Easiest will likely be to have 2 configurations to simulate: one clean, the other with shelves full of stone. Then compare the results of each.
Flow can calculate accumulation, but it won't change the regions from fluid to solid as stone accumulates in order to change the flow field.
I understand what you are saying but there is no flow of fluid into the tower other than the fluid being displaced by the incoming stone. I believe there is no way to introdce a solid as a flow medium which is where my issue resides. I am trying to study the affects of stone falling with gravity down the center of the tower and model the reflection of the material as it falls.
Thinking out loud:
If you have a conveyor feeding stuff in from the top left, you might be able to put in a small accompanying fluid flow from left to right across the top of the tower. Then it would calculate zero flow into the tower. But if Flow is accurate it should still calculate the particles being carried by that fluid flow and when they are unsupported they would fall into the tower.
Then if that works you could include solids to represent the buildup of stones.
But it won't show the gases moving upward as a result of the volume taken up by the stone. You would have to manually input a gas flow rate based on the stone accumulation (which in fact may be closer to reality).
I think I get what you're trying to do but I don't think it is possible in flow simulation.
the basic premise in flow simulation is that the volume will be full of fluid. so if you apply a mass flow rate at the top, and a pressure opening at the bottom, it will act like a continuum. it won't "fall" or "bounce" off of anything. it will flow. what you would see is the patterns of flow and how they change from with a shelf only and filled shelves. this might give you some idea of what is happening, but it won't be the same as particles falling.
it sounds to me like it might be better to do this as a motion study. basically dropping things from the top of your geometry downwards. it will a heavy contact problem but i think would be closer than assuming the material flow to be a continuum.
if you can assume that the volume is full of a stagnant fluid. you COULD potentially try a particle study where the particles are only acted on by gravity and maybe some initial velocity from the "flow".