**2. Experimental facility**

The experimental facility is capable of determining in plate heat transfer coefficients and measuring the pressure drops for the refrigerants. It consists of four main parts: a test section, a refrigerant loop, two water loops, and a data-acquisition system. A schematic of the test facility used in this study is shown in Figure-1, and detailed descriptions of the four main parts are mentioned below.

Fig. 1. Schematic diagram of the experimental system.

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

#### **2.1 Brazed plate heat exchangers**

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 rest of them.

#### **2.2 Refrigerant loop**

400 Heat Exchangers – Basics Design Applications

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

The experimental facility is capable of determining in plate heat transfer coefficients and measuring the pressure drops for the refrigerants. It consists of four main parts: a test section, a refrigerant loop, two water loops, and a data-acquisition system. A schematic of the test facility used in this study is shown in Figure-1, and detailed descriptions of the four

[4].

**2. Experimental facility** 

main parts are mentioned below.

Fig. 1. Schematic diagram of the experimental system.

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 controlled by a variable DC output motor controller.

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

The Characteristics of Brazed Plate Heat Exchangers with Different Chevron Angles 403

The power gained by the pre-heater is calculated by measuring the voltage and the current with a power meter. The change in the refrigerant quality inside the test section was evaluated from the heat transferred in the test section and the refrigerant mass flow

The condensing heat in the test section was calculated from an energy balance with water:

 Qw=mwCp,w(Tw,out-Tw,in) (7) The heat transfer coefficient of the refrigerant side (hr) was evaluated from the following

 1/hr= (1/U)-(1/hw)-Rwall (8) The overall heat transfer coefficient was determined using the log mean temperature

U=Qw/A X LMTD

 LMTD=(Tr,out-Tw,in)-(Tr,in-Tw,out)/ln{(Tr,out-Tw,in)-(Tr,in-Tw,out)} (9) The heat transfer coefficient of the water side (h W) was obtained by using Eq. (10). Equation (10) was developed from the single-phase water to water pre-tests by Kim [7]. If the leastsquares method and the multiple regression method are used, the heat transfer coefficient of the water side is correlated in terms of the Reynolds number, the Prandtl number, and the

hw=0.295(kw/DEq)Re0.64Pr0.32(π/2-β)0.09 (10)

And ∆P total is measured by using a differential pressure transducer. The two-phase friction

The port pressure loss in this experiment was less than 1 % of the total pressure loss. The static head loss can be written as and it has a negative value for vertical downward flow.

An uncertainty analysis was done for all the measured data and the calculated quantities based on the methods described by Moffat [9]. The detailed results of the uncertainty

∆Pp=1.4G2

The acceleration pressure drop for condensation is expressed as

The thermal resistance of the wall is negligible compared to the effect of convection.

For the vertical downward flow, the total pressure drop in the test section is defined as

∆x=xin-xout=Qw/mrXifg (6)

∆Ptotal=∆Pfr+∆Pa+∆Ps+∆Pp (11)

∆Pfr=fLvNcpG2Eq/Dhρf (12)

p/(2ρm) (13)

rate (6)

equation:

difference

chevron angle:

factor, f, is defined as

analysis are shown in Table-1.

the water cooled by the chiller and went into a liquid receiver. The subcooled refrigerant returned to the magnetic gear pump and circulated through the refrigerant loop repeatedly. Calibrated T-type thermocouples were used to measure the temperatures of the refrigerant at the inlet/outlet of the test section. The entire loop was insulated with fiberglass to prevent heat transfer to the environment.

#### **2.3 Water loop**

There are two closed water loops in this facility. One is for determining the condensation heat flux at the test section. The other is for making the subcooled refrigerant state at two double-pipe heat exchangers before it enters the magnetic gear pump. The water flow rates of the test section were measured by using a turbine flow meter, and T-type thermocouples were installed to evaluate the gain of the heat flux of the water of the test section.

#### **2.4 Data acquisition**

The data were recorded by a computer-controlled data-acquisition system with 40 channels scanned at the speed of 30 data per minute. The temperature and the pressure of both fluids were continuously recorded, and the thermodynamic properties of the refrigerant were obtained from a computer program. After steady-state conditions had been reached in the system, all measurements were taken for 10 minutes.

#### **3. Data reduction and uncertainty analysis**

The hydraulic diameter of the channel, Dh, is defined as

$$\mathbf{D\_{h}} = 4\mathbf{X} \mathbf{C} \mathbf{h} \text{annel flow area/Wetted perimeter=} 4\mathbf{b} \mathbf{L\_{w}}/2\mathbf{L\_{w}} \mathcal{O} \tag{1}$$

Where is **Ø** =1.17. This value is given by the manufacturer.

The mean channel spacing, b, is defined as

$$\mathbf{b} \triangleq \mathbf{p} - \mathbf{t}; \quad \mathbf{t} \triangleq \text{Plate Thickness} \tag{2}$$

and the plate pitch p can be determined as, N t=Total Number of plates

$$\mathbf{p} = \mathbf{L}\_c / \mathbf{N}\_t \mathbf{1} \tag{3}$$

The procedures to calculate the condensation heat transfer coefficient of the refrigerant side are described below. At first, the refrigerant quality at the inlet of the test section (x in) should be selected to evaluate the condensation heat at a given quality. Its value is calculated from the amount of heat given by a pre-heater, which is the summation of the sensible heat and the latent heat:

$$\mathbf{Q\_{prc}} = \mathbf{Q\_{sens}} + \mathbf{Q\_{lat}}$$

$$\mathbf{I} = \mathbf{m\_r} \mathbf{C\_{p,r}} (\mathbf{T\_{r,sat}} \mathbf{T\_{r,pre,in}}) + \mathbf{m\_r} \mathbf{i\_{fg}} \mathbf{x\_{in}} \tag{4}$$

The refrigerant quality at the inlet of the test section can be written as

$$\mathbf{X}\_{\rm in} = 1/\mathrm{i}\_{\rm lg} \left[ \mathbf{Q}\_{\rm pre}/\mathrm{m}\_{\rm r} - \mathbf{C}\_{\rm p,r} \left( \mathbf{T}\_{\rm r,sat} - \mathbf{T}\_{\rm r,pre,in} \right) \right] \tag{5}$$

the water cooled by the chiller and went into a liquid receiver. The subcooled refrigerant returned to the magnetic gear pump and circulated through the refrigerant loop repeatedly. Calibrated T-type thermocouples were used to measure the temperatures of the refrigerant at the inlet/outlet of the test section. The entire loop was insulated with fiberglass to prevent

There are two closed water loops in this facility. One is for determining the condensation heat flux at the test section. The other is for making the subcooled refrigerant state at two double-pipe heat exchangers before it enters the magnetic gear pump. The water flow rates of the test section were measured by using a turbine flow meter, and T-type thermocouples

The data were recorded by a computer-controlled data-acquisition system with 40 channels scanned at the speed of 30 data per minute. The temperature and the pressure of both fluids were continuously recorded, and the thermodynamic properties of the refrigerant were obtained from a computer program. After steady-state conditions had been reached in the

Dh= 4XChannel flow area/Wetted perimeter=4bLw/2LwØ (1)

 p= Lc/Nt-1 (3) The procedures to calculate the condensation heat transfer coefficient of the refrigerant side are described below. At first, the refrigerant quality at the inlet of the test section (x in) should be selected to evaluate the condensation heat at a given quality. Its value is calculated from the amount of heat given by a pre-heater, which is the summation of the

Qpre= Qsens+ Qlat

Xin = 1/ifg [Qpre/mr –Cp,r (Tr, sat – Tr,pre,in)] (5)

**b = p - t;** t= Plate Thickness (2)

= mrCp,r(Tr,sat-Tr,pre,in) + mrifgxin (4)

were installed to evaluate the gain of the heat flux of the water of the test section.

system, all measurements were taken for 10 minutes.

**3. Data reduction and uncertainty analysis** 

The mean channel spacing, b, is defined as

sensible heat and the latent heat:

The hydraulic diameter of the channel, Dh, is defined as

Where is **Ø** =1.17. This value is given by the manufacturer.

and the plate pitch p can be determined as, N t=Total Number of plates

The refrigerant quality at the inlet of the test section can be written as

heat transfer to the environment.

**2.3 Water loop** 

**2.4 Data acquisition** 

The power gained by the pre-heater is calculated by measuring the voltage and the current with a power meter. The change in the refrigerant quality inside the test section was evaluated from the heat transferred in the test section and the refrigerant mass flow rate (6)

$$
\Delta \mathbf{x} = \mathbf{x}\_{\text{irr}} \mathbf{x}\_{\text{out}} = \mathbf{Q}\_{\text{w}} / \mathbf{m}\_{\text{r}} \mathbf{X} \mathbf{i}\_{\text{f} \nmid \mathbf{g}} \tag{6}
$$

The condensing heat in the test section was calculated from an energy balance with water:

$$\mathbf{Q\_{w}} = \mathbf{m\_{w}} \mathbf{C\_{p,w}} \langle \mathbf{T\_{w,out}} \mathbf{T\_{w,in}} \rangle \tag{7}$$

The heat transfer coefficient of the refrigerant side (hr) was evaluated from the following equation:

$$1/\text{h}\_{\text{t}} = (1/\text{U}) \text{-} (1/\text{h}\_{\text{w}}) \text{-} R\_{\text{wall}} \tag{8}$$

The overall heat transfer coefficient was determined using the log mean temperature difference

$$\mathbf{U} = \mathbf{Q}\_{\mathbf{w}} / \mathbf{A} \,\,\mathbf{X} \,\,\mathrm{LMTD}$$

$$\mathrm{LMTD} = (\mathbf{T}\_{\mathrm{r,out}} \mathbf{T}\_{\mathrm{w,in}}) \cdot (\mathbf{T}\_{\mathrm{r,in}} \mathbf{-T}\_{\mathrm{w,out}}) / \ln \{ (\mathbf{T}\_{\mathrm{r,out}} \mathbf{T}\_{\mathrm{w,in}}) \cdot (\mathbf{T}\_{\mathrm{r,in}} \mathbf{-T}\_{\mathrm{w,out}}) \} \tag{9}$$

The heat transfer coefficient of the water side (h W) was obtained by using Eq. (10). Equation (10) was developed from the single-phase water to water pre-tests by Kim [7]. If the leastsquares method and the multiple regression method are used, the heat transfer coefficient of the water side is correlated in terms of the Reynolds number, the Prandtl number, and the chevron angle:

$$\mathbf{h\_w} = \mathbf{0.295(k\_w/D\_{liq})} \text{Re}^{0.64} \text{Pr}^{0.32} \text{(n/2-\beta)}^{0.09} \tag{10}$$

The thermal resistance of the wall is negligible compared to the effect of convection.

For the vertical downward flow, the total pressure drop in the test section is defined as

$$
\Delta \mathbf{P}\_{\text{total}} = \Delta \mathbf{P}\_{\text{fr}} + \Delta \mathbf{P}\_{\text{a}} + \Delta \mathbf{P}\_{\text{s}} + \Delta \mathbf{P}\_{\text{p}} \tag{11}
$$

And ∆P total is measured by using a differential pressure transducer. The two-phase friction factor, f, is defined as

$$
\Delta \mathbf{P}\_{\rm fr} = \mathbf{f} \mathbf{L}\_{\rm r} \mathbf{N}\_{\rm cr} \mathbf{G}^2 \mathbf{z}\_{\rm Eg} / \mathbf{D}\_{\rm hf} \mathbf{q} \tag{12}
$$

The port pressure loss in this experiment was less than 1 % of the total pressure loss. The static head loss can be written as and it has a negative value for vertical downward flow. The acceleration pressure drop for condensation is expressed as

$$
\Delta \mathbf{P}\_{\mathrm{P}} = \mathbf{1}.4 \mathbf{G}^2 \mathbf{p} / \text{(}\mathbf{2} \mathbf{p}\_{\mathrm{m}}\text{)}\tag{13}
$$

An uncertainty analysis was done for all the measured data and the calculated quantities based on the methods described by Moffat [9]. The detailed results of the uncertainty analysis are shown in Table-1.

The Characteristics of Brazed Plate Heat Exchangers with Different Chevron Angles 405

superficial liquid (jf) and vapor velocities (jg) by using water and air under adiabatic conditions. They only simulated a mixture of water and air as a two-phase fluid. According to their work, the flow patterns in a PHE are significantly different from those inside the vertical round tubes. They detected 3 types of flow patterns. The first was a gas continuous pattern with a liquid pocket at flow water flow rates (jf < 0.025 m/s) over wide range of air

The second was the slug flow pattern, which was detected at sufficiently high air (jg > 2 m/s) and water flow rates (jf > 0.025 m/s). Thirdly, the liquid continuous pattern with a gas pocket or a gas bubble at the high water flow rates (jf >0.1 m/s) and low air flow rates (jg < 1 m/s).According to the flow regime map proposed by Vlasogiannis *et al*., the expected flow pattern in this experimental study is the gas continuous flow pattern with liquid pockets. However, their flow regime map has a significant limitation for use since many important features, such as the phase-change, the heating or cooling conditions, the densities or specific volumes of the working fluids, the geometries of the PHEs, etc., were not considered in detail. According to the flow regime map proposed by Crawford *et al.* [11], which was developed for vertical downward flow in a round tube, all experimental flow patterns are located in the intermittent flow regime, but this flow regime can not represent the correct

Figure-3 shows the effects of the refrigerant mass flux, the chevron angle, and the condensation temperature on the averaged heat transfer coefficient for R410A. The term "averaged heat transfer coefficient" means the average of the heat transfer coefficients calculated by varying the quality of the refrigerant from 0.15 to 0.9, and the coefficients were

Where hl is the local heat transfer coefficient at the local vapor quality. The experimental results indicate that the averaged heat transfer coefficients vary proportionally with the mass flux and inversely with the chevron angles and the condensation temperature. The small chevron angle forms narrow pitches to the flow direction, creating more abrupt changes in the velocity and the flow direction, thus increasing the effective contact length and time in a BHPE. The zigzag flow increases the heat transfer, and the turbulence created by the shape of the plate pattern is also important in addition to the turbulence created by the high flow rates. Increasing the mass flux at a given condensation temperature showed that the differences in the averaged heat transfer coefficients were significantly enlarged with decreasing chevron angle. This indicates that a PHE with the small chevron angle is

The averaged heat transfer coefficient of R410A decreases with increasing condensation temperature. The vapor velocity is a more influential factor than the liquid film thickness for the heat transfer. Vapor bubbles in the flow enhance the disturbance in the bubble wake as a turbulence promoter, and the turbulence induced by the vapor bubbles increases with the vapor velocity. Also, since the specific volume of the vapor increases with decreasing condensation temperature, the vapor velocity increases for a fixed mass flux and quality.

more effective at a large mass flux (Gc > 25 kg/m2s) than at a small mass flux.

Haverged = Σhlocalxlocal / Σxlocal (19)

flow regime in a BPHE due to the different geometries.

**4.2 Condensation heat transfer** 

obtained from Eq. (19):

flow rates.


Table 1. Estimated uncertainty.

Where

$$\mathbf{G\_{P}} = 4 \mathbf{m\_{Fig}} / \mathbf{n} \mathbf{D\_{P}} \tag{14}$$

And

$$(\mathbf{1}/\rho\_{\mathbf{m}}) = (\mathbf{x}/\rho\_{\mathbf{y}}) + [(\mathbf{1}\cdot\mathbf{x})/\rho\_{\mathbf{l}}].\tag{15}$$

The equivalent mass flow rate, meq, is defined as

$$\mathbf{m}\_{\rm eq} = \mathbf{m} \left[ 1 \mathbf{-} \mathbf{x} + \mathbf{x} (\mathbf{q} \mathbf{f} / \, \! \! \mathbf{q} \mathbf{g})^{0.5} \right] \tag{16}$$

The port pressure loss in this experiment was less than 1% of the total pressure loss. The static head loss can be written as

$$
\Delta \mathbf{P}\_{\mathbf{s}} = \mathbf{\bar{s}} \mathbf{\bar{g}} \mathbf{m} \mathbf{L}\_{\mathbf{v}} \tag{17}
$$

And it has a negative value for vertical downward flow, The acceleration pressure drop for condensation is expressed as

$$
\Delta \mathbf{P}\_{\rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \rm \$$

#### **4. Results and discussions**

The condensation heat transfer coefficients and the pressure drops of R410A and R22 were measured in three BPHEs with chevron angles of 20°, 35°, and 45° by varying the mass flux (13 - 34 kg/m2s), the vapor quality (0.9 - 0.15), and the condensing temperature (20°C and 30°C) under a given heat flux condition (4.7 -5.3 kW/m2). R22 was tested under identical experimental conditions for comparison with R410A.

#### **4.1 Flow regime**

Before the behaviors of heat transfer are considered, it is necessary to predict what flow regime exists at a given set of operating conditions. The detailed flow regime map for the PHE has not been proposed yet because of the difficulty of flow visualization. Vlasogiannis *et al*., [10] suggested the criterion of a two-phase flow regime for a PHE in terms of superficial liquid (jf) and vapor velocities (jg) by using water and air under adiabatic conditions. They only simulated a mixture of water and air as a two-phase fluid. According to their work, the flow patterns in a PHE are significantly different from those inside the vertical round tubes. They detected 3 types of flow patterns. The first was a gas continuous pattern with a liquid pocket at flow water flow rates (jf < 0.025 m/s) over wide range of air flow rates.

The second was the slug flow pattern, which was detected at sufficiently high air (jg > 2 m/s) and water flow rates (jf > 0.025 m/s). Thirdly, the liquid continuous pattern with a gas pocket or a gas bubble at the high water flow rates (jf >0.1 m/s) and low air flow rates (jg < 1 m/s).According to the flow regime map proposed by Vlasogiannis *et al*., the expected flow pattern in this experimental study is the gas continuous flow pattern with liquid pockets. However, their flow regime map has a significant limitation for use since many important features, such as the phase-change, the heating or cooling conditions, the densities or specific volumes of the working fluids, the geometries of the PHEs, etc., were not considered in detail. According to the flow regime map proposed by Crawford *et al.* [11], which was developed for vertical downward flow in a round tube, all experimental flow patterns are located in the intermittent flow regime, but this flow regime can not represent the correct flow regime in a BPHE due to the different geometries.

#### **4.2 Condensation heat transfer**

404 Heat Exchangers – Basics Design Applications

(1/ρm) = (x/ρg) + [(1-x)/ρf]. (15)

 meq = m [1-x+x(ρf/ ρg)0.5] (16) The port pressure loss in this experiment was less than 1% of the total pressure loss. The

And it has a negative value for vertical downward flow, The acceleration pressure drop for

eqx/ρfg)in – (G2

The condensation heat transfer coefficients and the pressure drops of R410A and R22 were measured in three BPHEs with chevron angles of 20°, 35°, and 45° by varying the mass flux (13 - 34 kg/m2s), the vapor quality (0.9 - 0.15), and the condensing temperature (20°C and 30°C) under a given heat flux condition (4.7 -5.3 kW/m2). R22 was tested under identical

Before the behaviors of heat transfer are considered, it is necessary to predict what flow regime exists at a given set of operating conditions. The detailed flow regime map for the PHE has not been proposed yet because of the difficulty of flow visualization. Vlasogiannis *et al*., [10] suggested the criterion of a two-phase flow regime for a PHE in terms of

ΔPa = - [(G2

Temperature ±0.2 0C Pressure ±4.7 Pa Pressure Drop ±250 Pa Water Flow Rate ±2% Refrigerant mass flux ±0.5% Heat flux of test section ±5.7% Vapor Quality ±0.03

Heat Transfer coefficients of water side ±10.1% Heat transfer coefficients of refrigerant ±9.1%

Table 1. Estimated uncertainty.

static head loss can be written as

condensation is expressed as

**4. Results and discussions** 

**4.1 Flow regime** 

Gp=4mEq/πD2

The equivalent mass flow rate, meq, is defined as

experimental conditions for comparison with R410A.

Where

And

Parameters Uncertainty

p (14)

ΔPs = -ρmgLv (17)

eqx/ ρfg)out] (18)

Figure-3 shows the effects of the refrigerant mass flux, the chevron angle, and the condensation temperature on the averaged heat transfer coefficient for R410A. The term "averaged heat transfer coefficient" means the average of the heat transfer coefficients calculated by varying the quality of the refrigerant from 0.15 to 0.9, and the coefficients were obtained from Eq. (19):

$$\mathbf{H}\_{\text{averaged}} = \boldsymbol{\Sigma} \mathbf{h}\_{\text{local}} \mathbf{x}\_{\text{local}} / \boldsymbol{\Sigma} \mathbf{x}\_{\text{local}} \tag{19}$$

Where hl is the local heat transfer coefficient at the local vapor quality. The experimental results indicate that the averaged heat transfer coefficients vary proportionally with the mass flux and inversely with the chevron angles and the condensation temperature. The small chevron angle forms narrow pitches to the flow direction, creating more abrupt changes in the velocity and the flow direction, thus increasing the effective contact length and time in a BHPE. The zigzag flow increases the heat transfer, and the turbulence created by the shape of the plate pattern is also important in addition to the turbulence created by the high flow rates. Increasing the mass flux at a given condensation temperature showed that the differences in the averaged heat transfer coefficients were significantly enlarged with decreasing chevron angle. This indicates that a PHE with the small chevron angle is more effective at a large mass flux (Gc > 25 kg/m2s) than at a small mass flux.

The averaged heat transfer coefficient of R410A decreases with increasing condensation temperature. The vapor velocity is a more influential factor than the liquid film thickness for the heat transfer. Vapor bubbles in the flow enhance the disturbance in the bubble wake as a turbulence promoter, and the turbulence induced by the vapor bubbles increases with the vapor velocity. Also, since the specific volume of the vapor increases with decreasing condensation temperature, the vapor velocity increases for a fixed mass flux and quality.

The Characteristics of Brazed Plate Heat Exchangers with Different Chevron Angles 407

Increasing the vapor quality at the same mass flux induces a faster bubble velocity, which increases the turbulence level and the convection heat transfer coefficient. The difference of heat transfer coefficients between the low-quality region and the high-quality region becomes larger with decreasing chevron angle. The PHE with a low chevron angle shows a better heat transfer performance in the high-quality region (i.e., the high vapor velocity region). Figure-4 also shows the variation of the heat transfer coefficients with the condensation temperatures. Like Figure-3, the heat transfer coefficients decreased with increasing condensation temperature. Also, the variations of the heat transfer coefficients with the condensation temperature are larger in the high-quality region. From the experimental results in Figures, 3 and 4, lowering the chevron angle and the condensation

The frictional pressure loss in a BPHE is obtained by subtracting the acceleration pressure loss, the static head loss, and the port pressure loss from the total pressure loss. Figure-5 shows the trend of the pressure drop along the mass flux, and Figure-6 shows the trend of the pressure drop along the quality at a mass flux of 34 kg/m2s and a heat flux of 4.7-5.3 kW/m2. The frictional pressure drops in the BPHEs increase with increasing mass flux and quality and decreasing condensation temperature and chevron angle. This trend is similar to that of the condensation heat transfer. As mentioned above, since the vapor velocity is much faster than the liquid velocity during the two-phase flow in the tube, the vapor velocity is the dominant influence on the pressure drop, as well as the heat transfer. A high vapor velocity also tends to increase the turbulence of the flow. From Figures 3, 4, 5 and 6, we may concluded that since the trends of the the condensation heat transfer and the pressure loss in BPHEs are similar, those effects must be carefully considered in the

The ratios of R410A to R22 for the condensation heat transfer coefficients and pressure drops at a condensation temperature of 30°C are shown in the Figure-7. The ratios for the heat transfer coefficients are relatively constant in the range of 1 -1.1, regardless of the mass flux, while the ratios for the pressure drops decrease with increasing mass flux, except for the data at a chevron angle of 20° in the present experimental range. For a chevron angle of 20°, the heat transfer ratios of R410A to R22 are about 1.1, and the pressure drop ratios about 0.8, which is a 10 % higher heat transfer and a 20 % lower pressure drop.The smaller specific volume of the vapor of R410A relative to that of R22 makes the vapor velocity slower and yields a small pressure drop under the same conditions of the mass flux. While the two fluids have almost equal values of their latent heats, the liquid-phase thermal conductivity of R410A is larger than that of R22. The higher thermal conductivity for R410A helps to produce better heat transfer even if a reduction in the specific volume occurs. Also, a BPHE with a small chevron angle is known to have more effective performance from the ratios

temperature gives the desired heat transfer effect.

**4.3 Frictional pressure loss** 

design of a BPHE.

**4.4 Comparison of R410A with R22** 

when replacing R22 with R410A.

The vapor velocity at 20°C is faster than that at 30°C. The rates of the averaged heat transfer coefficients between condensation temperatures of 20°C and 30°C increased 5 % for a chevron angle of 45°, 9 % for 35°, and 16 % for 20°. These results show that different chevron angles lead partly to different flow pattern. Thus, we may conclude that the flow regime map should be modified by geometric considerations. The heat transfer coefficients in the high-quality region (fast velocity region) are larger than those in the low-quality region (slow velocity region). As mentioned above, this happens because the vapor velocity is the dominant effect on the heat transfer mechanism.

Fig. 3. Effect of mass flux on the averaged condensation heat transfer coefficient.

Fig. 4. Effect of quality on the condensation heat transfer coefficient.

Increasing the vapor quality at the same mass flux induces a faster bubble velocity, which increases the turbulence level and the convection heat transfer coefficient. The difference of heat transfer coefficients between the low-quality region and the high-quality region becomes larger with decreasing chevron angle. The PHE with a low chevron angle shows a better heat transfer performance in the high-quality region (i.e., the high vapor velocity region). Figure-4 also shows the variation of the heat transfer coefficients with the condensation temperatures. Like Figure-3, the heat transfer coefficients decreased with increasing condensation temperature. Also, the variations of the heat transfer coefficients with the condensation temperature are larger in the high-quality region. From the experimental results in Figures, 3 and 4, lowering the chevron angle and the condensation temperature gives the desired heat transfer effect.

## **4.3 Frictional pressure loss**

406 Heat Exchangers – Basics Design Applications

The vapor velocity at 20°C is faster than that at 30°C. The rates of the averaged heat transfer coefficients between condensation temperatures of 20°C and 30°C increased 5 % for a chevron angle of 45°, 9 % for 35°, and 16 % for 20°. These results show that different chevron angles lead partly to different flow pattern. Thus, we may conclude that the flow regime map should be modified by geometric considerations. The heat transfer coefficients in the high-quality region (fast velocity region) are larger than those in the low-quality region (slow velocity region). As mentioned above, this happens because the vapor velocity is the

Fig. 3. Effect of mass flux on the averaged condensation heat transfer coefficient.

Fig. 4. Effect of quality on the condensation heat transfer coefficient.

dominant effect on the heat transfer mechanism.

The frictional pressure loss in a BPHE is obtained by subtracting the acceleration pressure loss, the static head loss, and the port pressure loss from the total pressure loss. Figure-5 shows the trend of the pressure drop along the mass flux, and Figure-6 shows the trend of the pressure drop along the quality at a mass flux of 34 kg/m2s and a heat flux of 4.7-5.3 kW/m2. The frictional pressure drops in the BPHEs increase with increasing mass flux and quality and decreasing condensation temperature and chevron angle. This trend is similar to that of the condensation heat transfer. As mentioned above, since the vapor velocity is much faster than the liquid velocity during the two-phase flow in the tube, the vapor velocity is the dominant influence on the pressure drop, as well as the heat transfer. A high vapor velocity also tends to increase the turbulence of the flow. From Figures 3, 4, 5 and 6, we may concluded that since the trends of the the condensation heat transfer and the pressure loss in BPHEs are similar, those effects must be carefully considered in the design of a BPHE.

#### **4.4 Comparison of R410A with R22**

The ratios of R410A to R22 for the condensation heat transfer coefficients and pressure drops at a condensation temperature of 30°C are shown in the Figure-7. The ratios for the heat transfer coefficients are relatively constant in the range of 1 -1.1, regardless of the mass flux, while the ratios for the pressure drops decrease with increasing mass flux, except for the data at a chevron angle of 20° in the present experimental range. For a chevron angle of 20°, the heat transfer ratios of R410A to R22 are about 1.1, and the pressure drop ratios about 0.8, which is a 10 % higher heat transfer and a 20 % lower pressure drop.The smaller specific volume of the vapor of R410A relative to that of R22 makes the vapor velocity slower and yields a small pressure drop under the same conditions of the mass flux. While the two fluids have almost equal values of their latent heats, the liquid-phase thermal conductivity of R410A is larger than that of R22. The higher thermal conductivity for R410A helps to produce better heat transfer even if a reduction in the specific volume occurs. Also, a BPHE with a small chevron angle is known to have more effective performance from the ratios when replacing R22 with R410A.

The Characteristics of Brazed Plate Heat Exchangers with Different Chevron Angles 409

Based on the experimental data, the following correlations for Nu and f during condensation for the tested BPHEs are established: Where Ge1, Ge2, Ge3, and Ge4 are nondimensional geometric parameters that involve the corrugation pitch, the equivalent diameter, and the chevron angle. ReEq is the equivalent Reynolds number, and GEq the equivalent mass flux: where Gc is the channel mass flux. The suggested correlations for the Nusselt number and the friction factor can be applied in the range of ReEq from 300 to 4000. Figure-8(a) shows a comparison of the Nusselt number among the experimental data, the correlation proposed in this paper, and the correlation of Yan *et al.,* [5]. The correlation of

Nu = Ge1ReEqGe1Pr1/3 (20)

Ge1 = 11.22 (pco/Dh) -2.83 (Π/2 – β) -4.5 (21)

Ge2 = 0.35 (pco / Dh) 0.23 (Π/2 – β) 1.48 (22)

Ge3 = 3521.1 (pco/Dh) 4.17 (Π/2 – β) -7.75 (24)

ReEq = GEqDh / µf (26)

G Eq = Gc[1-x+x(ρf / ρg)

and is obtained from one PHE with a chevron angle of 30° for R134a. Regardless of the BPHE types and refrigerants, most of the experimental data are within 20 % for the

The correlation of Yan *et al*.(5), matched the data relatively well β for β: 20 and 35 within30 %, but over-predicted the data quite a bit for 45. This discrepancy results from the correlation of Yan *et al*., being developed for only a +30 PHE. Also,the correlation of Yan *et* 

for the Nusselt number only adopted the equivalent Reynolds number and Prandtl number without any geometric parameters. Because a BPHE has a strong geometric effect, the correlation with geometric parameters must be developed for general applications. The root-

r.m.s. = <sup>2</sup>

The r.m.s. deviation for the correlation of Yan *et al*., [Eq. (29)] is 50.2 % and for Eq. (20), it is only 10.9 %. Figure-8(b) shows a comparison of the friction factor between the experimental

Nu = 4.118Reeq

f = Ge3ReGe4Eq (23)

Gc = m / NepbLw (28)

1/2] (27)

0.4Pr1/3 (29)

Ge4 = -1.024 (pco/Dh) 0.0925 (Π/2 – β) -1.3 (25)

data pred exp exp 1 / N Nu Nu /Nu x 100 % (28)

**4.5 Correlations of Nusselt number and friction factor for tested BPHEs** 

Yan *et al*., is

*al*.

correlation proposed in this paper.

mean-square (r.m.s.) of the deviations is defined as

Fig. 5. Variation of the averaged condensation pressure drop with mass flux.

Fig. 6. Variation of the condensation pressure drop wih quality.

Fig. 7. Condensation heat transfer coefficient ratio and pressure drop ratio between R410A and R22.

Fig. 5. Variation of the averaged condensation pressure drop with mass flux.

Fig. 6. Variation of the condensation pressure drop wih quality.

and R22.

Fig. 7. Condensation heat transfer coefficient ratio and pressure drop ratio between R410A

#### **4.5 Correlations of Nusselt number and friction factor for tested BPHEs**

Based on the experimental data, the following correlations for Nu and f during condensation for the tested BPHEs are established: Where Ge1, Ge2, Ge3, and Ge4 are nondimensional geometric parameters that involve the corrugation pitch, the equivalent diameter, and the chevron angle. ReEq is the equivalent Reynolds number, and GEq the equivalent mass flux: where Gc is the channel mass flux. The suggested correlations for the Nusselt number and the friction factor can be applied in the range of ReEq from 300 to 4000. Figure-8(a) shows a comparison of the Nusselt number among the experimental data, the correlation proposed in this paper, and the correlation of Yan *et al.,* [5]. The correlation of Yan *et al*., is

$$\mathbf{N}\_{\rm u} = \mathbf{G}\_{\rm e1} \mathbf{R}\_{\rm e2} \mathbf{G}\_{\rm le1}^{\rm e1} \mathbf{P} \mathbf{r}^{1/3} \tag{20}$$

$$\text{Ge}\_1 = 11.22 \, (\text{p}\_{\text{co}}/\text{D}\_{\text{h}})^{\text{-}2.83} \, (\Pi/2 - \text{\textdegree })^{\text{-}4.5} \tag{21}$$

$$\text{Ge}\_2 = 0.35 \, (\text{p}\_{\text{co}} \, / \text{ D}\_{\text{h}})^{0.23} \, (\Pi / 2 - \beta)^{1.48} \tag{22}$$

f = Ge3ReGe4Eq (23)

$$\text{Ge}\_3 = 3521.1 \, (\text{p}\_{\text{co}}/\text{D}\_{\text{h}})^{4.17} \, (\Pi/2 - \text{\textdegree })^{5.75} \tag{24}$$

$$\text{Gee} = \text{-1.024} \left( \text{p}\_{\text{co}} / \text{D}\_{\text{h}} \right)^{0.0925} \left( \text{Tl} / 2 - \text{\textdegree } \right)^{-1.3} \tag{25}$$

$$\text{Re}\_{\text{liq}} = \text{G}\_{\text{liq}} \text{D}\_{\text{h}} / \,\mu\text{t} \tag{26}$$

$$\mathbf{G}\_{\rm xq} = \mathbf{G}\_{\rm t} \mathbf{[l-x+x(p\_t/p\_t)]^{1/2}} \tag{27}$$

$$\mathbf{G}\_{\mathbf{c}} = \mathbf{m} \mid \mathbf{N}\_{\mathbf{e}\mathbf{p}} \mathbf{b} \mathbf{L}\_{\mathbf{w}} \tag{28}$$

and is obtained from one PHE with a chevron angle of 30° for R134a. Regardless of the BPHE types and refrigerants, most of the experimental data are within 20 % for the correlation proposed in this paper.

The correlation of Yan *et al*.(5), matched the data relatively well β for β: 20 and 35 within30 %, but over-predicted the data quite a bit for 45. This discrepancy results from the correlation of Yan *et al*., being developed for only a +30 PHE. Also,the correlation of Yan *et al*.

$$\mathbf{Nu} = \mathbf{4.118Re\_{eq}04Pr^{1/3}} \tag{29}$$

for the Nusselt number only adopted the equivalent Reynolds number and Prandtl number without any geometric parameters. Because a BPHE has a strong geometric effect, the correlation with geometric parameters must be developed for general applications. The rootmean-square (r.m.s.) of the deviations is defined as

$$\text{tr.m.s.} = \sqrt{1 / \text{ N}\_{\text{data}} \Sigma \left( \text{Nu}\_{\text{pred}} - \text{Nu}\_{\text{exp}} \, \Big/ \text{Nu}\_{\text{exp}} \right)^2 \times 100 \left( \% \right)}\tag{28}$$

The r.m.s. deviation for the correlation of Yan *et al*., [Eq. (29)] is 50.2 % and for Eq. (20), it is only 10.9 %. Figure-8(b) shows a comparison of the friction factor between the experimental

The Characteristics of Brazed Plate Heat Exchangers with Different Chevron Angles 411

original plate heat exchanger and to reduce the computational demands. The geometry studied in the CFD simulations (similar to the test section) is shown in **Figure 10**. The Reynolds numbers examined are 400, 900, 1000, 1150, 1250 and 1400, which are based on the distance between the plates at the entrance (*d*=10mm), the mean flow velocity and the properties of water at 60oC. In addition to isothermal flow, heat transfer simulations are carried out for the same Reynolds numbers, where hot water (60oC) is cooled in contact with a constant-temperature wall (20oC). The latter case is realized in condensers and evaporators. Additionally, it is assumed that heat is transferred only through the corrugated

plate, while the rest of the walls are considered adiabatic.

Fig. 9. Simplified model and detail of the corrugated plate.

Fig. 10. CFD model.

data and the proposed correlation. Similar to the correlation of the Nusselt number, the correlation of the friction factor includes the equivalent Reynolds number and the geometric parameters. Regardless of the BPHE types and refrigerants, most of the experimental data are within 15 % of the correlation proposed in this paper; the r.m.s. deviation for Eq. (23) is 10 %.

Fig. 8. Comparison of the correlations with the experimental data.

#### **5. Study of a simplified geometry**

In an effort to simulate the flow configuration, a **simple** channel was designed and constructed in order to conduct experiments and obtain formation on the flow pattern prevailing inside the furrows of the conduit. The flow configuration, apart from affecting the local momentum and heat transfer rates of a plate heat exchanger, suggests the appropriate flow model for the CFD simulation. A module of a plate heat exchanger is a single pass of the exchanger, consisting of only two plates. The simple channel examined is a single pass made of Plexiglas (**Figure 9**). It is formed by only **one** corrugated plate comprised of fourteen equal sized and uniformly spaced corrugations as well as a flat plate and it is used for pressure drop measurements and flow visualization. Details of the plate geometry are presented in **Table 2**. This model was chosen in an attempt to simplify the complexity of the

data and the proposed correlation. Similar to the correlation of the Nusselt number, the correlation of the friction factor includes the equivalent Reynolds number and the geometric parameters. Regardless of the BPHE types and refrigerants, most of the experimental data are within 15 % of the correlation proposed in this paper; the r.m.s. deviation for Eq. (23) is

Fig. 8. Comparison of the correlations with the experimental data.

In an effort to simulate the flow configuration, a **simple** channel was designed and constructed in order to conduct experiments and obtain formation on the flow pattern prevailing inside the furrows of the conduit. The flow configuration, apart from affecting the local momentum and heat transfer rates of a plate heat exchanger, suggests the appropriate flow model for the CFD simulation. A module of a plate heat exchanger is a single pass of the exchanger, consisting of only two plates. The simple channel examined is a single pass made of Plexiglas (**Figure 9**). It is formed by only **one** corrugated plate comprised of fourteen equal sized and uniformly spaced corrugations as well as a flat plate and it is used for pressure drop measurements and flow visualization. Details of the plate geometry are presented in **Table 2**. This model was chosen in an attempt to simplify the complexity of the

**5. Study of a simplified geometry** 

10 %.

original plate heat exchanger and to reduce the computational demands. The geometry studied in the CFD simulations (similar to the test section) is shown in **Figure 10**. The Reynolds numbers examined are 400, 900, 1000, 1150, 1250 and 1400, which are based on the distance between the plates at the entrance (*d*=10mm), the mean flow velocity and the properties of water at 60oC. In addition to isothermal flow, heat transfer simulations are carried out for the same Reynolds numbers, where hot water (60oC) is cooled in contact with a constant-temperature wall (20oC). The latter case is realized in condensers and evaporators. Additionally, it is assumed that heat is transferred only through the corrugated plate, while the rest of the walls are considered adiabatic.

Fig. 9. Simplified model and detail of the corrugated plate.

Fig. 10. CFD model.

The Characteristics of Brazed Plate Heat Exchangers with Different Chevron Angles 413

Fig. 11A. Typical flow pattern for the: a) simple channel, CFD results, Re=900.

**Figure 12** shows details of the flow inside a furrow for the simple model, where swirling flow is identified. This secondary flow is capable of bringing new fluid from the main stream close to the walls, augmenting heat transfer rates. Focke & Knibbe[18], who performed visualization experiments in similar geometries, also describe this kind of swirling flow. The values of the *z*-component of shear stress (**Figure13a**) increase with the Reynolds number –as expected–and the maximum value occurs at the crests of the corrugations. It may be argued that, during gas-liquid counter-current flow in such geometries, the shear stress distribution tends to prevent the liquid layer from falling over

Fig. 11B. Flow visualization by Focke & Knibbe[7], Re=125.

A commercial CFD code, namely the *CFX* ® *5.6* code developed by *AEA Technology*, was employed to explore its potential for computing detailed characteristics of this kind of flow. In general, the models used in CFD codes give reasonably good results for single-phase flow systems. The first step in obtaining a solution is the division of the physical domain into a solution mesh, in which the set of equations is discretised.

The grid size used is selected by performing a grid dependence study, since the accuracy of the solution greatly depends on the number and the size of the cells. The resulting mesh was also inspected for inappropriate generated cells (e.g. tetrahedral cells with sharp angles) and fixed, leading to a total number of 870,000 elements. The *SST* model was employed in the calculations for the reasons explained in the previous chapter. The mean velocity of the liquid phase was applied as boundary condition at the channel entrance (i.e. Dirichlet BC on the inlet velocity) and no slip conditions on the channel walls. A constant temperature boundary condition was applied only on the corrugated wall, whereas the rest of the walls are considered adiabatic. Calculations were performed on a *SGI O2* R10000 workstation with a 195MHz processor and 448Mb RAM. The *CFX* ®*5.6* code uses a finite volume method on a non-orthogonal body-fitted multi-block grid. In the present calculations, the *SIMPLEC*  algorithm is used for pressure-velocity coupling and the *QUICK* scheme for discretisation of the momentum equations [31],[32].


Table 2. Simple Channel's plate geometric characteristics.

The results of the present study suggest that fluid flow is mainly directed inside the furrows and follows them (*Figure 11a*). This type of flow behavior is also described by Focke & Knibbe[7], who made visual observations of the flow between two superposed corrugated plates *(Figure 11b*). They confirm that the fluid, after entering a furrow, mostly follows it until it reaches the side wall, where it is reflected and enters the anti-symmetrical furrow of the plate above, a behavior similar to the one predicted by the CFD simulation. It seems that, in both cases, most of the flow passes through the furrows, where enhanced heat transfer characteristics are expected.

A commercial CFD code, namely the *CFX* ® *5.6* code developed by *AEA Technology*, was employed to explore its potential for computing detailed characteristics of this kind of flow. In general, the models used in CFD codes give reasonably good results for single-phase flow systems. The first step in obtaining a solution is the division of the physical domain into a

The grid size used is selected by performing a grid dependence study, since the accuracy of the solution greatly depends on the number and the size of the cells. The resulting mesh was also inspected for inappropriate generated cells (e.g. tetrahedral cells with sharp angles) and fixed, leading to a total number of 870,000 elements. The *SST* model was employed in the calculations for the reasons explained in the previous chapter. The mean velocity of the liquid phase was applied as boundary condition at the channel entrance (i.e. Dirichlet BC on the inlet velocity) and no slip conditions on the channel walls. A constant temperature boundary condition was applied only on the corrugated wall, whereas the rest of the walls are considered adiabatic. Calculations were performed on a *SGI O2* R10000 workstation with a 195MHz processor and 448Mb RAM. The *CFX* ®*5.6* code uses a finite volume method on a non-orthogonal body-fitted multi-block grid. In the present calculations, the *SIMPLEC*  algorithm is used for pressure-velocity coupling and the *QUICK* scheme for discretisation of

Plate Length 0.200 m Plate width 0.110 m Maximum spacing between plates 0.010 m

Number of corrugations 14 Corrugation angle 45 o

Table 2. Simple Channel's plate geometric characteristics.

Corrugation pitch 0.005 m Corrugation width 0.014 m Plate length before and after corrugations 0.050 m

Heat transfer area 2.7 x 10 -2 m2

The results of the present study suggest that fluid flow is mainly directed inside the furrows and follows them (*Figure 11a*). This type of flow behavior is also described by Focke & Knibbe[7], who made visual observations of the flow between two superposed corrugated plates *(Figure 11b*). They confirm that the fluid, after entering a furrow, mostly follows it until it reaches the side wall, where it is reflected and enters the anti-symmetrical furrow of the plate above, a behavior similar to the one predicted by the CFD simulation. It seems that, in both cases, most of the flow passes through the furrows, where enhanced heat transfer

solution mesh, in which the set of equations is discretised.

the momentum equations [31],[32].

characteristics are expected.

Fig. 11A. Typical flow pattern for the: a) simple channel, CFD results, Re=900.

Fig. 11B. Flow visualization by Focke & Knibbe[7], Re=125.

**Figure 12** shows details of the flow inside a furrow for the simple model, where swirling flow is identified. This secondary flow is capable of bringing new fluid from the main stream close to the walls, augmenting heat transfer rates. Focke & Knibbe[18], who performed visualization experiments in similar geometries, also describe this kind of swirling flow. The values of the *z*-component of shear stress (**Figure13a**) increase with the Reynolds number –as expected–and the maximum value occurs at the crests of the corrugations. It may be argued that, during gas-liquid counter-current flow in such geometries, the shear stress distribution tends to prevent the liquid layer from falling over

The Characteristics of Brazed Plate Heat Exchangers with Different Chevron Angles 415

the experimental friction factors, obtained from the Plexiglas test section of **Figure 9**, as well as the CFD predictions for the simple geometry studied, as a function of the Reynolds

Fig. 13. Typical results of the CFD simulation for Re=900; distributions of: (a) *z*-shear stress

Where *m* and *n* constants with values 0.27 and 0.14 respectively. Heavner et al.[14] proposed a similar empirical correlation based on their experimental results on a single pass of a plate heat exchanger with 45º corrugation angle, but with two corrugated plates. In spite of the differences in geometry, it appears that the present results are in good agreement with the experimental data of Heavner et al.[14] (0.687 and 0.141 for the variables *m* and *n*,

component, (b) local Nusselt number.

respectively).

f = m Re –n (32)

number. It appears that the experimental values follow a power law of the form:

the crest of the corrugations and to keep it inside the furrows. The visual observations of Paras et al.[14] seem to confirm the above behavior. The heat flux through the wall of the corrugated plate was calculated by the CFD code. In addition, the local Nusselt number was calculated (by a user-Fortran subroutine) using the expression:

Fig. 12. Swirling flow inside a furrow; Re=900.

$$\mathbf{Nu\_{x} = qd} \;/\; (\mathbf{T\_{b^{-}}T\_{w})} \; \mathbf{k} \tag{31}$$

Where *q'* is the local wall heat flux, *d* the distance between the plates at the entrance, *Τw* the wall temperature, *Tb* the local fluid temperature and *k* the thermal conductivity of the fluid. In addition to the local Nusselt number, mean Nusselt numbers were calculated as follows:

\* A *mean Nu* calculated by numerical integration of the local *Nu* over the *corrugated* area **only**, and

\* An *overall* average *Nu* calculated using the total wall heat flux through the *whole* plate and the fluid temperatures at the channel entrance/exit.

The comparison of the values of the above Nusselt numbers shows that they do not differ more that 1%; therefore, the smooth part of the corrugated plate does not seem to influence the overall heat transfer. **Figure 13b** shows a typical local Nusselt number distribution over the corrugated wall for Re=900. All the Reynolds numbers studied exhibit similar distributions.

It is noticeable that local Nusselt numbers attain their maximum value at the top of the corrugations. This confirms the strong effect of the corrugations, not only on the flow distribution, but also on the heat transfer rate. To the best of author's knowledge, experimental values of heat transfer and pressure drop are very limited in the open literature for the corrugated plate geometry, since these data are proprietary. Therefore, the data of Vlasogiannis et al.[16] were used to validate the simulation results. These data concern heat transfer coefficients measurements of both single (Re<1200) and two-phase flow in a plate heat exchanger with corrugated walls and a corrugation inclination angle of 60o. Heavner et al.[14] proposed a theoretical approach, supported by experimental data, to predict heat transfer coefficients of chevron-type plate heat exchangers. **Figure 14** presents

the crest of the corrugations and to keep it inside the furrows. The visual observations of Paras et al.[14] seem to confirm the above behavior. The heat flux through the wall of the corrugated plate was calculated by the CFD code. In addition, the local Nusselt number was

 Nux = qd / (Tb- Tw) k (31) Where *q'* is the local wall heat flux, *d* the distance between the plates at the entrance, *Τw* the wall temperature, *Tb* the local fluid temperature and *k* the thermal conductivity of the fluid. In addition to the local Nusselt number, mean Nusselt numbers were calculated as follows: \* A *mean Nu* calculated by numerical integration of the local *Nu* over the *corrugated* area

\* An *overall* average *Nu* calculated using the total wall heat flux through the *whole* plate and

The comparison of the values of the above Nusselt numbers shows that they do not differ more that 1%; therefore, the smooth part of the corrugated plate does not seem to influence the overall heat transfer. **Figure 13b** shows a typical local Nusselt number distribution over the corrugated wall for Re=900. All the Reynolds numbers studied exhibit similar

It is noticeable that local Nusselt numbers attain their maximum value at the top of the corrugations. This confirms the strong effect of the corrugations, not only on the flow distribution, but also on the heat transfer rate. To the best of author's knowledge, experimental values of heat transfer and pressure drop are very limited in the open literature for the corrugated plate geometry, since these data are proprietary. Therefore, the data of Vlasogiannis et al.[16] were used to validate the simulation results. These data concern heat transfer coefficients measurements of both single (Re<1200) and two-phase flow in a plate heat exchanger with corrugated walls and a corrugation inclination angle of 60o. Heavner et al.[14] proposed a theoretical approach, supported by experimental data, to predict heat transfer coefficients of chevron-type plate heat exchangers. **Figure 14** presents

calculated (by a user-Fortran subroutine) using the expression:

Fig. 12. Swirling flow inside a furrow; Re=900.

the fluid temperatures at the channel entrance/exit.

**only**, and

distributions.

the experimental friction factors, obtained from the Plexiglas test section of **Figure 9**, as well as the CFD predictions for the simple geometry studied, as a function of the Reynolds number. It appears that the experimental values follow a power law of the form:

Fig. 13. Typical results of the CFD simulation for Re=900; distributions of: (a) *z*-shear stress component, (b) local Nusselt number.

Where *m* and *n* constants with values 0.27 and 0.14 respectively. Heavner et al.[14] proposed a similar empirical correlation based on their experimental results on a single pass of a plate heat exchanger with 45º corrugation angle, but with two corrugated plates. In spite of the differences in geometry, it appears that the present results are in good agreement with the experimental data of Heavner et al.[14] (0.687 and 0.141 for the variables *m* and *n*, respectively).

The Characteristics of Brazed Plate Heat Exchangers with Different Chevron Angles 417

Fig. 15. Comparison of *j*-Colburn factor predictions (CFD) with experimental data.

Plate length 0.430 m Plate width 0.100 m Mean spacing between plates 0.024 m Corrugation angles 60 o Corrugation area length 0.352 m

Table 4. Geometric characteristics of the model with two corrugated plates.

The results for the simplified geometry confirm the validity of the CFD code and strongly encourage the simulation of a module (pass) consisting of two corrugated plates of a compact heat exchanger (**Figure16a**). In order to quantitatively evaluate the results of this simulation, the experimental setup of Vlasogiannis et al.[16] was used as the design model (**Figure 16b**). Due to the increased computational demands, an AMD AthlonXP 1.7GHz workstation with 1GB RAM was used. The geometric characteristics of the new model are

Preliminary results of the present study, which is still in progress, are shown in **Figure 17**. It is obvious that the herringbone design promotes a symmetric flow pattern (**Figure 16b**). Focusing on the left half of the channel (**Figure 17a**), a close-up of the flow streamlines (**Figure17b**) reveals a "*peacock-tail*" pattern as the liquid flows inside the furrows and over the corrugations. The same flow pattern, which is characteristic for this type of geometry, has also been observed by Paras et al.[14] in similar cross-corrugated geometries (**Figure17c**), where "dry areas" of ellipsoidal shape are formed around the points where the

**6. Study of a heat exchanger channel** 

presented in **Table 4.** 

It must be noted that Focke et al.[15] , who also measured heat transfer coefficients in a corrugated plate heat exchanger having a partition of celluloid sheet between the two plates, reported that the overall heat transfer rate is the 65% of the corresponding value without the partition. **Figure 15** shows that the mean *j-*Colburn factor values calculated using the *overall*  Nusselt number are practically equal to the 65% of the values measured by Vlasogiannis et al. This holds true for all Reynolds numbers except the smallest one (Re=400). In the latter case the Nusselt number is greatly overpredicted by the CFD code. This is not unexpected, since the *two-equation turbulence* model is not capable to predict correctly the heat transfer characteristics for such low Reynolds number.The CFD results reveal that the corrugations enhance the heat transfer coefficient, whereas the pressure losses due to the augmentation of friction factor *f* are increased **(Table 3)**, compared to a smooth-wall plate heat exchanger. Additionally, comparison of the normalized values of Nusselt number and the friction factor, with respect to the corresponding values for the smooth plate (*fsm*, *Nusm*), indicates that as the Reynolds number increases, heat transfer enhancement is slightly reduced, while the friction factor ratio, *f/f* , is increased. This is typical for plate heat exchangers with corrugations [16].


Table 3. Experimental values, calculated Nusselt numbers and normalised values of *N*u and *f*

Fig. 14. Comparison of friction factor predictions (CFD) with experimental data.

Fig. 15. Comparison of *j*-Colburn factor predictions (CFD) with experimental data.
