Analytical Solution of Three-Dimensional Steady State Temperature Field of Single-Piped Freezing

2013 ◽  
Author(s):  
Hu Xiangdong ◽  
Guo Wang ◽  
Zhang Luoyu
Keyword(s):  
Temperature Field ◽  
Steady State ◽  
Analytical Solution ◽  
Three Dimensional ◽  
Steady State Temperature

scholarly journals Application of Analytical Solution to Steady-State Temperature Field by Double-Row-Pipe Freezing and Verification with Field Measurement: A Case Study of Connected Aisle

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Zequn Hong ◽  
Xiangdong Hu
Keyword(s):  
Temperature Field ◽  
Steady State ◽  
Analytical Solution ◽  
Wall Thickness ◽  
Field Measurement ◽  
Field Analysis ◽  
Shield Tunnel ◽  
Double Row ◽  
Steady State Temperature ◽  
Frozen Wall

In order to solve the problem of sealing water and bearing capacity of a connected aisle in an underwater shield tunnel, a double-circle horizontal freezing method was adopted for ground reinforcement in the connected aisle of Maliuzhou Tunnel, which is China’s first shield tunnel with superlarge diameter built in a composite stratum. This paper proposed a new double-row-pipe freezing model for the calculation of frozen wall thickness based on analytical solution to steady-state temperature field. Besides, field measurement and transient numerical studies of the active freezing period were also carried out to study the freeze-sealing effect. The results show that frozen wall thickness obtained by analytical solutions agrees well with numerical simulation results, which verifies the applicability of the newly proposed calculation method. Field analysis indicates that soil temperature gradually approaches a stable value which is far below the freezing point, and a reliable water-sealing curtain can be formed around the designed connected aisle. Maximum impact of soil excavation on the frozen wall is about 10°C, and reducing exposure time of excavation surface can effectively alleviate the weakening of frozen wall. To obtain comprehensive analysis for freezing wall thickness, a more reasonable arrangement of temperature-measuring holes is expected in future freezing engineering.

scholarly journals Analytical Solution of Steady-State Temperature Field of Single Freezing Pipe under Action of Seepage Field

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Bin Wang ◽  
Chuanxin Rong ◽  
Hua Cheng ◽  
Haibing Cai ◽  
Shiqi Zhang
Keyword(s):  
Temperature Field ◽  
Steady State ◽  
Analytical Solution ◽  
Model Test ◽  
Freezing Temperature ◽  
Seepage Velocity ◽  
Distribution Law ◽  
Seepage Field ◽  
Steady State Temperature ◽  
Single Pipe

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.

Piezothermoelasticity and Control of Piezoelectric Laminates Exposed to a Steady-State Temperature Field

1993 ◽  
Author(s):  
H. S. Tzou ◽  
R. Ye
Keyword(s):  
Temperature Field ◽  
Steady State ◽  
Degrees Of Freedom ◽  
Sensors And Actuators ◽  
System Equation ◽  
Thermal Fields ◽  
Steady State Temperature ◽  
And Control ◽  
Internal Degrees Of Freedom

Abstract Piezothermoelastic effects of distributed piezoelectric sensors and actuators are investigated. Vibration control of piezoelectric laminates subjected to a steady-state temperature field is studied. A new 3-D piezothermoelastic finite element with three internal degrees of freedom is formulated using a variational formulation. A system equation for the piezoelectric continuum exposed to combined elastic, electric, and thermal fields is formulated. Distributed sensing and control equations are derived. All these effects are studied in a case study.

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