Учебное пособие 2210

A heat pump turns on in cycles with alterations of a supply (removal) of heat with stops. For the second stage, i.e. the cooling stage, the initial conditions are a complex temperature field formed during stationery operation of the heat pump over the first calculation period 0 < < 1:

where τ1 is the operation time of the heat pump setup of the second stage, sec.

For the third stage, i.e. when the heat pump turns on following a stop, the initial conditions for calculations will be a complex temperature field obtained following the cooling of the layer

1< < 2:

where τ2 is the operation time of the heat pump setup of the third stage, sec.

The boundary conditions at the face of the well are accepted depending on the technological modes of the first, second, and third order:

–– first order, where there is no influence of the wells and constant temperature

t ( , τ) = tbackground;

–– second order, on the surface of the casing pipe of the well; for the operating heat pump:

t(rc , ) q ;r

and for the non-operating heat pump:

t(rc , ) 0;

r

–– for the second order, on the lower generating line of the calculation cylinder, the earth’s warmth, the heat flow is considered constant:

t(r, ) q ;r

–– the third order, on the Earth’s surface, due to a significantly larger thermal conductivity coefficient on the surface in relation to the heat transfer coefficient of a soil from the surface to the heat exchange part of the well can be changed by the first order: t (r, ) = tclimate.

The solution for modeling a temperature field is obtained by means of the method of finite differences using an implicit difference scheme (Fig. 2) [8].

The equation (2) in the discrete form is as follows:

where i, j are the indices (numbers) of the corresponding nod point along the axis Х and У.

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Fig. 2. A grid and a control volume in polar coordinates r, ϴ

2. Calculation prediction of the distribution of temperature fields considering a filtration flow of groundwater

Determining the effect of a filtration flow of groundwater is reduced to solving the problem of flowing of a circular cylinder. In Fig. 3—6 there are the results of the influence of groundwater during the operation of the well for 5 years for a heat load on the well of 200 Watt seasonally. The prediction results are performed using a numerical model implemented using the applied software MathLab.

TPeak TAxis

Displacement

of the field

Fig. 3. Results of the operation of a heat pump setup over 6 months:

а) a temperature field of the soil; b) a temperature graph in direction to a filtration flow;

Тaxis is the temperature along the well axis; Тpeak is the peak temperature of the soil in operation over 6 months

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As seen from Fig. 3, a heat flow is distributed radially from the well. In Fig. 3b the temperature graph is displaced in relation to the main axis of the well (the area is 10 meters and it is accepted to be the centre of the well) along the axis Х, the deviation is close to 0.3 m.

Fig. 4 shows the results of the experiment of the first year of the operation when the heat pump is not in operation (the downtime period).

As seen from Fig. 4а, the distribution of a heat flow is radial similarly to Fig. 3. As during the downtime period the heat pump is not in operation, the temperature field around the well yields to the background temperature of the soil.

The boundaries of the temperature graph (Fig. 4b) from both sides of the axis approach the contour of the influence of the external boundary if the task is accepted to be along the radius and is 10 m. Thus when the heat pump setup is not in operation, there is no displacement along the main axis under the influence of a filtration flow.

Approaching the influence boundaries

Fig. 4. Results of the first year of the operation of the well during the downtime period of the heat pump setup: а) a temperature field;

b) a graph of a change in the temperature in direction to a filtration flow

As the operation time increases, there is no displacement along the axis Х. Stabilization of the temperature of the soil in operation takes place as early as during the second year of the seasonal operation of the heat pump setup.

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Displacement

of the field

Fig. 5. Results of the operation of the heat pump setup over 3.5 years:

а) a temperature field of the soil; b) a temperature graph in direction to a filtration flow Тpeak is the peak temperature of the soil in operation over 6 months

3. Summarizing the obtained results for more complex filtration

The obtained results for different operation modes of the heat pump setup are processed in order to come up with a method of dependencies for engineering and technical and economic calculations [8]. Fig. 6 presents the temperature fields and graphs for different rates of groundwater. In order to allow the results to be further employed in experimental and theoretical studies of a wide range of engineering objects, the similarity theory was used.

Fig. 7 presents the results of the effect of the filtration rate on heat exchange. To make it easier for the obtained data to be processed, the following dimensionless values are introduced as part of the study: С is the criterion of the multiplicity coefficient of water exchange, θ is a dimensionless temperature, Q is a dimensionless heat flow, P is a correction for a filtration flow, kP is a regeneration coefficient.

As seen from the graph, there are two modes. The first mode is when the filtration rate is slow and has no effect on a temperature field, the second one is when as the filtration rate is on the rise, the temperature pressure drops.

Based on the processing of the obtained results, the correction modes were identified. If 0 < С < 78, P = 1, a filtration flow has no effect, if C > 78, a filtration flow has an effect on the temperature of the soil.

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I

Displacement

of the field

II

Break along the length of the well

Fig. 6 (beginning). A field and a temperature for different rates of groundwater:

I — υ = 0,000000001 m/seс;

II — υ = 0,00000009 m/sec

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Russian Journal of Building Construction and Architecture

III

Break along the length of the well

Bend of the field

IV

Tends to the axis

of the well

Fig. 6 (end). The field and temperature at different rates of groundwater:

III — υ = 0.0000005 m/seс; IV — υ = 0.000006 m/seс

We have identified the effect of a filtration flow on the temperature field and the criterion equation [11] (7) where the corrections for a filtration flow are taken into account:

where Fo is the Fourier criterion; Q is a dimensionless heat flow; kp is a regeneration coeffi-

cient; С is the criterion of the multiplicity coefficient of water exchange (a dimensionless value).

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No effect

Boundary of a filtration flow

Effect is present

Fig. 7. Dependence of the correction for the filtration flow P on the water exchange criterion С

Using the similarity theory and calculations of the coefficients with the corrections, the obtained equation can be employed as a modified equation for obtaining the results of the prediction of the operation of the heat pump for long operation periods considering the effect of a filtration flow of groundwater.

Conclusions

Based on the research, the following conclusions can be made.

1.During active operation of the heat pump setup there is a displacement of a temperature field ranging from 0.1 to 0.4 m due to the effect of filtration of groundwater.

2.During the downtime of the heat pump there was no deviation from the axis of the temperature field under the influence of groundwater, but a temperature wave approaches the influence boundary of a heat flow.

3.Stabilization of a temperature field of the soil during active operation of the heat pump setup occurs during the second year of operation and a temperature field tends to the background temperature during the downtime period. Such a temperature distribution remains through the entire operation period of the non-active mode.

4.The rate flow of filtration water was divided into four modes: the first one was when the rate of a filtration flow is slow and has no effect on changes in the temperature field of the soil; the second one was when the rate increases and so does the displacement of a temperature field of the soil. Thus the influence of a flow in areas with plain rivers but it has to be taken into account during long operation.

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5. The criterion equation introduced with the correction for a filtration flow allows one to determine changes in the temperature of a soil body making an engineering calculation during the designing stage easier as a tool of a technical and economical analysis of the heat pump setup.

References

1.Vasil'ev G. P. Teplokhladosnabzhenie zdaniy i sooruzheniy s ispol'zovaniem nizkopotentsial'noy teplovoy energii poverkhnostnykh sloev zemli. Diss. dokt. tekhn. nauk [Teplogazosnabzhenie of buildings using low-grade thermal energy of the surface layers of the earth. Dr. eng. sci. diss.]. Moscow, 2006. 423 p.

2.Kostikov A. O., Kharlampidi D. Kh. Vliyanie teplovogo sostoyaniya grunta na effektivnost' teplonanosnoy ustanovki s gruntovym teploobmennikom [The influence of the thermal state of the soil on the effectiveness of teplonasos installing ground heat exchanger]. Energetika: ekonomika, tekhnologiya, ekologiya, 2009, no. 1, pp. 32—40.

3.Krylov V. A., Chernoozerskiy V. A., Nikitin A. A., Baranov I. V. Uchet neravnomernosti temperaturnogo polya v geotermal'noy skvazhine teplovogo nasosa [The account of the irregularity of the temperature field in the geothermal well heat pump]. Vestnik MAX, 2015, no. 1, pp. 75—80.

4.Lykov A. V. Teoriya teploprovodnosti [Theory of thermal conductivity]. Moscow, Vysshaya shkola Publ., 1967. 600 p.

5.Malykh V. V., Udalov S. N., Zakharov A. A. [The method of calculation of a soil battery]. Trudy nauchnoprakticheskoy konferentsii «Energo- i resusoeffektivnogst' maloetazhnykh zdaniy» [Proc. of scientific-practical conference "Energy - and respeetively low-rise buildings"]. Moscow, 2013, pp. 317—318.

6.Maslov N. N. Osnovy mekhaniki gruntov i inzhenernoy geologii [Fundamentals of soil mechanics and engineering Geology]. Moscow, Vysshaya shkola Publ., 1982. 511 p.

7.Nerpin S. V., Chudnovskiy A. F. Fizika pochvy [Physics of soil]. Moscow, Nauka Publ., 1967. 584 p.

8.Patankar S. Chislennye metody resheniya zadach teploobmena i dinamiki zhidkosti [Physics of soil]. Energoatomizdat Publ., 1984. 152 p.

9.Rudenko N. N., Fursova I. N. Modelirovanie temperaturnogo polya v grunte [Modeling of the temperature field in the soil]. Available at: http://www.ivdon.ru/magazine/archive/n2y2013/1697

10.Rukovodstvo po primeneniyu teplovykh nasosov s ispol'zovaniem vtorichnykh energeticheskikh resursov i netraditsionnykh vozobnovlyaemykh istochnikov energii: (utv. i vved. v deystvie ukazaniem Moskomarkhitektury ot 31.01.2011 № 8). [Guidance on the application of heat pumps using secondary energy resources and nontraditional renewable energy sources: (approved and put into effect an indication of the architectural Committee from 31.01.2011 No. 8)]. Moscow, GUP «NIATs», 2001. 32 p.

11.Saprykina N. Yu., Yakovlev P. V. [Statement of the problem of determining the temperature field of a geothermal heat pump for the oil industry]. Trudy VI Mezhdunarodnoy nauchno-prakticheskoy konferentsii [Proc. of the VI International scientific-practical conference]. Astrakhan, Izd-vo AGTU, 2015, pp. 126—130.

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12.Smirnov S. S. Teoreticheskie osnovy i tekhnologii izvlecheniya geotermal'noy energii s ispol'zovaniem absorbtsionnykh teplovykh nasosov. Avtoref. diss. dokt. tekhn. nauk [Theoretical bases and technologies of extraction of geothermal energy using absorption heat pumps. Dr. eng. sci. diss.]. Novocherkassk, 2011. 19 p.

13.Fedyanin V. Ya., Karpov M. K. Ispol'zovanie gruntovykh teploobmennikov v sistemakh teplosnabzheniya [The use of ground heat exchangers in heating systems]. Polzunovskiy vestnik, 2006, no. 4, pp. 98—103.

14.Shishkin N. D., Prosvirina I. S. Otsenka effektivnosti primeneniya teplonasosnykh ustanovok v sistemakh teplosnabzheniya Astrakhanskoy oblasti [Evaluation of the effectiveness of heat pump systems in heating systems in Astrakhan region]. Izvestiya AZhKKh, 2000, no. 4, p. 7.

15.RETScreen®International. Ground-source Heat Pump Project Analysis: Chapter // RETScreen®Engineering & Cases Textbook. Ministry of Natural Sources of Canada, 2005. 70 p.

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Russian Journal of Building Construction and Architecture

UDC 697.9:621.3

V. P. Shackij1, V. A. Gulevskij2

COOLING OF THE SEALED VOLUMES

USING WATER EVAPORATION COOLERS

Voronezh State University of Agriculture

Russia, Voronezh, tel.: (473)29-103-39, e-mail: sha.vladim@yandex.ru 1D. Sc. in Engineering, Head of the Dept. of Mathematics and Physics 2D. Sc. in Engineering, Prof. of the Dept. of Mathematics and Physics

Statement of the problem. We consider the problem of cooling a sealed volume, in particular electronic equipment using counter-flow water evaporation cooler of indirect principle.

Results. A heat balance equation for limited volume including cooling closed-loop cooling is proposed. A mathematical model of processes of heat and mass transfer in counter-flow evaporation of water chillers of indirect principle, which consists of parabolic and elliptic differential equations with distributed parameters as well as a method of numerical realization of this model were set forth.

Conclusions. The results of the study allow us to conclude about the possibility of lowering the temperature in a sealed volume using an affordable eco-friendly water evaporation coolers of indirect principle.

Keywords: pressurized volume, electronic equipment, water evaporation cooler.

Introduction

Cooling a variety of electronic equipment has long been an urgent task in its construction. An oscillation particularly a dramatic increase in the temperature in similar schemes might change thresholds of comparators, coefficients of increasing the power of transistors, nominal values of resistors and condensers. In digital technology oscillations in temperature are also hazardous. They might lead to breakdowns including thermal ones, a reduction in the measurement accuracy, etc. A growth of the temperature in power equipment that might cause a power source and power blocks to break down poses the most threat.

Cooling systems of insulated premises can be classed into two main groups: passive and active ones. The first group is when the heat is diverted using convection, heat conductivity and radiation. The second group is forced thermal diversion by means ofventilation,thermal electri coolers

© Shatskiy V. P., Gulevskiy V. А., 2017

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