Calculation of Di Felice's drag force in the source code of CFDEM

Submitted by Rachel on Mon, 04/23/2018 - 19:48

Dear all,

Have anyone checked the formula of Di Felice drag force used in CFDEM pavkage?

As I see from the source code (DiFeliceDrag.C) and the refered paper Zhou et al. (2010), the drag coefficient is calculated as:
dragCoefficient=0.125*Cd*rho*M_PI*ds*ds*pow(voidfraction,(2-Xi))*magUr.

However, as I see from Di Felice (1994), the power law coefficient is -Xi while not (2-Xi). In fact, In the literature, there are several variations for the power law coefficient, including 2-Xi (Zhou et al, 2010), -Xi (Felice, 1994), 1-Xi (used in Xu et al, 2000).

Therefore, my question is: Why there are such variation of the power law coefficient? Which one is better or correct? Any suggestion or discussion is greatly appreciated. Many thanks!

Best,
Rachel

References:
Di Felice, R. (1994). The voidage function for fluid-particle interaction systems. International Journal of Multiphase Flow, 20(1), 153-159.
Zhou, Z. Y., Kuang, S. B., Chu, K. W., & Yu, A. B. (2010). Discrete particle simulation of particle–fluid flow: model formulations and their applicability. Journal of Fluid Mechanics, 661, 482-510.
Xu, B. H., Yu, A. B., Chew, S. J., & Zulli, P. (2000). Numerical simulation of the gas–solid flow in a bed with lateral gas blasting. Powder Technology, 109(1-3), 13-26.

Forums:

medvedeg | Tue, 04/24/2018 - 13:43

Hi Rachel,

formulation depends on what is magUr: relative velocity or superficial velocity. Superficial velocity is the relative velocity multiplied by the void fraction. In this case correct coefficient is -Xi. If magUr is the relative velocity, than the correct coefficient is 2-Xi, like in CFDEM. Note that this dragCoefficient is later multiplied again by magUr. So the coefficient is correct.

Alexander Podlozhnyuk

Rachel | Wed, 04/25/2018 - 17:56

Thanks. I get your idea~

gelinhan | Wed, 04/25/2018 - 08:13

Hi Rachel,

Totally agree with Alexander's explanation. Please also note that the formulation of model type ("A", "B" or "Bfull") might affect the coefficient as well.

Cheers,
Linhan

Rachel | Wed, 04/25/2018 - 17:57

Hi Linhan,

Thanks for your suggesiton. I now understand~