Motions of particles in Taylor Green vortex with

TaylorGreenParticles is a single python script to simulate motions of particles in Taylor Green vortex. The animations can help to understand the phenomenon of preferential concentration of inertial particles in turbulence, see Preferential concentration. The fortran code is added by Guo Chen.

The analytical solution for 2D Taylor Green vortex is given by:

where u,v,\omega are respectively the x-velocity,y-velocity and vorticity. In this simulation, we set both x and y in range [0,2*pi]. And they are discretized into a PERIODIC mesh with shape of 64*64 (change it as you wish).

The particle dispersed in fluid experiences a hydrodynamic force, and this force will drive the particle's motion following the Newton's Second Law. The procedure to caculate the force lists as follows.

• First, caculate the particle Reynolds number :

• Next, caculate the drag coefficient :

• If we define the particle relaxation time as , we can get:

• Finally, the particle translation motion (location) is governed by :

• In practice, the particle velocity and location is updated by:

The particle relaxation time (or particle inertia) can be changed by adjusting either dp or rho_p. Here we give five typical results.

• If tau_p = 5.56, it means particle has small inertia, so it will exactly follow the motion of fluid.

• If we increase tau_p to 555.56, the particle will have similar inertia with the fluid. There will be a strong competition between the particle and fluid vortex. It turns out that the particle's power is much smaller than the vortex core, so they choose to stay in the edge of the vortexs.

• Further increase tau_p to 55555.56, the particles now can cross the outer part of the vortex, but they can still not penetrate into the vortex core.

• Finally, tau_p is increased to 277777.78, now they have much higher inertia than the vortex, so they just freely move in the whole domain. Particles win!

Send me an email at [email protected] (Zhuo Wang) or [email protected] (Guo Chen) if you have any suggestion.