induced flows form intensive pressure deficiency zones around an obstacle, which may lead to generation of propulsion mechanism resulting in self-movement of neutral buoyancy bodies in a continuously stratified fluid, e.g. horizontal movement of a wedge, rotation of a sloping plate, etc.Conclusions. Diffusion-induced flows are a wide-spread phenomenon in biology, medicine, and environmental systems, since such flows inevitably occur in any inhomogeneous media, including different solutions, suspensions, mixtures, etc. A complex multilevel vortex structure of diffusion-induced flows on an obstacle becomes even more complicated due to self-motion of the obstacle itself and displacement of various admixtures, suspended particles, additives, etc., which are always present in the real systems.
O.M. Phillips, “On flows induced by diffusion in a stably stratified fluid”, Deep-Sea Res., vol. 17, pp. 435–443, 1970. doi: 10.1016/0011-7471(70)90058-6
H.E. Huppert and J.S. Turner, “On melting icebergs”, Nature, vol. 271, pp. 46–48, 1978. doi: 10.1038/271046a0
M. Gurnis, “Large-scale mantle convection and the aggregation and dispersal of supercontinents”, Nature, vol. 332, pp. 695–699, 1988. doi: 10.1038/332695a0
L. Prandtl, Führer durch die Strömungslehre. Braunschweig: Vieweg, 1942, 638 p.
L. Thompson and G.C. Johnson, “Abyssal currents generated by diffusion and geothermal heating over rises”, Deep-Sea Res., vol. 43, pp. 193–211, 1996. doi: 10.1016/0967-0637(96)00095-7
M.R. Allshouse et al., “Propulsion generated by diffusion-driven flow”, Nature Phys., vol. 6, pp. 516–519, 2010. doi: 10.1038/nphys1686
C. Wunsh, “On oceanic boundary mixing”, Deep-Sea Res., vol. 17, pp. 293–301, 1970. doi: 10.1016/0011-7471(70)90022-7
P.F. Linden and J.E. Weber, “The formation of layers in a double-diffusive system with a sloping boundary”, Fluid Mech., vol. 81, pp. 757–773, 1977. doi: 10.1017/S002211207700233X
A.V. Kistovich and Yu.D. Chashechkin, “The structure of transient boundary flow along an inclined plane in a continuously stratified medium”, Appl. Math. Mech., vol. 57, pp. 633–639, 1993. doi: 10.1016/0021-8928(93)90033-I
L. Landau and E. Lifshitz, Fluid Mechanics, vol. 6, Course of Theoretical Physics. Oxford, UK: Pergamon Press, 1987, 731 p.
Yu.D. Chashechkin and Ia.V. Zagumennyi, “Non-equilibrium processes in non-homogeneous fluids under the action of external forces”, Physica Scripta, T155, paper 014010, 2013. doi: 10.1088/0031-8949/2013/T155/014010
Ya.V. Zagumennyi and Yu.D. Chashechkin, “Unsteady vortex pattern in a flow over a flat plate at zero angle of attack (2D problem)”, Fluid Dynamics, vol. 51, no. 3, pp. 343–359, 2016. doi: 10.1134/S0015462816030066
Ia.V. Zagumennyi and Yu.D. Chashechkin, “Fine structure of unsteady diffusion-induced flow over a fixed plate”, Fluid Dynamics, vol. 48, no. 3, pp. 374–388, 2013. doi: 10.1134/S0015462813030113
Ia.V. Zagumennyi and Yu.D. Chashechkin, “Diffusion-induced flow on a strip: theoretical, numerical and laboratory modelling”, Procedia IUTAM, vol. 8, pp. 257–266, 2013. doi: 10.1016/j.piutam.2013.04.032
Ia.V. Zagumennyi and N.F. Dimitrieva, “Diffusion-induced flow on a wedge-shaped obstacle”, Physica Scripta, vol. 91, paper 084002, 2016. doi: 10.1088/0031-8949/91/8/084002
Yu.D. Chashechkin and V.V. Mitkin, “A visual study on flow pattern around the strip moving uniformly in a continuously stratified fluid”, J. Visualiz., vol. 7, no. 2, pp. 127–134, 2004. doi: 10.1007/BF03181585
GOST Style Citations
Copyright (c) 2017 NTUU KPI