Condensation and Evaporation Heat Transfer Characteristics of Low Mass Fluxes in Horizontal Smooth Tube and Three-Dimensional Enhanced Tubes

Two-phase flow studies have attached the attention of a variety of researchers in recent years. Condensers and evaporators are commonly used in various industrial systems (the refrigerators, air conditioners, heat pump, etc.). In order to improve the efficiency of these heat exchangers, the field of the enhanced heat transfer technology has become an important consideration; many works have evaluated methods to generate higher heat transfer coefficients. Enhanced heat transfer tubes have become an important consideration in the desire to increase performance; these tubes directly affect the efficiency and energy consumption of the heat exchanger. Over time, various types of enhanced tubes have been developed and are widely used in industrial production to improve the heat transfer coefficients.

There are many types of enhanced tubes, they include micro-fin, herringbone, corrugated, flattened, and dimpled tubes. Several previous studies [1–10] on the condensation and evaporation heat transfer characteristics of these tubes have been performed.

Miyara et al. [11] studied the condensation performance of horizontal micro-fin and herringbone tubes. Kim [12] investigated the effect of various parameters on the tube-side condensation of micro-fin tubes using R410A. Sarmadian et al. [13] performed condensation experiments of R600a in horizontal, smooth, and helically dimpled tubes with a mass flux that varied from 114 to 368 kg/m²s. Aroonrat and Wongwises [14] studied the condensation heat transfer and pressure drop characteristics of R134a flowing inside horizontal smooth and dimpled tubes (8.1 mm in diameter and 1500 mm in length) at saturated temperatures of 30 °C, 40 °C, and 50 °C. From the results, it appears that the average heat transfer coefficient and the frictional pressure drop tend to increase with an increasing average vapor quality and mass flux. The Nusselt number of the dimpled tubes are 1.3–1.4 times larger than those found in a smooth tube for similar conditions and the two-phase friction factor is 2.8–4.1 times larger. In the studies [15,16], condensation heat transfer and pressure drop results of the dimpled tubes with different helical, dimpled pitches, and depths are also found. Li et al. [17] showed an experimental investigation of the shell-side flow condensation inside a smooth tube and 2EHT enhanced tubes. They analyzed the effect of the saturated temperature, mass flux, and vapor quality on the heat transfer coefficients; they also present a new heat transfer model (based on the Nusselt's theory) for outside condensation.

A number of studies (Dalkilic et al. [18], Lu et al. [19], Jiangzhi et al. [20], Guo et al. [21]) evaluated the evaporation heat transfer coefficient of micro-fin tubes for a variety of parameters. Guo et al. [21] performed an experimental investigation on the condensation and evaporation heat transfer characteristics for various refrigerants (R22/R32/R410A) inside smooth, herringbone, and enhanced surface tubes. Mass flux ranged from 55 to 181 kg/(m²s) and heat flux ranged from 9.8 to 36 kW/m², with the vapor quality ranging from 0.1 to 0.9. The results showed that the condensation heat transfer coefficient of the 1EHT is about 1.3–1.95 times larger than that of a smooth tube; however, the herringbone tube produced the highest condensation heat transfer enhancement. For evaporation, the 1EHT tube produced the highest evaporation heat transfer performance when using R22/R32/R410A. The authors found the Cavallini et al. correlation [22] to predict condensation results for a smooth tube and the modified Wojtan et al. correlation [23] to predict evaporation results. Li et al. [24] tested the heat transfer coefficients and friction pressure drop during the condensation and evaporation of R410A inside a horizontal smooth tube and 2EHT tubes. They showed that the evaporation heat transfer coefficient of 2EHT tubes is 11–44% larger than that of the smooth tube, and 10–16% larger for condensation. Wang et al. [25] obtained the condensation heat transfer and pressure drop characteristics of R134A inside a plain tube and four enhanced tubes with different pin fins structures, for saturation pressures of 13.4 bars and 11.6 bars. They conducted the experiments for a mass flux range of 50–150 kg/m²s. They concluded that the heat transfer coefficient of the four enhanced tubes is about 1.5–2.5 times that of the smooth tube.

The purpose of this investigation is to study the condensation and evaporation heat transfer characteristics at a low mass flux for 15.88-mm-OD and 12.7-mm-OD enhanced tubes (1EHT/3EHT) and compare the results with a smooth tube using R410A and R134A. During the experiment, the average heat transfer coefficient is determined and the effect of saturation temperature and tube diameter on the condensation and evaporation heat transfer coefficients was also discussed. Finally, experimental data were compared with previously reported empirical models.

Schematic diagram of the experimental system used for this investigation is given in Fig. 1(a); it consisted of a preheat section, a test section, and a subcooling section. The experimental apparatus has been previously used and discussed in Refs. [2,3]. As can be seen in Fig. 1, the preheat section controls the inlet vapor quality that enters into the test section, it is accomplished by changing the water temperature and mass velocity. The test section is shown in Fig. 1(b); it consists of a straight, horizontal, counterflow, tube-in-tube heat exchanger (heating length of two meters). The refrigerant flows into the tube side, water flows through the shell side to heat/cool the refrigerant. The entire test section was insulated (in order to minimize the heat loss) using polyurethane rigid foam and rubber foam.

During the experiment, the refrigerant and water temperature were measured by a Platinum 100 RTD at the inlet and outlet of the preheat and test section, respectively. All the thermocouples were calibrated with an uncertainty of ±0.1 °C. The pressure transducers (with an accuracy of 0.075% of the full scale) at the inlet and outlet of the test section were installed to measure the refrigerant pressure; a differential pressure transducer was located between the inlet and outlet of the test section in order to obtain the total pressure drop. A Coriolis mass flow meter (with an accuracy of 0.2% of full scale) was used to measure the mass flux between 50 and 200 kg/m²s in this refrigerant loop.

Figure 2 shows the three-dimensional view and surface structures of the enhanced tubes (1EHT/3EHT). Tested tubes include (a) a stainless steel smooth tube with outer diameter of 15.88-mm-OD and 12.7-mm-OD; (b) 1EHT stainless steel tube, as shown in Fig. 2(a), the surface structure of the 1EHT tube is composed of dimpled protrusions with secondary petal arrays. There are five rows of main rounded dimples, in which the depth of the dimple is 2.36 mm and the diameter of the dimple is 3.00 mm; and (c) 3EHT stainless steel tube, as shown in Fig. 2(b), unlike a 1EHT tube, the enhancement structure of the 3EHT tube is a series of rectangular cavities and grooves. The length, width, and depth of rectangular cavities are 7.20 mm, 3.20 mm, and 1.00 mm, respectively. Obviously, these surface enhancement structures can increase the heat transfer area and provide more heat flux. The inner heat transfer area of the 1EHT tube is approximately 1.20 times than that of the smooth tube; for the 3EHT tube, it has a heat transfer area ratio (A_e/A_s) that is 1.25. Three tested tubes have the same outer diameter (d_o) of 15.88 mm.

Condensation tests using R134A and R410A were conducted at saturation temperatures of 35 °C, 40 °C, and 45 °C, with a mass flux ranging from 80 to 200 kg/(m²s), heat flux range from 11 to 29 kW/m², with an inlet vapor quality of 0.8, and an outlet vapor quality of 0.2. Evaporation heat transfer tests using R134A and R410A are investigated at a saturation temperature of 6 °C and 10 °C; with a mass flux ranging from 50 to 180 kg/(m²s), heat flux in the range from 9 to 35 kW/m², and a vapor quality that varies from 0.2 to 0.8. The summary of the operating conditions is given in Table 1. During the experiment, the inlet and outlet vapor quality values remained constant; mass flux and heat flux varied. Experimental data were collected every ten continuous data points (time interval of every data is 20 s) when the deviations of temperature, pressure, and vapor quality were below 0.1 °C, 3 kPa, and 0.05, respectively. All thermodynamic properties of refrigerant (R134 and R410A) and water were acquired from NIST REFPROP 9.0 database [26] shown in Table 2.

In Eq. (7), A_i and A_o are the nominal internal and external heat transfer area based on d_i and d_o of the test tubes, respectively; k is the thermal conductivity of tube material (stainless steel k = 17 W/m K).

The property ratio (μ_bulk/μ_wall)^0.14 is a temperature difference factor reflecting the effect of the temperature distribution on the fluid properties. Additionally, k_w and d_h are the thermal conductivity of water and the shell-side hydraulic diameter (d_h = D − d_o).

However, the Gnielinski correlation [27] cannot be directly used to calculate the annulus side heat transfer coefficients due to the existence of the dimples and rectangular cavities on the outer surface of the 1EHT tube and 3EHT tube. Therefore, the Wilson plot method needs to be used in order to obtain the enhancement ratio (C) of the two enhanced tubes.

The theoretical basis of the Wilson plot method is given in Fig. 4. As the tube-side refrigerant mass velocity (V_ref) increases, the total thermal resistance 1/(UA_o) is considered as a function of V^−0.8. Hence, when the refrigerant mass flux is infinite, the tube-side thermal resistance, 1/(h_iA_i), tends to zero and the total thermal resistance, 1/(UA_o), can be approximately equal to the shell-side thermal resistance, 1/(h_oA_o) and the tube wall thermal resistance, d_oln(d_o/d_i)/(2kA_o). In addition, in order to ensure both tube-side and shell-side turbulence, evaluations were conducted by changing the water mass flux and the refrigerant mass flux while keeping the tube wall thermal resistance fixed.

During the Wilson plot method evaluation, the refrigerant mass flux is constant at 200 kg/(m²s), and the water mass flux ranges from 600 to 900 kg/(m²s) (corresponding to Reynolds number from 3200 to 4800). According to the experimental results shown in Fig. 5, the enhancement ratio of the 1EHT tube is 2.03 and 3EHT tube enhancement ratio is 1.81.

In this study, the heat balance of the test section was evaluated using single-phase experiments in order to ensure the accuracy of the two-phase experimental results. As is shown in Fig. 6, the heat loss is well controlled within 5% (comparing the heat flux of the refrigerant and water). The uncertainties of measurements and calculated parameters are listed in Table 3. A detailed description of the experimental uncertainties is given in Ref. [24].

Figure 7(a) shows the single-phase variation of Nusselt number with Reynolds number in a stainless steel smooth tube and 1EHT tube; each with a 12.7-mm-OD, using R134A and R410A. The Nu number of the 1EHT tube is much higher at the same Re number. The enhancement of single-phase heat transfer coefficient is caused by swirling flow in the dimples and petal array. In addition, strong swirling enhances interfacial turbulence and disrupts the boundary layer. It can be seen that the single-phase heat transfer coefficients of the tested tubes have little difference using R134A and R410A. Figure 7(b) compares the experimental Nu numbers with the empirical correlations of Dittus–Boelter [29] and Gnielinski [27] for smooth tube; the results fit well with the predicted values with an error band ±5%.

Condensation heat transfer characteristics were evaluated inside 1EHT, 3EHT, and a smooth tube using R134A and R410A. Figure 8 shows the variation of the average heat transfer coefficients as a function of mass flux for a saturation temperature of 45 °C. It is observed that the two enhanced tubes produce better heat transfer performances over the tested range of mass flux; this is the result of its larger heat transfer surface area. It appears that some of the condensate liquid film on the bottom surface of the enhanced tubes was disrupted by the dimples/rectangle cavities and this increases the turbulence. The heat transfer coefficients increase slightly with the increase of mass flux. It appears that for low mass flux, the flow pattern is stratified flow; the effect of the mass flux on the condensation heat transfer coefficient is weak and negligible. It can be seen that the condensation heat transfer coefficient increases gradually for mass flux values over 120 kg/m²s. This can be explained by the liquid film thickness decreasing with the mass flux increasing; this results in a decrease of liquid thermal resistance. Moreover, the vapor velocity increases and results in an increase in the shear stress on the liquid–vapor interface; this leads to more droplet entrainment. Enhancement of the condensation heat transfer coefficient results from the decrease of the liquid thermal resistance and the increase of the two-phase flow velocity.

Condensation heat transfer coefficient of the 1EHT tube is approximately 1.64–1.95 times than that of the smooth tube and for the 3EHT tube it is approximately 1.42–1.57 times. Reasons for the enhanced heat transfer in the 1EHT tube include increased heat transfer surface area of enhanced tubes, decreasing heat transfer resistance (dimples of the 1EHT tube can destroy the liquid film of the boundary layer), the structure of the 1EHT tube promotes condensate drainage from the boundary to the center by the shear stress, and enhanced mixing and turbulence. Finally, a thinner liquid film is formed on the surface of the enhanced tubes which causes an increase to the heat transfer coefficient. However, the rectangular cavities of 3EHT are an inefficient method to the enhancement of the condensation heat transfer coefficient since the condensate liquid remains on the bottom of the rectangular cavities, so the flow turbulence is weakened.

Finally, the condensation heat transfer coefficient of the smooth tube was compared with three existing correlations (Shah correlation [30], Cavallini et al. correlation [22], and Dorao and Fernandino correlation [31]) in Fig. 8. It is noticed that the Cavallini et al. correlation [22] shows better predictive ability (at a low mass flux) than the other two condensation heat transfer correlations (regardless if R134A or R410A is used). Table 4 shows the mean absolute deviations (MAD) between the predictive values and experimental values. Cavallini et al. correlation [22] produces a mean absolute deviation of 8.5%, while a larger scatter is determined when using the Shah correlation [30] or the Dorao and Fernandino correlation [31]. This is probably due to the fact that they tend to be used in forced convective condensation and it is not accurate at a low mass flux. It is concluded that the condensation heat transfer coefficient of two enhanced tubes cannot be correlated with the empirical correlations.

Figure 9 presents the evaporation heat transfer coefficient as a function of mass flux for 1EHT, 3EHT, and smooth stainless steel tubes when using R134A and R410A. Among all three test tubes, the heat transfer coefficient of the 1EHT tube is the largest, followed by the 3EHT tube and finally the smooth tube. The evaporation heat transfer coefficient of the enhanced tubes is in the range of 1.04–1.42 times than that of the smooth tube. The heat transfer enhancement is caused by the larger heat transfer area of enhanced tubes; additionally, the dimples and petal arrays in the surface of enhanced tubes generate more nucleation sites and swirl turbulence, which also increases the heat transfer coefficient. The surface structure also creates stronger interfacial turbulence and boundary layer disruption. Unlike the condensation results, the evaporation heat transfer coefficient increases significantly with increasing mass flux. On one hand, the low vapor density at a low saturation temperature tends to increase vapor velocity and this enhances the flow boiling heat transfer. On the other hand, a larger mass flux requires more heat flux, which in turn requires a greater degree of superheat; the greater degree of superheat has a large effect on nucleate boiling. As far as the experimental conditions discussed in this paper are concerned, the increase of the heat flux and the degree of superheat has a strengthening effect on nucleate boiling. It is speculated (based on the Wojtan et al. [32] flow pattern map) that the 1EHT enhanced tube could achieve a transformation from stratified flow to stratified-wavy flow earlier due to the dimple enhancement units. The same is not true for the 3EHT tube; it doesnot show enhanced evaporation heat transfer for low mass flux values. As is shown in Fig. 9, the evaporation heat transfer coefficients of the 3EHT tube is only slightly larger than that of a smooth tube even though there is a larger heat transfer area ratio (1.25). The rectangular cavities on the surface of the 3EHT tube are obviously more inefficient for these evaporation conditions. This may be explained by the depth of the ribs; the rib height is less than liquid film thickness and the shorter ribs couldnot change the flow direction and cause strong swirls.

Evaporation is composed of nucleate or convective components or both, at low mass flux the nucleate flow regime is dominant. Comparison of the evaporation heat transfer coefficients' predictive effect is presented in Fig. 9; Liu and Winterton correlation [33], Kandlikar correlation [34], and Wojtan et al. correlation [23] show good predictive ability for evaporation heat transfer at a low mass flux. The predictive accuracy of evaporation heat transfer correlations is given in Table 4. The accuracy of the Kandlikar correlation [34] decreases with increasing the mass flux, while the Liu and Winterton correlation [33] can predict all experiment data points with a relatively small deviation.

For evaporation heat transfer in the tubes that were evaluated, R410A performs much better than R134A. This is because of the larger shear stress that is present in R410A between the liquid phase and vapor phase; this produces a thinner liquid film than that which is produced using R134A. In addition, the higher liquid thermal conductivity and higher vapor density also contribute to the higher heat transfer coefficients.

Figure 10 displays the effect of saturation temperature on the condensation and evaporation heat transfer coefficient. The condensation heat transfer coefficient decreases as the saturation temperature rises for both the 1EHT and 3EHT tubes. This is due to the liquid thermal conductivity being lower at higher saturation temperatures, which results in higher liquid thermal resistance. In addition, the higher saturation temperature leads to a higher vapor density, which creates shear stress between the liquid film and tube wall; this weakens the interaction of the liquid–vapor interface. The low latent heat of vaporization present under a high saturation temperature is also a significant factor affecting the heat transfer characteristics. As shown in Fig. 10, the condensation heat transfer coefficients for T_sat = 35 °C and the evaporation heat transfer coefficients for T_sat = 6 °C are higher under the test conditions.

From Fig. 11, it can be seen that for the most part, the heat transfer coefficients of the 12.7-mm-OD tubes are higher than that of 15.88-mm-OD tubes. The solid lines denote the measured heat transfer coefficients in R410A for 1EHT and smooth tube of 12.7-mm-OD; the dotted line symbol denotes those of tubes of 15.88-mm-OD. This can partially be explained by the fact that as tube diameters increased, the condensation and evaporation heat transfer characteristics are more dominated by gravity. At a low mass flux, the flow regime is mainly stratified or stratified-wavy; the gravitational force is more dominant than viscosity and shear forces; and the liquid film deposits more at the bottom of the tube, which serves as a thermal resistance and decreases the heat transfer coefficient. Furthermore, the effect of the surface tension and shear stress forces both the gas–liquid interface and the liquid film/tube wall to be reduced for two-phase flow at a low mass flux. An interesting phenomenon shown in Fig. 11 is that the heat transfer coefficient of the 12.7-mm-OD smooth tube is less than that of the 15.88-mm-OD 1EHT tube under the same test conditions. This is because the dimples and protrusions have obvious and significant enhancement effect for condensation and evaporation heat transfer characteristics under a low mass flux. It can be concluded that the heat transfer coefficient decreases with increasing the tube diameter.

As is shown in Fig. 12(a), the enhancement factor for condensation of the 1EHT tube varies from 1.7 to 2.0 for 15.88-mm-OD and 12.7-mm-OD tube using R134A and R410A, while those for 3EHT tube it varied from 1.4 to 1.6 as the mass flux increases from 80 to 140 kg/(m²s). The EF decreases gradually with an increase of mass flux, indicating a good enhancement effect at low mass flux. For evaporation, unlike condensation, there is a larger enhancement factor using R134A as the working fluid. Figure 12(b) shows that the EF of the 1EHT tube (with R134A and R410A) is approximately 1.4 and 1.2, respectively. In summary, the 1EHT and 3EHT tubes present excellent condensation heat transfer performance at relatively low mass flux values.

An experimental investigation of condensation (T_sat = 45 °C) and evaporation (T_sat = 6 °C) heat transfer characteristics was performed in a smooth tube and two three-dimensional enhanced tubes (1EHT, 3EHT) using R134A and R410A. The following conclusions are made

1. For condensation, the 1EHT and 3EHT tube produces higher heat transfer coefficients than a stainless steel smooth tube. Cavallini et al. correlation [22] shows a good predictive ability for a smooth tube.

2. For evaporation, the heat transfer coefficients increase significantly with increasing mass flux. It can be speculated that the higher vapor velocities will lead to strong interfacial turbulence and that the surface structure increases the nucleation sites. Liu and Winterton correlation [33] can accurately predict the current evaporation experiment data with a mean absolute deviation of 3.06%.

3. R410A presents better heat transfer characteristics than R134A due to its higher vapor density and liquid thermal conductivity. The low saturation temperature and small tube diameter also have a beneficial effect on the heat transfer characteristics.

4. The condensation heat transfer coefficient for 1EHT and 3EHT tubes are 70–200% and 40–60% higher than the smooth tube, while for evaporation they are 20–45% and 5–20% higher at similar test conditions.

• National Science Foundation of Zhejiang Province (Grant No.: LY19E060004; Funder ID: 10.13039/100000001)

f =

Fanning friction factor, —

h =

heat transfer coefficient, W/(m² K)

k =

thermal conductivity, W/(m K)

l =

heat length, m

m =

mass flow rate, kg/s

q =

heat flux, W/m²

x =

vapor quality, —

A =

heat transfer area, —

C =

enhancement ratio, —

D =

inner diameter of the outer tube, m

H =

enthalpy, kJ/kg

Q =

heat transfer amount, W

T =

temperature, K

U =

total heat transfer coefficient, W/(m² K)

c_p =

specific heat, J/(kg K)

d_h =

hydraulic diameter, m

h_lv =

latent heat of vaporization, J/kg

A_i =

inner surface area of the test tube, m²

A_o =

outer surface area of the test tube, m²

d_i/ID =

inner diameter of the test tube, m

d_o/OD =

outer diameter of the test tube, m

EF =

enhancement factor, —

EHT =

enhanced heat transfer tube, —

G/V =

mass flux, kg/(m²s)

LMTD =

logarithmic mean temperature, K

MAD =

mean absolute deviation, —

Pr =

Prandtl number, —

Re =

Reynolds number, —

γ =

heat loss, —

μ =

dynamic viscosity, Pa s

ρ =

density, kg/m³

e =

enhanced

exp =

experiment

i =

inner

in =

inlet

l =

liquid phase

o =

outer

out =

outlet

pre =

preheat section

ref =

refrigerant

s =

smooth

sat =

saturated

v =

vapor phase

w =

water