The hydronic snow melting pavement (HSMP) system is an environmentally friendly, clean, and sustainable alternative to traditional approaches for bridge deck snowmelt. The objective of this paper is to investigate the temperature field and thermal responses of HSMP by a three-dimensional finite element (3D FE) model based on the thermal-fluid coupling method. Considering the full fluid domain, the model simulates the dynamic temperature field and obtains the dynamic heat load of HSMP. Results show that the model factually simulates the decrease of fluid temperature along the pipe. The insulation of bridge deck bottom reduces heat loss, and heating demand can be lowered. Due to the ambient temperature changes, preheating is an effective approach of energy conservation and the start time of heating proposed is at 10 : 00 to 16 : 00. The flow velocity has a slight influence, and the recommended magnitude is 0.6 m/s. The shallower pipe embedded depth and the narrower pipe spacing can improve the surface temperature of HSMP and the uniformity of snowmelt process. Under ambient temperature loads, the maximum principle tensile stress of HSMP is induced at the contact interface between pipes and surrounding concrete, and the magnitude is greater than that of the conventional pavement. Under ambient temperature loads and fluid circulation, heated pipes can effectively prevent thermal shrinkage cracking and extend service life of HSMP. With increase of the pipe embedded depth and decrease of the pipe spacing, the chance of thermal shrinkage cracks decreases. For both optimum snowmelt efficiency and thermal cracking reduction, the pipe embedded depth of 7 cm and pipe spacing of 10 cm are recommended for HSMP with the inlet fluid temperature of 15°C.
To prevent snow accumulation and ice formation on pavement surfaces and improve traffic safety during winter, the applications of chemical salt are the most common means. As reported, annually nearly 35 million tons of salt was used to melt snow and deice ice worldwide, and this dosage has apparently risen in recent years [
The hydronic snow melting pavement (HSMP) system is that heated fluid circulates through a series of serpentine or parallel embedded pipes inside the pavement to transfer heat to the pavement and consequently melt snow on the top surface. Therefore, the cleaner and more sustainable hydronic snow melting system has received increasing attention in recent years. Research on the hydronic snowmelt system has been performed since the introduction of the technology in 1948 in Klamath Falls, Oregon, USA [
In the open literature, a number of models could predict the surface temperature of hydronic snowmelt pavement, while only a few [
The effects of embedded pipes on the mechanical properties of HSMP have been the subject of many studies. Numerical models have been developed and validated by experimental results, which are applicable to perform design with respect to the structural aspect [
The present paper is aimed to evaluate the effects of heat pipes on the temperature field and thermal responses of conventional pavement and HSMP. Based on the thermal-fluid coupling method, a 3D FE model of HSMP was developed by applying ANSYS. The model simulated the dynamic temperature field under ambient temperature and heat pipes and obtained the temperature load of HSMP. In order to obtain the optimal performance of the HSMP system, influence factors such as boundary conditions of the bottom, start time of heating, flow velocity, pipe embedded depth, and pipe spacing on the thermal analyses of HSMP were studied. Simultaneously, the thermal responses of conventional pavement and HSMP were simulated to identify the effects of pipe layout. Finally, the recommended pipe embedded depth and pipe spacing were proposed for the HSMP with the inlet fluid temperature of 15°C. The study presented would provide theoretical support for the design and application of the bridge deck snow melting system.
Aiming to evaluate the effects of the heat pipe on the HSMP temperature distribution and thermal responses, the transient conduction and dynamic heat load are taken into account in the thermal analyses and responses for the low temperature (15°C) HSMP system. In this study, the thermal-fluid coupling method models the heat conduction between pipes and concrete by applying the thermal-fluid pipe element, which can fully reflect temperature change law of the place near the pipe or far from the pipe and consider temperature changes of the fluid along pipes [
The model of the HSMP system is performed in pipes and concrete materials for bridge decks. The important assumptions applied in this model are as follows [ The heat transfer process of the hydronic snow melting system is transient Neglect the thermal contact resistance between different materials The velocity profile is fully developed within the entire pipe section Materials are uniform, continuous, and isotropic elastic The interface between materials is fixed
The heat conduction in the surface course is a three-dimensional and transient conduction process. The energy equation in the surface course can be written by using Fourier’s law as follows:
Figure
Heat exchange of the coupled thermal-fluid pipe.
The governing equation for heat transfer and conservation of energy is described as
The geometrical model of fluid temperature calculations along the pipe is shown in Figure
Geometrical model of the 3D domain with segments used for fluid temperature calculations.
In the numerical simulation of fluid-structure interactions, the fluid in heating pipes is considered to be one-dimensional steady flow fluid. According to Fourier’s law, the heat flux of concrete in contact with pipes is The heat flux The fluid heat flux The fluid heat flux where The fluid heat flux difference between section where, Based on the energy balance, the governing equation is described as
The fluid temperature difference
Due to the smaller volume of flows and slight change of fluid temperature, equation (
The inlet temperature of segments is
The object of this study is shown in Figure
Schematic diagram of HSMP: (a) layout plan; (b) cross-sectional view of Section
Thermal parameters and elastic parameters of HSMP.
Parameter | AL | CL | Pipe | Fluid |
---|---|---|---|---|
Material | Asphalt | Concrete | 304 steel | Water |
Specific heat capacity (J/(kg·°C)) | 1680 | 966 | 467 | 4187 |
Density (kg/m3) | 2100 | 2450 | 7860 | 1000 |
Thermal conductivity (W/(m·°C)) | 1.54 | 2.68 | 11.94 | 0.6 |
Dynamic viscosity (10−3 Pa·s) | — | — | — | 1.1 |
Elastic modulus (MPa) | 3000 | 25000 | 206000 | — |
Poisson’s ratio | 0.25 | 0.2 | 0.3 | — |
Linear expansion coefficient (×10−5/°C) | 2.0 | 1.5 | 1.6 | — |
A 3D FE model of HSMP was developed to solve the thermal analyses and responses by applying ANSYS. The meshing for the whole model and pipes is presented in Figure
3D FE model meshing for: (a) whole model, (b) serpentine pipes, and (c) pipes and surrounding concrete.
Design parameters of pipe layouts.
Parameter | Parameter levels | Number of variations |
---|---|---|
Pipe spacing (cm) | 10, 15, 20, 30 | 4 |
Pipe embedded depth (cm) | 7, 9, 11 | 3 |
Fluid temperature (°C) | 15, 20, 25, 30 | 4 |
Flow velocity (m/s) | 0.6, 1, 1.5, 2 | 4 |
The temperature field of HSMP is dynamic during the 1st day, which produces the dynamic heating loads. To ensure the efficiency of HSMP, the control design needs to know the conditions of the heating pipes to start. In this paper, the periodic ambient condition was adopted. The air temperature is expanded into periodic functions in the linear combination form of two sinusoidal functions, involving a 24 h cycle, as shown in the following equation [
As reported in Ref. [
This section presents influence of factors (e.g., insulation, start time of heating, flow velocity, pipe embedded depth, and pipe spacing) on HSMP surface temperature distribution. The relationship between surface temperature and factors were analysed.
Figures
Surface temperature distribution (°C) of HSMP with insulating the bottom (a) at 6 : 00 and (b) at 16 : 00.
Surface temperature distribution (°C) of HSMP without insulating the bottom (a) at 6 : 00 and (b) at 16 : 00.
Figure
Surface temperature distribution of HSMP: (a) with insulating the bottom; (b) without insulating the bottom.
Pipe temperature distribution (°C): (a) with insulating the bottom; (b) without insulating the bottom.
As shown in Figure
Heat flux of the bottom time-history curve.
Due to ambient temperature changes, it is necessary to preheat the HSMP at an approriate time for satisfactory snowmelt effect, and it is an effective approach of energy conservation. As Hu [
Heating hours at different points in time.
The fluid is turbulent and meets equation (
Temperature of the HSMP surface time-history curve.
The pipe embedded depth represents the heat transfer distance from the pipe to the HSMP surface. Figure
Temperature of HSMP surface at the outlet section with different pipe embedded depths: (a) pipe spacing of 15 cm; (b) pipe spacing of 30 cm.
The pipe spacing is the horizontal distance between two adjacent pipes that affects the heat-transfer areas of the heat pipes. Figure
Temperature of the HSMP surface at the outlet section with different pipe spacing: (a) pipe embedded depth of 7 cm; (b) pipe embedded depth of 11 cm.
It can be inferred that the pipe layouts have dominated influence on the uniformity of HSMP surface temperature. The shallower the pipe embedded depth and the narrower the pipe spacing, the higher the surface temperature and the lower the stripe distribution in the snowmelt process. Table
The numbers of hours for HSMP surface temperature below 0°C.
Spacing (cm) |
10 | 15 | 20 |
---|---|---|---|
7 | 1 | 1.25 | 1.75 |
9 | 1.25 | 1.5 | 2 |
11 | 1.5 | 1.75 | 2.25 |
In this section, the influence of pipe layouts on HSMP thermal responses was analysed and compared with the conventional pavement (without embedded pipes) under temperature load based on the 3D FE model. As the layer interface and contact interface between pipes and surrounding concrete almost have no effect on thermal responses [
For the sake of investigating the difference of thermal responses between HSMP and conventional pavement under ambient temperature loads, a 3D FE model of conventional pavement with the same size was modelled. The temperature distribution of pavement at 6 : 00 is considered as temperature loads. The maximum principle tensile stress is generated at the bottom of the conventional pavement under a positive temperature gradient load, and the magnitude of AL and CL are 0.4 MPa and 2.2 MPa, respectively. However, the HSMP stress distribution features (e.g., maximum stress position, distribution shape, and magnitude) are evidently different with the conventional pavement. As shown in Figure
Maximum principle stress distribution (MPa) of HSMP under ambient temperature loads: (a) AL; (b) CL.
Thermal responses of the pipe under ambient temperature loads: (a) maximum principle stress distribution (MPa); (b) vertical displacement (mm).
Table
Maximum principle stress extreme values of HSMP under ambient temperature loads (pipe spacing of 15 cm).
Layers | Depth (cm) | Maximum principle stress (MPa) | |
---|---|---|---|
Min | Max | ||
AL | 7 | 0.393 | 0.431 |
9 | 0.397 | 0.407 | |
11 | 0.397 | 0.404 | |
|
|||
CL | 7 | 2.012 | 2.782 |
9 | 2.032 | 2.743 | |
11 | 2.043 | 2.734 | |
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Pipe | 7 | 15.741 | 28.512 |
9 | 16.123 | 27.632 | |
11 | 16.224 | 27.714 |
Maximum principle stress extreme values of HSMP under ambient temperature loads (pipe embedded depth of 7 cm).
Layers | Spacing (cm) | Maximum principle stress (MPa) | |
---|---|---|---|
Min | Max | ||
AL | 10 | 0.392 | 0.424 |
15 | 0.393 | 0.431 | |
20 | 0.393 | 0.434 | |
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CL | 10 | 2.011 | 2.713 |
15 | 2.012 | 2.782 | |
20 | 2.012 | 2.791 | |
|
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Pipe | 10 | 15.821 | 27.844 |
15 | 15.741 | 28.521 | |
20 | 15.691 | 28.712 |
In this section, the thermal response of HSMP is simulated when HSMP suffers the ambient temperature (at 6 : 00) and fluid circulation (15°C). In Figure
Maximum principle stress distribution (MPa) of HSMP with fluid circulation: (a) AL; (b) CL.
Figure
Thermal responses of the pipe with fluid circulation: (a) maximum principle stress distribution (MPa); (b) vertical displacement (mm).
In Table
Maximum principle stress extreme values of HSMP with fluid circulation (pipe spacing of 15 cm).
Layers | Depth (cm) | Maximum principle stress (MPa) | |
---|---|---|---|
Min | Max | ||
AL | 7 | −0.336 | 0.091 |
9 | −0.113 | 0.063 | |
11 | −0.654 | 0.042 | |
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CL | 7 | −2.983 | 1.523 |
9 | −3.134 | 1.132 | |
11 | −3.143 | 1.073 | |
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Pipe | 7 | −4.244 | 3.484 |
9 | −4.322 | 3.072 | |
11 | −4.412 | −1.134 |
Maximum principle stress extreme values of HSMP with fluid circulation (pipe embedded depth of 7 cm).
Layers | Spacing (cm) | Maximum principle stress (MPa) | |
---|---|---|---|
Min | Max | ||
AL | 10 | −0.291 | 0.098 |
15 | −0.336 | 0.091 | |
20 | −0.337 | 0.122 | |
|
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CL | 10 | −2.832 | 1.274 |
15 | −2.983 | 1.523 | |
20 | −3.042 | 1.773 | |
|
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Pipe | 10 | −4.123 | 1.551 |
15 | −4.244 | 3.484 | |
20 | −4.321 | 5.672 |
For the bridge deck hydronic snow melting system utilizing low temperature water, a 3D FE model of HSMP was built. Influence factors on the temperature distribution and thermal responses of HSMP were studied, respectively. The following conclusions are drawn from this study: The 3D FE model of HSMP based on the thermal-fluid coupling method was developed to solve the heat transmission and thermal responses of HSMP. Particularly, the insulation, start time of heating, pipe embedded depth, and pipe spacing have significant impacts on the snowmelt performance, while the flow velocity has a slight influence. The pipe layout has little impact on the thermal response of HSMP under ambient temperature loads. However, the principle tensile stress and the chance of thermal shrinkage cracks decreases for HSMP with fluid circulation as the pipe embedded depth is deeper and the pipe spacing is narrower. The pipe embedded depth of 7 cm and pipe spacing of 10 cm for HSMP with the inlet fluid temperature of 15°C are recommended for both optimum snowmelt efficiency and the reduction of thermal shrinkage cracking risk.
The data used to support the findings of this study are included within the supplementary information files.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported by the Doctoral Fund of the Ministry of Education of China (grant no. 20130205110014), the Natural Science Basic Research Plan in Shaanxi Province of China (grant no. 2014JM1005), the Science and Technology Program of the Department of Transportation in Shaanxi Province of China (grant no. 13-16k), and the Science and Technology Planning Project in Henan Province of China (grant no. 182102311091).
In the “insulated bottom” folder, two text files are, respectively, the command-flow of the 3D FE model of HSMP (pipe spacing of 30 mm and pipe embedded depth of 11 cm) and conventional pavement (without embedded pipes) with the insulation at the bottom. In the “noninsulated bottom” folder, two text files are, respectively, the command-flow of the 3D FE model of HSMP (pipe spacing of 30 mm and pipe embedded depth of 11 cm) and conventional pavement (without embedded pipes) without the insulation at the bottom. In the “spacing of 10 mm” folder, three text files are, respectively, the command-flow of the 3D FE model of HSMP with pipe spacing of 10 mm and different pipe embedded depths (7 mm, 9 mm, and 11 cm). In the “spacing of 15 mm” folder, three text files are, respectively, the command-flow of the 3D FE model of HSMP with pipe spacing of 15 mm and different pipe embedded depths (7 mm, 9 mm, and 11 cm). In the “spacing of 20 mm” folder, three text files are, respectively, the command-flow of the 3D FE model of HSMP with pipe spacing of 20 mm and different pipe embedded depths (7 mm, 9 mm, and 11 cm). In the “spacing of 30 mm” folder, three text files are, respectively, the command-flow of the 3D FE model of HSMP with pipe spacing of 30 mm and different pipe embedded depths (7 mm, 9 mm, and 11 cm).