Analytical solution to steady-state temperature field of two freezing pipes with different temperatures

Hu, Xiangdong; Luoyu, Zhang

doi:10.1007/s12204-013-1453-7

Cited by 19 publications

(12 citation statements)

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“…(21) is consistent with the analytical solution derived by Tobe and Akimoto (1979) and Kato et al (2007), which is a particular solution of our solution when T 0 =0 °C. Another solution to the steady-state temperature field frozen by two freezing pipes with different temperatures was given by Hu and Zhang (2013a). In their study, the boundary conditions were set differently and as a result, the expressions of the solution had different forms.…”

Section: Temperature Field Of Two Freezing Pipesmentioning

confidence: 99%

Mathematical models of steady-state temperature fields produced by multi-piped freezing

Guo

Luoyu

et al. 2016

J. Zhejiang Univ. Sci. A

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Abstract:The multi-piped freezing method is usually applied in artificial ground freezing (AGF) projects to fulfill special construction requirements, such as two-, three-, or four-piped freezing. Based on potential superposition theory, this paper gives analytical solutions to steady-state frozen temperature for two, three, and four freezing pipes with different temperatures and arranged at random. Specific solutions are derived for some particular arrangements, such as three freezing pipes in a linear arrangement with equal or unequal spacing, right and isosceles triangle arrangements, four freezing pipes in a linear arrangement with equal spacing, and rhombus and rectangle arrangements. A comparison between the analytical solutions and numerical thermal analysis shows that the analytical solutions are sufficiently precise. As a part of the theory of AGF, the analytical solutions of temperature fields for multi-piped freezing with arbitrary layouts and different temperatures of freezing pipes are approached for the first time.

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Section: Temperature Field Of Two Freezing Pipesmentioning

confidence: 99%

Mathematical models of steady-state temperature fields produced by multi-piped freezing

Guo

Luoyu

et al. 2016

J. Zhejiang Univ. Sci. A

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“…e formation process of frozen soil is basically a physical and mechanical process. During this process, the properties of soil have changed essentially [12][13][14][15]. As the freezing temperature increases, the frost heave caused by the ice-water phase transition and the thaw settlement caused by the thawing of the frozen soil curtain will increase sharply after the completion of the support of the connecting channel [16].…”

Section: Introductionmentioning

confidence: 99%

Research on the Ground Subsidence Mechanism of Cross Passage Caused by Freezing Method Construction

Zhang

Cheng

et al. 2021

Advances in Civil Engineering

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At present, the built or newly built underground structures are mostly concentrated in developed areas along the coast, lakes, and rivers, while deep soft soil is widely distributed in these areas. The cold heat treatment method is one of the advanced foundation treatments and has broad application prospect. However, geothermal exchange and temperature field change are complex Stefan problems with mobile boundaries, internal heat sources, and phase changes. It is important to determine the freezing area and freezing temperature reasonably under the premise of ensuring the safety of the frozen construction. Therefore, this paper summarizes the research methods of freezing method construction of cross passage and introduces the research on the constitutive model of freezing undisturbed soil, the theory of freezing wall calculation, and the evolution mechanism of the temperature field. Then, a brief evaluation is made in view of the lack of research, and the development direction of this field is put forward with the research characteristics. It is to deepen the understanding of the deformation mechanism of cross passage embedded in soft soil caused by the freezing and melting.

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“…Hu et al established a set of methods for solving the steady-state temperature field of artificial ground freezing based on the principle of superposition of potential functions. Combining this principle with mathematical methods, a series of analytical results for the steady-state temperature field were obtained [24][25][26][27][28]. In order to benchmark flow and energy transport models that include pore water phase change, Kurylyk et al…”

Section: Introductionmentioning

confidence: 99%

“…After the artificial formation freezing enters the stable freezing stage, the temperature drop rate of the freezing temperature field becomes very slow; therefore, the transient temperature field at this time can be approximated by the steady-state temperature field [24][25][26][27][28]. When a seepage field exists in the stratum, after entering the stable freezing phase, the convective heat transfer between the water and the frozen soil on the freezing front and the heat transfer of the frozen pipe cancel each other out under the condition that the seepage velocity and the water temperature are constant.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Steady‐State Temperature Field of Single Freezing Pipe under Action of Seepage Field

Wang

Rong

Cheng

et al. 2020

Advances in Civil Engineering

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To accurately describe the distribution law of the temperature field formed by a single freezing pipe under the action of a seepage field, the shape of the freezing front was simplified using a segmentation-equivalent method. The analytical solution of the steady-state temperature field was derived, and the accuracy was verified using a physical model test. Combined with the results of the model test and the calculation results of the analytical solution, the distribution law of the freezing temperature field formed by a single pipe under different seepage velocities was analyzed. It was found that compared with the no flow rate, when the seepage velocity was 3, 6, and 9 m/day, the frozen area was reduced from 17.97 × 104 mm2 to 15.77 × 104, 3.84 × 104, and 3.05 × 104 mm2, respectively. The proportion of frozen area below −5°C increased from 39.43% to 40.19%, 49.84%, and 51.52%, respectively. The average freezing temperature field reduced from −5.78 to −5.86, −7.31, and −7.50°C, respectively. As the seepage velocity increased, the frozen area formed by a single pipe decreased while the proportion of the low-temperature zone increased and the average temperature of the temperature field decreased.

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Analytical solution to steady-state temperature field of two freezing pipes with different temperatures

Cited by 19 publications

References 1 publication

Mathematical models of steady-state temperature fields produced by multi-piped freezing

Mathematical models of steady-state temperature fields produced by multi-piped freezing

Research on the Ground Subsidence Mechanism of Cross Passage Caused by Freezing Method Construction

Analytical Solution of Steady‐State Temperature Field of Single Freezing Pipe under Action of Seepage Field

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