Experimental study and modeling on effective thermal conductivity of ...

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Bulletin of the JSME

Vol.11, No.2, 2016

Journal of Thermal Science and Technology Experimental study and modeling on effective thermal conductivity of EPS lightweight concrete Yi XU*,**, Linhua JIANG*, Jiaping LIU**, Yan ZHANG*, Jinxia XU* and Gongqing HE* *College of Mechanics and Materials, Hohai University 8 Fochengxi Road, Nanjing 211100, China E-mail: [email protected] **School of Materials Science and Engineering, Southeast University 2 Southeast University Road, Nanjing 211189, China

Received 14 September 2015 Abstract The effect of expanded polystyrene (EPS) inclusions on thermal conductivity of lightweight concrete is studied. Various mixtures are produced by incorporating EPS aggregate at different volumes (0%, 10%, 20%, 30% and 40%) in concrete with three water/cement ratios (0.55, 0.50 and 0.45). The apparent density and thermal conductivity values of expanded polystyrene concrete decrease as the volume of EPS increases. The thermal conductivity increases with an exponential function of the apparent density whatever the water/cement ratios. The general thermal conductivity models can not well predict the present experimental results. Based on experimental results and composite approach, a new simplified model is proposed to evaluate the effective thermal conductivity with an equation of the plain concrete thermal conductivity, the EPS thermal conductivity, the density and the percentage of EPS particles. The model is applicable to the EPS lightweight concretes with different water and cement ratios. Key words : EPS concrete, Ultra lightweight aggregate, Thermal conductivity, Model

1. Introduction Lightweight concrete (LWC) produced through replacing normal aggregate partially or totally by lightweight aggregate has been widely used in building constructions, highway foundations and marine structures recently (Chia et al., 2002; Rajamane et al., 2012; Alshihri et al., 2009; Gao et al. 2013). Expanded polystyrene (EPS) which is classified as ultra-lightweight aggregate is one of the promising aggregates, owing to its properties of ultra-low density, thermal insulation and energy absorption comparing to ordinary concrete, so EPS concrete can be regarded as a considerable lightweight concrete (Miled et al., 2004; Babu et al., 2006; Sadrmomtazi et al., 2012). A number of research studies have been conducted on the EPS lightweight aggregate concrete. The scientific researchers are mainly focusing on their mechanical properties. As far back as 1973, Cook (Cook et al., 1973) investigated EPS as an aggregate for concrete. Thereafter, Perry and Bischoff (Perry et al., 1991) researched the mechanical properties of polystyrene aggregate concrete over a compressive strength from 3MPa to 10MPa and stated the relationship between strength and density. Babu (Babu, et al., 2003, 2004, 2005) added mineral admixtures to gain better bonding between EPS beads and cement, and discussed the effect of EPS sphere size on compressive strength of EPS concrete. Kan (Kan et al., 2009) evaluated the usability of modified waste EPS as an aggregate for concrete and investigated the freezing and thaw resistance. Chen (Chen et al., 2004, 2005, 2007) applied steel fiber or styrene butadiene rubber latex to reinforce the concrete with EPS lightweight aggregates and studied the characteristics such as strength and shrinkage. Le Paper No.15-00504 [DOI: 10.1299/jtst.2016jtst0023]

© 2016 The Japan Society of Mechanical Engineers

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Yi Xu, Jiang, Liu, Zhang, Jinxia Xu and He, Journal of Thermal Science and Technology, Vol.11, No.2 (2016)

Roy (Le Roy et al., 2005; Miled et al., 2007, 2009) improve the workability of EPS concrete by used superplasticizer and developed a 2D numerical model to analyze size effects on mechanical properties. Sadrmomtazi (Sadrmomtazi et al., 2012, 2013) proposed neural network and adaptive network-based fuzzy inference system models for calculating the compressive strength of EPS concrete containing rice husk ash. In our previous investigation (Xu et al., 2012, 2015), the correlation of the elementary composition and the characteristics such as density, compressive strength and stress-strain behavior of EPS concrete was produced, and the EPS concrete hollow bricks were manufactured by applying the optimal mixture proportion of EPS concrete. As above mentioned, the literatures in this field are mostly devoted to characterizing the mechanical properties of EPS concrete. Meanwhile, several researches about the thermal properties were carried out in recent years due to the requirement of building energy conservation. Bonacina (Bonacina et al., 2003) studies the thermal performance of polystyrene pearls light concrete at different mean temperatures and moisture content. Bouvard (Bouvard et al., 2007) investigated the effect of EPS sphere size and mass fraction on thermal conductivity and draw the conclusion that the differential effective medium model was fitted with the experimental data. According to the published research, we find that EPS lightweight concrete with different water to cement ratio (w/c), one of the most important factors, is rarely discussed. It could be interesting to develop a new simplified model to predict the effective thermal conductivity of EPS concretes with different water/cement ratios. The model should be a useful support for designing thermal properties of EPS lightweight concrete to satisfy the requirements of Chinese energy-efficient standard GB50176-93, GB50189-2005, JGJ75-2012, and JGJ134-2010 for different building engineering. In this article, a series of experimental tests with different EPS aggregate volumes and water/cement ratios and modeling of effective thermal conductivity are performed. First, the apparent density of fresh EPS concrete and the thermal conductivity of hardened EPS concrete are tested. Then, results analysis shows that the existing effective thermal conductivity methods are not suitable for the experimental results. A new semi-empirical model approach to assess the effect of EPS inclusions on the effective thermal conductivity of EPS lightweight concrete as a two-phase material is proposed. Finally, the present model is calibrated by one group test (w/c=0.55) and extended to the other two group test (w/c=0.50 and w/c=0.45). It is shown that the model is well suitable to experimental results of EPS concrete with different water cement ratios.

2. Experimental study Ordinary Portland cement was used in the experiments. The maximum size of normal coarse aggregates (crushed granite) is 10mm nominal. The normal fine aggregates were siliceous sands with medium-graded. The EPS aggregates (Fig. 1) were commercially lightweight aggregates with the bulk density of 30 kg/m3 and the grain size of 3 mm. Fig. 2 is the micro morphology of EPS bead investigated by SEM (Scanning Electron Microscopy). The surface of EPS is of hydrophobic nature. The mixtures were divided into series A, B and C with water/cement(w/c) ratio of 0.55, 0.50 and 0.45, respectively. The EPS beads were used to replace 0%, 10%, 20%, 30% and 40% of the volume of plain concrete at each water/cement ratio. Mixture proportions are given in Table 1.

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Fig. 1

The macroscopic appearance of EPS

(b)

(a)

Fig. 2

(c)

The microscopic appearance of EPS (a)×20000; (b)×2000; (c)×500 Table 1 Mixture proportions

Mixture

EPS volume (%)

Cement (kg/m3)

Water (kg/m3)

Sand (kg/m3)

Gravel (kg/m3)

0 10 20 30 40

500 450 400 350 300

275 248 220 192 165

713 642 570 499 428

872 784 697 610 523

0 10 20 30 40

500 450 400 350 300

250 225 200 175 150

725 652 580 507 435

886 797 708 620 532

0 10 20 30 40

500 450 400 350 300

225 203 180 158 135

736 662 589 515 441

899 809 719 629 540

Series A (w/c=0.55) A1 A2 A3 A4 A5 Series B (w/c=0.50) B1 B2 B3 B4 B5 Series C (w/c=0.45) C1 C2 C3 C4 C5

The apparent densities of fresh EPS lightweight concretes were twice performed after mixing. The thermal conductivities of hardened EPS lightweight concretes were measured on slab specimens (300mm× 300mm×35mm, see Fig. 3) at the age of 28 days, according to Chinese Standard GB10294-2008. It is a stationary method which has been discussed by Shi (Shi et al., 2014) as well as by various other authors (Liu et al., 2014; Ng et al., 2010). Six specimens which were divided into three groups were used for each mix proportion. The thermal conductivity measuring apparatus in this study (CD-DR3030A model produced by Shenyang Ziwei Electromechanical Equipments Co., Ltd.) is shown in Fig. 4. The measurement range

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of this instrument is within 0.01~1.00 W(/m·K). The specimen was placed between the heat plate and the cold plate whose temperatures could be controlled automatically. The temperatures at each face of the specimen were monitoring by the thermocouples until thermal equilibrium (steady state) is achieved. Two specimens could be measured simultaneously. The schematic illustration of this standard test method for steady-state thermal transfer mechanism is shown in Fig. 5. The thermal conductivity was deduced from Fourier's law:

 Where



Q T1  T2   S  t

is the thermal conductivity of EPS concrete,

（1）

Q is the heat conducted across the specimen, 

is the specimen thickness, S is the metering area of specimen, t is the heat transport time, T1 is the metering plate (heated plate) temperature, T2 is the cold plate temperature. The heat and the temperature were measured automatically by the power sensor and temperature sensor.

Fig. 3

Specimens for testing thermal conductivity

Fig. 4

Thermal conductivity detector

Fig. 5 Schematic illustration of the test method

3. Experimental results The experiments results are listed in Table 2. Table 2 EPS volume (%) Series A (w/c=0.55) A1 0 Mixture

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Properties of test specimens

Experimental density (kg/m3)

Theoretical density* (kg/m3)

Thermal conductivity (W(/m·K))

2380

2360

0.91


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A2 A3 A4 A5 Series B (w/c=0.50) B1 B2 B3 B4 B5 Series C (w/c=0.45) C1 C2 C3 C4 C5

10 20 30 40

2090 1970 1750 1530

2127 1893 1660 1427

0.71 0.65 0.56 0.48

0 10 20 30 40

2400 2130 1880 1590 1400

2360 2127 1893 1660 1427

0.92 0.69 0.61 0.50 0.45

0 10 20 30 40

2440 2150 1810 1450 1200

2360 2127 1893 1660 1427

0.94 0.69 0.55 0.42 0.40

* Theoretical density, i.e., the assumed fresh apparent density, is equal to the sum of weight per unit volume of cement, water, sand, gravel and EPS.

The measured apparent densities of the fresh normal concrete and the fresh EPS lightweight concrete are plotted in Fig. 6. The apparent density of EPS lightweight concrete was lower than that of normal concrete without EPS aggregates, and the decrease was larger as the EPS content increased. In theory, the relationship between apparent density and EPS volume of lightweight concrete is linear. The experimental results of specimens in series B (w/c=0.50) agreed well with the theoretical values. The experimental results of specimens in series A (w/c=0.55) are slightly overestimating the theoretical values due to the hydrostatic pressure on EPS aggregates in concrete. This fact is in accordance with the previous analysis (Perry et al., 1991; Chen et al., 2005). While, the measured results of specimens in series C (w/c=0.45) is generally underestimating the calculated values when the EPS volume is high. It can be concluded that the workability of concrete is reduced as the EPS percentage is increased, resulting in a lower degree of compaction in the test. Fig. 7 shows the thermal conductivities of hardened normal concrete and EPS lightweight concrete detected in dry conditions. The experimentally thermal conductivities vary from 0.40W(/m·K) to 0.94W(/m·K), within the measurable ranges of the instrument. It can be observed that the values of thermal conductivity decrease with the increasing values of EPS aggregate contents. The error bars are used to represent the standard deviations. The coefficient of variations are mostly within ±10% when the EPS volume fraction does not exceed 20%. Higher errors occurred with the increasing EPS volume fraction, but the coefficient of variations are less than 15%. Otherwise, the thermal conductivities of EPS concretes in series A are larger than the results in series B and C, owing to the higher dense degree of the series A specimens. The relationship between the thermal conductivity and the apparent density of EPS concrete is plotted in Fig. 8. The thermal conductivity is decreasing as the density decreases with the increasing of EPS percentage. The thermal conductivity increases with an exponential function of the apparent density.

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Fig. 6

The relationship between apparent density and

Fig. 7

and EPS particle content

EPS volume

Fig. 8

The relationship between thermal conductivity

The relationship between thermal conductivity and the apparent density

4. The existing thermal conductivity approaches 4. 1 Thermal conductivity bounds The two generally accepted models are parallel model and series model (Côté et al., 2009). The parallel model which is shown in Fig. 9 and Eq. (2) provides the upper bound of effective thermal conductivity, and the series model which is shown in Fig. 10 and Eq. (3) gives the lower bound.

  V11  V22

（2）

12 V12  V2 1

（3）

 Where



is the effective thermal conductivity,

1 and 2 are thermal conductivity of each phase, V1

and

V2 are volume fractions.

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Fig. 9

Parallel model

Fig. 10 Series model

4. 2 Campbell-Allen and Thorne model Campbell-Allen and Thorne proposed the theoretical model (Campbell-Allen et al., 1963; Khan et al., 2002) assumed that the concrete was composed of continuous mortar phase and dispersed coarse aggregate phase (Fig. 11). Following this premise, the effective thermal conductivity is expressed by:

  1  M    1  2M  M   1 2 2 M  1 1  M  2

2

（4）

M  1  V21/ 3

（5）

Where

Where

1

phase,

V2 is the volume fractions of dispersed phase.

is the thermal conductivity of continuous phase,

2

is the thermal conductivity of dispersed

Fig. 11 Campbell-Allen and Thorne model

4. 3 Maxwell-Eucken model The Maxwell-Eucken model (Sundstrom et al., 1972; Wang et al., 2008) represents one continuous phase and one or more discontinuous phases, which the dispersed phase is randomly dispersed without relevant interaction (Fig. 12). The expression for thermal conductivity of this model suggested is given by

  1

21  2  2  1  2  V2 21  2   1  2  V2

Fig. 12

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（6）

Maxwell-Eucken model


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4. 4 Hamilton and Crosser model Of the above fundamental models, it is noted that the effective thermal conductivity of heterogeneous materials is strongly affected by the volume fraction and the thermal conductivity of each phase. Furthermore, Hamilton and Crosser (Hamilton et al., 1962) improved the Maxwell-Eucken model considering the shape factor of the dispersed phase. The theoretical model developed by Hamilton and Crosser can be expressed as follows:

V11  V2 2 V1  V2

（7）

n1  n  1 1  2

（8）

 

Where n is the shape factor depending on experiment. It is noted that n values of 1, 3 and 50 yield thermal conductivity relationships that are mathematically equivalent to the well known series model, Maxwell-Eucken model and parallel model respectively.

4. 5 Generalized effective medium theory The Effective medium theory model (Wang et al., 2006) is based on the phases being mutually dispersed (Fig. 13). This model provides unlimited possibilities for theoretical models, which can be expressed by:

V1

1      V2 2 0 1  2 2  2

（9）

Eq. (9) can be modified as Eq. (10).

1

    3V2  1 2   3 1  V2   1 1  4 

Fig.13

  3V

2

 1 2   3 1  V2   1 1



2

  812  （10） 

Effective medium theory model

As a matter of fact, the effective thermal conductivity using the parallel, series, Maxwell-Eucken and effective medium theory models can be derived as a unifying equation for composite structures by suitable choice of the parameters d and

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' :


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d' iVi   d  1  '  i i 1  2 d' V  i  d  1  '  i i 1 2

（11）

4.6 Discussion The expanded polystyrene concrete can be considered as a two phase composite material consisting of a bulk plain concrete matrix containing spherical randomly dispersed expanded polystyrene inclusions. The experimental results are compared with the values simulated by using aforementioned models. The thermal conductivity of 0.041W/(m·K) of EPS aggregates was taken for the model calculations (Hu et al., 2012). Table 3 summarizes the calculated results of existing theoretical models for thermal conductivity. It is noted that the parallel model completely overestimates the experimental thermal conductivity while the series model completely underestimates the experimental results. In series A and B, the other three models (Campbell-Allen and Thorne, Maxwell-Eucken, Effective Media Theory) have thermal conductivities neighboring the experimental results. However, in series C, the thermal conductivity values for the three models move away from the experimental values. In this case, the water to cement ratio of concrete is comparatively low. That is to say the water usage is so less that the workability of fresh concrete is reduced, especially when the volume fraction of EPS particles is high. It will lead to low compactness of hardened concrete because some more air pores are introduced to the concrete. On the one hand, the thermal conductivity of air is very small. On the other hand, the actual volume of dispersed phase is higher than the ideal volume used in the models. The model of Hamilton and Crosser matches quite well with experimental data. However, the values of model parameter n in Series A, B, C are set equal to 3, 2, 1.5 respectively by applying inversion method, i.e., n is different with different w/c. Therefore, the model of Hamilton and Crosser has limited usefulness in its practical use. Table 3

Calculated value of theoretical model for thermal conductivity Thermal conductivity （W(/m·K)）

Mixture

Parallel model

Series A (w/c=0.55) A1 0.91 A2 0.82 A3 0.74 A4 0.65 A5 0.56 Series B (w/c=0.50) B1 0.92 B2 0.83 B3 0.74 B4 0.66 B5 0.57 Series C (w/c=0.45) C1 0.94 C2 0.85 C3 0.76 C4 0.67 C5 0.58

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Series model

Campbell model

Maxwell model

Hamilton model

EMT model

Experimental rsults

0.91 0.29 0.17 0.12 0.10

0.91 0.73 0.62 0.53 0.45

0.91 0.79 0.68 0.57 0.48

0.91 0.79 0.68 0.57 0.48

0.91 0.78 0.66 0.53 0.41

0.91 0.71 0.65 0.56 0.48

0.92 0.29 0.17 0.12 0.10

0.92 0.74 0.63 0.53 0.45

0.92 0.80 0.68 0.58 0.49

0.92 0.77 0.64 0.52 0.43

0.92 0.79 0.66 0.54 0.42

0.92 0.69 0.61 0.50 0.45

0.94 0.29 0.17 0.12 0.10

0.94 0.75 0.64 0.54 0.46

0.94 0.81 0.70 0.59 0.49

0.94 0.73 0.57 0.45 0.36

0.94 0.81 0.68 0.55 0.42

0.94 0.69 0.55 0.42 0.40


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5. A new thermal conductivity prediction equation It has been found that the above general thermal conductivity models could not well predict the present experimental results and it has to be subject to modification. Based on the preceding discussion, it is proposed that the effective thermal conductivity of EPS concrete can be related to not only the thermal conductivity of each phase but also the apparent density of EPS concrete owing to the density could be affected by the changes of w/c and EPS volumes:

 ) 0

  f (1 , 2 ,  ,

（12）

The equation can be represented as Eq. (13) by modifying the Maxwell and Eucken model:

 21  2  2  1  2      21  2   1  2   

  E 1 exp  F Where



（13）

is EPS volume fractions, E and F are dimensionless empirical parameters associated with the

structure of EPS lightweight concrete which can be expressed as Eq. (14) and Eq. (15). It indicates the contribution of concrete compactness to the effective thermal conductivity.

   E  A   0    F  B 0     where



3

（14）

2

is the experimental apparent density of EPS concrete,

（15）

0

is the theoretical apparent density of

EPS concrete, A and B are dimensionless coefficients. The experimental results are used for inversing and validating the proposed model. Constants A and B are deduced as 0.25 and 1.35 respectively based on the test values in series A. Then the serviceability of such a model is evaluated on the basis of data in series B and C. Fig. 14 demonstrates the comparison of the proposed model with the present experimental results. It can be seen that the calculated effective thermal conductivity is fitted well with the measurements, and increasing EPS volume fractions leads to a decrease of thermal conductivity. It is considered that Eq. (13) is useful as an estimation equation for effective thermal conductivity of EPS lightweight concrete. The model is also applicable to the concrete with different water and cement ratio.

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(a)

(b)

(c) Fig. 14

Comparison between experimental and calculated thermal conductivity of EPS concrete (a) W/C=0.55; (b) W/C=0.50; (c) W/C=0.45

6. Conclusion In this work, the mixtures are produced by incorporating EPS aggregate at different volumes in concrete with different water/cement ratios. The thermal conductivity test results of EPS concretes show that the apparent density and thermal conductivity values of EPS concrete decrease with the volume of EPS increases. A simplified model has been proposed for assess the effective thermal conductivity with different EPS volume fraction and water/cement ratio, based on the test results of EPS lightweight concrete. The calculated effective thermal conductivity is fit well with the measurements. It is considered that Eq. (12) is a useful estimation equation for effective thermal conductivity incorporating the effects of EPS inclusions and concrete compactness.

Acknowledgments The authors would like to acknowledge the financial support received from the National Natural Science Foundation of China (No. 51508158 and 51579088), the Fundamental Research Funds for the Central Universities (No. 2015B21714) and China Postdoctoral Science Foundation (No. 2015M571643).

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