Experimental Study on Flow Boiling Heat Transfer of Zeotropic Mixture R290/R601a in a Mini-Channel

Abstract

The flow boiling heat transfer characteristics of zeotropic mixture R290/R601a in a horizontal mini-channel with an inner diameter of 2 mm were experimentally studied. The experiments were conducted at saturation pressure from 1 to 1.5 MPa, mass flux from 100 to 500 kg/(m²·s), heat flux from 20 to 30 kW/m², and vapor quality from 0 to 1. The effects of mass fraction, mass flux, saturation pressure, heat flux, and vapor quality on the flow boiling heat transfer coefficient in a mini-channel were analyzed. The experimental results show that the boiling heat transfer coefficient initially decreases and then increases with a decrease in the R290 mass fraction. The boiling heat transfer coefficient increases with the increase in mass flux and heat flux and decreases with the increase in saturation pressure. In addition, due to the dry-out phenomenon, the boiling heat transfer coefficient first increases and then decreases with the increase in vapor quality. The experimental data were compared and evaluated with existing correlations. Finally, a new prediction correlation for the boiling heat transfer coefficient is proposed, and the mean absolute relative deviation is 13.7%. This work provides key data for the development of green refrigeration technology, which is helpful in promoting the application of low-GWP natural refrigerants in new refrigeration systems. It also offers experimental guidance for the energy efficiency optimization of the ORC system and the structural design improvement of the compact heat exchanger.

1. Introduction

Improving the utilization of medium and low-temperature heat energy has become one of the more effective approaches to address increasing environmental pollution and energy consumption [1]. The Organic Rankine Cycle (ORC) is considered one of the most promising methods with which to improve the utilization of low-temperature heat sources due to its many advantages, such as high safety, high thermal efficiency, a wide range of heat source temperatures, stable operation, and easy maintenance [2,3]. In the ORC system, the irreversible loss and heat transfer area of the evaporator occupy its main proportion, which has a significant impact on the thermal economic benefits of the system. Because of this, it is particularly important to study the heat transfer characteristics of working fluids in flow boiling [4]. As a result of the Kigali Amendment to the Montreal Protocol, high global warming potential (GWP) refrigerants are now being restricted [5,6]. Compared with the widely used synthetic working fluids such as chlorofluorocarbons and hydrofluorocarbons, natural working fluids have received special attention from researchers and developers because of their zero ozone depletion potential (ODP) and extremely low global warming potential (GWP) [7]. In addition, mixed refrigerants can achieve low-GWP alternative mixtures with similar or even better system performance [8]. The zeotropic mixture can form a good temperature match with the heat transfer fluid due to its temperature glide characteristics. The zeotropic working fluid with a large temperature glide can be applied to thermal systems, such as high-temperature air source heat pump systems, Joule–Thomson refrigeration systems with large temperature rise/temperature drop, and trans-critical ORC systems [9,10,11]. Therefore, this paper mainly considers the zeotropic mixture composed of hydrocarbons as the research object.

Refrigeration systems containing hydrocarbons and their mixtures need to be designed to minimize the refrigerant charge in the system, thereby reducing their safety risks [12]. The miniaturization of the heat exchanger has become one of the best choices for reducing the refrigerant charge because of its high heat transfer coefficient, reduced volume and weight, and improved energy efficiency [13,14]. Further, mini-channel heat exchangers with HCs as the working medium exhibit higher heat transfer efficiency [15]. Due to the increasing demand for zeotropic mixtures and the miniaturization of heat exchangers, some scholars have begun to study their boiling characteristics in depth.

The existing research shows that the heat transfer coefficient of saturated liquid flow boiling is mainly affected by nucleate boiling and film boiling [16,17]. Nucleate boiling is characterized by the formation of vapor bubbles at the vaporization core (bubble flow/elastic flow), and its heat transfer is dominated by heat flux and saturation pressure and has nothing to do with mass flux and vapor quality [18]. The film boiling corresponds to the annular flow, and the heat transfer depends on the evaporation of the liquid film and the change of mass flux [19]. Some scholars have compared the boiling heat transfer characteristics of pure refrigerants and zeotropic mixtures by experimental methods. For example, Kundu et al. [14] compared the flow boiling heat transfer coefficients of pure R134a, R401a, and R407C. They found that the heat transfer coefficient of R407C is always lower than that of R134a and R410A. The heat transfer coefficient of pure refrigerant and mixed refrigerant always increases with the increase in mass flux. Similarly, the experimental study of Mohammed et al. [20] showed that the boiling heat transfer coefficient of the zeotropic refrigerant R1270/R600a was higher than that of R22. Compared with R22, the boiling heat transfer coefficient of R1270/R600a increased by 19.04–67.32%. Moreover, the effect of saturation pressure on the heat transfer coefficient for boiling is directly proportional, while Wang et al. [21] found that the effect of saturation pressure on the heat transfer coefficient for boiling is inversely proportional. The above literature shows that the boiling heat transfer coefficient of zeotropic mixtures is usually lower than that of pure working fluids, but their core advantage is the temperature glide effect. This feature enables the phase change process of the working fluid to form a better temperature match with the heat source/heat sink fluid, thereby reducing the heat transfer energy loss and improving the system energy efficiency. Especially in the high-temperature rise system, the mixed working fluid shows significant advantages. Pan et al. [22] pointed out that the R600/R245fa mixture has better thermal performance and more stable operating pressure than pure R245fa. Sarkar et al. [23] also reported that the performance of CO₂/butane mixture in a heat pump system is better than that of a single component. Although the heat transfer coefficient of zeotropic refrigerants is not high, it achieves an optimal balance in system efficiency, operation safety, and working condition adaptability, especially suitable for heat pump systems and refrigeration systems with large temperature spans.

In addition, some scholars have compared the boiling heat transfer characteristics of various mixtures through experimental methods. Liu et al. [24] experimentally studied the boiling heat transfer performance of three alternative refrigerants and analyzed the characteristics of each parameter on the heat transfer characteristics to evaluate the feasibility of R1234yf and R1336mzz(Z) replacing R134a and R245fa. The results show that the heat transfer coefficient of R134a/R245fa is the highest, while that of R1234yf/R1336mzz(Z) is the lowest. In addition, Berto et al. [25] measured the flow boiling heat transfer coefficient of R455A and R452B ternary mixtures in two horizontal smooth tubes with inner diameters of 8.0 mm and 0.96 mm, respectively. They found that, under the same operating conditions, R452B exhibits a higher heat transfer coefficient than R455A, and the reduced heat transfer performance of R455A is due to fluid properties and additional mass transfer resistance related to temperature glide. In addition, the effect of tube diameter on boiling heat transfer characteristics was also compared. It was found that the heat transfer coefficient in the 0.96 mm channel was higher than that in the 8.0 mm diameter channel.

Boiling heat transfer characteristics are the same as condensation heat transfer characteristics, and mass transfer resistance is the main factor affecting heat transfer characteristics. Dai et al. [26] experimentally analyzed the flow boiling characteristics of three mass fractions of CO₂/R152a in a 2 mm horizontal tube. The boiling heat transfer coefficient of CO₂/R152a increases with the increase in heat flux, mass flux, and saturation temperature. Guo et al. [27] and Dang et al. [28] also found the same trend. They found that mass transfer resistance and sensible heat resistance had a serious deteriorating effect on flow boiling heat transfer due to high-temperature glide. The researchers in [7] found that the heat transfer degradation of zeotropic mixtures flow boiling in microchannels is similar to that in conventional channels. This degradation is essentially caused by the increase in liquid–vapor interface temperature affected by the mass transfer effect. Qi et al. [29] also pointed out that heat transfer deterioration is a unique phenomenon of zeotropic mixtures. Heat transfer deterioration increases with the increase in the mass fraction difference of R134a in the liquid. Li et al. [30] later found that the non-equilibrium of the two-phase flow affects the concentration gradient of the two phases, which in turn affects the HTC of the high-temperature glide mixture. For mixtures with extremely low-temperature glide, this non-equilibrium effect is not significant [31].

In previous research, Wu et al. [32] screened the working fluid of a high-temperature recuperative heat pump system and confirmed that the R290/R601a zeotropic mixed working fluid was an ideal working fluid suitable for this purpose. When the molar ratio is 0.9/0.1, the system COP reaches 3.51, and the compressor pressure is always in a safe range, avoiding the risk of negative pressure. Thermodynamic analysis shows that the working fluid reduces the exergy loss of the recuperator and condenser and increases the exergy efficiency of the system to 40.9%. The 70 °C temperature glide highly matches the 75 °C water temperature demand, which reduces the possibility of heat loss. However, the heat transfer mechanism of the two-phase flow in the evaporation process is not clear, and the change in the mixing ratio will significantly affect the system performance. In addition, although the miniaturization of heat exchangers can improve the efficiency of equipment, it will change the flow and heat transfer characteristics [33]. It is necessary to clarify the flow and heat transfer law of R290/R601a in mini-channels through experimental research, establish an accurate heat transfer prediction model, and provide key data support for heat pump system optimization. In addition, although current research has begun to study the flow boiling of zeotropic mixtures, correlation mainly depends on conventional channel data, ignoring the synergistic effect of microchannel limitation and mass transfer resistance under large temperature glide. When applied to small-scale channels, this can lead to significant deviations. Therefore, in the present work, a universal correlation between ensemble temperature glide effect and two-phase flow dynamics is proposed for the flow boiling heat transfer mechanism of R290/R601a in mini-channels. This method is fundamentally different from the existing superposition or asymptotic models and quantifies the dynamic competition between nucleate boiling suppression and convection enhancement.

Therefore, the fluid-boiling heat transfer characteristics of R290/R601a in a horizontal mini-channel were experimentally studied under the conditions of saturation pressure of 1 to 1.5 MPa, mass flux of 100 to 500 kg/(m²·s), heat flux of 20 to 30 kW/m² and vapor quality of 0 to 1. The effects of mass fraction, mass flux, saturation pressure, heat flux, and vapor quality on flow boiling characteristics are analyzed. The existing heat transfer correlation is evaluated. Finally, by introducing the dimensionless temperature glide parameter and the modified nucleate boiling suppression factor, a new correlation for the boiling heat transfer coefficient of zeotropic refrigerants is proposed. Studying the flow boiling characteristics of zeotropic working fluids in mini-channels can not only reveal the internal mechanism of heat transfer deterioration but also provide theoretical support for the development of efficient and compact heat exchangers and the improvement of the comprehensive performance of heating systems. The research results provide a key data basis for the upgrading of green refrigeration technology, which can directly guide the design optimization of energy-efficient compact heat exchange equipment. It also provides a practical basis for the selection of mixed refrigerant ratios and optimization of operating parameters in new refrigeration and heat pump systems.

2. Experimental Apparatus

2.1. Experimental System

A schematic diagram of the experimental system is shown in Figure 1. The experimental system is composed mainly of a refrigerant cycle and three cooling water cycles. The experimental working fluid enters the system through the filling valve and is stored in a liquid reservoir with a volume of 0.26 L. After the working fluid leaves the liquid reservoir, it enters the subcooling section to keep the working fluid in the supercooling state. The experimental working fluid in the supercooled state is driven by a magnetically driven gear pump (Oerlik Pump Valve Co., MG204XK/DC24W-50, Nanjing, China) and enters a mass flow meter to measure the flow rate of the working fluid. The preheater, which is electrically heated, converts the subcooled working fluid into a vapor–liquid two-phase mixture with a specific vapor quality by adjusting its heating power. The temperature control switch is installed around the preheater, which can be over-temperature protected. Next, it enters the boiling test section and is heated to the desired vapor quality by the heating wire. Finally, it is returned to the liquid reservoir to complete the refrigerant side circulation. In order to prevent damage to the differential pressure sensor (Baker Hughes Co., UNIK-5000, Houston, TX, USA) when charging with refrigerant, a bypass branch is installed around it. By controlling the ball valve on the branch, the differential pressure sensor can adapt to the sudden change in pressure. To reduce the energy loss of the experimental system, it is necessary to carry out thermal insulation treatment. The various components of the system and tube are wrapped with thermal insulation foam, with a thickness of not less than 20 mm.

In the experimental system, the control of each influencing parameter is achieved by the following methods: the precise control of the mass fraction is achieved by collecting the full liquid phase samples before the preheating section, using the chromatograph to perform real-time component detection, and adjusting the mixing ratio of R290 and R601a according to the detection results; the mass flux is dynamically controlled by adjusting the speed of the magnetically driven gear pump, and the flow rate is monitored in real time with the Coriolis mass flowmeter (RHEONIK); the regulation of saturation pressure changes the overall pressure of the system by adjusting the temperature of the cooling water circulation of the liquid reservoir, and synchronously fine-tunes the electric heating power of the preheating section; The heat flux is directly controlled by the DC power supply in the boiling test section. The power is calculated by accurately adjusting the voltage and current. Combined with the thermal efficiency calibrated by the single-phase verification experiment, the heat flux is uniformly applied in the range of 20–30 kW/m²; the vapor quality is achieved mainly by adjusting the electric heating power of the preheating section, and the pre-heating is used to convert the supercooled liquid working medium into a vapor–liquid two-phase flow with a specific vapor quality. The cooperative operation of each equipment hinders the independence of parameters, which provides a reliable basis for studying the flow boiling heat transfer characteristics under different working conditions.

2.2. Test Section

The boiling test section is a copper tube with an inner diameter of 2 mm and a length of 350 mm. The specific structure is visible in Figure 2. The heating method of the boiling test section is via electric heating wire. To prevent short circuits in the heating process, the insulating tape is wound around the copper tube and then evenly wound with the nichrome heating wire at intervals of 3 mm. Finally, more than two layers of glass cloth are wound around the heating wire to play the role of heat insulation. Three T-type thermocouples were arranged at each of the three sections outside the tube in the test section. The average value was taken to calculate the inner wall temperature of the boiling test section.

2.3. Data Reduction

The heat flux of the boiling test section is provided by the Joule heat generated by the direct current. The specific formula is as follows:

$$q={\displaystyle \frac{{\eta }_{\mathrm{test}}UI}{\mathsf{\pi }{d}_{\mathrm{i}}L}}$$

(1)

where q is the heat flux of the boiling test section; η_test is the thermal efficiency of the boiling test section. After the single-phase verification experiment, the electric heating efficiency of the preheating section is 0.89; U and I are the voltage and current of the heater in the boiling test section, respectively.

Three thermocouples were arranged on the three sections of the boiling test section. The outer wall temperature of the test section at each section is equal to the average temperature measured by the three thermocouples. The specific form of the outer wall temperature of the test section is as follows:

$$T_{\mathrm{w},\mathrm{out}}={\displaystyle \frac{1}{3}}{\displaystyle \sum _{i=1}^3{T}_{\mathrm{w},\mathrm{out},\mathrm{i}}}$$

(2)

According to Newton’s law of cooling, the local heat transfer coefficient h of the boiling test section can be calculated as follows:

$$h={\displaystyle \frac{q}{\left(T_{\mathrm{w},\mathrm{in}}-T_{\mathrm{s}\mathrm{at}}\right)}}$$

(3)

where T_sat is the saturation temperature of the refrigerant; T_w,in is the inner wall temperature of the test section. The inner wall temperature of the test section can be calculated from the outer wall temperature by using the one-dimensional radial steady-state heat conduction equation. The calculation formula is

$$T_{\mathrm{w},\mathrm{in}}=T_{\mathrm{w},\mathrm{out}}-{\displaystyle \frac{{\eta }_{\mathrm{test}}UI}{2\mathsf{\pi }\lambda L}}\ln {\displaystyle \frac{d_{\mathrm{i}}}{d_{\mathrm{o}}}}$$

(4)

where d_i and d_o are the inner diameter and outer diameter of the boiling test section, respectively; L is the effective heat transfer length of the boiling test section; and λ is the thermal conductivity of the copper tube.

Since the boiling test section is arranged after the condensation test section, the outlet vapor quality of the condensation test section is the inlet vapor quality x_in of the boiling test section. The calculation formula for the vapor quality change Δx in the boiling test section is

$$\Delta x={\displaystyle \frac{{\eta }_{\mathrm{test}}UI}{m_{\mathrm{r}}{H}_{\mathrm{lv}}}}$$

(5)

where m_r is the mass flux of the refrigerant; H_lv is the latent heat of the refrigerant.

The outlet vapor quality x_out of the refrigerant in the boiling test section can be calculated as

$$x_{\mathrm{out}}=x_{\mathrm{in}}+{\displaystyle \frac{{\eta }_{\mathrm{test}}UI}{m_{\mathrm{r}}{H}_{\mathrm{lv}}}}$$

(6)

The refrigerant vapor quality x is the average of the inlet and outlet vapor quality of the test section:

$$x={\displaystyle \frac{x_{\mathrm{in}}+x_{\mathrm{out}}}{2}}$$

(7)

2.4. Measurement Uncertainties

Uncertainty analysis is an important concept used to evaluate the reliability of measurement results, especially widely used in experimental methods. The measurement error of the parameters directly measured by the experimental instrument can be obtained by the range and accuracy of the instrument. The model, range, and accuracy of each parameter instrument are shown in

Table 1. Measurement instruments and their uncertainties.

Parameters	Instruments	Range	Uncertainties
Absolute pressure	Baker Hughes Co., UNIK-5000 pressure sensors, US	0~3 MPa	±0.04%FS
Differential pressure	Baker Hughes Co., UNIK-5000 differential pressure sensors, US	0~100 kPa	±0.02%FS
Mass flow	RHEONIK Co., RHM-03, Coriolis mass flow meter, Odelzhausen, Germany	0.038~5 kg/min	±0.1%
Voltage	HSPY Co., DC-regulated power supply, Beijing, China	0~200 V	±0.1%
Direct current	HSPY Co., DC-regulated power supply, Beijing, China	0~5 A	±0.5%
Temperature	Ou Chuang Co., T-type thermocouples, Hangzhou, China	−200~260 °C	±0.2 °C

. Using the method recommended by Kline [34], the calculation formula is shown below. The uncertainty of the indirect measurement parameters in the experiment is shown in

Table 2. Uncertainties of indirect experimental parameters.

Parameters	Uncertainties
Heat flux	±3.1%
Pressure gradient	±6.25%
Vapor quality	±3.2%
Boiling heat transfer coefficient	±7.49%

.

$$\delta R=\pm \sqrt{{\displaystyle \sum _{k=1}^n{\left(\frac{\delta R}{\partial x_k}\delta x_k\right)}^2}}$$

(8)

According to Equation (3), the uncertainty of the local boiling heat transfer coefficient can be calculated by the following formula:

$${\displaystyle \frac{\delta h}{h}}=\pm \sqrt{{\left({\displaystyle \frac{\delta q}{q}}\right)}^2+{\left({\displaystyle \frac{\delta \Delta T}{\Delta T}}\right)}_{\mathrm{wall}}^2}$$

(9)

After synthesizing various uncertainties, the uncertainty of the local boiling heat transfer coefficient is 7.49%.

2.5. Single-Phase Verification Experiment

In order to verify the reliability of the experimental system, the single-phase verification experiment of R290 in a 2 mm copper tube was experimentally studied. The accuracy of the whole experimental system is analyzed by comparing the single-phase experimental data with the empirical correlation. Figure 3 shows the variation trend of Nu with Re in the single-phase experiment, and the range of Re is 2000–12,000. The experimental results were compared with the predicted values of the Gnielinski correlation [35]. The results show that the Nu of the experiment is in good agreement with the prediction results of the empirical correlation, and the relative deviation is within 10%.

3. Experimental Results for the Boiling Heat Transfer Coefficient

Pure R290 and zeotropic refrigerants R290/R601a with mass fractions of 75/25, 50/50, and 30/70 were selected for the experimental study of boiling heat transfer. When the saturation pressure is 1 MPa and the vapor quality is 0.5, the temperature glide is 20.97 K, 31.31 K, and 31.81 K, respectively. The effects of mass fraction, mass flux, saturation pressure, vapor quality, and heat flux on the flow boiling heat transfer characteristics of R290/R601a were analyzed. The experimental conditions are shown in

Table 3. Experimental conditions.

Parameters	Ranges
Inner diameter	2 mm
Mass fractions of R290/R601a mixtures (by mass)	1/0; 0.75/0.25; 0.5/0.5; 0.3/0.7
Mass flux	100/200/300/400/500 kg/(m2·s)
Saturation pressure	1/1.25/1.5 MPa
Heat flux	20/30 kW/m2
vapor quality	0~1

.

3.1. Effect of Mass Fraction

Figure 4 shows the trend for the flow boiling heat transfer coefficient of R290/R601a with vapor quality under different mass fractions. Figure 4b shows the trend for boiling heat transfer coefficient with R290 mass fraction under a certain vapor quality. The experimental data show that the heat transfer coefficient of pure R290 is always higher than that of mixed refrigerants. The heat transfer coefficient of the mixed working fluid first decreases and then increases slightly with the decrease in R290 mass fractions. The main reason for this phenomenon is the dynamic competition between thermophysical properties and mass transfer resistance. Pure R290 has no mass transfer resistance, has high bubble formation and detachment efficiency, and nuclear boiling dominates heat transfer. When the mass fraction of R290 in the mixture decreases, the temperature glide increases. R290, with a lower boiling point, is more volatile, so that the content of R290 component in the liquid phase is reduced. The content of R601a at the vapor–liquid interface was significantly higher than that of R290. R290 needs to overcome the mass transfer resistance caused by the concentration gradient at the interface to evaporate, which inhibits the phase change heat transfer efficiency. However, with the increase in R290 mass fraction, the liquid viscosity of the mixture increases. This leads to an increase in the stability of the liquid film, delays the local drying phenomenon, and offsets the negative effects of some mass transfer resistance. According to Appendix A, it can be seen that the mixture with the low mass fraction of R290 (such as 0.3/0.7) has higher surface tension, which leads to the limitation of bubble coalescence and the enhancement of micro-scale flow disturbance. Finally, the heat transfer coefficient increased slightly. When the vapor quality is 0.13–0.17, the boiling heat transfer coefficient of R290/R601a (0.3/0.7) is 11.2% higher than that of R290/R601a (0.5/0.5).

3.2. Effect of Mass Flux and Vapor Quality

Figure 5 shows the trend in the flow boiling heat transfer coefficient of R290/R601a with vapor quality under different mass fluxes. It can be seen that the boiling heat transfer coefficient first increases and then decreases in the whole vapor quality range, and there is a dry vapor quality [26]. When the vapor quality value is less than the dry-out vapor quality, the boiling heat transfer is mainly dominated by nucleate boiling, and the boiling heat transfer coefficient increases slowly with the vapor quality. When the vapor quality value is greater than the drying vapor quality, the thickness of the liquid film decreases or even partially dries out. At this time, the working fluid flowing in the tube is mainly vapor phase, and the vapor phase heat transfer coefficient is lower than the liquid phase heat transfer coefficient, resulting in a rapid decrease in the boiling heat transfer coefficient. In addition, the boiling heat transfer coefficient increases with the increase in mass flux. This is attributed to the fact that the increase in mass flux will enhance the turbulent disturbance of vapor–liquid two-phase flow, which promotes the formation and detachment of bubbles, thus enhancing the heat transfer efficiency between the wall and the fluid. In addition, with the increase of mass flux, the dry-out vapor quality gradually tends to the direction of low vapor quality. Taking Figure 5b as an example, as the mass flux of R290/R601a (0.75/0.25) gradually increased from 200 kg/(m²·s) to 400 kg/(m²·s), the dry-out vapor quality decreased from 0.52 to 0.48, and finally to 0.24. This indicates that the phenomenon of instability or drying out of the liquid film occurs earlier under high-quality flux conditions. The mass flux significantly affects the boiling heat transfer performance by controlling the two-phase flow pattern and liquid film dynamic behavior. However, the difference in thermal properties and mass transfer resistance of the mixed working fluid aggravates the nonlinear variation of the heat transfer coefficient with vapor quality. The heat transfer coefficient of R290/R601a (0.75/0.25) increased by 9.7% on average when the mass flux increased by 100 kg/(m²·s).

3.3. Effect of Saturation Pressure

Figure 6 shows the trend in the flow boiling heat transfer coefficient of R290/R601a with vapor quality under different saturation pressures. The experimental data indicate that the boiling heat transfer coefficient of R290/R601a decreases overall with increasing saturation pressure (1–1.5 MPa), especially in the high vapor quality region. Li et al. [30] also observed a similar trend. The main reason for this phenomenon is that the increase in saturation pressure leads to the change in thermal properties of the working fluid: on the one hand, the liquid phase density decreases, the vapor phase density increases, and the two-phase velocity glide decreases, which weakens the disturbance of the vapor–liquid interface shear force on the liquid film, thereby reducing the turbulent heat transfer efficiency; on the other hand, the liquid thermal conductivity and latent heat decrease with the increase in saturation pressure, which further inhibits the phase change heat transfer performance. From Appendix A, the changing trend in the thermophysical properties of the working fluid can be more clearly seen. In addition, the increase in saturation pressure will directly affect the bubble behavior and flow pattern in the mini-channel. As the saturation pressure increases, the surface tension of the liquid phase decreases, resulting in a decrease in the bubble departure diameter and an increase in the bubble generation frequency [21]. However, the increase in liquid phase viscosity under high saturation pressure will hinder the timely replenishment of the liquid film after the bubble is detached, which will aggravate the local drying phenomenon. At the same time, the increase in saturation pressure reduces the vapor–liquid density ratio and weakens the stability of the annular flow liquid film, thus promoting the transition of the flow pattern to intermittent flow. This transition reduces the core region of effective boiling heat transfer and relies on unstable thin film evaporation for heat transfer. This explains the decrease in heat transfer coefficient under high saturation pressure. When the saturation pressure increases from 1 MPa to 1.5 MPa, the boiling heat transfer coefficient of R290/R601a (0.75/0.25) decreases by 9.4% on average.

3.4. Effect of Heat Flux

Figure 7 shows the trend in the boiling heat transfer coefficient of R290/R601 (0.75/0.25) with vapor quality under two different heat fluxes. From Figure 7, it can be seen that the boiling heat transfer coefficient of the mixed working fluid increases with the increase of heat flux before the dry-out point. This is because the increase in heat flux leads to a gradual increase in the superheat of the wall and an acceleration of the bubble formation rate before the drying point. Nuclear boiling is intensified, so the heat transfer coefficient of the flow boiling increases. However, the trend in the boiling heat transfer coefficient changing with heat flux is not obvious after the dry-out point. In addition, with the increase in heat flux, the dry-out point of R290/R601a (0.75/0.25) gradually tends in the direction of low vapor quality. Under the condition of saturation pressure of 1 MPa and mass flux of 300 kg/(m²·s), with the increase in heat flux of R290/R601a (0.75/0.25) from 20 kW/m² to 30 kW/m², the dry-out vapor quality decreases from 0.5 to 0.48. This is because the increase in heat flux will increase the superheat of the fluid, resulting in easier drying. In addition, the ability of the vapor to entrain droplets during the flow process is enhanced. The damage to the liquid film at the wall surface is increased, resulting in a decrease in the thickness of the liquid film. As a result, the dry-out point of zeotropic mixtures occurs in advance. When the heat flux increases from 20 kW/m² to 30 kW/m², the boiling heat transfer coefficient of R290/R601a (0.75/0.25) increases by 5.3% on average.

4. Prediction Correlation for the Boiling Heat Transfer Coefficient

4.1. Study on the Existing Correlation of the Boiling Heat Transfer Coefficient

Due to the complex boiling heat transfer process, there are many influencing factors. Therefore, there is little literature studying the boiling heat transfer correlation of mixed refrigerants. The existing flow boiling heat transfer correlations are usually developed based on three models: the superposition model, the asymptotic model, and the enhancement model [36]. To verify the prediction accuracy of the existing boiling heat transfer model for the boiling experimental data of zeotropic mixture R290/R601a, six commonly used semi-empirical boiling heat transfer correlations were selected from the published literature (Guo et al. [37], Dai et al. [26], Liu and Winterton [38], Zhang et al. [39], Choi et al. [40] and Shah et al. [41]).

Mean absolute relative deviation (MARD), mean relative deviation (MRD), and percentage of points calculated within the deviation bandwidth of ±30% (η_30%) were selected to evaluate the predictive power of existing correlations. The calculation methods for MARD and MRD are as follows:

$$\mathrm{MRD}={\displaystyle \frac{1}{n}}{\displaystyle \sum _1^n\left[\frac{h_{\mathrm{cal}}-h_{\exp }}{h_{\exp }}\right]}\times 100\%$$

(10)

$$\mathrm{MARD}={\displaystyle \frac{1}{\mathrm{n}}}{\displaystyle \sum _1^{\mathrm{n}}\left|\frac{h_{\mathrm{cal}}-h_{\exp }}{h_{\exp }}\right|}\times 100\%$$

(11)

The comparison results for the six boiling heat transfer correlations with the experimental data of R290/R601a can be found in Figure 8 and

Table 4. Comparisons of R290/R601a experimental data with existing correlations.

Correlations	MRD (%)	MARD (%)	η30% (%)
Guo et al. [37]	−24.3	26.55	63.81
Dai et al. [26]	39.16	47.99	35.24
Liu and Winterton [38]	2.78	28.83	53.33
Zhang et al. [39]	56.31	60.22	27.62
Choi et al. [40]	46.1	46.68	26.67
Shah et al. [41]	30.25	42.74	40

. The MARD of the six boiling heat transfer coefficient correlation formulas was greater than 30%. Among them, Guo et al. [37] and Liu and Winterton [38] have the best prediction results, with 63.81% and 53.33% data in the 30% error band, respectively. Both of their boiling heat transfer correlations adopt the asymptotic model. The model of Guo et al. [37] is modified based on the model of Liu and Winterton [38]. Their correlation can accurately predict the flat surface behavior and clearly distinguish the nuclear boiling and forced convection effects. However, there are not many data points in their database, and most of the working fluids are pure, so their applicability to zeotropic mixtures is poor. The models of Zhang et al. [39] and Choi et al. [40] have the worst prediction results, and data in the 30% error band is less than 30%. All adopted the superposition model. Zhang et al. [39] considered the effect of mass diffusion near the vapor–liquid interface on nucleate boiling and forced convection vaporization. Choi et al. [40] proposed a correction factor for heat transfer deterioration of zeotropic refrigerant mixtures. However, due to the limited types of experimental working fluids, the narrow range of experimental conditions, and the use of conventional channels in the test section of the experimental data, it is impossible to accurately predict the boiling heat transfer coefficient of zeotropic mixtures in mini-channels.

4.2. The Corrected Correlation of the Boiling Heat Transfer Coefficient

According to the results of Section 4.1, the prediction results of these six boiling heat transfer correlations are much lower than expected. It is necessary to propose a new correlation for the boiling heat transfer coefficient of the mixed refrigerant. Referring to the boiling heat transfer prediction correlation of Zhang et al. [42], 10 dimensionless numbers affecting the boiling heat transfer characteristics of the mixed refrigerant were subjected for multiple regression. Finally, the corrected correlation of the boiling heat transfer coefficient is obtained.

Temperature glide ΔT_glide and saturation temperature T_sat play important roles in the boiling heat transfer process. At higher saturation temperatures, nucleate boiling dominates. The dimensionless number T* is introduced, i.e., the ratio of temperature glide to saturation temperature:

$$T*={\displaystyle \frac{\Delta T_{\mathrm{glide}}}{T_{\mathrm{sat}}}}$$

(12)

To minimize the relative deviation of the predicted values, T* ≤ 0.06 is used to describe the accompanying process of nucleate and convective boiling, and T* > 0.06 to explain the dominant process of convective boiling. The boiling heat transfer correlation adopts the power-law notation, and the correlation is established by using a variety of dimensionless terms and multiple regression analysis. Then, the regression is improved based on two T* regions. After eliminating the dimensionless terms that do not improve the predictive ability of the correlation, the final correlation is as follows:

When T* ≤ 0.06,

$$h_{\mathrm{tp}}=3.66R{e}_{\mathrm{l}}^{1.134}R{e_{\mathrm{vo}}}^{-0.7}B{o}^{-0.128}F{r_{\mathrm{v}}}^{-0.3}T{*}^{2.053}Q{*}^{-2.372}C{o}^{-1.125}{F_{\mathrm{T}\mathrm{S}}}^{1.03}P{r_{\mathrm{l}}}^{5.31}p{r}^{3.51}\left({\displaystyle \frac{{\lambda }_{\mathrm{l}}}{d_{\mathrm{i}}}}\right)$$

(13)

When T* > 0.06,

$$h_{\mathrm{tp}}=2.55R{e_{\mathrm{l}}}^{0.845}R{e_{\mathrm{vo}}}^{-0.241}B{o}^{0.102}F{r_{\mathrm{v}}}^{-0.128}T{*}^{3.01}Q{*}^{-2.905}C{o}^{-0.785}{F_{\mathrm{T}\mathrm{S}}}^{-0.595}P{r_{\mathrm{l}}}^{4.061}p{r}^{2.087}\left({\displaystyle \frac{{\lambda }_{\mathrm{l}}}{d_{\mathrm{i}}}}\right)$$

(14)

where the Reynolds number Re_vo and Re_l denote the ratio of inertial force to viscous force in a fluid; reduced pressure pr is the ratio of saturation pressure to critical pressure; the vapor Froude number Fr_v is defined as the ratio of flow inertia to gravity field; the boiling number Bo represents the ratio of the mass rate of vapor produced per unit area to the mass flux, quantifying the intensity of the nuclear state boiling; the liquid Prandtl number Pr_l is the ratio of momentum diffusion rate to thermal diffusion rate in the liquid phase, indicating the effect of fluid properties on heat transfer; the dimensionless term Q* = C_pvT_s/H_lv represents the ratio of sensible heat to latent heat during the boiling process; the convection number Co reflects the effect of vapor–liquid two-phase ratio and density difference on heat transfer. Then, considering the effect of mass transfer resistance on bubble nucleation, the Thome–Shakir correction factor F_TS [43] was introduced to correct the contribution of nucleate boiling:

$$F_{\mathrm{TS}}={\left[1+{\displaystyle \frac{h_{\mathrm{id}}}{q}}\Delta T_{\mathrm{glide}}\left\{1-\exp \left(-{\displaystyle \frac{Bq}{{\rho }_{\mathrm{l}}{H}_{\mathrm{lv}}{\beta }_{\mathrm{l}}}}\right)\right\}\right]}^{-1}$$

(15)

where h_id is the ideal heat transfer coefficient of nuclear boiling, which is calculated by Cooper correlation [44]; B is the ratio of the latent heat transferred to the bubble interface, and B is assumed to be 1. It is assumed that all the heat transferred to the bubble interface is converted into latent heat. The liquid mass transfer coefficient β_l is a constant value of 0.0003 m/s [41]. The corrected correlation is compared with the experimental data of the R290/R601a mixture, and the results are shown in Figure 9. The corrected boiling heat transfer correlation has a more accurate prediction ability. The MARD of the model is 13.7%, and 93.27% of the experimental data are within the 30% deviation band.

4.3. Evaluation of the New Correlation of the Boiling Heat Transfer Coefficient

In order to objectively evaluate the prediction ability of the newly proposed correlation formula for boiling heat transfer coefficients, a total of 423 boiling heat transfer experimental data points were collected from three pieces of literature (Dai et al. [26], Li et al. [30] and Zhu et al. [45]). It can be seen from Figure 10 that the new boiling heat transfer correlation can predict well the experimental data points from the literature. The predicted MARD of all data is 15.62%, and 90.78% of the experimental data points are within the 30% deviation band.

Table 5. Comparison of experimental data in the literature with the new correlation.

Correlations	Data Points	Fluids	MARD (%)	η30% (%)
Dai et al. [26]	153	CO2/R152a	17.21	87.22
Li et al. [30]	90	R32/R1234yf	14.9	86.27
Zhu et al. [45]	180	CO2/R290	13.67	94.44
Total	423		15.62	90.78

shows the prediction results of the new boiling heat transfer coefficient correlation for the three pieces of literature.

5. Conclusions

In this paper, zeotropic working fluid R290/R601a is taken as the research object, and the flow boiling heat transfer phenomenon in a horizontal mini-channel with an inner diameter of 2 mm is experimentally studied. In the experiment, the saturation pressure range is 1 to 1.5 MPa, the mass flux is 100 to 500 kg/(m²·s), the heat flux is 20 to 30 kW/m², and the vapor quality range is 0 to 1. The effects of mass fraction, mass flux, saturation pressure, heat flux, and vapor quality on the boiling heat transfer coefficient were analyzed in detail. Then, the prediction ability of the six selected correlations of the boiling heat transfer coefficient was evaluated. A new correlation of the boiling heat transfer coefficient is proposed. The following conclusions can be drawn from this study:

• The boiling heat transfer coefficient of R290/R601a first decreases and then increases with the decrease in R290 mass fraction, which is mainly affected by thermophysical properties and mass transfer resistance. Due to the thinning of the liquid film during the boiling heat transfer process, there will be a dry-out point. The boiling heat transfer coefficient will first increase and then decrease with the increase in vapor quality. With the increase in mass flux and heat flux, the dry-out point will gradually shift in the direction of low vapor quality. In addition, the boiling heat transfer coefficient will increase with the increase in mass flux and heat flux, and decrease with the increase in saturation pressure.
• The boiling heat transfer experimental data of R290/R601a were compared with the predicted results of six known boiling heat transfer coefficient correlations. The prediction results for the six boiling heat transfer coefficient correlations are lower than expected. Among them, the asymptotic models of Guo et al. [37] and Liu and Winterton [38] have the best prediction effect, and the mean absolute relative deviation is 26.55% and 28.83%.
• Then, the correlation of the mixed boiling heat transfer coefficient is modified, mainly referring to the boiling heat transfer prediction correlation of Zhang et al. [42]. The dimensionless number affecting the boiling heat transfer characteristics of the mixture was subjected to multiple regression and fitted with the experimental data of R290/R601a. The corrected boiling heat transfer correlation has a more accurate prediction ability. The MARD of the model is 13.7%, and 93.27% of the experimental data deviation is within the 30% deviation band. Finally, to verify the applicability of the new boiling heat transfer coefficient correlation, it is necessary to select data from the literature to establish a database. The new correlation of the boiling heat transfer coefficient has a good prediction effect on the database. The MARD is 15.62%, and 90.78% of the experimental data points are within the 30% deviation band.

There are still many aspects to be studied in this work. In the future, it may be necessary to carry out experimental research on the heat transfer characteristics of enhanced tubes. The liquid phase accumulation problem and component migration mechanism of the mixture under different flow patterns can also be discussed, and the influence of component migration on phase change heat transfer can be analyzed in depth. For the test section of the mini-channel, the frictional pressure drop will affect its heat transfer characteristics. It is necessary to find the relative relationship between frictional pressure drop and heat transfer.