Thermal performance of clay bricks with different fillings: a CFD analysis

The thermal conductivity of 15 loadbearing and infill bricks was calculated through a Computational Fluid Dynamic (CFD) analysis. Clay bricks filled with air, expanded polystyrene EPS, and graphitized expanded polystyrene were selected from the catalogue of the manufacturer F.B.M. - Fornaci Briziarelli Marsciano. The company provided the geometric features of each block and the thermal characteristics of the clay mix and the filling. The thermal conductivity value of each air cavity was calculated in compliance with UNI EN ISO 6946. Each volume was discretized in triangular meshes. The equivalent thermal conductivity of each block was calculated starting from the simulation of the isotherms trend inside the sample and from the heat flux passing through it. The obtained results were discussed depending on the filling, the geometry, and the hole percentage. In general, thermal conductivity increases with hole percentage in the bricks with air. Similar geometries have similar thermal behaviour. EPS or graphitized EPS involve better thermal performance as the hole percentage increases. Finally, the influence of the different orientations of the blocks was investigated. Equivalent thermal conductivity values increase for horizontally-brick placed, especially in homogeneous and compact geometries.


Introduction
In recent years, there was a growing emphasis on energy efficiency and sustainable constructions, considering that buildings account for more than 40% of social energy consumption [1].For this reason, building energy saving has a great relevance in order to reduce the energy crisis and protecting the environment [2].Since heat loss in building envelopes accounts for 60-80% of the total loss [3], it is crucial to create a high level of comfort and to reduce the energy consumption by improving the thermal performance of the envelopes, particularly of the opaque walls.As a result, researchers and engineers are working to develop materials that offer enhanced thermal insulation properties while minimizing energy consumption.Among these, hollow bricks represent a promising standard solution able to provide excellent insulation, due to the hollow cores.However, further improvements in their thermal performance are still desirable.Expanded polystyrene (EPS) is a widely used insulation material known for its low thermal conductivity (0.033 -0.039 W/mK) and lightweight properties [4].It was successfully employed in several applications to enhance the thermal resistance of building envelopes.Recently, researchers started to explore the potential of incorporating EPS into hollow bricks as a filling material to enhance their thermal insulation performance.The introduction of EPS as a filling material has the potential to significantly avoid the convective heat transfer within the holes, resulting in a high thermal resistance [5].Moreover, the field of materials science has witnessed the advent of graphitized EPS, a novel derivative of EPS with enhanced thermal conductivity properties (λ=0.031W/mK) [6].It opens new possibilities for enhancing the thermal performance of hollow bricks by incorporating graphitized EPS as a filling material.
However, despite the potential benefits of using air, EPS and graphitized EPS in hollow bricks, a comprehensive and systematic understanding of their effects on the thermal performance of such building materials is still lacking.This knowledge gap underscores the need for systematic investigations that evaluate and compare the thermal characteristics of hollow bricks filled with EPS and graphitized EPS.Therefore, this study aims to address this research gap by investigating the effect of air, EPS and graphitized EPS filling on the thermal performance of hollow bricks.Equivalent thermal conductivity values of several bricks were calculated by means of CFD analysis and the results were discussed taking into account the geometry, the hole percentage, and the orientation of the blocks, in order to establish the correlations between the features of the block and its thermal performance.

Materials and Methods
Several clay bricks were selected from the catalogue of the manufacturer F.B.M. -Fornaci Briziarelli Marsciano [7] (Table 1, Figure 1).They are both load-bearing bricks (BTP) and partition clay blocks (BTT), some with joints (inc) and some smooth (lis) among the most marketed.The clay mixture used to produce the bricks is characterized by a thermal conductivity λ equal to 0.328 W/mK, a density ρ equal to 1800 kg/m 3 , and a specific heat ϒ of 937 J/kgK.Air, EPS (λ = 0.038 W/mK, ρ = 30 kg/m 3 and ϒ = 1450 J/kgK), and graphitized EPS (λ = 0.031 W/mK, ρ = 20 kg/m 3 and ϒ = 1450 J/kgK) were considered to fill the holes in each block.The geometric features of the bricks and those of the clay mixture and fillings were provided by the company.The dimensions are in the 45x30x18 cm 3 (brick 1) -30x25x18 cm 3 (brick 15).Blocks 2, 5-9, 11, 12, 14, 15 are characterized by homogeneous holes (height in the 8.8 -25.4 mm range), whereas holes of different sizes are present in the bricks 1, 3, 4, 10, 13.Hole percentages are in the 44.65 (brick 8) -65.53 (brick 11).Thermal resistance of the air gaps in each brick was calculated in compliance with UNI EN ISO 6946 [8].The analyses were carried out by means of a finite volume approach.The 2D model from the external CAD software was imported in the software component called Design Modeler.Each continuum was discretized into elements of finite volume, choosing triangular meshes with an average element size of 0.001 m, as shown in Figure 2-a (block 14, as an example).The boundary conditions of the model (right and left adiabatic sides, convective conditions on the upper and lower sides) and the features of the materials (thermal conductivity, density, and specific heat of the clay, air/EPS/graphitized

Results and discussion
Figure 3 shows the equivalent thermal conductivity values obtained for the bricks with three different fillings of the gaps.Increasing hole percentage, the thermal performance of the bricks with air tend to worsen.However the trend is rather scattered with respect to the trend-line and the great variability is related to the geometry of the brick, especially the height of the holes, as discussed in the following.
When the holes are filled with EPS or graphited EPS, an improvement in thermal performance is obtained as the hole percentage increases (reduction of equivalent thermal conductivity is in the 8 -61% and 12 -65% ranges with EPS and graphitized EPS, respectively).The trends with the insulation materials are practically parallel; lower λeq-values are obtained with graphitized EPS, according to the thermal performance of the materials; the reduction is about 4-12%.
A detailed discussion should be made with respect to the geometric characteristics (Figure 4).Increasing the hole percentage in the air-filled bricks with very small holes (high hole of 8.8 and 9.3 mm in 8 and 5 bricks, respectively), λeq increases (Figure 4-a).When both the percentage and the height of the holes are about equal (yellow bars), similar thermal performance are obtained.For hole percentages in the 53.9 -65.5 range, the higher holes (n.15, 2, 14, 12, 11, blue bars) involve a worsening of the thermal performance of the brick.Conversely, the increase in drilling leads to a reduction in λeqvalues, in geometries with non-homogeneous cavities (red dotted bars).
The increase in the percentage of both EPS and graphited EPS leads to an improvement in thermal performance, especially in bricks with non-homogeneous holes (λeq is reduced up to 42% and 45% with EPS and graphitized EPS from brick n. 13 to brick n. 3) (Figure 4-b and c, red dotted bars).A particular behavior is found in block 8 (hole percentage of 44.7%), which is characterized by the smallest gaps (8.8 mm): this behavior is probably due to a reduction in convection heat transfer.Similar geometry has comparable performance.The influence of the geometry is less marked as the performance of the material inside the cavities increases; with graphitized EPS, when the hole percentages is higher than 60%, the performance is approximately equal in all the bricks (λeq=0.059-0.06 W/mK) (Fig. 4-c).
The shaping does not affect the thermal properties with any filling (blocks 6 and 7 with equal size but one smooth and one with joints).
Furthermore, 4 blocks (n. 8, 13, 15, 1) which can be installed on site also according to a horizontal arrangement were selected.The comparison of the equivalent thermal conductivity values obtained with respect to the vertical position is shown in Figure 5.The horizontal position involves a worsen behavior in thermal performance, especially in the homogeneous and compact bricks (8 and 15); the thermal conductivity-value increases by 50 and 49% with air, 45 and 43% with EPS, and 47 and 45% with graphitized EPS for blocks number 8 and 15, respectively, regardless of geometry.In bricks with large holes (n. 13 and 1), the increase in λeq due to the horizontal position is much higher as the % of holes increases (from 26% to 40% with air, from 18% to 37% with EPS, from 19% to 26% with graphitized EPS).

Conclusion
In the present study, thermal performance of 15 clay bricks in terms of equivalent thermal conductivity were calculated by means of CFD simulations.The brick-cavities are filled with air (thermal conductivity of each gap calculated according to UNI EN ISO 6946), EPS (λ=0.035W/mK), or graphitized EPS (λ=0.031W/mK).For each geometry, starting from the simulated trend of the isotherms and the calculated heat flux, the thermal resistance and the corresponding equivalent thermal conductivity values of the block were determined.A critical analysis of the results is presented in this paper and the following main conclusions are highlighted: -increasing the hole percentage from about 45% to 66%, the thermal conductivity decreases when the cavities are filled with insulation materials (up to 44% and 46% with EPS and graphitized EPS, respectively), whereas it increases with air (up to 48%); -in air-filled bricks, the height of the holes greatly influences the thermal performance: the higher holes result in a thermal deterioration (up to 30% with holes about 25-mm high); -in geometries with non-homogeneous holes, the increase of the drilling with EPS and graphitized EPS involves a reduction of the λeq-values with three different fillings; similar geometry is characterized by similar thermal properties; bricks with holes greater than 60% filled with graphitized EPS have a similar thermal behavior; -the horizontal positioning of the brick leads to an increase in thermal conductivity, especially in geometries with homogeneous and compact holes (increases up to 50, 45, and 47% with air, EPS, and graphitized EPS, respectively).
defined in the dedicated software.The thermal resistance and the corresponding equivalent thermal conductivity λeq of each block was obtained by means of the simulated isotherms (Figure2-b) and the calculated heat flux.

Table 1 .
Features of the selected bricks.
a small/large hole height.