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

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Old   October 22, 2020, 22:05
Post Equation in Burns.C of Turbulent dispersion model of Burns et al.
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Chaoran Guan
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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).

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
           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?
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Old   November 24, 2020, 04:43
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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.
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multiphase flows, multiphase modelling

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