Chapter 13

THE PROGNOSIS OF UNDERGROUND REFRIGERATORS' TEMPERATURE REGIME IN THE PERMAFROST ZONE

A.S. Kurilko Mining Institute of the North, the Siberian Department of the Academy of Science of Russia, Yakutsk, Russia	V.V. Kiselev Yu.A. Khokholov E.K. Romanova Mining Institute of the North, the Siberian
	Department of the Academy of Science of Russia, Yakutsk, Russia

ABSTRACT

Tasks concerning the operation of underground refrigerators in condition of permafrost area are studied. Rational regimes of cold accumulation by atmospheric cold during winter as well as the power required for refrigerating units, are calculated.

KEYWORDS

Underground refrigerators (UR), temperature regime, cold accumulating

INTRODUCTION

From immemorial time the indigenous people of the North built semi-deepened in other words underground refrigerators. It is used for food (meat, fish) storage adopting natural resources such as ice and cold that are accumulated by rocks. During winter refrigerators are opened in order to be frozen through by natural (atmospheric) cold. Low efficiency of such a freezing method is compensated by river ice that is piled in storage chambers during winter.

The opening up of the North with following development of mining industry and rise of inhabited localities have brought about new UR's construction methods that apply more profound volume-planing decisions and constructions. Construction has been conducted using mining technologies and on larger scale (Galkin, et al., 1996).

Pre-freezing of containing rocks is crucial for recently built refrigerators. It is important because natural temperature of rock is -4 -8°C. It is not enough for food (meat, fish) storage. Yearly conducted accumulation of cold is necessary. It provides with progressing cold accumulation in order to keep required temperature for food storage.

Conducted observations have revealed, that rock's freezing-through occurs very slowly in spite of forced ventilation. The reasons are as follows: ventilation schemes are out of date; fan-power is inefficient; control under process of freezing-through (cold accumulation) is low; calculating method as well as temperature regime prognosis, which allow to choose optimal freezing regimes, are absent.

Due to the reasons stated above, UR's have to be maintained with additional refrigerating units even in regions with low temperature where natural rock temperature is low. However, preliminary calculations show sufficiency of natural cold, that in its turn lowers material and energy expenses (Recommendations on designs, reconstructions and using the underground refrigerators in Yakutia ASSR, 1982). Thus it significantly lowers operational expenses.

Formation of UR's temperature regime depends on its geometric size, heat capacity of containing rocks, mass of storing food and its initial temperature, regime of winter cold accumulation (ventilation longevity, air expenditure).

Taking into account all the factors stated above, the UR's 3D mathematical model has been specially designed to forecast temperature regime. It is accepted, that cross-section of UR workings (storage chambers) are of rectangle shape, where h is for height and a is for width. Variable UR ventilation regime (with different consumption) is designed for atmospheric air ventilation during winter. Computer designed numeral methods are used to decide task of heat exchange (Samarsky, 1977; Popov, 1995; Hoholov, 1999).

The mathematical model is adapted for operating conditions of functioning UR. It is located in Yakutsk and belongs to join-stock company “Yakutenergo”.

THE INFLUENCE OF COLD ACCUMULATING REGIME ON UR TEMPERATURE REGIME

Cold accumulating regime and temperature regime have been studied according to the UR's 3D mathematical model. When chambers are ventilated according to circular scheme, the existing scheme of winter ventilation is taken as a starting point. Natural observations' data are taken as initial data for numeral calculations. Natural observations have been conducted by Mining Institute of the North for temperature regime of rocks surrounding refrigerators' chambers.

The influence of longevity of cool accumulating on dynamics of air temperature, is shown in Fig. 1 for summer time. Air consumption equals ≈ 3 m³/sec. for cool accumulation during winter. According to demonstrated consumption, the extension of longevity of cool accumulation from one to four months leads to decrease in UR air temperature by 3°C.

Figure 1. Changes of air temperature that occur during different cold accumulation periods in summer time.
1 - 4 months (November-February); 2 - 3 months (December-February); 3 - 2 months (January, February); 4 - 1 months (February)

In addition to longevity of ventilating, air consumption for cool accumulation is also very important to formation of UR temperature regime. In case of small air consumption during winter, accumulation of cold by surrounding rocks is inefficient. Thus reserve of cold could be insufficient for keeping temperature required for food storage during summer time. The more air consumption is, the more cold is accumulated by rock surrounding chamber. We have researched the dependence of air temperature in UR from consumption of air delivered with a purpose of cold accumulation. It is shown in Fig. 2. The calculations show, that winter air consumption of 25 m³/sec. and more guaranties air temperature of -12°C in chambers during summer time.

Figure 2. Dynamic of air temperature in UR chambers during different consumption of the air (G), delivered for cold accumulation purpose

Refrigerating units become necessary when required storage temperature (≤ -12°C) can not be maintained by the offered method of accumulation of natural cold.

CALCULATION OF THE REQUIRED POWER
OF REFRIGERATING UNITS

Let's define necessary power of refrigerating units to keep required air temperature in chambers (in addition to accumulation of natural cold used in UR) by the value of heat flow passing through chamber's walls as follows.

Q = S⋅α ⋅ (T₂-T₁), W (1)

Where S is area of chamber's surface, m²; α is coefficient of heat exchange between the air and chamber's walls, W/(m²⋅K); T1 is temperature of chamber's wall, °C; T₂ is temperature required for the air in a chamber, °C.

During summer heat exchange occurs by means of free conversion due to discontinuance of air supply in UR. Coefficient of heat exchange (α) depends on air temperature and temperature of chamber's walls. It is calculated as follows (Bogoslovsky, 1982):

α = 1.66 ⋅ ( T₂-T₁)¹/₃, W/(m² ⋅ K) (2)

Calculation of required power of refrigerating units is shown in Fig. 3 and 4. It is conducted according to suggested method of calculation used for UR chambers, that are frozen-through by natural cold during winter applying different regimes. Two levels of required air temperature are -18 and -24°C. It can not be achieved by the method of natural freezing-thorough. The graphs show dependence of the amount of machine cold, required to compensate lost of cold during summer, on winter regime of cold accumulation, and consequently on the amount of natural cold accumulated by surrounding rock.

As it is shown in Fig. 3, the more incoming air is consumed during winter freezing-through, the later refrigerating units are going to be operated, in order to maintain required temperature (-18°C) in chambers by periodic increase of units' power. Due to the described temperature regime, maintenance of required temperature of food storage required comparatively small amount of machine cold.

Figure 3. Calculated power of UR chambers' refrigerating units during different consumption of the air, delivered for cold accumulation purpose (T = -18°C)

Different situation is observed, if it is necessary to maintain lower temperature (-24°C). In this case, a large amount of power is used to initially cool down rock containing in chamber to -18°C. Existing level of air expenditure (Q = 1 m³/sec.) as well its increase to
3 m³/sec. can not guaranty required accumulation of cold in winter time. It brings the situation, where powerful refrigerating units are going to be used to produce large amount of artificial cold during first month of operation. As it is shown in Fig. 4, a function of dependence of refrigerating units' power on time is a decreasing one.

Figure 4. Calculated power of UR chambers' refrigerating units during different consumption of the air, delivered for cold accumulation purpose (T = -24°C)

Evidently, a value of refrigerating units' power asymptoticly approaches constant value. It practically doesn't depend on expenditure of the air incoming with purpose of cold accumulation.

CALCULATION OF TEMPERATURE REGIME
OF UR LOADED WITH FOOD SUPPLY

It is known, that storied food has heat-accumulation capacity. It accumulates cold, that influences formation of UR temperature regime, the same way as rock. Numeric experiments have been conducted in order to define a level of dependence of a load (total mass of storied food) to temperature regime.

For instance, in winter for 1,5 months, UR chamber is being frozen-through by the atmospheric air forced by a fan. By the end of March the freezing-through is stopped. A chamber loads with meat, pre-cooled to the temperature of external air.

The graphs in Fig. 5 illustrate temperature dynamic of food during storage period from the regime of freezing-through and the amount of storied food. Therefore let's assume that the larger food mass accumulating cold is storied and the more intensive freezing-through process is, that guaranties accumulation of required cold by surrounding rock, the longer the storing period. For instance, 100 tons of meat can be stored in temperature of ≤-12°C until June, if consumption of air during freezing-through process is 9m³/sec. The increase of a load to 200 tons guaranties normative temperature in chambers for one more month. Refrigerating units are used to maintain normative temperature in a chamber in case of further extension of storing period.

Figure 5. Temperature dynamic of UR stored food supply depending on freezing-through regime conducted by natural cold. 1 - external air temperature;
2 - temperature of food (meat) with G = 3 m³/sec.;
3 - temperature of food (meat) with G= 9 m³/sec

CONCLUSION

1. Developed mathematical model has allowed to study the influence of different freezing-through (cold accumulation) regimes of UR, conducted by natural cold, to dynamics of temperature regime in chambers during summer time.

2. The required power of refrigerating units to maintain temperature of -18 and -24°C (in addition to winter cold accumulation by natural cold) is defined by means of the developed method.

3. The limits for food storing period are defined depending on pre-cooled food mass (t_cool< -12°C) and winter cold accumulation regime of UR (t_c.a.<=
   -12°C).

REFERENCES

Bogoslovsky V.N., 1982, Heat physics of Building. Higher school, Moscow

Galkin A.F., Kiselev V.V., Scherstov V.A., 1996, “Experience and perspectives of underground refrigerators building in the North,” Proceeding, Int. Symposium Cold Regions Engineering, Harbin, China, pp. 49-51

Hoholov Y.A, 1999, “Three-dimensional mathematical model for the calculation of temperature regime in underground construction,” Proceeding, Int. Conf. on Computational Haet and Mass Transfer, CHMT99. Easter Mediterranean University, G. Magusa. April 26-29, 1999. N. Cyprus, Turkey,pp 158-161

Popov F.S., 1995, Computational methods of engineering geocryology. Nauka, RAS Siberian Publ. Firm, Novosibirsk

Recommendations on building, reconstructions and using the underground refrigerators in Yakutia ASSR, 1982, Yakutsk

Samarsky A.A., 1977, The theory of finite differences. Nauka, Moscow

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THE PROGNOSIS OF UNDERGROUND REFRIGERATORS' TEMPERATURE

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