Equation in Burns.C of Turbulent dispersion model of Burns et al.

Chaoran · October 22, 2020, 22:05

Hello, Foamers. I was using the reactingTwoPhaseEulerFoam of OF6.0 Version.
A turbulent dispersion model called Burns is used which located in applications/solvers/multiphase/reactingEulerFoam/interfacialModels/turbulentDispersionModels/Burns. And the reference is

Burns, A. D., Frank, T., Hamill, I., & Shi, J. M. (2004, May).The Favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows.In 5th international conference on multiphase flow, ICMF (Vol. 4, pp. 1-17). https://www.researchgate.net/publica...ti-Phase_Flows

The equation used in Burns.C from the reference is
$\vec M_{\alpha}^{TD}=-\vec M_{\beta}^{TD}=-\frac{3}{4}C_D\frac{\overline r_{\beta}\rho_{\alpha}}{d_\beta}|\vec{U_\beta}-\vec{U_\alpha}|\frac{\nu_{t\alpha}}{\sigma_{r\alpha}}(\frac{1}{\overline r_{\alpha}}+\frac{1}{\overline r_{\beta}})\nabla \overline r_{\alpha}$
And the correspponding source code in Burns.C from OF version 6.0 is

Code:

        0.75
       *drag.CdRe()
       *pair_.continuous().nu()
       *continuousTurbulence().nut()
       /(
            sigma_
           *sqr(pair_.dispersed().d())
        )
       *pair_.continuous().rho()
       *pair_.dispersed()
       *(
           1.0/max(pair_.dispersed(), residualAlpha_)
         + 1.0/max(pair_.continuous(), residualAlpha_)
        );

I tried to translate it into the mathematical form as
$\frac{3}{4}C_D\frac{\nu_\alpha\rho_\alpha \overline r_\beta}{d^2_\beta}\frac{\nu_{t\alpha}}{\sigma_{r\alpha}}(\frac{1}{\overline r_{\alpha}}+\frac{1}{\overline r_{\beta}})$
The two equations seem not to be the same. The interphase velocity term $|\vec{U_\beta}-\vec{U_\alpha}|$ is missed in the source code and there is an additional term $\frac{\nu_\alpha}{d_{\beta}}$ in it.
Is there any relationship between these two terms?

geth03 · November 24, 2020, 04:43

drag.CdRe() in the code means C_d x Re (Reynolds number),
it cancels out the additional terms (kin. viscosity / bubble diameter)
and leaves your missing term (velocity difference).

so in the end it is implemented correctly although not in a way that
makes sense at first sight.

October 22, 2020, 22:05	Equation in Burns.C of Turbulent dispersion model of Burns et al.	#1
Chaoran New Member Chaoran Guan Join Date: Aug 2019 Posts: 5 Rep Power: 7	Hello, Foamers. I was using the reactingTwoPhaseEulerFoam of OF6.0 Version. A turbulent dispersion model called Burns is used which located in applications/solvers/multiphase/reactingEulerFoam/interfacialModels/turbulentDispersionModels/Burns. And the reference is Burns, A. D., Frank, T., Hamill, I., & Shi, J. M. (2004, May).The Favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows.In 5th international conference on multiphase flow, ICMF (Vol. 4, pp. 1-17). https://www.researchgate.net/publica...ti-Phase_Flows The equation used in Burns.C from the reference is $\vec M_{\alpha}^{TD}=-\vec M_{\beta}^{TD}=-\frac{3}{4}C_D\frac{\overline r_{\beta}\rho_{\alpha}}{d_\beta}\|\vec{U_\beta}-\vec{U_\alpha}\|\frac{\nu_{t\alpha}}{\sigma_{r\alpha}}(\frac{1}{\overline r_{\alpha}}+\frac{1}{\overline r_{\beta}})\nabla \overline r_{\alpha}$ And the correspponding source code in Burns.C from OF version 6.0 is Code: 0.75 drag.CdRe() pair_.continuous().nu() continuousTurbulence().nut() /( sigma_ sqr(pair_.dispersed().d()) ) pair_.continuous().rho() pair_.dispersed() *( 1.0/max(pair_.dispersed(), residualAlpha_) + 1.0/max(pair_.continuous(), residualAlpha_) ); I tried to translate it into the mathematical form as $\frac{3}{4}C_D\frac{\nu_\alpha\rho_\alpha \overline r_\beta}{d^2_\beta}\frac{\nu_{t\alpha}}{\sigma_{r\alpha}}(\frac{1}{\overline r_{\alpha}}+\frac{1}{\overline r_{\beta}})$ The two equations seem not to be the same. The interphase velocity term $\|\vec{U_\beta}-\vec{U_\alpha}\|$ is missed in the source code and there is an additional term $\frac{\nu_\alpha}{d_{\beta}}$ in it. Is there any relationship between these two terms?

November 24, 2020, 04:43		#2
geth03 Senior Member Join Date: Dec 2019 Location: Cologne, Germany Posts: 369 Rep Power: 8	drag.CdRe() in the code means C_d x Re (Reynolds number), it cancels out the additional terms (kin. viscosity / bubble diameter) and leaves your missing term (velocity difference). so in the end it is implemented correctly although not in a way that makes sense at first sight. lourencosm, KasperWayne, Chaoran and 1 others like this.

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