Simulation of a geothermal heat pump with non-azeotropic mixture

Applied Thermal Engineering 23 (2003) 1515–1524 www.elsevier.com/locate/apthermeng

Simulation of a geothermal heat pump with non-azeotropic mixture P.C. Zhao, G.L. Ding *, C.L. Zhang, L. Zhao Department of Power and Energy Engineering, Institute of Refrigeration and Cryogenics Engineering, Shanghai Jiaotong University, No. 1954, Huashan Road, Shanghai 200030, PR China Received 14 November 2002; accepted 5 April 2003

Abstract The paper sets up a simulation of a geothermal heat pump with a non-azeotropic mixture. The model is modified and verified with experimental data. The results of the simulation show that the systematic model can predict the performance within
12% of the experimental data. As a result, some improvements can be provided on the basis of the simulation platform. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Non-azeotropic; Geothermal heat pump; Model; System; Optimization

1. Introduction Geothermal heat pumps can aid in the conservation of energy and reduce heat pollution. The system is like most of other heat pumps except the different working conditions. For example, in Ref. [2], the geothermal heat pumps has condensation temperature from 80 to 100 °C and evaporation temperature from 25 to 35 °C. So far, preliminary experimental and theoretical researches [1–3] have been done. Mathematical simulation has been proved to be an effective approach to analysis. If a model can be arranged to simulate the system, and some performance analysis and optimization can be done on the basis of the model, then the periodic time and the cost to develop a practical system can be greatly shortened. This paper continues the researches [2] and aims at simulating the system. The geothermal heat pump has the following four major components: a hermetic compressor, a plate condenser,

*

Corresponding author. Tel.: +86-21-62932110; fax: +86-21-62932601. E-mail address: [email protected] (G.L. Ding).

1359-4311/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S1359-4311(03)00102-9

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Nomenclature Ac b Bo Ch cp Dh f F G h ifg k pb Pr q00w Q Re T U V W x

cross-sectional area of plate exchanger (m2 ) channel spacing (m) boiling number charge of working fluid (kg) heat capacity at constant pressure (J kg1 K1 ) hydraulic diameter of plate exchanger (m) friction factor heat transfer area (m2 ) mass flux (kg m2 s1 ) heat transfer coefficient (W m2 K1 ) enthalpy of vaporization (J kg1 ) thermal conductivity (W m1 K1 ) pressure provided by temperature sensing bulb (Pa) PrandtlÕs number imposed wall heat flux (W m2 ) heat transfer rate (W) Reynolds number temperature (K) overall heat transfer coefficient (W m2 K1 ) theoretic compressor displacement (m3 s1 ) compressor input power (W) vapor quality (kg kg1 )

Greeks l dynamic viscosity (Pa s) k volumetric efficiency of compressor q density (m3 kg1 ) indicated efficiency of compressor gi motor efficiency of compressor gmo mechanical efficiency of compressor gme acceleration pressure drop (or pressure rise) (Pa) Dpa friction pressure drop (Pa) Dpf gravity pressure drop (Pa) Dpg DpTP pressure drop in two phases (Pa) static pressure provided by the TEV spring (Pa) Dp P st DpNi pressure drop in connection pipe and interface (Pa) v kinematic viscosity (m2 s1 ) d thickness of plate (m) Subscripts ave average

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com compressor cond, c condenser crit critical eq equivalent evap,e evaporator l liquid phase in inside out outside r working fluid sat saturate TP two phase val valve w water wall plate wall

a thermostatic expansion valve (TEV), and a plate evaporator, and uses mixture refrigerant as working fluids. First, all component models are set up from the viewpoint of system, and then they are concatenated to the entire system.

2. Systematic models The objective of the system model is to acquire steady performance data, given the construction parameters, inlet water temperature and flow in the two exchangers. 2.1. The compressor model From the viewpoint of a systematic algorithm, inputs to the compressor model are inlet state parameters (temperature and pressure) and back pressure while the outputs are outlet state parameters and flow. Flow model mcom ¼ kVcom qin

ð1Þ

The volumetric efficiency of a compressor is represented as the linear function of pressure ratio regressed though experimental data.   Pc;in þ 0:8133 ð2Þ k ¼ 0:0548 Pe;out Compressor power W ¼

mcom ðhcom;out  hcom;in Þ gi gmo gme

ð3Þ

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where gi , gmo and gme are the indicated efficiency, motor efficiency and mechanical efficiency, respectively. Their values are 0.8, 0.85 and 0.95, respectively. 2.2. The thermostatic expansion valve model Inputs to the TEV model are inlet state parameters (temperature and pressure) and back pressure while the outputs are outlet state parameters and flow. Flow model [4] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð4Þ mval ¼ Cval qc;out ðpc;out  pe;in Þðpb  pe;in  Dpst Þ where Cval is the characteristic constant of TEV (dependent mainly on the throttling section). 2.3. The plate condenser Plate condensers are getting increasingly more attention because of their compact construction and high heat efficiency. Plate condensers have been used in the refrigeration field for a relatively short period, and so far their heat transfer research with refrigerants is less done. A onedimensional, distributed parameter model has been set up in order to consider non-linear variation of properties in the two-phase area. The flow is countercurrent. Inputs to the model are pc;in , Tc;in , mcom , Tc;w;in and mc;w while the outputs are pc;out , Tc;out and Tc;w;out . Like other patterns of heat exchangers, the basic model includes the following three equations: As Fig. 1 shows, heat transfer dQ through infinitesimal area dF is ð5Þ dQ ¼ U ðTr  Tw Þ dF Hot fluid (refrigerant mixture) ð6Þ

dQ ¼ mr cp;r dTr Cool fluid (water) dQ ¼ mw cp;w dTw

ð7Þ

Fig. 1. Schematic of counter-flow heat transfer.

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U is the total heat transfer coefficient 1 1 d 1 ¼ þ þ U hr k hw

ð8Þ

The heat transfer model and pressure drop model will be discussed in detail in the Sections 2.3.1–2.3.4. The heat transfer coefficient model includes the two-phase heat transfer coefficient model, the single-phase heat transfer coefficient model and the heat transfer model of water. The pressure drop model includes the two-phase pressure drop model and the single-phase pressure drop model. The pressure drop model does not include that of water, because the pressure drop is relatively small and has little influence on systematic performance. 2.3.1. Heat transfer coefficient in two-phase area After comparing with the experimental results, YanÕs model [5] is recommended for plate condenser. Nu ¼

hr Dh 0:33 ¼ 4:118Re0:4 eq Prl kl

ð9Þ

where the equivalent Reynolds number is Reeq ¼

Geq Dh ll

Geq is the equivalent mass flux "  0:5 # ql Geq ¼ G 1  x þ x qv

ð10Þ

ð11Þ

As for the mixtures, there are two kinds of vapor quality: mass quality and molar quality. The x in Eq. (11) is mass quality and considers the influence of condensed liquid film. The influence of vapor pressure on heat transfer is taken into account by the term ðql =qv Þ. 2.3.2. The heat transfer coefficient in the single-phase area Nu ¼ 0:2121Re0:78 Pr0:33

ð12Þ

The model not only applies to single-phase refrigerants but also to liquid water. 2.3.3. The pressure drop in the two-phase area The pressure drop in plate condensers is usually large because of their compact configuration. The working fluid studied is a mixture with about a 20 °C temperature glide. The findings show that a 2 °C deviation of outlet temperature will result if the pressure drop is ignored. The total pressure drop in plate condenser is X DpNi ð13Þ DpTP ¼ Dpf þ DPg þ DPa þ where Dpf accounts for the majority of the total pressure drop (about 93–99%). YanÕs model [5] is recommended here.

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fTP

 0:8 Dpf Dh 0:0467 0:4 0:5 pave ¼ 2 Re Bo ¼ 94:75Reeq 2G vm L pcrit

where Bo is the boiling number q00 Bo ¼ w Gifg

ð14Þ

ð15Þ

2.3.4. The pressure drop in the single-phase area The pressure drop model in the single-phase area is not involved in the literatures previously mentioned. Therefore, the water model [6] is introduced to the refrigerant mixture f ¼ 2956:1Re0:12

ð16Þ

2.4. The plate evaporator The basic models are like those of the plate condenser. The flow is also countercurrent. Inputs of the plate evaporator model are pe;out , Te;out , mcom , Te;w;in and me;w while the outputs are pe;in , Te;in and Te;w;out . 2.4.1. The heat transfer coefficient in the two-phase area [7] hr;sat ¼ hr;l ð88Bo0:5 Þ

ð17Þ

where hr;l is the non-boiling coefficient of heat transfer with full liquid, which is regressed through experimental data with full liquid.    0:14 kl lave 0:78 0:33 hr;l ¼ 0:2092 Re Pr ð18Þ Dh lwall Note that the viscosity modification factor ðlave =lwall Þ can be ignored because the infinitesimal unit can be divided into very small and then lave is nearly equal to lwall . 2.4.2. The heat transfer coefficient in the single-phase area Eq. (18) is adopted as the heat transfer coefficient model in the single-phase area. 2.4.3. The pressure drop in the two-phase area The total pressure drop in plate evaporator is X DpNi DpTP ¼ Dpf þ Dpg þ Dpa þ

ð19Þ

As reported in the literature [7], Dpf covers more than 95% of the total pressure drop, so the accuracy of the Dpf model defines the accuracy of the total pressure drop. The friction factor is fTP ¼ 

Dpf Dh ¼ 1444600Re1:25 eq 2G2 vm L

2.4.4. Pressure drop in the single-phase area Eq. (16) is adopted as a pressure drop model in the single-phase area.

ð20Þ

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2.5. The charge model The brazing plate exchanger has a narrow and wavy construction and flow model between plates is highly turbulent, so the mixture can be treated as homogeneous across the plates, and then the charge model can also be homogeneous. Z Ch ¼ qAc dL ð21Þ As for the charge model in the hermetic compressor, if the refrigerants inside the hermetic compressor are only in the gaseous state, the whole refrigerant gas can be treated as heated gas at some temperature; if the state is two-phase, the charge model will be difficult to set up. In the work, the relationship for the charge model in two phases is regressed from the experimental data. It adopts the following form: Chcom ¼ f ððxin þ xout Þ=2Þ

ð22Þ

if ðxin þ xout Þ=2 < 0:88, Chcom ¼ 0:1695ðxin þ xout Þ=2 þ 0:8430

ð23Þ

if ðxin þ xout Þ=2 > 0:88, Chcom ¼ 13:099ðxin þ xout Þ=2  10:29

ð24Þ

3. Systematic algorithms Systematic algorithms are designed to acquire a systematic steady performance, given systematic structural parameters and inlet water temperature and mass flow in the two exchangers. To validate the model expediently, the working fluid in the model is the same as that in the experiment [2], that is R290/R123,50%/50%. The mixture of working fluid (R290/R123, 50%/50%) studied here has a large temperature glide (about 20 °C), and then distributed parameter model needs to be built to consider non-linear variation of properties along the exchangers. In the paper, REFPROP 6.1 [8] is adopted to calculate thermodynamic properties of the working fluid. The detailed algorithms are followed (see Fig. 2): (1) assume the following three parameters, pc;in , pe;out and Te;out ; (2) calculate the compressor model from the above three parameters to get the compressor mass flow mcom , input power W and compressor outlet state; (3) calculate the condenser model, given pc;in , Tc;in and mcom to get the condenser outlet state; (4) calculate the evaporator model, given mcom , pe;out and Te;out to get the evaporator inlet state (pe;in and Te;in1 ); (5) calculate the TEV model from pc;out , Tc;out and pe;in to get mval and Te;in ; (6) compare the two mass flows mcom and mval , if the error is out of the set range, return to step 1 to adjust pc;in , or continue; (7) compare the two evaporator inlet temperatures Te;in1 and Te;in2 , if the error is out of the set range, return to step 1 to adjust Te;out , or continue; (8) add up all charge in all of the components, and compare the calculated value with the experimental value, if the error is out of the set range, return to step 1 to adjust pe;out , or continue; (9) output systematic performance parameters.

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Fig. 2. Chart of systematic algorithms.

Before designing the systematic algorithms, the relationship between assumed parameters and adjusted parameters should be reviewed to determine proper algorithms. A dichotomizing search can be used for the solution.

4. Validation of model For the purpose of checking the accuracy of the systematic model, the model results are compared with the experimental data. The geothermal heat pump shown in Fig. 3 is a single stage vapor compression system, which consists of three loops: the evaporator water loop, the condenser water loop, and the working fluid loop. Condenser (4) and evaporator (10) are plate-type heat exchangers with a heat transfer area of 0.76 m2 .

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Fig. 3. Schematic of the experimental apparatus.

A computer is used for data acquisition with the aid of 8 temperature sensors and 4 pressure sensors. The temperature sensors are T-type thermocouples calibrated at 0–90 °C by using a standard water bath, and the accuracy is found to be 0.1 °C. Thermocouple wires are isolated from surrounding noises. The accuracy of the pressure sensors is 1.0 kPa, and the effective measurement range is 0–2500 kPa. The accuracy of the flow meter is 0.01 kg/s. The function of the geothermal heat pump is not only to provide winter heating, but also to lower the temperature of discharged geothermal water for pollution prevention. Therefore, the main interests are the following parameters: COP, thermal load, condenser outlet water temperature ðTc;w;out Þ and evaporator outlet water temperature ðTe;w;out Þ. Some comparisons are given in Table 1 to show that the systematic model has a desirable accuracy and can serve as prediction model.

Table 1 Comparison between simulation model and experimental results COP

Thermal load (W)

Tc;w;out (K)

Te;w;out (K)

Model

Data

Error %

Model

Data

Error %

Model

Data

Error %

Model

Data

Error %

2.52 2.67 3.04 2.84 3.38 3.28 3.99 4.12

2.79 2.88 3.08 2.73 3.19 3.10 3.73 3.69

)9.9 )7.0 )1.3 4.0 6.0 5.8 7.0 11.6

5328 5476 5605 5491 5840 5826 6194 6289

5597 5809 5905 5343 5614 5523 5969 5907

)4.8 5.7 5.1 2.8 4.0 5.5 3.8 6.5

351.1 347.8 343.2 349.4 340.0 345.7 335.3 332.5

351.8 348.4 344.0 348.6 339.5 344.3 334.7 331.8

)0.7 )0.6 )0.8 0.8 0.5 1.4 0.6 0.7

306.7 307.0 304.3 304.7 303.9 304.8 303.8 303.4

306.9 306.6 303.9 304.1 303.3 303.7 303.0 303.0

)0.2 0.4 0.4 0.6 0.6 1.1 0.8 0.4

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5. Conclusions The steady-state simulation model for the geothermal heat pump with non-azeotropic mixture is presented here. The model can predict performance within
12% of the experimental data. WhatÕs more, the systematic model can serve as a basis for improvements to the system.

Acknowledgement This research is supported by the State Key Fundamental Research Program of China under the contract no. 2000026309.

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