Study on the heat transfer performance of boiling in vertical buried tube of direct expansion ground source heat pump

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10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, China(ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China

Study on the heat transfer performance of boiling in vertical buried Study ontube the transfer performance boiling in vertical Theheat 15th International Symposium on District Heating and Cooling buried of direct expansion groundofsource heat pump tube of direct expansion ground source heat pump a a a Assessing the feasibility using Yuefen Gao *of , Tingting Gao the , Zhaoheat Liu demand-outdoor a a a Yuefen Gao *, Tingting Gaodistrict , Zhao Liu heat demand forecast temperatureNorthfunction for University, a long-term China Electric Power 619 Yonghua North Street, Baoding 071003, China a a

North China Electric Power University, 619 Yonghua North Street, Baoding 071003, China

I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc a Abstract IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract Two kinds ofcphysical phenomena of phase change heat transfer- IMT and Atlantique, gas-liquid 4two-phase flow co-exist in the buried Département Systèmes Énergétiques et Environnement rue Alfred Kastler, 44300 Nantes, France tube of the directkinds expansion ground source heat pump change system.heat Thetransfer performance of boiling heat transfer processininthe vertical Two of physical phenomena of phase and gas-liquid two-phase flow co-exist buriedU-tube tube ofwas the discussed in this ground study. Firstly, the refrigerant flow equation and the change heat in transfer process the direct expansion source the heatmodels pump of system. The performance of boiling heatphase transfer process vertical U-tubein was vertical U-tube, heatFirstly, transfertheprocess and outsideflow wellequation heat transfer were established. Based on the models, discussed in this the study. modelsinternal of the refrigerant and the phase change heat transfer process in the Abstract changes U-tube, of the refrigerant parameters alonginternal the length tube were and analyzed during boiling process. vertical the heat transfer process andofoutside wellsimulated heat transfer were established. Basedheat on transfer the models, the District networks are that commonly addressed in as one and of the most effective solutions the The simulation results showed thealong pressure and temperature of refrigerant rise in the downward tube, while thedecreasing pressure and changes ofheating the refrigerant parameters the length of the tubeliterature were simulated analyzed during boiling heatfor transfer process. greenhouse gas emissions from therapidly building sector. These systems require high which aredownward returned through heat temperature of refrigerant declined in the upward tube. Soofthe evaporation kept slow rate in the tube butthe fastand in The simulation results showed that the pressure and temperature refrigerant riseinvestments in the downward tube, while the pressure sales. Duetube. to the conditions and tube building renovation policies, heat influence demand in the soil future could decrease, the upward Thechanged effectdeclined ofclimate heat rapidly transfer inthe upward is better. the same time, of the initial temperature of refrigerant in upward tube. So theAtevaporation kept the slow rate in the downward tubetemperature but fast in prolonging the investment return period. is as the initial temperature declining, the changes andofpressure in the temperature buried tube thesimulated. upward tube. Thesoil effect of heat transfer in upward tube is better.ofAtthe therefrigerant same time,temperature the influence the soil initial The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand are smaller.The And thesoil changes oftemperature the soil temperature field with theof running time the different depth of theisinborehole areoftube also is simulated. as district the initial declining, the(Portugal), changes the used refrigerant temperature and pressure the buried forecast. of Alvalade, located in Lisbon was asand a case study. The district consisted 665 simulating simulation show that the temperature around thescenarios buried decreases operating are smaller.studied. Andvary theThe changes of theresults soil temperature with the running time and thetube different depthalong ofhigh) thewith borehole aredistrict also buildings that in both construction period andfield typology. Three weather (low, medium, andthe three renovation scenarios developed (shallow, intermediate, To in estimate the gradient. error, obtained heat were time, and the temperature diffusion radius around the buried tubedeep). increases athe descent simulating studied. Thewere simulation results show that the temperature around buried tube decreases alongdemand with thevalues operating compared with results from a dynamic heat demand model, previously developed and validated by the authors. time, and the temperature diffusion radius around the buried tube increases in a descent gradient. The results that when weather change is considered, the margin of error could be acceptable for some applications Copyright © showed 2018 Elsevier Ltd. only All rights reserved. ©(the 2019 The Published by responsibility Elsevier Ltd.20% error inAuthors. annual demand was lower than weathercommittee scenarios considered). However, after introducing Conference onrenovation Applied Selection and peer-review under of for the all scientific of the 10th International Copyright © 2018 Elsevier Ltd. All the rights reserved. This is an open access article under CC BY-NC-ND license on (http://creativecommons.org/licenses/by-nc-nd/4.0/) scenarios, the error value increased up to 59.5% (depending the weather and renovation scenarios combination considered). th Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10 International Conference on Peer-review under responsibility the scientific committee of ICAE2018 10thupInternational Applied Applied Energy. The value of slope coefficient of increased on average within the range –ofThe 3.8% to 8% per Conference decade, thatoncorresponds to the Energy (ICAE2018). decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and Keywords: direct expansion ground source heat pump; vertical U-tube, boiling heat transfer; phase change heat transfer renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the Keywords: direct expansion ground source heat pump; vertical U-tube, boiling heat transfer; phase change heat transfer coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations.

© 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +086-312-752-2792; fax: +086-312-752-2440.

address:author. [email protected]. * E-mail Corresponding Tel.: +086-312-752-2792; fax: +086-312-752-2440. Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected]. 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. th Selection peer-review under responsibility the scientific 1876-6102and Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10 International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.596

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1. Introduction In the direct expansion ground source heat pump system, refrigerant is flowing in the buried tube heat exchanger and directly exchanging heat with the soil. There exists refrigerant phase change heat transfer in the buried pipe. And the refrigerant presents gas-liquid two-phase flow. In other words, there are two kinds of physical phenomena of phase change heat transfer and gas-liquid flow in the buried tube during the fluid flow process. In recent years, many researches on the vertical U-tube heat exchanger have been done. The temperature field of the single well and the influence radius and its influencing factors of the underground heat exchanger in a directexpansion ground-source heat pump system were obtained.[1] The thermal performance of direct expansion ground coupled heat pump system under cooling and heating conditions was obtained by testing and simulating the heat transfer performance of the direct thermal exchange U-tube under different hydrologic geology, initial soil temperature, climatic regions, etc.[2] A two-phase flow boiling heat transfer model of a vertical U-tube heat exchanger was established to simulated the 3-D heat transfer process from backfills to fluid under different inlet parameters and the flow evolution and heat transfer mechanism. The influence of fluid inlet parameters on outlet parameters was also tested.[3] The distribution parameter method was used to establish the mathematical model of the system.[4] The soil temperature field distribution, diffusion radius, heat flux, the temperature distribution around the tube group and the interaction between the tube groups under different operating modes, different soil types and different backfills with different thermal conductivity were simulated.[5] The previous researches often ignored the effect of pressure drop, gravity and friction in the U-tube. All the factors would change the evaporation pressure, and further affect evaporation performance. Considering the evaporation pressure change along the U-tube, a group of new models including the refrigerant flow equation, phase change heat transfer model in the vertical U-tube, heat transfer in and out of the borehole need to be established. Based on these models, the changes of temperature, pressure, dryness of refrigerant in the tube with the length of Utube in boiling heat transfer process are simulated and analyzed. 2. Phase change heat transfer model of refrigerant in vertical U-tube Refrigerant absorbs heat to evaporate in the vertical U-tube, as shown in Fig. 1. The state parameters, such as gasliquid component, temperature and pressure, are changing under the action of gravity, friction and inertia. Refrigerant is in the state of turbulent flow in the U-tube. It is assumed that heat transfer only existed in radial direction, but longitudinal heat transfer was neglected. Liquid refrigerant enters into the downward tube and extracts heat from the surroundings. The gravity and the inertial force are along the flow direction, the friction is in the opposite direction, as shown in Fig. 2(a). The gravity is dominated. The resultant force acting on the refrigerant is in the flow direction. Both the fluid pressure and the temperature increase along the downward tube. This causes liquid refrigerant to be vaporized uneasily. The dryness of fluid may increase little or even possibly reduce when the heat flux is small. Refrigerant then flows upward in the tube after it reaches the tube bottom and continues absorbing heat from the surroundings. The friction and the gravity are keeping in downward direction, while the inertial force is in upward direction, as shown in Fig. 2(b). The fluid pressure decreases under the combined action of friction and gravity. The refrigerant will vaporize easily and rapidly. The dryness of the fluid also increases greatly.

Fig. 1. Diagram of refrigerant flow and heat transfer in a vertical U-tube.

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(a)

3

(b)

Fig. 2. Schematic diagram of refrigerant force analysis in the U-tube: (a) downward tube; (b) upward tube

2.1. Refrigerant flow heat transfer model in vertical U-tube It is assumed that the gas-liquid two-phase of refrigerant is homogeneous when the refrigerant flows in the tube. The heat transfer process of refrigerant in tube can be described by a one-dimensional homogeneous flow equation. 1) mass conservation equation (1)  Gm   0  L    l (1   )   g

According to the principle of minimum entropy, the void fraction is obtained (Zivi, 1964). 1  1  x g 2/3 1 ( )( ) l x 2) momentum conservation equation Gm Gm 2 /  P 4 c       g g sin   L L di The formula can be rewritten as: G G 2 /  P 4 c     g g sin   ( m  m ) L di  L where θ is the fluid flow angle drifting off the horizontal line, the angle is 90° for upward tube and -90° for downward tube. 3) energy conservation equation h h Gm  qv    0 L 

(2)

(3)

(4)

(4a)

(5)

2.2. Pressure Drop of the Refrigerant The refrigerant pressure changes along the flow direction under the combined action of friction force, gravity and inertia force. Accordingly, the total pressure drop of the refrigerant consists of friction pressure drop, gravity pressure drop and acceleration pressure drop. [6] dP dPfr dPg g dPa (6)     dL dL dL dL Eq. (6) is actually corresponding to Eq. (4a). 1) friction pressure drop

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Friction pressure drop can be calculated and corrected using Lockhart-Martinelli formula for single-phase liquid or gas. [7] If Re is more than 4000, dPfr dP (7a)  l ,tt 2 ( )l dL dL If Re is less than 4000, dPfr dP (7b)   g ,tt 2 ( ) g dL dL The pressure drop of the single-phase liquid or gas can be calculated by dP  ( )l 4 fl (1/ di )Gm 2 (1  x)2 1/(2l ) (8a) dL dP ( ) g  4 f g (1/ di )Gm 2 x 2 1/(2  g )  (8b) dL Fluid friction coefficient (fl and fg) in single phase region is obtained by f  0.079 Re 0.25

（9）

The correction factor of liquid or gas is calculated by C 1 l ,tt 2  1  2 X tt X tt

(10a)

g ,tt 2  1  CX tt  X tt 2 X tt  (

(10b)

1  x 0.9 l 0.1  g 0.5 ) ( ) ( ) g l x

(11)

where C is a constant and depends on the flow regime of liquid or gas. When the flow regime is tt, C is equal to 20.[7] 2) gravity pressure drop Gravity pressure drop can be calculated by dPg g (12)   g  (1   ) l  g g dL 3) acceleration pressure drop Acceleration pressure drop can be calculated by 2   1  x  2 dPa x 2   1  x1  x 2   2   2   1  Gm 2   dL   l 1  2   g 2   l 1  1   g 1   Assuming that the inlet liquid was in saturated state, the above equation could be simplified as  1 dPa 1     Gm 2 x    g l  dL  

(13)

(14)

2.3. Convective heat transfer model between refrigerant and tube In convective heat transfer process, heat flux between refrigerant and tube can be expressed as  q  f , c1 Tt  T f



where q is heat flux, q=qv di/4. The refrigerant convective heat transfer coefficient calculated in the following two situations. 1) single phase flow zone

Nu  0.023Re0.8 Pr 0.4

(15) is different in tube at different phase state. It is usually

(16)

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5

2) two-phase flow zone Convective heat transfer coefficient in two-phase flow zone is calculated according to improved Kandlikar generalized correlation formula. [8]

i , f ,c1  C1 (Co)C2 (25Frl )C5  C3 ( Bo)C4 Ff l i ,l  G (1  x) di   i  0.023  m  l   0.8  1  x   g  Co       x   l  q Bo  Gm 

0.8

(17)

Prl 0.4 l di

(18)

0.5

(19) (20)

Gm 2 9.8l 2 di where Ffl is the fluid characteristic coefficient linked with the refrigerant. For R134a, Ffl is 1.63. [9] Frl 

(21)

Table 1. Relation between C1 - C5 and CO.

CO<0.65 CO>0.65

C1

C2

C3

C4

C5

1.136 0.6683

-0.9 -0.2

667.2 1058

0.7 0.7

0.3 0.3

3. Heat transfer model between vertical U-tube and soil In the direct expansion ground source heat pump system, heat transfer process between vertical U-tube heat exchanger and soil includes the heat conduction process through U-tube wall, backfill materials and soil. The thermal resistance of the tube and backfill material is much smaller than that of the soil. But the specific heat capacity of the tube and backfill materials is much bigger than that of the soil. So the heat conduction process in the drilling is usually regarded as quasi steady state, while the heat conduction process out of drilling is regarded as unsteady state. 3.1. Heat transfer model in drilling The heat transfer process in drilling is usually analyzed using a 2-D thermal model. The model considers heat transfer occurred only in radial direction. By analyzing the 2-D temperature field caused by the two branch tube, the thermal resistance between the fluid in the tube and the drilling wall is determined. In practical engineering, it is assumed that the U-tube is symmetrically installed in the drilling well. The tube pitch is 2D, as shown in Fig. 3. Heat transfer model in drilling is Td  Tt  qL Rc Thermal resistance from the tube inner wall to the drilling wall is expressed as  g  s dd (d d 2) 4  d 1  dd 1 Rc   ln  ln( o ) ln( )  ln( )   4 g  d o 4 D g  s (d d 2) 4  D 4  2t di where ql is the heat flux per unit buried tube length, ql  2 d i q .

(22) (23)

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dd Td 2D

q1

q2

do di

Tf1

Tf2 Backfill material Soil

Drilling well

Fig. 3. Cross-section schematic diagram of U-tube.

3.2. Heat transfer model of soil around the drilling The one-dimensional cylindrical heat transfer model is usually used to analyze the heat transfer process out of drilling. It is assumed that the soil was infinite medium with uniform constant properties; the drilling well had good contact with soil; there was a constant heat flux q between the buried tube and soil. According to the cylindrical heat transfer model, the soil temperature field around the drilling is assumed to be qL Ts (r , )  Ts ,0  G ( Fo , E ) (24) s where ts(r, τ) is the soil temperature at radius of r at τ time; t0 is the initial soil temperature; G(Fo, P) is named G function only related to r and τ, it is calculated by

G ( Fo , E )

1 2





0

2

e   Fo  1 d  J 0 E  )Y1 ( )  J1 (  )Y0 ( E  ) 2 2 J1 (  )  Y 12 (  ) 

a r ; E  ;   urd . 2 rd rd The drilling wall temperature Tb is calculated according to the fitting G function. [10] G ( Fo , E ) Ts , o  Td  qL s G ( F When E=1, the value of o ,1) is written as

(25)

where F0 is Fourier number, F0 

 0.89129  0.36081lg( Fo )  0.05508lg2 ( Fo )  3.59617103 lg3 ( Fo ) 

G( Fo ,1)  10

(26)

(27)

4. Simulation condition of boiling heat transfer in vertical U-tube The phase change heat transfer performance of R134a in vertical U-tube is simulated. The single U-tube is copper pipe with diameter of Φ12.7 × 1.0 mm, total length of 60 m. Thermal conductivity of copper pipe is 398 Wm-1K-1, the specific heat capacity is 393 Jkg-1K-1, and the density is 8900 kgm-3. The diameter of the drilling is 300 mm. Shank spacing of the U-tube is 200 mm, and it is symmetrically arranged in the drilling. The backfill material is sand mixture of 10% bentonite clay and 90% SiO2, whose thermal conductivity is 2.08 Wm-1K-1. The soil consists of compacted clay with 5% moisture content. Its thermal conductivity is 1.4 Wm-1K-1, the diffusion rate is 0.71 ×

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10-6 m2s-1 and the density is 1925 kgm-3. The soil initial temperature is 15 °C. R134a absorbs heat and evaporates in the tube. It is assumed that the inlet refrigerant temperature was 0 °C, the inlet pressure was 2.928 bar and the inlet mass flow rate was 0.018 kgs-1. It is also assumed that R134a reached saturated gas state at the outlet. The heat capacity of the buried heat exchanger is assumed as 3500 W. The heat flux per unit length of tube is assumed as 58.3 Wm-1. Based on the above conditions, the changes of the pressure, temperature and dryness of refrigerant along the tube length are simulated. Furthermore, the effects of soil initial temperature on the temperature and pressure of refrigerant are also studied. 5. Results and analysis 5.1. Refrigerant performance parameters in the vertical U-tube during boiling heat transfer In this section, the distribution of pressure, temperature and dryness of the refrigerant along the tube length during the boiling heat transfer are studied. The change of pressure, temperature and dryness in upward tube and downward tube are analyzed respectively. 1) distribution of refrigerant pressure along the tube length It is assumed that the entrance starts at 0 m. During boiling heat transfer, the change of the refrigerant pressure along the tube length is shown in Fig. 4. 360

管长 为60m

340

压力 (kPa)

320 300 280 260 240 220 200

0

10

20

30

40

50

60

管长 (m)

Fig. 4. Changes of refrigerant pressure along the tube length.

In this model, the depth of drilling in the vertical direction is 30 m. As the impact of gravity on the refrigerant is large, it cannot be ignored. It can be seen from Figure 4, when the refrigerant flows in downward tube, the direction of gravity is the same as the direction of the refrigerant flow. The friction and inertial force have an opposite direction to refrigerant flow, which hinders the flow of refrigerant. At the beginning of the tube, liquid refrigerant occupies a larger proportion. As gravity is the dominated force, the refrigerant pressure increases along the flow direction under the combined action of three forces. The refrigerant pressure increases rapidly at the beginning. As the refrigerant continues flowing on and evaporating, gas gradually occupies more proportion. The friction increases, the effect of gravity decreases and the refrigerant pressure change tends to be slow. After refrigerant enters the upward tube, the flow direction becomes vertical upward. Gravity, friction and inertia force are all in the opposite direction to the flow, so the refrigerant pressure decreases significantly in the upward tube. 2) distribution of refrigerant temperature along the tube length During boiling heat transfer, the change of the refrigerant temperature along the tube length is shown in Fig. 5.

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280

管长 为60m

278 276

温度 (K)

274 272 270 268 266 264 262 260

0

10

20

30

40

50

60

管长 (m)

Fig. 5. Changes of refrigerant temperature along the tube length.

It can be seen from Fig. 5, the refrigerant temperature slowly rises in downward tube and reaches the maximum at the bottom of the U-tube. This is because the ascension range of the refrigerant pressure is small in the downward tube and the evaporation temperature changes little. Then the refrigerant enters into the upward tube, the refrigerant temperature drops rapidly with the increase of the rising height. Because the pressure drops faster in the upward tube, the refrigerant evaporation temperature becomes smaller and it is easy to evaporate. 3) distribution of refrigerant dryness along the tube length When the refrigerant is boiling in the U-tube, the change of the refrigerant dryness along the tube length is shown in Fig. 6. the tube length is 60m

1.0

Dryness

0.8 0.6 0.4 0.2 0.0 0

10

20

30

40

50

60

Tube length(m)

Fig. 6. Changes of refrigerant dryness along the tube length.

The refrigerant enters into the downward tube in a saturated liquid state at the beginning. The heat transfer coefficient is small on the refrigerant side. As the refrigerant flows in the tube, the refrigerant pressure and evaporation temperature both increase. It is difficult for refrigerant to evaporate. So the dryness changes little. It can be seen from Figure 6, the refrigerant dryness in the whole downward tube increases by only 0.3. However, after the refrigerant flows upward, the refrigerant pressure and evaporation temperature decrease obviously, and liquid refrigerant rapidly changes into gas. The phase change speed accelerates with the increase of the rising height. At the exit, the refrigerant is completely gasified and the dryness reaches 1.0.

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5.2. Influence of initial soil temperature on refrigerant temperature and pressure Assuming all the simulation conditions kept unchanged except for the soil initial temperature changing from 15 °C to 13 °C, the change of refrigerant temperature and pressure in the tube is studied on the condition of boiling heat transfer. Soil initial temperature directly affects the design length of the buried tube. When soil initial temperature is at 15 °C, the design length of the buried tube is 60 m. But the length of the buried tube needs to be 68 m when the soil initial temperature reduces to 13 °C, because the temperature difference between soil and refrigerant reduces.

Fig. 7. Temperature distribution along the tube under different soil temperature

. Fig. 8. Pressure distribution along the tube under different soil temperature conditions.

The temperature and pressure distribution at different depths of the tube are presented in Fig.7 and Fig. 8 under the two kinds of soil temperature. The inlet position and the outlet position are regarded as at 0 m. It can be seen from Fig. 7 and Fig. 8, when the temperature difference between soil and refrigerant decreases, the refrigerant phase change goes on slowly in the buried tube. In downward tube, the proportion of liquid refrigerant is large, so the gravity effect is large. The refrigerant pressure increases greatly. The evaporation temperature is high,

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so the refrigerant evaporates more difficultly. When the soil temperature decreases, the refrigerant temperature and pressure drop remarkably in upward tube. 6. Conclusions The models of boiling heat transfer process in the vertical U-tube are established firstly in this study. Based on the models, the changes of the refrigerant parameters along the length of the tube are simulated and analyzed. The simulation results show that the pressure and temperature of refrigerant rise in the downward tube, while the pressure and temperature of refrigerant decline rapidly in the upward tube. So the evaporation keeps slow rate in the downward tube but fast rate in the upward tube. The initial soil temperature affects the tube length. As the soil initial temperature is declining, the buried tube needs lengthening, the changes of the refrigerant temperature and pressure are remarkable due to the effects of gravity and friction. Acknowledgements The authors are grateful to the financial support by Natural Science Foundation of Hebei Province in 2014 (E2014502123). References [1] Jia shaoqiang. Experimental study of direct expansion type ground source heat pump and analysis of underground heat transfer system [D]. Hunan University, 2008. [2] Gao yuefen. Study on performance and regional adaptability of direct - expansion ground source heat pump system[D].North China Electric Power University, 2013. [3] Zhaohong. Direct expansion soil source heat pump underground heat exchange system of two-phase flow heat transfer research[D].Shenyang Architecture University, 2012. [4] Cao xiaolin, Wang fangfang, Chenhui, Cao shuangjun, Zengwei. Theoretical and experimental study on direct - expansion ground source heat pump system[J].Journal of Central South University (Science and Technology), 2012,02:738-742. [5] Zhao honglei. Research on Heat Transfer Simulation of Direct - expanding Ground - tube Heat Exchanger[D].North China Electric Power University, 2013:66. [6] American Society of Heating, Refrigerating and Air-conditioning Engineers, Inc. 2009 ASHRAE Handbook-Fundamentals (SI), 1791 Tullie Circle, N.E., Atlanta, GA 30329 [7] R.W. Lockhart, R.C.Martinelli. Proposed correlation of data for isothermal two-phase, two-component flow in pipes[J]. Chem. Eng. Pro., 1 (1949), pp. 39-48 [8] Kandlikar S.G. A General Correlation for Saturated Two-Phase Flow Boiling[J]. Heat Transfer Inside Horizontal and Vertical Tubes. 1990. [9] Yan qisen, Shi wenxing, Tian changqin. Refrigeration Technology for Air Conditioning[M]. Beijing, China Construction Industry Press, 2011 [10] Klein S. A. EES Engineering Equation Solve,F-chart software. 2000.