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Dear all Transys users,
Hi,
There are a few questions I have regarding discretization of Type 10 (Rock bed storage tank) represented on page 560 in the "04-MathematicalReference" document.
1 - What are the boundary conditions for the first and last segments?
2- What finite difference method is used for discretizing the space second derivatives for the first and last segments?
It would be greatly appreciated if anyone could provide me with some guidance in this regard.
Best Regards,
Ali
Ali,
The rock bed storage model is more similar to a tank model than it is to a ground storage model. As such, it does not have boundary conditions quite like you would find with another solid state storage model, like a ground storage model (adiabatic boundary, conduction to far field at boundary, conduction or convection to ambient air at boundary, and so forth).
For each segment (or node) of the storage bed, the model calculates the change in internal energy of that node over the time step as a function of only the following influences:
- The temperature and flow rate of the air entering this node from above (if any);
- The temperature and flow rate of the air entering this node from below (if any);
- Conduction to the node immediately above this node (unless it's the top node of the storage bed);
- Conduction to the node immediately below this node (unless it's the bottom node of the storage bed);
- Thermal losses between this node and the ambient environment. These are calculated as a function of the vertical surface area of each node, the loss coefficient of the bed (Parameter 7), and the environment temperature (Input 5). The model does not assume any additional losses to the environment from the top or bottom surface of the storage bed, only from the vertical sides of the bed.
In the first node of the storage bed, there is no conduction to the node immediately above, and (if there is air flow from top to bottom) the temperature of the entering air is set to "Temperature into top" (Input 1 in Type 10's proforma), otherwise the equations are the same as for any other node. In the last node of the storage bed, there is no conduction to the node immediately below, and (if there is air flow from bottom to top) the temperature of the entering air is set to "Temperature into bottom" (Input 3 in Type 10's proforma), otherwise the equations are the same as for any other node.
Equations 4.10.1-6 through 4.10.1-11, found on pages 4-561 and 4-562 of the Mathematical Reference, spell out how the energy balances are calculated for a storage bed with N nodes at node i = 1 (the first segment), nodes 2 through N - 1, and node i = N (the last segment) for both top-to-bottom and bottom-to-top air flow cases.
