Commit 74532e98 authored by William D. Fullmer's avatar William D. Fullmer
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WIP wdf fix bad error in fluid equations

parent 28635041
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+5 −5
Original line number Diff line number Diff line
@@ -47,18 +47,18 @@ The conservation of fluid momentum is:
   = \nabla \cdot \tau + M_{sg} + \varepsilon_g \rho_g g

where :math:`M_{sg} = - M_{gs}` is the generalized interfacial momentum transfer from 
the solid particles to the gas-phase to the gas-phase. Like :math:`\varepsilon_s`, 
the solid particles to the fluid-phase. Like :math:`\varepsilon_s`, 
:math:`M_{gs}` is determined from the L-E transfer kernel by setting :math:`A_i = F_{gi}`, 
where :math:`F_{gi}` is the force due to the gas-phase on the ith particle. Following 
where :math:`F_{gi}` is the force due to the fluid-phase on the ith particle. Following 
MFiX classic (and many other CFD-DEM codes designed for high density ratio gas-solids 
flows), only buoyancy (pressure gradient) and steady drag are considered: 

.. math::
   F_{gi} = - \mathcal{V}_i \nabla p_g 
   - \frac{1}{2} C_D \rho_g \boldsymbol{V}_{ig} -  \left|\boldsymbol{V}_{ig}\right| A_i^{(proj)}
   - \frac{1}{2} C_D \rho_g \boldsymbol{V}_{ig} \left|\boldsymbol{V}_{ig}\right| A_i^{(proj)}

where :math:`\boldsymbol{V}_{ig} = \boldsymbol{V}_i - \boldsymbol{U}_g ( \boldsymbol{X}_i )` 
is the velocity of ith particle relative to the gas-phase (at the particle position 
is the velocity of ith particle relative to the fluid-phase (at the particle position 
:math:`\boldsymbol{X}_i`). :math:`F_{gi}` is closed by the specification of a drag 
coefficient, :math:`C_D`. Currently, MFiX-Exa includes Wen-Yu, Gidaspow and BVK2 drag laws.

@@ -73,7 +73,7 @@ coefficient, :math:`C_D`. Currently, MFiX-Exa includes Wen-Yu, Gidaspow and BVK2

In chemical engineering literature, it is common to lump all drag-related terms of 
:math:`M_{gs}` into :math:`\beta`. With this simplification and some re-arrangement, 
the flud momentum takes the more convenient form: 
the fluid momentum takes the more convenient form: 

.. math:: \frac{ \partial (\varepsilon_g \rho_g U_g)}{\partial t} 
   + \nabla \cdot (\varepsilon_g \rho_g U_g U_g) + \varepsilon_g \nabla p_g