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Review of heat transfer and pressure drop correlations for evaporation of fluid flow in plate heat exchangers (RP-1352).

INTRODUCTION

Plate heat exchangers are designed to achieve high heat transfer capacity in a small volume. Due to their compact size, plate heat exchangers have clear advantages over shell-and-tube heat exchangers and are rapidly replacing conventional shell-and-tube evaporators. Several types of plate heat exchangers are currently used in industry, including conventional gasket plate-and-frame, compact brazed, semiwelded plate-and-frame, and shell-and-plate (Ayub 2003). The disadvantage of conventional gasket heat exchangers is leakage due to failure of gasket material. Brazed heat exchangers were initially designed for cooling oil and liquid-to-liquid applications. They are also used as evaporators and condensers in the refrigeration industry. When used as evaporators, brazed heat exchangers showed poor performance at high load capacities, and failures were reported for low temperature applications (Ayub 2003). Shell-and-plate is the newest design in the plate exchanger technology. It has high mechanical integrity and superior thermal characteristics (Ayub 2003).

Some main geometric features of a heat exchanger plate are discussed below and are shown in Figure 1.

[FIGURE 1 OMITTED]

Chevron Angle: [beta], typically varying from 20[degrees] to 65[degrees], is the measure of softness (large [beta], low thermal efficiency and low pressure drop) and hardness (small [beta], high thermal efficiency and high pressure drop) of thermal and hydraulic characteristics of plates. Some authors use ([pi] - [beta]) in their investigations to represent the chevron angle.

Surface Enlargement Factor: [phi] is the ratio of developed area, based on corrugation pitch [P.sub.c] and plate pitch p, to the projected area (i.e., [L.sub.w] x [L.sub.p]). [L.sub.w] and [L.sub.p] are estimated from port distances [L.sub.v] and [L.sub.h] and port diameter [D.sub.p]: [L.sub.w] = [L.sub.h] + [D.sub.p], and [L.sub.p] = [L.sub.v] - [D.sub.p].

Mean Flow Channel Spacing: b = p - t is the difference between plate pitch p and the plate thickness, t.

The boiling of refrigerants in shell-and-tube heat exchangers has been studied and reported by a number of researchers. Relatively fewer similar studies have been conducted for plate heat exchangers. Two-phase flow heat transfer in a plate heat exchanger is a function of parameters such as quality, heat flux, mass flux, incipient boiling, surface structure, local flow regimes, dry out, film thickness, oil concentration, etc. Panchal et al. (1983), Panchal and Hillis (1984), Jonsson (1985), Hesselgreaves (1990), Kumar (1993), Thonon (1995), and Thonon et al. (1995) briefly discussed two-phase flow in plate evaporators. Boccardi et al. (1999) reported performance of plate heat exchangers using R-134a, R-407C, R-410A and R-22. Panchal et al. (1983) and Panchal and Hillis (1984) performed experimental work on plate heat exchangers as ammonia evaporators. Palm and Claesson (2006) presented methods for predicting single and two-phase flows in plate heat exchangers by studying the effect of various geometric parameters on heat transfer and pressure drop in single and two phases. Contrary to previous work by others, their work indicated a predominant effect of heat flux over mass flux. The heat transfer performance was correlated by conventional pool boiling correlations.

The potential threat of ozone depletion and global warming has increased interest in the use of natural refrigerants in the air-conditioning and refrigeration industry. Ammonia, a low-cost, environmentally safe natural fluid with excellent thermophysical properties, has received increased attention in light of the phasing out of CFCs, HCFCs, and the potential/possible phase-out of HFCs. Ayub (2006) suggested ammonia as an attractive and viable replacement for HFCs. Ammonia as a refrigerant has played an important role in the industry, particularly in the fields of food processing, dairy, and marine refrigeration. Ammonia has four- to six-fold better heat transfer characteristics compared to halocarbon refrigerants (Stoecker 1998). Djordjevic and Kabelac (2008) studied flow boiling of R-134a and ammonia in a plate heat exchanger with two chevron plate configurations. Heat transfer coefficient was reported to be a strong function of vapor quality, which also increased with an increase in heat and mass flux. Experimental data were presented, but a correlation for heat transfer coefficient based on their study was not reported. However, ammonia was reported to have better heat transfer characteristics compared to R-134a.

A disadvantage of ammonia is its toxicity, which has impeded its wider use. However, taking advantage of the large area-to-volume ratio offered by compact heat transfer equipment, such as plate heat exchangers, and the superior heat transfer characteristics of ammonia, a significant reduction in the operating charge of refrigerants can be achieved. Plate heat exchangers are therefore particularly suitable for ammonia. However, for plate heat exchangers to cope with high-pressure applications for ammonia and carbon dioxide, economic brazing techniques need to be developed.

This paper provides a review of heat transfer and pressure drop correlations for fluid flow evaporating in plate heat exchangers. Emphasis is placed on the application of a plate heat exchanger as ammonia evaporator in a refrigeration system. Effects of compressor oil/lubricant on the evaporator heat transfer performance are also covered.

CORRELATIONS FOR AMMONIA

Ayub (2003) presented extensive literature review of available single-phase and two-phase correlations for plate heat exchangers. The single-phase correlations are geometry and plate specific. It was suggested that the augmented single-phase heat transfer performance of a plate heat exchanger is due to mechanisms such as disruption and reattachment of boundary layers, vortex and swirl flows, and secondary circulations. For evaporating two-phase flow in a plate heat exchanger, due to its complex narrow passages, it is possible that heat transfer mostly takes place by two-phase flow convection, except at the lower section of the evaporator plate where nucleate boiling may play an important role. In plate heat exchanger evaporators, flow is vertical and against gravity; therefore, the flow regime is relatively simple, and phase separation is not a severe issue even at low mass fluxes. Ayub (2003) proposed the following two-phase heat transfer coefficient correlation for the evaporation of ammonia and R-22 in direct expansion (DX) and flooded evaporators. The correlation was developed based on field data, and no detailed experimental work was performed in a laboratory environment:

[h.sub.tp] = C([k.sub.l]/[D.sub.e])[([[[Re.sub.l.sup.2][h.sub.fg]]/[L.sub.p]]).sup.0.4124][(p/[p.sub.cr]).sup.0.12][[(65/[beta])].sup.0.35] (1)

where C is a constant, [k.sub.l] is thermal conductivity of liquid, and [D.sub.e] is equivalent diameter. Re is the Reynolds number based on [D.sub.e], [h.sub.fg] is latent heat of vaporization, [L.sub.p] is effective plate length, p is pressure, [p.sub.cr] is critical pressure, and [beta] is the chevron angle in degrees.

C = 0.1121 for flooded and thermo-siphon

C = 0.0675 for DX

Ayub (2003) also proposed to evaluate evaporation pressure drop using the following correlation for Fanning friction factor:

f = (n/[Re.sup.m])(-1.89 + 6.56R - 3.69[R.sup.2]) (30[degrees] [less than or equal to] [beta] [less than or equal to] 65[degrees]) (2)

where f is the Fanning friction factor, R = 30[degrees]/[beta], and

m = 0.137, n = 2.99 for Re [less than or equal to] 4000

m = 0.172, n = 2.99 for 4000 < Re [less than or equal to] 8000

m = 0.161, n = 3.15 for 8000 < Re [less than or equal to] 16,000

m = 0.195, n = 2.99 for Re > 16,000

The author concluded that this study served as a starting point for further research in the field of plate heat exchangers, where effects of several geometric, thermal and fluid flow characteristics should be explored.

Sterner and Sunden (2006) conducted experimental work on various semiwelded plate heat exchangers with ammonia in a DX configuration. They studied the effects of plate dimensions, corrugation angles, and number of channels on Nusselt number, and presented results on flow boiling of ammonia in plate heat exchangers. The following correlation was developed for five different combinations of plate heat exchangers:

Nu = C[[Re.sub.fo.sup.m][Ja.sup.n][Co.sup.p] (3)

where Co is the convection number, Ja is the Jakob number and [Re.sub.fo] is the Reynolds number for liquid only and ranges from 50 to 250. Values of constants C, m, n, and p depend on parameters such as plate geometry, Reynolds number, quality, mass flux, etc., and are reported by Sterner and Sunden (2006). The study showed that uniform distribution of flow at the inlet improves evaporation heat transfer. However, to establish generalized correlations, data in a wider range are required.

CORRELATIONS FOR OTHER REFRIGERANTS

Yan and Lin (1999) performed experiments on evaporation heat transfer and pressure drop of R-134a in plate heat exchangers. The test facility included two vertical counter-flow channels in a heat exchanger using three commercial plates with a plate corrugation inclination angle [beta] = 60[degrees]. The overall heat transfer coefficient, U, and convective heat transfer coefficient of R-134a were related as follows:

[1/[h.sub.r]] = [1/U] - [1/[h.sub.w,h]] - [R.sub.wall]A (4a)

where [h.sub.r] and [h.sub.w,h] are the heat transfer coefficients for refrigerant and hot water side, respectively. [h.sub.w,h] is determined from correlation developed for single-phase, water-to-water heat transfer. [R.sub.wall] A is the wall thermal resistance, and A is the actual corrugated heat transfer surface area of the plate. U is given by the following:

U = [[Q.sub.w,h]/[A * LMTD]] (4b)

where LMTD is the log mean temperature difference, and [Q.sub.w,h] is the total heat transfer rate from the hot-water side.

Heat transfer coefficients in plate heat exchangers were higher than in circular tubes, especially at high vapor quality convective regimes. The effect of heat flux was minimal, while mass flux played a major role in overall heat transfer performance and pressure drop. The increase in heat transfer coefficient due to quality was larger than that in pressure drop. Based on Yan and Lin's (1990) experimental data, the heat transfer correlation for the single-phase flow is as follows:

[Nu.sub.sp] = 0.2121[Re.sup.0.78][Pr.sup.1/3][([[mu].sub.m]/[[mu].sub.wall]).sup.0.14] (5)

where [Nu.sub.sp] is single-phase Nusselt number; Re and Pr are Reynolds and Prandtl numbers, respectively; and [mu] is dynamic viscosity. Subscripts m and wall correspond to bulk and wall conditions, respectively. The evaporation heat transfer data of R-134a flow in the plate heat exchanger were correlated with an average deviation of 8.3% by the following equation:

[Nu.sub.tp][[Pr.sub.l.sup.[-1/3]][Re.sub.l.sup.0.5][Bo.sub.eq.sup.[-0.3]] = 1.926[Re.sub.eq] for 2000 < [Re.sub.eq] < 10,000 (6a)

where Bo is Boiling number. The equivalent values for mass flux G, Reynolds number, and boiling number are as follows:

[G.sub.eq] = G * [C.sub.x]

[Re.sub.eq] = [Re.sub.l] * [C.sub.x] = [[G.sub.eq][D.sub.h]/[[mu].sub.l]]

[Bo.sub.eq] = [Bo/[C.sub.x]] = [[q.sub.wall]"/[G.sub.eq][h.sub.fg]] (6b)

where q" is heat flux, and [h.sub.fg] is latent heat of vaporization. The coefficient [C.sub.x], a function of mean vapor quality ([x.sub.m]) and the liquid-to-vapor-density ratio, is given as follows:

[C.sub.x] = (1 - [x.sub.m]) + [x.sub.m][([[rho].sub.l]/[[rho].sub.g]).sup.0.5] (6c)

where [[rho].sub.l] and [[rho].sub.g] are liquid and vapor densities, respectively. Correlations of Fanning friction factor, [C.sub.f] for evaluation of pressure drop of evaporating R-134a flow, with an average deviation of 7%, are as follows:

[C.sub.f,tp][Re.sup.0.5] = 6.947 x [10.sup.5][Re.sub.eq.sup.[-1.109]] for [Re.sub.eq] < 6000 (7)

[C.sub.f,tp][Re.sup.0.5] = 31.21[[Re.sub.eq.sup.0.04557] for [Re.sub.eq] [greater than or equal to] 6000 (8)

Ouazia (2001) investigated heat transfer and pressure drop of R-134a for upward flow boiling inside a typical plate heat exchanger. The test configuration included three sets of plates with chevron angles of 0[degrees], 30[degrees], and 60[degrees]. A heat transfer correlation was proposed based on the ratio of two-phase to single-phase heat transfer coefficients as follows:

F = [[h.sub.tp]/[h.sub.l]] (9a)

where [h.sub.tp] and [h.sub.l] represent two-phase and single-phase (liquid only) heat transfer coefficients, respectively, with [h.sub.l] given by the following equation:

[h.sub.l] = a[[k.sub.l]/[D.sub.h]][([[G(1 - x)[D.sub.h]]/[[mu].sub.l])].sup.b][[Pr.sub.l.sup.[1/3]][([[mu].sub.l]/[[mu].sub.wall]).sup.0.17] (9b)

where a and b are constants for the different corrugation angles. The factor F is a function of the Lockhart--Martinelli parameter ([X.sub.tt]):

F = 1 + [C.sub.1][(1/[X.sub.tt]).sup.[C.sub.2]] (9c)

[1/[X.sub.u]] = [[(x/[1 - x])].sup.[1 - [n/2]]][([[rho].sub.l]/[[rho].sub.v]).sup.0.5][([[mu].sub.v]/[[mu].sub.l]).sup.[n/2]] (9d)

where [C.sub.1] and [C.sub.2] are constants. The frictional pressure drop, [DELTA][p.sub.fr], was correlated using a two-phase friction multiplier:

[[PHI].sub.l.sup.2] = [[[DELTA][p.sub.fr]]/[[DELTA][p.sub.l]]] (10a)

where the liquid pressure drop, [DELTA][p.sub.l], is obtained by

[DELTA][p.sub.l] = [C.sub.f,l][[2L]/[D.sub.h]][[[G.sup.2][[(1 - x)].sup.2]]/[[rho].sub.l]] (10b)

The two-phase friction multiplier, [[PHI].sub.l], is a function of the Lockhart--Martinelli parameter ([X.sub.tt]):

[[PHI].sub.l.sup.2] = 1 + [C/[X.sub.tt]] + [1/[X.sub.[tt].sup.2]] (10c)

where C is a constant.

Hsieh et al. (2002) explored subcooled flow boiling heat transfer and associated bubble characterization of R-134a in a plate heat exchanger. They used the same facility as Yan and Lin (1999). An almost linear rise in the cross-channel superheat was observed as the heat flux at the plate was raised gradually. Boiling hysteresis was important only at low refrigerant mass flux levels, i.e., 50 kg/[m.sup.2.]s. The subcooled flow boiling curves indicated an increase in heat transfer with saturation temperature. It was also reported that an increase in the saturation temperature of the refrigerant resulted in enhanced heat transfer. However, in the single-phase region before onset of nucleate boiling, saturation temperature showed negligible effects on heat transfer in the refrigerant flow. The boiling heat flux was higher for a higher subcooling in the single-phase heat transfer region. Also, at a given mass flux, boiling heat transfer coefficient increased slightly with the heat flux. Photographic evidence of subcooled flow boiling indicated that, at a higher heat flux, a larger fraction of the plate surface is covered by the bubbles, and bubble generation frequency and bubble rising velocity are higher. The heat transfer coefficient in the subcooled flow boiling of R-134a in a plate heat exchanger was correlated as following (Hsieh et al. 2002):

[h.sub.r,sub] = [h.sub.r,l](1.2[Fr.sup.0.75] + 13.5[Bo.sup.1/3] [Ja.sup.1/4]) (11a)

where [h.sub.r,l], the liquid refrigerant heat transfer coefficient, is defined as follows:

[h.sub.r,l] = 0.2092([k.sub.l]/[D.sub.h])[[Re.sub.l.sup.0.78][[Pr.sub.l.sup.1/3][([[mu].sub.ave]/[[mu].sub.wall]).sup.0.14] (11b)

Fr, Bo, and Ja are Froude, Boiling, and Jakob numbers, respectively, and are defined as follows:

Fr = [[G.sup.2]/[[[rho].sub.l.sup.2]g[D.sub.h]]]

Bo = [q/[[Gh.sub.fg]]]

Ja = [[[[rho].sub.l][C.sub.p][DELTA][T.sub.sat]]/[[[rho].sub.g][h.sub.fg]]] (11c)

[[rho].sub.g], [C.sub.p], and [DELTA][T.sub.sat] are vapor density, specific heat, and cross-channel super heat, respectively.

Hsieh et al. (2002) also proposed an empirical correlation for the average bubble departure diameter, [d.sub.p], for subcooled upward flow boiling in a vertical annular channel as follows:

[[d.sub.p]/[square root of ([sigma]/g[DELTA][rho])] = [[0.93[([[rho].sub.l]/[[rho].sub.g]]).sup.1.23]]]/[[[Re.sup.0.35][Ja + 165[([[rho].sub.l]/[[rho].sub.g]).sup.1.23]/[Bo.sup.0.487][Re.sup.1.58]]] (12)

where [sigma] is surface tension, while [[rho].sub.l] and [[rho].sub.g] are liquid and vapor densities, respectively. [Delta][rho] is the difference of liquid and vapor densities. The above correlation was reported to fit experimental data with an average deviation of 12.8%.

Hsieh and Lin (2002) conducted a study of saturated flow boiling heat transfer and pressure drop of R-410A in a vertical plate heat exchanger using the same facility as that used by Yan and Lin (1999). Refrigerant mass flux and heat flux were varied for three sets of saturation temperatures and respective pressures. Both boiling heat transfer coefficient and frictional pressure drop increased almost linearly with imposed heat flux. Refrigerant mass flux was reported to have significant effect on heat transfer coefficient only at high heat flux levels. With a rise of refrigerant pressure, the frictional pressure drop was reported to be lower. However, the effect of refrigerant pressure on saturated flow boiling heat transfer coefficient was reported to be less significant. Based on Hsieh and Lin's (2002) experimental data, the following correlation was developed for boiling heat transfer coefficient:

[h.sub.r,sat] = [h.sub.r,l](88[Bo.sup.0.5]) (13a)

where [h.sub.r,sat] is heat transfer coefficient of a refrigerant at saturated state, and [h.sub.r,l] is the all-liquid single-phase heat transfer coefficient for liquid R-410A given below:

[h.sub.r,l] = 0.2092([k.sub.l]/[D.sub.h])[Re.sup.0.78][Pr.sup.1/3][([[mu].sub.m]/[[mu].sub.wall]).sup.0.14] (13b)

Bo = [q/[[Gh.sub.fg]]] (13c)

where [k.sub.l] is thermal conductivity for liquid, [D.sub.h] is hydraulic diameter, [[mu].sub.m] is the average viscosity for the two-phase mixture between the inlet and the exit, [[mu].sub.wall] is viscosity at the wall of plate heat exchanger, q is average imposed heat flux, G is the mass flux, and [h.sub.fg] is the latent heat of vaporization.

The measured frictional pressure drop was reported in terms of the friction factor as follows:

[f.sub.tp] = 61,000([[Re.sub.eq.sup.[-1.25]]) (14a)

where [Re.sub.eq] is the equivalent Reynolds number and is defined as follows:

[Re.sub.eq] = [[[G.sub.eq][D.sub.h]]/[[mu].sub.l]] (14b)

[G.sub.eq] is the equivalent mass flux, which is a function of R-410A mass flux; mean quality [x.sub.m], defined as average value between inlet and exit; and density [rho] at the saturation condition:

[G.sub.eq] = G[(1 - [x.sub.m]) + [x.sub.m][([[rho].sub.l]/[[rho].sub.g]).sup.1/2]] (14c)

Hsieh and Lin (2003) conducted another study of evaporation heat transfer and pressure drop of R-410A in a plate heat exchanger using the same facility used by Yan and Lin (1999). They observed that evaporation heat transfer coefficient and frictional pressure drop increased with mass flux and vapor quality. However, at a low vapor quality, refrigerant mass flux had little effect on heat transfer coefficient. Also, pressure drop increased more with the vapor quality compared to heat transfer coefficient. The heat transfer coefficient of R-410A was found to be higher than that of R-134a, except at high vapor quality, where R-134a was reported to be more effective due to different thermal conductivities of the refrigerants for liquid and vapor phases. For vapor quality greater than 50%, the frictional pressure drop for R-410A was considerably lower compared to that for R-134a, but was still much higher than that of a smooth horizontal pipe for all values of quality. This was attributed to lower densities and viscosities of R-410A vapor and liquid compared to R-134a. The following heat transfer correlation for two-phase flow was proposed:

[h.sub.tp] = [Eh.sub.l] + [Sh.sub.pool] for 2000 < Re < 12,000 and 0.0002 < Bo < 0.002 (15a)

where [h.sub.l] is the liquid heat transfer coefficient, and [h.sub.pool] is the pool boiling heat transfer coefficient given in Equation 15b.

[h.sub.l] = 0.023[Re.sub.l.sup.0.8][Pr.sup.0.4]([k.sub.l]/[D.sub.h])

[h.sub.pool] = 55[[P.sub.r.sup.0.12][(-[log.sub.10][P.sub.r])].sup.-0.55][M.sup.[-0.5]][q.sup.0.67] (15b)

where M is the molecular weight, while E and S are enhancement and suppression factors:

E = 1 + 24,000[Bo.sup.1.16] + 1.37[(1/[X.sub.tt]).sup.0.86]

S = [[(1 + 1.15 x [10.sup.[-6]][E.sup.2][[Re.sub.l.sup.1.17])].sup.[-1]] (15c)

where [X.sub.tt] is the Lockhart-Martinelli parameter. The friction factor was correlated as

[f.sub.tp] = 23,820[[Re.sub.eq.sup.[-1.12]] for 2000 < Re < 12,000 and 0.0002 < Bo < 0.002. (16)

Park and Kim (2003) experimentally investigated effects of mass and average heat flux, saturation temperature, and vapor quality on heat transfer characteristics of R-134a in a plate-and-shell heat exchanger. The heat transfer coefficient for a single-phase, water-to-water heat exchanger on the shell side was correlated in terms of Nusselt number as follows:

Nu = 0.55[Re.sup.0.92][Pr.sup.1/3] (17)

The refrigerant heat transfer coefficient was reported to increase with mass flux at high vapor quality. For a given vapor quality, the heat transfer coefficient increased with heat flux and decreased with saturation temperature. The two-phase heat transfer coefficient was correlated by a modified Yan et al. (1999) correlation:

[[Nu]/[Pr.sup.1/3]][Re.sup.0.5] [Bo.sub.eq.sup.[-0.3]] = 532.2[[Re.sub.eq.sup.0.3237] (18a)

where [Re.sub.eq] and [Bo.sub.eq] are equivalent Reynolds and Boiling numbers, respectively, given as follows:

[Re.sub.eq] = [[[G.sub.eq][D.sub.h]]/[[mu].sub.l]] (18b)

[Bo.sub.eq] = [[q.sub.w]/[[G.sub.eq][h.sub.fg]]] (18c)

where [G.sub.eq] is the equivalent mass flux. This two-phase flow correlation was reported to cover the experimental data within [+ or -]15%.

Han et al. (2003) performed experiments on evaporation of refrigerants R-410A and R-22 in plate heat exchangers with the plate corrugation inclination angles of 45[degrees], 35[degrees], and 20[degrees]. Data were taken under temperatures of 41[degrees]F (5[degrees]C), 50[degrees]F (10[degrees]C), and 59[degrees]F (15[degrees]C) and heat fluxes of 792.5 Btu/h*[ft.sup.2] (2.5 kW/[m.sup.2]), 1743.5 Btu/h*[ft.sup.2] (5.5 kW/[m.sup.2]), and 2694.5 Btu/h*[ft.sup.2] (8.5 kW/[m.sup.2]) in the mass flux range of 2.66 to 6.96 lb/[ft.sup.2]*s (13-34 kg/[m.sup.2]*s). Churn flow regime was observed in all test conditions for both R-410A and R-22. Both evaporation heat transfer coefficient and pressure drop were reported to increase with increasing mass flux and vapor quality and with decreased evaporation temperature and chevron angle. The average heat transfer coefficient showed increasing trend with increasing mass flux with maximum average heat transfer coefficient for 5[degrees]C temperature and smallest corrugation angle of 20[degrees]. The authors explained that with increasing evaporation temperature, the saturated vapor specific volume decreases and the vapor velocity at a given mass flux decreases. Vapor velocity--the main parameter to increase heat transfer--causes a decrease in the average heat transfer coefficient. As for vapor quality, during evaporation, quality and increase in specific volume caused the vapor velocity and, hence, the heat transfer coefficient to increase. Effect of quality was reported to be more significant at lower corrugation angles. It was reported that the evaporation heat transfer coefficient of R-410A was 0% to 15% higher, and the pressure drop of R-410A was about 15% to 35% lower than that of R-22. R-410A was therefore considered to be a more suitable refrigerant than R-22. The following correlation for Nusselt number was proposed:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19a)

where

[Ge.sub.l] = 2.81[([P.sub.co]/[D.sub.h]).sup.[-0.041]][[([pi]/2 - [beta])].sup.2.83] (19b)

and

[Ge.sub.2] = 0.746[([P.sub.co]/[D.sub.h]).sup.[-0.082]][[([pi]/2 - [beta])].sup.0.61] (19c)

where [p.sub.co] is the corrugation pitch and [beta] is the chevron angle. A correlation for friction factor was also proposed:

[f.sub.tp] = [Ge.sub.3][Re.sub.eq.sup.[[Ge.sub.4]]] (20a)

where

[Ge.sub.3] = 64,710[([p.sub.co]/[D.sub.h]).sup.[-5.27]][[([pi]/2 - [beta])].sup.[-3.03]] (20b)

[Ge.sub.4] = -1.314[([p.sub.co]/[D.sub.h]).sup.[-0.62]][[([pi]/2 - [beta])].sup.[-0.47]] (20c)

Longo et al. (2004) presented heat transfer data for vaporization and condensation of R-22 in plate heat exchanger with a plate corrugation inclination angle of 25[degrees]. They also investigated the effect of surface roughness of the plates on refrigerant heat transfer characteristics. It was reported that compared to smooth surface plates, roughened surface plates in the plate heat exchanger provided an increase of heat transfer rate up to 40% for the vaporization and 60% for the condensation. They compared vaporization data with two well known correlations developed for nucleate pool boiling by Cooper (1984) and Gorenflo (1993), respectively. The mean absolute percentage deviations were around 9% and 5%, respectively. Cooper (1984) reported the following correlation for pool boiling heat transfer coefficient for R-22:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

where P* = P/[P.sub.cr] is reduced pressure, [R.sub.p]([mu]m) is the plate surface roughness, q is heat flux, and M is molecular weight of the fluid. Gorenflo (1993) reported the following correlation for pool boiling heat transfer coefficient for R-22:

[h.sub.r] = [h.sub.o][C.sub.w]F(P*)[(q/[q.sub.o]).sup.n] (22a)

where [h.sub.o] = 3930 W * [m.sup.-2] * [K.sup.-1] is the reference value, and [C.sub.w] = [([R.sub.a]/0.4)].sup.0.1333] accounts for the effect of arithmetic mean roughness [R.sub.a] ([mu]m). F(P*), which accounts for reduced pressure P* effect, is given as follows:

F(P* ) = 1.2[P*.sup.0.27] + [2.5 + 1/[(1-P*)]]P* (22b)

and

[(q/[q.sub.o]).sup.n] = [(q/[20,000]).sup.[0.9-0.3[[(P*)].sup.0.3]]] (22c)

The condensation data of Longo et al. (2004) were reported to be within 11% of that of Yan et al. (1999), a semi-empirical correlation based on a single set of R-134a condensation data for only herring-bone type heat exchanger with 30[degrees] corrugation. The Yan et al. (1999) correlation is given as follows:

[h.sub.r] = 4.118([[lambda].sub.l]/[d.sub.h])[[Re.sub.eq.sup.0.4][[Pr.sub.l.sup.1/3] (23a)

where [Re.sub.eq] is the equivalent Reynolds number and is given as follows:

[Re.sub.eq] = G[(1 - [x.sub.m]) + [x.sub.m][([[rho].sub.l]/[[rho].sub.v]).sup.1/2]][[d.sub.h]/[[mu].sub.l]]

[Pr.sub.l] = [[mu].sub.l][[C.sub.pl]/[[lambda].sub.l]] (23b)

[x.sub.m] is the mean vapor quality, while [mu], [lambda], and [rho] are viscosity, thermal conductivity, and density, respectively.

Claesson (2005a, 2005b) studied the thermohydrodynamics of brazed-plate heat exchangers and presented a detailed survey of single-phase heat transfer and two-phase adiabatic and flow boiling applications. A correlation for pressure drop of adiabatic two-phase flow based on the Lockhart--Martinelli approach was presented. This correlation, defining the Chisholm parameter for the experimental data, was proposed as follows:

C(X,[Re.sub.lo]) = - 67.6 + 0.1[Re.sub.lo] + [27.7/X] - [0.8/[X.sup.2]] (24)

where [Re.sub.lo] is the Reynolds number assuming all mass flow as liquid, and X is the Lockhart--Martinelli parameter.

Claesson (2005b) also proposed the dryout quality correlation as follows:

[x.sub.dryout] = (0.308 + 0.1241n)(1/[Bo]))(0.98 + 0.36[NTU.sub.sp]) (25)

where Bo is the boiling number and [NTU.sub.sp] is the number of transfer units based on single-phase heat transfer coefficient. Results of this study indicated that plates of larger chevron angles ([pi] - [beta]) are more beneficial for large heat flux applications, and plates with smaller chevron angles should be selected for lower total heat loads. The refrigerant heat transfer coefficient was reported to increase with brine mass flow rate. Based on literature review, the author also concluded that there is no agreement on whether in flow boiling the convective boiling or nucleate boiling or a combination of both dominates.

Jokar et al. (2006) performed dimensional flow analysis on evaporation and condensation of R-134a for three plate heat exchangers of similar interior plate design but different number of plates. The Fanning friction factor for single-phase flow was correlated as follows:

[C.sub.f,sp] = 6.431[Re.sup.[-0.25]] (26)

where Re is the Reynolds number based on the hydraulic diameter, defined as twice the mean plate spacing. The two-phase Fanning friction factor for the refrigerant flow was correlated as follows:

[C.sub.f,tp] = 3.521 x [10.sup.4][[Re.sub.l.sup.[-1.35]][C.sub.x.sup.[-1]] 70 [less than or equal to] [Re.sub.l] [less than or equal to] 420 (27)

where the subscript l symbolizes liquid, and [C.sub.x] is the coefficient based on vapor quality. The Nusselt number correlation for single phase was proposed as follows:

[Nu.sub.sp] = 0.089[Re.sup.0.79][Pr.sup.n] (28)

where n = 0.3 for cooling and 0.4 for heating. They reported at least 12 independent variables to be important for correlating the data of two-phase flows in the plate heat exchangers under study. The following dimensionless correlations for evaporation and condensation, respectively, were proposed for R-134a:

[Nu.sub.tp] = 0.603[[Re.sub.l.sup.0.5][[Pr.sub.l.sup.0.1][x.sup.[-2]][([G.sup.2]/[[[rho].sub.l.sup.2][C.sub.p,l][DELTA]T]).sup.[-0.1]][([[[rho].sub.l.sup.2][h'.sub.fg]]/[G.sup.2]).sup.[-0.5]][([[[rho].sub.l][sigma]]/[[[mu].sub.l]G]).sup.1.1][[([[rho].sub.l]/[[[rho].sub.l]-[[rho].sub.v]])].sup.2] (29)

[Nu.sub.tp] = 3.371[[Re.sub.l.sup.0.55][[Pr.sub.l.sup.0.3][([G.sup.2]/[[[rho].sub.l.sup.2][C.sub.p,l][Delta]T]).sup.1.3][([[[rho].sub.l.sup.2][h'.sub.fg]]/[G.sup.2]).sup.1.05][([[[rho].sub.1][sigma]]/[[[mu].sub.l]G]).sup.0.05][[([[rho].sub.l]/[[[rho].sub.l] - [[rho].sub.v]])].sup.2] (30)

where x is the vapor quality and [sigma] is the surface tension. The results of this study showed that the existing two-phase flow theories and correlations for conventional macrochannel heat exchangers may not be directly applicable to mini/microchannel heat exchangers, such as plate heat exchangers.

Jassim et al. (2006) investigated refrigerant pressure drop in chevron and bumpy-style plate heat exchangers. Chevron-style flat-plate heat exchangers are used for industrial refrigeration, while bumpy-style flat-plate heat exchangers are commonly used for automotive air conditioners. Two-phase pressure drop was reported to be the highest for chevron plate, while 1:1 aspect ratio bumpy plate had the lowest two-phase pressure drop. At constant quality values, there was a strong relationship between kinetic energy per unit volume of flow and pressure drop for both single and two-phase flow. It was concluded that inertial effects dominate the pressure drop for both flows. The authors developed a void fraction model to relate two-phase flow data with single-phase flow data. The model predicted two-phase frictional pressure drop data within 15% of experimental measurements.

Longo and Gasparella (2007a) studied vaporization of R-134a in a ten-plate brazed-plate heat exchanger with chevron angle of 25[degrees]. They showed that heat transfer coefficient was affected by heat flux and evaporator outlet conditions, while saturation temperature had little effect. Heat transfer rate was reported to decrease with increasing vapor quality and vapor superheat. In this study, nucleate boiling was the dominant mode of vaporization. There was a linear dependency of frictional pressure drop on kinetic energy per unit volume (KE/V) of the refrigerant. Based on the experimental data, the following relation for frictional pressure drop, [[Delta].sub.pf], was reported.

[[DELTA].sub.pf] = 1.425[[KE]/V] (31a)

Longo and Gasparella (2007b), in a similar study, reported that frictional pressure drop of HFC-410A shows a linear dependence on kinetic energy per unit volume and non-linear (quadratic) dependence on refrigerant mass flux. They also reported that the refrigerant vaporization rate is mainly governed by heat flux. Longo and Gasparella (2007c) extended their study further by comparing heat transfer and pressure drop characteristics of HFC-134a, HFC-410A, and HFC-236fa in a brazed-plate heat exchanger. They investigated effects of heat and mass flux, saturation temperatures, and exit vapor quality on heat transfer and pressure drop during refrigerant evaporation. Heat transfer was reported to be significantly affected by heat flux, exit vapor quality, and fluid properties, while the effect of saturation temperature was not significant. HFC-410A was reported to show better heat transfer and pressure drop characteristics compared to the other two refrigerants, probably because of higher liquid thermal conductivity and low liquid dynamic viscosity. For the three refrigerants, the following empirical correlation was developed to predict frictional pressure drop and is reported to reproduce the experimental data within [+ or -]8.8%:

[[Delta].sub.pf] = 1.49[KE/V] (31b)

Kim et al. (2007) experimentally investigated evaporation heat transfer characteristics of R-410A in an oblong shell and plate heat exchanger. For a Reynolds number range of 600 to 2300, the following correlation for single phase was proposed:

[Nu.sub.sp] = 0.05[Re.sup.0.95][Pr.sup.1/3] (32)

It was reported that evaporation heat transfer rate increased with both mass and average heat flux. However, heat flux had a little effect on heat transfer coefficient compared to mass flux. It was also reported that at a given saturation temperature, heat transfer coefficient increased with increasing vapor quality. For a fixed vapor quality, heat transfer coefficient was reported to decrease with saturation temperature. Based on the data, the following Nusselt number correlation was proposed for the two-phase flow:

Nu = 5.323[[Re.sub.eq.sup.0.42][[Pr.sub.l.sup.1/3] (33a)

where [Re.sub.eq] is the equivalent Reynolds number, as defined by Park and Kim (2003), in which [G.sub.eq], the equivalent mass flux, is given as follows:

[G.sub.eq] = G[1 - [x.sub.m] + [x.sub.m][([[rho].sub.l]/[[rho].sub.v]).sup.1/2]] (33b)

where [x.sub.m] is the mean vapor quality, and [[rho].sub.l] and [[rho].sub.v] are liquid and vapor densities, respectively. The average deviation between the correlation and experimental data was found to be within [+ or -]10%.

EFFECTS OF OIL/LUBRICANT

Immiscible mineral oils are usually used for lubrication in ammonia systems. Liquid oil film forms on the tube wall in a tubular DX system (Koster 1986). The heat transfer performance of the evaporator is reduced due to the formation of the oil film. A 30% reduction in tube-side heat transfer coefficient was reported by Shah (1975) due to such oil film. Chaddock (1986) and Chaddock and Buzzard (1986) also reported that heat transfer coefficient was reduced by 50% to 90% due to the presence of immiscible mineral oil layer on the heat transfer surface. Experimentation with refrigerant and oil mixtures boiling in a planar confined space between a heated plate and an opposing adiabatic plate was reported by Marvillet and De Carvahlo (1994). It was noted that, while the presence of oil was observed to have only a relatively minor effect on low heat flux nucleate boiling, it caused a serious degradation of boiling performance in high heat flux range. This deterioration was more severe with a higher oil concentration and a smaller gap size. However, for a given gap size, the critical heat flux increased with oil concentration accompanied by greater surface superheats. The effects of refrigerant/oil solubility of mixture of refrigerants and oils on system performance were analyzed by Hewitt and McMullan (1997). Their focus was on refrigerants that can replace chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs), and on synthetic oils. Refrigerant solubility with compressor lubricant oils was reported to affect composition of fluid mixtures and to reduce the system performance.

Effects of synthetic oil on the operation of a plate heat exchanger-type condenser and evaporator with R410A were studied by Lottin et al. (2003). Lubricant quantity in refrigerant ranged from [10.sup.-5]% to 5%. Existing two-phase flow correlations with corrections to account for mass transfer thermal resistance of zeotropic mixtures, such as R410A, were incorporated for both condensation and evaporation studies. Different existing correlations produced scattered results; however, the same results were reported at 0.01% oil mass fraction in condenser with all correlations used. The lubricant effect on temperature within the condenser was found to be insignificant. However, results of different correlations used in evaporator analysis showed heat transfer coefficient decreasing with lubricant mass fraction. Heat transfer coefficient was the highest at 0.1% lubricant mass fraction in the evaporator. Also, temperature decreased with oil mass fraction in the evaporator, reducing the overall evaporator performance. Pressure loss in the condenser was reported to be negligible; however, it increased several times in the evaporator as oil quantity reached 5%, reducing suction pressure and, hence, compressor efficiency, as well as favoring release of more refrigerant and enhancing heat transfer in the evaporator. Therefore, a balance between these two phenomena is important.

Zheng et al. (2001) investigated shell-side flooded boiling of ammonia mixed with lubricant on a horizontal plain tube. It was reported that the effect of miscible lubricant depends strongly on saturation temperature and weakly on heat flux. Under a particular saturation temperature and heat flux, generally the heat transfer coefficient first decreased with lubricant concentration up to 5% and then increased significantly with a further increase in concentration to 10%. The heat transfer degradation depended strongly on temperature. At a low temperature of -9.94[degrees]F (-23.3[degrees]C), the degradation could be as high as 33%.

Zheng et al. (2006) further studied flooded boiling of pure ammonia and ammonia/lubricant mixture on a plain horizontal tube subjected to a vapor quality at the inlet of the evaporator. Their results showed that the heat transfer coefficient increased with both saturation temperature and heat flux. Depending on heat flux and saturation temperature, heat transfer performance increased, decreased, or did not change with lubricant oil concentration. However, lubricant effect, in general, was more significant compared to inlet quality effect. A correlation for flooded boiling of lubricant/ammonia mixture on a horizontal plain tube with [+ or -]15% error was presented as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (34a)

where [[rho].sub.f] and [[rho].sub.g] represent liquid and vapor densities, respectively. The experimentally determined empirical constants were as follows:

[c.sub.1] = 4.663

[c.sub.2] = 1.156 - 16.3Pr + 206.79[Pr.sup.2] + 1.742w - 29.214[w.sup.2]

[c.sub.3] = -16.759[x.sub.in]

[c.sub.4] = - 3.573 (34b)

where Pr is the Prandtl number, w is mass concentration of lubricant, and [x.sub.in] is the inlet quality of vapor.

The current literature survey revealed no previous study conducted using ammonia mixed with oil/lubricant evaporating in a plate heat exchanger.

A summary of the heat transfer and pressure drop correlations for evaporation of fluid flow in plate heat exchangers is tabulated in Table 1.

[TABLE 1 OMITTED]

CONCLUSION

A literature review was carried out to identify available heat transfer and pressure drop correlations for plate heat exchangers. The main focus of this review is on plate heat exchangers used as evaporators. A substantial amount of work was reported regarding correlations for heat transfer and pressure drop for plate heat exchangers using CFCs and HFCs as refrigerants. Due to their compactness and better area-to-volume ratio, plate heat exchangers may have advantages over shell-and-tube heat exchangers with toxic natural refrigerants, such as ammonia. However, the current review shows a lack of work on plate heat exchangers with natural refrigerants. There has been no previous study reported to quantify the effect of oil/lubricant mixed in ammonia evaporating in a plate heat exchanger. Heat transfer and pressure drop correlations are needed for ammonia flow evaporating in plate heat exchangers based on thorough research of related thermal--hydraulic phenomena. There is also a need to quantify the effects of plate geometry, plate material, oil concentration, and several operating parameters on heat transfer coefficient and pressure drop for plate heat exchangers.

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Tariq S. Khan

Mohammad S. Khan, PhD

Member ASHRAE

Ming-C. Chyu, PhD

Zahid H. Ayub, PhD

Fellow Member ASHRAE

Javed A. Chattha, PhD

Received May 21, 2008; accepted October 3, 2008

This paper is based on findings resulting from ASHRAE Research Project RP-1352.

Tariq S. Khan is a doctoral student, Mohammad S. Khan is an assistant professor, and Javed A. Chattha is a professor and dean of the Faculty of Mechanical Engineering, GIK Institute of Engineering Sciences and Technology, Topi, Pakistan. Ming-C. Chyu is a professor in the Department of Mechanical Engineering, Texas Tech University, Lubbock, TX. Zahid H. Ayub is a researcher at ISOTHERM, Inc., Arlington, TX.
COPYRIGHT 2009 American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc.
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Author:Khan, Tariq S.; Khan, Mohammad S.; Chyu, Ming-C.; Ayub, Zahid H.; Chattha, Javed A.
Publication:HVAC & R Research
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Date:Mar 1, 2009
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