Three-dimensional numerical modeling and simulation of the thermal properties of foamed concrete

doi:10.1016/j.conbuildmat.2013.09.027

Construction and Building Materials

Volume 50, 15 January 2014, Pages 421-431

https://doi.org/10.1016/j.conbuildmat.2013.09.027 Get rights and content

Highlights

•
A random generation method was extended from 2D to 3D.
•
Finite volume method was used to solve the heat transfer equations.
•
3D effects on the effective thermal conductivity predictions were discussed.

Abstract

In this paper, a three-dimensional method was developed for modeling the heat transfer of foamed concretes with a large range of densities (300–1700 kg/m³). A random generation method was extended from two dimensions (2D) to three dimensions (3D) for reproducing the microstructure of foamed concrete. A finite volume method (FVM) was then used to solve the energy transport equations for two phase coupled heat transfer through the porous structure. The effective thermal conductivities (ETCs) of foamed concretes were thus numerically calculated and the 3D predictions were compared with the existing experimental data and other analytical models. The numerical results show that the predicted effective thermal conductivity varies with the lattice number in the third dimension following an exponential relationship, and it needs at least 20 lattices along the third dimension to stabilize the simulation results. In addition, the 3D numerical predictions agree more with the experimental results, since the heat conduction in the third direction is omitted in 2D simulation, leading to the underestimation of effective thermal conductivities prediction in the same boundary conditions. Finally, a correlation was then derived between the results computed with 3D and 2D numerical models.

Introduction

Nowadays, various kinds of lightweight concretes have been widely used in construction industry [1], [2], [3], [4]. The interest is of course to decrease the amount of load-bearing elements, as well as to get better thermal properties compared with conventional concrete. The latter point especially makes sense with regard to relieve the energy crisis and ecological problems in developing countries, where the large-scale construction of urbanization is proceeding. Lightweight concrete can normally be produced by replacing totally or partially the standard aggregate with low weight and usually low cost components (e.g., EPS, perlite and clay), or by directly introducing gas or foam into the cement or mortar paste, forming the so called foamed concrete.

Foamed concrete has been widely used in non-structural applications [5], [6], [7], [8], mostly for cast-in-place applications in roof slopes, floor leveling and insulating layers of wall constructions, and for any kind of void filling projects (mines, tunnels, road basements, ground stabilization and others), owing to its self-compacting, light weight, excellent thermal insulation properties and affordable strength values. In many application cases, there are no strict requirements to strength characteristics, and thermal conductivity plays the more dominant role [9], [10], [11], [12]. In addition, it is possible to design the properties of foamed concrete to meet the construction requirement by varying material parameters such as cement paste composition, foam size and volume friction. To this end an accurate evaluation of the relationship between the microstructure and thermal transfer properties of such porous lightweight building materials is required.

At ambient temperature, the heat transfer in solid foams is dominated by thermal conduction. Numerous of authors proposed empirical, analytical or numerical model depending on the porous morphology and on the conductivity of the phases to estimate the effective thermal conductivity (ETC) of this type of materials.

Some analytical models which are often used to describe the effect of pore volume fraction as a variable on the thermal conductivity of a porous material are summarized in Table 1. In each case, the expression is based on a geometrical simplification of the microstructure concerning the spatial distribution of the two phase system. For example, the Hashin and Shtrikman [14] expressions give the most restrictive upper and lower limits of the effective thermal conductivity (ETC) for a two-phase system where spherical inclusions are placed in a continuous matrix. Landauer [15] derived a practical expression in which the connectivity of the phases is taken into account. This approach is also called “Effective medium percolation theory” (EMPT). These approaches become limited when the pore volume fraction increases and the isolated pores become connected. Recently, owing to the rapid developments in computer and computational techniques, some numerical models have also been used to predict the thermal conductivity of porous materials [16], [17], [18], [19], [20], [21]. Coquard and Baillis [20] calculated the ETC of two-phase heterogeneous materials by using a numerical finite volume method. The work of Wang and Pan [21] who solved the energy transport equation through random open-cell porous foams using a high-efficiency Lattice Boltzmann method can also be cited. Wei et al. [22] presented a random method to predict the effective thermal conductivity of foamed concrete, which included a random generation method to reproduce microstructure of foamed concrete and a resistor network analogy method to solve the energy transport equations for fluid–solid coupled heat transfer. Wei’s predictions agreed well with the experimental data when the porosity is less than 35%. However, this kind of 2D models underestimated the predictions of ETC in high porosity cases, attributed to the inherent approximations in the 2D analysis.

Based on the previous work [22], this paper developed a three-dimensional random generation method to reproduce the 3D microstructure of foamed concretes. A finite volume method (FVM) was also developed which allows the effective thermal conductivity of foamed concretes with flexible microstructure to be predicted numerically. Finally, the proposed model was validated by the comparison with the two-dimensional predictions, the experimental data and other existing models. The 3D effect of prediction of ETC of foamed concrete was therefore discussed.

Section snippets

Random generation of 3D porous structure

As mentioned in the introduction, the existing analysis models are based on the geometrical simplification of the microstructure. In such models, the stochastic natures of the porous material are neglected. To bring the random characteristics of porous materials into modeling, the random effect has to be introduced during the generation of porous media structure. The random location of lattices is the most easy and popular method to construct an artificial porous medium [16], [23], [24].

Results

The aforementioned numerical method will be used to predict the effective thermal conductivity of the three-dimensional foamed concrete in this section. First, the method is validated by comparing with the two analytical models for two simple structures (parallel mode and series mode). Second, the three-dimensional predictions with proper simulation parameters will be compared with the two-dimensional cases and experimental results so that the third dimensional influence on the ETC predictions

Discussion

The differences between 3D and 2D numerical prediction of ETCs are mainly due to the different assumptions of basic heat transfer unit. In the 2D model, each lattice exchanges heat with its neighbors in the plane so that the heat flow perpendicular to the section is not taken into account. In principle, this assumption is uniquely applicable if the microstructure in the third dimension is totally repetitive or symmetrical. In other words, this assumption is not representative of the case of

Conclusions

A random generation method has been extended from 2D to 3D for reproducing much more realistic microstructure of foamed concretes by computer algorithms. The steady heat equilibrium equations through the 3D porous structures were then solved by a finite volume method (FVM). The numerical results show that the 3D numerical predictions are related to both the generated structure and the lattice number in the third dimension. The predicted effective thermal conductivity varies with the lattice

Acknowledgements

Authors gratefully acknowledge the financial support from open projects from state key laboratory of high performance civil engineering materials (2010CEM002), China National Natural Science Fund of China (51178106, 51138002), Program for New Century Excellent Talents in University (NCET-08-0116), 973 Program (2009CB623200), Program sponsored for scientific innovation research of college graduate in Jiangsu province (CXLX_0105). Thanks are also due to the Concrete Technology Unit, University of

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Three-dimensional numerical modeling and simulation of the thermal properties of foamed concrete

Highlights

Abstract

Introduction

Section snippets

Random generation of 3D porous structure

Results

Discussion

Conclusions

Acknowledgements

Cem Concr Res

Appl Therm Eng

Front Architect Res

Cem Concr Compos

J Phys D Appl Phys

Acta Mater

Int J Heat Mass Transfer

Constr Build Mater

Int J Heat Fluid Flow

Effective thermal conductivity of clayey aerated concrete in the dry state: experimental results and modeling