Rayleigh time?

Submitted by xinze_l on Tue, 12/14/2010 - 16:13

Hi, Christoph. I have a question about Rayleigh time:

Question 1:
in code:

rayleigh_time_i=M_PI*r[i]*sqrt(density[i]/shear_mod)/(0.1631*nu->values[type[i]-1]+0.8766)

in doc
dt_r =PI*r*sqrt(rho/Y)/(0.1631*n+0.8766),

but in doc Young Modulus instead of shear_mod, I want to known, which was right?

Question 2:

what are the Rayleigh time and Hertz time relationship with timestep of run, and how timestep should be determined.

Question 3:
Are there some references about this topic?

Thank you
xz

Forums:

cstoltz | Tue, 12/14/2010 - 20:35

Q1 - I think that the code is correct in using shear modulus, not Young's modulus.

Q2 - Common guideline for timestep is to use ~20% of Rayleigh time, though this is situation dependent. Often times, you can get away with as much as 40% if you're doing something simple like dropping some particles into a container. However, you might need to go smaller than 20% if you're doing a simulation in which the particles achieve high velocities (e.g. high speed mixer). I'd start at 20% and make sure you do some consistency checks.

Q3 - I don't know any one definitive resource. The following have some discussion of timestep choice. As mentioned above, part of it comes down to practice.
* Mishra, Intl Jrnl Mineral Processing, 2003
* Raji & Favier, J. Food Engineering, 2003
* Ning & Ghadiri, Chem. Eng. Sci, 2006
* Li / Xu / Thornton, Powder Technology, 2005

ckloss's picture

ckloss | Thu, 12/16/2010 - 14:32

Hi xinze and chris,

>>I want to known, which was right
As chris said, the code is right, I will fix this for the next release

>>dt_r =PI*r*sqrt(rho/Y)/(0.1631*n+0.8766),
This formula is from the Li/Xu paper mentioned by Chris

>>However, you might need to go smaller than 20% if you're doing a simulation in which the particles achieve high velocities (e.g. high speed mixer)
Basically Chris is right that one needs to go lower than 20% Rayleigh time here, but the issue itself is related to Hertz time, not Rayleigh-time.
That's the reason why fix check/timestep/gran checks for both criteria

Cheers,
Christoph