Experimental investigation on pinch points and maximum temperature differences in a horizontal tube-in-tube evaporator using zeotropic refrigerants

Energy Conversion and Management 56 (2012) 22–31

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Experimental investigation on pinch points and maximum temperature differences in a horizontal tube-in-tube evaporator using zeotropic refrigerants W. Wu a, L. Zhao a,⇑, T. Ho b a b

Department of Thermal Energy and Refrigeration, School of Mechanical Engineering, Tianjin University, No. 92 Weijin Road, Tianjin 300072, China Department of Mechanical Engineering, University of California – Berkeley, Etcheverry Hall, Berkeley, CA 94720, USA

a r t i c l e

i n f o

Article history: Received 1 September 2010 Received in revised form 10 October 2011 Accepted 12 November 2011 Available online 14 December 2011 Keywords: Zeotropic Refrigerant mixture Pinch point Maximum temperature difference Experimental

a b s t r a c t An experimental investigation is conducted on the occurrence and location of either a pinch point (PP) or maximum temperature difference (MTD) between a zeotropic refrigerant mixture and a heat transfer fluid (HTF) in a tube-in-tube evaporator. The zeotropic refrigerant used in the PP investigation is a R290/R600 mixture with a 0.15/0.85 mass fraction; the refrigerant used in the MTD investigation is a R245fa/R152a mixture with a 0.6/0.4 mass fraction. The inlet HTF temperature and the HTF and refrigerant flow rate were chosen as variable parameters at several sets of different working conditions to observe their effects on the location of a PP or MTD. The collected experimental data was then analyzed to determine the position of the PP or MTD. The position of the PP or MTD from the experiments did not show good agreement compared to predictions using existing available theoretical methods. The disagreement between theoretical and experimental results can be attributed in part to the nonlinear temperature change of the HTF along the evaporator which is not accounted for with existing theoretical methods. Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved.

1. Introduction In light of the Montreal Protocol, many chlorofluorocarbons (CFCs) have been phased out and replaced by zeotropic and azeotropic refrigerant mixtures that possess lower global warming potentials (GWPs) and ozone depression potentials (ODPs). For zeotropic refrigerant mixtures, current research has shown that they have broad applicability in a number of applications with potential to increase thermal efficiency in devices such as Organic Rankine Cycles (ORCs) powered by solar energy [1] and high temperature water source heat pumps [2]. Zeotropic refrigerant mixtures exhibit two unique characteristics during isobaric liquid–vapor phase change: temperature gliding and a nonlinear temperature–enthalpy relationship [3,4]. Temperature gliding is known as the characteristic in which the mixture’s equilibrium temperature varies during isobaric phase change. This characteristic is what distinguishes zeotropic refrigerants from azeotropic and pure refrigerants which remain at a constant temperature during phase change. By matching the temperature glide of zeotropic mixtures to the HTF, heat exchanger performance can be significantly enhanced, particularly for countercurrent tube in tube heat exchanger [3]. Researchers hope to use this property to more closely emulate the Lorenz cycle and approach the ideal efficiencies for air-conditioning and heat pump systems [5–7].

⇑ Corresponding author. Tel.: +86 22 27892823. E-mail address: [email protected] (L. Zhao).

The nonlinear temperature–enthalpy relationship exhibited by zeotropes often can reduce heat exchanger stream temperature matching and degrade performance. Temperature mismatching between streams causes destruction of the fluid’s potential work, or exergy, as a result of greater irreversibilities generated by heat transfer across a larger finite temperature difference. The heat transfer fluid (HTF) is often a single-phase fluid in the heat exchanger. Assuming only small changes in the heat capacity of the HTF, its temperature profile along the heat exchanger would then be expected to be linear with respect to heat transferred to the fluid, or its enthalpy change. For ideal temperature matching in the evaporator, the refrigerant would also need to have a linear temperature–enthalpy relationship during phase change. As previously mentioned though, zeotropic mixtures possesses a nonlinear temperature–enthalpy relationship during phase change; therefore, some temperature mismatching is inevitable making approaching the Lorenz cycle difficult. Minimizing temperature mismatching thus is important in improving heat pump and refrigerator performance when using zeotropic fluids [8]. Temperature mismatching between the HTF and the refrigerant reduces heat exchanger effectiveness and cause pinch points (PPs) or maximum temperature differences (MTDs) to occur [3]. A PP occurs when temperature mismatching causes the refrigerant’s and HTF’s temperature profiles along the heat exchanger to first converge and then diverge; creating a point where the temperature difference between the two streams is at a minimum. A MTD occurs when the temperature profiles of the two streams, diverges at first and then converges. The occurrence of either of these phenomena

0196-8904/$ - see front matter Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2011.11.009

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W. Wu et al. / Energy Conversion and Management 56 (2012) 22–31

Nomenclature A cp d f Fr G g Gr h hconv k L _ m Nu p Pr Q Ra Re T V x z

area (m2) specific heat (J/kg K) diameter (m) friction factor Froude number mass flux (kg/m2 s) acceleration due to gravity (9.81 m/s2) Grashof number enthalpy (J/kg) natural convection heat transfer coefficient (W/m2 K) thermal conductivity (W/m K) length (m) mass flow rate (kg/s) Nusselt number pressure (Pa) Prandtl number heat transfer rate (W) Rayleigh number Reynolds number temperature (K) average velocity (m/s) vapor quality or vapor mass fraction position (m)

causes irreversibilities in the heat exchanger to increase. Solar ORCs and air-conditioning and heat pump systems can be better designed and optimized by understanding how PPs and MTDs form for zeotropic refrigerants. Although many researchers have published information regarding the occurrence of PPs and MTDs and how mixture composition affects the formation of them [3,4], to date there exists very few experimental studies on how other important system parameters affect PPs and MTDs. Experimental studies to verify proposed models would significantly enhance the basic understanding of PPs and MTDs and could help improve the design and development of thermal systems using zeotropic fluids. The present study utilizes an experimental system to determine the PP or MTD location in a typical countercurrent tube-in-tube evaporator. Variable system parameters are also identified and analyzed to determine their effects on the location of the PP or MTD along the evaporator. Experimental results are compared to predictions from a theoretical model available in the literature. In this study, R245fa/R152a and R290/R600 have been selected as the mixture components to investigate MTD and PP respectively, because these fluids possess good stability and are relatively environmentally benign. R245fa and R152a both have zero ODP, and they possess a GWP of only 1030 and 124, respectively. A study conducted by Zhang et al. [2] showed that when utilizing a R245fa/R152a mixture for a heat pump system, the highest coefficient of performance was achieved when using a mass fraction of 0.6/0.4. Therefore, in this present MTD study, a zeotropic mixture of R245fa/R152a with a mass fraction of 0.6/0.4 is used. R290 and R600 both have zero ODP and GWP and have been shown to have potential in heat pump and refrigeration applications. Since the vapor pressure of R600 is too low for typical heat pump applications, this present PP study uses a R290/R600 mixture with 0.15/0.85 mass fraction as it allows for a more desirable fluid vapor pressure in typical heat pump applications.

2. Theoretical prediction of PP or MTD position in the evaporator Following the theoretical model developed by Venkatarathnam et al. [3], the evaporator and condenser are assumed to be in a coun-

Greek symbols b volumetric thermal expansion coefficient (K1) c relative error parameter e void fraction l dynamic viscosity (Pa s) q density (kg/m3) t kinematic viscosity (m2/s) r surface tension (N/m) Ugd two-phase multiplier Superscripts/subscripts 1 ambient f heat transfer fluid (HTF) in inlet of evaporator L loss to ambient l liquid out outlet of evaporator p constant pressure r refrigerant v vapor w wall

terflow configuration and the variation in thermal properties of the HTF is small enough that they can be assumed constant in the temperature range considered. Assuming no heat loss from the heat exchanger to the ambient, an energy balance across an infinitesimal element of the counterflow heat exchanger is given in Eq. (1) [3],

_ f cp m

    dT dh _r ¼m dz f dz r

ð1Þ

_ is mass flow rate, cp is the fluid’s specific heat, T is temperwhere m ature, h is enthalpy, z is position with respect to the inlet of the refrigerant in the heat exchanger, and the subscripts f and r refer to the HTF and the refrigerant, respectively. Using the chain rule and assuming that the pressure drop across the heat exchanger is negligible, the energy balance of Eq. (1) can be rewritten as Eq. (2), where the subscript p denotes constant pressure [3].

"   #       dT dh dT @h dT _r _r _ f Cp ¼m ¼m m dz f dT p dz @T p;r dz r

ð2Þ

r

To achieve ideal temperature matching, the change in temperature across each infinitesimal part of the heat exchanger must be exactly the same for both the HTF and refrigerant. In other words, the slope of the HTF’s temperature profile must match that of the refrigerants such that Eq. (3) is satisfied [3].

    dT dT ¼ dz f dz r

ð3Þ

Combining Eqs. (2) and (3), the resulting expression yields that for perfect temperature matching, the refrigerant’s derivative of enthalpy with respect to temperature under constant pressure must be a constant, as shown in Eq. (4) [3].



@h @T

 ¼ p;r

_ f cp m ¼ constant mr

ð4Þ

Eqs. (3) and (4) show that in order for ideal temperature matching to the HTF to be achieved, a linear refrigerant enthalpy-temperature relationship is necessary. Venkatarathnam et al. [3] concluded that for a PP or MTD to occur, Eqs. (5), (6) needs to be satisfied, respectively [3],

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W. Wu et al. / Energy Conversion and Management 56 (2012) 22–31

Fig. 1. Schematic diagram of the experimental system.



@h @T



@h @T

 <

  dhr @h < @T p;r;out dT f

ð5Þ

>

  dhr @h > @T p;r;out dT f

ð6Þ

p;r;in

 p;r;in

where the subscripts in and out represent the fluid’s inlet and outlet. Using Eqs. (5) and (6), predictions for the occurrence of a PP or MTD can be made by obtaining the necessary thermodynamic properties from NIST REFPROP 8.0 [9]. For the experimental working conditions considered, it was seen that Eqs. (5), (6) were satisfied. Therefore, it is expected in the experiments that a PP will occur using the zeotropic mixture R290/R600 (0.15/0.85 mass fraction) and a MTD will occur using the zeotropic mixture R245fa/R152a (0.6/0.4 mass fraction). 3. Experimental system and procedure The R290/R600 and R245fa/R152a mixtures were provided by the Lantian Company (China) with a certified purity greater than 99.95%. Water is used as the HTF to investigate PPs and ethyl alcohol is used as the HTF to investigate MTDs. Both the water and ethyl alcohol were purchased from Reagent (China) with a guaranteed purity higher than 99.7%. A schematic diagram of the experimental system is shown in Fig. 1; the main components of the experimental system consists of an evaporator, condenser, refrigerant feed pump, pressure damper, constant temperature tank, and a storage tank. The adjustable system parameters in the system include the inlet temperature of the refrigerant and HTF, the refrigerant and HTF flow rate, the inlet refrigerant pressure, and the elevation angle of the evaporator. The evaporator is a brass, countercurrent, tube-in-tube type heat exchanger; a cross sectional view of the evaporator is provided in Fig. 2. The HTF flows in the outer tube, and the refrigerant flows in the inner tube. The evaporator has been equipped with two small windows at either ends for observational purposes. The length of evaporator is about 2000 mm, the diameters of the inner and outer tube are about 10 mm and 20 mm, respectively. The condenser is similar in geometry and material as the evaporator. To measure the temperature of the evaporator’s outer wall, 41 T-type thermocouples with accuracy of ±0.1 °C were distributed 50 mm apart along the outer periphery of the evaporator. The outside of the heat exchanger is thermally insulated so that heat loss from the evaporator to the ambient is minimized. The inlet and outlet pressures of the evaporator are measured using pressure

Fig. 2. A cross-sectional view of the experimental evaporator.

transducers with accuracy of ±0.0018 MPa (TIG-SIEMENS, model TDS4033, 0–2.4 MPa). In the experimental system, the refrigerant and HTF flow rate is measured using two mass flowmeters: Rheonik Instruments model RHM015GNT (0–0.6 kg/s) and RHM04GNT (0–10 kg/s) with respective accuracies of ±0.0003 kg/s and ±0.005 kg/s. The inlet HTF temperatures both in the evaporator and condenser are regulated by using constant temperature tanks (Julabo model FP59 and Julabo model F32 that can operate from 35 to 200 °C and 50 to 200 °C, respectively). To maintain the inlet refrigerant pressure in the evaporator and mitigate pressure transients, a pressure damper was installed. A photo of the experimental system is shown in Fig. 3. Note that the evaporator is at an incline in the photo to better show the experimental setup; however, the evaporator was completely horizontal during the actual experiments. All current and voltage signals in the experimental system are collected using a data collector, Agilent model 34980A. Typical operation of the experiment began with the refrigerant being pumped to the evaporator by the refrigerant feed pump; the high pressure liquid is then heated in the evaporator, causing a phase transition to occur. Next, the high pressure refrigerant vapor goes through the flowmeter and then through the condenser where it is cooled and transitions back to a liquid. The condensed liquid refrigerant then flows to the storage tank, where it is stored until it is pumped through the pressure damper, and then to the evaporator again by the refrigerant feed pump.

W. Wu et al. / Energy Conversion and Management 56 (2012) 22–31

25

hconv ;i ¼ Nui k=d

ð11Þ

Q L;i ¼ hconv ;i AðT w;i  T 1 Þ

ð12Þ

To solve for Tw,i and QL,i, an iterative solution incorporating Eq. (9)–(12) is required. The refrigerant enthalpy difference (Dhr,i) across an element i in the evaporator can be determined using the following equation.

_r Dhr;i ¼ DQ r;i =m

ð13Þ

Combining with Eqs. (7), (8), and (12), Eq. (13) can be rewritten to Eq. (14). Fig. 3. Photo of experimental system.

Dhr;i ¼

4. Model correlations and relations 4.1. Determining the local refrigerant temperature along the evaporator The local refrigerant temperature inside the evaporator cannot be measured directly; therefore, experimental data is used in conjunction with available empirical correlations to calculate the refrigerant temperature along the inside tube of the evaporator. The details of the methodology and the empirical correlations used in determining the refrigerant temperature are now discussed. At steady state, conservation of energy stipulates that heat released by the HTF, Qf, is either absorbed by the refrigerant, Qr, or loss through the heat exchanger and insulation to the environment, QL, as shown in the following equation:

Qf ¼ Qr þ QL

ð7Þ

Experimental data for the outer tube wall temperature is available every 50 mm along the evaporator using the aforementioned 41 thermocouples. The heat exchanger can be divided into 40 corresponding elements and the energy conservation relation shown in Eq. (7) can be applied to each element along the evaporator using a finite difference approach. Since the temperature change across each element is small, the HTF’s specific heat is assumed to be constant for a given element. The heat released by the HTF across element i is given by the following equation.

_ f cp;i DT f ;i Q f ;i ¼ m

ð8Þ

For the temperature ranges examined, heat loss from the evaporator to the environment is dominated by natural convection; therefore, readily available empirical correlations to determine the heat transfer coefficient are employed. To determine the Grashof (Gr) and Nusselt (Nu) number at a particular element, Eqs. (9) and (10) are used respectively [10], 3

Gri ¼

gbðT w;i  T 1 Þd

t2

Nui ¼ 0:48Ra0:25 i

ðfor 104 < Ra < 107 Þ

ð9Þ ð10Þ

where b is the volumetric thermal expansion coefficient, g is the acceleration due to gravity, Tw,i is the average wall temperature of element i, T1 is the environment temperature, d is the outer diameter of the insulation, t is kinematic viscosity, and Ra = GrPr is the Rayleigh number, where Pr is the Prandtl number. The local natural convective heat transfer coefficient hconv,i and the heat loss rate from the evaporator at element i can be determined using Eqs. (11) and (12), where k is thermal conductivity, and A is the surface area exposed to the environment.

_ f cp;i DT f ;i  hconv ;i AðT w;i  T 1 Þ m _r m

ð14Þ

The distribution of 41 thermocouples along the evaporator naturally lends itself to be divided into 40 elements of length of 50 mm each, as shown in Fig. 4. The inlet and outlet enthalpies of the refrigerant in the evaporator would be hr,1 and hr,41, respectively. For a given element i, the inlet enthalpy hr,i and the change in enthalpy over the element can be used to calculated the outlet enthalpy hr,i+1, as shown in the following equation.

hr;iþ1 ¼ hr;i þ Dhr;i

ð1  i  40Þ

ð15Þ

For a two-phase binary mixture, Gibbs phase rule states that only two thermodynamic properties are required to define a thermodynamic state and determine the remaining state properties. Therefore, from the measured refrigerant temperature and pressure at the inlet of the evaporator, the inlet refrigerant enthalpy hr,1, can be determined using a thermodynamic property database such as REFPROP 8.0 [9]. Using the known inlet enthalpy and the successive energy balances summarized in Eqs. (14) and (15), the local refrigerant enthalpy along the evaporator can be determined. These enthalpy values are then used with calculated pressure values for the refrigerant to obtain the required two thermodynamic properties to satisfy Gibbs phase rule and define a state. With the local refrigerant pressure and enthalpy known, the refrigerant temperature along the inside tube of evaporator can be determined using REFPROP 8.0 [9]. The methods and correlations to calculate the local refrigerant pressure are described in the following section. 4.2. Determining the local refrigerant pressure along the evaporator To determine the refrigerant temperature along the evaporator, in addition to the known local refrigerant enthalpy, one other state variable is required such as pressure. The refrigerant inlet and outlet pressure for the evaporator can be measured directly from the experimental system. The working conditions in the condenser are maintained such that the refrigerant temperature at the inlet is slightly lower than the bubble point, and that the refrigerant is slightly subcooled before entering the evaporator. Therefore, the vapor mass fraction, or quality, of the refrigerant at the evaporator inlet is near zero. As the refrigerant flows through the evaporator though, its quality will increase due to heat absorption from the HTF. To determine the local pressure along the evaporator then,

Fig. 4. Enthalpy transfer in a segment of evaporator.

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W. Wu et al. / Energy Conversion and Management 56 (2012) 22–31

two-phase flow pressure drop correlations are necessary. Twophase flow dynamics has been studied and developed for many years now, and a number of prediction methods are available in the literature. In this study, the well known separated flow model is used [11]. The pressure drop during phase change consists of three contributions: the static pressure drop, the momentum pressure drop, and the frictional pressure drop. This is expressed mathematically in Eq. (16) [11].

Dptotal ¼ Dpstatic þ Dpmom þ Dpfric

ð16Þ

4.2.1. Static pressure drop Although the elevation angle of the evaporator is adjustable in this experimental system, for the present study, the evaporator is maintained horizontal making its elevation angle zero. Therefore, there is no static contribution to the total pressure drop and Dpstatic = 0 in Eq. (16). Fig. 5. The relative error parameter (c) for the different experimental trials.

4.2.2. Momentum pressure drop The flow’s change in kinetic energy is manifested in the momentum pressure drop term of Eq. (15). The momentum pressure drop is defined in Eq. (17) [11],

("

Dpmom ¼ G2total

# ð1  xÞ2 x2 þ ql ð1  eÞ qv e

" 

out

# ) ð1  xÞ2 x2 þ ql ð1  eÞ qv e

ð17Þ

in

where Gtotal is the total mass flux (both liquid and vapor), q is density, e is the void fraction, and the subscripts l and v are for the liquid and vapor quantities, respectively. Thome [11] recommends the adapted Rouhani and Axelsson drift flow rate model [12] developed by Steiner [13] for calculating the flow’s void fraction for horizontal flow. This relationship is given in the following equation,

   x x 1x e¼ ð1 þ 0:12ð1  xÞÞ þ

qv

þ

qv

1:18ð1  xÞ½g rðql  qv Þ0:25 G2total q0:5 l

ð20Þ

where fl is the liquid friction factor, L is the length of the pipe, di is the pipe inside diameter, and V is the average velocity of the liquid flow. The liquid friction factor is a function of the liquid Reynolds number Rel; both f and Rel can be calculated from Eqs. (21) and (22), respectively, with l being dynamic viscosity.

fl ¼ 0:079Re0:25

ð21Þ

Rel ¼ Gdi =ll

ð22Þ

The two-phase multiplier Ugd can be determined using Eq. (23) [11],

ql

#1 ð18Þ

where r is the fluid’s surface tension. Using the measured experimental quantities and calculated thermodynamic properties from REFPROP [9], the momentum pressure drop can be determined using Eqs. (17) and (18). 4.2.3. Frictional pressure drop To the authors’ knowledge, an experimentally verified prediction method for frictional pressure drop developed specifically for a zeotropic R245fa/R152a mixture does not exist. However, Ould Didi et al. [14] conducted a study that compared available experimental data to the following seven popular prediction methods for two-phase frictional pressure drops: Lockhart and Martinelli [15], Friedel [16], Grönnerud [17], Chisholm [18], Bankoff [19], Chawla [20], and Müller-Steinhagen and Heck [21]. Ould Didi et al. concluded that the method of Müller-Steinhagen and Heck and the method of Grönnerud consistently yielded the most accurate prediction of those examined, and the method of Friedel was third best. Since Grönnerud method was developed specifically for refrigerants [11], it was the method selected for the present study. The method of Grönnerud [17] quantifies the two-phase frictional pressure drop as a product of the two-phase multiplier Ugd and the pressure drop if the flow was completely liquid Dpl as shown in the following equation:

Dpfric ¼ Dpl Ugd

    1 L ql V 2 L 2 1 G Dpl ¼ fl ¼ 4f l 2 di 2 d 2ql

ð19Þ

The pressure drop for the flow treated as completely liquid can be calculated using the well known Darcy–Weisbach equation [11],



Ugd ¼ 1 þ fFr x þ 4ðx

1:8





x10 fFr0:5 Þ

"

ðql =qv Þ

ðll =lv Þ0:25

# 1

ð23Þ

where fFr is the Froude friction factor based on the liquid Froude number Frl. The Froude friction factor and the Froude number can be calculated from Eqs. (24) and (25), respectively [11].

fFr ¼ 1

for Fr l  1

fFr ¼

Fr 0:3 l

Frl ¼

G2 gdi q2l

þ

0:0055lnðFr1 l Þ

for Fr l < 1

ð24Þ

ð25Þ

Further details on the method of Grönnerud or other frictional pressure drop correlations often used in the separated flow model can be found in reference [11]. The total pressure drop across each element along the evaporator can be solved by summing together the static, momentum, and frictional contributions across the given element, as shown in Eq. (16). The local pressure of the refrigerant along the evaporator can be calculated using the measured pressure of the refrigerant at the inlet of the evaporator and the calculated pressure drop across each segment of the tube from the separated flow model. 5. Experimental results and discussion 5.1. Verifying the heat balance along the evaporator Due to the large number of thermocouples applied to the evaporator, the temperature difference between consecutive measuring points along the evaporator was small, typically only about 0.5 °C.

27

W. Wu et al. / Energy Conversion and Management 56 (2012) 22–31 Table 1 Description of the working conditions. Working condition

Inlet pressure Flow rate of of refrigerant refrigerant (g/min) (MPa)

HTF flow HTF inlet temperature (°C) rate (kg/min)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

1.1070 1.1076 1.1114 1.1117 1.0001 1.0129 1.0158 1.0284 1.1145 1.1017 1.1170 1.1141 1.1031 1.1138 1.1211 1.1050 1.1154 1.1262 1.1256 1.1175 1.1000 1.1045 1.1114 1.1124 1.1111 1.1123 0.5896

0.652 0.660 0.657 0.659 0.367 0.359 0.379 0.373 0.359 0.483 0.813 0.359 0.489 0.813 0.360 0.361 0.350 0.358 0.359 0.358 0.496 0.483 0.825 0.839 0.353 0.350 0.173

42.14 42.25 42.17 42.37 33.99 35.46 34.56 35.56 41.92 42.28 42.22 41.92 41.90 42.36 22.71 33.55 38.61 22.83 33.93 38.88 42.04 41.93 41.83 42.25 41.74 42.01 24.89

89.1 91.1 93.0 94.9 85.7 87.5 89.4 91.2 91.0 91.1 91.0 93.1 93.0 93.0 91.0 91.1 91.1 93.1 93.0 93.0 89.1 94.8 89.1 94.9 89.3 94.8 60.6

Fig. 7. Experimental results in r working condition 27: (a) Refrigerant and HTF temperature as a function of position. (b) Temperature difference between refrigerant and HTF as a function of position.

Table 2 Grid of working conditions for horizontal plane in Fig. 8a. Working condition grid No. No. No. No.

25 2 1 24

No. No. No. No.

9 10 2 11

No. No. No. No.

12 13 3 14

No. No. No. No.

26 23 4 25

To verify the reliability of the experimental results and the correlations used from the previous section, a heat balance over the entire evaporator is conducted and a relative error parameter defined in Eq. (26), is introduced as a way to quantify the uncertainties in the experiments.



c¼ 1

Fig. 6. Experimental results in working condition 1: (a) Refrigerant and HTF temperature as a function of position. (b) Temperature difference between refrigerant and HTF as a function of position.

Qr þ QL Qf

  100%

ð26Þ

The relative error parameters for the 29 experimental trials conducted are shown in Fig. 5 with the relative error parameter being limited to ±7%. The authors believe that the errors introduced into the system can mainly be attributed to the inaccuracy of the correlations used for determining the natural convection heat transfer coefficient between the air and the thermal insulation material outside the evaporator tube.

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W. Wu et al. / Energy Conversion and Management 56 (2012) 22–31

5.2. Occurrence of pinch point (PP) and maximum temperature difference (MTD) 5.2.1. Pinch point (PP) For studying pinch points, R290/R600 (mass fraction 0.15/0.85) mixture is utilized as a zeotropic refrigerant and water is used as the HTF. The different working conditions imposed during the

different experimental trials are briefly summarized in Table 1. For the PP investigation, working condition 1 was utilized. Using experimental data and the previously described methods, the local temperatures of the refrigerant and HTF along the evaporator are calculated. In Fig. 6a, the refrigerant and HTF temperatures along the evaporator, as well as the refrigerant bubble point and dew point, are plotted for working condition 1.

Fig. 8. The influence of HTF on the position of pinch point: (a) 3D presentation of the influence of HTF parameters. (b) The influence of HTF flow rate. (c) The influence of inlet HTF temperature.

W. Wu et al. / Energy Conversion and Management 56 (2012) 22–31

In Fig. 6a, the inlet refrigerant temperature is approximately 70.2 °C (point a), the refrigerant bubble point temperature is about 70.6 °C (point b), the dew point temperature is about 77.3 °C (point c), and the outlet refrigerant temperature is about 78.6 °C (point d). The refrigerant temperature curve in Fig. 6a can be separated into three parts: a ? b which represents the refrigerant while it is a subcooled liquid, b ? c where the refrigerant is transitioning from liquid to vapor phases, and c ? d where the fluid is a superheated vapor. To locate the position of the PP for the experiments, the difference between the HTF and refrigerant temperature is plotted as a function of position along the evaporator in Fig. 6b. A clear PP can be seen in Fig. 6b, and is marked for emphasis. Note that experimental measurement points were taken every 50 mm; therefore, in reality the exact location of the PP could actually fall 25 mm ahead or behind the location marked in Fig. 6b. The exact location of the PP, for working conditions 1 is therefore, somewhere between 725 mm and 775 mm along the evaporator. 5.2.2. Maximum temperature difference (MTD) For studying the MTD, R245fa/R152a (mass fraction 0.6/0.4) mixture is used as zeotropic refrigerant. The enthalpy change per °C during phase change for R245fa/R152a is small compared to the cp of water. Therefore, if water is used as the HTF, a very small temperature difference will be observed between two adjacent measurement points. Instead, ethyl alcohol was used for the HTF as it has a lower specific heat. For the MTD investigation, condition 27 was utilized. The local refrigerant temperatures along the evaporator are plotted in Fig. 7a, and the local temperature difference between the HTF and refrigerant is plotted in Fig. 7b. Here, the position of MTD is determined to be between 225 mm and 275 mm away from the cold end of evaporator, where the refrigerant enters. For the remaining set of working conditions, experimental data is analyzed using this same methodology to determine the positions of the PP or MTD.

29

(0.350–0.360 kg/min), and inlet HTF temperature (91.0–91.1 °C); the difference in these conditions are less than 3%. Assuming the differences in these parameters for these four working conditions are negligible, the variable parameter for these four working conditions then is the refrigerant flow rate. The PP is determined using the previously described methods and plotted for these four working conditions in Fig. 9a. Working conditions 12, 18, 19, and 20 also have similar inlet refrigerant pressures (1.1141–1.1262 MPa), HTF flow rates (0.358–0.359 kg/min), and inlet HTF temperatures (93.0–93.1 °C). Again, assuming these differences are negligible, the calculated PP location can be plotted for these working conditions as a function of the refrigerant flow rate, as shown in Fig. 9b. From Fig. 9a and b, it can be concluded that as the refrigerant flow rate increases, the PP position moves closer to the cold end of the evaporator. Moreover, results indicate that increasing the HTF flow rate has the same net effect on the position of the PP as decreasing the refrigerant flow rate. The position of the PP moves closer to the cold end of evaporator when the HTF flow rate decreases or when the refrigerant flow rate increases.

6. Comparison of experimental results to theoretical predictions Theoretical predictions for the PP and MTD using methods from Venkatarathnam et al. [3] are compared data collected from the

5.3. System parameters that influence the position of the PP 5.3.1. HTF inlet temperature and flow rate The HTF inlet temperature and flow rate are variables which can affect the position of the PP. To determine how these two factors influence the PP location, experimental data from the 16 working conditions listed in Table 2 were used. For the working conditions in Table 2, the refrigerant inlet pressure range is 1.1000– 1.114516 MPa and the refrigerant flow rate is 41.74–42.37 g/min. As shown, the variations in refrigerant inlet pressure and flow rate are very small and can be regarded as negligible for these 16 working conditions. Therefore, the HTF flow rate and inlet temperature are the variable parameters for this set of experimental data. For a given row of conditions in Table 2, it can be seen that the HTF flow rate is nearly the same. The HTF inlet temperature is then the only variable parameter in each row. Likewise, for a given column of working conditions in Table 2, the HTF inlet temperature can be regarded as nearly the same. Therefore, the HTF flow rate is the only variable parameter in each column. Using previously applied methods to determine the PP, Fig. 8a-c were constructed with an linear interpolation method in Matlab to illustrate the PP locations for a given set of working conditions. Note for Fig. 8a, Table 2’s working conditions are intentionally listed in a grid such that it corresponds to the bottom x–y plane of the 3D figure. It can be observed from Fig. 8b and c that as the inlet HTF temperature increases or as the HTF flow rate decreases, the position of the PP moves closer to the cold end of evaporator. 5.3.2. Refrigerant flow rate From Table 1, working conditions 9, 15, 16 and 17, have similar inlet refrigerant pressures (1.1050–1.1211 MPa), HTF flow rates

Fig. 9. (a) and (b) The influence of refrigerant flow rate on the position of pinch point.

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Fig. 10. Comparison of experimental PP position with theoretical PP position in working condition 10: (a) Refrigerant and HTF temperature as a function of position. (b) Temperature difference between refrigerant and HTF as a function of position.

experiments. For the theoretical predictions, the parameters of working conditions 10 and 27 are used for the calculation. The parameters used include the inlet and outlet temperature of the HTF and the inlet pressure and flow rate of the refrigerant. The theoretical prediction method assumes that the HTF specific heat is constant and that the HTF temperature changes linearly along evaporator. Results from the theoretical prediction method [3] are shown in Figs. 10a and b, 11a, and b. In Figs. 10a and 11a, the HTF temperature profile along the evaporator is predicted by theory [3] to be a straight line. However, the HTF temperature profile obtained from the experiments is quite different, as the HTF has a nonlinear temperature-position relationship along the length of evaporator. This difference between the theoretical method and experimental data underscores the possible errors from assuming a constant HTF specific heat for the entire evaporator. Another possible reason for the discrepancy may be due to the vapor mass quality of the refrigerant changing along the evaporator. As the vapor mass quality increases along the evaporator, vapor can begin to coat the tube walls at higher qualities as the flow regime approaches dry out; this can significantly reduce the heat transfer coefficient and the heat transfer rate. This can be seen in Fig. 10a, as the slope of temperature curve becomes smaller further and further along the evaporator in Fig. 10a. These processes are not accounted for when using the theoretical prediction methods, which may have lead to differences from what was seen during the experiments.

Fig. 11. Comparison of experimental MTD position with theoretical MTD position in working condition 27: (a) Refrigerant and HTF temperature as a function of position. (b) Temperature difference between refrigerant and HTF as a function of position.

In Figs. 10b and 11b, the local HTF and refrigerant temperature difference is plotted for the theoretical predictions (solid line) and for the experimental results (solid line with data points). As Fig. 10b shows, these two curves have the same overall trend, and both show the occurrence of a PP. However, the PP positions calculated from the theoretical model and from the experiments are different. The theoretical position of the PP is at a position between 925 mm and 975 mm away from the cold end of evaporator, whereas the experimental PP is at a position between 225 mm and 275 mm. In Fig. 11b, the positions of these two MTDs are also different, although to a much smaller degree. The theoretical MTD is predicted to be at a position between 175 mm and 225 mm away from the cold end of evaporator and the experimental MTD is at a position between 225 mm and 275 mm. Therefore, if the precise MTD or PP location is necessary, care should be taken in applying the assumption that the HTF temperature profile is linear along the evaporator. 7. Conclusion This paper described and analyzed an effective experimental method for investigating the PP or MTD location of zeotropic refrigerants in a horizontal tube-in-tube evaporator. Experimental studies which used R290/R600 (mass fraction: 0.15/0.85) and R245fa/R152a (mass fraction: 0.6/0.4) as refrigerants were carried

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out to determine the PP or MTD position. This also paper discussed and analyzed how several different system parameters can influence the PP or MTD position. In addition, a comparison made between experimental results and predictions from currently available theoretical models. The conclusions of this study can be summarized as follows: (1) An experimental system used to detect and determine the PP or MTD position for zeotropic refrigerants in a tube-in-tube evaporator is described. (2) Experimental results showed that the PP position moves closer to the cold end of the evaporator when the inlet HTF temperature increases or when the HTF flow rate decreases. (3) Comparison of the experimental results to theoretical predictions showed that the assumption of a linear temperature-evaporator position can lead to inaccurate PP or MTD location predictions. Care should be taken to ensure that this assumption of the theoretical model actually corresponds to the physical situation.

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