Enhancement of phase-change evaporators with zeotropic refrigerant mixture using metal foams

International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Enhancement of phase-change evaporators with zeotropic refrigerant mixture using metal foams Gholamreza Bamorovat Abadi, Kyung Chun Kim ⇑ School of Mechanical Engineering, Pusan National University, San 30, Jangjeon-dong, Geumjeong-gu, Busan 609-735, Republic of Korea

a r t i c l e

i n f o

Article history: Received 18 May 2016 Received in revised form 6 October 2016 Accepted 6 October 2016 Available online xxxx Keywords: Metal foam Phase change Zeotropic mixture Heat exchanger Temperature glide

a b s t r a c t Almost all thermal systems use some kind of heat exchanger. In many cases, evaporators are needed for systems such as organic Rankine cycle (ORC) systems. Evaporators contribute to a big portion of the capital cost, and their price is directly related to their size or transfer area. Highly porous open-cell metal foams are being considered to improve performance while keeping the size of heat exchangers small. This study experimentally investigates the degradation of the heat transfer coefficient of zeotropic mixtures during phase change in a plate heat exchanger with metal-foam-filled channels. The working fluids were pure R245fa and a zeotropic mixture of R245fa/R134a (0.6/0.4 molar ratio). The results show that the metal foams significantly increase the recovered heat, overall heat transfer coefficient, and effectiveness of the heat exchanger for mass flux ranging from 90 to 290 kg/m2s, but at the expense of increasing the pressure drop. The same improvement was observed for the mixture of refrigerants. The degraded heat transfer coefficient of the mixture compared to the pure refrigerants was recovered by the introduction of metal foams to the system. New correlations are proposed to predict the two-phase heat transfer coefficient of both pure R245fa and the refrigerant mixture in metal foam evaporators. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction The sizing of phase-change heat exchangers such as evaporators is one of the main design parameters of thermal systems that use these components. There have been extensive studies on the two-phase heat transfer mechanism in horizontal and vertical tubes, which represent the tube side of a shell-and-tube heat exchanger [1–3]. However, plate heat exchangers have not been investigated as much [4–6], and manufacturers have only published general performance data. Therefore, the available research on plate heat exchangers is not comprehensive [22]. The available data show that the performance of these heat exchangers could be improved by various means [11]. High-porosity open-cell metal foams have been proposed as a feasible solution to improve the thermal performance of evaporators while keeping their sizes compact [7–10]. Hsieh and Lin studied vertical plate heat exchangers [6]. They reported on the saturated flow boiling and associated frictional pressure drop for R410A as the working fluid. Corrugated sinusoidal shapes were used on the plates with a chevron angle of 60°. They examined mass flux ranging from 50 to 125 kg/m2s, heat ⇑ Corresponding author. E-mail address: [email protected] (K.C. Kim).

flux of 5 to 35 kW/m2, and saturation pressure between about 10 and 14 bar. They showed that the heat transfer coefficient and pressure drop increase with the heat flux and mass flux. Hsieh et al. studied the subcooled flow boiling of the refrigerant R134a [4] in the same type of plate heat exchanger. For subcooled boiling, their data suggest that the mass flux has a greater effect on the heat transfer coefficient than the mass flux or the inlet subcooling degree. Han et al. [5] performed experiments on the boiling of R410A and R22 refrigerants in brazed plate heat exchangers with chevron angles of 20, 35, and 45°. Their results show that for a given mass flux, an increase in the inlet vapor quality or a decrease in the saturation temperature increases the heat transfer coefficient. An increase in the mass flux or the vapor quality increases the pressure drop. They concluded that the R410A refrigerant has a higher heat transfer coefficient and a lower pressure drop than R22. Longo and Gasparella [12] also performed experiments on the vaporization of R134a in brazed plate heat exchangers. Their plate heat exchanger had macro-scale herringbone corrugation with a chevron angle of 65°. The evaporative heat transfer coefficient of R134a increased with the heat flux or the outlet conditions. The pressure drop also increased with the mass flux. Longo and Gasparella also compared the data for vaporization of R134a to that of R410A and R236fa [13]. Their results indicate increases of

http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.10.039 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.

Please cite this article in press as: G. Bamorovat Abadi, K.C. Kim, Enhancement of phase-change evaporators with zeotropic refrigerant mixture using metal foams, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.10.039

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Nomenclature A Atotal Aempty Bo cp Dh dp f G g h hfg k L M _ m P Pr Pr q_ Q_ Re t T U x Xtt

area, m2 total surface area of the metal-foam-filled channel, m2 surface area of the empty channel, m2 boiling number specific heat, J/kg
K hydraulic diameter, m pore diameter, m2 friction factor mass flux, kg/m2s gravitational acceleration, m/s2 enthalpy, kJ/kg latent heat of evaporation, J/kg thermal conductivity, W/mK distance, m molecular mass, kg/kmol mass flow, kg/s pressure, bar Prandtl number reduced pressure Heat flux, kW/m2 heat, W Reynolds number thickness, m2 temperature, K overall heat transfer coefficient, W/m2 K vapor quality martinelli number

40–60% in the heat transfer coefficient and a decrease in the pressure drop for R410A compared to R134a and R236fa. Zeotropic mixtures are also used in plate evaporators. Taboas et al. [14] experimented with the saturated flow boiling heat transfer of zeotropic mixtures of ammonia and water in a plate heat exchanger. The heat transfer coefficient was influenced far more by the mass flux than the heat flux or saturation pressure. The increase in mass flux and quality greatly increased the frictional pressure drop. No relation between the heat flux and the frictional pressure drop was reported. A mixture of R134a and ammonia was also investigated. Djordjevic and Kabelac [15] studied the evaporation of this mixture in plate heat exchangers with chevron-pattern corrugation. Parallel flow yielded a higher overall heat transfer coefficient than counter-flow. Lower chevron angles of the corrugations also resulted in a lower heat transfer coefficient. Lee and Lee [16] proposed a correlation for predicting the two-phase evaporative heat transfer coefficient in small rectangular channels similar to those found in plate heat exchangers. The heat transfer coefficient of R113 is directly related to the mass flux and the vapor quality, but the heat flux had only a small influence. When experiments are not an option, models can be used to predict the performance of evaporators with good accuracy. Some models use a moving boundary method, while others use a discretized method. Discretized models are less cumbersome and easier to implement [20,21], but the moving boundary method is probably the most accurate. This method directly uses the Navier–Stokes equations of mass, momentum, and energy conservation [17–19]. By dividing the evaporator into three subsections for the liquid phase, two-phase, and vapor phase, the heat transfer coefficient and the pressure drop of the evaporator can be obtained using the Navier–Stokes partial differential equations for each part, especially the two-phase section. However, the right-hand side of these equations need assumptions for simplification.

X Y

liquid mole fraction vapor mole fraction

Greek symbols heat transfer coefficient, W/m2 K effectiveness porosity viscosity, Pa
s Density, kg/m3 surface tension, N/m

a e e0 l q r

Subscript c cb h i id int l nb o p r sh tp v w

cold side convective boiling hot side inlet ideal intermediate liquid nucleate boiling outlet port, pore refrigerant superheat two phase vapor water

Most if not all of commercialized plate heat exchangers use a method of surface enhancement (most commonly chevron corrugation). However, inserting metallic foam in plain rectangular channels could be even more beneficial in terms of thermal enhancement. Although metal foam has been around for a while, its application in heat transfer enhancement has gained attraction recently. Kim et al. [23] investigated the pressure drop and heat transfer of plate-fin heat exchangers with aluminum metal foams. They reported that the friction factor and heat transfer coefficient are significantly affected by the permeability and porosity of the metal foams. They concluded that metal foams are preferable for compactness of the heat exchanger. They also provided correlations for both the friction factor and j-factor, which were verified in experiments by other researchers. Calmidi and Mahajan [24] studied the convective heat transfer in aluminum metal foams with air as the fluid medium. They correlated their Nusselt number data with the Reynolds number of the pores. Mancin et al. [25,26] and Hamadouche et al. [27] did similar experiments for the air flow in aluminum metal foams. Two-phase flow in metal foam channels has not been investigated as much. Diani et al. [28] and Mancin et al. [29] studied the boiling of R134a, R1234yf, and R1234ze(E) in a 5-PPI (pores per inch) copper foam. Mancin et al. [29] reported the effects of the mass flow, heat flux, and vapor quality on the heat transfer coefficient, and they visualized the boiling phenomena using a high-speed camera. In their experiments, the ratio of the twophase heat transfer in a metal foam tube to that in a smooth, empty tube varied between 1.8 and 4.8. The best improvement was achieved at low mass velocity and heat flux. Zhu et al. [30,31] visualized the boiling of R410A refrigerant in a 7.9-mm tube filled with 5-PPI metal foams and provided a correlation for the two-phase heat transfer data. They provided flow maps for the two-phase flow of the refrigerant in the copper foam and

Please cite this article in press as: G. Bamorovat Abadi, K.C. Kim, Enhancement of phase-change evaporators with zeotropic refrigerant mixture using metal foams, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.10.039

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concluded that the flow pattern has a great effect on the heat transfer enhancement. The metal foam was observed to promote the annular flow. Heat transfer enhancement by up to 1.5 times that in smooth tubes was observed at low mass fluxes. Bamorovat Abadi et al. [8] studied the enhancement of the evaporative heat transfer coefficient. They used high-porosity metal foams to increase the heat duty of their evaporator prototype. The metal foam increases the two-phase frictional pressure drop of R245fa but also increases the waste heat recovered from the heat source and the overall heat transfer coefficient by up to 2–3 times compared to a conventional evaporator. They also visualized the two-phase flow of R245fa in a mini-tube filled with copper foam [9,10]. They studied the single-phase heat transfer in plate heat exchangers with metal foams and provided a correlation for the Nusselt number [7]. The two-phase flow in metal foam channels has not been fully investigated and understood yet. Studies on the two-phase flow of zeotropic mixtures in metal-foam-filled ducts are virtually non-existent. The aim of this study is to experimentally verify the heat transfer enhancement in plate heat exchangers with metal-foam-filled channels. To this end, a plate heat exchanger with three channels was manufactured from aluminum and filled with copper foams. Pure R245fa and a mixture of R245fa and R134a were used as the working fluid. New correlations are proposed for the evaporator with zeotropic mixtures in plate heat exchangers. 2. Experimental setup The experimental setup is shown in Fig. 1 and is identical to that used in previous studies [7,8]. It consists of a hot water loop that feeds hot water to the hot side of the evaporator, a cooling water loop that cools down the superheated refrigerant after the evaporator in a condenser, and the main refrigerant loop where the evaporator is installed. All three loops have a pump, a pump frequency inverter, and a flowmeter. A positive displacement flowmeter is installed in the main loop, while turbine flowmeters are used in the other two loops. A thermocouple and pressure transducer are installed before and after each component so that the

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thermodynamic states of the hot water, cold water, and refrigerant are always known. The hot water temperature can be adjusted from room temperature to 150 °C with pressure of 1–2 bar and flowrate of up to 12.1 m3/h. The cooling water is provided by a chiller that uses a cooling tower. Its temperature can be adjusted to as low as 5 °C with flowrate as high as 10 m3/h. The main loop uses a gear pump that can provide a flowrate of up to 4 liters per minute. The pressure in the main loop is adjusted with a globe valve right after the evaporator. The temperature of the refrigerant entering the evaporator is adjusted by controlling the condenser’s cooling water temperature and a preheater (not shown in Fig. 1). The thermocouples, pressure transducer, and flowmeter data are connected to a computer through a data acquisition device and converted to digital output through a customized LabView program with online indicators of the desired parameters. Post-processing of the data is performed using the Refprop library [32] to determine the thermodynamic properties of the fluids. Fig. 2 shows the test section evaporator. Details are explained in previous studies [7,8]. The test section evaporator has aluminum plates with 3-mm thickness and 5-mm channel depth. The portto-port length of the evaporator is 245 mm, and the maximum width of the channel is 100 mm. Three channels were used: two for the hot side and one for the refrigerant side. The refrigerant flows upward while the hot water flows downward in a countercurrent heat exchanger. Aside from thermocouples and absolute pressure transducers, a very accurate pressure difference transducer is installed between the inlet and the outlet of the evaporator to accurately measure the pressure drop inside the evaporator channels. The evaporator channels are filled with high-porosity copper foams obtained from a local manufacturer and cut with electrical discharge machining. The metal foams have 20, 30, and 60 PPI and a porosity of 0.9. These physical properties are provided by the manufacturer, while other properties such as the pore diameter and the ligament diameter were determined by scanning electron microscope (SEM), as shown in Fig. 3. Both pure R245fa and the mixture of R245fa and R134a were used in previous studies on organic Rankine cycle (ORC) applications [33]. Separate studies

Fig. 1. Schematics of the test setup.

Please cite this article in press as: G. Bamorovat Abadi, K.C. Kim, Enhancement of phase-change evaporators with zeotropic refrigerant mixture using metal foams, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.10.039

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Fig. 2. Metal foam evaporator port configuration and the flow direction from the front and side views.

showed the flow boiling heat transfer of these refrigerants by means of visualization [34,35,46]. 2.1. Data reduction Two major parameters are determined for the performance test of an evaporator: the refrigerant-side boiling heat transfer coefficient through the overall heat transfer coefficient of the evaporator, and the frictional pressure drop. The overall heat transfer coefficient of the evaporator can be expressed as:

U¼

Q_ A  DT ln

ð1Þ

where A is the total heat transfer area (2*0.0226 m2 for the threechannel evaporator), and DTln is the logarithmic mean temperature defined using the inlet and outlet conditions of the fluids. Q_ is the total heat rate of the exchanger and can be found using an energy balance over the evaporator on either the water side or the refrigerant side. Since the water side is always single-phase with a limited temperature drop, Q_ h can be used in place of Q_ :

_ h cp;h ðT h;i  T h;o Þ Q_ h ¼ m

ð2Þ

_ h is the mass flowrate of the hot water, and cp;h is its speciwhere m fic heat capacity, which is assumed to be constant over the limited temperature and pressure drop on the hot side of the evaporator. Using the hot water side, the heat rate can be verified since single-phase heat balance tests showed that the heat loss is less than 6% for the evaporator. In Case A, the fluid entering and exiting the evaporator is always two-phase. In this case, DTln is defined using Eq. (3):

DT ln ¼

T h;o þ T c;o  T c;i  T h;i
 T T c;i ln T h;oT c;o

ð3Þ

h;i

For zeotropic mixtures, Tc,o and Tc,i are not the same since the mixtures experience a temperature glide while boiling. But for pure fluids, T c;o ¼ T c;i ¼ T sat is the saturation temperature of the pure fluid at the corresponding saturation pressure, which is averaged between the inlet and outlet values in consideration of the pressure drop. The subcooling degree might still be negligible (<3 °C), but the inlet flow is assumed to be in saturated liquid phase (x = 0).

Fig. 3. SEM images of a 60-PPI metal foam with 25 (left side) and 150 (right side) times magnification showing the pore and ligament diameters.

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In Case B, the fluid exiting the evaporator is further superheated, and the same assumption is made for the fluid state at the inlet of the evaporator. Eq. (4) is used to find the logarithmic meant temperature difference [12]:

DT ln ¼ h


Q_ tp DT ln;tp



Q_ þ




Q_ sh DT ln;sh

i

ð4Þ

where tp and sh stand for two-phase and superheated, respectively, and [12,13]:

flow should also be removed. Finally, the port pressure drop is removed from the total pressure drop, and the remaining head difference is interpreted as the friction pressure drop:

DPfriction ¼ DPtotal  DPstatic  DPport  DPacceleration

ð11Þ

The static pressure drop is [4,36]:

DPstatic ¼ gLqmean

ð12Þ

where qmean is the mean density of the two-phase flow. The acceleration pressure drop is given by the momentum difference at the inlet and outlet of the channel [4]:

_ h cp;h ðT h;int  T h;o Þ Q_ tp ¼ m

ð5Þ

_ h cp;h ðT h;i  T h;int Þ Q_ sh ¼ m

ð6Þ

DPacceleration ¼ G2

T h;o þ T c;o  T c;i  T h;int
 T T ln T h;o Tc;ic;o

ð7Þ

Dx is the difference between the vapor quality at the inlet and outlet of the channel. The port pressure loss is calculated by [4,36]:

T h;int þ T c;o  T c;i  T h;i
 T T ln Th;intT c;oc;i

ð8Þ

DT ln;tp ¼

h;int

DT ln;sh ¼

h;i

Th,int is the water temperature in the location where the superheating starts. The summation of Eqs. (5) and (6) should be equal to Eq. (2), and Th,int is bounded between the minimum and maximum values of the hot water inlet and outlet temperatures. Thus, Th,int is first found by iteration over the energy balance for each zone, especially for the mixture where the local saturation temperature changes with the local pressure and vapor quality value. The logarithmic temperature in each zone is calculated with this method, and the overall heat transfer coefficient is averaged over the two zones. When the overall heat transfer coefficient of the evaporator is found, the following equation can be used to determine the refrigerant-side heat transfer coefficient:

1 1 1 t ¼ þ þ U ar aw k

ð9Þ

where ar and aw are the heat transfer coefficient of the refrigerant and water side, respectively, k is the thermal conductivity of the aluminum wall, t is its thickness, and aw is determined by separate water-to-water experiments under similar experimental conditions with single-phase water on both sides [7].Without visualization or local temperature measurement, the data for local vapor quality is not available. But for Case A, it is still possible to calculate the vapor quality at the outlet of the evaporator. Given the heat rate to the refrigerant Q_ h in Eq. (2), the heat of vaporization hfg, and assuming a saturated liquid phase at the evaporator inlet, the vapor quality at the outlet of vapor is:

xo ¼

Q_ h _ c hfg m

ð10Þ

The heat of vaporization hfg is sensitive to the saturation pressure, and it is averaged between the inlet and outlet values considering the pressure drop of the refrigerant side. It is even more difficult to define hfg for the mixture because the local pressure and composition are changing. Therefore, the composition of the mixture is assumed to be constant during the phase change and is found by iteration of hfg. The total pressure difference between the inlet and outlet of the refrigerant side is directly measured by an accurate pressure difference transducer. Because the evaporator has a vertical configuration, the static pressure drop should be removed from this total pressure drop. Furthermore, the two-phase nature of the evaporator means that the pressure drop due to the acceleration of the



DPport

1

qo



1

qi

G2p G2p ¼ 0:75 þ 2qo 2qi

 Dx

ð13Þ

! ð14Þ

Gp is the mass flux at the port, and qo and qi are the density values at the outlet and inlet of the evaporator, respectively. Substituting Eqs. (12)–(14) in Eq. (11) gives the frictional pressure drop. Hereafter, ‘‘pressure drop” is used to refer to the frictional pressure drop. The experimental conditions are summarized in Table 1. Data points are obtained by increasing the refrigerant-side mass flow while maintaining the inlet conditions for both the refrigerant and hot water sides. A control volume is considered over the heat exchanger, where the cold side and hot side inlet conditions are the input, while the outlet conditions are the output of different equations as the outlet conditions. The mass flux is reported based on the inlet port since the area inside the channels changes along the flow direction due to the channel geometry. The hot water inlet temperature and mass flow are fixed for all cases, which results in different values for the heat input. The heat rate is reported as one of the result parameters. A total of four cases were studied: three cases with 20, 30, and 60-PPI metal foam, and one case with no metal foam (an empty channel). In cases with metal foam on the refrigerant side, 20-PPI metal foam is used on the hot water side. The empty channel case does not have any metal foam in any channel.

Table 1 Experimental conditions. Hot side

Cold side

Mass flow rate (kg/s)

0.49

Mass flow rate (kg/s)

Inlet temperature

80 °C

Pressure Fluid

2.5 bar Water

Inlet temperature Pressure Fluid

Area

2 channels: Empty Channel or 20 PPI

Area

0.011 0.015 0.022 0.027 0.032 0.038 Saturated liquid 4 bar Pure R245fa or R245fa/R134a (0.6/0.4) mixture 1 channel: Empty Channel 20 PPI 30 PPI 60 PPI

Please cite this article in press as: G. Bamorovat Abadi, K.C. Kim, Enhancement of phase-change evaporators with zeotropic refrigerant mixture using metal foams, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.10.039

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2.2. Uncertainty analysis Similar to a previous study [8], the uncertainty in measuring the length of the plates is estimated to be within ±0.2 mm. The uncertainty of the temperature measurement with K-type thermocouples is within ±1.5 K. The mass flux is calculated based on the measured volume flow rate and calculated density, resulting in an uncertainty of up to ±4%. The pressure measurement was achieved using pressure transducers across the setup and is reported with an uncertainty of ±5%. A Yokogawa pressure difference transmitter that is accurate to 0.1 kPa was used for the pressure drop. The system error and the random error pertaining to the sample number and standard deviation of the measured data were calculated, from which the maximum uncertainty of the pressure drop was estimated to be ±4.5%. The uncertainty for the heat transfer coefficient was calculated based on Eq. (1) using a method suggested by Moffat [37]. Table 2 summarizes the uncertainties in this experiment. The properties of the refrigerant and water that were not directly measured were calculated by REFPROP 9.1. 3. Experimental results The two main parameters for testing an evaporator are the refrigerant-side heat transfer coefficient and its pressure drop. In the following sections, the experimental data of these parameters are presented based on the data reduction method of previous sections. Next, new correlations for an evaporator with pure refrigerants and their mixtures are suggested, which can predict evaporator parameters such as the heat transfer coefficient and the pressure drop. 3.1. Heat transfer coefficient The evaporator test was performed by fixing the hot water and refrigerant inlet temperatures at 80 °C and at the saturation liquid state, respectively. A globe valve controls the operating pressure of the evaporator, while the inlet temperature of the refrigerant is controlled by the cooling water temperature and a pre-heater. In these conditions, the mass flowrate of the refrigerant is increased with increments of 0.5 liters per minute. For each case, enough time is allowed to reach steady state. The reported heat transfer coefficient is the refrigerant-side boiling heat transfer coefficient averaged over a period of time. Fig. 4 shows the heat transfer coefficient of the refrigerant side of the evaporator with pure R245fa. The coefficient increases with the mass flux, which indicates the possible dominance of the convective boiling heat transfer mechanism (the heat flux increases too, but the dominance of the convective heat transfer is proven in Section 4). This trend is the same for the empty channel and cases with metal foam. Another conclusion from Fig. 4 is that increasing the PPI value of the metal foam decreases the heat transfer coefficient, with 20 PPI showing the highest heat transfer

Fig. 4. Refrigerant side heat transfer coefficient – Pure R245fa.

coefficient. This is explained by the fact that the heat flux (or heat duty) of the evaporator is not fixed. The inlet conditions such as the temperature and the mass flowrate of the hot water are kept fixed to simulate a real-life heat source, such as the outlet of a gas turbine. Compared to the empty channel evaporator, the one with the 20-PPI metal foam showed a maximum increase of 2.3 times in the heat transfer coefficient, while the increases are 2 and 1.3 times for the 30 and 60-PPI foams, respectively. Fig. 5 presents the heat duty of the evaporator calculated using the temperature drop of the hot water. As expected, more heat is absorbed from the heat source with increasing mass flux of the refrigerant side. The 20-PPI metal foam can recover more heat from the heat source at the same mass flux. Fig. 5 shows that the 20-PPI metal foam evaporator recovered 20% more heat from the heat source compared to the empty channel evaporator. Absorbing more heat from a waste heat source is especially useful in ORC applications that recover waste heat and turn it into electricity. Fig. 4 and 5 show obvious enhancement of the heat transfer mechanism when high-porosity metal foam is inserted in the channels. But this thermal enhancement comes with a penalty of increased pressure drop, which is discussed in Section 3.2. The vapor quality of the refrigerant at the outlet of the evaporator is especially important in ORC applications, where the outlet of the evaporator directly flows into the inlet of an expander that is usually not designed to work with two-phase flows. Table 3 shows

Table 2 Experimental uncertainties. Parameter

Uncertainty

Mass flux (kg/m2s) Temperature (K) Pressure (bar) Pressure drop (kPa) Length (m) Vapor quality Heat duty (kW) Heat transfer coefficient (W/m2K)

±4% ±1.5 ±5% ±4.5% ±0.2 ±1% ±4.5% ±8–15%

Fig. 5. Heat duty of the evaporator – Pure R245fa.

Please cite this article in press as: G. Bamorovat Abadi, K.C. Kim, Enhancement of phase-change evaporators with zeotropic refrigerant mixture using metal foams, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.10.039

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G. Bamorovat Abadi, K.C. Kim / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx Table 3 Outlet vapor quality – Pure R245fa.

Table 4 Outlet vapor quality – R245fa/R134a (0.6/0.4).

Mass flux

Empty channel

20 PPI

30 PPI

60 PPI

Mass flux

Empty channel

20 PPI

30 PPI

60 PPI

90 127 162 205 250 286

4.2 1 0.69 0.63 0.58 0.54

11.3 10.8 5.6 3 0.76 0.64

9.3 8 4.6 0.76 0.7 0.66

5.6 5 0.82 0.81 0.76 0.71

90 127 162 205.5 250.1 286.6

11.8 9.2 7.7 5.4 3.9 1.5

17.9 15.7 14.7 12.8 11.7 10.2

15.62 13.82 11.63 9.4 8.47 7.32

13.21 11.1 9.54 7.71 5.38 4.24

the outlet vapor quality of the refrigerant with increasing mass flux. Values more than one indicate superheated vapor. The table shows that while the outlet conditions of the empty channel evaporator are mostly two-phase, the 20-PPI foam insert promotes the occurrence of dry superheated refrigerant at the outlet. The performance of the metal foam evaporator with pure R245fa was compared with that of a mixture of R245fa/R134a (0.6/0.4 molar ratio). Zeotropic mixtures are a promising substitute for pure refrigerants since their non-isothermal phase change in evaporation enables them to increase the total exergy efficiency of ORC systems by following the temperature line of the heat source and reducing irreversibility. But there is little study on their performance in metal-foam-filled heat exchangers. To the best of our knowledge, this is the first such data. Heat transfer degradation is well known for zeotropic mixtures during the phase change process. The reasons for this degradation are well discussed in the literature [38]. The degradation of the heat transfer coefficient of the mixtures compared to the original pure refrigerants is mainly due to the higher mass diffusion resistance of the refrigerant mixtures compared to their parent pure refrigerants [34]. Here, we focused on the heat transfer enhancement in metal foam evaporators and determine how much of the degradation is recovered by using metal foam inserts. Fig. 6 shows the heat transfer coefficient of the mixture in the metal foam evaporator. Comparing Fig. 4 and Fig. 6, it is clear that the general trend is the same for both the pure refrigerant and the binary mixture. In both cases, the heat transfer coefficient increases with the mass flux, and the 20-PPI foam has the highest heat transfer coefficient. But compared to Fig. 4, the heat transfer coefficient of the mixture is lower. The amount of heat transfer degradation varies from case to case, depending on the mass flux and vapor quality value. Fig. 6 shows that the zeotropic mixture evaporator with 20-PPI foam increases the heat transfer coefficient up to 2.3 times compared to the empty channel evaporator. This increase is up to 1.9 and 1.28 times for the evaporators with 30-

Fig. 7. Effectiveness of the heat exchanger with Pure R245fa.

PPI and 60-PPI foams, respectively, which is very similar to the enhancement factors for the pure R245fa refrigerant. However, the heat transfer coefficient for the empty channel evaporator is 11% less than that with pure R245fa at the maximum mass flux. This degradation is up to 14% for the case with 20-PPI foam. The heat duty of the evaporator with the binary mixture was very similar to that with the pure refrigerant and is not presented in a separate figure. There was a small increase (less than 10%) in the heat duty of the evaporator with the mixture due to the lower inlet temperature of the refrigerant than that for the pure fluid (keeping both the pure fluid and the mixture at the saturated liquid state). Table 4 shows the outlet vapor quality of the refrigerant mixture with increasing mass flux. Under the experimental conditions, the outlet of the evaporator with the binary mixture is always in the superheated vapor state, with the 20-PPI foam showing the highest superheating degree. The effectiveness of the heat exchanger is also an important parameter. The effectiveness of the evaporator is defined as the ratio of the recovered heat to the maximum recoverable heat from the heat source according to the second law of thermodynamics:

Q_

e¼ _ Q max

Fig. 6. Refrigerant side heat transfer coefficient – R245fa/R134a (0.6/0.4) mixture.

Qmax is the maximum possible amount of heat that can be transferred from the hot side to the cold side when the refrigerant outlet temperature hypothetically reaches the hot water inlet temperature. Fig. 7 shows the effectiveness of the evaporator with pure R245fa. The effectiveness decreases as the PPI value of the metal foam increases, and the lowest effectiveness is associated with the empty-channel heat exchanger. If the inlet conditions are kept fixed, the mixture has higher effectiveness compared to pure R245fa, as shown in Fig. 8. The increase in heat exchanger effectiveness for the mixture is promising for improvement of the overall exergy efficiency of ORCs.

Please cite this article in press as: G. Bamorovat Abadi, K.C. Kim, Enhancement of phase-change evaporators with zeotropic refrigerant mixture using metal foams, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.10.039

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G. Bamorovat Abadi, K.C. Kim / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx

Fig. 8. Effectiveness of the heat exchanger with R245fa/R134a (0.6/0.4) mixture.

3.2. Pressure drop The two-phase pressure drop of the refrigerant side was measured directly with a pressure difference transducer and corrected by subtracting the unwanted static, acceleration, and port contributions. Fig. 9 shows the frictional pressure drop for the phase change of pure R245fa in the evaporator prototype. As expected, the metal foam with higher PPI causes a higher pressure drop. The two-phase flow in 60-PPI foam has the highest pressure drop. At the maximum mass flux of 290 kg/m2s, the pressure drop reaches up to 36 kPa/m for 60-PPI foam, which is 6 times higher than that of the empty channel evaporator. The increases in pressure drop were 4 and 2.5 times for the 30-PPI and 20-PPI foam evaporators, respectively. The frictional pressure drop of the R245fa/R134a mixture is shown in Fig. 10. Since the working pressure strongly affects the pressure drop (increasing the working pressure would decrease the pressure drop), all the experiments were performed at a fixed working pressure of 4 bar. Fig. 10 shows the same trends for the frictional pressure drop of the mixture as those in Fig. 9 for pure R245fa. For the mixture, the maximum pressure drop with 60PPI foam was 4.5 times that in the empty channel evaporator.

Fig. 10. Pressure drop values of the heat exchanger with R245fa/R134a (0.6/0.4) mixture.

The increases in pressure drop were 3 and 2 times for the 30-PPI and 20-PPI foam evaporators, respectively. Comparing Fig. 9 and 10 shows that the pressure drop of the mixture is higher than that of pure R245fa at the same inlet conditions. The 60-PPI foam has the highest pressure drop and a maximum of 45 kPa/m at the maximum mass flux of 290 kg/s, in contrast to the 36-kPa/m value for the pure R245fa. Also, compared to the heat exchanger without any metal foam, the pressure drop is increased by up to two times by the 20-PPI foam, which had the best thermal performance. For pure R245fa, the pressure drop in channels with 20-PPI foam reaches 15 kPa/m at a mass flux of 290 kg/m2s, while it is around 20 kPa/m for the mixture at the same mass flux. This increase of about 20–30% is associated with the fact that the mixture exits the channel at higher temperatures, and it changes phase in the channel sooner than R245fa does. Therefore, the mixture exists as vapor in the channel for a longer time than R245fa, resulting in higher pressure drop due to the higher velocity of the vapor. Also, while boiling at 4 bar, the mixture has 18% higher surface tension than pure R245fa. It has been suggested that the pressure drop might be different between mixtures and pure refrigerants [39]. However, other studies suggest that the same method can be used for predicting the pressure drop for both pure refrigerants and mixtures [40,41]. 4. Predictive methods for two-phase heat transfer coefficient Refrigerant evaporation in ducts occurs by two mechanisms: nucleate boiling and convective boiling. Using the criterion by Thonon et al. [42] is useful for determining which mechanism is dominant [12,13]. According to this criterion, the convective boiling is dominant if the product of the boiling number (Eq. (15)) and the Martinelli parameter (Eq. (16)) is smaller than 0.00015.

Bo ¼

q_ Ghfg 

X tt ¼

Fig. 9. Pressure drop values of the heat exchanger with pure R245fa.

1x x

ð15Þ 0:9 

qv ql

0:5 

lv ll

0:1 ð16Þ

where q is the heat flux, hfg is the heat of vaporization, and q and l are the density and viscosity, respectively. The empty channel evaporator has the lowest mass flux G inside the channels (which has the highest cross-sectional area due to the lack of metal foam). There-

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fore, the boiling number is the highest for this evaporator. The analysis for the given experimental conditions shows that the product of Eqs. (15) and (16) is always smaller than 0.00015 for vapor quality greater than 0.12, indicating dominant convective boiling. The determination of the two-phase heat transfer coefficient in metal foam channels has not been fully discussed in the literature. A few studies correlate the two-phase heat transfer coefficient in high-porosity metal foams in tubes based on their flow patterns [10,31]. A correlation is suggested based on previous studies that can be used for plate heat exchangers with metal foam inserts. The heat input from the hot water is considered as the heat flux. Both nucleate and convective boiling mechanisms are considered. First, the heat transfer coefficient of the pure R1245 and the mixture in the empty channel evaporator are correlated, and then the concept is extended to channels with metal foams using an improvement factor. It has been shown that a correlation based on Liu and Winterton’s correlation [43] is the most useful for predicting the heat transfer coefficient of both pure R245fa and its mixture with R134a [34]: 2 0:5

atp ¼ ½ðF
acb Þ þ ðK
S
anb Þ  2

ð17Þ

where the convective boiling contribution acb is:

k acb ¼ 0:023 l Re0:8 Pr0:4 l Dh l

ð18Þ

9

Fig. 11 shows a comparison between the experimental values of the heat transfer coefficient of the empty channel evaporator and those predicted by Eq. (17). Fig. 11(a) presents this comparison for pure R245fa with K = 1, while Fig. 11(b) shows the same comparison for the mixture of R245fa/R134a (0.6/0.4). In both cases, this equation captures the experimental data within a ±20% error band. If the heat transfer coefficient of the empty channel is known, it is possible to predict the heat transfer coefficient of a metal-foamfilled channel using an equation with the following form [10]:

aMF ¼ IF  aEmpty

ð28Þ

Since aEmpty is already predicted by Eq. (17), a method to predict the improvement factor is given. By neglecting the effect of the heat flux on the enhancement of the heat transfer coefficient, the improvement factor can be predicted by Eq. (29) [10,31]:

 IF ¼

Atotal Aempty

/ ð29Þ

The enhancement of the heat transfer coefficient is associated with the increase in the surface area and the change in the flow pattern. The total heat transfer area is calculated with Eq. (30) [10,31]:

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Atotal ¼ 0:25pD2 ð231:156 pð1  porosityÞPPIÞ þ Aempty

ð30Þ

and the nucleate boiling contribution anb is: 0:55 0:5 0:67 anb ¼ 55P0:12 ðlogPr Þ M q_ r

ð19Þ

Pr is the reduced pressure (Pr = P/Pcr), and M is the molecular weight. S is the suppression factor and F is the enhancement factor, which are calculated using the following equations:

  0:35 ql F ¼ 1 þ xPrl 1

ð20Þ

qv

S¼

1

ð21Þ

1 þ 0:55F 0:1 Re0:16 l

K accounts for the mixture effect and equals 1 for pure R245fa. For the mixture of R245fa and R134a in a plate heat exchanger, K is found by curve fitting the heat transfer coefficient data to Eq. (22) to find the constants a, b, and c:

K¼

1 1þ

DT bp DT id

_ jY  Xj ðP=100Þ ½1  c  expðq=ð3  105 ÞÞ a

b

ð22Þ

DT bp is the temperature difference between the dew and bubble points of the mixture at a given saturation pressure, and DT id is found by:

DT id ¼ 1

aid

¼

q_

ð23Þ

aid

X1

a1

þ

1  X1

ð24Þ

a2

X and Y are the liquid and vapor phase mole fractions, respectively, and 1 and 2 represent each component of the mixture. Using the average values for the vapor quality, a, b, and c are found to be 0.34, 0.81, and 1.03 respectively [34]. The single-phase heat transfer coefficient is calculated by the Gnielinsky correlation:

Nu ¼

k ðf =8ÞðRe  1000ÞPr Dh 1 þ 12:7ðf =8Þ1=2 ðPr 2=3  1Þ

f ¼ ð0:79 ln Re  1:64Þ

2

ð26Þ ð27Þ

Fig. 11. Comparison of the experimental heat transfer coefficient of the empty channel evaporator with (a) pure R245fa and (b) mixture of R245fa and R134a with values predicted by Eq. (17).

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G. Bamorovat Abadi, K.C. Kim / International Journal of Heat and Mass Transfer xxx (2016) xxx–xxx

Fig. 12. Comparison of the experimental improvement factor of the metal foam evaporators with pure R245fa and mixture of R245fa and R134a with values predicted by Eq. (29).

Aempty is the heat transfer area when there is no metal foam. The exponent in Eq. (29) can be expressed as:

/ ¼ aRep þ bq_

dp G

S ¼ 4:867

½1  0:971ð1  e0 Þ0:5 

e0 l

ð32Þ

dp ¼ 0:0254=PPI

ð33Þ

e0 is the porosity of the metal foam. The Reynolds number changes

"

e0

a¼

ð36Þ

dw ð1  e0 Þ0:5

ð31Þ

a and b are found by curve fitting to be 0.0015 and 0.002, respectively, while Rep is the Reynolds number based on the pore diameter:

Rep ¼

Fig. 13. Comparison of the experimental pressure drop of the metal foam evaporators with pure R245fa and mixture of R245fa and R134a with values predicted by Eq. (34).

1  0:971ð1  e0 Þ0:5

#1 ð37Þ

0:6164ð1  e0 Þ0:5

" b ¼ ð1  e0 Þ

1  0:971ð1  e0 Þ0:5

#

0:6164ð1  e0 Þ0:5

ð38Þ

dw is the mean diameter of the ideal tetrakaidecahedra window. The liquid multiplier is given by [44]:

automatically from the mixture to the pure refrigerant based on the viscosity of the fluid. The improvement factor of the metal foam evaporator is predicted by Eq. (29) and compared to the experimental vales in Fig. 12. The figure shows that Eq. (29) predicts 85% of the experimental values for the improvement factor of the metal foam evaporators within a ±30% error band. Substituting Eqs. (29) and (17) into Eq. (28) easily gives the heat transfer coefficient of the metal foam evaporator. There is no similar study available for comparison on heat transfer enhancement in metal foam plate heat exchangers with zeotropic mixtures.

The coefficient C in Eq. (39) is modified for the pressure drop in metal foam heat exchangers and has to reflect all the parameters introduced by the metal foam to the pressure drop increase. Considering no oil, Hu et al. [44] defined C as:

5. Predictive methods for two-phase frictional pressure drop

C ¼ c1 Gc2 ec3 x dp4

/2l ¼ 1 þ

C 1 þ X tt X 2tt

The Martinelli parameter Xtt is calculated as:

 X tt ¼

1x x

0:5 

qv ql

c

He et al. [44] recently provided a prediction method for the two-phase pressure drop in metal-foam-filled channels. They experimented with the heat transfer and pressure drop of metalfoam-filled tubes and proposed a correlation to predict the twophase frictional pressure drop. We extended their model to plate heat exchangers. The two-phase pressure drop is given as:

DPtp ¼ u2l DP l

ð34Þ

where DPl is the liquid-phase pressure drop calculated according to Ergun and Orning [45].

DPl aS2 ð1  e0 Þ2 ll G bSð1  e0 ÞG2 þ ¼ L q0 e30 ql e30

ð35Þ

a, b, and S are the following coefficients for an ideal tetrakaidecahedra model [45]:

ð39Þ

0:5 

ll lv

0:5 ð40Þ

ð41Þ

The original equation was developed for small tubes. Therefore, it was modified to find the constants c1, c2, c3, and c4. By curve fitting to experimental data, these constants are experimentally found to be 0.1, 0.17, 0.018, and 0.16, respectively. dp is the pore diameter. The frictional two-phase pressure drop of the metal foam evaporator is predicted by Eq. (34) and compared to the experimental values in Fig. 13. Almost all of the experimental values are predicted within a ±30% error band. No similar studies are available for comparison. 6. Conclusion We studied the enhancement of the heat transfer coefficient in plate heat exchangers by experimenting with different aspects of a customized plate heat exchanger and metal foam inserts.

Please cite this article in press as: G. Bamorovat Abadi, K.C. Kim, Enhancement of phase-change evaporators with zeotropic refrigerant mixture using metal foams, Int. J. Heat Mass Transfer (2016), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.10.039

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Both pure R245fa refrigerant and its mixture with R134a were considered. Compared to a conventional evaporator, the one with 20-PPI foam showed an increase of up to 2.3 times in the heat transfer coefficient, while the increases were up to 2 and 1.3 times for 30 and 60-PPI foams, respectively. The zeotropic mixture evaporator with metal foams also increased the heat transfer coefficient. The increase compared to the empty channel evaporator was up to 2.3, 1.9, and 1.28 times for 20, 30, and 60-PPI foam evaporators, which is very similar to the enhancement factors for the pure R245fa refrigerant. The degradation of the heat transfer coefficient for the mixtures was up to 11% for the empty channel evaporator and up to 14% for the 20-PPI foam. The 60-PPI foam increased the pressure drop by a maximum factor of 6. The increases were 4 and 2.5 times for the 30-PPI and 20-PPI foam evaporators, respectively. For the mixture, the evaporator with 60-PPI foam had a maximum increase in pressure drop of 4.5 times. The increases were 3 and 2 times for the 30-PPI and 20-PPI foam evaporators, respectively. Both the heat transfer coefficient and pressure drop experimental data are predicted well by the suggested correlations within a reasonable error band.

Acknowledgments This study was supported by the Energy Efficiency & Resources Core Technology Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) granted financial resources from the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20132020000390). This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) through GCRC-SOP (No. 20110030013).

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