FLUENT 6.2  Mass imbalance in simulating gassolid flow with Eulerian granular model when having solid sink in the bed and when solid volume fraction approaches packing limit
We met with a problem that mass imbalance occurred while using a udf sink in extracting solid from the solid bed. The solid volume fraction of 0.29 was patched into the bed as the initial condition to start the unsteady simulation. The udf extracts a constant total mass rate out of a fluidized bed over time, where there is no inlet and outlet for solid, and there is only gas coming into the domain from bottom and leaving the domain from top (solid leaving top boundary was monitored as zero). It is intended that the mass in the bed is reduced linearly at a constant slope, which is equal to the solid sink mass rate. The sink term udf is formulated based on the assumption of constant solid surface rate, so that the cell sink term is proportional to the cell volume fraction. The volume integral of the sink term is prescribed as a constant in the udf. The simulation shows the result as expected in the initial stage, 00.6 second, but changed to a steeper slope (extra mass sink extracting solids more than the given total rate) afterward. It was seen from the solid volume fraction contour that the solid volume fraction began reaching packing limit after 0.6 s. It is thought that the mass imbalance is related to the solid's approaching packing limit. (Another simulation was also done, where the maximum solid volume fraction was always well below the packing limit. The mass imbalance problem didn't occur.) It was also tested in the same simulation without the sink, that the bed mass was kept as constant, which means that there is no mass imbalance problem if the udf sink is not used, even when the packing limit is approached. The mass imbalance also occurs when using the sink term in the bed volume by inputting the constant value in the entry of the mass equation in the gui panel (without using udf). The mass imbalance problem is resolved in FLUENT 6.3. 

