Reduction of interior temperature of massive concrete using an enhanced heat transfer pipe array with spiral fins

Abstract

The interior temperature of the massive concrete should be controlled to avoid cracks caused by the trapped hydration heat. In this paper, an enhanced heat transfer pipe array with spiral fins (PSF) is proposed to reduce the interior temperature of concrete blocks. Numerical simulations of massive concrete blocks embedded with traditional cooling water pipe (TCWP) and newly proposed PSF were conducted to investigate the interior temperature distribution of massive concrete. Meanwhile, validity of the finite element model was verified by both theoretical results and available experimental data. Based on the calculated temperature distribution of the points located in the interior area of the massive concrete, it is shown that when the TCWP was replaced by the PSF, the interior temperature can be significantly reduced. Therefore, compared to the TCWP, the proposed PSF has excellent heat transfer performance for cooling the interior temperature of massive concrete.

Keywords

cooling water pipe enhanced heat transfer pipe interior temperature massive concrete spiral fins

Introduction

Powerful purchases of electricity over the last few decades have led to the construction of large hydro dams. Meanwhile, number of long span suspension bridges is increasing to meet the demands of the transportation industry. Massive concrete blocks are poured during the construction of the hydro dam and long span suspension bridge as shown in Figure 1(a). The hydration heat released by an exothermic reaction between water and cement raises the interior temperature of the massive concrete block. As the interior temperature of the massive concrete rises, cracks will occur which will hinder safety of the concrete structure. Therefore, it is necessary to develop effective temperature reduction technologies to prevent cracks in massive concrete.

Figure 1.

Schematics of the massive concrete: (a) massive concrete without cooling water pipe system and (b) massive concrete with cooling water pipe system.

Pre- and post-cooling methods are usually employed to change temperature distribution in massive concrete at an early age (American Concrete Institute, 2005). The pre-cooling method is a technology by lowering the temperature of concrete-forming component. In contrast with the pre-cooling method, a technology by employing cooling pipe system in massive concrete is defined as post-cooling method.

The post-cooling system shown in Figure 1(b) as a main temperature control measure was employed in the Hoover dam (Mead, 1933). After then, the post-cooling method has become a popular temperature control technology during the construction process of massive concrete. Therefore, this research field has been investigated intensively. Zhu and Cai (1989) proposed a numerical method for analyzing the effect of simultaneous cooling through embedded pipes. Massive concrete embedded with the non-metal cooling pipes was investigated by Zhu (1999). Convenient methods which can calculate the temperature distribution were presented for the massive concrete cooling by nonmetal pipes.

In the past two decades, the post-cooling method has drawn attention of many researchers. Kim et al. (2001) developed a finite element program for calculating thermal distribution of massive concrete structures embedded with a pipe cooling system. The predicted results by the numerical model had good agreements with the monitoring data. Yang et al. (2012) analyzed the thermal distribution of a concrete block embedded with double-layer cooling pipes. Cooling functions of the double layer cooling pipes were derived. Qian and Gao (2012) employed the suspension of phase change materials as cooling fluid to reduce the peak value of temperature in the massive concrete. It was concluded that when water was replaced by suspension of phase change materials as cooling fluid, interior temperature reduction ratio of the massive concrete can be increased. A data mining approach to analyze thermal performance of the cooling pipe technology via in situ monitoring was presented by Zuo et al. (2014). The data mining results showed that iron pipes have better heat exchange performance. Liu et al. (2015) proposed a method for a heat-fluid coupling model to calculate thermal distribution of massive concrete, and it can accurately reflect temperature distribution near the pipe. Wu et al. (2019) tested the effect of sodium hydroxide on hydration of low carbon cementitious materials. Hong et al. (2017, 2019) proposed a numerical algorithm that can solve the transient temperature field in the massive concrete. Tasri and Susilawati (2019a, 2019b) numerically investigated thermal stresses of the massive concrete embedded with a cooling pipe system. It was found that the cooling water temperature at the inlet location and the distance between two adjacent pipes are two key points which can dominate the temperature distribution and thermal stress near the cooling pipe. Chen et al. (2019) proposed a theoretical solution for the cooling system using non-metal pipes. The proposed formulae are convenient for direct calculation. A new method based on equivalent surfaces for simulation of the post-cooling in concrete arch dams was proposed by Conceição et al. (2020). The new method was also employed to predict the thermal behavior of a real arch dam monolith during construction. An acceptable agreement between the results calculated by the new method and data obtained from monitoring process was observed. Kheradmand et al. (2020) proposed a new method for the embedment of flexible PVC holes that allows their removal a few hours after casting. This paper intended to show the proof of concept carried out in laboratory context conditions, highlighting the features that led to the selection and phasing procedure of the solution proposed.

From the literature review on the interior temperature of massive concrete, it is clear that cooling water pipes embedded in the massive concrete can reduce the interior temperature. In this paper, based on the work of the previous researchers, an enhanced heat transfer pipe array with spiral fins (PSF) is proposed to reduce the interior peak value of the temperature of massive concrete. Computation results obtained by the finite element models of massive concrete embedded with the traditional cooling water pipe and the proposed PSF are compared. The peak value of the interior temperature of the massive concrete is analyzed to investigate the performance of the proposed PSF.

Numerical model description

The heat exchange between the core region of massive concrete and the cooling water pipe does not seem so ideal due to the poor conductivity of concrete. Therefore, heat transfer efficiency between the cooling water pipe and the adjacent concrete should be enhanced in order to reduce the temperature values.

Layout of the numerical model

In Figure 2, schematics of the proposed enhanced heat transfer pipe arrayed with spiral fins (PSF) are demonstrated. Through Figure 2, it can be seen that heat exchange efficiency between the concrete and the cooling water pipe will be raised due to the increased heat absorption area contributed by the surrounding fins of the pipe. The external diameter of the cooling water pipe is D and a row of fins with height h_p, screw pitch w_p, and thickness w_f are attached to the surface. Length of the surrounding fins is defined as l_p. w_d stands for thickness of the cooling water pipe. l_c, d_c, and h_c as shown in Figure 1 represent the geometric dimensions of the massive concrete along x, y and z directions, respectively. O means the geometric center of the massive concrete, and its coordinates are defined as (0.0, 0.0, 0.0). For the traditional post-cooling pipe system (without the spiral fins), the heat exchange between Point A shown in Figure 2(c) and the cooling water flowing in the cooling pipe is not efficient due to the poor thermal conductivity of concrete (the distance between Point A and the surface of the cooling pipe is l₁). However, for the enhanced heat transfer pipe array with spiral fins, the distance between Point A and the surface of the cooling pipe is reduced to l₂. Accordingly, the efficiency of the heat exchange between Point A and the cooling water flowing in the cooling pipe can be enhanced. In other words, the highest temperature and corresponding appearance time of the highest temperature of the interior area of the massive concrete can be reduced.

Figure 2.

Schematics of massive concrete embedded with PSF: (a) three dimensional, (b) enlarged schematics of PSF, and (c) two dimensional cross section of the x–z plane.

Numerical simulation is conducted by using Ansys V.17.0. Tetrahedron elements are employed for the concrete, pipe and fluid in the pipe as shown in Figure 3(a). Maximum layers of the inflation of the fluid adjacent to the pipe are set as 5, and the growth rate of the inflation is 1.2, as shown in Figure 3(b). The average value of the element quality of the tetrahedron elements is controlled above 0.8, and the value of the skewness of the tetrahedron elements is controlled around 0.2.

Figure 3.

Massive concrete divided into tetrahedron meshes: (a) three-dimensional meshing and (b) inflation setting of the fluid.

Governing equations

The finite volume method is used to calculate unsteady conduction with the following governing equation:

ρ C_{p} \frac{\partial T}{\partial t} = \nabla k \nabla T + S_{h}

(1)

where $C_{p}$ , $ρ$ , $S_{h}$ , T, and k are the hydration heat per unit of thermal conductivity, density, hydration heat per unit of volume, temperature, and thermal conductivity, respectively.

The employed function of the total hydration heat of the employed material is:

Q = (k_{1} + k_{2} - 1) Q_{0}

(2)

where k₁ and k₂ are the adjustment coefficients of the hydration heat when the cement mixed with fly ash and slag powder, respectively. Q₀ is the total hydration heat of the cement. It can be obtained by the following function:

Q_{0} = \frac{4}{7 / Q_{7} - 3 / Q_{3}}

(3)

where Q₃ and Q₇ are the accumulated hydration heats of the cement at 3 days and 7 days age, respectively.

The adiabatic temperature rise of concrete is shown as follow:

T (t) = \frac{WQ}{C ρ} (1 - e^{- mt})

(4)

In equation (4), W represents consumption of the cementitious materials in per cubic meter of the concrete; $ρ$ stands for density of the concrete; C means the specific heat capacity of the concrete; t is the concrete age; m is the coefficient of the cementitious, and it is related to properties of the cement, as shown below:

m = (k_{1} + k_{2} - 1) (AW + B)

(5)

where A and B are the coefficients related to casting temperature of the concrete.

The standard $k - ε$ model is used to simulate movement of water flow through the pipe. The turbulence kinetic energy, k, and its rate of dissipation, $ε$ , used in the standard $k - ε$ model are shown as follows:

\begin{matrix} \frac{\partial}{\partial t} (ρ k) + \frac{\partial}{\partial x_{i}} (ρ k u_{i}) = \frac{\partial}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{k}}) \frac{\partial k}{\partial x_{j}}] \\ + G_{k} + G_{b} - ρ ε - Y_{M} + S_{k} \end{matrix}

(6)

\begin{matrix} \frac{\partial}{\partial t} (ρ ε) + \frac{\partial}{\partial x_{i}} (ρ ε u_{i}) = \frac{\partial}{\partial x_{j}} [(μ + \frac{μ_{t}}{σ_{ε}}) \frac{\partial ε}{\partial x_{j}}] \\ + C_{1 ε} \frac{ε}{k} (G_{k} + C_{3 ε} G_{b}) - C_{2 ε} ρ \frac{ε^{2}}{k} + S_{ε} \end{matrix}

(7)

In the above equations, $G_{b}$ stands for generation of turbulence kinetic energy due to buoyancy; $G_{k}$ represents generation of turbulence kinetic energy due to the mean velocity gradients; $C_{1 ε}$ , $C_{2 ε}$ , and $C_{3 ε}$ are constants; $Y_{M}$ represents contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate; $S_{k}$ and $S_{ε}$ are user-defined source terms; $σ_{k}$ and $σ_{ε}$ are the turbulent Prandtl numbers for k and $ε$ , respectively.

Numerical results

Validation of the numerical model

In order to validate accuracy of the numerical model, the calculated internal temperature of a cylindrical concrete as shown in Figure 4(a) by the numerical model based on governing equations employed in Section 2 is compared to the theoretical solution proposed by Zhu (1999). The cylindrical concrete is 0.845 m in radius. The cooling water flows through the pipe which located at the axial direction of the cylindrical volume. The outer and inner radii of the pipe are 0.016 m and 0.014 m, respectively. The casting temperature of the concrete is 273 K, the temperature of the inlet water is 273 K. The adiabatic temperature rise of concrete is:

T_{c} = T_{0} (1 - e^{- mt})

(8)

Here, T₀ and m are assumed to be 25 and 0.35, respectively. According to the theoretical method proposed by Zhu (1999), the theoretical solution of the concrete embedded with steel cooling pipe can be expressed as:

T_{c} = 32.7 (e^{- 0.8242 t} - e^{- 0.35 t})

(9)

The temperature of the concrete calculated by the numerical model is compared to the theoretical solution, as shown in Figure 4(b) and (c). It can be readily observed that the temperature of the concrete predicted by the numerical model is almost identical with the theoretical one.

Figure 4.

Comparison results between the numerical model and the theoretical method: (a) sketch of the concrete and the cooling pipe, (b) without cooling pipe, and (c) with cooling pipe.

To further prove the validity of the numerical model, two specimens presented in Qian and Gao (2012) with a size of 50 cm × 50 cm × 50 cm were modeled by the present numerical method. Specimen 1 is the concrete without the cooling system, and Specimen 2 is the concrete with the traditional cooling system (water was adopted as cooling fluid). The arrangement of measuring point within the concrete specimens is shown in Figure 5. Properties of the concrete and cooling system can be referred from Qian and Gao (2012). Point C is selected for comparison, and Figure 6 shows the comparison results between the numerical results and the experimental data obtained from Qian and Gao (2012). Through the comparison results, it can be known that in the early stage of concrete pouring, for examples at 6.5 h (points A and A₁) and at 10.5 h (points B and B₁), the temperature difference are a bit large (the temperature difference is about 8°C). In the middle and late stages of concrete pouring, numerical results show good agreement with the experimental data (the temperature difference is around 3°C). Overall, the numerical result and the experimental data are in good agreement. Therefore, the numerical model based on the governing equations depicted in Section 2 can be used to simulate the internal temperature of a concrete block embedded with cooling pipes.

Figure 5.

Measurement points in concrete (Qian and Gao, 2012).

Figure 6.

Comparison between the numerical results and the experimental data: (a) temperature of point C (without cooling system) and (b) temperature of point C (with cooling system).

Cooling effect of PSF

The reduction of the interior temperature of the massive concrete using the PSF is compared with that for the massive concrete using the TCWP in this section. Geometric and thermal parameters of the massive concrete and the pipe are depicted in Table 1. Water flow rate at the inlet of the pipe is 0.6 m/s, and the temperature of the inlet water is 298 K. The temperature of the pouring concrete is assumed to be 308 K. Thermal convection boundary condition is used to simulate the heat transfer between the concrete surface and the surrounding environment, and the heat transfer coefficient is assumed to be 3.6 W/m²K. The free stream temperature of the surrounding environment is assumed to be 303 K. Plane A is selected as shown in Figure 7(a) to analyze the cooling range of the cooling pipe system. The values of the temperature distributions are examined along line ab as shown in Figure 7(b), the coordinates of points a, b, c, and d are (0 m, 0.1 m, 0.1 m), (0 m, 0.2 m, 0.2 m), (0 m, 0.3 m, 0.3 m), and (0 m, 0.4 m, 0.4 m), respectively.

Table 1.

Geometric and thermal properties of the concrete and pipes.

Properties	Concrete block	PSF	TCWP
Sizes (m)	l_c = 2.3	D = 5.0 × 10⁻²	D = 5.0 × 10⁻²
	h_c = 1.3	h_p = 1.0 × 10⁻¹	w_d = 5.0 × 10⁻²
	d_c = 1.3	w_f = 4.36 × 10⁻²
		w_d = 5.0 × 10⁻²
		w_p = 1.0 × 10⁻¹
Adiabatic temperature rise (K)	$T (t) = 52.9 \times (1 - e^{(- t)})$	/	/
Specific heat (J/kgK)	970	871	871
Thermal conductivity (W/mK)	1.28	202.4	202.4

Figure 7.

Schematics of selected plane and points of the massive concrete: (a) selected plane and (b) selected points.

Figure 8 represents the thermal field of plane A for t = 1.0, 2.0, and 3.0 days. It can be observed that for the concrete embedded with the TCWP or the PSF, the interior temperature of the concrete decreased compared to that of the concrete without the cooling water pipe. Meanwhile, comparisons of Figure 8(b) and (c), show that the cooling range of the concrete with the PSF is larger than that of the concrete with the TCWP. Therefore, a conclusion that the PSF has a better cooling effect than the TCWP can be obtained.

Figure 8.

Cooling effects of cooling water pipe with time vibration: (a) concrete without cooling water pipe, (b) concrete with TCWP, and (c) concrete with PSF.

The temperature along line ad as shown in Figure 8(b) is collected and depicted in Figure 9. Figure 9 shows that the temperature of the massive concrete and the peak value of the temperature in the concrete decrease quickly for those with the cooling water pipe. Meanwhile, the cooling efficiency of the massive concrete with the PSF is improved compared with the massive concrete with the TCWP. The above phenomenon is much more apparent for the points those are adjacent to the cooling pipe. The reduction of concrete temperature at point d which is far away from the cooling pipe is mainly attributed to the atmosphere convection between the surfaces of the massive concrete and the surrounding environment. Through Figure 9, it can be also observed that the appearance time of the highest temperature of the massive concrete with the cooling pipe system decreased compared with that without the cooling pipe system. For point a, the appearance time of the highest temperature is 2.0 days, 1.5 days, and 1.0 days for the massive concrete without TWCP, with TWCP and with PSF, respectively. Moreover, the appearance time of the highest temperature for the concrete with the PSF has been further advanced compared with the case with the TCWP.

Figure 9.

Variations of the inertial temperature of the concrete: (a) point a, (b) point b, (c) point c, and (d) point d.

Three sections shown in Figure 10 are selected to depict the temperature distribution along the depth of the concrete. It can be seen from the calculated results (Figure 11) that the reduction of the temperature is remarkable at section B. Meanwhile, for sections B, C, and D, the cooling efficiency of the massive concrete with the PSF is obviously better than that of the massive concrete with the TCWP.

Figure 10.

Schematics of sections B, C, D: (a) plane A in xz and (b) plane A in yz.

Figure 11.

Profiles of concrete temperature at different sections: (a) section B, (b) section C, and (c) section D.

Cooling efficiency of PSF with variation of the screw pitch of the spiral fin

In this section, cooling efficiency of the PSF with variation of the pitch of screw is further investigated. The total length of the spiral fin l_p is 2200 mm. Three types of the pitch of screw: 440 mm, 200 mm, and 100 mm are selected for numerical study. Geometric and physical parameters of the massive concrete and the other parameters of the numerical model are the same as those given in Section 3.1.

Temperature distributions of the massive concrete along line ad with variation of the pitch of screw are shown in Figure 12. It can be known that the cooling efficiency decreases with increase of the value of pitch of screw. This phenomenon is due to a reason that with increase of the value of screw pitch, the heat exchange surface area decreases. Thus, the cooling efficiency is reduced. The above mentioned phenomenon is not remarkable for point d which is far away from the cooling pipe. This is due to a reason that for point d the reduction of concrete temperature is mainly attributed to the atmosphere. Thus, the cooling pipe has a small impact on the area far away from it.

Figure 12.

Variations of the inertial temperature of the concrete: (a) point a, (b) point b, (c) point c, and (d) point d.

A concrete block embedded with a snakelike cooling pipe system

The snakelike arrangement of the cooling pipe is always employed to reduce the interior temperature during the construction process of the massive concrete. Therefore, the temperature distribution of a concrete block embedded with the snakelike cooling pipe as shown in Figure 13 is calculated in this section. Geometric parameters of the concrete block and the cooling pipe are listed in Table 2. The thermal properties of the concrete and the cooling pipe are the same as shown in Table 1. Water flow rate at the inlet of the pipe is 0.6 m/s, and the temperature of the inlet water is 298 K. The heat transfer coefficient is assumed to be 1.6 W/m²K. The free stream temperature of the surrounding environment is 303 K. The pouring temperature of the concrete is 308 K.

Figure 13.

Concrete block embedded with the snakelike arrangement cooling pipe: (a) concrete block, (b) snakelike arrangement of TCWP, and (c) snakelike arrangement of PSF.

Table 2.

Geometric parameters of the concrete block and the cooling pipe.

Properties	Concrete block	PSF	TCWP
Sizes (m)	l_c = 3.0	D = 5.0 × 10⁻²	D = 5.0 × 10⁻²
	h_c = 1.2	h_p = 5.0 × 10⁻²	w_d = 5.0 × 10⁻²
	d_c = 8.0	w_f = 4.36 × 10⁻²	l₁ = 2.45
	d₁ = 0.5	w_d = 5.0 × 10⁻²	l₂ = 0.9
	d₂ = 0.5	w_p = 2.0×10^-1	l₃ = 1.9
	d₃ = 0.5	l_x1 = 2.2	r = 5.0 × 10⁻²
	d₄ = 0.5	l_y1 = 0.8
		l_x2 = 1.8

Plane B which is parallel to xy plane with z-coordinate zero is selected, and the temperature distributions of Plane B for t = 1.5 days, 3.0 days, and 4.5 days are shown in Figures 14 and 15. Through the comparison results shown in Figures 14 and 15, it can be seen that the interior temperature of the concrete embedded with the PSF can be reduced compared with the case with the TCWP.

Figure 14.

Temperature distributions of plane B (concrete embedded with TCWP): (a) 1.5 days, (b) 3.0 days, and (c) 4.5 days.

Figure 15.

Temperature distributions of plane B (concrete embedded with PSF): (a) 1.5 days, (b) 3.0 days, and (c) 4.5 days.

It is known that the hydration heat of the concrete is partly absorbed by the cooling pipe. Thus, temperature of the water will rise when it is running through the pipe. Figure 16 shows the temperature history of the cooling water at inlet and outlet of the PSF. It clearly shows that the temperature of the water at outlet is higher than that at inlet. In addition, the value of the temperature of the water at outlet varies with time changes. The reason of the variation is that the generated hydration heat of the concrete changes with the time.

Figure 16.

Inlet and outlet temperatures of the cooling water (PSF).

Eight points with the coordinates shown in Table 3 are selected to investigate the temperature variation of the water. The selected points have a characteristic that they have the same x and y coordinates but different z coordinates. With the increase of the number of points, the distance between the point and the inlet location increases (defined as D). The temperature of the points for t = 1.0 days, 3.0 days, 5.0 days, and 7.0 days are depicted in Figure 17. It can be found that with the distance D increases, the temperature of the cooling water rises. The above phenomenon reflects that a remarkable heat exchange generated between the running water and the surrounding concrete.

Table 3.

Coordinates of the selected points of the water.

Point	Coordinates (m)
Point	x	y	z
1		−3.5
2		−2.5
3		−1.5
4	0.0	−0.5	0.0
5		0.5
6		1.5
7		2.5
8		3.5

Figure 17.

Temperatures of the cooling water at each point (PSF).

Conclusion

An enhanced heat transfer pipe array with spiral fins was proposed in this paper. Three dimensional finite element models for studying temperature distribution of the massive concrete with a cooling pipe system were developed. Numerical simulations have been performed on massive concrete cooled by a post-cooling system to determine the effectiveness of the proposed enhanced heat transfer pipe. Several conclusions can be drawn:

For the concrete embedded with the TCWP and the PSF, the interior temperature of the concrete will decrease compared with that of the concrete without the cooling water pipe. Meanwhile, the cooling range of the concrete with the PSF is larger than that of the concrete with the TCWP. Therefore, the PSF has a better cooling effect than the TCWP.

The appearance time of the highest temperature of the massive concrete with the cooling pipe system advanced compared with that without the cooling pipe system. Meanwhile, the appearance time of the highest temperature for the concrete with the PSF has been further advanced compared with the case with the TCWP.

The cooling efficiency of the PSF decreases with increase of the value of pitch of screw. This phenomenon is due to the reason that with increase of the value of screw pitch, the heat exchange surface area decreases. Thus, the cooling efficiency is reduced.

Footnotes

Authors’ Note

Lemu Zhou is also affiliated with Hubei Provincial Road & Bridge Company Group, Wuhan, China.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors gratefully acknowledge the financial support for this research provided by the National Key Research and Development Plan of China (Grant No. 2017YFC1500705) and National Natural Science Foundation of China (Grant No. 51878314, 51308243).

ORCID iDs

Fangyuan Zhou

Hanbin Ge

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