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Engineering
Materials and Chemical Engineering
Modelling of two phase flow in packed bed using conservation equations
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[QUOTE="casualguitar, post: 6560630, member: 695787"] Ok great. It seems we will only need the energy conservation equation here then for both the fluid and solid separately, not the mass/momentum equations. Is this correct? So taking the energy conservation equation: [ATTACH type="full" width="365px" alt="1636111963025.png"]291806[/ATTACH] [B]Assumptions: 1) [/B]No temperature variation along the bed in any direction for both the fluid and solid (dT/dx,dT/dy,dT/dz) will all be zero) [B]2)[/B] No pressure variation (Dp/Dt = 0) [B]3)[/B] The velocity gradient is small enough such that shear stresses will be zero (shear stress term will be zero) [B]4)[/B] We're dealing with a single phase [B]Point of confusion: [/B] I'm going to say that q here is due to only convection, not the sum of convection and conduction. The reason I'm confused here is because the the temperature in the bed is constant. So this might mean there is no conduction between solid particles. Is this correct? So for those reasons, I think the answer to model 2 is the same as the original equations I posted, minus the dTf/dx fluid term, the conduction terms in both equations, and the losses to the environment term. I'm going to write the equations out using LaTex (I haven't done this before so I guess it'll take a few attempts to get right): $$\epsilon\ * \rho_{f} *C_{pf}*dT_{f}/dt = h_{fp}*a_{s}*(Ts-Tf)$$ $$(1-\epsilon) * \rho_{s} *C_{ps}*dT_{s}/dt = h_{fs}*a_{s}*(Tf-Ts)$$ These equations say the following to me: LHS: The temperature of the fluid/solid will change over time RHS: The temperature change is driven by convection (the difference between Tf and Ts) Note: f and s subscripts are fluid and solid Is this the right direction? I will edit this if I see any corrections! I'm now going to look into how to adapt this for the phase change case. My initial thought is that it seems that it might be possible to have an 'if statement' of sorts, where we check the boiling point of the fluid. For T>Tsat we use the gas parameters, and for T<Tsat we use liquid parameters. This could avoid the need for a phase change term. However obviously it tells us nothing about the phase change itself. I'm going to think about the addition of a phase change term now. [/QUOTE]
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Modelling of two phase flow in packed bed using conservation equations
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