**1. Introduction**

Plate heat exchangers (PHEs) were introduced in the 1930s and were almost exclusively used as liquid/liquid heat exchangers in the food industries because of their ease of cleaning. Over the years, the development of the PHE has generally continued towards larger capacity, as well as higher working temperature and pressure. Recently, a gasket sealing was replaced by a brazed material, and each thermal plate was formed with a series of corrugations (herringbone or chevron). These greatly increased the pressure and the temperature capabilities.

The corrugated pattern on the thermal plate induces a highly turbulent fluid flow. The high turbulence in the PHE leads to an enhanced heat transfer, to a low fouling rate, and to a reduced heat transfer area. Therefore, PHEs can be used as alternatives to shell-and-tube heat exchangers. Due to ozone depletion, the refrigerant R22 is being replaced by R410A (a binary mixture of R32 and R125, mass fraction 50 %/50 %). R410A approximates an azeotropic behavior since it can be regarded as a pure substance because of the negligible temperature gliding. The heat transfer and the pressure drop characteristics in PHEs are related to the hydraulic diameter, the increased heat transfer area, the number of the flow channels, and the profile of the corrugation waviness, such as the inclination angle, the corrugation amplitude, and the corrugation wavelength. These geometric factors influence the separation, the boundary layer, and the vortex or swirl flow generation. However, earlier experimental and numerical works were restricted to a single-phase flow. Since the advent of a Brazed PHE (BPHE) in the 1990s, studies of the condensation and/or evaporation heat transfer have focused on their applications in refrigerating and air conditioning systems, but only a few studies have been done. Much work is needed to understand the features of the two-phase flow in the BPHEs with alternative refrigerants. Xiaoyang *et al*., [1] experimented with the two-phase flow distribution in stacked PHEs at both vertical upward and downward flow orientations. They indicated that non-uniform distributions were found and that the flow distribution was strongly affected by the total inlet flow rate, the vapor quality, the flow channel orientation, and the geometry of the inlet port Holger [2].Theoretically predicted the performance of chevron-type PHEs under singlephase conditions and recommended the correlations for the friction factors and heat transfer coefficients as functions of the corrugation chevron angles. Lee *et al*., [3] investigated the characteristics of the evaporation heat transfer and pressure drop in BPHEs with R404A and

The Characteristics of Brazed Plate Heat Exchangers with Different Chevron Angles 399

abutting, with their corrugations forming narrow passages. This type of equipment offers high thermal effectiveness and close temperature approach, while allowing ease of inspection and cleaning [1],[2]. In order to be able to evaluate its performance, methods to predict the heat transfer coefficient and pressure drop must be developed. In this direction, CFD is considered an efficient tool for momentum and heat transfer rate estimation in this

The type of flow in such narrow passages, which is associated with the choice of the most appropriate flow model for CFD simulation, is still an open issue in the literature. Due to the relatively high pressure drop, compared to shell-and-tube heat exchangers for equivalent flow rates, the Reynolds numbers used in this type of equipment must be lower so as the resulting pressure drops would be generally acceptable[1]. Moreover, when this equipment is used as a reflux condenser, the limit imposed by the onset of flooding reduces the maximum Reynolds number to a value less than 2000[3]. Ciofalo et al.[4], in a comprehensive review article concerning modeling heat transfer in narrow flow passages, state that, for the Reynolds number range of 1,500-3,000, transitional flow is expected, a kind

On the other hand, Shah & Wanniarachchi[1] declare that, for the Reynolds number range 100-1500, there is evidence that the flow is already turbulent, a statement that is also supported by Vlasogiannis et al.[5], whose experiments in a plate heat exchanger verify that the flow is turbulent for Re>650. Lioumbas et al.[6], who studied experimentally the flow in narrow passages during counter-current gas-liquid flow, suggest that the flow exhibits the basic features of turbulent flow even for the relatively low gas Reynolds numbers tested (500<Re<1200).Focke & Knibbe[7] performed flow visualization experiments in narrow passages with corrugated walls. They concluded that the flow patterns in such geometries are complex, due to the existence of secondary swirling motions along the furrows of their test section and suggest that the local flow structure controls the heat transfer process in

The most common two-equation turbulence model, based on the equations for the turbulence energy *k* and its dissipation *ε*, is the *k-ε* model[8]. To calculate the boundary layer, either "wall functions" are used, overriding the calculation of *k* and *ε* in the wall adjacent nodes[8], or integration is performed to the surface, using a "low turbulent Reynolds (*low-Re*) *k-ε*" model[9]. Menter & Esch[9] state that, in standard *k-ε* the wall shear stress and heat flux are over predicted (especially for the lower range of the Reynolds number encountered in this kind of equipment) due to the over prediction of the turbulent length scale in the flow reattachment region, which is a characteristic phenomenon occurring on the corrugated surfaces in these geometries. Moreover, the standard *k-ε*, model requires a course grid near the wall, based on the value of *y+*=11 [9],[10], which is difficult to accomplish in confined geometries. The low-Re *k-ε* model, which uses "dumping functions" near the wall[8],[9], is not considered capable of predicting the flow parameters in the complex geometry of a corrugated narrow channel[4], requires finer mesh near the wall, is computationally expensive compared to the standard *k-ε* model and it is unstable in

An alternative to *k-ε* model, is the *k-ω* model, developed by Wilcox[11]. This model, which uses the turbulence frequency *ω* instead of the turbulence diffusivity *ε*, appears to be more robust, even for complex applications, and does not require very fine grid near the wall[8].

of flow among the most difficult to simulate by conventional turbulence models.

type of heat exchangers.

such narrow passages.

convergence.

R407C. Kedzierski [4] reported the effect of inclination on the performance of a BPHE using R22 in both the condenser and the evaporator. Several single-phase correlations for heat transfer coefficients and friction factors have been proposed, but few correlations for the two-phase flow have been proposed. Yan *et al*., [5] suggested a correlation of condensation with a chevron angle of 30º for R134a. Yan *et al*., reported that the mass flux, the vapor quality, and the condensation pressure affected the heat transfer coefficients and the pressure drops. Hieh and Lin [6] developed the correlations for evaporation with a chevron angle of 30º for R410A.

The main objective of this work was to experimentally investigate the heat transfer coefficients and the pressure drops during condensation of R410A inside BPHEs. Three BPHEs with different chevron angles of 45º, 35º, and 20º were used. The results were then compared to those of R22. The geometric effects of the plate on the heat transfer and the pressure drop were investigated by varying the mass flux, the quality, and the condensation temperature. From the results, the geometric effects, especially the chevron angle, must be considered to develop the correlations for the Nusselt number and the friction factor. Correlations for the Nusselt number and the friction factor with the geometric parameters are suggested in this study.

Experiments to measure the condensation heat transfer coefficient and the pressure drop in brazed plate heat exchangers (BPHEs) were performed with the refrigerants R410A and R22. Brazed plate heat exchangers with different chevron angles of 45°, 35°, and 20° were used. Varying the mass flux, the condensation temperature, and the vapor quality of the refrigerant, we measured the condensation heat transfer coefficient and the pressure drops. Both the heat transfer coefficient and the pressure drop increased proportionally with the mass flux and the vapor quality and inversely with the condensation temperature and the chevron angle.

Correlations of the Nusselt number and the friction factor with the geometric parameters are suggested for the tested BPHEs. In an effort to study and optimize the design of a plate heat exchanger comprising of corrugated walls with herringbone design, a CFD code is employed. Due to the difficulties induced by the geometry and flow complexity, an approach through a simplified model was followed as a first step. This simple model, comprised of only one corrugated plate and a flat plate, was constructed and simulated. The Reynolds numbers examined are 400, 900, 1000, 1150, 1250 and 1400. The SST turbulence model was preferred over other flow models for the simulation.

The case where hot water (60oC) is in contact with a constant-temperature wall (20oC) was also simulated and the heat transfer rate was calculated. The results for the simplified model, presented in terms of velocity, shear stress and heat transfer coefficients, strongly encourage the simulation of one channel of the typical plate heat exchanger, i.e. the one that comprises of two corrugated plates with herringbone design having their crests nearly in contact. Preliminary results of this latter work, currently in progress, comply with visual observations.

In recent years, compact heat exchangers with corrugated plates are being rapidly adopted by food and chemical process industries, replacing conventional shell-and-tube exchangers. Compact heat exchangers consist of plates embossed with some form of corrugated surface pattern, usually the chevron (herringbone) geometry[1].The plates are assembled being

R407C. Kedzierski [4] reported the effect of inclination on the performance of a BPHE using R22 in both the condenser and the evaporator. Several single-phase correlations for heat transfer coefficients and friction factors have been proposed, but few correlations for the two-phase flow have been proposed. Yan *et al*., [5] suggested a correlation of condensation with a chevron angle of 30º for R134a. Yan *et al*., reported that the mass flux, the vapor quality, and the condensation pressure affected the heat transfer coefficients and the pressure drops. Hieh and Lin [6] developed the correlations for evaporation with a chevron

The main objective of this work was to experimentally investigate the heat transfer coefficients and the pressure drops during condensation of R410A inside BPHEs. Three BPHEs with different chevron angles of 45º, 35º, and 20º were used. The results were then compared to those of R22. The geometric effects of the plate on the heat transfer and the pressure drop were investigated by varying the mass flux, the quality, and the condensation temperature. From the results, the geometric effects, especially the chevron angle, must be considered to develop the correlations for the Nusselt number and the friction factor. Correlations for the Nusselt number and the friction factor with the geometric parameters

Experiments to measure the condensation heat transfer coefficient and the pressure drop in brazed plate heat exchangers (BPHEs) were performed with the refrigerants R410A and R22. Brazed plate heat exchangers with different chevron angles of 45°, 35°, and 20° were used. Varying the mass flux, the condensation temperature, and the vapor quality of the refrigerant, we measured the condensation heat transfer coefficient and the pressure drops. Both the heat transfer coefficient and the pressure drop increased proportionally with the mass flux and the vapor quality and inversely with the condensation temperature and the

Correlations of the Nusselt number and the friction factor with the geometric parameters are suggested for the tested BPHEs. In an effort to study and optimize the design of a plate heat exchanger comprising of corrugated walls with herringbone design, a CFD code is employed. Due to the difficulties induced by the geometry and flow complexity, an approach through a simplified model was followed as a first step. This simple model, comprised of only one corrugated plate and a flat plate, was constructed and simulated. The Reynolds numbers examined are 400, 900, 1000, 1150, 1250 and 1400. The SST turbulence

The case where hot water (60oC) is in contact with a constant-temperature wall (20oC) was also simulated and the heat transfer rate was calculated. The results for the simplified model, presented in terms of velocity, shear stress and heat transfer coefficients, strongly encourage the simulation of one channel of the typical plate heat exchanger, i.e. the one that comprises of two corrugated plates with herringbone design having their crests nearly in contact. Preliminary results of this latter work, currently in progress, comply with visual

In recent years, compact heat exchangers with corrugated plates are being rapidly adopted by food and chemical process industries, replacing conventional shell-and-tube exchangers. Compact heat exchangers consist of plates embossed with some form of corrugated surface pattern, usually the chevron (herringbone) geometry[1].The plates are assembled being

model was preferred over other flow models for the simulation.

angle of 30º for R410A.

are suggested in this study.

chevron angle.

observations.

abutting, with their corrugations forming narrow passages. This type of equipment offers high thermal effectiveness and close temperature approach, while allowing ease of inspection and cleaning [1],[2]. In order to be able to evaluate its performance, methods to predict the heat transfer coefficient and pressure drop must be developed. In this direction, CFD is considered an efficient tool for momentum and heat transfer rate estimation in this type of heat exchangers.

The type of flow in such narrow passages, which is associated with the choice of the most appropriate flow model for CFD simulation, is still an open issue in the literature. Due to the relatively high pressure drop, compared to shell-and-tube heat exchangers for equivalent flow rates, the Reynolds numbers used in this type of equipment must be lower so as the resulting pressure drops would be generally acceptable[1]. Moreover, when this equipment is used as a reflux condenser, the limit imposed by the onset of flooding reduces the maximum Reynolds number to a value less than 2000[3]. Ciofalo et al.[4], in a comprehensive review article concerning modeling heat transfer in narrow flow passages, state that, for the Reynolds number range of 1,500-3,000, transitional flow is expected, a kind of flow among the most difficult to simulate by conventional turbulence models.

On the other hand, Shah & Wanniarachchi[1] declare that, for the Reynolds number range 100-1500, there is evidence that the flow is already turbulent, a statement that is also supported by Vlasogiannis et al.[5], whose experiments in a plate heat exchanger verify that the flow is turbulent for Re>650. Lioumbas et al.[6], who studied experimentally the flow in narrow passages during counter-current gas-liquid flow, suggest that the flow exhibits the basic features of turbulent flow even for the relatively low gas Reynolds numbers tested (500<Re<1200).Focke & Knibbe[7] performed flow visualization experiments in narrow passages with corrugated walls. They concluded that the flow patterns in such geometries are complex, due to the existence of secondary swirling motions along the furrows of their test section and suggest that the local flow structure controls the heat transfer process in such narrow passages.

The most common two-equation turbulence model, based on the equations for the turbulence energy *k* and its dissipation *ε*, is the *k-ε* model[8]. To calculate the boundary layer, either "wall functions" are used, overriding the calculation of *k* and *ε* in the wall adjacent nodes[8], or integration is performed to the surface, using a "low turbulent Reynolds (*low-Re*) *k-ε*" model[9]. Menter & Esch[9] state that, in standard *k-ε* the wall shear stress and heat flux are over predicted (especially for the lower range of the Reynolds number encountered in this kind of equipment) due to the over prediction of the turbulent length scale in the flow reattachment region, which is a characteristic phenomenon occurring on the corrugated surfaces in these geometries. Moreover, the standard *k-ε*, model requires a course grid near the wall, based on the value of *y+*=11 [9],[10], which is difficult to accomplish in confined geometries. The low-Re *k-ε* model, which uses "dumping functions" near the wall[8],[9], is not considered capable of predicting the flow parameters in the complex geometry of a corrugated narrow channel[4], requires finer mesh near the wall, is computationally expensive compared to the standard *k-ε* model and it is unstable in convergence.

An alternative to *k-ε* model, is the *k-ω* model, developed by Wilcox[11]. This model, which uses the turbulence frequency *ω* instead of the turbulence diffusivity *ε*, appears to be more robust, even for complex applications, and does not require very fine grid near the wall[8].

The Characteristics of Brazed Plate Heat Exchangers with Different Chevron Angles 401

Three BPHEs with chevron angles of 45°, 35°, and 20° were used as the test sections. The angles of corrugation were measured from the horizontal axis. Each BPHE was composed of 4 thermal plates and 2 end plates, forming 5 flow channels. The dimensions of the BPHEs are shown in Figure-2. The refrigerant and cooling water were directed into the alternate passages between the plates through corner ports, creating counter flow conditions. The cooling water owed from the bottom to the top of every other channel on the basis of a central channel. On the other hand, the refrigerant owed from the top to the bottom in the

Refrigerant was supplied to the test section at specific conditions (i.e., temperature, flow rate, and quality) through the refrigerant loop. This loop contained a pre-heater, a doublepipe heat exchanger, a receiver, a magnetic gear pump, a differential pressure transducer, and a mass flow meter. Also included were thermocouples probes and pressure taps at the inlet/outlet of the test section. The refrigerant pump was driven by a DC motor which was

The refrigerant flow rate was measured by using a mass flow meter installed between the magnetic gear pump and the pre-heater with an accuracy of 0.5 %. The pre-heater located before the test section was used to evaporate the refrigerant to a specified vapor quality at the inlet of the test section. The pressure drop of the refrigerant owing through the test section was measured with the differential pressure transducer, to an accuracy of 0.25 kPa. The refrigerant through the test section was subcooled at a double-pipe heat exchanger by

Fig. 2. Dimensions of the brazed plate heat exchangers.

controlled by a variable DC output motor controller.

**2.1 Brazed plate heat exchangers** 

rest of them.

**2.2 Refrigerant loop** 

However, it seems to be sensitive to the free stream values of turbulence frequency *ω* outside the boundary layer. A combination of the two models, *k-ε* and *k-ω*, is the *SST* (Shear-Stress Transport) model, which, by employing specific "blending functions", activates the Wilcox model near the wall and the *k-ε* model for the rest of the flow[9] and thus it benefits from the advantages of both models. Some efforts have been made wards the effective simulation of a plate heat exchanger. Due to the modular nature of a compact heat exchanger, a common practice is to think of it as composed of a large number of unit *cells*  (Representative Element Units, *RES*) and obtain results by using a single cell as the computational domain and imposing periodicity conditions across its boundaries[4],[12]. However, the validity of this assumption is considered another open issue in the literature [4].
