How does this flow sound to you?
Pressure Gradient:
1) Independently implement the Ergun equation to get a sense of the expected pressure drop for liquid only and gas only flow across the packed bed i.e. don't include it in the spatial variation model initially.
2) Make a function that allows calculation of the pressure at any point along the bed. I guess this will just be the Ergun equation again except instead of taking the total bed length as input, this function would take a distance from the inlet as input. This would give the ##\Delta P## between the inlet and that point. Then we just take that ##\Delta P## from the inlet pressure to get the pressure at that point.
3) This function could then go into the spatial variation model. It just affects the density and ##\frac{d\rho}{dh}## functions currently so its easy to slot in
4) Later, this function can be used to get the input pressure for real mixture heat capacity, density, etc. Not priority as you say because it won't affect the accuracy that much, but just to clear my heat and for model completion, I'll add it in
The author of the thermo library I mentioned also has some other nice libraries. The 'fluids' library has packed bed pressure drop functionality, here:
https://fluids.readthedocs.io/fluids.packed_bed.html?highlight=ergun
This will give an immediate sense of the pressure drop
The real system:
I've chosen non-exact volume, mass, area, solid property values, etc. I know the dimensions of the actual tank being used and any information about the material (diameter, ##C_p##, etc). I'll add in these so that model output resembles the real system:
- tank volume
- solid area
- inlet fluid mass flow
- solid particle diameter
- solid density
- solid ##C_p##
- voidage
- tank length
- tank diameter
Heat transfer coefficient:
I don't know much about this. I know there are a few correlations used to get the Nusselt number, like Gnielinski and Achenbach, and we can use this with the Reynolds number I think to get the heat transfer coefficient.
This library (another from the same author) called 'heat transfer' calculates the Nusselt number for a packed bed given the particle diameter, voidage, superficial velocity, fluid density, fluid viscosity and the Prandtl number
: https://ht.readthedocs.io/en/release/ht.conv_packed_bed.html?highlight=packed bed
So again we can get an immediate sense of the heat transfer coefficient using this (I am keen to use these libraries where possible, mostly out of interest in the functionality available)
I think the heat transfer coefficient modelling sounds like something that would slot into the model best after the above two sections are done (they shouldn't take long given the available functionality).
Question: Does '##n##', the number of tanks, correspond to a real length?
