Numerical simulation of jet‐forced flow in a circular reservoir using discrete and random vortex methods

Abstract

SUMMARYThis paper describes a BiotSavart discrete vortex model for simulating the flow patterns which occur when a single high-velocity inflow jet is used to stir the fluid within a circular container. The first stage of the model consists of conformally mapping the circular perimeter of the container onto a rectangle by means of a Schwarz-Christoffel transformation. A potential flow solution is then obtained for the flow inside the rectangle and this is transformed to give the potential flow inside the circle. In the second stage of the simulation, discrete vortices are added at the inlet of the physical system in order to model the inflow shear layers. Velocity components resulting from the discrete vortices and their images in the walls of the cylinder are superimposed on the uniform potential flow solution. The positions of the vortices are updated using a Lagrangian tracking procedure. Viscous effects are incorporated through the use of random walks. From the results it is shown that the discrete vortex method does predict qualitatively the important features of jetforced reservoir flow.

Numerical simulation of laminar jet-forced flow using lattice Boltzmann method

“…For the laminar jet-forced flow problems, only a few papers [11][12][13][14][15][16][17][18] can be hitherto found because of the complexity of nonlinear flow phenomena in irregular domains. Natural flow domains have the complicated boundary configurations, which may strongly influence the interior flow patterns.…”

Vortex-induced chaotic mixing in wavy channels

“…The standard deviation of these random walks must be compatible with the analytical Gaussian solution of pure diffusion, and therefore the fluctuating random velocity components of a particle are written as u r = r 1 2ν/∆t, v r = r 2 2ν/∆t, (7.1a, b) where the subscript r indicates random component; ν and ∆t are the diffusion coefficient and time step respectively; and r 1 and r 2 are independent normally distributed random numbers, each with zero mean and unit standard deviation (e.g. Borthwick & Barber 1992).…”