Diffusion induced flow on a wedge-shaped obstacle

Abstract

In this paper the problem of evolution of diffusion induced flow on a wedge-shaped obstacle is analyzed numerically. The governing set of fundamental equations is solved using original solvers from the open source OpenFOAM package on supercomputer facilities. Due to breaking of naturally existing diffusion flux of a stratifying agent by the impermeable surface of the wedge a complex multi-level vortex system of compensatory fluid motions is formed around the obstacle. Sharp edges of the obstacle generate extended high-gradient horizontal interfaces which are clearly observed in laboratory experiments by high-resolution Schlieren visualization. Formation of an intensive pressure depression zone in front of the leading vertex of the wedge is responsible for generation of propulsive force resulting in a self-displacement of the obstacle along the neutral buoyancy horizon in a stably stratified environment. The size of the pressure deficiency area near the sharp vertex of a concave wedge is about twice that for a convex one. This demonstrates a more intensive propulsion mechanism in case of the concave wedge and, accordingly, a higher velocity of its self-movement in a continuously stratified medium.

Diffusion-Induced Effects in a Stratified Fluid Around a Motionless Wedge

“…Numerical simulation of the equations set (1-2) is realized in frame of the open source computational package OpenFOAM using the finite volume method. It is based on the original solver which supplements the standard codes of the package with the programming modules accounting for the stratification and diffusion effects [16]. New variables ( ρ , s ), the additional equations and new physical parameters ( N , Λ , S k , g ) were supplemented to the standard solver icoFoam.…”

Modeling of Molecular Diffusion in Non-Homogeneous Media

“…In this section, numerical results are presented on steady-state structure and dynamics of diffusion-induced flows around an impermeable motionless sloping plate and a wedge with finite length, which are immersed into a stably stratified medium [10,14,15]. Such investigations are of a great scientific and practical interest since both the stationary and non-stationary analytical solutions of the problem are constructed only in the approximation of an infinite plane.…”

“…1. The general structure of the flow consists of a four-level sequence of horizontally oriented circulating cells, which are located symmetrically relative to the plate's horizon and its central vertical plane [14,15]. The contacting cells circulate in opposite directions and are mutually coordinated in contrast to the case of thermal convection where circulations in adjacent cells have the same signs.…”

“…5 cm 2 /s [15]. The parameters of stratified fluid are chosen to be typical for the laboratory experiments [16], which significantly exceed typical values of stratification in the natural systems, i.e.…”

“…An extended area with virtually unperturbed distribution of salinity perturbation is located close to the base of the wedge, which supplements the obstacle to a symmetrical form relative the base ("a reflected wedge with curvilinear boundaries"). Near the edges of the base fine structural asymmetrical perturbations are formed, which penetrate into the bottom area behind the wedge like in case of a sloping plate [14,15].…”