# Dynalene/water correlations to be used for condensation of [CO.sub.2] in brazed plate heat exchangers.

INTRODUCTION

Global warming concerns are gaining momentum in the twenty-first century and as such, environmentally friendly refrigerants are quickly becoming a necessity rather than just an interesting topic to speculate about for the future. R-744 or carbon dioxide ([CO.sub.2]) is a top contender, as instigated in the Montreal protocol, to phase out the use of ozone depleting chlorofluorocarbon (CFC) and the greenhouse gas contributing hydrochlorofluorocarbon (HCFC) refrigerants, especially in low temperature applications. As mentioned by Bodinus (1999), the idea of using carbon dioxide as a refrigerant started in the mid 19th Century by Alexander Twining; however, it was not readily implemented until Franz Windhausen made a [CO.sub.2] compressor in 1886. [CO.sub.2] refrigeration systems gained popularity until the late 1920s and early 1930s in the great depression. Due to the rise in demand for smaller systems in the non-commercial refrigeration market, coupled with the extremely high pressures required to use [CO.sub.2] as a refrigerant, an innovation was needed. Companies such as General Motors and DuPont funded research to develop new refrigerants that could operate under much lower pressures, Pearson (2005). Thus, synthetic CFC refrigerants were invented, which allowed refrigeration units to be sized much smaller and cheaper due to lower working pressure requirements. When these new refrigerants were developed, research and use of R-744 was greatly reduced.

With the introduction of new CFCs/HCFCs refrigerants, such as R-12 and R-22, the refrigeration market's needs were met, but at the same time these innovations created environmental problems. The chlorine molecules in CFCs/HCFCs proved to be harmful when leaked and released into the atmosphere. The ozone molecules in the stratosphere, which protect humans from harmful ultra-violet rays, are absorbed and destroyed by the chlorine molecules through a chemical reaction. In the early 1990s, a few hydrofluorocarbon (HFC) refrigerants, such as R-134a, were developed in which chlorine molecules were totally replaced by hydrogen molecules. In spite of the improvement regarding the ozone depletion dilemma, HFCs are still not perfect refrigerants due to their excess carbon, which contributes to the potential for global warming. In general, the existing refrigerants in today's market have two measured potential harmful effects on the environment: Global Warming Potential (GWP) and Ozone Depletion Potential (ODP). Global Warming Potential measures how harmful a greenhouse gas can be compared to carbon dioxide, which is defined as the GWP base reference having a value of 1. Ozone Depletion Potential characterizes how harmful a chemical compound can be in depleting the ozone layer on a scale of 0 to 1. These two measured potentials are typically presented for common refrigerants in Table 1.

Comparing GWPs and ODPs of R-744 to R-134a, R-22, and R-12 in Table 1, one can find that more research and application must be established to further the progress of [CO.sub.2] as an eco-friendly refrigerant.

Not only is carbon dioxide promising as a refrigerant with respect to the environment's protection, but it also works as a great refrigerant due to its abundance, safety, as well as its thermophysical properties. Halder and Sarkar (2001) found that [CO.sub.2] had several advantages over conventional refrigerants, which included lower pumping power requirements (attributed to a lower required volumetric flow rate), higher efficiency in heat exchangers, and higher latent heat. However, one of the leading factors in the decline of [CO.sub.2] as a practical refrigerant in the early 20th century was due to the lack of technology in using this refrigerant under its high pressure demands in smaller applications. With the substantial recent development in heat exchanger and compressor technologies however, [CO.sub.2] can now be seriously considered a potential working refrigerant in industrial as well as non-commercial applications.

Since the 1930s, plate heat exchangers have served well for single-phase heat transfer applications, e.g., beverage and food processing, pharmaceutical industries, paper and rubber industries, and dairy pasteurization, as mentioned by Shah and Wanniarachchi (1992). The introduction of brazed plate heat exchangers in the 1970s, which brazed the plates together rather than using gaskets, bolts, and carrying bars, unlocked the possibilities of using refrigerants that require higher operating pressures and larger temperature ranges. Plate heat exchangers are innovative in several different aspects of heat transfer; total heat transfer area per total volume is quite large compared to other types of heat exchangers, and high turbulence can be achieved even at low flow rates which results in high heat transfer coefficients. One of the drawbacks to the brazed plate heat exchangers however, is the difficulty of freeing the plates of fouling, unlike the earlier plate heat exchangers that could be disassembled, cleaned, and reassembled.

The focus of this research is to understand the condensation behavior of [CO.sub.2] in three brazed plate heat exchangers with differing interior plate geometries. To date, no research has been reported in literature on condensing [CO.sub.2] in brazed plate heat exchangers. Nevertheless, there has been research on other refrigerants being condensed in brazed plate heat exchangers as well as [CO.sub.2] being used in refrigeration systems.

LITERATURE REVIEW

Single-Phase Flow in Plate Heat Exchangers

To be able to formulate two-phase flow in the BPHEs, comprehensive single-phase flow experimentation is first required to establish single-phase formulation. Table 2 and Table 3 show typical well-established experimental correlations for single-phase heat transfer coefficients and friction factors, respectively, in PHEs, as presented by Ayub (2003).

Condensation in PHEs

While heat transfer coefficients and pressure drops have been studied extensively in the single-phase realm in PHEs, as documented by Ayub (2003), two-phase vaporization and condensation have not received as much attention, let alone in BPHEs.

A comprehensive condensation table of plate channels has been presented by Wurfel and Ostrowski (2004). Various entries of that table, as well as more recent findings, are focused on in the present section of literature review.

Panchal (1985) observed condensation heat transfer of ammonia in Alfa-Laval PHEs. Two exchangers with chevron angles of 60[degrees] and 30[degrees] were used. Heat transfer was observed using the different parameters of film Reynolds numbers (200-2000) in the high angle plate and low angle plates. Experimental data was compared against theoretical calculations. The conclusion that was made stated that for both low and high angle plates the heat transfer coefficients increased with the film Reynolds number or remained constant. This behavior was attributed to high interfacial shear stress for laminar-film condensation and the occurrence of the shear-stress-controlled condensation at low Reynolds numbers. Although no analytical relationship was made from Panchal's (1985) experiments, it was compared to Tovazhnyanski's (1984) Nusselt numbers for high and low angle plates:

Nu = 0.34924 [Re.sup.[0.75]] [Pr.sup.[0.4]] (high-angle plates) (1)

Nu = 0.11159 [Re.sup.[0.75]] [Pr.sup.[0.4]] (low-angle plates) (2)

Water-steam condensation was studied by Wang and Zhao (1993) in a plate heat exchanger with a chevron angle of 45 degrees, consisting of three channels. Parameters measured were flow, steam content, temperature differences, and pressures to obtain heat transfer coefficients. Condensation heat transfer was directly proportional to pressure drop. The heat flux in the plate heat exchanger was consistently larger than shell and tube condensers, this was due in part by the complex configurations of the channels, small cross sections, and shearing of steam flow with high velocities.

Arman and Rabas (1995) reported their results using ammonia in their PHEs with chevron angles of 30[degrees] and 60[degrees] to test single component condensation correlation equations. A propane/butane mixture was used in a plate heat exchanger (angle not specified) to study binary-component condensation as well. The single component condensation results revealed that the high chevron angle achieved high pressure drops at Reynolds numbers (5000-7500), where the low angle plate achieved the same pressure drop at almost three times the Reynolds numbers. Also, from the tables in the paper, it appeared that the high angle chevron plate required a lower mass flow rate than the low angle chevron plate to achieve the same heat transfer coefficients.

Yan et al. (1999) found that condensation trends for R-134a in PHEs showed greater heat transfer coefficients as well as pressure drops as vapor quality increased. Their experimental parameters included mass flux, average imposed heat flux, saturated pressure, and vapor quality. Using an inclination angle of 60[degrees] in the 500 mm (19.68 in.) by 120 mm (4.72 in.) plates, it was noted that the chevron configuration in PHEs create high turbulence at low Reynolds numbers which increased heat transfer at slower flow rates. The following heat transfer coefficient and friction factor were correlated:

Nu = 4.118 [Re.sub.eq.sup.[0.4]] [Pr.sub.l.sup.[1/3]] (3)

[f.sub.tp][Re.sup.[0.4]][Bo.sup.[-0.5]][([p.sub.m]/[p.sub.c]).sup.[-0.8]] = 94.75 [Re.sub.eq.sup.[-0.0467]] (4)

Jokar et al. (2006) explored single and two-phase heat transfer and pressure drop correlations of R-134a that were found in three heat exchanger depths (34, 40, and 54 plates) of 112 mm (4.41 in.) by 311 mm (12.24 in.) plates all having a corrugation inclination angles of 60[degrees]. These heat exchangers were used as both evaporators as well as condensers in an auto-motive dual refrigeration system. The two-phase flow correlations proved to be much more complex than that of the single-phase. The following correlations were proposed for the two-phase condensation heat transfer and pressure drop:

[Nu.sub.tp] = 3.371[Re.sup.[0.55]][Pr.sup.[0.3]][([G.sup.2]/[[rho].sup.2][C.sub.p][DELTA]T).sup.[1.3]][([[rho].sup.2][i'.sub.fg]/[G.sup.2]).sup.[1.05]][([rho][sigma]/[mu]G).sup.[0.05]][([rho]/([rho] - [[rho].sub.v])).sup.2] (5)

[C.sub.f, tp] = 2.139 * [10.sup.7][([GD.sub.hyd]/[[mu].sub.m, sat]).sup.[-1.6]] for 960 [less than or equal to] ([GD.sub.hyd]/[[mu].sub.m, sat]) [less than or equal to] 4169 (6)

Important two-phase behaviors were observed in the experimentation of condensation in the BPHEs; e.g., when the temperature differences were not large, film condensation proved to be the dominant characteristic when determining heat transfer correlations. Also, as the mass flow rates increased within the minichannels of the BPHEs, convection proved to be more important in driving heat to transfer.

Longo and Gasparella (2007) studied the condensation of R-134a in BPHEs. Three parameters were observed to conclude how each affected the heat transfer coefficients and pressure drop in the BPHE; mass flux, saturated R-134a vapor, and super heated R-134a vapor. The BPHEs used consisted of 10 plates, 72 mm (2.83 in.) by 310 mm (12.20 in.) that had the inclination chevron angle of 65[degrees]. It appeared that gravity controlled condensation occurred at mass fluxes less than 20 kg/[m.sup.2]*s (4.10 [lb.sub.m]/[ft.sup.2]*s), but when the flux exceeded this, forced convection condensation was achieved, producing a 30% increased heat transfer coefficient when the mass flux was 40 kg/[m.sup.2]*s (8.19 [lb.sub.m]/[ft.sup.2]*s). The behavior of the saturated vapor versus the super heat was similar, with the super heat yielding only an 8-10% increase in heat transfer over the saturate. Saturation temperature however played no great significance in heat transfer in the BPHE. For saturated vapor condensation Longo and Gasparella (2007) proposed the average heat transfer coefficient on the vertical plate as

[h.sub.r] = [PHI]0.943[[([[lambda].sub.l.sup.3][[rho].sub.l.sup.2]g[[DELTA]J.sub.lg])/([[mu].sub.l][DELTA]TL)].sup.[1/4]] (7)

where [PHI] is the enlargement factor equal to the ratio between the actual area and the projected area of the plates due to corrugation. For forced convection condensation the average heat transfer coefficient was found to be modeled closely to

[h.sub.r] = (1/S)[S.[integral].0][PHI]5.03([[lambda].sub.L]/[d.sub.h])[Re.sub.eq.sup.[1/3]][Pr.sub.L.sup.[1/3]]dS (8)

for equivalent Reynolds numbers less than 50,000. Pressure drop was derived from the experimental data as

[[DELTA]p.sub.f] = 1.816 KE/V (9)

Longo et al. (2004) also researched the correlations between surface smoothness within PHEs and condensation and evaporation heat transfer coefficients. Three types of smoothness were observed; smooth, rough, and cross-grooved. The plates were all of the chevron or herringbone type with inclination angles of 65[degrees]. It was concluded that the increased roughness was only advantageous in vaporization, whereas the cross-grooved plates improved both vaporization and condensation by 30%-40% and 60% respectively when compared to smooth plates.

Carbon Dioxide in Refrigeration Systems

Searching and reviewing the open literature, there is no single work reported on the condensation of [CO.sub.2] in BPHEs to date. However, there is research that has been done on carbon dioxide being used in refrigeration systems, as outlined in Table 4.

As far as research on developing [CO.sub.2] as a refrigerant, Hwang et al. (2005) explored [CO.sub.2] behavior and produced a database to provide a better understanding of the environmentally friendly compound. The researchers utilized fin and tube as well as microchannel heat exchangers to explore [CO.sub.2] condensation and evaporation properties. Airside pressure drops were compared according to different air frontal velocities. As inlet pressure of [CO.sub.2] increased, its heating capacity did the same up to a pressure of about 10 or 11 MPa (1450 to 1600 psi). Various overall heat transfer coefficients were measured, tabulated, and graphically presented. As air frontal velocities increased, heat transfer values increased. As mass flow rates increased heat transfer values increased as well.

Rigola et al. (2005) compared numerically and experimentally a [CO.sub.2] transcritical refrigeration system and sub-critical R-134a refrigeration cycle. Although the research heavily biased numerical analysis, two prototyped single stage hermetic reciprocating compressors (one being an improvement of the other) were used in the [CO.sub.2] refrigeration cycle to validate the numerical results. Both numerical and experimental results showed only a 10% lower COP in the [CO.sub.2] refrigeration cycle than that of R-134a under similar cooling capacity parameters.

EXPERIMENTAL FACILITY

Single-Phase Experimentation Set Up

A thorough single-phase analysis, including water/water and dynalene/water (2008), was conducted since single-phase heat transfer and pressure drop coefficients are needed in the two-phase analysis of [CO.sub.2] condensation. The single-phase test facility is depicted in Figure 1. To match the two-phase behavior of [CO.sub.2] condensing (rejecting heat) in the middle of three channels within the heat exchanger, single-phase hot water entered the top of the exchanger, flowing through the middle channel. On the other side, cold water entered from the bottom of the exchanger, flowing through the side channels, to produce counter flow heat transfer. The hot water line contained the instrumentation to record temperature, pressure drop, and flow rate; however, the cold water line recorded only temperature and flow rate. The pressure transducers on the hot line were positioned as close as possible to the inlet and outlet of the exchanger, followed by temperature reading and flow metering devices.

[FIGURE 1 OMITTED]

For the dynalene/water experimentation, the single phase flow configuration was similar, i.e., hot water flowing through the middle channel and chilled dynalene flowing through the side channels. But the instrumentation used for the hot side in the water/water configuration (temperature, pressure drop, flow rate) was switched to record data for the cold side in the dynalene/water test, in order to obtain more precise measurements on the dynalene side.

Two-Phase Experimentation Set Up

Once the single-phase analysis has been completed, the two-phase experimentation can commence. Two refrigeration loops will be used to complete the study, one being the two-phase [CO.sub.2] loop while the other, a single-phase dynalene loop. Figure 2 shows the plan for the two-phase experimentation equipment.

[FIGURE 2 OMITTED]

Brazed Plate Heat Exchangers

Three brazed plate heat exchangers are used in the present study. Dimensions and geometries of the plates are expressed in Table 5. Graphical descriptions of various BPHE dimensions are expressed in Figure 3.

[FIGURE 3 OMITTED]

The counter flow, also detailed in Figure 3, shows how the three channels are utilized having the outside channels direct flow opposite the middle channel. This counter flow method, coupled with alternating corrugated plates, allows for high heat transfer rates due to forced turbulence and an increase in pressure drop across the plates.

[CO.sub.2] Pump

In order to study the condensation of carbon dioxide, a [CO.sub.2] refrigeration loop must be built. The specifications for the test conditions state the temperature range of saturated [CO.sub.2] span from -17.8[degrees]C (0[degrees]F) to -34.4[degrees]C (-30[degrees]F) and the heat flux in the heat exchanger spans 800 Btu/hr*[ft.sup.2] (2.5 kW/[m.sup.2]) to 5000 Btu/hr*[ft.sup.2] (15.7 kW/[m.sup.2]). Not knowing initially the size of plates being used for the heat exchanger, maximum and minimum flow rates and pressures were calculated from the possible plate geometries to size the [CO.sub.2] pump. By multiplying the given heat fluxes by the approximate possible plate areas, minimum and maximum power loads were found. These loads were then divided by the latent heat of vaporization of [CO.sub.2] at the low and high temperatures to yield a mass flow rate. The mass flow was then converted to a volumetric flow based on appropriate properties of [CO.sub.2]. The flow range that was calculated was on the order of 0.01 gpm (0.00227 [m.sup.3]/sec) for the smallest plate and lowest heat flux, while for the largest plates and highest heat flux, 0.4 gpm (0.0909 [m.sup.3]/sec). A proper [CO.sup.2] pump was purchased that satisfies flow requirements as well as withstanding the extreme low working temperatures.

Chiller

A packaged water-cooled chiller was selected with a capacity of 39,275 Btu/h (3.27 tons) at -40[degrees]C (-40[degrees]F), which uses R507a as the working fluid to chill the secondary cooling fluid dynalene (HC-50). Dynalene was found to be a better fluid for this project compared to ethylene glycol since dynalene is less viscous at very low temperatures. Furthermore, a 50/50 ethylene glycol water mixture may freeze at -37[degrees]C (-34.6[degrees]F). Table 6 shows some of the thermo-physical properties of the two cooling fluids at -35[degrees]C (-31[degrees]F). Although dynalene is 25% more dense and its specific heat value is 20% less than glycol at this temperature, it is 75% less viscous than the ethylene glycol mixture. The chiller uses a 75 gallon (0.284 [m.sup.3]) stainless steel tank insulated with 3 inch (0.0762 m) expanded foam in a 0.080 inch (0.002032 m) aluminum jacket to store and maintain the dynalene at desired temperatures.

Temperature Reading Devices

a. Resistance Temperature Detectors (RTD): Temperature must be measured accurately at the inlets and outlets of the plate heat exchangers, and as such, RTDs provide the highest accuracy possible to deliver reliable temperatures. Just as thermocouples, there are several kinds of RTDs that are configured differently and have different accuracies. Of the three different wire configurations (2-wire, 3-wire, 4-wire) that are available, the 4-wire RTD were used in the test set up. The 4-wire design touts the highest accuracy and reliability of the different configurations because the resistance error due to lead wire resistance is nonexistent in this design. There are five different tolerance classes that depict temperature accuracy; Class B, Class A, DIN 1/3, DIN 1/5, and DIN 1/10. Table 7 shows comparison of four of the temperature reporting tolerances for RTDs. The RTDs in this experiment were of the accuracy following the 1/3 DIN. The 100 [ohm] platinum RTDs used conform to the Pt 3851 calibration curve. Each of the RTDs had sheath lengths of 6 inches (0.1524 m) to minimize stem conduction effects. This measurement surpassed the recommended minimum sheath length of 20 times the RTD diameter, and with the diameter of 1/8 inch (3.175 mm), the 6 inch (0.1524 m) sheath is 48 times the diameter, therefore temperature reading disturbances from ambient temperatures did not influence experimental data.

b. Thermocouples: For areas of the condensing loop that did not require high accuracy temperature readings, type T thermocouples sufficed. The temperature range of type T thermocouples was adequate for the present experimentation parameters. The thermocouples were classified in tolerance class 1, which for type T is [+ or -] 0.5[degrees]C between -40[degrees]C to 125[degrees]C (-40[degrees]F to 257[degrees]F). This accuracy was three times better than the more common K and J type thermo-couples, which were rated at [+ or -]1.5[degrees]C between -40[degrees]C to 375[degrees]C (-40[degrees]F to 707[degrees]F). Again the stem lengths were 6 inches (0.1524 m) as to minimize stem conduction interference.

Pressure Reading Devices

Obtaining accurate pressure drop data was critical in the project, and as such, high accuracy gauge and differential pressure transducers were utilized to measure pressure behaviors. The gauge and differential pressure transducers had a compensated temperature range which covers -40[degrees]C (-40[degrees]F). They were made of all stainless steel and hermetically sealed. The differential pressure transmitter required a 10 V ac or dc excitation voltage and returned a 3 mV/V [+ or -]1% with an accuracy of 0.25% linearity, with hysteresis and repeatability combined. The gauge pressure transducer was designed to work in a range of 0-500 psi (0-3.45 MPa). The transmitter is capable of working off of an excitation voltage from 6-42 Vdc and output either a 4-20 mA or 1-5 Vdc signal. The gauge pressure transducer had an accuracy of [+ or -]0.1% of the upper range limit or [+ or -]0.15% of full scale.

Flow Reading Devices

To accurately measure the flow of dynalene, which will ultimately condense the [CO.sub.2] refrigerant, a turbine flow meter made of stainless steel using a ceramic journal bearing with a RF pickoff signal to ensure the widest flow metering range of 0.3 to 15 gpm (0.068 to 3.41 [m.sup.3]/sec) was utilized. The ceramic journal bearing was necessary for the dynalene due to its high viscosity. The flow meter had two 10 point calibrations with viscosities of 1 cSt and 20 cSt to give an accuracy of [+ or -]0.05%. The flow meter's temperature and pressure operating ranges were -100[degrees]F to 800[degrees]F (-73.3[degrees]C to 426.7[degrees]C) and up to 5000 psig (34.5 MPa). The flow meter used an input DC voltage range of 8 to 30V and produced 0 to 5V pulses ranging from 5 to 5000 Hz.

Data Acquisition System

All of the experimental equipment was integrated into a data acquisition system program which recorded and displayed all the temperatures, pressures, and flow rates necessary. A power supply was used to power the flow meter as well as the differential pressure transmitter.

Test Procedure

To be as consistent as possible in the data collection process, identical steps were used for each heat exchanger.

1. Both hot and cold water ran until maximum hot and minimum cold temperatures were achieved.

2. Data collecting began by finding the maximum flow rates permitted by each side of each plate (1 channel side and 2 channel side) and assigning flow increments to be analyzed.

3. The DAQ recorded the inlet and outlet temperatures, gauge and differential pressures, as well as the flow from the turbine flow meter every 2 seconds for a duration of 2 minutes yielding a total of 60 data points per data collection set.

4. Data collection sets started by recording max flows of cold and hot. The hot flow stayed constant as the cold flow decreased for each iteration. When the minimum cold flow iteration was completed, the next permeation of reduced hot flow was set constant and the cold flow increased for each iteration. Data collection followed this fashion until all combinations of low and high flows for cold and hot water were recorded.

5. Statistical analysis was performed on each data set before moving to the next data set to ensure low standard deviations and acceptable precision intervals.

6. Data was then verified by the energy balance equation, assuming the specific heats of the hot and cold water to be equal. The ratio of cold mass flow rate with cold side temperature difference and hot mass flow rate with hot side temperature difference should equal unity.

SINGLE-PHASE ANALYSIS

The raw data collected by the data acquisition system are used to obtain the single-phase heat transfer and pressure correlations within the three BPHEs. This section reviews the data reduction method, and discusses the resulted correlations.

Modified Wilson Plot for Heat Transfer

As the first step in analyzing the collected data, properties of water for each test point were calculated at bulk temperatures averaged between the inlet and outlet ports on each side.

Each property, including density, specific heat, conductivity, and viscosity, was evaluated and correlated, using third order logarithmic regressions. These properties were then used to find the flow characteristics in the channels for each plate.

The Reynolds number of the flow within the channels was calculated by:

Re = [[GD.sub.hyd]/[mu]] (10)

where the hydraulic diameter was defined as two times the average plate spacing ([D.sub.hyd] = 2b), and the mass flux was calculated based on the minimum free flow area ([A.sub.o]) between the plates, as described by Shah and Wanniarachchi (1992):

G = [[[rho][??]]/[A.sub.o]] (11)

Due to the complicated geometries that brazed plate heat exchangers contain, this minimum free flow area is difficult to estimate and has not been universally standardized. However for the sake of simplicity, many studies have considered this free flow area as the average plate spacing, b, multiplied by the width of the plate:

[A.sub.o] [approximately equal to] bw (12)

It is noteworthy that the minimum free flow area (MFFA) between the two neighboring plates, which depends on the corrugation angle, is much less than the area given by Equation (12). A more thorough description of the minimum free flow area is given in the appendix of this manuscript, while Equation (12) is used for data reduction in this study.

An energy balance was applied in order to obtain heat transfer rates on both hot and cold sides:

Q = m[c.sub.p][DELTA]T (13)

Using the log-mean temperature difference

[[DELTA]T.sub.lm] = [[([T.sub.h, i] - [T.sub.c, o]) - ([T.sub.h, o] - [T.sub.c, i])]/[ln[([T.sub.h, i] - [T.sub.c, o])/([T.sub.h, o] - [T.sub.c, i])]]] (14)

the overall heat transfer coefficient in the heat exchanger was calculated by:

U = [[Q.sub.h]/[2[A.sub.S][[DELTA]T.sub.lm]]] (15)

where [A.sub.s] is the effective heat transfer surface area, which was calculated by the projected heat transfer area multiplied by the enlargement factor.

A common analysis method of single-phase heat transfer in BPHE is the modified Wilson plot technique. Due to the possibility of large property variations, especially the viscosity of dynalene, the heat transfer correlation format was chosen similar to the Sieder-Tate equation, as explained in Incropera and DeWitt (2002):

Nu = [CRe.sup.P][Pr.sup.[1/3]][[([mu]/[[mu].sub.S])].sup.[0.14]] (16)

The heat transfer coefficients for the hot and cold sides of the BPHE are thus obtained by:

[h.sub.c] = ([k.sub.c]/[D.sub.hyd])[C.sub.c] [Re.sub.c.sup.P] [Pr.sub.c.sup.[1/3]] [[([mu]/[[mu].sub.S])].sub.c.sup.[0.14]] (17)

and

[h.sub.h] = ([k.sub.h]/[D.sub.hyd])[C.sub.h] [Re.sub.h.sup.P] [Pr.sub.h.sup.[1/3]] [[([mu]/[[mu].sub.S])].sub.h.sup.[0.14]] (18)

In the original Wilson plot technique, used for shell-and-tube heat exchangers, [C.sub.h] and [C.sub.c] are the only coefficients that need to be found to be able to find Nusselt numbers. Reynolds number exponent (0.8), Prandtl number exponent (1/3), as well as the viscosity ratio exponent (0.14) for the tube side are assumed constant due to the widely accepted characteristics of in tube flow. The shell side Reynolds number exponent, however, is not necessarily 0.8 and can be optimized, based on the magnitude of Reynolds number, in the Wilson plot calculations. Plate geometries in BPHEs are so complex and varied among different manufacturers, the flow regimes, and as a result the Reynolds number exponents, cannot be assumed like the in-tube flow. Due to the similarity in geometries and configurations on the cold and hot channels of a BPHE, the flow regimes and the Reynolds number exponents on both sides can be assumed identical in certain ranges of Reynolds numbers. Prandtl number exponent and viscosity ratio exponent, which account for the fluid properties, can also be assumed constant at 1/3 and 0.14, respectively. The original Wilson plot technique requires the data to be recorded at constant flow rates and constant average bulk fluid temperatures on both hot and cold sides, which is not easily accomplished. However, the modified Wilson plot technique, devised by Briggs and Young (1969), allows data to be taken at varying flow rates and varying bulk fluid temperatures on hot and cold sides. The overall heat transfer equation based on this method is obtained through the following thermal resistance equation:

[1/U] - [(t/k).sub.wall] = [1/[[C.sub.c][[k.sub.c]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.c.sup.P][([[c.sub.p][mu]]/k).sub.c.sup.[1/3]][([mu]/[[mu].sub.S]).sub.c.sup.[0.14]]]] + [1/[[C.sub.h][[k.sub.h]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.h.sup.P][([[c.sub.p][mu]]/k).sub.h.sup.[1/3]][([mu]/[[mu].sub.S]).sub.h.sup.[0.14]]]] (19)

Multiplying both sides of the above equation by

[[k.sub.c]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.c.sup.P][([[c.sub.p][mu]]/k).sub.c.sup.[1/3]][([mu]/[[mu].sub.S]).sub.c.sup.[0.14]] (20)

gives

(1/U - [(t/k).sub.wall])[[k.sub.c]/[D.sub.hyd][([[D.sub.hyd]G]/[mu]).sub.c.sup.P][([[c.sub.p][mu]]/k).sub.c.sup.[1/3]][([mu]/[[mu].sub.S]).sub.c.sup.[0.14]]] = [1/[C.sub.c]] + [[[[k.sub.c]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.c.sup.P][([[c.sub.p][mu]]/k).sub.c.sup.[1/3]][([mu]/[[mu].sub.S]).sub.c.sup.[0.14]]]/[[C.sub.h][[k.sub.h]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.h.sup.P][([[c.sub.p][mu]]/k).sub.h.sup.[1/3]][([mu]/[[mu].sub.S]).sub.h.sup.[0.14]]]] (21)

which is in the form of

Y = mX + b (22)

where

Y = (1/U - [(t/k).sub.wall])[[k.sub.c]/[D.sub.hyd][([[D.sub.hyd]G]/[mu]).sub.c.sup.P][([[c.sub.p][mu]]/k).sub.c.sup.[1/3]][([mu]/[[mu].sub.S]).sub.c.sup.[0.14]]] (23)

X = [[[[k.sub.c]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.c.sup.P][([[c.sub.p][mu]]/k).sub.c.sup.[1/3]][([mu]/[[mu].sub.S]).sub.c.sup.[0.14]]]/[[[k.sub.h]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.h.sup.P][([[c.sub.p][mu]]/k).sub.h.sup.[1/3]][([mu]/[[mu].sub.S]).sub.h.sup.[0.14]]]] (24)

m = [1/[C.sub.h]] (25)

and

b = [1/[C.sub.c]] (26)

Since the viscosity ratio groups and the Reynolds number exponents are relaxed with the fluid flow rates and temperatures, successive linear regressions can be performed to execute the nonlinear regression that these equations require. These two linear regressions consist of evaluating X [Equation (24)] and Y [Equation (23)] and X ' [Equation (27)] and Y ' [Equation (28)].

X' = ln([Re.sub.c]) (27)

Y' = ln([C.sub.c][Re.sub.c.sup.P]) (28)

The X and Y regression starts with an initial P value as well as a guess for the [C.sub.h] value. These values have an impact on the wall temperature calculations; therefore, the viscosity ratio must be adjusted in both linear regression processes. From the X and Y regression, [C.sub.c] and [C.sub.h] coefficients are found. This [C.sub.h] coefficient is then used to relax the viscosity ratio in the X ' and Y ' linear regression, producing values of P and [C.sub.c]. The new P is used in the next iteration of regressions (which has new viscosity ratios to be relaxed), and this [C.sub.c] is compared to the [C.sub.c] of the X and Y regression. Calculations continue following this procedure until the difference between the successive P and [C.sub.h] values and the [C.sub.c] values from the X - Y and X' - Y' linear regressions reach some allowable error. These values can then be verified by executing a reverse calculation that requires multiplying both sides of Equation (19) by the hot side heat transfer denominator instead of the cold side heat transfer denominator, and undergoing the same process to converge at similar P, [C.sub.c] and [C.sub.h] coefficients. Both calculation procedures were done in this study and minute differences were observed, so the average of the two methods' coefficients was taken into account.

Fanning Friction Factor for Pressure Drop

To determine the single-phase pressure drop due to friction across the BPHEs, the manifold pressure loss was subtracted from the measured pressure drop recorded by a differential pressure transmitter.

[[DELTA]P.sub.f] = [[DELTA]P.sub.total] - [[DELTA]P.sub.man] (29)

The contribution of pressure loss due to gravitation was zero in this case since the pressure drop was measured using a single differential pressure transducer. The manifold pressure loss was estimated by 1.5 times the inlet velocity head, as reported by Shah and Wanniarachchi (1992),

[[DELTA]P.sub.man] = 1.5([[u.sub.m.sup.2][rho]]/2) (30)

where [u.sub.m] is the mean velocity of the fluid at the manifold.

The Fanning friction factor is given by

[C.sub.f] = [[DELTA]P.sub.f][[[D.sub.hyd][rho]]/[2[L.sub.p][G.sup.2]]] (31)

where [L.sub.p] is the characteristic length, which was here defined as the distance from the middle of the top inlet port to the middle of the bottom outlet port. The Fanning friction factor in the turbulent

regime can then be correlated based on the Reynolds number by the following general form:

[C.sub.f] = C'[Re.sup.-P'] (32)

Single-Phase Heat Transfer Results

The single-phase analysis was conducted on the three previously described BPHEs. Data are presented of the water/water analysis as well as the dynalene/water analysis. Implementing the modified Wilson plot technique and reverse calculations for the three different plates gave correlations with an average standard deviation less than 1%. The plots of the modified Wilson method for each plate are shown in Figure 4, while the heat transfer correlations are presented in Table 8.

[FIGURE 4 OMITTED]

It is common practice that in most BPHEs, defining plate orientation with hot and cold fluid flow direction in single phase study is not as critical as it is in two phase flow. However, based upon the present experimentation, it is interesting to note that mixed angle plates do require such a definition. Because the neighboring plates alternate chevron angles, mixed-angle exchangers exhibit different behavior for opposite flow directions. For example, if a 30/60 mixed-angle exchanger consists of plates where the high-profile (30[degrees]) plates are pointed up and the low-profile (60[degrees]) plates are pointed down, the middle channel's fluid would have a different flow pattern in this orientation compared to the opposite orientation, where the high-profile (30[degrees]) plates are pointed down and the low-profile (60[degrees]) plates are pointed up. In the 60/60 and 30/30 exchangers, this problem is eliminated because the fluid's flow pattern is similar regardless of flow direction. This was apparent in the dynalene/water data which demonstrated that in one orientation the [C.sub.c], [C.sub.h], and P values were 0.272, 0.136, and 0.759, respectively, and in the opposite orientation the corresponding values were 0.278, 0.143, and 0.745. The latter data is reported here because its orientation is similar to the two phase experimentation.

In order to properly compare the findings presented in this paper with those by other authors in the field, a meticulous comparison of definitions and calculations needed to be accomplished to make sure that continuity was maintained. For the most part, parameters were commonly defined, but there were still discrepancies among them. One of these was the definition and use of the flow characteristic length. It is important to note that the length (and resulting area) along the plate that experiences heat transfer is not the same length that contributes to a pressure drop, and as such, different lengths should be defined and utilized for each calculation. In reported literature, common definitions of length include "heat transfer length", "port to port length", "length between ports", "length of channel", "chevron area length", "distribution region length", and just "length". As these researched calculations and correlations will ideally be used in industry, simple, externally measured, and logical lengths should be used. The length used to find the amount of heat transfer area is most easily attained by measuring the distance between the ports ([L.sub.HT]), i.e., the distance measured from the top of the bottom port to the bottom of the top port. No heat transfer occurs at the entrance of each port and it is impossible to know, by external examination, exactly where the entrance or distribution length of the plate ends, and the chevron area begins, and exactly how much of the distribution length actually transfers heat. The pressure drop length, however, is affected by the distance that the fluid travels through the ports, therefore an easy measurement between the middle of each port suffices ([L.sub.P]). The data from other authors being compared with the present data has been mapped to eliminate the discrepancies that arise from the inconsistencies of definitions and calculations. For example, the heat transfer area from other studies was converted to the definition in the present study. Comparing these results shows consistency in heat transfer behavior, as shown in Figure 5 through Figure 7 for the three plates, although there are still quantitative differences that can be explained mainly due to their different geometrical plate configurations and flow conditions.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

Single-Phase Pressure Drop Results

The pressure drop through the middle channel of the three BPHEs was recorded by a differential pressure transducer. The pressure drop reported is based on the assumption of [L.sub.P], meaning that the length used in the calculations was not that of the heat transfer length but the length measured from the middle of the top port to the middle of the bottom port. The resulted correlations are summarized in Table 9, and compared with other studies in Figure 8 through Figure 10.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

Uncertainty Analysis

The instrumentation used in the experimental process detected and recorded temperatures, pressures, and flow rates. Each devise had unique responses and uncertainties, all of which were taken into account when performing a propagation of error analysis. These accuracies were found in Table 10.

CONCLUSION

The single-phase flow of water/water as well as dynalene/water through three brazed plate heat exchangers with different interior configuration, each consists of three channels, were experimentally analyzed in this study. Hot water was pumped into the middle channel while cold water or chilled dynalene into the side channels. The temperature, pressure, and flow rates were precisely measured and collected by a data acquisition unit. The collected data were analyzed to obtain single-phase heat transfer coefficients, using modified Wilson plot method, as well as the Fanning friction factor for each plate configuration. The resulted correlations were within reasonable range of standard deviation and uncertainty. These correlations were also compared with other well established studies on single-phase flow in plate heat exchangers. This comparison qualitatively showed good consistencies; however, considerable differences were observed among different studies that could be explained due to several factors: (1) geometrical configuration of the plates, such as size, corrugation angle, pitch, and spacing were not exactly identical, (2) overall size and aspect ratio of the heat exchangers were different, (3) flow conditions and regimes were different, (4) thermal boundary conditions were not similar, and (5) thermo-hydrodynamic parameters, such as free flow and heat transfer areas, were not consistently defined and used. The latter looks to be a major issue on discrepancies among different studies on PHEs, which needs to be carefully and extensively investigated in the future.

ACKNOWLEDGMENT

This research project was collaborative between Washington State University Vancouver and the American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. The authors are grateful to those individuals in these institutions who have sponsored and supported this research project, especially the PMS members: Dr. Zahid Ayub (chair), James Bogart, and Joseph Huber.

NOMENCLATURE

[A.sub.s] = heat transfer surface area, [m.sup.2] ([in.sup.2])

[A.sub.o] = minimum free flow open area between two neighboring plates, [mm.sup.2] ([in.sup.2])

[A.sub.onepass] = single smallest cross sectional area of flow within channel in BPHE, [mm.sup.2] ([in.sup.2])

b = average plate spacing, mm (in.)

C = constant

[C.sub.p] = specific heat, J/kg * K (Btu/lbm*[degrees]F)

[C.sub.f] = Fanning friction factor

D = diameter, m (in.)

[D.sub.hyd] = hydraulic diameter (taken as twice the mean plate spacing in PHEs), m (in.)

G = mass flux, kg/[m.sup.2] * s ([lb.sub.m]/[ft.sup.2] * s)

H = dimensionless parameter accounting for sub-cooling in the condensate film

h = heat transfer coefficient, W/[m.sup.2] * K (Btu/[ft.sup.2] * s * [degrees]F)

[h.sub.fg] = latent heat, J/kg (Btu/[lb.sub.m])

i = enthalpy, J/kg (Btu/[lb.sub.m])

[[DELTA]h.sub.fg] = specific enthalpy of vaporisation, J/kg (Btu/[lb.sub.m])

Ja = Jacob number

k = thermal conductivity, W/m * K (Btu/ft * s)

[L.sub.T] = plate length, mm (in.)

[L.sub.HT] = heat transfer length (bottom of top port to top of bottom port), mm (in.)

[L.sub.P] = pressure drop length (middle of top port to middle of bottom port), mm (in.)

m = mass flow rate, kg/s ([lb.sub.m]/s)

N = number of plates

Nu = Nusselt number

P = Reynolds number power coefficient

p = system pressure, Pa (psi)

Pr = Prandtl number

q" = heat flux, W/[m.sup.2] (Btu/[ft.sup.2]*s)

Re = Reynolds number

T = temperature, [degrees]C ([degrees]F)

t = plate thickness, mm (in.)

U = overall heat transfer coefficient, W/[m.sup.2] * K (Btu/[ft.sup.2] * s * [degrees]F)

u = flow velocity, m/s (in/s)

[??] = volume flow rate, [m.sup.3]/s (gpm)

w = width of BPHE, mm (in.)

Greek Symbols

[beta] = plate corrugation inclination angle (deg.) measured from horizontal

[lambda] = corrugation pitch, mm (in.)

[DELTA]P = pressure drop, Pa (psi)

[DELTA]T = temperature difference, [degrees]C ([degrees]F)

[mu] = dynamic viscosity, cP ([lb.sub.m]/ft * s)

[rho] = density, kg/[m.sup.3] ([lb.sub.m]/[ft.sup.3])

[PHI] = enlargement factor

Subscripts

c = cold side (heat absorption channels)

eq = equivalent values

f = frictional

fg = difference between liquid and vapor phase properties

film = film condensation

gr = gravitational

h = hot side (heat rejection channel)

ht = heat transfer

hyd = hydraulic

i = in, entrance side of system

l = liquid

lm = logarithmic mean

m = mean values

man = manifold

o = out, exit side of system

p = plate

s = at surface condition

sat = saturation

sp = single-phase

t = thickness

tot = total

tp = two-phase

w = water

REFERENCES

Arman, B. and Rabas, T.J. 1995. Condensation analysis for plate-frame heat exchangers. National Heat Transfer Conference 12: 97-104.

Ayub, Z.H. 2003. Plate heat exchanger literature survey and new heat transfer and pressure drop correlations for refrigerant evaporators. Heat Transfer Engineering 24(5): 8-12.

Bodinus, W.S. 1999. The rise and fall of carbon dioxide systems: The first century of air conditioning. ASHRAE Journal 41(4): ProQuest Education Journals p 37.

Briggs, D.E. and Young, E.H. 1969. Modified Wilson plot techniques for obtaining heat transfer correlations for shell and tube heat exchangers. Chemical Engineering Progress Symposium, AIChE Heat Transfer-Philadelphia 65(92):35-45.

Brown, M., Rosario, L. and Rahman, M.M. 2005. Thermo-dynamic analysis of transcritical carbon dioxide cycles. AES 45: 59-70.

Dynalene Inc. 2008. WhiteHall, PA (www.dynalene.com).

Focke, W.W., Zacharides, J., and Oliver, I. 1985. The effect of the corrugation inclination angle on the thermohydraulic performance of plate heat exchangers. International Journal of Heat and Mass Transfer 28(8):1469-1479.

Halder, G.N. and Sarkar. 2001. S.C. Scope of carbon dioxide as a natural refrigerant for replacements of CFCs. Journal of energy in Southern Africa 12(3): 408-411.

Hwang, Y., Radermacher, R., Jin, D. and Hutchins, J.W. 2005. Performance measurement of [CO.sub.2] heat exchangers. ASHRAE Transactions 111(Part 2):306-316.

Jokar, A., Hosni, M.H. and Eckels, S.J. 2006. Dimensional analysis on the evaporation and condensation of refrigerant R-134a in minichannels plate heat exchangers. Applied Thermal Engineering 25:2287-2300.

Kim, S.G. and Kim, M.S. 2002. Experiment and simulation on the performance of an autocascade refrigeration system using carbon dioxide as a refrigerant. International Journal of Refrigeration 25:1093-1101.

Longo, G.A. and Gasparella, A. 2007. Heat transfer and pressure drop during HFC-134a condensation inside a commercial brazed plate heat exchanger. International Congress of Refrigeration, Beijing.

Longo, G.A., Gasparella, A. and Sartori, R. 2004. Experimental heat transfer coefficients during refrigerant vaporization and condensation inside herringbone-type plate heat exchangers with enhanced surfaces. International Journal of Heat and Mass Transfer 47:4125-4136.

Muley, A. and Manglik, R.M. 1999. Experimental study of turbulent flow heat transfer and pressure drop i a plate heat exchanger with chevron plates. Journal of Heat Transfer 121(1):110-117.

Panchal, C.B. 1985. Condensation heat transfer in plate heat exchangers. American Society of Mechanical Engineers, Heat Transfer Division 44:45-52.

Pearson, A. 2005. Carbon dioxide-new uses for an old refrigerant. International Journal of Refrigeration 28:1140-1148.

Pettersen, J., Hafner, A., Skaugen, G. and Rekstad, H. 1998. Development of compact heat exchangers for [CO.sub.2] air-conditioning systems. International Journal of Refrigeration 25(3):180-193.

Raush, G., Rigola, J., Perez-Segarra, C.D. and Oliva, A. 2005. Thermal and fluid dynamic behavior of a trans-critical carbon dioxide small cooling system: Experimental investigation. International conference on compressors and their systems, Sept 4-7:293-300.

Rigola, J., Perez-Segarra, C.D., Oliva, A. and Raush, G. 2005. Thermal and fluid dynamic behavior of a trans-critical carbon dioxide small cooling system: Numerical analysis. International conference on compressors and their systems, Sept. 4-7:301-309.

Rigola, J., Perez-Segarra, C.D., Oliva, A. and Raush, G. 2005. Numerical simulation and experimental validation of vapour compression systems. Special emphasis on CO2 trans-critical cycles. International Journal of Refrigeration, 28:1225-1237.

Robinson, D.M. and Groll, E.A. 1998. Heat transfer analysis of air-to-carbon dioxide two-phase heat absorption and supercritical heat rejection. HVAC&R Research, Oct., 4(4):327-344.

Shah, R.K. and Wanniarachchi, A.S. 1992. Plate heat exchanger design theory, J.-M. Bushlin (Ed.), Industrial Heat Exchangers, Lecture Series #1991-04, Von Karman Institute for Fluid Dynamics, Belgium.

Thonon, B. 1995. Design method for plate evaporators and condensers. 1st International Conference on Process Intensification for the Chemical Industry, BHR Group Conference Series Publication, 18:37-47.

Tovazhnyanski, L.L. and Kapustenko, P.A. 1984. Intensification of heat and mass transfer in channels of plate condensers. Chemical Engineering Communications, 31(1-6):351-366.

UNEP (United Nations Environmental Programme). 2006. Report of the Refrigeration, Air Conditioning and Heat Pumps Technical Options Committee. RTOC Assessment Report 2006, p 32.

Wang, Z. and Zhao, Z. 1993. Analysis of performance of steam condensation heat transfer and pressure drop in plate condensers. Heat Transfer Engineering 14(4): 32-41.

Wurfel, R. and Ostrowski, N. 2004. Experimental investigations of heat transfer and pressure drop during the condensation process within plate heat exchangers of the herringbone-type. International Journal of Thermal Sciences 43:59-68.

Yan, Y., Lio, H. and Lin, T. 1999. Condensation heat transfer and pressure drop of refrigerant R-134a in a plate heat exchanger. International Journal of Heat and Mass Transfer 42:933-1006.

APPENDIX: Minimum Free Flow Area Calculation

Utilizing computer modeling software can shed extra light on the minimum free flow area (MFFA) in the BPHEs under study. With parametric modeling it is possible to better estimate the area based not only on average plate spacing, but also corrugation pitch and chevron angle. As Figure A1 (a, b, c) shows, the three plates have different corrugations pitches and the angles by which the plates meet, giving different geometries for which fluid to flow through.

[FIGURE A1 OMITTED]

Although the three different plates demonstrate different corrugation pitches and angles, the individual passes all seem to have similar areas, 5.7 mm (0.00884 [in.sup.2]) to 5.8 mm (0.00899 [in.sup.2]) on average. When taking into account all the individual passes collectively, Figure A2 (a, b, c), at any given cross section for the different plates, the three plates' minimum free flow areas are dissimilar as shown in Table A1.

[FIGURE A2 OMITTED]

Instead of having to model each plate in the future to find the minimum free flow area, the following formulation is proposed.

[A.sub.o] = f([beta], [lambda], w, [A.sub.onePass]) (33)

[A.sub.o] = [[2(0.000095[[beta].sup.2] - 0.0074[beta] + 1.0716)wsin([pi][beta]/180)]/[lambda]] * [A.sub.onePass] (34)

where [beta] (in degrees) is the average of the chevron angled plates from the horizontal axis of the vertically installed exchanger.

Setting the definitions of the geometries of the plates, such as minimum free flow area and hydraulic diameter, is essential in accurately analyzing the pressure drop and heat transfer of BPHEs. In fact, calculating the minimum free flow area corresponds to the maximum flow velocity in the channels. This velocity in turn can characterize the Reynolds number and flow regimes in the BPHEs. It was found that the conventional flow area, Equation (12), is 1.3 to 2.5 times the minimum free flow area, Equation (34), for the three BPHEs in this study. This leads to an augmentation in Reynolds numbers of 30% and 150% between the two methods, which can represent different flow regimes.

The resulting heat transfer coefficients utilizing the MFFA method are shown in Table A2.

While the Reynolds number exponents do not deviate substantially from the b * w method, the cold and hot coefficients do (by as much as 94%) yielding discrepancies in the relationships between Nu and Re.

Niel Hayes

Student Member ASHRAE

Amir Jokar, PhD

Member ASHRAE

This paper is based on findings resulting from ASHRAE Research Project RP-1394.

Niel Hayes is a graduate research assistant and Amir Jokar is an assistant professor in the School of Engineering and Computer Science, Washington State University Vancouver, Vancouver, WA.

Global warming concerns are gaining momentum in the twenty-first century and as such, environmentally friendly refrigerants are quickly becoming a necessity rather than just an interesting topic to speculate about for the future. R-744 or carbon dioxide ([CO.sub.2]) is a top contender, as instigated in the Montreal protocol, to phase out the use of ozone depleting chlorofluorocarbon (CFC) and the greenhouse gas contributing hydrochlorofluorocarbon (HCFC) refrigerants, especially in low temperature applications. As mentioned by Bodinus (1999), the idea of using carbon dioxide as a refrigerant started in the mid 19th Century by Alexander Twining; however, it was not readily implemented until Franz Windhausen made a [CO.sub.2] compressor in 1886. [CO.sub.2] refrigeration systems gained popularity until the late 1920s and early 1930s in the great depression. Due to the rise in demand for smaller systems in the non-commercial refrigeration market, coupled with the extremely high pressures required to use [CO.sub.2] as a refrigerant, an innovation was needed. Companies such as General Motors and DuPont funded research to develop new refrigerants that could operate under much lower pressures, Pearson (2005). Thus, synthetic CFC refrigerants were invented, which allowed refrigeration units to be sized much smaller and cheaper due to lower working pressure requirements. When these new refrigerants were developed, research and use of R-744 was greatly reduced.

With the introduction of new CFCs/HCFCs refrigerants, such as R-12 and R-22, the refrigeration market's needs were met, but at the same time these innovations created environmental problems. The chlorine molecules in CFCs/HCFCs proved to be harmful when leaked and released into the atmosphere. The ozone molecules in the stratosphere, which protect humans from harmful ultra-violet rays, are absorbed and destroyed by the chlorine molecules through a chemical reaction. In the early 1990s, a few hydrofluorocarbon (HFC) refrigerants, such as R-134a, were developed in which chlorine molecules were totally replaced by hydrogen molecules. In spite of the improvement regarding the ozone depletion dilemma, HFCs are still not perfect refrigerants due to their excess carbon, which contributes to the potential for global warming. In general, the existing refrigerants in today's market have two measured potential harmful effects on the environment: Global Warming Potential (GWP) and Ozone Depletion Potential (ODP). Global Warming Potential measures how harmful a greenhouse gas can be compared to carbon dioxide, which is defined as the GWP base reference having a value of 1. Ozone Depletion Potential characterizes how harmful a chemical compound can be in depleting the ozone layer on a scale of 0 to 1. These two measured potentials are typically presented for common refrigerants in Table 1.

Table 1. Adverse Affects of Refrigerants on the Environment from the United Nations Environment Program (UNEP-2006) Refrigerants ODP GWP (100 Year Time Horizon) R-12 (CFC) 1.00 10,890 R-22 (HCFC) 0.050 1810 R-134a (HFC) 0 1430 R-744 or [CO.sub.2] (nature 0 1 friendly)

Comparing GWPs and ODPs of R-744 to R-134a, R-22, and R-12 in Table 1, one can find that more research and application must be established to further the progress of [CO.sub.2] as an eco-friendly refrigerant.

Not only is carbon dioxide promising as a refrigerant with respect to the environment's protection, but it also works as a great refrigerant due to its abundance, safety, as well as its thermophysical properties. Halder and Sarkar (2001) found that [CO.sub.2] had several advantages over conventional refrigerants, which included lower pumping power requirements (attributed to a lower required volumetric flow rate), higher efficiency in heat exchangers, and higher latent heat. However, one of the leading factors in the decline of [CO.sub.2] as a practical refrigerant in the early 20th century was due to the lack of technology in using this refrigerant under its high pressure demands in smaller applications. With the substantial recent development in heat exchanger and compressor technologies however, [CO.sub.2] can now be seriously considered a potential working refrigerant in industrial as well as non-commercial applications.

Since the 1930s, plate heat exchangers have served well for single-phase heat transfer applications, e.g., beverage and food processing, pharmaceutical industries, paper and rubber industries, and dairy pasteurization, as mentioned by Shah and Wanniarachchi (1992). The introduction of brazed plate heat exchangers in the 1970s, which brazed the plates together rather than using gaskets, bolts, and carrying bars, unlocked the possibilities of using refrigerants that require higher operating pressures and larger temperature ranges. Plate heat exchangers are innovative in several different aspects of heat transfer; total heat transfer area per total volume is quite large compared to other types of heat exchangers, and high turbulence can be achieved even at low flow rates which results in high heat transfer coefficients. One of the drawbacks to the brazed plate heat exchangers however, is the difficulty of freeing the plates of fouling, unlike the earlier plate heat exchangers that could be disassembled, cleaned, and reassembled.

The focus of this research is to understand the condensation behavior of [CO.sub.2] in three brazed plate heat exchangers with differing interior plate geometries. To date, no research has been reported in literature on condensing [CO.sub.2] in brazed plate heat exchangers. Nevertheless, there has been research on other refrigerants being condensed in brazed plate heat exchangers as well as [CO.sub.2] being used in refrigeration systems.

LITERATURE REVIEW

Single-Phase Flow in Plate Heat Exchangers

To be able to formulate two-phase flow in the BPHEs, comprehensive single-phase flow experimentation is first required to establish single-phase formulation. Table 2 and Table 3 show typical well-established experimental correlations for single-phase heat transfer coefficients and friction factors, respectively, in PHEs, as presented by Ayub (2003).

Table 2. Single-Phase Heat Transfer Correlations Using an Enlargement Factor of Unity ([PHI] = 1) General Single-Phase Heat Transfer Correlation: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [beta] Re [C.sub.1] [C.sub.2] [C.sub.3] 30 >1000 0.09 0.70 1/3 Muley and 45 >1000 0.08 0.76 1/3 Manglik (1999) 60 >1000 0.08 0.78 1/3 20-150 1.89 0.46 0.50 30 150-600 0.57 0.70 0.50 600-16,000 1.11 0.60 0.50 45-300 1.67 0.44 0.50 Focke et al. 45 300-2000 0.41 0.70 0.50 (1985) 2000-20,000 0.84 0.60 0.50 60 120-1000 0.77 0.54 0.50 1000-42,000 0.44 0.64 0.50 30 50 [less 0.29 0.70 1/3 than or equal to] Re [less than or equal to] 15,000 Thonon 45 50 [less 0.30 0.65 1/3 (1995) than or equal to] Re [less than or equal to] 15,000 60 50 [less 0.23 0.63 1/3 than or equal to] Re [less than or equal to] 15,000 [C.sub.4] 0.14 Muley and 0.14 Manglik (1999) 0.14 0.00 0.00 0.00 0.00 Focke et al. 0.00 (1985) 0.00 0.00 0.00 0.00 Thonon 0.00 (1995) 0.00 Table 3. Single-Phase Pressure Drop Correlations using an Enlargement Factor of Unity ([PHI] = 1) General Friction Factor Correlation: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [beta] Re [C.sub.5] [C.sub.6] [C.sub.7] 30 10-100 19.40 0.59 0 Muley and 45 15-300 18.29 0.65 0 Manglik (1999) 60 40-400 3.24 0.63 0 30 90-400 188.75 1.00 1.26 400-16,000 6.70 0.21 0 Focke et al. 45 150-1800 91.75 1.00 0.30 (1985) 1800-30,000 1.46 0.18 0 60 260-3000 57.50 1.00 0.09 3000-50,000 0.90 0.26 0 [less than 45.57 0.67 0 or equal to] 160 30 >160 3.7 0.17 0 [less than 18.19 0.68 0 or equal to] 200 Thonon 45 >200 0.69 0.17 0 (1995) [less than 26.34 0.83 0 or equal to] 550 60 >550 0.57 0.22 0

Condensation in PHEs

While heat transfer coefficients and pressure drops have been studied extensively in the single-phase realm in PHEs, as documented by Ayub (2003), two-phase vaporization and condensation have not received as much attention, let alone in BPHEs.

A comprehensive condensation table of plate channels has been presented by Wurfel and Ostrowski (2004). Various entries of that table, as well as more recent findings, are focused on in the present section of literature review.

Panchal (1985) observed condensation heat transfer of ammonia in Alfa-Laval PHEs. Two exchangers with chevron angles of 60[degrees] and 30[degrees] were used. Heat transfer was observed using the different parameters of film Reynolds numbers (200-2000) in the high angle plate and low angle plates. Experimental data was compared against theoretical calculations. The conclusion that was made stated that for both low and high angle plates the heat transfer coefficients increased with the film Reynolds number or remained constant. This behavior was attributed to high interfacial shear stress for laminar-film condensation and the occurrence of the shear-stress-controlled condensation at low Reynolds numbers. Although no analytical relationship was made from Panchal's (1985) experiments, it was compared to Tovazhnyanski's (1984) Nusselt numbers for high and low angle plates:

Nu = 0.34924 [Re.sup.[0.75]] [Pr.sup.[0.4]] (high-angle plates) (1)

Nu = 0.11159 [Re.sup.[0.75]] [Pr.sup.[0.4]] (low-angle plates) (2)

Water-steam condensation was studied by Wang and Zhao (1993) in a plate heat exchanger with a chevron angle of 45 degrees, consisting of three channels. Parameters measured were flow, steam content, temperature differences, and pressures to obtain heat transfer coefficients. Condensation heat transfer was directly proportional to pressure drop. The heat flux in the plate heat exchanger was consistently larger than shell and tube condensers, this was due in part by the complex configurations of the channels, small cross sections, and shearing of steam flow with high velocities.

Arman and Rabas (1995) reported their results using ammonia in their PHEs with chevron angles of 30[degrees] and 60[degrees] to test single component condensation correlation equations. A propane/butane mixture was used in a plate heat exchanger (angle not specified) to study binary-component condensation as well. The single component condensation results revealed that the high chevron angle achieved high pressure drops at Reynolds numbers (5000-7500), where the low angle plate achieved the same pressure drop at almost three times the Reynolds numbers. Also, from the tables in the paper, it appeared that the high angle chevron plate required a lower mass flow rate than the low angle chevron plate to achieve the same heat transfer coefficients.

Yan et al. (1999) found that condensation trends for R-134a in PHEs showed greater heat transfer coefficients as well as pressure drops as vapor quality increased. Their experimental parameters included mass flux, average imposed heat flux, saturated pressure, and vapor quality. Using an inclination angle of 60[degrees] in the 500 mm (19.68 in.) by 120 mm (4.72 in.) plates, it was noted that the chevron configuration in PHEs create high turbulence at low Reynolds numbers which increased heat transfer at slower flow rates. The following heat transfer coefficient and friction factor were correlated:

Nu = 4.118 [Re.sub.eq.sup.[0.4]] [Pr.sub.l.sup.[1/3]] (3)

[f.sub.tp][Re.sup.[0.4]][Bo.sup.[-0.5]][([p.sub.m]/[p.sub.c]).sup.[-0.8]] = 94.75 [Re.sub.eq.sup.[-0.0467]] (4)

Jokar et al. (2006) explored single and two-phase heat transfer and pressure drop correlations of R-134a that were found in three heat exchanger depths (34, 40, and 54 plates) of 112 mm (4.41 in.) by 311 mm (12.24 in.) plates all having a corrugation inclination angles of 60[degrees]. These heat exchangers were used as both evaporators as well as condensers in an auto-motive dual refrigeration system. The two-phase flow correlations proved to be much more complex than that of the single-phase. The following correlations were proposed for the two-phase condensation heat transfer and pressure drop:

[Nu.sub.tp] = 3.371[Re.sup.[0.55]][Pr.sup.[0.3]][([G.sup.2]/[[rho].sup.2][C.sub.p][DELTA]T).sup.[1.3]][([[rho].sup.2][i'.sub.fg]/[G.sup.2]).sup.[1.05]][([rho][sigma]/[mu]G).sup.[0.05]][([rho]/([rho] - [[rho].sub.v])).sup.2] (5)

[C.sub.f, tp] = 2.139 * [10.sup.7][([GD.sub.hyd]/[[mu].sub.m, sat]).sup.[-1.6]] for 960 [less than or equal to] ([GD.sub.hyd]/[[mu].sub.m, sat]) [less than or equal to] 4169 (6)

Important two-phase behaviors were observed in the experimentation of condensation in the BPHEs; e.g., when the temperature differences were not large, film condensation proved to be the dominant characteristic when determining heat transfer correlations. Also, as the mass flow rates increased within the minichannels of the BPHEs, convection proved to be more important in driving heat to transfer.

Longo and Gasparella (2007) studied the condensation of R-134a in BPHEs. Three parameters were observed to conclude how each affected the heat transfer coefficients and pressure drop in the BPHE; mass flux, saturated R-134a vapor, and super heated R-134a vapor. The BPHEs used consisted of 10 plates, 72 mm (2.83 in.) by 310 mm (12.20 in.) that had the inclination chevron angle of 65[degrees]. It appeared that gravity controlled condensation occurred at mass fluxes less than 20 kg/[m.sup.2]*s (4.10 [lb.sub.m]/[ft.sup.2]*s), but when the flux exceeded this, forced convection condensation was achieved, producing a 30% increased heat transfer coefficient when the mass flux was 40 kg/[m.sup.2]*s (8.19 [lb.sub.m]/[ft.sup.2]*s). The behavior of the saturated vapor versus the super heat was similar, with the super heat yielding only an 8-10% increase in heat transfer over the saturate. Saturation temperature however played no great significance in heat transfer in the BPHE. For saturated vapor condensation Longo and Gasparella (2007) proposed the average heat transfer coefficient on the vertical plate as

[h.sub.r] = [PHI]0.943[[([[lambda].sub.l.sup.3][[rho].sub.l.sup.2]g[[DELTA]J.sub.lg])/([[mu].sub.l][DELTA]TL)].sup.[1/4]] (7)

where [PHI] is the enlargement factor equal to the ratio between the actual area and the projected area of the plates due to corrugation. For forced convection condensation the average heat transfer coefficient was found to be modeled closely to

[h.sub.r] = (1/S)[S.[integral].0][PHI]5.03([[lambda].sub.L]/[d.sub.h])[Re.sub.eq.sup.[1/3]][Pr.sub.L.sup.[1/3]]dS (8)

for equivalent Reynolds numbers less than 50,000. Pressure drop was derived from the experimental data as

[[DELTA]p.sub.f] = 1.816 KE/V (9)

Longo et al. (2004) also researched the correlations between surface smoothness within PHEs and condensation and evaporation heat transfer coefficients. Three types of smoothness were observed; smooth, rough, and cross-grooved. The plates were all of the chevron or herringbone type with inclination angles of 65[degrees]. It was concluded that the increased roughness was only advantageous in vaporization, whereas the cross-grooved plates improved both vaporization and condensation by 30%-40% and 60% respectively when compared to smooth plates.

Carbon Dioxide in Refrigeration Systems

Searching and reviewing the open literature, there is no single work reported on the condensation of [CO.sub.2] in BPHEs to date. However, there is research that has been done on carbon dioxide being used in refrigeration systems, as outlined in Table 4.

Table 4. Carbon Dioxide Used in Refrigeration Systems, as Reported in Open Literature Researcher Heat Exchanger Type Remarks Robinson and Single straight tubes with [CO.sub.2] and R-22 Groll (1998) outside fins of constant two-phase behavior was thickness and spacing compared and [CO.sub.2] heat exchanger dimension ratios were proposed. Pettersen et al. Small diameter Discussed advantages and (1998) mechanically expanded disadvantages of how round-tube heat exchanger various exchangers may be and brazed micro-channel used for [CO.sub.2] type heat exchanger refrigeration cycles in automotive and residential air conditioning. Kim and Kim Counter flow-type heat Experimentation and (2002) exchanger with concentric simulation were performed dual tubes using showing that as mass R-774/134a and R-744/290 fractions of R-744 mixtures. increased, cooling capacity and compressor power increased but COP decreased. Raush et al. Double pipe heat Numerical and experimental (2005) exchangers results of trans-critical [CO.sub.2] cycle discovering optimal gas cooler pressure values in the trans-critical [CO.sub.2] cycle. Rigola et al. Double pipe counter flow Numerical analysis was (2005) performed. Brown et al. Evaporator and condensers Visual Basic programs were (2005) not specified in Visual used to simulate single Basic program and two-phase [CO.sub.2] vapor compression cycles.

As far as research on developing [CO.sub.2] as a refrigerant, Hwang et al. (2005) explored [CO.sub.2] behavior and produced a database to provide a better understanding of the environmentally friendly compound. The researchers utilized fin and tube as well as microchannel heat exchangers to explore [CO.sub.2] condensation and evaporation properties. Airside pressure drops were compared according to different air frontal velocities. As inlet pressure of [CO.sub.2] increased, its heating capacity did the same up to a pressure of about 10 or 11 MPa (1450 to 1600 psi). Various overall heat transfer coefficients were measured, tabulated, and graphically presented. As air frontal velocities increased, heat transfer values increased. As mass flow rates increased heat transfer values increased as well.

Rigola et al. (2005) compared numerically and experimentally a [CO.sub.2] transcritical refrigeration system and sub-critical R-134a refrigeration cycle. Although the research heavily biased numerical analysis, two prototyped single stage hermetic reciprocating compressors (one being an improvement of the other) were used in the [CO.sub.2] refrigeration cycle to validate the numerical results. Both numerical and experimental results showed only a 10% lower COP in the [CO.sub.2] refrigeration cycle than that of R-134a under similar cooling capacity parameters.

EXPERIMENTAL FACILITY

Single-Phase Experimentation Set Up

A thorough single-phase analysis, including water/water and dynalene/water (2008), was conducted since single-phase heat transfer and pressure drop coefficients are needed in the two-phase analysis of [CO.sub.2] condensation. The single-phase test facility is depicted in Figure 1. To match the two-phase behavior of [CO.sub.2] condensing (rejecting heat) in the middle of three channels within the heat exchanger, single-phase hot water entered the top of the exchanger, flowing through the middle channel. On the other side, cold water entered from the bottom of the exchanger, flowing through the side channels, to produce counter flow heat transfer. The hot water line contained the instrumentation to record temperature, pressure drop, and flow rate; however, the cold water line recorded only temperature and flow rate. The pressure transducers on the hot line were positioned as close as possible to the inlet and outlet of the exchanger, followed by temperature reading and flow metering devices.

[FIGURE 1 OMITTED]

For the dynalene/water experimentation, the single phase flow configuration was similar, i.e., hot water flowing through the middle channel and chilled dynalene flowing through the side channels. But the instrumentation used for the hot side in the water/water configuration (temperature, pressure drop, flow rate) was switched to record data for the cold side in the dynalene/water test, in order to obtain more precise measurements on the dynalene side.

Two-Phase Experimentation Set Up

Once the single-phase analysis has been completed, the two-phase experimentation can commence. Two refrigeration loops will be used to complete the study, one being the two-phase [CO.sub.2] loop while the other, a single-phase dynalene loop. Figure 2 shows the plan for the two-phase experimentation equipment.

[FIGURE 2 OMITTED]

Brazed Plate Heat Exchangers

Three brazed plate heat exchangers are used in the present study. Dimensions and geometries of the plates are expressed in Table 5. Graphical descriptions of various BPHE dimensions are expressed in Figure 3.

Table 5. BPHE Geometries Used in Present Study L Plate Chevron Angle, degrees 60[degrees]/60[degrees] (measured from horizontal in a vertical instillation) [[beta]] [Length.sub.Total], mm 533.4 (21) (in.) [[L.sub.Total]] [Length.sub.Heat 444.5 (17.5) Transfer] (top of bottom port to bottom of top port), mm (in.) [[L.sub.HT] [Length.sub.Pressure 476.25 (18.75) Drop] (middle of top port to middle of bottom port), mm (in.) [[L.sub.Port] Width, mm (in.) [w] 127 (5) Port diameter, mm (in.) 25.4 (1) Corrugation pitch, mm 6.27 (0.2468) (in.) [[lambda]] Enlargement factor [[PHI]] 1.2 Projected surface area, 0.05645 (87.5) [m.sup.2] ([in..sup.2]) Effective surface area, 0.06774 (105) [m.sup.2] ([in..sup.2])[[A.sub.s]] Plate thickness, mm (in.) [t] 0.4 (0.0157) Mean channel spacing, mm 2 (0.0787) (in.) [b] Number of channels 3 M Plate Chevron Angle, degrees 27[degrees]/60[degrees] (measured from horizontal in a vertical instillation) [[beta]] [Length.sub.Total], mm 533.4 (21) (in.) [[L.sub.Total]] [Length.sub.Heat 444.5 (17.5) Transfer] (top of bottom port to bottom of top port), mm (in.) [[L.sub.HT] [Length.sub.Pressure 476.25 (18.75) Drop] (middle of top port to middle of bottom port), mm (in.) [[L.sub.Port] Width, mm (in.) [w] 127 (5) Port diameter, mm (in.) 25.4 (1) Corrugation pitch, mm 6.19 (0.2437) (in.) [[lambda]] Enlargement factor [[PHI]] 1.2 Projected surface area, 0.05645 (87.5) [m.sup.2] ([in..sup.2]) Effective surface area, 0.06774 (105) [m.sup.2] ([in..sup.2])[[A.sub.s]] Plate thickness, mm (in.) [t] 0.4 (0.0157) Mean channel spacing, mm 2 (0.0787) (in.) [b] Number of channels 3 H Plate Chevron Angle, degrees 27[degrees]/27[degrees] (measured from horizontal in a vertical instillation) [[beta]] [Length.sub.Total], mm 533.4 (21) (in.) [[L.sub.Total]] [Length.sub.Heat 444.5 (17.5) Transfer] (top of bottom port to bottom of top port), mm (in.) [[L.sub.HT] [Length.sub.Pressure 476.25 (18.75) Drop] (middle of top port to middle of bottom port), mm (in.) [[L.sub.Port] Width, mm (in.) [w] 127 (5) Port diameter, mm (in.) 25.4 (1) Corrugation pitch, mm 6.03 (0.2374) (in.) [[lambda]] Enlargement factor [[PHI]] 1.2 Projected surface area, 0.05645 (87.5) [m.sup.2] ([in..sup.2]) Effective surface area, 0.06774 (105) [m.sup.2] ([in..sup.2])[[A.sub.s]] Plate thickness, mm (in.) [t] 0.4 (0.0157) Mean channel spacing, mm 2 (0.0787) (in.) [b] Number of channels 3

[FIGURE 3 OMITTED]

The counter flow, also detailed in Figure 3, shows how the three channels are utilized having the outside channels direct flow opposite the middle channel. This counter flow method, coupled with alternating corrugated plates, allows for high heat transfer rates due to forced turbulence and an increase in pressure drop across the plates.

[CO.sub.2] Pump

In order to study the condensation of carbon dioxide, a [CO.sub.2] refrigeration loop must be built. The specifications for the test conditions state the temperature range of saturated [CO.sub.2] span from -17.8[degrees]C (0[degrees]F) to -34.4[degrees]C (-30[degrees]F) and the heat flux in the heat exchanger spans 800 Btu/hr*[ft.sup.2] (2.5 kW/[m.sup.2]) to 5000 Btu/hr*[ft.sup.2] (15.7 kW/[m.sup.2]). Not knowing initially the size of plates being used for the heat exchanger, maximum and minimum flow rates and pressures were calculated from the possible plate geometries to size the [CO.sub.2] pump. By multiplying the given heat fluxes by the approximate possible plate areas, minimum and maximum power loads were found. These loads were then divided by the latent heat of vaporization of [CO.sub.2] at the low and high temperatures to yield a mass flow rate. The mass flow was then converted to a volumetric flow based on appropriate properties of [CO.sub.2]. The flow range that was calculated was on the order of 0.01 gpm (0.00227 [m.sup.3]/sec) for the smallest plate and lowest heat flux, while for the largest plates and highest heat flux, 0.4 gpm (0.0909 [m.sup.3]/sec). A proper [CO.sup.2] pump was purchased that satisfies flow requirements as well as withstanding the extreme low working temperatures.

Chiller

A packaged water-cooled chiller was selected with a capacity of 39,275 Btu/h (3.27 tons) at -40[degrees]C (-40[degrees]F), which uses R507a as the working fluid to chill the secondary cooling fluid dynalene (HC-50). Dynalene was found to be a better fluid for this project compared to ethylene glycol since dynalene is less viscous at very low temperatures. Furthermore, a 50/50 ethylene glycol water mixture may freeze at -37[degrees]C (-34.6[degrees]F). Table 6 shows some of the thermo-physical properties of the two cooling fluids at -35[degrees]C (-31[degrees]F). Although dynalene is 25% more dense and its specific heat value is 20% less than glycol at this temperature, it is 75% less viscous than the ethylene glycol mixture. The chiller uses a 75 gallon (0.284 [m.sup.3]) stainless steel tank insulated with 3 inch (0.0762 m) expanded foam in a 0.080 inch (0.002032 m) aluminum jacket to store and maintain the dynalene at desired temperatures.

Table 6. Cooling Fluid Property Comparison -35[degrees]C Density, kg/[m.sup.3] Dynamic Viscosity, (-31[degrees]F) ([lb.sub.m]/[ft.sup.3]) cP ([lb.sub.m]/ft*s) dynalene 1370.5 (85.56) 15.7 (0.0101) 50/50 ethylene 1089.94 (68.04) 66.93 (0.0450) glycol -35[degrees]C Specific Heat, kJ/kg*K (-31[degrees]F) (Btu/[lb.sub.m]*[degrees]F) dynalene 2.59 (10.84) 50/50 ethylene 3.07 (12.85) glycol

Temperature Reading Devices

a. Resistance Temperature Detectors (RTD): Temperature must be measured accurately at the inlets and outlets of the plate heat exchangers, and as such, RTDs provide the highest accuracy possible to deliver reliable temperatures. Just as thermocouples, there are several kinds of RTDs that are configured differently and have different accuracies. Of the three different wire configurations (2-wire, 3-wire, 4-wire) that are available, the 4-wire RTD were used in the test set up. The 4-wire design touts the highest accuracy and reliability of the different configurations because the resistance error due to lead wire resistance is nonexistent in this design. There are five different tolerance classes that depict temperature accuracy; Class B, Class A, DIN 1/3, DIN 1/5, and DIN 1/10. Table 7 shows comparison of four of the temperature reporting tolerances for RTDs. The RTDs in this experiment were of the accuracy following the 1/3 DIN. The 100 [ohm] platinum RTDs used conform to the Pt 3851 calibration curve. Each of the RTDs had sheath lengths of 6 inches (0.1524 m) to minimize stem conduction effects. This measurement surpassed the recommended minimum sheath length of 20 times the RTD diameter, and with the diameter of 1/8 inch (3.175 mm), the 6 inch (0.1524 m) sheath is 48 times the diameter, therefore temperature reading disturbances from ambient temperatures did not influence experimental data.

Table 7. Temperature Tolerances for RTDs Temp, Class B ([+ or -] Class A ([+ or -] 1/3 DIN ([+ or -] [degrees]C [degrees]C) [degrees]C) [degrees]C) ([degrees]F) -40 (-40) 0.50 0.25 0.13 -30 (-22) 0.45 0.23 0.13 -20 (-4) 0.40 0.20 0.12 -10 (14) 0.35 0.18 0.11 Temp, 1/10 DIN ([+ or -] [degrees]C [degrees]C) ([degrees]F) -40 (-40) 0.05 -30 (-22) 0.045 -20 (-4) 0.04 -10 (14) 0.035

b. Thermocouples: For areas of the condensing loop that did not require high accuracy temperature readings, type T thermocouples sufficed. The temperature range of type T thermocouples was adequate for the present experimentation parameters. The thermocouples were classified in tolerance class 1, which for type T is [+ or -] 0.5[degrees]C between -40[degrees]C to 125[degrees]C (-40[degrees]F to 257[degrees]F). This accuracy was three times better than the more common K and J type thermo-couples, which were rated at [+ or -]1.5[degrees]C between -40[degrees]C to 375[degrees]C (-40[degrees]F to 707[degrees]F). Again the stem lengths were 6 inches (0.1524 m) as to minimize stem conduction interference.

Pressure Reading Devices

Obtaining accurate pressure drop data was critical in the project, and as such, high accuracy gauge and differential pressure transducers were utilized to measure pressure behaviors. The gauge and differential pressure transducers had a compensated temperature range which covers -40[degrees]C (-40[degrees]F). They were made of all stainless steel and hermetically sealed. The differential pressure transmitter required a 10 V ac or dc excitation voltage and returned a 3 mV/V [+ or -]1% with an accuracy of 0.25% linearity, with hysteresis and repeatability combined. The gauge pressure transducer was designed to work in a range of 0-500 psi (0-3.45 MPa). The transmitter is capable of working off of an excitation voltage from 6-42 Vdc and output either a 4-20 mA or 1-5 Vdc signal. The gauge pressure transducer had an accuracy of [+ or -]0.1% of the upper range limit or [+ or -]0.15% of full scale.

Flow Reading Devices

To accurately measure the flow of dynalene, which will ultimately condense the [CO.sub.2] refrigerant, a turbine flow meter made of stainless steel using a ceramic journal bearing with a RF pickoff signal to ensure the widest flow metering range of 0.3 to 15 gpm (0.068 to 3.41 [m.sup.3]/sec) was utilized. The ceramic journal bearing was necessary for the dynalene due to its high viscosity. The flow meter had two 10 point calibrations with viscosities of 1 cSt and 20 cSt to give an accuracy of [+ or -]0.05%. The flow meter's temperature and pressure operating ranges were -100[degrees]F to 800[degrees]F (-73.3[degrees]C to 426.7[degrees]C) and up to 5000 psig (34.5 MPa). The flow meter used an input DC voltage range of 8 to 30V and produced 0 to 5V pulses ranging from 5 to 5000 Hz.

Data Acquisition System

All of the experimental equipment was integrated into a data acquisition system program which recorded and displayed all the temperatures, pressures, and flow rates necessary. A power supply was used to power the flow meter as well as the differential pressure transmitter.

Test Procedure

To be as consistent as possible in the data collection process, identical steps were used for each heat exchanger.

1. Both hot and cold water ran until maximum hot and minimum cold temperatures were achieved.

2. Data collecting began by finding the maximum flow rates permitted by each side of each plate (1 channel side and 2 channel side) and assigning flow increments to be analyzed.

3. The DAQ recorded the inlet and outlet temperatures, gauge and differential pressures, as well as the flow from the turbine flow meter every 2 seconds for a duration of 2 minutes yielding a total of 60 data points per data collection set.

4. Data collection sets started by recording max flows of cold and hot. The hot flow stayed constant as the cold flow decreased for each iteration. When the minimum cold flow iteration was completed, the next permeation of reduced hot flow was set constant and the cold flow increased for each iteration. Data collection followed this fashion until all combinations of low and high flows for cold and hot water were recorded.

5. Statistical analysis was performed on each data set before moving to the next data set to ensure low standard deviations and acceptable precision intervals.

6. Data was then verified by the energy balance equation, assuming the specific heats of the hot and cold water to be equal. The ratio of cold mass flow rate with cold side temperature difference and hot mass flow rate with hot side temperature difference should equal unity.

SINGLE-PHASE ANALYSIS

The raw data collected by the data acquisition system are used to obtain the single-phase heat transfer and pressure correlations within the three BPHEs. This section reviews the data reduction method, and discusses the resulted correlations.

Modified Wilson Plot for Heat Transfer

As the first step in analyzing the collected data, properties of water for each test point were calculated at bulk temperatures averaged between the inlet and outlet ports on each side.

Each property, including density, specific heat, conductivity, and viscosity, was evaluated and correlated, using third order logarithmic regressions. These properties were then used to find the flow characteristics in the channels for each plate.

The Reynolds number of the flow within the channels was calculated by:

Re = [[GD.sub.hyd]/[mu]] (10)

where the hydraulic diameter was defined as two times the average plate spacing ([D.sub.hyd] = 2b), and the mass flux was calculated based on the minimum free flow area ([A.sub.o]) between the plates, as described by Shah and Wanniarachchi (1992):

G = [[[rho][??]]/[A.sub.o]] (11)

Due to the complicated geometries that brazed plate heat exchangers contain, this minimum free flow area is difficult to estimate and has not been universally standardized. However for the sake of simplicity, many studies have considered this free flow area as the average plate spacing, b, multiplied by the width of the plate:

[A.sub.o] [approximately equal to] bw (12)

It is noteworthy that the minimum free flow area (MFFA) between the two neighboring plates, which depends on the corrugation angle, is much less than the area given by Equation (12). A more thorough description of the minimum free flow area is given in the appendix of this manuscript, while Equation (12) is used for data reduction in this study.

An energy balance was applied in order to obtain heat transfer rates on both hot and cold sides:

Q = m[c.sub.p][DELTA]T (13)

Using the log-mean temperature difference

[[DELTA]T.sub.lm] = [[([T.sub.h, i] - [T.sub.c, o]) - ([T.sub.h, o] - [T.sub.c, i])]/[ln[([T.sub.h, i] - [T.sub.c, o])/([T.sub.h, o] - [T.sub.c, i])]]] (14)

the overall heat transfer coefficient in the heat exchanger was calculated by:

U = [[Q.sub.h]/[2[A.sub.S][[DELTA]T.sub.lm]]] (15)

where [A.sub.s] is the effective heat transfer surface area, which was calculated by the projected heat transfer area multiplied by the enlargement factor.

A common analysis method of single-phase heat transfer in BPHE is the modified Wilson plot technique. Due to the possibility of large property variations, especially the viscosity of dynalene, the heat transfer correlation format was chosen similar to the Sieder-Tate equation, as explained in Incropera and DeWitt (2002):

Nu = [CRe.sup.P][Pr.sup.[1/3]][[([mu]/[[mu].sub.S])].sup.[0.14]] (16)

The heat transfer coefficients for the hot and cold sides of the BPHE are thus obtained by:

[h.sub.c] = ([k.sub.c]/[D.sub.hyd])[C.sub.c] [Re.sub.c.sup.P] [Pr.sub.c.sup.[1/3]] [[([mu]/[[mu].sub.S])].sub.c.sup.[0.14]] (17)

and

[h.sub.h] = ([k.sub.h]/[D.sub.hyd])[C.sub.h] [Re.sub.h.sup.P] [Pr.sub.h.sup.[1/3]] [[([mu]/[[mu].sub.S])].sub.h.sup.[0.14]] (18)

In the original Wilson plot technique, used for shell-and-tube heat exchangers, [C.sub.h] and [C.sub.c] are the only coefficients that need to be found to be able to find Nusselt numbers. Reynolds number exponent (0.8), Prandtl number exponent (1/3), as well as the viscosity ratio exponent (0.14) for the tube side are assumed constant due to the widely accepted characteristics of in tube flow. The shell side Reynolds number exponent, however, is not necessarily 0.8 and can be optimized, based on the magnitude of Reynolds number, in the Wilson plot calculations. Plate geometries in BPHEs are so complex and varied among different manufacturers, the flow regimes, and as a result the Reynolds number exponents, cannot be assumed like the in-tube flow. Due to the similarity in geometries and configurations on the cold and hot channels of a BPHE, the flow regimes and the Reynolds number exponents on both sides can be assumed identical in certain ranges of Reynolds numbers. Prandtl number exponent and viscosity ratio exponent, which account for the fluid properties, can also be assumed constant at 1/3 and 0.14, respectively. The original Wilson plot technique requires the data to be recorded at constant flow rates and constant average bulk fluid temperatures on both hot and cold sides, which is not easily accomplished. However, the modified Wilson plot technique, devised by Briggs and Young (1969), allows data to be taken at varying flow rates and varying bulk fluid temperatures on hot and cold sides. The overall heat transfer equation based on this method is obtained through the following thermal resistance equation:

[1/U] - [(t/k).sub.wall] = [1/[[C.sub.c][[k.sub.c]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.c.sup.P][([[c.sub.p][mu]]/k).sub.c.sup.[1/3]][([mu]/[[mu].sub.S]).sub.c.sup.[0.14]]]] + [1/[[C.sub.h][[k.sub.h]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.h.sup.P][([[c.sub.p][mu]]/k).sub.h.sup.[1/3]][([mu]/[[mu].sub.S]).sub.h.sup.[0.14]]]] (19)

Multiplying both sides of the above equation by

[[k.sub.c]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.c.sup.P][([[c.sub.p][mu]]/k).sub.c.sup.[1/3]][([mu]/[[mu].sub.S]).sub.c.sup.[0.14]] (20)

gives

(1/U - [(t/k).sub.wall])[[k.sub.c]/[D.sub.hyd][([[D.sub.hyd]G]/[mu]).sub.c.sup.P][([[c.sub.p][mu]]/k).sub.c.sup.[1/3]][([mu]/[[mu].sub.S]).sub.c.sup.[0.14]]] = [1/[C.sub.c]] + [[[[k.sub.c]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.c.sup.P][([[c.sub.p][mu]]/k).sub.c.sup.[1/3]][([mu]/[[mu].sub.S]).sub.c.sup.[0.14]]]/[[C.sub.h][[k.sub.h]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.h.sup.P][([[c.sub.p][mu]]/k).sub.h.sup.[1/3]][([mu]/[[mu].sub.S]).sub.h.sup.[0.14]]]] (21)

which is in the form of

Y = mX + b (22)

where

Y = (1/U - [(t/k).sub.wall])[[k.sub.c]/[D.sub.hyd][([[D.sub.hyd]G]/[mu]).sub.c.sup.P][([[c.sub.p][mu]]/k).sub.c.sup.[1/3]][([mu]/[[mu].sub.S]).sub.c.sup.[0.14]]] (23)

X = [[[[k.sub.c]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.c.sup.P][([[c.sub.p][mu]]/k).sub.c.sup.[1/3]][([mu]/[[mu].sub.S]).sub.c.sup.[0.14]]]/[[[k.sub.h]/[D.sub.hyd]][([[D.sub.hyd]G]/[mu]).sub.h.sup.P][([[c.sub.p][mu]]/k).sub.h.sup.[1/3]][([mu]/[[mu].sub.S]).sub.h.sup.[0.14]]]] (24)

m = [1/[C.sub.h]] (25)

and

b = [1/[C.sub.c]] (26)

Since the viscosity ratio groups and the Reynolds number exponents are relaxed with the fluid flow rates and temperatures, successive linear regressions can be performed to execute the nonlinear regression that these equations require. These two linear regressions consist of evaluating X [Equation (24)] and Y [Equation (23)] and X ' [Equation (27)] and Y ' [Equation (28)].

X' = ln([Re.sub.c]) (27)

Y' = ln([C.sub.c][Re.sub.c.sup.P]) (28)

The X and Y regression starts with an initial P value as well as a guess for the [C.sub.h] value. These values have an impact on the wall temperature calculations; therefore, the viscosity ratio must be adjusted in both linear regression processes. From the X and Y regression, [C.sub.c] and [C.sub.h] coefficients are found. This [C.sub.h] coefficient is then used to relax the viscosity ratio in the X ' and Y ' linear regression, producing values of P and [C.sub.c]. The new P is used in the next iteration of regressions (which has new viscosity ratios to be relaxed), and this [C.sub.c] is compared to the [C.sub.c] of the X and Y regression. Calculations continue following this procedure until the difference between the successive P and [C.sub.h] values and the [C.sub.c] values from the X - Y and X' - Y' linear regressions reach some allowable error. These values can then be verified by executing a reverse calculation that requires multiplying both sides of Equation (19) by the hot side heat transfer denominator instead of the cold side heat transfer denominator, and undergoing the same process to converge at similar P, [C.sub.c] and [C.sub.h] coefficients. Both calculation procedures were done in this study and minute differences were observed, so the average of the two methods' coefficients was taken into account.

Fanning Friction Factor for Pressure Drop

To determine the single-phase pressure drop due to friction across the BPHEs, the manifold pressure loss was subtracted from the measured pressure drop recorded by a differential pressure transmitter.

[[DELTA]P.sub.f] = [[DELTA]P.sub.total] - [[DELTA]P.sub.man] (29)

The contribution of pressure loss due to gravitation was zero in this case since the pressure drop was measured using a single differential pressure transducer. The manifold pressure loss was estimated by 1.5 times the inlet velocity head, as reported by Shah and Wanniarachchi (1992),

[[DELTA]P.sub.man] = 1.5([[u.sub.m.sup.2][rho]]/2) (30)

where [u.sub.m] is the mean velocity of the fluid at the manifold.

The Fanning friction factor is given by

[C.sub.f] = [[DELTA]P.sub.f][[[D.sub.hyd][rho]]/[2[L.sub.p][G.sup.2]]] (31)

where [L.sub.p] is the characteristic length, which was here defined as the distance from the middle of the top inlet port to the middle of the bottom outlet port. The Fanning friction factor in the turbulent

regime can then be correlated based on the Reynolds number by the following general form:

[C.sub.f] = C'[Re.sup.-P'] (32)

Single-Phase Heat Transfer Results

The single-phase analysis was conducted on the three previously described BPHEs. Data are presented of the water/water analysis as well as the dynalene/water analysis. Implementing the modified Wilson plot technique and reverse calculations for the three different plates gave correlations with an average standard deviation less than 1%. The plots of the modified Wilson method for each plate are shown in Figure 4, while the heat transfer correlations are presented in Table 8.

[FIGURE 4 OMITTED]

Table 8. Current Study Single-Phase Heat Transfer Correlations Nu = C*[Re.sup.P]*[Pr.sup.(1/3)]* [([mu]/[[mu].sub.s]).sup.0.14] Water/Water 60/60 Plate 27/60 Plate 27/27 Plate Dynalene/Water [C.sub.h] 0.134 0.214 0.240 [C.sub.c] P 0.712 0.698 0.724 P Water/Water 60/60 Plate 27/60 Plate 27/27 Plate [C.sub.h] 0.177 0.278 0.561 P 0.744 0.745 0.726

It is common practice that in most BPHEs, defining plate orientation with hot and cold fluid flow direction in single phase study is not as critical as it is in two phase flow. However, based upon the present experimentation, it is interesting to note that mixed angle plates do require such a definition. Because the neighboring plates alternate chevron angles, mixed-angle exchangers exhibit different behavior for opposite flow directions. For example, if a 30/60 mixed-angle exchanger consists of plates where the high-profile (30[degrees]) plates are pointed up and the low-profile (60[degrees]) plates are pointed down, the middle channel's fluid would have a different flow pattern in this orientation compared to the opposite orientation, where the high-profile (30[degrees]) plates are pointed down and the low-profile (60[degrees]) plates are pointed up. In the 60/60 and 30/30 exchangers, this problem is eliminated because the fluid's flow pattern is similar regardless of flow direction. This was apparent in the dynalene/water data which demonstrated that in one orientation the [C.sub.c], [C.sub.h], and P values were 0.272, 0.136, and 0.759, respectively, and in the opposite orientation the corresponding values were 0.278, 0.143, and 0.745. The latter data is reported here because its orientation is similar to the two phase experimentation.

In order to properly compare the findings presented in this paper with those by other authors in the field, a meticulous comparison of definitions and calculations needed to be accomplished to make sure that continuity was maintained. For the most part, parameters were commonly defined, but there were still discrepancies among them. One of these was the definition and use of the flow characteristic length. It is important to note that the length (and resulting area) along the plate that experiences heat transfer is not the same length that contributes to a pressure drop, and as such, different lengths should be defined and utilized for each calculation. In reported literature, common definitions of length include "heat transfer length", "port to port length", "length between ports", "length of channel", "chevron area length", "distribution region length", and just "length". As these researched calculations and correlations will ideally be used in industry, simple, externally measured, and logical lengths should be used. The length used to find the amount of heat transfer area is most easily attained by measuring the distance between the ports ([L.sub.HT]), i.e., the distance measured from the top of the bottom port to the bottom of the top port. No heat transfer occurs at the entrance of each port and it is impossible to know, by external examination, exactly where the entrance or distribution length of the plate ends, and the chevron area begins, and exactly how much of the distribution length actually transfers heat. The pressure drop length, however, is affected by the distance that the fluid travels through the ports, therefore an easy measurement between the middle of each port suffices ([L.sub.P]). The data from other authors being compared with the present data has been mapped to eliminate the discrepancies that arise from the inconsistencies of definitions and calculations. For example, the heat transfer area from other studies was converted to the definition in the present study. Comparing these results shows consistency in heat transfer behavior, as shown in Figure 5 through Figure 7 for the three plates, although there are still quantitative differences that can be explained mainly due to their different geometrical plate configurations and flow conditions.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

Single-Phase Pressure Drop Results

The pressure drop through the middle channel of the three BPHEs was recorded by a differential pressure transducer. The pressure drop reported is based on the assumption of [L.sub.P], meaning that the length used in the calculations was not that of the heat transfer length but the length measured from the middle of the top port to the middle of the bottom port. The resulted correlations are summarized in Table 9, and compared with other studies in Figure 8 through Figure 10.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

Table 9. Current Study Fanning Friction Factor Correlations Cf = C'*[Re.sup.P'] Water/Water 60/60 Plate 27/60 Plate 27/27 Plate Dynalene/Water C' 1.18 1.56 3.09 C' P' -0.10 -0.08 -0.06 P' Water/Water 60/60 Plate 27/60 Plate 27/27 Plate C' 0.57 21.40 3.15 P' 0 -0.46 -0.08

Uncertainty Analysis

The instrumentation used in the experimental process detected and recorded temperatures, pressures, and flow rates. Each devise had unique responses and uncertainties, all of which were taken into account when performing a propagation of error analysis. These accuracies were found in Table 10.

Table 10. Uncertainty of Data Collecting Devices and Calculated Correlations Parameter Instrument (Range of Uncertainty Measurement in Tests) Temperature RTD 4-wire DIN 1/3 [+ or -]0.16[degrees]C (10[degrees] to 50[degrees]C) Pressure Gauge Transducer (< 50 [+ or -]0.1 psi psi) Differential pressure Differential Transmitter [+ or -]0.1 psi (<40 psi) Flow In-Line Turbine Type [+ or -]0.1 gpm (0.3-15 gpm) Single-phase Fanning [C.sub.f] (0.2-2.3) [+ or -]1.3% friction factor Single-phase heat h [8-27 kW/([m.sup.2]*K)] [+ or -]4.4% transfer coefficient

CONCLUSION

The single-phase flow of water/water as well as dynalene/water through three brazed plate heat exchangers with different interior configuration, each consists of three channels, were experimentally analyzed in this study. Hot water was pumped into the middle channel while cold water or chilled dynalene into the side channels. The temperature, pressure, and flow rates were precisely measured and collected by a data acquisition unit. The collected data were analyzed to obtain single-phase heat transfer coefficients, using modified Wilson plot method, as well as the Fanning friction factor for each plate configuration. The resulted correlations were within reasonable range of standard deviation and uncertainty. These correlations were also compared with other well established studies on single-phase flow in plate heat exchangers. This comparison qualitatively showed good consistencies; however, considerable differences were observed among different studies that could be explained due to several factors: (1) geometrical configuration of the plates, such as size, corrugation angle, pitch, and spacing were not exactly identical, (2) overall size and aspect ratio of the heat exchangers were different, (3) flow conditions and regimes were different, (4) thermal boundary conditions were not similar, and (5) thermo-hydrodynamic parameters, such as free flow and heat transfer areas, were not consistently defined and used. The latter looks to be a major issue on discrepancies among different studies on PHEs, which needs to be carefully and extensively investigated in the future.

ACKNOWLEDGMENT

This research project was collaborative between Washington State University Vancouver and the American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. The authors are grateful to those individuals in these institutions who have sponsored and supported this research project, especially the PMS members: Dr. Zahid Ayub (chair), James Bogart, and Joseph Huber.

NOMENCLATURE

[A.sub.s] = heat transfer surface area, [m.sup.2] ([in.sup.2])

[A.sub.o] = minimum free flow open area between two neighboring plates, [mm.sup.2] ([in.sup.2])

[A.sub.onepass] = single smallest cross sectional area of flow within channel in BPHE, [mm.sup.2] ([in.sup.2])

b = average plate spacing, mm (in.)

C = constant

[C.sub.p] = specific heat, J/kg * K (Btu/lbm*[degrees]F)

[C.sub.f] = Fanning friction factor

D = diameter, m (in.)

[D.sub.hyd] = hydraulic diameter (taken as twice the mean plate spacing in PHEs), m (in.)

G = mass flux, kg/[m.sup.2] * s ([lb.sub.m]/[ft.sup.2] * s)

H = dimensionless parameter accounting for sub-cooling in the condensate film

h = heat transfer coefficient, W/[m.sup.2] * K (Btu/[ft.sup.2] * s * [degrees]F)

[h.sub.fg] = latent heat, J/kg (Btu/[lb.sub.m])

i = enthalpy, J/kg (Btu/[lb.sub.m])

[[DELTA]h.sub.fg] = specific enthalpy of vaporisation, J/kg (Btu/[lb.sub.m])

Ja = Jacob number

k = thermal conductivity, W/m * K (Btu/ft * s)

[L.sub.T] = plate length, mm (in.)

[L.sub.HT] = heat transfer length (bottom of top port to top of bottom port), mm (in.)

[L.sub.P] = pressure drop length (middle of top port to middle of bottom port), mm (in.)

m = mass flow rate, kg/s ([lb.sub.m]/s)

N = number of plates

Nu = Nusselt number

P = Reynolds number power coefficient

p = system pressure, Pa (psi)

Pr = Prandtl number

q" = heat flux, W/[m.sup.2] (Btu/[ft.sup.2]*s)

Re = Reynolds number

T = temperature, [degrees]C ([degrees]F)

t = plate thickness, mm (in.)

U = overall heat transfer coefficient, W/[m.sup.2] * K (Btu/[ft.sup.2] * s * [degrees]F)

u = flow velocity, m/s (in/s)

[??] = volume flow rate, [m.sup.3]/s (gpm)

w = width of BPHE, mm (in.)

Greek Symbols

[beta] = plate corrugation inclination angle (deg.) measured from horizontal

[lambda] = corrugation pitch, mm (in.)

[DELTA]P = pressure drop, Pa (psi)

[DELTA]T = temperature difference, [degrees]C ([degrees]F)

[mu] = dynamic viscosity, cP ([lb.sub.m]/ft * s)

[rho] = density, kg/[m.sup.3] ([lb.sub.m]/[ft.sup.3])

[PHI] = enlargement factor

Subscripts

c = cold side (heat absorption channels)

eq = equivalent values

f = frictional

fg = difference between liquid and vapor phase properties

film = film condensation

gr = gravitational

h = hot side (heat rejection channel)

ht = heat transfer

hyd = hydraulic

i = in, entrance side of system

l = liquid

lm = logarithmic mean

m = mean values

man = manifold

o = out, exit side of system

p = plate

s = at surface condition

sat = saturation

sp = single-phase

t = thickness

tot = total

tp = two-phase

w = water

REFERENCES

Arman, B. and Rabas, T.J. 1995. Condensation analysis for plate-frame heat exchangers. National Heat Transfer Conference 12: 97-104.

Ayub, Z.H. 2003. Plate heat exchanger literature survey and new heat transfer and pressure drop correlations for refrigerant evaporators. Heat Transfer Engineering 24(5): 8-12.

Bodinus, W.S. 1999. The rise and fall of carbon dioxide systems: The first century of air conditioning. ASHRAE Journal 41(4): ProQuest Education Journals p 37.

Briggs, D.E. and Young, E.H. 1969. Modified Wilson plot techniques for obtaining heat transfer correlations for shell and tube heat exchangers. Chemical Engineering Progress Symposium, AIChE Heat Transfer-Philadelphia 65(92):35-45.

Brown, M., Rosario, L. and Rahman, M.M. 2005. Thermo-dynamic analysis of transcritical carbon dioxide cycles. AES 45: 59-70.

Dynalene Inc. 2008. WhiteHall, PA (www.dynalene.com).

Focke, W.W., Zacharides, J., and Oliver, I. 1985. The effect of the corrugation inclination angle on the thermohydraulic performance of plate heat exchangers. International Journal of Heat and Mass Transfer 28(8):1469-1479.

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Hwang, Y., Radermacher, R., Jin, D. and Hutchins, J.W. 2005. Performance measurement of [CO.sub.2] heat exchangers. ASHRAE Transactions 111(Part 2):306-316.

Jokar, A., Hosni, M.H. and Eckels, S.J. 2006. Dimensional analysis on the evaporation and condensation of refrigerant R-134a in minichannels plate heat exchangers. Applied Thermal Engineering 25:2287-2300.

Kim, S.G. and Kim, M.S. 2002. Experiment and simulation on the performance of an autocascade refrigeration system using carbon dioxide as a refrigerant. International Journal of Refrigeration 25:1093-1101.

Longo, G.A. and Gasparella, A. 2007. Heat transfer and pressure drop during HFC-134a condensation inside a commercial brazed plate heat exchanger. International Congress of Refrigeration, Beijing.

Longo, G.A., Gasparella, A. and Sartori, R. 2004. Experimental heat transfer coefficients during refrigerant vaporization and condensation inside herringbone-type plate heat exchangers with enhanced surfaces. International Journal of Heat and Mass Transfer 47:4125-4136.

Muley, A. and Manglik, R.M. 1999. Experimental study of turbulent flow heat transfer and pressure drop i a plate heat exchanger with chevron plates. Journal of Heat Transfer 121(1):110-117.

Panchal, C.B. 1985. Condensation heat transfer in plate heat exchangers. American Society of Mechanical Engineers, Heat Transfer Division 44:45-52.

Pearson, A. 2005. Carbon dioxide-new uses for an old refrigerant. International Journal of Refrigeration 28:1140-1148.

Pettersen, J., Hafner, A., Skaugen, G. and Rekstad, H. 1998. Development of compact heat exchangers for [CO.sub.2] air-conditioning systems. International Journal of Refrigeration 25(3):180-193.

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Rigola, J., Perez-Segarra, C.D., Oliva, A. and Raush, G. 2005. Thermal and fluid dynamic behavior of a trans-critical carbon dioxide small cooling system: Numerical analysis. International conference on compressors and their systems, Sept. 4-7:301-309.

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APPENDIX: Minimum Free Flow Area Calculation

Utilizing computer modeling software can shed extra light on the minimum free flow area (MFFA) in the BPHEs under study. With parametric modeling it is possible to better estimate the area based not only on average plate spacing, but also corrugation pitch and chevron angle. As Figure A1 (a, b, c) shows, the three plates have different corrugations pitches and the angles by which the plates meet, giving different geometries for which fluid to flow through.

[FIGURE A1 OMITTED]

Although the three different plates demonstrate different corrugation pitches and angles, the individual passes all seem to have similar areas, 5.7 mm (0.00884 [in.sup.2]) to 5.8 mm (0.00899 [in.sup.2]) on average. When taking into account all the individual passes collectively, Figure A2 (a, b, c), at any given cross section for the different plates, the three plates' minimum free flow areas are dissimilar as shown in Table A1.

[FIGURE A2 OMITTED]

Table A1. Brazed Plate Heat Exchanger Dimensions Plate Chevron Corrugation Passes Minimum Free b*w Area, Designation Angle, Pitch, mm Across Flow Area, [mm.sup.2] [degrees] (in) Width [mm.sup.2] ([in.sup.2]) of ([in.sup.2]) Plate 8964 H 27/27 6.03 18 103.5 254 (0.394) (0.2374) (0.160) 9866 M 27/60 6.19 26 149.5 254 (0.394) (0.2437) (0.232) 8965 L 60/60 6.27 34 195.5 254 (0.394) (0.247) (0.303)

Instead of having to model each plate in the future to find the minimum free flow area, the following formulation is proposed.

[A.sub.o] = f([beta], [lambda], w, [A.sub.onePass]) (33)

[A.sub.o] = [[2(0.000095[[beta].sup.2] - 0.0074[beta] + 1.0716)wsin([pi][beta]/180)]/[lambda]] * [A.sub.onePass] (34)

where [beta] (in degrees) is the average of the chevron angled plates from the horizontal axis of the vertically installed exchanger.

Setting the definitions of the geometries of the plates, such as minimum free flow area and hydraulic diameter, is essential in accurately analyzing the pressure drop and heat transfer of BPHEs. In fact, calculating the minimum free flow area corresponds to the maximum flow velocity in the channels. This velocity in turn can characterize the Reynolds number and flow regimes in the BPHEs. It was found that the conventional flow area, Equation (12), is 1.3 to 2.5 times the minimum free flow area, Equation (34), for the three BPHEs in this study. This leads to an augmentation in Reynolds numbers of 30% and 150% between the two methods, which can represent different flow regimes.

The resulting heat transfer coefficients utilizing the MFFA method are shown in Table A2.

Table A2. Current Study- Modified Single-Phase Heat Transfer Correlations Based on MFFA Nu = C*[Re.sup.P]*[Pr.sup.(1/3)]* [([mu]/[[mu].sub.s]).sup.0.14] Water/Water 60/60 Plate 27/60 Plate 27/27 Plate Dynalene/Water [C.sub.h] 0.111 0.148 0.124 [C.sub.c] P 0.715 0.702 0.729 P Water/Water 60/60 Plate 27/60 Plate 27/27 Plate [C.sub.h] 0.147 0.182 0.288 P 0.748 0.760 0.733

While the Reynolds number exponents do not deviate substantially from the b * w method, the cold and hot coefficients do (by as much as 94%) yielding discrepancies in the relationships between Nu and Re.

Niel Hayes

Student Member ASHRAE

Amir Jokar, PhD

Member ASHRAE

This paper is based on findings resulting from ASHRAE Research Project RP-1394.

Niel Hayes is a graduate research assistant and Amir Jokar is an assistant professor in the School of Engineering and Computer Science, Washington State University Vancouver, Vancouver, WA.

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Title Annotation: | carbon dioxide |
---|---|

Author: | Hayes, Niel; Jokar, Amir |

Publication: | ASHRAE Transactions |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Jul 1, 2009 |

Words: | 10365 |

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