modelPB2Air_Bejan
Extends from TransiEnt.Storage.Heat.PackedBedStorage_L4.Basics.HeatTransfer.PackedBedToAir.HeatTransferBasePB2Air (Partial heat transfer model for packed Bed 2 Air heat transfer).
Information
1. Purpose of model
Heat Transfer Correlation for packed bed to adjacent air volume according to Bejan et al.
2. Level of detail, physical effects considered, and physical insight
The correlation is derived for a lateral fluid penetration due to natural convection into a porous structure from the side.
A weighting function is introduced in order to distribute the transferred heat to the different finite volumes inside the packed bed.
It need the penetration length as parameter, which thus has to be iteratively corrected.
3. Limits of validity
(Description)
4. Interfaces
(none)
5. Nomenclature
(no elements)
6. Governing Equations
(no equations)
7. Remarks for Usage
(none)
8. Validation
(no validation or testing necessary)
9. References
D.A. Nield, A. Bejan, Convection in porous media, 4th ed., Springer, New York, 2013., page 366
A. Bejan. “Lateral Intrusion of Natural Convection into a Horizontal Porous Structure.” In: Journal of Heat Transfer 103 (1981), pages 237–241.
10. Version History
Model created by Michael von der Heyde (heyde@tuhh.de) for the FES research project, March 2021
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| String | gas (from HeatTransferBasePB2Air) | "true" | |
| Boolean | useHomotopy (from HeatTransferBasePB2Air) | ||
| SI.Length | lx_set | if inlet then geo.max_height[1]/2 else geo.max_height[iCom.N_cv]/2 | Penetration length set by user (must be adopted to lx_check manually!) |
| Integer | N_cv_eff | integer(ceil(x_rel*iCom.N_cv)) | Number of effected cells |
| Integer | N_cv_den | integer(N_cv_eff*(N_cv_eff + 1)/2) | denumerator for partition function |
| Real[iCom.N_cv] | weight | if inlet then cat(1, {(N_cv_eff + 1 - i)/(N_cv_den) for i in 1:N_cv_eff}, {0 for i in N_cv_eff + 1:iCom.N_cv}) else cat(1, {0 for i in 1:iCom.N_cv - N_cv_eff}, {(i - (iCom.N_cv - N_cv_eff))/(N_cv_den) for i in iCom.N_cv - N_cv_eff + 1:iCom.N_cv}) | Weights for each cell |
| Internals | |||
| Boolean | inlet (from HeatTransferBasePB2Air) | true | |
| Heat Transfer | |||
| Real | x_rel | min(0.25, lx_set/geo.length) | Penetration length of heat flux in relation to storage length (should be lower than 0.25) |
Connectors
| Type | Name | Default | Description |
|---|---|---|---|
| ClaRa.Basics.Interfaces.HeatPort_a[iCom.N_cv] | heat (from HeatTransferBasePB2Air) |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| TransiEnt.Storage.Heat.PackedBedStorage_L4.Basics.Records.IComPackedBedControlVolume_L4 | iCom (from HeatTransferBasePB2Air) | ||
| TransiEnt.Storage.Heat.PackedBedStorage_L4.Basics.PackedBedGeometry.PackedBedGeometry_N_cv | geo (from HeatTransferBasePB2Air) | ||
| SI.MassFlowRate[iCom.N_cv + 1] | m_flow (from HeatTransferBasePB2Air) | Mass flow rate | |
| SI.Temperature[iCom.N_cv] | T_mean (from HeatTransferBasePB2Air) | ||
| SI.CoefficientOfHeatTransfer | alpha (from HeatTransferBasePB2Air) | Heat transfer coefficient | |
| TILMedia.Gas_ph[iCom.N_cv] | fluid | ||
| Real | beta | Thermal expansion coefficient | |
| Real | alpha_m | thermal diffusion coefficient according to Nield page 223 | |
| Real | Ra | Rayleigh number according to Nield page 334 with Delta T and H from page 367 | |
| SI.Length | lx_check | Penetration length (see Reference for more detail) |