Abstract
In this work, latent heat thermal energy storage system composed of porous metal foams with phase change material subject to pulsating fluid flow is investigated. The pulsating admission of such systems has not been thoroughly studied so far. Thus, the main motivation of the present study has been the investigation of the effect of pulsating admission in comparison with the constant through flow. The investigation is carried out numerically, utilizing the thermal lattice Boltzmann method, adopting a dual distribution function approach for calculating the dynamic and thermal fields, within the framework of an in-house developed code. The porous media is modeled at a macroscopic level by the representative elementary volume scale approach, utilizing the Brinkman–Forchheimer extended Darcy model, without assuming thermal equilibrium between the fluid phase and the solid foam. The phase change is modeled by an enthalpy–porosity approach. The main novelty of the work resides in the analysis of pulsating flow effects on melting and solidification of a phase change material embedded in porous metal foam, as this has not been investigated that thoroughly before. Furthermore, in difference to the previous work, detailed energy and exergy analyses incorporating entropy generation rates are presented, making up a further important novel aspect of the present work. A parametric study is performed covering a range of the porosity (0.7, 0.8, 0.9). For pulsating flow, variations in the amplitude (0.1, 0.5, 0.9) and Strouhal number (0.1, 1.0) are investigated. The analysis of the pulsating flow shows that small pulsation amplitudes speed up the melting rate and the heat spread. The overall system irreversibility is observed to decrease with decreasing Strouhal number. The dependence of the system irreversibility on the pulsation amplitude has been observed, however, to be different between charging and discharging phases, which has been an interesting result. During charging, it is observed that low amplitudes lead to low irreversibility. However, high amplitudes are observed to be correlated with low irreversibility during discharging. By comparison with the previous work, the superiority of pulsating flow compared to the constant flow in picking up the maximum energy storage while minimizing thermal losses is demonstrated.
Article Highlights
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Numerical study of a pulsed flow’s effects on the phase change within a porous channel.
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The pulsating flow is more useful than steady flow to pick up the maximum energy amount.
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Pulsating flow with a low Strouhal number and large pulsating amplitude is advised to mitigate the system's irreversibility during melting/solidifying process.
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Abbreviations
- BGK:
-
Bhatnagar–Gross–Krook
- BFD:
-
Brinkman–Forchheimer extended Darcy
- DDF:
-
Double distribution function
- LBM:
-
Lattice Boltzmann method
- LBE:
-
Lattice Boltzmann equation
- LHTESSs:
-
Latent heat thermal energy storage systems
- LTE:
-
Local thermal equilibrium
- LTNE:
-
Local thermal nonequilibrium
- MDF:
-
Multi-distribution function
- PCM:
-
Phase change material
- PPI:
-
Pore per inch
- REV:
-
Representative elementary volume
- TESSs:
-
Thermal energy storage systems
- A :
-
Pulsating amplitude
- \(a_{sf}\) :
-
Specific solid–fluid interfacial area \(\left( {{\text{m}}^{{ - {1}}} } \right)\)
- \(Be\) :
-
Bejan number
- \(Bi\) :
-
Biot number, \(Bi = h_{{{\text{sf}}}} a_{{{\text{sf}}}} H^{2} /\lambda_{s}\)
- \(c\) :
-
Lattice speed \(\left( {{\text{m}}\,{\text{s}}^{ - 1} } \right)\)
- \(C_{p}\) :
-
Specific heat capacity at constant pressure \(\left( {\rm{kJ}\,\rm{kg}^{ - 1} \,\rm{K}^{ - 1} } \right)\)
- \(c_{s}\) :
-
Sound speed \(\left( {{\text{m}}\,{\text{s}}^{ - 1} } \right)\)
- \(\overline{\overline{D}}\) :
-
Strain tensor \(\left( {\rm{s}^{{ - \rm{1}}} } \right)\)
- \(Da\) :
-
Darcy number, \(Da = K/H^{2}\)
- \(d_{f}\) :
-
Ligament diameter \(\left( {\text{m}} \right)\)
- \(d_{p}\) :
-
Average pore diameter\(\left( {\text{m}} \right)\)
- \(Ec\) :
-
Eckert number, \(Ec = U_{0}^{2} /(C_{f} .(T_{{\text{h}}} - T_{c} ))\)
- \(e_{i}\) :
-
Discrete velocity in direction i
- \(F_{\varepsilon }\) :
-
Forchheimer form coefficient
- \(F\) :
-
Body force per unit mass \(\left( {\rm{N}\,\rm{kg}^{ - 1} } \right)\)
- \(F_{ei}\) :
-
Discrete body force in direction i \(\left( {\rm{kg}\;\rm{m}^{ - 3} \;\rm{s}^{ - 1} } \right)\)
- \(f_{i} ,\;g_{i}\) :
-
Distribution function in direction i
- \(f_{i}^{eq} ,\;g_{i}^{eq}\) :
-
Equilibrium distribution function in direction i
- \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{f}\) :
-
Pulsating frequency (Hz)
- \(H\) :
-
Characteristic length scale \(\left( \rm{m} \right)\)
- \(h_{{\rm{sf}}}\) :
-
Interfacial heat transfer coefficient \(\left( {{\text{W}}\,{\text{m}}^{{ - {2}}} \,{\text{K}}^{{ - {1}}} } \right)\)
- \(K\) :
-
Porous medium permeability \(\left( {\rm{m}^{2} } \right)\)
- \(K_{R}\) :
-
Solid-to-fluid thermal conductivities ratio, \(K_{R} = \lambda_{s} /\lambda_{f}\)
- \(L_{a}\) :
-
Latent heat \(\left( {\rm{J}\,\rm{kg}^{ - 1} } \right)\)
- \(Ns\) :
-
Entropy generation Number
- \(p\) :
-
Pressure \(\left( {\rm{Pa}} \right)\)
- \(P\) :
-
Dimensionless pressure
- \({\text{Pr}}\) :
-
Prandtl number, \({\text{Pr}} = \nu_{f} /\alpha_{f}\)
- \({\text{Re}}\) :
-
Reynolds number, \({\text{Re}} = u_{in} H/\nu_{f}\)
- \({\text{Re}}_{d}\) :
-
Particle Reynolds number, \({\text{Re}}_{d} = \sqrt {U^{2} + V^{2} } d_{f} /\varepsilon \nu_{f}\)
- \({\text{R}} c\) :
-
Heat capacities' ratio, \(Rc = (\rho C_{p} )_{s} /(\rho C_{p} )_{f}\)
- \(Ste\) :
-
Stefan number, \(Ste = C_{p} (T_{h} - T_{m} )/L_{a}\)
- \(St\) :
-
Strouhal number, \(St = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{f} H/U_{0}\)
- \(T\) :
-
Temperature \(\left( K \right)\)
- \(T_{m}\) :
-
PCM melting temperature \(\left( K \right)\)
- \(\Theta\) :
-
Dimensionless temperature
- \(t\) :
-
Time (s)
- \(u,\,v\) :
-
Velocity \(\left( {{\text{m}}\,{\text{s}}^{ - 1} } \right)\)
- \(U,\,V\) :
-
Dimensionless velocity
- \(x,\,y\) :
-
Cartesian coordinates \(\left( \rm{m} \right)\)
- \(w\) :
-
Pulsation (rad.s−1)
- \(X,\,Y\) :
-
Dimensionless coordinates
- E:
-
Effective or equivalent
- F:
-
Fluid
- S:
-
Solid
- H:
-
Hot
- M:
-
Melting
- \(\circ\) :
-
Initial state
- In:
-
Inlet
- Out:
-
Outlet
- Ref:
-
Reference
- \(\nabla\) :
-
Gradient operator
- \(\nabla .\) :
-
Divergence operator
- \(\nabla^{2}\) :
-
Laplacian operator
- \(\Delta x\) :
-
Lattice step
- \(\Delta t\) :
-
Time step
- \(\overline{\overline{\tau }}\) :
-
Stress tensor \(\left( {Pa} \right)\)
- \(\alpha\) :
-
Thermal diffusivity \(\left( {{\text{m}}^{2} \,{\text{s}}^{ - 1} } \right)\)
- \(\varepsilon\) :
-
Media porosity
- \(\eta\) :
-
Energy efficiency
- \(\lambda\) :
-
Thermal conductivity \(\left( {\rm{W}\,\rm{m}^{{\rm{ - 1}}} \,\rm{K}^{{\rm{ - 1}}} } \right)\)
- \(\mu_{f}\) :
-
Dynamic fluid viscosity \(\left( {kg\,m^{ - 1} \,s^{ - 1} } \right)\)
- \(\Gamma\) :
-
PCM's melting fraction
- \(\nu\) :
-
Kinematic viscosity \(\left( {{\text{m}}^{2} \,{\text{s}}^{ - 1} } \right)\)
- \(\omega\) :
-
Pore density (PPI)
- \(\psi\) :
-
Exergy efficiency
- \(\rho\) :
-
Density \(\left( {{\text{kg}}\,{\text{m}}^{ - 3} } \right)\)
- \(\tilde{t}\) :
-
Dimensionless time
- \(\tau\) :
-
Dimensionless relaxation time
- \(w_{i}\) :
-
Weight coefficient in direction i
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Mabrouk, R., Benim, A.C., Naji, H. et al. Investigation of Pulsed Flow Effects on the Phase Change Within an Open-Cell Metal Foam Using Thermal Lattice Boltzmann Method. Transp Porous Med 147, 225–257 (2023). https://doi.org/10.1007/s11242-023-01903-x
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DOI: https://doi.org/10.1007/s11242-023-01903-x