Applied Thermal Engineering 23 (2003) 49–64 www.elsevier.com/locate/apthermeng
Influence of reversing methods on the performance of a reversible water-to-water heat pump L. Rajapaksha, K.O. Suen
*
Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK Received 20 March 2002; accepted 29 August 2002
Abstract Steady state performance of a reversible water-to-water heat pump are analysed using a computer simulation. The simulation adopts a distributed parameter modelling approach. The operation of the system and its components are described based on the principles of mass and energy conservation. The heat exchanger models are designed especially to address issues related to refrigerant mixture, such as two-phase property non-linearity and temperature glide, using an element by element analysis. The use of two refrigerants, R407C and R134a, are considered. The study emphasis on the influence of the heat exchanger volume ratio on the performance of both forward and reversed modes of the cycle. In the case of mixture application, the effects of glide mismatch resulting from reversing are investigated. Three different reversing methods are examined. Two of these methods use four-way reversing valve and the third method involves redirection of heat transfer fluid between the condenser and the evaporator to implement change of mode. The third method appears to be the best reversing technique for both refrigerants considered. With all the three methods, in the reversed mode, the R407C system performs better than the R134a system over a large range of volume ratios. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Simulation; Reversible heat pumps; Temperature glide matching; System performance
1. Introduction Reversible heat pump, whether using pure refrigerant or mixtures, can be designed to deliver specified duties in a selected mode (heating or cooling) of operation. When using a refrigerant mixture, the design can further incorporate TG matching in heat exchanger sizing to obtain
*
Corresponding author. Tel.: +44-20-7679-3926; fax: +44-20-7679-3926/7388-0180. E-mail address:
[email protected] (K.O. Suen).
1359-4311/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 2 ) 0 0 1 3 6 - 9
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Nomenclature A COP dT f G h HTC HTF m n NRV Nu P Pr Q Re RHP T TEV TG U v Vr W w x y z
area (m2 ) coefficient of performance temperature difference (°C) friction factor mass flux (kg/s m2 ) enthalpy (kJ/kg) heat transfer coefficient (W m2 /K) heat transfer fluid mass flow rate (kg/s) polytropic index, number of components non-return valve Nusselt number pressure (Pa) Prandtl number capacity (kW) Reynolds number reversible heat pump temperature (°C) thermostatic expansion valve temperature glide (°C) overall heat transfer coefficient (W m2 /K) specific volume (m3 /kg) volume ratio (refrigerant side volumes; condenser/evaporator) power absorbed by compressor (kW) mass (kg) vapour quality mass fraction direction of flow
Subscripts 2ph two-phase related bub bubble point con condenser related cx cross section del compressor delivery side evp evaporator related fg latent quantity go vapour only i element or component number in refers to inlet liq liquid phase
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lo out P Ref sc sp suc vap Greek h b a Ddb / q /2 c g
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liquid only refers to exit constant pressure refrigerant related subcool single phase compressor suction side vapour phase letters gradient of ÔdT Õ along heat exchanger liquid mass transfer coefficient void fraction glide temperature difference heat flux (W/m2 ) density (kg/m3 ) two-phase multiplier isentropic index isentropic efficiency
improved performance [1]. However, RHP designed to deliver a specified duty at a certain COP in a selected mode is expected to exhibit a variation of performance, when reversed, due to changes in surrounding and operating conditions, and in the case of refrigerant mixtures, changes in glide match conditions. These changes affect the heat transfer process in the condenser and evaporator, and the mass flow rate through the compressor causing variations in delivered capacities. Method of reversing, type and flow configuration of heat exchangers contribute in different degrees in this regard. Changing the mode of operation of RHPs can be implemented by using a four-way reversing valve (Fig. 1). With certain types of heat exchangers, such as concentric-tube, this method would result in changes of heat exchanger flow configuration, say, from counter flow to parallel flow. However, this can be avoided by simultaneously reversing the flow directions of HTF. Another method is to switch the HTF flows between two heat exchangers, thus maintaining the original flow configurations. Previous work, for examples Jung et al. [2] and Stefanuk et al. [3], primarily looked at the performance in one mode of heat pump operation, studying the thermodynamic aspects of different working fluids, etc. This paper presents an investigation into steady state performance emphasising on the reversed mode operation of a water-to-water heat pump. Three reversing methods are examined for their influence on the reversed mode performance when using 407C (a ternary mixture) and R134a (a pure refrigerant); the influences of heat exchanger sizing are also studied. In the case of mixture application, the effects of glide mismatch resulting from reversing are investigated with individual reversing method.
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Fig. 1. Schematic of the heat pump systems.
2. System configuration and methods of reversing The system considered in this study, as shown in Fig. 1, is a single stage vapour compression water-to-water RHP. It communicates with the space being heated or cooled (load) via the HTF (water) loop in concentric-tube heat exchangers. When using a four-way reversing valve two techniques can be considered. The first technique is to redirect refrigerant flow between condenser and evaporator while leaving HTF directions unchanged. The condenser in designed (or forward) mode then becomes the evaporator in the
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reversed mode and vice versa. The second technique is reversing the directions of HTF too, thus preserving the original counter-flow arrangement. A third method is to switch the heating HTF loop over to evaporator, while the HTF flow of evaporator (in heating mode) is directed to the condenser, but still maintaining the designed heat exchanger flow configuration. In this paper, the notations RC1, RC2 and RC3 are used to refer to the above three methods respectively. The system in the study was initially designed, using either R407C or R134a, to provide a given heating duty, where heat exchangers for the mixture system include glide matching considerations. Even under similar load and operating conditions, the heat exchanger sizes for mixture systems could vary significantly over that of a pure fluid system [4]. The change of performance from heating to cooling when using two refrigerants is compared.
2.1. Glide matching considerations Zeotropic mixtures offer the opportunity to match the temperature profiles of refrigerant and the HTF in counter-flow configuration during condensation and evaporation, thus reducing irreversibility in heat transfer and improving system performance [1,5]. To achieve this, the refrigerant mixture should have linear two-phase thermal properties. Accordingly, a main requirement for glide matching of a refrigerant mixture with a HTF that exhibits linear temperature profile can be derived from first principles as (see Ref. [6] for example):
oh oT
¼ constant
ð1Þ
P ;Ref
Evaluation with Eq. (1) for R407C, condensing at 1800 kPa and evaporating at 600 kPa respectively, suggests the requirement for glide matching is met within around 5%. Therefore, for the purpose of this investigation, it is reasonable to assume that R407C exhibits linear property variation during phase change process. Hence, the temperature of R407C at any given vapour quality, xi , during evaporation or condensation can be estimated using the following equation: TRef;i ¼ Tbub þ ðTGxi Þ
ð2Þ
Perfect glide matching can only be obtained at one specific HTF flow rate that is estimated based on heat transfer within the phase-changing section. This results in a constant temperature difference ðdT Þ between the refrigerant and the HTF along the heat exchanger. The influence of HTF flow rate on glide matching can be shown in Fig. 2, which presents three cases of different flow rates, plotting dT versus vapour quality. When the HTF flow rate for obtaining TG match is not available, under or over glide condition occurs. A horizontal line (case a) represents perfect TG match. For cases b and c, the inclinations hb and hc correspond respectively to a certain degree of mismatch due to lower (i.e. dT is decreasing along the length, relatively to the cold end of the HTF) and higher flow rates (i.e. dT is increasing along the length) than that of case a. A large gradient implies a higher mismatch that generally leads to poor performance.
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Case c mc HTF > ma HTF
dT/ degree C
54
θ
Case a
Case b mb HTF < ma HTF
θ
vapour quality (or heat exchanger length) Fig. 2. Degree of TG match (relative to the cold end of HTF).
3. Formulation of analysis 3.1. Heat exchanger and compressor models Both the condenser and the evaporator use a phase-wise calculation approach [3,7,8]. Singlephase sections are considered as single elements of average fluid properties. The phase-changing section is divided into a number of small elements. Evaluation of thermal quantities in each element are based on local pressure, temperature and refrigerant state. Heat transfer within a given two-phase element can be estimated using the following equation (Eq. (3)): DQðiÞ ¼ UðiÞ DAðiÞ DTðiÞ
ð3Þ
The continuity of fluid properties across the phase boundaries, for example from desuperheating to condensing in condenser, is maintained by checking the refrigerant state, enthalpy and temperature at the entry and exit of each element along the heat exchanger. When sizing the condenser and the evaporator, stream to stream temperature differences, dT s, are specified. To obtain a range of different volume ratios, evaporator dT s are varied while those for the condenser are kept at around 10 °C. The term Ôvolume ratioÕ denotes the ratio of the refrigerant side volume of the condenser to that of the evaporator in the designed mode. With pure fluids, the HTF flow rates are set to match the same load and the same temperature change of HTF as that of the mixture system. For TEV, isenthalpic expansion is assumed and the superheat at evaporator exit is specified. Single-phase HTCs for refrigerant are estimated using the correlation proposed by Petukhov [9] (Eq. (4)) Nu ¼
ðf =8ÞRePr 1:07 þ 12:7ðf =8Þ1=2 ðPr2=3 1Þ
ð4Þ
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To estimate local values of condensation HTC for both mixture and pure refrigerants, the following empirical correlation by Bivens and Yokozeki [10] is selected, (5). In which the HTCi represent the HTC of ith component of the mixture, obtained using ShahÕs correlation [11] " c #1=c n X yi ð5Þ HTC ¼ ðHTCi ÞF i¼1 F ¼ 0:78738 þ 6187:89G2 c ¼ 0:85 0:014545ðDdb Þ;
for G > 160
c ¼ fð0:10676 þ 0:12483 loge GÞð1:25 0:04545Ddb Þg;
for G 6 160
For evaporation, the following correlation developed by Collier and Thome [12] is used (Eq. (6)) in which HTCgo and HTClo are HTCs when only one phase is present, which are estimated using Dittus–Belter [13] correlation. HTCideal is obtained using transport properties of refrigerant mixture in a pure refrigerant boiling correlation [12] as shown in (6) !#1 " HTC HTCideal / ¼ 1þ ð6Þ Ddb 1 exp HTCideal qliq hfg b / 1=2
HTCideal ¼ hlo ½A2:2 B2
0:01
A ¼ ð1 xÞ þ 1:2x0:4 ð1 xÞ
qliq qvap
!0:37
8 !0:67 9 = < qliq HTCgo 0:01 0:7 B¼ x 1 þ 8ð1 xÞ ; : HTClo qvap In single-phase flow, the frictional pressure gradient is estimated using the standard pressure drop relationship applicable for pipe flow [14]. For two-phase frictional pressure drop, a twophase multiplier proposed by Friedel [15] is used and the pressure drop is estimated using following equation (7): dP dP ¼ /2 ð7Þ dz 2ph dz sp Compression is represented by a polytropic process. A reciprocating compressor is assumed in sizing the compressor displacement rate, which is necessary to obtain refrigerant mass flow rate during iterations at different evaporator pressures. The compressor work can be estimated as follows: Qevp ¼ mRef ðhout hin Þevp
ð8aÞ
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n W ¼ Psuc vsuc n1
"
n 1 ðc 1Þg ¼ n c
Pdel Psuc
ðn1Þ=n
½1
# 1 mRef
ð8bÞ
ð8cÞ
Required refrigerant properties are estimated by internally calling up property subroutines of NIST database 23, commonly known as REFPROP [16]. 3.2. System refrigerant charge The mass of the refrigerant in the system at design stage is estimated by separating the condenser and the evaporator into sections according to refrigerant phases. Two-phase quantity is derived using the appropriate void fraction correlation (Humark void fraction model [17,18]). The amount of liquid and vapour masses could be estimated for a tube length ÔLÕ as Z L adl ð9aÞ wvap ¼ qvap Acx 0
wliq ¼ qliq Acx
Z
L
ð1 aÞ dl
ð9bÞ
0
where a (¼ Avap =Acx ) is the void fraction at a given cross section, which is generally some function of vapour quality, refrigerant properties, local pressure and mass flux or heat flux. Estimated refrigerant content in the evaporator and condenser together with the quantity in the liquid line gives the total system charge at the design stage. However, for simplicity the charge in liquid line is not considered in this investigation. 3.3. Simulation strategy 3.3.1. Design and operation in heating mode The condenser and the evaporator areas (Acon , Aevp ) are sized to match the given design heating duty based on certain specified inlet temperatures of HTF and dT s. The cycle operation is simulated using component models described earlier. When system energy balance (that meets the required capacity) is met, system charge is estimated, and the compressor is sized to match the refrigerant flow rate. 3.3.2. Operation in reversed mode (cooling) Using the solution logic given in Fig. 3, the iteration starts by seeking an approximate evaporating pressure. The refrigerant mass flow rate is then estimated based on the compressor displacement rate. The energy and refrigerant charge balances of the system are then checked against certain specified margins. It is important to note that in developing the algorithm, the system charge in the forward mode must be conserved when the mode is reversed. If the balance conditions of this approximate system (energy, area and refrigerant charge) indicate possibility of
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Start Check avialable forward system design parameters Assign heat exchanger functions for selected reversing method Set HTF flow configurations for selected reverseing method Assign values for T HTF.in.con, T HTF.in.evp mHTF.con & m HTF.evp
Estimate: P con & Pevp
Adjust P con & P evp
Estimate enthalpy values at state points
Run Compressor module: Get m Ref
Run Evaporator module: Get Q evp
No
Adjust dTsc
Run Condenser module: Get Q con
System energy & Area balance satisfied ?
Yes Estimate: System charge
System charge: Estimated = Designed ?
No
Yes Write operating parameters and element data modules Stop
Fig. 3. Solution logic for reversed cycle.
convergence, the iteration is continued with refined margins. If any of the three balances is not met, the iteration starts again with another guess of evaporator pressure.
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4. Results and discussion 4.1. Performance in designed mode Fig. 4 presents the heating COPs of R407C and R134a heat pumps, both delivering the same capacity of 7.6 kW, as a function of heat exchanger volume ratios. The volume ratio (Vr ) was varied by changing the evaporator temperature difference, hence its volume and area, while keeping the condenser volume constant. For a given heating load, this also results in a small change in the dT in the condenser. The corresponding evaporator dT s (for R407C) are also shown in Fig. 4. Some selected system design parameters are given in Table 1. At present, only a medium output temperature of 41.5 °C can be obtained when glide match with R407C is employed. To get a higher output temperature with glide match, another refrigerant mixture (for example R32 þ R134a) could be used. Throughout the considered range of Vr from 0.92 to 3.7 (the corresponding area ratio ranges from 0.41 to 1.62), R407C and R134a heat pumps respectively exhibit a variation of about 23%
Fig. 4. Designed (heating) mode COP versus volume ratio or area ratio.
Table 1 Design parameters of R407C and R134a heating systems Parameter
R407C system
R134a system
Capacity (kW) Pipe diameters: inner and outer (mm) HTF inlet and exit temperatures of condenser (°C) HTF inlet and exit temperatures of evaporator (°C)
7.60 20.0/35.0 35.0/41.5 14.0/(9.4–9.8)
7.60 20.0/35.0 35.0/41.5 14.0/(9.0–9.4)
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and 20% in COP. As expected a higher COP can be achieved at the expense of using a larger evaporator size, therefore smaller Vr and dT . Over the range, R407C system outperforms R134a system by an average of 10%; the improvement is credited mainly on glide matching. A simulation exercise in which the glide effect in the heat exchangers are mathematically ‘‘suppressed’’ shows that the COP of the two systems are nearly the same at similar conditions (Fig. 4). When Vr increases from 0.92 to 3.7, the required compressor displacement rate for R407C and R134a increases about 40% and 45% respectively. The analysis indicates that the average overall HTC for R407C evaporators are about 10% lower than that of the R134a, whereas the condensing U values are similar in both cases. In addition, higher proportions of single-phase heat transfer area, leading to smaller heat transfer rate, for both evaporator and condenser are observed in R407C systems. The combined effects result in larger (by 30–40%) heat exchanger sizes for R407C, as compared to the R134a system. The compressor displacement rates for R407C systems are smaller than the corresponding R134a systems due to the higher suction vapour density of R407C. 4.2. Performance in reversed mode Performance evaluation of the two systems is based on both COP and the delivery capacity. When the operation mode is changed using a four-way valve, refrigerant flow within the evaporator is conveyed from the inner tube to the annulus while the opposite takes place in the condenser. This reduces the refrigerant mass flux in the reversed mode evaporator and considerably deteriorates the HTC and the performance. In addition, exchange of condenser and evaporator functions causes large variations in operating pressure levels when the two heat exchangers have considerably different heat transfer areas. 4.2.1. R134a system Fig. 5 represents the performance of the R134a system in cooling mode with the three reversing methods. All methods show reductions in COPs with increasing volume ratio, due to increases in pressure ratios, and RC3 outperforms the other two particularly at high Vr , though all of them offer less COP when compared to the design mode. For RC3, the increase in pressure ratio with Vr is relatively small. Higher performance of RC3 is due to the fact that it retains both the designed flow configuration and heat exchanger functions resulting in relatively small changes in operating conditions. As shown in Fig. 5, the cooling capacities of RC1 and RC2 improve while that of RC3 slightly deteriorates with increasing Vr . Over the range, the RC3 once again offers a higher capacity relative to the other two methods, particularly at low Vr . The evaporator U value and the inlet vapour quality of RC3 are respectively about 80% higher and 37% lower than that of RC1 and RC2, resulting in a significantly higher capacity difference at low Vr . An increase of evaporator inlet vapour quality with Vr (from about 0.28 to about 0.37 for RC3) combined with a small decrease in refrigerant mass flow rate (about 5.0% drop compared to 64% increase in other two methods) causes a slight decrease in capacity of RC3 across the range. On the other hand, RC1 and RC2 exhibit similar capacities regardless of Vr . In both methods, the increase of refrigerant flow with Vr improves the average evaporator U value by about 45%, leading to improved capacities at higher Vr .
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Fig. 5. Reversed mode (cooling) performance of R134a systems.
4.2.2. R407C system For R407C system, the observed trends (Fig. 6) are similar to that of R134a, showing a reduction of COP with Vr for all the three methods, and an increase in capacity with RC1 and RC2 as Vr increases. However, two major differences in the trends could be observed. First, there are appreciable differences in COP for the three methods at low Vr . RC3 in fact performs significantly better than RC2 for the entire range of Vr . RC2 has in turn performed well when compared to RC1 especially at low Vr . The difference in COP of RC1 and RC3 at low Vr can be explained in
8.0
COP or Capacity (kW)
7.0
6.0
5.0
RC1 RC2 RC3 Design (heating)
4.0
3.0
COP Capacity 2.0 0.5
1.0
1.5
2.0
2.5
3.0
3.5
Volume ratio
Fig. 6. Reversed mode (cooling) performance of R407C systems.
4.0
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relation to the degree of glide matching in evaporator and condenser. Secondly, although RC2 offers a higher capacity than RC1 at low volume ratios, the situation reverses at medium to high volume ratios due to the changes in pressure ratios. Figs. 7 and 8 show the normalised dT (normalised by dividing the temperature difference along the heat exchanger by the average difference) against vapour quality for the evaporator and condenser respectively at Vr ¼ 0:93. As shown in Fig. 7 even in design mode, setting a HTF flow rate to achieve a perfect TG match is not attainable. This is attributed to the fact that the HTF flow rate cannot be set completely independently of the inlet vapour quality. In addition, the pressure drop (1–2% of the inlet evaporator pressure) within the evaporator changes the corresponding local saturation temperature, hence increases the amount of glide and degree of mismatching. Among the three reversing methods, in the evaporator, RC2 achieves a better glide match than RC3, which in turn matches better than RC1. As expected, RC1 results in a parallel flow configuration that does not correspond to a viable condition for TG match. A similar analysis shows that the condenser has a complete TG match in the design mode (Fig. 8). Unlike the evaporator, the effect of pressure drop is very small (
