Thermo-mechanical analysis of copper-encapsulated NaNO3–KNO3
Introduction
Thermal energy storage (TES) has received an increasing interest over the past years in different applications such as waste heat recovery, thermal solar capture, zero-heat houses, aerospace applications, and for thermal protection purposes. In the thermal solar applications or for heat recovery from hot industrial flue gases, it is very interesting as high temperature thermal energy storage (HTTES) provides continuity and enhances the potential of a solar system allowing this technology to get a faster development and acceptation due to its increase of efficiency and usability (Zhang et al., 2013a, Pitié et al., 2013, Cáceres et al., 2013, Fernandez et al., 2012). For thermal protection applications, there is a strong interest in understanding and predicting the conditions where it is possible to cool damaged electrical equipments and/or electronics and telecommunication devices, and even severely damaged nuclear reactor cores (Lipinski, 1984). Thermal management utilizing solid–liquid PCMs is one of the most interesting passive thermal storage techniques, due to their inherent advantage of simplicity and reliability. TES techniques can be classified as sensible heat storage and latent heat storage. The latter is particularly attractive, since it provides a high energy storage density and can store the energy as the latent heat of fusion at a constant temperature. The latent heat absorption phenomenon, associated with melting of a suitable PCM, could be efficiently used to delay or modify the temperature rise of the surface subjected to a high heat flux (Zhang et al., 2013b).
Despite PCMs being widely promoted for HTTES systems due to their capability of storing significant amounts of energy within a small PCM volume and at a moderate temperature variation, most PCMs suffer the problem of low thermal conductivity which extends the charging and discharging periods. In order to improve the thermal conductivity of PCMs, extensive investigations have studied the addition of different high thermal conductivity materials, such as either mixing graphite within nitrate salts under isotropic pressure (Lopez et al., 2010), or using metal foams (Zhao et al., 2010, Neville and Rabiei, 2007, Elgafy and Lafdi, 2005, Ismail and Trullenque, 1993, Ho and Chu, 1996, Lopez, 2007). Past and current researches have demonstrated that porous foams (graphite, copper, aluminum or metal alloys) embedded within PCMs are a feasible storage material for low temperature applications, whereas applications at high temperatures are less documented. The objectives of the present paper will be focused on HTTES, as is supposed to be used in thermal solar capture system (Zhang et al., 2013a, Pitié et al., 2013, Cáceres et al., 2013, Chen et al., 2010), where the discontinuity of solar energy can be overcome by an integrated system with PCMs.
Many models have been presented in order to determine the heat transfer behavior in porous media (Bear, 1988, Pinder and Gray, 2008, Cushman, 1997), but due to the specific conditions of this problem, such studies require a different treatment of the transport equations involved in the system. A mathematical method, known as the volume averaging method, was developed by Whitaker (1999), and has subsequently been used in the modeling process of diffusion equations in porous media (Valdés-Parada and Alvarez-Ramírez, 2011), turning the intrinsic micro-analysis of this problem into an averaged approach on a macro scale. These models are generally solved by numerical methods: due to the complexity of the differential partial equations, analytical solutions are seldom possible and simulations are more efficient on computing resources. Some of these numerical approaches were previously presented in literature (Zabaras and Deep, 2004, Smith, 2005, Garcia, 2007). Porous media models, applying the volume averaging method, have been very useful to describe and simulate the fluids behavior in these geometries. These models have been used in thermal control applications that extend from temperature managing on nuclear reactor cores to thermal protections of electronic equipment and specific devices as mentioned before (Ismail and Trullenque, 1993, Ho and Chu, 1996, Cao and Faghri, 1990, Bain et al., 1971). Since thermal control applications have been developed from these models, they are of growing importance (Oddou et al., 2011, Chapotard and Tondeur, 1983). One of the most important model applications considers heat storage. The theoretical treatment of a variety of models has been assessed by Quintard and Whitaker, 1996, Quintard and Whitaker, 1998a, Quintard and Whitaker, 1998b and by Ahmadia and Quintarda (1998): these treatments deal with heterogeneous porous media using the volume averaging method in the transport equations of momentum, mass and energy. In this context, heat storage models are trying to improve the efficiency of a PCM assessment, by simulations with specific boundary conditions. The current research is based on the model of the closed solid sphere developed by Lopez et al. (2010) and later extended by Pitie et al. (2011). These authors present a model of confined melting in composite materials made of graphite-nitrates and ceramic-nitrates respectively. In order to model heat storage at high temperature, and therefore the melting of the salt, these authors have proposed phase change models accounting for the pressure effects of the molten salt within the thermo-mechanical analysis.
In the context of HTTES, a copper and nitrates composite is proposed in the present paper, considering the high thermal conductivity of copper and better mechanical strength in comparison with previously studied graphite composites. The present paper therefore proposes a first attempt to understanding salt melting within a copper spherical coating, by providing an appropriate thermo-mechanical treatment.
Section snippets
Geometry and hypotheses
Consider a 25 mm O.D. sphere of solid salt (rm = 12.5 mm) with a 40% KNO3 + 60% NaNO3 composition and a concentric coating sphere of 28 mm O.D. (R = 14 mm), made of copper (Fig. 1). The wall of the sphere allows heat transfer inside the material. The thermodynamic behavior of material properties and therefore thermo-mechanical coupling will be studied, especially toward heat capacity, average temperature and internal energy as affected by a constant temperature during a definite time. The melting front
Mathematical model
The numerical model is based on solving the heat diffusion equation to both copper coating and to the phase change material inside the coated shell. Since it is assumed that there is no velocity field in the molten PCM phase, convective heat transfer in the salt is neglected.
Because of the symmetry, the system was formulated in one-dimensional polar coordinates. The outer side of the enclosure was assumed to be subjected to free convection at external temperature, while the inner surface is
Background information
To validate the Lopez model, the thermodynamic properties of the KNO3–NaNO3 salt are listed in Table 1. The initial temperature of PCM is 293.15 K.
For the shell, the study will focus on geometrical and mechanical values of copper.
For the shell, the study will focus on geometrical and mechanical properties of copper.
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Ecopper = 117 GPa and αcopper representing the copper shell Young's module, and coefficient of thermal expansion respectively.
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Transition temperature of copper is 1357.77 K.
Comsol
Conclusions
The thermo-mechanical model of a PCM coated in a spherical copper shell was examined for the charging and discharging cycles.
Charging was predicted to take ∼1000 s from 293 till 550 K. A discharging period of ∼1600 s is needed to cool the E-PCM to 400 K. The cooling rate of the melt is possibly enhanced by the occurring natural convection.
The volume expansion upon melting and associated pressure increase is beyond the acceptable mechanical properties of the copper shell and shell cracking is not
Acknowledgements
This work was supported in Chile by the projects CONICYT/FONDAP/15110019 (SERC-CHILE), CONICYT/FONDECYT/1120490 and by Center for the Innovation in Energy of UAI. The authors moreover acknowledge the European Commission for co-funding the “CSP2” Project – Concentrated Solar Power in Particles (FP7, Project No. 282932).
References (39)
- et al.
Thermal protection from intense localized moving heat fluxes using phase change material
Int. J. Heat Mass Transfer
(1990) - et al.
Effect of carbon nanofiber additives on thermal behavior of phase change materials
Carbon
(2005) - et al.
Influence of residual stress, surface roughness and crystallographic texture induced by machining on the corrosion behavior of copper in salt-fog atmosphere
Corros. Sci.
(2012) - et al.
Thermal protection characteristics of a vertical rectangular cell filled with PCM/air layer
Heat Mass Transfer
(1996) - et al.
Physical and mechanical properties of copper and copper alloys
- et al.
Confined melting in deformable porous media: a first attempt to explain the graphite/salt composites behaviour
Int. J. Heat Mass Transfer
(2010) - et al.
Circulating fluidized bed heat recovery/storage and its potential to use phase-change material particles
Appl. Energy
(2013) - et al.
Transport in chemically and mechanically heterogeneous porous media. I: Theoretical development of region-averaged equations for slightly compressible single-phase flow
Adv. Water Resour.
(1996) - et al.
Transport in chemically and mechanically heterogeneous porous media—III. Large-scale mechanical equilibrium and the regional form of Darcy's law
Adv. Water Resour.
(1998) - et al.
Transport in chemically and mechanically heterogeneous porous media. IV: Large-scale mass equilibrium for solute transport with adsorption
Adv. Water Resour.
(1998)
Review on thermal energy storage with phase change materials, heat transfer analysis and applications
Appl. Therm. Energy
Concentrated solar power plants: review and design methodology
Renew. Sustain. Energy Rev.
Heat transfer enhancement for thermal energy storage using metal foams embedded within phase change materials (PCMs)
Solar Energy
Study of corrosion behaviour of mild steel and copper in thin film salt solution using the wire beam electrode
Corros. Sci.
Transport in chemically and mechanically heterogeneous porous media. V. Two-equation model for solute transport with adsorption
Adv. Water Resour.
Gravity induced free convection effects in melting phenomena for thermal control
ASME J Spacecraft
Dynamics of Fluids in Porous Media
Performance of molten salt solar power towers in Chile
J. Renew. Sustain. Energy
Dynamics of latent heat storage in fixed beds, a non-linear equilibrium, the analogy with chromatography
Chem. Eng. Commun.
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These authors contributed equally to the research.