Effective thermal conductivities in packed beds: Review of correlations and its influence on system performance

Díaz-Heras, M.; Belmonte, J.F.; Almendros-Ibáñez, J.A.

doi:10.1016/j.applthermaleng.2020.115048

Cited by 49 publications

(15 citation statements)

References 71 publications

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“…Therefore, when the Bi is smaller than 1.0 (less than 1.05 in case 1), the deviation between model 1 and model 3 is less than 2%, and model 1 can accurately simulate the charging process of the PBTES system. This conclusion coincides with the investigation in Díaz-Heras et al 31 Besides, it is found from the numerical results of model 3 that the charging duration decreases when the diameter of the PCM capsule decreases, which is because that the heat transfer between the PCM capsules and HTF is enhanced with the reduction of the diameter of the PCM capsules, as shown by Equations ( 9) and (10). The model 2 considers the effect of temperature gradient inside the PCM capsule by introducing the thermal resistance, therefore the effective convective heat T A B L E 1 The numerical setting of the operating parameters of the PBTES system transfer coefficient, obtained by Equation ( 15) is adopted to evaluate the heat transfer, thus the results of model 2 show good agreement with those of model 3 at different Bi, which confirms the feasibility of model 2 at small Ste.…”

Section: Resultssupporting

confidence: 93%

“…

h_{vol} = \frac{6 h ((), 1 - ε)}{d_{p}}

h = \frac{k_{f}}{d_{p}} italicNu = \frac{k_{f}}{d_{p}} ((), 2 + 1.1 {Re}^{0.6} \Pr^{1 / 3})

The heat transfer of the HTF includes heat conduction, radiation, and natural convection. These complex heat transfer processes are made equivalent to the heat conduction of the HTF using the effective thermal conductivity 31 which could be estimated by the formula summarized by Gonzo 32

k_{f, italiceff} = k_{f} \cdot \frac{1 + 2 β^{3} ϕ + ((), 2 β^{3} + 0.1 β) ϕ^{2} + 0.05 ϕ^{3} \exp ((), 4.5 β)}{1 - italicβϕ}

where β = 1 − ε , ϕ = ( k p − k f )/( k p + 2 k f ) and k f is the thermal conductivity of the HTF.…”

Section: Numerical Modelmentioning

confidence: 99%

“…To avoid this, Equation () is applied when the liquid fraction is in the range of 0 < γ < 0.999. The natural convection inside the PCM capsule significantly affects the melting of PCM 31 . The natural convection enhances the heat transfer and it is considered as the enhancement of the thermal conductivity which can be formulated as a piecewise function.

k_{p} = ({, \begin{array}{l} k_{p, italicsol}, T \leq T_{sol} \\ \frac{k_{p, italicsol} + k_{p, italicliq}}{2}, T_{sol} < T < T_{liq} \\ k_{p, italicliq} {Nu}_{conv}, T \geq T_{liq} \end{array})

The Nu conv shows the effect of natural convection and it is obtained by an empirical formula of Ra 33 …”

Section: Numerical Modelmentioning

confidence: 99%

See 2 more Smart Citations

A comprehensive investigation of the mathematical models for a packed bed latent heat thermal energy storage system

Guo

Meng

et al. 2021

Intl J of Energy Research

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The numerical simulation is effective to investigate the thermal performance of the packed bed latent heat thermal energy storage system which can provide more detailed information. There are three most commonly used numerical models developed based on the porous medium model: the continuous solid phase model, improved continuous solid phase model, and concentric dispersion model. The applicability of these models is compared by evaluating the variations of fluid temperature, temperature difference inside phase change material capsule, thermocline thickness, charging power, and computational time. The results show that the concentric dispersion model can accurately simulate the charging processes with a deviation of less than 5% between the results of the concentric dispersion model and experimental results. When the Bi is smaller than 1, the effect of the temperature gradient inside the capsule can be neglected and the continuous solid phase model shows a deviation less than 2%. When the Ste is smaller than 0.1, the sensible heat is negligible and the improved continuous solid phase model shows a deviation less than 2%.The computational time of the concentric dispersion model is generally 30% more than the other two models.

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Section: Resultssupporting

confidence: 93%

“…

h_{vol} = \frac{6 h ((), 1 - ε)}{d_{p}}

h = \frac{k_{f}}{d_{p}} italicNu = \frac{k_{f}}{d_{p}} ((), 2 + 1.1 {Re}^{0.6} \Pr^{1 / 3})

k_{f, italiceff} = k_{f} \cdot \frac{1 + 2 β^{3} ϕ + ((), 2 β^{3} + 0.1 β) ϕ^{2} + 0.05 ϕ^{3} \exp ((), 4.5 β)}{1 - italicβϕ}

where β = 1 − ε , ϕ = ( k p − k f )/( k p + 2 k f ) and k f is the thermal conductivity of the HTF.…”

Section: Numerical Modelmentioning

confidence: 99%

k_{p} = ({, \begin{array}{l} k_{p, italicsol}, T \leq T_{sol} \\ \frac{k_{p, italicsol} + k_{p, italicliq}}{2}, T_{sol} < T < T_{liq} \\ k_{p, italicliq} {Nu}_{conv}, T \geq T_{liq} \end{array})

The Nu conv shows the effect of natural convection and it is obtained by an empirical formula of Ra 33 …”

Section: Numerical Modelmentioning

confidence: 99%

See 1 more Smart Citation

A comprehensive investigation of the mathematical models for a packed bed latent heat thermal energy storage system

Guo

Meng

et al. 2021

Intl J of Energy Research

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“…bau eff bau (18) The radiative effective conductivity is chosen from Sih and Barlow [26], as reviewed by Diaz-Heras [27].…”

Section: Description Of the Numerical Modelmentioning

confidence: 99%

Experimental and numerical analysis of a packed-bed thermal energy storage system designed to recover high temperature waste heat: an industrial scale up

Touzo

Olivès

Dejean³

et al. 2020

Journal of Energy Storage

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An industrial-scale air-ceramic horizontal packed-bed thermal energy storage (Eco-Stock®) has been designed and built by Eco-Tech Ceram and tested during an experimental campaign of 500h. The goal is to provide experimental data and analysis of a horizontal and containerized packed bed TES at high temperature, with performance indicators specific to waste heat recovery. A single charge-discharge at 525°C and 3 cycles at 500°C were carried out (300 kW Th for charge, 350 kW Th for discharge). The unit was able to store up to 1.9 MWh Th in a TES system (1.7 × 1.7 × 3.08 m 3 ) composed by 16-ton of bauxite ceramic media. The packed bed was able to valorize up to 90% of the heat source, which demonstrates the system ability to recover waste heat up to 525°C at industrial scale. No channeling effect and moderate radial thermal gradient were detected, even though the tank had a horizontal geometry. The plug and play TES presents a non-negligible part of its energy stored in the insulant, which can be recovered during discharge. To take into account such phenomenon, a one-dimension 3 temperature model is proposed. The model fitted well with experimental results, with a root mean standard deviation of the model below 20°C for the temperature profiles.

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“…The equivalent capacitance (C ij ) could be computed by combining three capacitances using Eq. ( 6) [27].…”

Section: Heat Transfer Formulation In Dem and Cfdmentioning

confidence: 99%

Evaluating the effective thermal conductivity of geothermal pavements constructed using demolition wastes by DEM and 3D printing techniques

et al. 2021

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This paper studies the effect of various parameters on the effective thermal conductivity (k eff ) of the geothermal pavement system when constructed using construction and demolition (C&D) materials. Recycled asphalt pavement (RAP) and recycled concrete aggregates (RCA) were utilized to experimentally model the geothermal pavement system, consisting of copper tubes to circulate water in the pavement and harness thermal energy. Numerical computational fluid dynamics (CFD) and discrete element method (DEM) methods were used to simulate the geothermal pavement system. Six samples of RAP and RCA aggregates with different particle size distributions were utilized to study the effect of important parameters in the geothermal pavement system. According to the results, coupled CFD-DEM approach could simulate the heat transfer mechanism in geothermal pavement compared to the results of the CFD simulation. The results indicated that increasing porosity would decrease k eff . The decrease rate depended on the gravel content of the sample where samples with a higher gravel content experienced a higher rate of decrease. Also, simulation results showed that increasing the gravel content could increase the value of k eff . Increasing the axial stress resulted in an increase in the value of coordination number (CN) and k eff . Moreover, comparing the thermal power and contact distributions indicated that the morphology of the heat conduction was the same as the contact network distribution. To study the effect of the particle shape on k eff , a novel approach was used that comprised of 3D scanning and printing real particle shape of RCA aggregates by thermochromic material. Simulated assemblies with DEM were verified using 3D printed particles. The effect of aspect ratio (AR) on k eff was studied which indicated that increasing AR would increase k eff . Decreasing AR to one, on the other hand, increased the time needed to reach the steady state.

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Effective thermal conductivities in packed beds: Review of correlations and its influence on system performance

Cited by 49 publications

References 71 publications

A comprehensive investigation of the mathematical models for a packed bed latent heat thermal energy storage system

A comprehensive investigation of the mathematical models for a packed bed latent heat thermal energy storage system

Experimental and numerical analysis of a packed-bed thermal energy storage system designed to recover high temperature waste heat: an industrial scale up

Evaluating the effective thermal conductivity of geothermal pavements constructed using demolition wastes by DEM and 3D printing techniques

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