Evaluation of the thermal capacity of cement-based thermal energy storage components. A case study

In this paper, we evaluate the heat capacity performance of cement-based heat exchangers for thermal energy storage and analyze their structural integrity under elevated temperatures. Fluid flow is modeled using the Navier-Stokes equations, conservation of mass, and energy. The response of the cement-based material is modeled considering thermomechanical coupling, obtaining the temperature profile within the thermal energy storage. This study allows us to observe the thermal energy storage capabilities for different thermal energy storage designs: plain concrete and concrete with nanoparticles of SiO2. Finally, we use our model for the evaluation of the concrete thermal energy storage component, which has been previously functionalized for use in low to medium temperature ranges (i.e., 100 °C to 400 °C).


Introduction
Thermal energy storage (TES) systems are called to play a fundamental role in the coming years; they can be combined with renewable energy harvesters to avoid the grid problems associated with their dependence on natural resources [1].Concrete heat storage stands out as an economical, flexible, and high-energy-density solution for energy storage [2].Additionally, recent studies show that concrete as storage media has the potential to become an interesting solution due to its properties such as relatively high specific heat and thermal conductivity, good mechanical properties, a thermal expansion coefficient similar to that of steel pipe, and low cost of a material that is easy to obtain and process [3].However, high-temperature storage in concrete causes severe thermal loads, which can cause loss of thermal properties in the material, limiting the performance and durability of the system [4].
Nanotechnology has been increasingly applied in the construction industry, particularly in enhancing concrete properties.Studies have shown that using nanomaterials such as nano-silica, nano-TiO2, carbon nanotubes, and nanocellulose can significantly improve concrete's mechanical and thermal properties [5][6][7][8].These improvements include increased strength, durability, and ease of placement, as well as reduced thermal transfer rate for fire retardant and insulation.
On the other hand, fibers, as well as nanoparticles, can improve the thermal and mechanical properties of concrete [9][10][11][12].Basalt fiber has several advantages.First, basalt fiber is made from basalt ore, which is stable and safe for people and the environment.Secondly, it has high tensile strength, alkali and acid resistance, low heat transmission, and durability at high and low temperatures [13].Finally, basalt is chemically rich in oxides of magnesium, calcium, sodium, potassium, silicon, and iron, along with traces of alumina, with 52.8% composed of SiO2 [14].
In this work, we propose a model based on the finite element method (FEM) to evaluate the heat storage capacity of heat exchangers of cement-based materials for concrete thermal energy storage (CTES), considering each of the proposed conditions concrete and concrete + Nano SiO2 [5].The mass, Navier-Stokes, and energy conservation equations are used to describe the fluid motion.The thermal problem is strongly coupled to the mechanical problem in order to evaluate the structural stability of each CTE.

Methodology and materials
In our work, we compare the thermal storage capacity of different cement-based thermal energy storage devices, considering SiO2 nanoparticles, by means of the FEM.The mathematical description is presented below.On the other hand, the thermal evolution in the solid domain can be described as Equation ( 1) [15].
where ρ is the density, C % the specific heat, T the temperature, t is the time, and  the heat flow, which depends on the thermal conductivity (k) and the temperature gradient.Namely, Fourier's law as Equation ( 2) [15].
On the other hand, the heat transfer in the fluid domain is given by Equation (3) [15].
where  is the fluid velocity, Q a source term, Q ! the pressure work, and Q ∨' a viscous dissipation term; The fluid motion is described using the Navier-Stokes equations Equation (4) and the conservation of mass Equation (5) [15].In this study, we consider laminar conditions for the fluid flow.
where p is the fluid pressure, µ is the dynamic viscosity, and  is the volume force vector.

Results and discussions
For the simulations, we consider a cylindrical concrete heat exchanger with 50 cm length, 25 cm outer diameter, and 5 cm inner diameter, as depicted in Figure 1.As additional boundary conditions to those mentioned above, the outer boundary of the concrete is thermally insulated.This boundary condition means that there is no heat flow through the boundary, and the temperature gradient across the boundary is zero.To run the numerical model, we employed the Multiphysics simulation software COMSOL 6.1 [16], taking advantage of its capabilities to solve both fluid motion and heat transfer equations; our model incorporates the dynamics of heat transfer in fluid and solid media, which guarantees an analysis of the thermal behavior at different points in the material.The convergence of the mesh is established from the tetrahedral method with independent trajectory (see Table 1); this approach, as well as the selection of the appropriate mesh, allows us to simulate the behavior of the fluid efficiently and accurately.At the time of the simulation, the thermal properties were considered (see Table 2); in the case of concrete + nano SiO2, it was considered a concentration of 3%.   Figure 2, the dotted blue line represents the radius of the concrete that was considered for the analysis of the temperature behavior for this work.Figure 3 shows the temperature behavior at 1000 seconds, 5000 seconds, and 10000 seconds in the cement-based TES, and concrete +Nano SiO2, respectively, in a radius, represented in Figure 2; the two temperature graphs show remarkable variations but differ mainly in their thermal gradients.While the temperature gradient in Figure 1(a) shows a larger increase in temperature over time, Figure 1(b), shows the sample has a higher thermal inertia; that is, it has a higher storage capacity but is slower.This makes the thermomechanical response more expected, as it can better accommodate the gradients.

Conclusions
This study presents a comparison using the finite element method to examine the thermal attributes of concrete; our implementation of a mathematical model in COMSOL Multiphysics, employing the finite element methodology, has shown its benefits for component design.Specifically, our results suggest that the integration of SiO2 nanoparticles in concrete significantly affects its temperature gradient, allowing it to withstand elevated temperatures more effectively, which is considered an advantage when manufacturing thermal energy storage.Another relevant feature of this formulation is that it provides a higher thermal capacity; these results guide future research in which this basis can be expanded by exploring different varieties of nanoparticles or fibers.The aim of these explorations is not only to improve the thermal characteristics but also to enhance the mechanical properties of concrete, thus expanding the potential applications and strength of this material.

Figure 1 .
(a)  The geometry of the proposed concrete thermal energy storage, and (b) tetrahedral fine mesh.

Figure 2 .
Figure 2. The radius of the concrete.

Figure 3 .
(a) Temperature profile across the CTES concrete, and (b) Temperature profile across the CTES concrete + nano SiO2.