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The seasonally-operating cooling devices (SHOW) intended for freezing and cooling plastichnomorzlyh thawed soil at the base of a ventilated constructions underground and without, around transmission line supports and piping, along the embankments of railways and highways to increase their carrying capacity and to prevent buckling of piles in areas where permafrost. More information about the technology of thermal stabilization of soils can be on this page website.

The task of modeling the thermal effect on the seasonally active cooling devices today soils can be effectively addressed in the software package Frost 3D Universal. To do this, you need the following data:

1.Meteorological data (Table. 1): air temperature, wind speed, and the thickness of the snow cover;

2.Engineering and geological structure of the soil(Table. 2) and initial temperature at the start date of calculation (Table. 3);

3.Thermophysical properties of geological strata (Table. 4): thermal conductivity and heat capacity in the thawed state and morzlom, curve unfrozen water, phase transition temperature, soil density;

4.Technical characteristics of a thermal stabilizer (Table. 5).

Table. 1 - Climatic data

Parameter Month
1 2 3 4 5 6 7 8 9 10 11 12
Air temperature, aboutFROM -27,3 -24,3 -16 -5,3 4,8 13,2 16,4 12,5 4,1 -5 -19,5 -26,8
Wind speed, m / s 2,3 2,1 2,1 2,4 2,4 2,1 1,8 1,8 1,9 2,3 2,3 2,4
Snow depth, m 0,28 0,31 0,32 0,27 0 0 0 0 0 0,14 0,19 0,25
snow density, kg / m3 275 300 320 330 0 0 0 0 0 180 220 240

Table. 2 - Capacity of soils for each well

Power geological layer, m
Name of geo-cal layer wells. 1 wells. 2 wells. 3 wells. 4
IGE-1 1,5 1 1,9 0,7
IGE-2 1,9 1,2 3 1,5
IGE-3 0,8 1,2 1 2
IGE-4 2,4 2 1 4
IGE 5 3 3,8 2,5 1
IGE 6 2,7 2 4 4
IGE-7 1,7 1,8 0,6 0,8

Table. 3 - The temperature distribution on the soil depth 01.10.2016

Depth, m Temperature, aboutFROM
0 2,22
1 1,35
2 -0,42
3 -0,40
4 -0,38
5-6 -0,36
7-10 -0,35
11-14 -0,34

rice. 1 - Location of geologic wells in 2D Editor software package

Table. 4 - Thermal properties of soils

Parameter Identification of the substance Identification of the substance
Temperature, aboutFROM The temperature distribution on the ground at a depth of 01.10.2016
Volumetric heat capacity of the unfrozen soil, MJ /(m3aboutFROM) 2,78 3,17 3,17 2,78 2,31 2,39 2,31
Volumetric heat capacity of the frozen ground, MJ /(m3aboutFROM) 2,06 2,41 2,41 2,26 2,14 2,08 2,14
The thermal conductivity of unfrozen soil, W /(м•aboutFROM) 1,91 1,57 1,57 2,26 1,62 2 1,62
The thermal conductivity of frozen soil, W /(м•aboutFROM) 2,14 1,8 1,8 2,62 1,74 2,2 1,74
The total weight of soil moisture, d.e. 0,14 0,29 0,57 0,23 0,27 0,21 0,18
The density of dry soil, kg / m3 1550 1450 1030 1590 1470 1630 1710
plasticity, lp 0,01 0,10 0,10 0,01 0,05 0,01 0,06
the phase transition temperature, aboutFROM -0,1 -0,21 -0,26 -0,24 -0,31 -0,27 -0,32

Table. 5 - Technical characteristics and thermal stabilizer circuit


1 - part of the capacitor;

2 - the transport of the;

3 - evaporation of the

Diameter, mm 34
The length of the aerial part, m 1,5
ribbing condensers
type ribs cross, round
The diameter of the ribs, mm 70
step ribs, mm 2,5
The number of edges, PC, 300
The thickness of the ribs, mm 1
Material ribs; thermal conductivity, W /(m∙aboutFROM) Aluminum; 203,5
Evaporator (without inserts)
Diameter, mm 34
The length of the underground part, m 13
The length of the insulated portion, m 2

It is necessary to calculate the thermal state of the soil under impact seasonally active cooling device for 5 years of use with 01.10.2018 by 01.05.2024.

Three-dimensional Computational Domain

Geological lithology soil, consisting of various elements geotechnical (IGE), recovering on the basis of several geotechnical wells using three-dimensional interpolation methods.

The dimensions of the modeled area must be taken in such a way, to the annual variation of temperature does not affect the thermal condition of the soil deeper than zero temperatures of heat exchange. It is also necessary to take into account the impact of heat stabilizer and postpone the side and lower bounds on the computational domain as, so at this distance was not its effect on soil thermal distribution. On the basis of these considerations, it was decided to take the calculated area size 25h25h30 meters (rice. 2). tk. known geological structure of the ground only to 14 meters from the ground surface, it was decided to increase the capacity of the last layer of soil (IGE-7) More on 16 m.

rice. 2 - A three-dimensional computational domain

Thermal properties of soils (Table. 4) you need to create the database software package data (rice. 3), then assign them for each of the layers of soil, and set the initial temperature for the entire depth of the computational domain (rice. 4).

rice. 3 - Setting the thermo-physical properties of soils

rice. 4 - Setting the initial temperature distribution in the soil depth

For subsequent modeling of the effects on the SDA primers, you must create and arrange it in a three-dimensional computational domain (rice. 5). heat stabilizer work is described in the relevant section of the program complex database.

rice. 5 - A three-dimensional region with the calculated current-seasonally cooling device

FEATURES Simulation of heat stabilizers

The database for describing the operation of a thermal stabilizer is necessary to set the following values:

  1. The annual course of air temperature in the given area.
  2. Coefficient of heat exchange with the air condenser surface, that defines a convective heat transfer Finned tube heat stabilizer with air. This ratio can be calculated in the calculator heat transfer conditions Frost 3D Universal depending on the design features of the capacitor (rice. 7, 8).
  3. The temperature difference between the condenser and the evaporator - total thermal loss due to the pressure difference, in particular, hydrostatic pressure in the middle and upper layers of the boiling refrigerant.
  4. The thermal resistance of a heat stabilizer - characterizes the additional temperature losses in the transfer of heat from the soil to the evaporator. This value is determined from the experimental values ​​of the temperature on the evaporator and the condenser at a certain value of thermal stress on the JMA.
  5. The design parameters of the MCS:
  • evaporative pipe radius portion;
  • area of ​​the evaporator, the contacted ground;
  • area of ​​the condenser fins, contactee with the environment.

rice. 6 - Set parameters for describing the operation of seasonally active cooling device

rice. 7 - Calculation of the coefficient of heat exchange with the condenser part JMA air

rice. 8 - The calculated heat transfer coefficient for the condenser with air JMA

The boundary conditions ON THE VERGE computational domain

After creating the three-dimensional model of the computational domain, it is necessary to set the following facets of the boundary conditions, which also first need to create a database:

  • The top of the computational domain is necessary to set the boundary condition 3 kind (rice. 9), where it is necessary to introduce air temperature varies periodically with respect to time (rice. 10) and heat exchange coefficient (rice. 11). Soil heat transfer coefficient of air is calculated from the wind speed. In the cold season on the heat transfer coefficient is also affected by snow depth (rice. 12) and its density (rice. 13), the values ​​of which can be set in the corresponding parameters of the boundary condition.
  • On the side surface is set equal to zero heat flux, tk. the side faces are at a distance sufficiently distant from the MCS and supposed, that the soil temperature of the lateral boundary of the computational domain will match the estimated temperature inside the border region in its.
  • permafrost constant temperature is set at the lower face of the computational domain is equal to -0,34 OC, tk. the lower boundary lies at a sufficient distance from heat sources and it will not affect the work of the JMA.

rice. 9 - Setting the boundary conditions on the ground surface

rice. 10 - Dependence of temperature on time

rice. 12 - The dependence of the thickness of the snow cover on the time

rice. 11 - The dependence of heat transfer coefficient times

rice. 13 - Dependence of the density of the snow cover from time to time


Thermal design a computer model was made on 5 years, beginning with 1 October 2018 and ending the year 1 May 2024 of the year. Effect seasonally active cooling device is provided below the ground in the form of color temperature distribution and the proportion of unfrozen water in the simulated domain on 15 of each month (rice. 14, 15).

rice. 14 - Temperature regime Soil cross-sectional area in place of the simulated location JMA

rice. 15 - Ratio of unfrozen water in the ground cross-section area in place of the simulated location JMA

On the basis of the calculation results, automatically creates a graph of cooling capacity of the entire surface of the evaporator of the SDA (rice. 16). This graph can be used to assess thermal stabilizer effectiveness in these climates.

rice. 16 - Automatically create a graph the cooling capacity of the JMA for all time simulation