Grabowski-Berger rotational flow

palabos gbergerThe geometry and boundary condition of this 3D flow have cylindrical symmetry. This symmetry breaks at a critical Reynolds number, with a production of helix branches. A regime with a double-helix is shown in this demo. The flow is visualized through injected passive tracer particles.

A detailed description of the problem and solutions obtained with other numerical tools are provided in Ruith, Chen, Meiburg, Comp. Fluids 33 (2004) 1225–1250.

 

 

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Simulation setup

The simulation is contained in a cylinder of radius 10 and length 20 (in dimensionless units). The axial direction in the following referred to as z-direction. The inlet (z=0) is defined through a rotating velocity profile with a core of radius 1. In cylindrical coordinates, the velocity u_theta, u_r, u_z takes the shape

u_{theta}(0 le r le 1) = S r(2-r^2),

u_{theta}(1 le r) = S/r,

u_r(r) = 0,

u_z(0 le r le 1) = alpha + (1-alpha) r^2(6-8r+3r^2),

u_z(1 le r) = 1.

Numerical Parameters

Reynolds number 100
S 1.5
alpha 1

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