### Abstract

The relevance of the research is caused by the necessity to develop mathematical models of thermophysical processes occurring in thermosiphons. These models are significantly less complex than the known ones, where sophisticated hydrodynamics problems are solved for vapor channel. However, at the same time they provide the possibility of adequate predictive modeling of heat transfer processes in thermosiphons and determining their main characteristics (temperature, heat fluxes, and evaporation rates) which are necessary to create heat supply systems using geothermal and petrothermal energy of the deep layers of the earth when heat transfers by high thermosiphons system. The main aim of the research is the validation of new approach to description of heat transfer in thermosiphons, which are the main elements of the system for extracting heat from the deeper layers of the earth (geothermal and petrothermal energy) by comparing the results of mathematical modeling of temperatures within the framework of the new model at characteristic points of the coolant layer and experimental results. Object: twophase close thermosiphon Method. The formulated boundary problem of mathematical physics was solved by the finite difference method. Results. Based on the analysis and synthesis of experimental results, the authors have developed a new approach to mathematical modeling of thermal regime formation of high thermosiphons for using geothermal heat. We formulated mathematical modeling describing heat transfer in a coolant layer on the bottom cover of thermosiphon. This model provides to make reliable prediction of evaporation (or boiling) rates of a coolant. The model differs from the known ones by description of conduction, as well as natural convection in the coolant layer. A good agreement was established between the results of numerical calculations of temperature fields in the area of analysis and the experiments. Numerical studies were performed on a spatial grid of 36101, the time step was varied in the range from 10^{-3} to 10^{-6} s. We considered the range of heat fluxes q corresponding to the conditions of intense evaporation on the free surface of the coolant layer. Experimentally and numerically obtained temperatures at a point located on the symmetry axis of a thermosiphon at a distance of 6 mm from the surface of its bottom cover were compared. Npentane, a lowboiling liquid that can be used in thermosiphons at relatively low temperature (up to 40 °C) of rock or water, was considered as a coolant. The temperature fields obtained in the experiments and numerical simulations agree well. Natural convection in the coolant layer at sufficiently high heat fluxes to the lower surface of the thermosiphon plays an important role in formation of liquid temperature field and the rate of its evaporation from the free surface. The developed approach can be used for analysis of geothermal and petrothermal heat supply systems when extracting heat from the deeper layers of the earth using a group of high thermosiphons.

Original language | Russian |
---|---|

Pages (from-to) | 78-86 |

Number of pages | 9 |

Journal | Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering |

Volume | 330 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

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### ASJC Scopus subject areas

- Materials Science (miscellaneous)
- Fuel Technology
- Geotechnical Engineering and Engineering Geology
- Waste Management and Disposal
- Economic Geology
- Management, Monitoring, Policy and Law

### Cite this

*Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering*,

*330*(8), 78-86. https://doi.org/10.18799/24131830/2019/8/2214

**НОВЫЙ ПОДХОД К МОДЕЛИРОВАНИЮ ПРОЦЕССА ФОРМИРОВАНИЯ ТЕПЛОВОГО РЕЖИМА ТЕРМОСИФОНОВ БОЛЬШИХ РАЗМЕРОВ ДЛЯ ИСПОЛЬЗОВАНИЯ ГЕОТЕРМАЛЬНОЙ ТЕПЛОТЫ.** / Maksimov, Vyacheslav I.; Nurpeiis, Atlant E.

Research output: Contribution to journal › Article

*Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering*, vol. 330, no. 8, pp. 78-86. https://doi.org/10.18799/24131830/2019/8/2214

}

TY - JOUR

T1 - НОВЫЙ ПОДХОД К МОДЕЛИРОВАНИЮ ПРОЦЕССА ФОРМИРОВАНИЯ ТЕПЛОВОГО РЕЖИМА ТЕРМОСИФОНОВ БОЛЬШИХ РАЗМЕРОВ ДЛЯ ИСПОЛЬЗОВАНИЯ ГЕОТЕРМАЛЬНОЙ ТЕПЛОТЫ

AU - Maksimov, Vyacheslav I.

AU - Nurpeiis, Atlant E.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The relevance of the research is caused by the necessity to develop mathematical models of thermophysical processes occurring in thermosiphons. These models are significantly less complex than the known ones, where sophisticated hydrodynamics problems are solved for vapor channel. However, at the same time they provide the possibility of adequate predictive modeling of heat transfer processes in thermosiphons and determining their main characteristics (temperature, heat fluxes, and evaporation rates) which are necessary to create heat supply systems using geothermal and petrothermal energy of the deep layers of the earth when heat transfers by high thermosiphons system. The main aim of the research is the validation of new approach to description of heat transfer in thermosiphons, which are the main elements of the system for extracting heat from the deeper layers of the earth (geothermal and petrothermal energy) by comparing the results of mathematical modeling of temperatures within the framework of the new model at characteristic points of the coolant layer and experimental results. Object: twophase close thermosiphon Method. The formulated boundary problem of mathematical physics was solved by the finite difference method. Results. Based on the analysis and synthesis of experimental results, the authors have developed a new approach to mathematical modeling of thermal regime formation of high thermosiphons for using geothermal heat. We formulated mathematical modeling describing heat transfer in a coolant layer on the bottom cover of thermosiphon. This model provides to make reliable prediction of evaporation (or boiling) rates of a coolant. The model differs from the known ones by description of conduction, as well as natural convection in the coolant layer. A good agreement was established between the results of numerical calculations of temperature fields in the area of analysis and the experiments. Numerical studies were performed on a spatial grid of 36101, the time step was varied in the range from 10-3 to 10-6 s. We considered the range of heat fluxes q corresponding to the conditions of intense evaporation on the free surface of the coolant layer. Experimentally and numerically obtained temperatures at a point located on the symmetry axis of a thermosiphon at a distance of 6 mm from the surface of its bottom cover were compared. Npentane, a lowboiling liquid that can be used in thermosiphons at relatively low temperature (up to 40 °C) of rock or water, was considered as a coolant. The temperature fields obtained in the experiments and numerical simulations agree well. Natural convection in the coolant layer at sufficiently high heat fluxes to the lower surface of the thermosiphon plays an important role in formation of liquid temperature field and the rate of its evaporation from the free surface. The developed approach can be used for analysis of geothermal and petrothermal heat supply systems when extracting heat from the deeper layers of the earth using a group of high thermosiphons.

AB - The relevance of the research is caused by the necessity to develop mathematical models of thermophysical processes occurring in thermosiphons. These models are significantly less complex than the known ones, where sophisticated hydrodynamics problems are solved for vapor channel. However, at the same time they provide the possibility of adequate predictive modeling of heat transfer processes in thermosiphons and determining their main characteristics (temperature, heat fluxes, and evaporation rates) which are necessary to create heat supply systems using geothermal and petrothermal energy of the deep layers of the earth when heat transfers by high thermosiphons system. The main aim of the research is the validation of new approach to description of heat transfer in thermosiphons, which are the main elements of the system for extracting heat from the deeper layers of the earth (geothermal and petrothermal energy) by comparing the results of mathematical modeling of temperatures within the framework of the new model at characteristic points of the coolant layer and experimental results. Object: twophase close thermosiphon Method. The formulated boundary problem of mathematical physics was solved by the finite difference method. Results. Based on the analysis and synthesis of experimental results, the authors have developed a new approach to mathematical modeling of thermal regime formation of high thermosiphons for using geothermal heat. We formulated mathematical modeling describing heat transfer in a coolant layer on the bottom cover of thermosiphon. This model provides to make reliable prediction of evaporation (or boiling) rates of a coolant. The model differs from the known ones by description of conduction, as well as natural convection in the coolant layer. A good agreement was established between the results of numerical calculations of temperature fields in the area of analysis and the experiments. Numerical studies were performed on a spatial grid of 36101, the time step was varied in the range from 10-3 to 10-6 s. We considered the range of heat fluxes q corresponding to the conditions of intense evaporation on the free surface of the coolant layer. Experimentally and numerically obtained temperatures at a point located on the symmetry axis of a thermosiphon at a distance of 6 mm from the surface of its bottom cover were compared. Npentane, a lowboiling liquid that can be used in thermosiphons at relatively low temperature (up to 40 °C) of rock or water, was considered as a coolant. The temperature fields obtained in the experiments and numerical simulations agree well. Natural convection in the coolant layer at sufficiently high heat fluxes to the lower surface of the thermosiphon plays an important role in formation of liquid temperature field and the rate of its evaporation from the free surface. The developed approach can be used for analysis of geothermal and petrothermal heat supply systems when extracting heat from the deeper layers of the earth using a group of high thermosiphons.

KW - Condensation

KW - Evaporation

KW - Heat flux

KW - Heat transfer

KW - Mathematical modelling

KW - Thermo;gravitational convection

KW - Two;phase thermosiphon

UR - http://www.scopus.com/inward/record.url?scp=85071952453&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071952453&partnerID=8YFLogxK

U2 - 10.18799/24131830/2019/8/2214

DO - 10.18799/24131830/2019/8/2214

M3 - Статья

VL - 330

SP - 78

EP - 86

JO - Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering

JF - Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering

SN - 2500-1019

IS - 8

ER -