A Modified Correlative Model for Condensation Heat Transfer in Horizontal Enhanced Tubes with R32 and R410A Refrigerants

Abstract

An experimental study was performed that compared tube side condensation heat transfer characteristics of enhanced tubes (hydrophobic surface tubes (HYD), herringbone micro fin tube (HB), and a composite hydrophobic/herringbone (micro fin) tube (HYD/HB)) to the performance of a smooth tube (ST). The condensation heat transfer coefficient (HTC) was calculated from data that were recorded for smooth and enhanced tubes that had an outer diameter (OD) of 12.7 mm. Data were collected (as a function of mass flow rate) using a couple of refrigerants (R410A and R32), for saturated temperatures of 35 °C and 45 °C, with vapor qualities that ranged from 0.8 to 0.2. Several previously reported smooth tube HTC models were used to calculate values that could be compared to experimentally obtained HTC values. The correlation model that demonstrated the best accuracy (for the conditions considered) was then modified for use with the enhanced tubes from this study. Results from the modified correlation show differences with experimental values that ranged from −10% to +17%; the new modified correlation demonstrates high prediction accuracy. An accurate correlation allows the evaluation of enhanced heat transfer tubes for use in high-efficiency heat exchanger systems. The development of this new model is significant in the study of enhanced heat transfer.

1. Introduction

Heat exchangers have applications in many industries (i.e., chemical, energy, food, pharmaceuticals, aviation, transportation, refrigeration, HVAC, etc.). Optimized heat exchanger designs reduce the carbon footprint, improve energy efficiency, reduce production costs, extend equipment lifespan, improve product quality, lower operating costs, produce more energy, reduce the footprint of the unit, etc. Therefore, studies of newly developed enhanced heat transfer tubes are important in order to be able to design high efficiency heat transfer systems.

Heat transfer performance of a heat exchanger tube is influenced by several parameters (i.e., geometric shape of the tube, surface enhancement structure of the tube, type of refrigerant, mass flow rate, saturation temperature, vapor quality, etc.). Previous condensation studies have been typically performed on smooth tubes; some studies have evaluated enhanced tubes. Longo et al. [1] performed a comparative study on the condensation heat transfer characteristics of micro fin tubes using refrigerants R410A and R32 tubes with an inner diameter of 4.2 mm. This study investigated the effects of saturation temperature, vapor quality, and mass flow rate on the heat transfer coefficient (HTC) of micro fin tubes. Results indicate that micro fin tubes exhibited the best enhancement (when compared to smooth tubes) for mass flow rates ranging from 150 to 300 kg/m²·s. Additionally, they determined that when using R410A the condensation HTC and pressure drop were greater than when using R32. Ma et al. [2] conducted an experimental study that evaluated the condensation heat transfer performance of smooth tubes, micro-fin tubes, and enhanced three-dimensional (3D) tubes (with an inner diameter of 9.52 mm) using R410A and R32 as the working fluids. Under varying mass flow rates and vapor qualities, the results showed that the condensation heat transfer coefficient (when using R410A) in the micro-fin was 2.0~2.2 times the HTC found in smooth tubes, and for the 3D enhanced tubes, it was 1.4~1.5 times greater, while when using R32 it was 1.5~2.0 times (micro fin) and 1.5~1.6 times (3D tube) the HTC found in smooth tubes. By analyzing the flow pattern, they determined that the enhanced tubes promoted the occurrence of intermittent flow and annular flow and this produces an improvement to the condensation heat transfer coefficient (when compared with a smooth tube).

The emergence of hydrophobic surfaces provides a new direction and research area to consider when evaluating the performance of enhanced heat transfer tubes. Alwazzan et al. [3] studied the condensation heat transfer characteristics of a copper tube composed of alternating sections of hydrophobic and hydrophilic areas (studying tubes with different area ratios). As a result of their experimental evaluation and visual observations, they concluded that the use of alternating surface structures can significantly enhance the condensation heat transfer performance. When surfaces (composed of different width ratios) are compared with hydrophobic (with a uniform stripe width) and hydrophilic surfaces (with uniform stripe width), the heat transfer coefficients (for the surfaces composed of different width ratios) were increased by 480% and 180%, respectively. Additionally, it appears that there is an optimal width ratio that maximizes the enhancement effect. Wan et al. [4] experimentally studied the heat transfer performance of a composite surface enhanced tube with a hydrophobic inner cavity wall and a hydrophilic outer fin surface. They found that the condensation heat transfer coefficient and boiling heat transfer coefficient of the tube with a hydrophobic inner cavity wall and hydrophobic outer fin surface were 3 times and 1.8 times the HTC of a smooth tube, respectively. They go on to conclude that hydrophilic surface enhanced tubes should be preferred for boiling heat transfer, and hydrophobic surface enhanced tubes should be preferred for condensation heat transfer. Additional work in this area is needed.

Scholars have previously studied correlation formulas that are used to determine condensation heat transfer coefficients in tubes; some studies have proposed empirical formulas that can be used in the design and optimization of heat exchangers. Yun et al. [5] proposed a new correlation (based on previous research) for heat transfer coefficients and friction factors. They introduced correction factors (C1 and C2 for use with R134a and R410A) that are used in a comprehensive correlation (within a 25% error range) and had prediction accuracies of 88.1% and 73.2%, respectively. Hosseini et al. [6] collected in-tube condensation heat transfer data (6521 data points) from 40 published works and evaluated eight existing condensation correlations. They developed a new general correlation that can accurately estimate the condensation heat transfer coefficient in both microchannels and conventional channels. Li et al. [7] studied the condensation heat transfer characteristics of R410A in smooth tubes, herringbone micro fin tubes, dimpled tubes, and herringbone-dimpled composite tubes. They found that the condensation heat transfer coefficient and pressure drop increased with the refrigerant mass flow rate and average vapor quality. An improved Nusselt equation was developed for smooth tubes. Additionally, they introduced the mass flux factor (EUR) and the enhanced tube structure factor (Y) that could be used in order to predict the condensation HTC in the enhanced tubes. Shah [8] proposed modified correlation equations for condensation heat transfer in microchannels and conventional channels for use with horizontal or downward flows. Shah’s equations have a wide range of applications, covering 51 types of fluids (including water, low-temperature media, refrigerants, chemicals, etc.) for tubes with diameters ranging from 0.08 to 49.0 mm, with a mass flux range from 1.1 to 1400 kg/m²·s for use with various channel cross-sections (including circular, rectangular, triangular, etc.). Additional conditions considered include (i) single and multiple channels, (ii) annular flow, and (iii) horizontal or vertical downward flow conditions. These modified equations were validated using a database consisting of 8298 data points from 130 sources; the equations had a high prediction accuracy that had an average absolute error of 17.9%.

There are few studies on enhanced tube condensation heat transfer performance correlations that describe the condensation HTC for enhanced tubes. In order to advance the knowledge base for enhanced heat transfer tubes, a modification (for use in enhanced tubes) of an existing smooth tube condensation correlation was undertaken in the present study; the modified correlation will allow enhanced tubes to be used when trying to optimize the design of heat exchangers. This will improve heat transfer efficiency and reduce costs (production and operational). The condensation heat transfer performance of smooth (ST), hydrophobic (HYD), herringbone micro fin (HB), and hydrophobic/herringbone (HYD/HB) tubes was evaluated for various mass flow rates. Several previously reported empirical correlation equations have been assessed using the data from the current study. Finally, one correlation was selected for modification and use. The prediction accuracy of the modified equation was found to be high; this was verified after finding a small deviation between the predicted values from the modified correlation and experimental values.

2. Experimental Apparatus and Test Conditions

2.1. Experimental System

An experimental process was carried out on a high-precision test rig that can use various refrigerants (i.e., R410A, R32, R22, etc.) and can perform single-phase, condensation, and evaporation heat transfer performance tests on various types of heat exchange tubes. The test rig is able to test circular tubes, rectangular channel tubes, internally enhanced tubes, and three-dimensional tubes with outer tube diameters (OD) ranging from 6 mm to 19 mm. Various experimental conditions can be controlled: (i) inlet and outlet vapor qualities (0 to 1); (ii) refrigerant mass flow rate (10 kg/h to 300 kg/h); (iii) boiling conditions ranging from 5 °C to 15 °C; and (iv) condensation conditions ranging from 35 °C to 45 °C. The schematic diagram of the test setup is shown in Figure 1 and comprises a main refrigerant loop with three auxiliary loops.

The refrigerant flows out of the storage tank and enters the preheating section after passing through a digital gear pump and a Coriolis mass flow meter. After being preheated, the refrigerant flows into the test section (the heat transfer tube being evaluated is located here). The refrigerant flows out of the test section and enters the supercooling section. Finally, the refrigerant enters the storage tank to complete the cycle.

The testing section is the most critical part of the experimental system. It consists of a single tube counter-flow heat exchanger (the tube being evaluated is the inner tube of the heat exchanger). The length of the tube heat exchanger can be changed according to the experimental requirements. The inlet and outlet conditions of the heat exchanger are measured with temperature, pressure, and differential pressure sensors. The preheating section consists of the water bath heating system, and functions to control the required test conditions of the refrigerant and the gear pump deliver the fluid to the entrance of the experimental section. The subcooling section cools the refrigerant flowing out of the test section and reduces its temperature and pressure; this brings the refrigerant to a subcooled state and sends it to the storage tank for the next cycle. Temperatures in the test section, preheating section, and subcooling section are all controlled by PID temperature controllers with an accuracy of up to 0.01 °C. The pressure sensor (working temperature ranging from −40 °C to 100 °C) has a range of 0~6 MPa with an accuracy of 0.075% full-scale (FS). The differential pressure sensor is used to measure the pressure difference of the working medium between the inlet and outlet of the test section; it has a range of 50 kPa with an accuracy of 0.075% FS and a working temperature ranging from −40 to 100 °C. Additional experimental details and parameter uncertainties are given in [9].

2.2. Parameters and Operating Conditions

Tubes evaluated include smooth (ST), hydrophobic surface tubes (HYD), a herringbone micro fin tube (HB), and a composite hydrophobic herringbone micro fin tube (HYD/HB). All are 304 L stainless steel with a 12.7 mm OD with a test length of 1.7 m. Two types of herringbone micro fin enhanced tubes were considered, HB and HYD/HB. They have a herringbone pitch of 0.636 mm, a herringbone fin height of 0.052 mm, and a helix angle of 18°. Experimental results show that HB tubes significantly improve condensation heat transfer characteristics. Increasing the fin height increases the inner wall surface area and enhances heat transfer. The fin pitch affects the fluid flow pattern, and the helix angle influences flow behavior and velocity distribution, all contributing to the heat transfer performance. These parameters all affect the heat transfer performance of the tubes and make them suitable parameters to include in the correlation model. Additional tube parameters are given in

Table 1. Geometric parameters of the tubes evaluated.

Parameter	ST Tube	HYD Tube	HB Tube	HB/HYD Tube
Material	Stainless steel	Stainless steel	Stainless steel	Stainless steel
Inner diameter (mm)	11.5	11.5	11.5	11.5
Outer diameter (mm)	12.7	12.7	12.7	12.7
Thickness (mm)	0.61	0.61	0.61	0.61
Length (m)	1.7	1.7	1.7	1.7
Fin height (mm)	-	-	0.052	0.052
Fin pitch (mm)	-	-	0.636	0.636
Helix angle (°)	-	-	18	18
Addendum angle (°)	-	-	161.4	161.4
Contact angle (°)	-	107.35	48.23	53.37

. Condensation experiments of the enhanced tubes were carried out using R410A and R32, with saturation temperatures of 35 °C and 45 °C, respectively.

3. Data Processing and Discussion

3.1. Experimental Determination of the Heat Transfer Coefficient

Data are collected using the data acquisition system; this experimental data can be used to calculate the heat transfer coefficient for each heat transfer tube under different operating conditions. Since the tube in the tube heat exchanger is well insulated, the heat loss of the test section can be neglected. The total heat transfer in the test section can be calculated from the heat transfer of the water in the shell of the heat exchanger, $Q_{w,exp}$.

$$Q_{w,exp}=c_{pl,w,exp}{m}_{w,exp}\left(T_{w,exp,out}-T_{w,exp,in}\right)$$

(1)

where $Q_{w,exp}$, is the heat transfer of the water in the shell, W; $c_{pl,w,exp}$, the specific heat capacity corresponding to the average from the inlet and outlet temperature of the water, J/(kg · K); $m_{w,exp}$, the mass flow rate of the water, kg/s; $T_{w,exp,out}$, the outlet temperature of the water, K; $T_{w,exp,in}$, the outlet temperature of the water, K.

The total heat transfer of the refrigerant, $Q_{ph},$ is composed of two parts: the sensible heat, $Q_{lat}$, and the latent heat of vaporization, $Q_{sens}$.

$$Q_{ph}=Q_{lat}+Q_{sens}=c_{pl,w,ph}{m}_{w,ph}\left(T_{w,ph,in}-T_{w,ph,out}\right)$$

(2)

$$Q_{sens}=c_{pl,ref,ph}{m}_{ref}\left(T_{sat}-T_{ref,ph,in}\right)$$

(3)

$$Q_{lat}=m_{ref}{h}_{lv}{x}_{in}$$

(4)

Based on the thermal balance of the test section, the inlet quality, $x_{in}$, of the refrigerant can be calculated using Equation (5).

$$x_{in}=\frac{Q_{w,exp}-c_{pl,ref,ph}{m}_{ref}\left(T_{sat}-T_{ref,ph,in}\right)}{m_{ref}{h}_{lv}}$$

(5)

$\mathrm{where} T_{sat}$, is the saturation temperature of the refrigerant, K; $h_{lv}$, the latent heat of vaporization of the refrigerant, J/kg;$m_{ref}$, the mass flow rate of the refrigerant, kg/s; and $T_{ref,ph,in}$ is the inlet temperature of the refrigerant, K.

The test section refrigerant outlet vapor quality $x_{out}$ is calculated using Equation (6).

$$x_{out}=x_{in}+\frac{Q_{w,exp}}{m_{ref}{h}_{lv}}$$

(6)

The logarithmic mean temperature difference LMTD of the test section is calculated using:

$$\mathrm{LMT}=\frac{\left(T_{w,exp,in}-T_{ref,exp,out}\right)-\left(T_{w,exp,out}-T_{ref,exp,in}\right)}{\ln \left[\left(T_{w,exp,in}-T_{ref,exp,out}\right)-\left(T_{w,exp,out}-T_{ref,exp,in}\right)\right]}$$

(7)

with $T_{ref,exp,in},T_{ref,exp,out}$ representing the inlet and outlet temperatures of the refrigerant, K; $T_{w,exp,in},T_{w,exp,out}$ representing the inlet and outlet temperatures of water, K.

All of the test tubes are new tubes, so the effect of fouling thermal resistance can be ignored, and the condensation heat transfer coefficient inside the tubes can be calculated using Equation (8).

$$h_i=\frac{1}{A_i\left[\frac{\mathrm{LMTD}}{Q_{w,exp}}-\frac{1}{h_o{A}_o}-\frac{d_o\ln \left(d_o/d_i\right)}{2k{A}_o}\right]}$$

(8)

$\mathrm{where} A_i,A_o$ represents the inner and outer surface areas of the tube, m²; $d_o,d_i$ represents the inner and outer diameters of the tube, mm; k represents the thermal conductivity of the tube wall, W/(m · K); $h_i$ represents the inside heat transfer coefficient on the refrigerant side the tube and $h_o$ the heat transfer coefficient on the water side outside the tube, W/(m²·K).

The heat transfer coefficient of water on the shell side is calculated using the Gnielinski [10] correlation equation:

$$h_o=\frac{\left(f_w/2\right)\left(R{e}_w-1000\right)P{r}_w}{1+12.7{\left(f_w/2\right)}^{1/2}\left(P{r}_w{}^{2/3}-1\right)}{\left(\frac{{\mu }_{bulk}}{{\mu }_w}\right)}^{0.14}\frac{k_w}{d_h}$$

(9)

The fanning friction factor is calculated using the Petukhov [11] correlation equation:

$$f_w={\left(1.58R{e}_w-3.28\right)}^{-2}$$

(10)

3.2. Condensation Heat Transfer Coefficient as a Function of Refrigerant Mass Flux

Figure 2 compares the variation of the condensation heat transfer coefficient with the mass flow rate for the smooth and enhanced tubes.

As can be seen in Figure 2, the condensation heat transfer coefficients of R410A and R32 in the smooth tube increase linearly with the mass flow rate; however, in the three enhanced tubes (HB, HYD, and HYD/HB) the HTC first decreases and then increases. This may be due to the fact that when compared to smooth tubes, enhanced heat transfer is produced in the three enhanced tubes as a result of turbulence and an increase in the heat transfer surface area. Compared to smooth tubes, herringbone tubes have some special protrusions on the inner wall. These structural protrusions disrupt the fluid boundary layer, enhancing fluid disturbance and mixing. Additionally, the extended surface area generated by these protrusions is beneficial for enhanced heat transfer. The enhanced tubes with hydrophobic surfaces create a thin liquid film on the wall, which has lower surface tension. Therefore, when condensing fluid flows through the tubes, the presence of the liquid film makes it easier for the fluid to transition into turbulent flow within the tube. Turbulent flow disrupts the boundary layer and removes the thicker thermal resistance layer, thereby increasing the heat transfer coefficient. At low mass flow rates (below 60 kg·m⁻²s⁻¹), the refrigerant flow velocity is low, and the condensation process inside the tube is mainly the result of surface heat transfer. Turbulent heat transfer may only have a small contribution to the overall heat transfer process, so the heat transfer coefficient is high. As the mass flow rate increases, the refrigerant flow velocity increases; the heat transfer process gradually transitions from surface heat transfer to turbulent heat transfer. Turbulence suppresses the heat transfer process, resulting in a decrease in the heat transfer coefficient. As the flow rate continues to increase, the turbulence intensity reaches its peak and then gradually decreases. The degree of mixing between the refrigerant and the heat transfer surface gradually increases and, therefore, the heat transfer coefficient also gradually increases. This indicates that the three enhanced tubes are more suitable for condensation heat transfer under low mass flow rate (below 60 kg·m⁻²s⁻¹) and high mass flow rate conditions (above 120 kg·m⁻²s⁻¹). Additionally, the heat transfer coefficient is slightly lower for medium mass flow rates (60~120 kg·m⁻²s⁻¹) and condensation heat transfer designs in this range should be avoided.

The condensation heat transfer coefficient of refrigerant R32 is larger than that of R410A in all the tubes (under identical conditions). This can be explained from the physical properties of the two refrigerants; R32 has a smaller molecular weight and has a lower density and higher thermal conductivity. This means that in the condensation process inside the tube (when using R32) can release heat quicker and transfer it to the surface of the tube. Additionally, R410A has a higher density and viscosity; this can lower its flow rate and flow state inside the tube. This will reduce the condensation heat transfer coefficient inside the tube.

When two refrigerants are condensed under different conditions, the heat transfer coefficients of the three enhanced tubes are all enhanced to varying degrees. The tube with the largest enhancement ratio (enhanced tube HTC/smooth tube HTC) is the HB tube (1.55), followed by the HYD tube (1.4) and the HYD/HB tube (combines the hydrophobic surface and the herringbone microfin) has the lowest enhancement ratio (1.37). Both hydrophobic surfaces and herringbone microfins can enhance the condensation heat transfer inside the tube because they can increase the apparent contact angle of the surface and also reduce the contact area of the liquid condensate on the surface. This reduces the liquid film resistance and heat resistance of the heat transfer surface. Specifically, the hydrophobic surface can reduce surface tension and cause the condensate droplets to spontaneously detach from the surface. This reduces the thickness of the surface liquid film and increases the contact angle between the droplets and the surface. This improves the heat transfer coefficient. Herringbone microfins increase the heat transfer surface area and reduce the thickness of the liquid film at the surface. This reduces the heat resistance of the heat transfer surface.

However, the combination of the hydrophobic surface and the herringbone microfin results in a decrease in the condensation heat transfer coefficient. This may be because the combination increases the evaporation of the surface liquid film, causing a consumption of heat that lowers the condensation heat transfer coefficient. At the same time, the condensate droplets on the hydrophobic surface are blocked by the microfins and the droplets cannot completely detach from the surface; therefore, the diffusion and evaporation of the liquid film between the microfins consume more heat. This combination also increases the surface heat resistance and reduces the heat transfer coefficient.

3.3. Empirical Correlation for Smooth Tube Condensation

Table 2. Empirical correlation for condensation heat transfer coefficient of smooth tubes.

Authors	Equations	Experimental Conditions
Shah et al. [12] (1979)	$h_{tp}=h_L\left[{\left(1-x\right)}^{0.8}+\frac{3.8x^{0.76}{\left(1-x\right)}^{0.04}}{{\mathrm{P}}_{\mathrm{r}}^{0.38}}\right]$ $h_L=0.023{\mathrm{Re}}_L{}^{0.8}{\mathrm{Pr}}_l{}^{0.4}\frac{k_l}{D}$ ${\mathrm{Re}}_{\mathrm{l}}=\frac{GD}{{\mu }_l},{\mathrm{Pr}}_l=\frac{c_{pl}{\mu }_l}{k_l}, {\mathrm{P}}_{\mathrm{r}}=\frac{P}{P_c}$	Fluid: water, R11, R22, alcohol, etc. G = 10.8~210.6 kg m−2s−1 Tsat = 21~31 °C do = 7~40 mm
Cavallini et al. [13] (2006)	${\mathrm{J}}_{\mathrm{G}}^{\mathrm{T}}={\left\{{\left[\begin{array}{c}\frac{7.5}{4.3{\mathrm{X}}_{\mathrm{tt}}{}^{1.111}+1}\end{array}\right]}^{-3}+{\mathrm{C}}_{\mathrm{T}}^{-3}\right\}}^{-\frac{1}{3}}{C}_T=\{\begin{array}{cc}1.6& \mathrm{Hydrocarbon}\\ 2.6& \mathrm{Other}\mathrm{refrigerants}\end{array}$ $J_G=\frac{xG}{{\left[g{d}_h{\rho }_v\left({\rho }_l-{\rho }_v\right)\right]}^{\frac{1}{2}}}$ ${\mathrm{J}}_{\mathrm{G}}>{\mathrm{J}}_{\mathrm{G}}^{\mathrm{T}}:{\mathrm{h}}_{\mathrm{a}}={\mathrm{h}}_{\mathrm{lo}}[1+1.128{\mathrm{x}}^{0.8170}{(\frac{{\mathsf{\rho }}_l}{{\mathsf{\rho }}_v})}^{0.3685}{(\frac{{\mathsf{\mu }}_l}{{\mathsf{\mu }}_v})}^{0.2363}\times \left(1-\frac{{\mathsf{\mu }}_v}{{\mathsf{\mu }}_l}{)}^{2.44}{\mathrm{Pr}}_{\mathrm{l}}^{-0.1}\right]$ ${\mathrm{J}}_{\mathrm{G}}\le {\mathrm{J}}_{\mathrm{G}}^{\mathrm{T}}:{\mathrm{h}}_{\mathrm{d}}=\left[{\mathrm{h}}_{\mathrm{a}}{\left(\frac{{\mathrm{J}}_{\mathrm{c}}^{\mathrm{T}}}{{\mathrm{J}}_{\mathrm{G}}}\right)}^{0.8}-{\mathrm{h}}_{\mathrm{start}}\right]\left(\frac{{\mathrm{J}}_{\mathrm{c}}}{{\mathrm{J}}_{\mathrm{G}}^{\mathrm{T}}}\right)+{\mathrm{h}}_{\mathrm{start}},{\mathrm{h}}_{\mathrm{lo}}=\frac{0.023{\mathrm{Re}}_{\mathrm{lo}}^{0.8}P{r}_L{}^{0.4}{\mathsf{\lambda }}_{\mathrm{l}}}{\mathrm{D}}$ ${\mathrm{h}}_{\mathrm{stra}}=0.725{\left[1+0.74{\left(\frac{1-\mathrm{x}}{\mathrm{x}}\right)}^{0.3321}\right]}^{-1}\times {\left[\frac{{\mathsf{\lambda }}_{\mathrm{l}}^3{\mathsf{\rho }}_{\mathrm{l}}\left({\mathsf{\rho }}_{\mathrm{l}}-{\mathsf{\rho }}_v\right){\mathrm{gh}}_{\lg }}{{\mathsf{\mu }}_L\mathrm{D}△\mathrm{T}}\right]}^{0.25}+\left(1-{\mathrm{x}}^{0.087}\right){\mathrm{h}}_{\mathrm{lo}}$	Fluid: R410A, R32, R22, etc. G = 18~2240kg m−2s−1 Tsat-Twall = 0.6~28.7 °C Tsat = −15~302 °C do = 3.1~17mm
Cavallini and Zecchin [14] (1974)	$h_{lp}=0.05\mathrm{R}{e}_{eq}^{\mathrm{o}\mathrm{s}}{\mathrm{Pr}}_i^{\mathrm{o}.33}\frac{k_l}{d_i}$ ${\mathrm{Re}}_{\mathrm{eq}}={\mathrm{Re}}_{\mathrm{v}}\left(\frac{{\mu }_{\mathrm{v}}}{{\mu }_{l_v}}\right){\left(\frac{{\rho }_{\mathrm{l}}}{{\rho }_{\mathrm{v}}}\right)}^{0.5}+{\mathrm{Re}}_l$ ${\mathrm{Re}}_l=\frac{G\left(1-x\right)d_i}{{\mu }_v}$	Fluid: R22, etc. Re ≥ 1.2 × 103 0.1 ≤ x ≤ 0.9
Bohdal et al. [15] (2011)	$h=25.084R{e}_l^{0.258}P{r}_l^{-0.495}{p}_r^{-0.288}{(\frac{x}{1-x})}^{0.266}\frac{k_l}{D}$	Fluid: R134a, R404A G = 64~902 kg m−2s−1 do = 0.31~3.30 mm Tsat = 20~40 °C
Vu et al. [16] (2015)	$\mathrm{h}=0.023{\mathrm{Re}}_{l0}^{0.8}P{\mathrm{r}}_l^{0.4}\frac{{\lambda }_l}{d_i}\left[{\left(1-x\right)}^{0.8}+\frac{3.8}{P{\mathrm{r}}^{0.52}}{\left(\frac{x}{1-x}\right)}^{0.201}\right]$	Fluid: R410A G = 200~320 kg m−2s−1 do = 6.61~9.2 mm Tsat = 48 °C

lists several previously reported empirical correlations that model the condensation heat transfer coefficient for smooth tubes. Figure 3 compares the condensation heat transfer coefficient (based upon experimental data) in smooth tubes and the predicted results using five empirical models. The data points were collected under experimental conditions obtained using refrigerants R410A and R32 for saturated temperatures of 35 °C and 45 °C and a vapor quality ranging from 0.8 to 0.2.

As shown in Figure 3, the majority of the data points fall in an approximate error range of ±40%; therefore, the empirical models provide a reasonable prediction of results. Data points with large errors appear for lower experimental conditions. In this range the Cavallini et al. [13] and Shah [12] relations significantly underestimated the heat transfer coefficient. At those conditions, the deviation of some data points is more than −40%. Predicted values, when using the correlation of Bohdal et al. [15] for R32, showed a good linear relationship (closer to the experimental values) for the experimental values at conditions of both 35 °C and 45 °C. Predicted values when using R410A were lower than the experimental values. Here, the overall predicted values are relatively accurate (typical deviation ranging from −20% to −40%). Values predicted using the Cavallini and Zecchin [14] relation showed a large variation trend with increasing HTC. Predicted values were lower than experimental values in the low HTC region (maximum deviation of −40%). Predicted values were higher in the high heat transfer coefficient region (maximum deviation being approximately +20%).

Figure 3. Comparison of experimental condensation heat transfer coefficient values in ST tubes with values obtained using various empirical models [12,13,14,15,16].

Figure 3. Comparison of experimental condensation heat transfer coefficient values in ST tubes with values obtained using various empirical models [12,13,14,15,16].

3.4. Development of New HTC Correlations for Enhanced Tubes

Cavallini et al. [13] developed a prediction model using 5648 data points from eighteen references that covered a wide range of operating conditions. They also considered the influence of different flow patterns on the convective heat transfer coefficient inside the tube. Since the prediction accuracy for convective condensation heat transfer inside the tube was high, this relation has been widely recognized.

Conditions (refrigerants used (R410A and R32), saturated temperatures, vapor qualities, and tube diameters) considered in the current experiment were within the range of the Cavallini et al. model. These facts made the model developed by [13] the correlation that could be modified for use with the enhanced tubes from this study (HYD, HB, and HYD/HB tubes).

$${\mathrm{J}}_{\mathrm{G}}^{\mathrm{T}}={\left\{{\left[\begin{array}{c}\frac{7.5}{4.3{\mathrm{X}}_{\mathrm{tt}}{}^{1.111}+1}\end{array}\right]}^{-3}+{\mathrm{C}}_{\mathrm{T}}^{-3}\right\}}^{-\frac{1}{3}}{C}_T=\{\begin{array}{cc}1.6& \mathrm{Hydrocarbon}\\ 2.6& \mathrm{Other}\mathrm{refrigerants}\end{array}$$

(11)

$$J_G=\frac{xG}{{\left[g{d}_h{\rho }_v\left({\rho }_l-{\rho }_v\right)\right]}^{\frac{1}{2}}}$$

(12)

$${\mathrm{J}}_{\mathrm{G}}>{\mathrm{J}}_{\mathrm{G}}^{\mathrm{T}}:{\mathrm{h}}_{\mathrm{a}}={\mathrm{h}}_{\mathrm{lo}}[1+1.128{\mathrm{x}}^{0.8170}{(\frac{{\mathsf{\rho }}_l}{{\mathsf{\rho }}_{\mathrm{v}}})}^{0.3685}{(\frac{{\mathsf{\mu }}_l}{{\mathsf{\mu }}_v})}^{0.2363}\times (1-\frac{{\mathsf{\mu }}_v}{{\mathsf{\mu }}_l}{)}^{2.44}{\mathrm{Pr}}_{\mathrm{l}}^{-0.1}]$$

(13)

$${\mathrm{J}}_{\mathrm{G}}\le {\mathrm{J}}_{\mathrm{G}}^{\mathrm{T}}:{\mathrm{h}}_{\mathrm{d}}=\left[{\mathrm{h}}_{\mathrm{a}}{\left(\frac{{\mathrm{J}}_{\mathrm{c}}^{\mathrm{T}}}{{\mathrm{J}}_{\mathrm{G}}}\right)}^{0.8}-{\mathrm{h}}_{\mathrm{start}}\right]\left(\frac{{\mathrm{J}}_{\mathrm{c}}}{{\mathrm{J}}_{\mathrm{G}}^{\mathrm{T}}}\right)+{\mathrm{h}}_{\mathrm{start}},$$

(14)

$${\mathrm{h}}_{\mathrm{stra}}=0.725{\left[1+0.74{\left(\frac{1-\mathrm{x}}{\mathrm{x}}\right)}^{0.3321}\right]}^{-1}\times {\left[\frac{{\mathsf{\lambda }}_{\mathrm{l}}^3{\mathsf{\rho }}_{\mathrm{l}}\left({\mathsf{\rho }}_{\mathrm{l}}-{\mathsf{\rho }}_{\mathrm{v}}\right){\mathrm{gh}}_{\lg }}{{\mathsf{\mu }}_L\mathrm{D}△\mathrm{T}}\right]}^{0.25}+\left(1-{\mathrm{x}}^{0.087}\right)E{\mathrm{h}}_{\mathrm{lo}}$$

(15)

$${\mathrm{h}}_{\mathrm{lo}}=\frac{0.023{\mathrm{Re}}_{\mathrm{lo}}^{0.8}P{r}_L{}^{0.4}{\mathsf{\lambda }}_{\mathrm{l}}}{\mathrm{D}}$$

(16)

There were differences between the predicted values (using the unmodified Cavallini model) and experimental HTC values for the conditions considered here. In order to account for the enhanced tubes used in this study, an enhancement factor E (as shown in Equations (17) and (18)) is introduced to correct the condensation heat transfer coefficient calculated using the Cavallini et al. [13] correlation. The enhancement factor E includes parameters to characterize different tube features (i.e., contact angle α and the helix angle β), as well as additional coefficients (B1 and B2) that were introduced in order to make the Cavallini et al. [13] formula more accurate when using enhanced tubes. The specific parameters of the enhanced tubes used in this study (HYD, HB, and HYD/HB tubes) are listed in Table 1.

$$E={\left[{\left(B_1{e}^{cos\alpha }\right)}^2+\left(\frac{B_2{f}_h{f}_p{e}^{cos\alpha }}{d_{i}L{e}^{cos\beta }}\right)\right]}^{\frac{1}{2}}$$

(17)

$$B_1=\left\{\begin{array}{c}1.76, \mathrm{H}\mathrm{Y}\mathrm{D}\\ 0, \mathrm{H}\mathrm{B}\\ 0.602, \mathrm{H}\mathrm{Y}\mathrm{D}/\mathrm{H}\mathrm{B}\end{array}\right.,B_2=\left\{\begin{array}{c} 0, \mathrm{H}\mathrm{Y}\mathrm{D}\\ 0.93, \mathrm{H}\mathrm{B}\\ 0.1, \mathrm{H}\mathrm{Y}\mathrm{D}/\mathrm{H}\mathrm{B}\end{array}\right.$$

(18)

where as $f_h$, $f_p$, $\alpha$, $\beta$, and $d_i,L$, respectively, represent the fin height, fin pitch, contact angle, helix angle, inner diameter, and length of the tubes. The detailed parameters are listed in Table 1 and include the following: (i) when applied to HYD tubes, the values of B1 and B2 for use in Equation (17) are 1.76 and 0, respectively, (ii) for HB tubes, the values of B1 and B2 for use in Equation (17) are 0 and 0.93, respectively, and (iii) when applied to HYD/HB tubes, the values of B1 and B2 for use in Equation (17) are 0.602 and 0.1, respectively.

A comparison of differences between predicted and experimental HTC values of the enhanced (HYD, HB, and HYD/HB) tubes is shown in Figure 4, Figure 5 and Figure 6. Good results are obtained from the modified Cavallini et al. [13] formula. Deviations are within (i) −10%~+12% for the HYD tube (see Figure 4); (ii) −15%~+17% for the HB tube (see Figure 5); and (iii) −15%~+14% for the HYD/HB tube (see Figure 6). Predicted deviations for all the enhanced tubes are within ±17%. This indicates good prediction accuracy. This modified Cavallini et al. [13] formula has the best prediction accuracy when predicting the condensation of R32 in the HB and HYD/HB tubes. For these tubes, the predicted values are close to the experimental values. When using the modified condensation equation for use with R410A, the predicted values (for the three enhanced tubes in the low heat transfer coefficient region) are relatively close to the experimental values. As the HTC increases, the deviation between the predicted and experimental value increases; however, the error does not exceed +17% and this is still in the acceptable range.

The evaluation of correlation equations typically uses statistical parameters such as the mean absolute deviation (MAD) as a measure of how well the correlation performs (see Equation (19)). This parameter measures the prediction accuracy of the correlation equation. It is the measurement of the average absolute difference between actual observed values and the predicted values. An additional parameter, mean relative deviation (MRD), can also be used in order to determine whether the predictive correlation is biased high or low (see Equation (20)). This correlation equation evaluation index measures the average relative deviation between predicted values and the actual data. The use of these two indicators can effectively evaluate the predictive ability of the correlation and will determine whether it is applicable to specific operating conditions and applications.

$$MAD=\frac{1}{N}{\displaystyle \sum }_{i=1}^N\left|\frac{h{\left(i\right)}_{pred}-h{\left(i\right)}_{exp}}{h{\left(i\right)}_{exp}}\right|$$

(19)

$$MRD=\frac{1}{N}{\displaystyle \sum }_{i=1}^N\frac{h{\left(i\right)}_{pred}-h{\left(i\right)}_{exp}}{h{\left(i\right)}_{exp}}$$

(20)

The calculated MAD and MRD parameters for the three enhanced tubes are shown in

Table 3. MAD and MRD values of the enhanced tubes (HYD, HB, HYD/HB) considered in this study.

	HYD	HB	HYD/HB
MAD	4.50%	5.76%	4.18%
MRD	2.33%	0.12%	1.49%

. For all of the tubes, the MAD of the experimental data points is less than 6% and the MRD is less than 2.4%. This indicates that the modified Cavallini et al. [13] correlation has high prediction accuracy. Values of MAD for the three enhanced tubes are less than 6%, with the maximum MAD value (5.76%) associated with the HB tube and the minimum value (4.18%) coming from the HYD/HB tube. The MRDs of the three enhanced tubes are all greater than zero, indicating that the predicted values of the modified correlation will be slightly higher than the experimental values. The maximum MRD value comes from the HYD tube (2.33%) and the minimum value comes from the HB tube (0.12%). When considering the MAD parameter, the modified equation produces the best results for the HYD/HB tube; however, if you consider the MRD parameter, the modified formula produces the best results for the HB and HYD/HB tubes.

4. Conclusions

The heat transfer coefficient was measured experimentally for smooth (ST), hydrophobic (HYD), herringbone micro fin (HB), and hydrophobic/herringbone (HYD/HB) tubes for various mass flow rates. Several empirical correlation equations were evaluated using the experimental data points and the Cavallini et al. [13] correlation was modified for use with the enhanced tubes. Predicted values were compared with the experimental values. It was found that the deviation between the predicted values and the experimental values was small. This indicates that the prediction accuracy was high.

• Condensation heat transfer coefficients (when using R410A and R32) were measured experimentally for smooth and enhanced tubes. For the experimental range considered, the condensation heat transfer coefficient of the smooth tube increased linearly with the increasing flow rate; as the flow rates increased the heat transfer coefficient increased (with a larger slope). It was found that the condensation heat transfer coefficients (for enhanced tubes), when using either refrigerant, initially decreased and then increased with the increasing refrigerant flow rate. For flow rates ranging from 60 to 120 kg·m⁻²s⁻¹, the heat transfer coefficients were low. Use of these enhanced tubes in the mid-range of flow should be avoided.
• For the same refrigerant flow rate, the condensation heat transfer coefficient when using R32 was significantly higher than when using R410A. For the same conditions, the condensation heat transfer coefficient of R32 was approximately 1.03 to 1.48 times the HTC when using R410A.
• Five empirical correlation models were compared for their prediction accuracy in smooth tubes. With the exception of a few data points, the errors of most of the models were within ±40%. Among them, the correlation models of Cavallini and Bohal had better prediction accuracy (differences within −40% to +20%). The correlation model of Cavallini et al. [13] was modified for use with HYD, HB, and HYD/HB tubes. The fitted errors were within −10% to +17%, indicating a high prediction accuracy for the modified correlation.
• The Cavallini et al. [13] correlation was modified and the modified correlation had a mean absolute deviation (MAD) of <6% and the mean relative deviation (MRD) was <2.4%. The maximum MAD value was 5.76% (for the HB tube) and the minimum MAD value was 4.18% (for the HYD/HB tube). The MRD values of all three enhanced tubes were greater than zero, indicating that the predicted values of the new correlation model were slightly higher than the experimental values. The maximum MRD value was 2.33% (for the HYD tube) and the minimum value was 0.12% (for the HB tube). Overall, the modified Cavallini et al. [13] correlation accurately predicts the condensation heat transfer coefficients of the three enhanced tubes (HYD, HB, and HYD/HB). These are important new results that will allow these tubes to be used in the development of high-performance heat transfer systems.