Boiling and Condensing Two-Phase Frictional Pressure Drop Within Minichannel Tubes—Comparison and New Model Development Based on Experimental Measurements

Abstract

This study presents a comprehensive experimental investigation into the frictional pressure drop of two-phase flows—boiling and condensation—in horizontal minichannels, emphasizing its impact on the energy efficiency of vapor compression systems. A total of 3553 data points were obtained using six low-GWP refrigerants (R32, R134a, R290, R410A, R513A, and R1234yf) across a wide range of operating conditions in multiport aluminum tubes with hydraulic diameters of 0.715 mm and 1.16 mm. The dataset covers mass fluxes from 200 to 1230 $\mathrm{kg}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$, saturation temperatures between 5 °C and 55 °C, and vapor qualities from 0.05 to 0.95. Results showed a strong dependence of frictional pressure gradient on vapor quality, mass flux, and channel size. Boiling flows generated higher frictional losses than condensation, and high-density refrigerants such as R32 exhibited the largest pressure penalties, which can directly translate into increased compressor power demand. Conversely, higher saturation temperatures were associated with lower frictional losses, highlighting the role of thermophysical properties in improving energy performance. Additionally, an inverse correlation between saturation temperature and frictional pressure gradient was observed, attributed to variations in thermophysical properties such as viscosity and surface tension. Existing correlations from the literature were assessed against the experimental dataset, with notable deviations observed in several cases, particularly for R134a under high-quality conditions. Consequently, a new empirical correlation was developed for predicting the frictional pressure drop in two-phase flow through minichannels. The proposed model, formulated using a power-law regression approach and incorporating dimensionless parameters, achieved better agreement with the experimental data, reducing prediction error to within ±20%, improving the accuracy for the majority of cases. This work provides a robust and validated dataset for the development and benchmarking of predictive models in compact heat exchanger design. By enabling the more precise estimation of two-phase pressure drops in compact heat exchangers, the findings support the design of refrigeration, air-conditioning, and heat pump systems with minimized flow resistance and reduced auxiliary energy consumption. This contributes to lowering compressor workload, improving coefficient of performance (COP), and it ultimately advances the development of next-generation cooling technologies with enhanced energy efficiency.

1. Introduction

Refrigerants play a central role in a wide range of engineering and scientific applications, owing to their favorable thermophysical properties, such as low critical temperature, pressure, and boiling point. Nevertheless, many conventional refrigerants are associated with high global warming potential (GWP) and ozone depletion potential (ODP), raising serious environmental concerns. As a result, increasing research efforts have been directed toward the identification and development of alternative refrigerants that combine environmental sustainability with long-term applicability in heating and cooling systems.

The accurate estimation of two-phase frictional pressure drop is a cornerstone in the design of compact heat exchangers, particularly in systems employing minichannel configurations. Given their reduced hydraulic diameter and high surface-area-to-volume ratio, these devices offer enhanced heat transfer performance, but at the cost of elevated pressure losses that can significantly reduce the system’s overall thermal performance and increase energy consumption. The incorrect estimation of pressure drop can lead either to undersized equipment—resulting in excessive compressor or pump loads—or to oversized systems with increased capital cost, footprint, and refrigerant charge. Therefore, accurate predictive tools are essential for optimizing thermal performance while minimizing parasitic power consumption, as per Zu et al. [1].

In this context, Hontoria et al. [2], applied a multi-criteria decision-making (MCDM) approach to identify the most influential variables affecting pressure drop and heat transfer in minichannels. Their findings emphasize that thermophysical properties, flow regime, and geometric characteristics must be jointly considered to improve system design and operational efficiency. More recently, Calleja-Cayón et al. [3] analyzed mechanical vapor compression cycles in zero liquid discharge desalination systems and highlighted the role of precise pressure drop modeling in optimizing energy use. In particular, they showed that refined hydraulic modeling directly improves the performance of compression subsystems, which are typically the largest energy consumers in thermal systems.

Complementary studies have highlighted the need to integrate experimentally validated pressure drop correlations into simulation and design methodologies. For example, Xu et al. [4] numerically investigated flow distribution in the header of a microchannel heat exchanger, identifying appropriate void fraction, two-phase flow, and turbulence models through the direct comparison of simulation outcomes with experimental data. On the other hand, through the numerical modeling of electric vehicle battery cooling systems, it was found that deviations in pressure loss estimation can propagate into significant errors in cooling capacity and COP calculations. These findings reinforce the practical value of the empirical correlation developed in this work, which has been validated across multiple refrigerants, flow regimes, and geometries. The model enables more accurate thermal-hydraulic predictions in compact evaporators and condensers and supports better-informed decisions regarding compressor sizing, component matching, and overall energy performance.

By integrating this model into the design process, engineers can reduce the uncertainty associated with frictional losses and unlock the full energy-saving potential of minichannel technology. This is particularly relevant in the context of energy-intensive applications such as refrigeration, air conditioning, and water desalination. Such improvements in heat transfer behavior can lead to substantial reductions in primary energy demand for cooling and heating systems, where improvements in thermal efficiency translate directly into lower operating costs and reduced environmental impact.

Since the 1830s, when Parkin proposed the first vapor compression cycle employing ether as a refrigerant, a wide range of chemical substances have been evaluated as working fluids. While natural fluids were initially adopted, they were largely replaced in the 1930s by synthetic compounds specifically developed for refrigeration applications. By the 1970s, however, the detrimental impact of chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) on the ozone layer led to the signing of the Montreal Protocol, which mandated their gradual phase-out and required the use of refrigerants with zero ozone depletion potential. In the 1990s, hydrofluorocarbons (HFCs) emerged as substitutes for CFCs and HCFCs, but their high global warming potential raised new concerns in the context of greenhouse gas emissions, prompting the establishment of the Kyoto Protocol. More recently, the Kigali Amendment to the Montreal Protocol was introduced to progressively reduce the use of HFCs and further mitigate their climate impact.

The utilization of minichannels in refrigeration applications has attracted significant attention in recent years due to their potential to enhance system performance and efficiency. Their small hydraulic diameters increase the heat transfer surface-to-volume ratio, leading to intensified phase-change processes. However, these benefits are often accompanied by higher frictional pressure drops, making accurate predictive models essential for system design and optimization. Recent research has improved our understanding of phase-change heat transfer in minichannels. Liu et al. [5] looked at condensate removal and heat transfer performance of a minichannel heat exchanger working as an evaporator. They demonstrated how air velocity and humidity affect condensate buildup and thermal performance. Rafałko et al. [6] performed high-speed image analysis of boiling synchronization in two parallel 1 mm minichannels. They revealed flow instabilities that impact boiling dynamics. Kuczyński et al. [7] presented a model for the dynamic instabilities during the condensation of R1234yf and R1234ze in minichannels. This model predicts refrigerant phase-change behavior. Piasecka et al. [8] visualized flow structures during condensation of HFE 7000, HFE 7100, and Novec 649 refrigerants in minichannels (0.5–2.5 mm). They produced original flow regime maps based on void fraction and vapor quality. Together, these studies provide experimental, numerical, and modeling insights on evaporation and condensation in minichannel environments. We contribute to previous studies [9,10,11] by enlarging the experimental database to 3553 points, covering six low-GWP refrigerants, two minichannel geometries, and an extended range of saturation temperatures. Unlike our earlier publications, which treated evaporation and condensation separately, the present study proposes a unified correlation for two-phase frictional pressure drop valid for both boiling and condensation regimes, thereby providing a broader and more general predictive tool.

Two-Phases Pressure Drop Correlations for Minichannels

Minichannels have become increasingly relevant in refrigeration and heat transfer applications, where their compact geometry offers enhanced heat transfer performance but also introduces significant hydraulic challenges. Consequently, numerous studies have investigated their thermal–hydraulic behavior, leading to the development of various correlations and models. The following section summarizes the most relevant works in this area and identifies the specific research gap addressed in the present study.

Arcasi et al. [12] carried out an experimental investigation on the flow boiling heat transfer, pressure drop, and dry-out vapor quality of the low-GWP, non-azeotropic mixture R454C. Tests were performed in a smooth horizontal stainless-steel tube, assessing the influence of operating parameters such as mass flux, heat flux, and saturation pressure. Results indicated that both mass flux and heat flux enhanced the boiling heat transfer coefficient, whereas higher saturation pressure had a detrimental effect. Pressure drop was observed to increase with mass flux and heat flux, but to decrease with saturation pressure. Furthermore, dry-out vapor quality was shown to be strongly dependent on these parameters, with higher operating values leading to earlier onset of dry-out.

Similarly, Jige et al. [13] analyzed the condensation heat transfer and frictional pressure drop of the zeotropic mixture R32/R1123 inside two horizontal multiport extruded tubes of different geometries. The experiments, conducted at a mean saturation temperature of 40 °C, covered a wide range of mass fluxes, vapor qualities, heat fluxes, and channel shapes. By comparing the performance of R32/R1123 with pure R32, the authors reported that the mixture exhibited a lower heat transfer coefficient across all operating conditions, while frictional pressure drops were reduced by 20–30%. The experimental results aligned well with previous studies, with an average deviation of 17%. Additionally, the condensation heat transfer of the mixture was predictable within a mean deviation of −5.2% using existing correlations that account for temperature glide, offering valuable insights into the effects of operating conditions and geometry on mixture performance in minichannels.

Manova et al. [14] proposed a novel multiport minichannel (MPMC) thermosyphon design, using acetone as the working fluid, for the cooling of high heat flux electronic devices. The configuration, featuring 10 internal ports, was benchmarked against single-port cylindrical and flat minichannels. The experimental study examined the influence of heat load, filling ratio, and tilt angle on thermal performance. A 50% filling ratio yielded optimal results, reducing evaporator wall temperature by 9.31% and thermal resistance by 22.2%. The multiport structure promoted more effective condensation by enhancing surface tension effects transverse to the flow direction. In a related study, the same authors evaluated an air-cooled MPMC thermosyphon (10 ports, 1.18 mm hydraulic diameter), testing various heat loads (10–90 W), filling ratios (40–60%), inclination angles (30–90°), confluence lengths (0–10 mm), and airflow velocities (0.8–1.5 m/s), with acetone as the working fluid. A maximum heat dissipation of 90 W was achieved with an evaporator wall temperature of 72.2 °C at a 5 mm confluence length. The multiport configuration, acting as internal fins, increased surface area and enhanced boiling and evaporation, which reduced thermal resistance and wall temperature. At optimal conditions, irreversibility in heat transfer was reduced by 17.1% and pressure drop by 48.2%. Incorporating liquid reservoirs at both ends mitigated entrainment issues and prevented dry-out, while flow visualization revealed transitions between slug and geyser regimes. These findings provide key design guidance for thermal management in miniaturized electronics.

Varinder Singh et al. [15] explored the condensation heat transfer of R134a and R410A in rectangular, parallel microchannels with hydraulic diameters between 0.66 and 1 mm. Three geometries (MC-1, MC-2, and MC-3) with aspect ratios of 0.5, 0.7, and 1.0, respectively, were tested under mass fluxes of 200–600 kg/(m² s), vapor qualities of 0.05–0.83, and saturation temperatures of 30 °C and 40 °C. The results showed that condensation HTC increased with mass flux and vapor quality but decreased with higher saturation temperature. R134a consistently provided higher condensation HTC than R410A, and among the geometries, the lowest aspect ratio (MC-1) performed best. A new correlation for condensation HTC in microchannels was developed, achieving good agreement with experimental data (MAE = 5.40%) and predicted values within ±20%, thereby extending the predictive capabilities beyond existing conventional-channel correlations.

Nalbandian et al. [16] studied the flow boiling heat transfer of HFO-1234yf and HFC-134a in microchannel heat exchangers (0.5 mm channel size) employing extruded flat aluminum tubes, typical of automotive air-conditioning systems. The study aimed to assess the potential of HFO-1234yf as a low-GWP substitute for HFC-134a. Results showed that HFC-134a exhibited heat transfer coefficients up to 22% higher than HFO-1234yf depending on operating conditions. When compared to predictive models, the correlation of Kandlikar and Balasubramanian [17] provided the best agreement with the experimental data. Moreover, it was observed that the key properties governing flow boiling HTC in microchannels resemble those in larger circular tubes, being primarily dependent on two-phase flow patterns.

Kuczynski et al. [18] developed a regressive model to describe dynamic pressure and temperature instabilities during the condensation of R134a and HFO isomers R1234yf and R1234ze(E) in minichannels. Based on a Buckingham theorem–driven dimensional analysis, the model linked instability propagation velocities to acoustic speed and condensation front velocity. Validation was carried out with experiments on tubes with circular cross-sections and hydraulic diameters ranging from 1.40 to 3.30 mm. The model predictions showed satisfactory agreement within ±25% of experimental data, demonstrating its potential for accurately describing transient instabilities in confined geometries.

Azolin and Bortolin [19] examined HFC/HFO refrigerant blends as alternatives to high-GWP fluids in air-conditioning and refrigeration systems. Using a circular minichannel (0.96 mm diameter), condensation and flow boiling tests were conducted on an R32/R1234ze(E) blend (0.75/0.25 mass fraction). Condensation experiments at 21.8 bar and boiling tests at 17 bar revealed significant heat transfer penalization due to mass transfer resistance and temperature glide. Experimental results were benchmarked against data for pure fluids and other blend compositions. Comparisons with correlations demonstrated the need for improved predictive tools for such mixtures in confined geometries.

Overall, the reviewed studies confirm the sensitivity of pressure drop in minichannels to refrigerant properties, vapor quality, mass flux, and channel geometry. However, most existing correlations remain fluid-specific, geometry-dependent, or limited to either boiling or condensation regimes. Their predictive accuracy decreases significantly when applied to low-GWP refrigerants under broader operating conditions. This gap highlights the need for a unified and experimentally validated correlation capable of accurately predicting frictional pressure drop for both boiling and condensation in compact geometries. Addressing this limitation is the main contribution of the present study.

2. Description of the Experimental Installations

To study the processes of evaporation and condensation inside minichannels, two different installations had to be constructed at the Technical University of Cartagena. Both installations are located in the Laboratories Building and can operate simultaneously as they are fully instrumented. The following sections provide a detailed description of these installations, as well as their test sections. The interested reader can obtain further information in [9,10,11].

2.1. Boiling Installation

The experimental setup was developed to study flow boiling heat transfer and the associated two-phase pressure drop. The system operates by applying controlled AC electrical heating to a horizontally oriented multiport extruded aluminum tube. A schematic of the facility is provided in Figure 1. The installation is organized into three interconnected loops. The first loop (L1) is the refrigerant loop, which contains the test section. The second loop (L2) is a secondary circuit responsible for heat removal via a plate heat exchanger (7), using a 50% water–glycol solution. The third loop (L3), also employing a water–glycol mixture, is dedicated to regulating the overall system pressure. The inclusion of L2 and L3 provides the independent control of thermal conditions (temperature) and inlet pressure at the test section, ensuring flexibility and accuracy in experimental operation.

As seen in Figure 1, the refrigerant tank (1), which is, in fact, a shell and tube heat exchanger used in the refrigerant tank, contains approximately 3.5 L of liquid refrigerant. With the amount of energy removed with the water–glycol loop (L3), the pressure of the test rig is controlled. The magnetic gear pump (2) (10–2640 mL/min, 0.75 kW) is employed to circulate the refrigerant throughout the entire loop (L1). The pump is controlled by a commercial PID system connected to an AC variable frequency drive, with the refrigerant mass flow serving as the objective parameter. The refrigerant mass flow rate is measured using a Coriolis-type flow meter (3).

The subcooled coolant enters the test section (5), where the coolant receives a uniform heat output across the tube wall. This uniform heat output is produced by the heat generated by the Joule effect of the electric current passing through the tube from the two brass electrodes connected to the inlet and outlet headers of the test section. The effective heated length of the tube was 1.205 m, corresponding to the active boiling test section. The resulting saturated liquid–vapor mixture of refrigerant exits the test section and is subsequently condensed in the plate heat exchanger (7) using the water–glycol mixture previously mentioned. The experimental conditions at the test section inlet are controlled as follows: the refrigerant temperature is controlled by the pair of temperature and mass flow rate of water–glycol mixture in loop (L2) and the inlet test section pressure is controlled by the pair of temperature and mass flow rate of the water–glycol mixture of loop (L3).

Refrigerant temperatures are measured at the inlet and outlet of the test section using 3 mm diameter resistive temperature detector Pt100 sensors with an accuracy of ±0.03 °C. The wall temperature on the external surface of the tube is measured by fifteen 0.5 mm diameter T-type thermocouples, with an accuracy of ±0.5 °C. These thermocouples are directly affixed to the tube’s external wall using thermally conductive paste, with a layer of electrical insulating polypropylene tape of 20 µm separating the thermocouple junctions from the multiport tube’s external wall. The thermocouples are distributed along the tube wall as follows: the first thermocouple is positioned 10 cm from the inlet header, and the subsequent thermocouples are placed 7 cm apart from each other. The pressure at the inlet (PT) of the test section is measured using an absolute pressure transmitter, which is connected to a pressure port machined at the inlet header. The measurement range for all tested refrigerants was set at [0–32] bar. A differential pressure transmitter is utilized to measure the pressure drop (Dp) along the test section, with its range configured at [0–2] bar. Both transmitters have an accuracy below 0.09%. These accuracies correspond to the manufacturer’s specifications and are expressed as a percentage of the full scale (FS). Accordingly, the absolute transmitter (0–32 bar) had an accuracy of ±0.09% FS (±0.029 bar), and the differential transmitter (0–2 bar) had an accuracy of ±0.09% FS (±0.0018 bar).

Each test was conducted by fixing the following three variables: heat flux, mass flow rate, and system pressure. The tests were carried out with varying mass flow rates while keeping the remaining parameters constant. In order to increase the thermodynamic vapor quality, the mass flow rate was gradually decreased. A steady state for each operating point was declared when, over a 1200 s monitoring interval, the following thresholds were simultaneously satisfied: saturation temperature (or pressure) drift $<\pm 0.1\mathrm{K}$ (approximately <$\pm 5\mathrm{kPa}$), mass flux variation $<\pm 1\%$, electrical power (heat flux) variation $<\pm 1\%$, inlet subcooling/superheat variation $<\pm 0.2\mathrm{K}$, vapor quality drift $<\pm 0.01$ (absolute), and frictional pressure gradient variation $<\pm 0.5\%$. Once these conditions were met, signals were recorded for 120 s and time-averaged. Tests not fulfilling these criteria were extended or discarded. The mass flow rate was progressively reduced until the minimum tested value was reached. A Labview® state machine programme was used to monitor and modify all the variables defining each test. All temperature sensors, differential and absolute pressure transmitters, as well as voltage and electrical current measurements, are connected to two 20-channel armature multiplexers, connected to an Agilent data logger 34972A. Data are recorded every 30 s, with a steady-state sample of 20 min recorded for all measured variables.

2.2. Condensing Installation

The first of the experimental installations was specifically designed to study condensation processes within tubes. The experimental facility included one main refrigerant loop and three auxiliary circuits (two with cooling water and one with hot water). For simplicity, Figure 2 shows only the refrigerant circuit. The subcooled refrigerant from the condenser (1) is directed into a tank (2). A controlled gear pump (3) is connected to this tank and is magnetically coupled to a variable speed electric motor. During the condensation measurements, the fluid is pumped through the Coriolis-effect mass flow meter (4) and the evaporator (5), where the refrigerant vaporizes until it reaches the desired vapor quality. The evaporator (5) and the condenser (1) are both plate heat exchangers. The Coriolis-effect (4) flow meter mentioned earlier also allows for refrigerant density and mass flow rate readings to be obtained. Following its passage through the evaporator, the two-phase mixture flows through a 10-centimeter copper tube to the inlet header (6). It is assumed that a uniform two-phase flow is established in the copper section before entering the measuring section via the inlet header. Although this assumption is an approximation, it is a commonly adopted practice in similar experimental setups [20,21,22]. These references provide evidence of experimental test sections resembling the section being tested. In the measuring section, only partial condensation of the refrigerant occurs, and the variation in vapor quality remained under 0.08 in all runs. The condensing measuring section had a length of 259 mm, complemented by two additional adiabatic sections of 23.5 mm located within the inlet and outlet headers. In the measuring section, only partial condensation of the refrigerant occurs, and the variation in vapor quality remained under 0.08 in all runs. After passing the outlet header, the fluid was directed back to the condenser, where the circulation started again. A steady state for each operating point was declared when, over a 1200 s monitoring interval, the following thresholds were simultaneously satisfied: saturation temperature (or pressure) drift $<\pm 0.1\mathrm{K}$ (approximately <$\pm 5\mathrm{kPa}$), mass flux variation $<\pm 1\%$, electrical power (heat flux) variation $<\pm 1\%$, inlet subcooling/superheat variation $<\pm 0.2\mathrm{K}$, vapor quality drift $<\pm 0.01$ (absolute), and frictional pressure gradient variation $<\pm 0.5\%$. Once these conditions were met, signals were recorded for 1200 s and time-averaged. Tests not fulfilling these criteria were extended or discarded. All variables were recorded with an Agilent data logger 34972A with three 20-channel armature multiplexers. Steady state is controlled with a specifically programmed control system using the analog inputs and outputs of a National Instruments NI6229 PCI Card in a PC.

In condensation tests, two thermal baths are used. The first bath supplies the hot water used to heat the evaporator through the Joule effect, while the second bath feeds the measuring section and the condenser after the test section with cold water. The temperature of these two circuits can be set independently by means of two mixing valves. The inlet pressure of the test section is regulated by adjusting the energy removal in the condenser. The main tank serves as a two-phase reservoir, and the vapor phase pressure is utilized to control the system pressure. The amount of refrigerant charge is carefully determined to prevent the vapor phase from being suctioned by the pump. An electronic control system ensures steady-state conditions and the accuracy of the measurements. Pressure measurements are acquired using the following two digital pressure transducers: an absolute pressure sensor (PT) connected to the pressure port machined in the inlet header and a differential pressure sensor (Dp) linked to the outlet header. The range of the differential pressure sensor range is fixed at 0 to 1 bar. The uncertainty of the differential sensor is below 0.09%, and for both absolute sensors, it is below 0.08%. These values are also specified as percentages of the full scale (FS). For the condensation facility, the absolute transmitter was configured with a full-scale range of 40 bar absolute, resulting in an accuracy of ±0.08% FS (±0.032 bar). The differential transmitter (0–1 bar) had an accuracy of ±0.09% FS (±0.0009 bar). The overall accuracy also takes into account the precision of the data logger used to record the sensor measurements. Further details can be found in [9,10]

2.3. Test Section Geometries and Experimental Conditions

Two different geometries were tested in the installations described in the previous sections. The main geometric parameters of both multiport extruded tubes are presented in

Table 1. Geometrical parameters of the tested tubes.

Parameter	Triangular Ports	Square Ports
Hydraulic diameter (mm)	0.715	1.16
Free flow area (mm2)	10.16	1.54
Inner perimeter (mm)	57.04	43.23
Outer perimeter (mm)	40.17	40.17
Number of ports	19	10
Roughness (μm)	0.262	0.226

. The range of thermodynamic parameters modified while performing the condensing and boiling two-phase flow test are summarized in

Table 2. Experimental conditions.

Parameter	Boiling	Condensation
Refrigerants	R32, R134a	R32, R134a, R290, R410A, R513a, R1234yf
G (${\mathrm{kg}/\mathrm{m}}^2\mathrm{s}$)	270–1230	200–900
$T_{saturation}$ (°C)	5, 7.5, 10, 12.5	30, 35, 40, 45, 50, 55
x (kg/kg)	0.05–0.95	0.06–0.92
$D_h$ (mm)	0.715	0.715, 1.16
Test section length (mm)	1205	259
Roughness (μm)	0.262	0.262, 0.226
Pressure drop data	350	3203

For condensation tests, the 259 mm length corresponds to the measuring section; two additional adiabatic sections of 23.5 mm are located in the headers.

. The images obtained with an optical microscope to perform geometrical measurements of the hydraulic diameter, free flow area, and parimeters can be seen in Figure 3.

3. Frictional Pressure Drop Calculation

The pressure drop in a two-phase system is composed of three components: frictional losses, effects due to gravity, and those arising from acceleration. In the case of horizontal flow, the gravitational pressure gradient is zero. The acceleration pressure gradient can be estimated using Equations (4) and (5). There is no change in the cross-sectional area between the outlet section of the evaporator, the copper tube section, and the inlet header. However, there is a contraction and expansion process between the inlet and outlet headers and the multiport minichannel tube. The frictional pressure gradient in the two-phase flow is calculated by subtracting the acceleration and accessories pressure gradients from the measured experimental pressure gradient. The calculation of the acceleration pressure gradient is determined by the Equation (5), $\alpha$ denotes the void fraction. Several correlations exist in the literature to estimate void fraction; among them, Zivi’s [23] approach is most frequently adopted when the homogeneous mixture model is employed. The dimensionless groups used in the regression analysis are defined as follows. The Reynolds number of the liquid phase is given by the following:

$$R{e}_{liq}={\displaystyle \frac{G(1-x)D_h}{{\mu }_{liq}}},$$

(1)

which represents the ratio of inertial to viscous forces. The Weber number is defined as follows:

$$W{e}_{liq}={\displaystyle \frac{{\left(G(1-x)\right)}^2}{\sigma {\rho }_{liq}}},$$

(2)

which accounts for the relative importance of inertia and surface tension forces. Finally, the Lockhart–Martinelli parameter is expressed as follows:

$$X_{Martinelli}=\sqrt{{\displaystyle \frac{{\left(\frac{dp}{dz}\right)}_{liq}}{{\left(\frac{dp}{dz}\right)}_{gas}}}},$$

(3)

which compares the pressure gradients of the liquid and vapor phases. These parameters are subsequently employed in the development of the regression Formulas (6) and (8). Here, x is defined as the vapor quality, i.e., the mass fraction of vapor in the mixture, and therefore $(1-x)$ represents the liquid mass fraction. In this way, the dimensionless numbers are evaluated using the superficial mass flux of the liquid phase instead of the total mass flux.

The calculation of expansion and contraction pressure drop in the accessories pressure gradient takes into account the models proposed by Coleman and Krause [24] for sudden contraction losses and Schmidt and Friedel [25] for sudden expansion losses in two-phase flows. For single-phase flows, the models used were those of Kays and London [26] and Abdelall et al. [27].

$$\begin{array}{c}-{\left({\displaystyle \frac{dp}{dz}}\right)}_{2ph}=-{\left({\displaystyle \frac{dp}{dz}}\right)}_g-{\left({\displaystyle \frac{dp}{dz}}\right)}_f-{\left({\displaystyle \frac{dp}{dz}}\right)}_{ac}-{\left({\displaystyle \frac{dp}{dz}}\right)}_{acc}\end{array}$$

(4)

$$\begin{array}{c}-{\left({\displaystyle \frac{dp}{dz}}\right)}_{ac}=G^2·{\displaystyle \frac{d}{dz}}·\left[{\displaystyle \frac{x^2}{\alpha ·{\rho }_{gas}}}+{\displaystyle \frac{(1-x^2)}{(1-\alpha )·{\rho }_{liq}}}\right]\end{array}$$

(5)

The frictional pressure gradient was not measured directly but obtained from the differential pressure across the test section. For the condensation facility, the average gradient was calculated as the measured differential pressure divided by the effective length of the condensing section (259 mm). Owing to the relatively small variation of vapor quality along this short section, the average value is representative of the local behavior. For the boiling facility, with a longer test section (1205 mm), the onset of two-phase flow was determined from the imposed heat balance, and the single-phase liquid pressure drop up to this location was estimated. The two-phase contribution was then obtained by subtracting the calculated single-phase drop from the total differential pressure. In this way, the reported gradients correspond to the effective two-phase portion of the test section and represent average values over the region where vapor is present.

Uncertainty Analysis

Since the parameters of interest such as vapor quality or mass velocity are not directly measured, it is imperative to conduct an analysis of the uncertainties associated with the direct measurements and derived calculations in order to assess their accuracy. In accordance with this objective, the guidelines outlined in [28] were followed to calculate the uncertainty associated with all the measurements performed.

Table 3. Relative uncertainties (expressed as percentages of the measured value) of the main experimental parameters.

Fluid	Parameter
	Vapor Quality	Saturation Pressure	Frictional Pressure Gradient
R32	2.3–12.67	1.6–3.33	1.17–19.23
R134a	3.34–18.61	1.51–3.68	0.99–14.44
R290	1.75–14.75	1.35–2.78	1.48–13.34
R410A	2.4–17.53	1.57–3.28	1.23–15.21
R513a	2.01–14.95	1.63–3.88	1.17–17.44
R1234yf	4.3–15.09	1.64–5.92	0.87–18.36

displays the uncertainty ranges for the variables of interest in this study. As indicated in Table 3, all values are expressed as percentages relative to the measured variable. The highest relative uncertainty corresponds to the frictional pressure gradient, mainly due to the propagation of errors from absolute and differential pressure measurements coupled with heat balance over the entire installation and test sections. The uncertainties of the measured variables are primarily determined by the nature of the measurement process. While the saturation pressure is directly obtained from an absolute pressure transducer, other variables such as the frictional pressure gradient or the vapor quality result from mathematical derivations, where error propagation can significantly amplify the measurement uncertainty under certain conditions. A detailed analysis of the dataset shows that only a minority of points exhibit uncertainties greater than 13%; specifically, fewer than 6% of all data fall within this range, typically under conditions of very low pressure drop close to the resolution limit of the differential transducer. In contrast, more than 94% of the measurements present uncertainties below 10%, and over 70% are below 5%. To avoid overcrowding the figures with error bars, a histogram of the uncertainty distribution for the frictional pressure gradient is provided giving readers a clear overview of the spread of uncertainties across the database in Figure 4. In addition to pressure drop, the uncertainty associated with the vapor quality determination also deserves attention. As shown in Table 3, maximum relative uncertainties in vapor quality reached values up to 17.53%, mainly for R410A and 18.61% for R134a at the highest saturation temperatures and lowest mass fluxes. These conditions amplify the effect of small measurement errors in temperature, mass flow rate, and heat balance closure, which are used to calculate inlet and outlet enthalpies. Nevertheless, the distribution analysis indicates that most of the vapor quality data exhibit uncertainties well below 10%, with more than 65% of the points within 5%. Similar to the case of the pressure gradient as shown in Figure 5. These higher relative uncertainties are confined to a limited subset of data near the resolution limits of the instrumentation.

4. Experimental Measurements and Models Comparison

In this section, the experimental measurements obtained in both evaporation and condensation processes are presented. The behaviors of the two-phase pressure drop are analyzed in relation to the other variables that influence heat exchange processes in condensation and evaporation, such as mass flow rate, vapor quality, refrigerant fluid, and saturation pressure. Additionally, the results of predictions made using various models available in the open literature are also presented.

4.1. Boiling Experimental Data

Experiments were carried out with two different refrigerants (R134a and R32) in boiling tests and one geometry, at saturation temperatures of 5, 7.5, 10, and 12.5 degrees Celsius. Figure 6, Figure 7 and Figure 8 present the friction gradient measurements against the vapor quality at saturation temperatures of 5, 7.5 and 10 °C. The experiments indicated that greater mass flux and higher vapor quality consistently produced an increase in the two-phase pressure gradient. The images also show the decrease of frictional pressure gradient as the saturation temperature increases. This is also depicted in Figure 9 for a fixed value of mass velocity and different saturation temperatures.

Regarding the influence of vapor quality and mass velocity, the experimental data (Figure 6, Figure 7 and Figure 8) show a strong dependence of the frictional pressure gradient on vapor quality. At all saturation temperatures and for both refrigerants, an increase in vapor quality leads to a marked rise in frictional pressure drop. This behavior is consistent with the transition from liquid-dominated to vapor-dominated flow regimes, where shear stresses increase due to enhanced interfacial interaction and phase velocity differences. Such trends are expected in minichannel configurations, where confined geometries amplify wall and interfacial friction effects [20,22]. Similarly, increasing mass velocity also results in higher pressure gradients, as higher inertia contributes to elevated shear forces along the channel walls. The pressure drop scales approximately with the square of the mass velocity, as predicted by classical two-phase flow models. This effect becomes more pronounced at high vapor qualities, where the vapor phase’s contribution to momentum is more significant.

On the other hand, the influence of saturation temperature is illustrated in Figure 9. For constant mass velocity and heat input, raising the saturation temperature was observed to reduce the pressure gradient. This can be attributed to variations in fluid properties: specifically, a decrease in liquid viscosity and surface tension with temperature, as well as reduced density contrast between phases. These changes lead to a lower interfacial shear and, consequently, a reduction in total pressure loss. These observations align with results reported by Park et al. [29] and Kuczyński et al. [18], emphasizing the role of fluid property variation in two-phase flow within micro-scale geometries.

In addition, the comparison Between R32 and R134a R32 consistently exhibited higher frictional pressure gradients than R134a under identical operating conditions. This behavior is mainly due to R32’s higher vapor pressure and latent heat, as well as its lower molecular weight and viscosity. These properties enhance vapor generation and accelerate the shift to high-quality flow regimes, which are associated with increased wall and interfacial friction. Moreover, the higher density of R32 in vapor phase contributes to larger momentum fluxes and, therefore, increased pressure drop, particularly at high mass fluxes. These differences underscore the importance of refrigerant selection when designing high-performance minichannel evaporators.

Another important point is that the boiling dataset served as a critical benchmark for assessing the performance of established predictive models, including those of Cavallini et al. [20], Friedel [30], and Müller-Steinhagen and Heck [22]. These correlations, originally formulated for conventional or moderately compact geometries, consistently overpredicted pressure drops, particularly for R134a at low vapor qualities. This discrepancy highlights the limited validity of traditional correlations when applied to highly confined geometries and emphasizes their relevance for model validation and the development of new predictive approaches tailored to minichannel configurations.

4.2. Condensation Experimental Data

The two-phase flow pressure drop was measured for two different multiport extruded minichannel tubes with a hydraulic diameter of 0.715 and 1.16 mm, using R32, R134a, R290, R410A, R513a, and R1234yf as working fluids. The frictional two-phase pressure gradient was calculated as described in Section 3.

The contribution of the acceleration pressure gradient was minimal, accounting for less than 6% of the experimental pressure gradient in the biggest case. To verify the accuracy of the momentum pressure drop predictions in this study, diabatic and adiabatic two-phase flow tests were performed under similar conditions with vapor quality variations below 0.2. The experiments showed that the frictional pressure drop predictions were consistent between the diabatic and adiabatic tests, confirming the reliability of the momentum pressure drop calculation for our tests. Linear pressure drop was considered in this study, following the method presented by Park et al. [29], due to the small differences in saturation temperature between the inlet and outlet sections. Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14 show the experimental data recorded and the different effects on frictional pressure gradient of mass velocity, hydraulic diameter and saturation temperature. All of them are limited to a maximum mass velocity of 300 kg/m² s because of the pump displacement limitations. This value was established by its propane properties, since its density is approximately half of the other tested fluids and the displacement of the gear pump is fixed, which limits the maximun mass velocity of propane tests. Figure 10 depicts the effect over frictional pressure gradient for all tested fluids of mass velocity variation at 35 °C. The image shows two different values of mass velocity, 200 and 300 kg/m² s. Figure 11 shows the effect that saturation temperature has over frictional pressure drop at a fixed value of mass velocity. Figure 10 and Figure 11 are depicted for the multiport square tube. Similar results were obtained in the case of the triangular ports. Figure 12, Figure 13 and Figure 14 plot the effect of hydraulic diameter over frictional pressure gradient at saturation temperatures of 35, 45, and 55 °C for hydraulic diameters of 0.715 and 1.16 mm at one value of mass velocity.

The same results were registered at higher mass velocities in Figure 15, Figure 16 and Figure 17 for both hydraulic diameters. In all cases, frictional pressure drop increases with an increase in the values of vapor quality and a decrease in hydraulic diameter. These figures show the effect at a fixed value of mass velocity of 900 ${\mathrm{kg}/\mathrm{m}}^2\mathrm{s}$ of changing hydraulic diameter, refrigerant fluid, and vapor quality. The tendency across all fluids is similar, and the slope of the data depends on the fluid.

Figure 18 compares the frictional pressure drop of two fluids, R134a and R32, at the typical condensing and boiling temperatures of 50, 40, 10, and 5 °C in the same tube for a value of mass velocity of 500 ${\mathrm{kg}/\mathrm{m}}^2\mathrm{s}$. From the point of view of the frictional pressure gradient, and thus, power, we require to impulse the refrigerant through the heat exchanger (compressor power); the boiler presents higher resistance and therefore its design is much more critical for the optimization of thermal power devices involving minichannels.

The findings confirm that boiling flows in minichannels lead to considerably higher frictional losses than condensation flows (see Figure 18), highlighting the need for careful evaporator optimization in compact heat exchanger systems. While minichannels enhance heat transfer due to their high surface-to-volume ratio, this advantage is offset by significant hydraulic penalties that must be properly managed. Excessive pressure drops increase compressor power demand, potentially reducing overall thermal efficiency and diminishing the anticipated energy savings. Therefore, in the design of refrigeration systems—including applications such as automotive air conditioning, electronics cooling, and heat pumps—it is essential to perform a trade-off analysis between heat transfer enhancement and hydraulic performance.

The registered data are also compared against some models available in the open literature, such as Cavallini et al. [20], Müller Steinhagen and Heck [22], and Friedel [30] for the tested geometry used in boiling and condensing experimental campaigns. Figure 19, Figure 20 and Figure 21 show the predictions of the experimental data. These figures also include the 20% limits of under- and overestimation. The models proposed by Friedel and by Müller Steinhagen and Heck reproduced the pressure drop measurements with reasonable accuracy.rom them all, the Müller-Steinhagen and Heck model is the one that predicts all data with lower dispersion. The Friedel and Cavallini et al. models tend to overestimate the frictional pressure drop of R134a.

Table 4. Statistical performance of reference pressure-drop correlations.

Correlation	${\mathit{R}}^2$	MRD (%)	MARD (%)
Cavallini	0.974	−2.10	9.80
Friedel	0.921	+15.20	18.50
Müller–Steinhagen and Heck	0.945	+8.40	14.70

summarizes the quantitative performance of three widely used pressure-drop correlations. Cavallini’s correlation achieves the best agreement among the reference models, with $R^2=0.974$ and a MARD of 9.8%, and it shows a small tendency to underpredict the data (MRD = −2.1%). The Müller–Steinhagen and Heck correlation also provides reasonable agreement, with $R^2=0.945$, although it exhibits larger scatter (MARD = 14.7%) and a systematic positive bias (MRD = +8.4%). In contrast, the Friedel correlation shows the poorest performance, with the lowest $R^2$ (0.921), the largest deviations (MARD = 18.5%), and a strong overprediction trend (MRD = +15.2%). These results highlight the limitations of the classical correlations when applied to the present database, especially under conditions of low mass flux and high vapor quality where the discrepancies become more pronounced.

5. Update Model Proposal for Frictional Pressure Drop Estimation

After careful analysis, it has been observed that the existing correlations tend to exhibit slight discrepancies in estimating the frictional pressure drop for condensing flows through minichannels within the studied range of experimental conditions. It should be emphasized that most conventional correlations were developed for larger channels and their validity is intrinsically limited when extrapolated to minichannels. In particular, they often neglect confinement effects, which become increasingly important as the hydraulic diameter decreases and are usually quantified by the confinement number. These effects modify the balance between surface tension, inertia, and buoyancy forces, leading to discrepancies when classical models are applied at the microscale. This limitation further highlights the need for correlations specifically calibrated for confined geometries, as pursued in the present work.To address this limitation and improve the accuracy of predictions, a new correlation is proposed.

The newly proposed correlation focuses on calculating the liquid flow multiplier and takes into account various dimensionless parameters that consider fluid properties and differences between the liquid and vapor phases. In addition, it incorporates the ratio between the inertial and viscous forces of the liquid phase and the Martinelli parameter. The new correlation is based on the Reynolds number to take into account the viscous and inertial forces of refrigerant. It also includes the Weber number since there are free surface between liquid and vapor phase, and finally, the Lockhart–Martinelli parameter was also introduced to compute the liquid fraction of the flowing fluid.

To develop the new correlation, a non-linear regression method was applied to a dataset consisting of 3553 experimental data points. This new correlation, which represents the two-phase frictional pressure drop for two-phase flow in pipes, is presented in Equations (7)–(9); the considered friction factor is presented in Equation (6). The comparison of experimental data against the prediction is depicted in Figure 22.

The updated correlation developed in this work demonstrates the highest accuracy when evaluated against the present database. As shown in Table 4, the model achieves $R^2=0.9892$, with a mean absolute relative deviation (MARD) of only 3.12% and a negligible bias (MRD = +0.85%). This represents the following substantial improvement compared with the reference correlations: Cavallini ($R^2=0.974$, MARD = 9.8%), Müller–Steinhagen and Heck ($R^2=0.945$, MARD = 14.7%), and Friedel ($R^2=0.921$, MARD = 18.5%). The improvement arises from the broader calibration of the present model, which incorporates both boiling and condensation data over a wide range of mass fluxes, vapor qualities, and refrigerants with low global warming potential. By explicitly accounting for these conditions, the updated correlation reduces scatter and removes the systematic biases observed in the reference models. In particular, Friedel’s correlation consistently overpredicts pressure drops at high vapor quality, while that of Müller–Steinhagen and Heck tends to underpredict at low mass fluxes; both effects are effectively corrected by the new formulation. As a result, more than 90% of the database falls within ±20% error for the present correlation, compared to approximately 70–80% for the reference models. These results confirm that the updated model provides a more robust and reliable tool for predicting two-phase pressure drop in compact geometries.

$$\begin{array}{c}{f}_{lo}=0.25·lo{g}_{10}{\left({\displaystyle \frac{150.39}{R{e}_{liq}^{0.98865}}}-{\displaystyle \frac{152.66}{R{e}_{liq}}}\right)}^{-2}\end{array}$$

(6)

$$\begin{array}{c}{\left({\displaystyle \frac{dp}{dz}}\right)}_{lo}={\displaystyle \frac{f_{lo}·G^2}{2·D_h·{\rho }_{liq}}}\end{array}$$

(7)

$$\begin{array}{c}{\varphi }_{lo}^2=0.51294·x^{0.64245}·P_{red}^{-1.44326}·{\left({\displaystyle \frac{R{e}_{liq}}{X_{Martinelli}}}\right)}^{0.21176}·W{e}_{liq}^{0.11459}·F{r}_{2ph}^{-0.10117}·N_{conf}^{0.14297}\end{array}$$

(8)

$$\begin{array}{c}{\left({\displaystyle \frac{dp}{dz}}\right)}_{f2ph}={\varphi }_{lo}^2·{\left({\displaystyle \frac{dp}{dz}}\right)}_{lo}\end{array}$$

(9)

where the friction factor, Equation (6), corresponds to the correlation developed by Frang et al. [31].

In the above equations, the terms below are defined as follows:

• $f_{lo}$: friction factor for the liquid-only flow, obtained from the correlation of Fang et al. [31], Equation (6) [-].
• ${\left(\frac{dp}{dz}\right)}_{lo}$: frictional pressure gradient for liquid-only flow, Equation (7) [Pa m⁻¹].
• G: mass flux, defined as the mass flow rate divided by the flow area [kg m⁻² s⁻¹].
• $D_h$: hydraulic diameter of the channel [m].
• ${\rho }_{liq}$, ${\rho }_{gas}$: liquid and vapor densities, respectively [kg m⁻³].
• ${\mu }_{liq}$: dynamic viscosity of the liquid [Pa s].
• $\sigma$: surface tension [N m⁻¹].
• x: vapor quality, mass fraction of vapor in the two-phase mixture [-].
• ${\varphi }_{lo}^2$: two-phase multiplier defined by Equation (8) [-].
• ${\left(\frac{dp}{dz}\right)}_{f2ph}$: frictional pressure gradient for two-phase flow, Equation (9) [Pa m⁻¹].
• $P_{red}$: reduced pressure, defined as $P/P_{crit}$ [-].
• $R{e}_{liq}$: liquid Reynolds number, Equation (1) [-].
• $f_{liq}$, $f_{gas}$: friction factors for liquid-only and gas-only flows, respectively [-].
• $X_{Martinelli}$: Martinelli parameter, Equation (3), which compares liquid and gas phase pressure gradients [-].
• $W{e}_{liq}$: liquid Weber number, Equation (2), relating inertial to surface tension forces [-].
• $F{r}_{2ph}$: two-phase Froude number, defined as $F{r}_{2ph}=\frac{G^2}{g{D}_h{\rho }_m^2}$, where G is the mass flux [kg m⁻² s⁻¹], g the gravitational acceleration [m s⁻²], $D_h$ the hydraulic diameter [m], and ${\rho }_m$ the two-phase mixture density obtained from $\frac{1}{{\rho }_m}=\frac{x}{{\rho }_{gas}}+\frac{1-x}{{\rho }_{liq}}$ [-].
• $N_{conf}$: confinement number, defined as $N_{conf}=\sqrt{\frac{\sigma }{g{D}_h^2({\rho }_{liq}-{\rho }_{gas})}}$, where $\sigma$ is the surface tension [N m⁻¹] [-].

All thermophysical properties were evaluated with REFPROP v10 [32].

6. Conclusions

This work has presented an in-depth experimental investigation into two-phase frictional pressure drops during boiling and condensation processes in minichannel tubes. The outcomes are directly relevant to the design and operation of high thermal-performance systems, contributing to both environmental sustainability and reduced energy use. A total of 3553 experimental data points were obtained using six refrigerants—R32, R134a, R290, R410A, R513A, and R1234yf—across a broad range of operational conditions. The study considered varying mass velocities (from 200 to 1230 kg/m² s), saturation temperatures (from 5 °C to 55 °C), and vapor qualities (from 0.05 to 0.95), using two different multiport tube geometries with hydraulic diameters of 0.715 mm and 1.16 mm.

The results demonstrate consistent trends across all fluids and conditions. It was found that the frictional pressure gradient increases with higher vapor quality and mass velocity, and decreases with larger hydraulic diameters and higher saturation temperatures. These findings highlight the sensitivity of pressure drop to geometric and thermodynamic parameters, which is especially relevant in the design of compact thermal systems with enhanced heat transfer capability and energy efficiency. In particular, the study also confirms that boiling flows generally exhibit greater friction resistance than condensation flows, underscoring the critical need for careful design optimization in evaporators using minichannel configurations.

Another key contribution of this research lies in the comparative analysis between the experimental data and widely used predictive models in the literature. Although some existing correlations—such as those of Müller–Steinhagen and Heck [22], Cavallini et al. [20], and Friedel [30]- were able to capture general trends, they often failed to accurately predict pressure drops across all fluids and conditions. Discrepancies were particularly significant in flows involving R134a, suggesting that traditional models are not universally applicable to modern refrigerants or minichannel geometries.

To address these limitations, a new empirical correlation was developed based on nonlinear regression techniques applied to the full dataset. This model incorporates dimensionless parameters such as Reynolds number, Weber number, and the Lockhart–Martinelli parameter, effectively accounting for fluid properties and interfacial phenomena specific to minichannel two-phase flow. The new correlation shows a significantly improved prediction accuracy within ±20% of the experimental results, outperforming the existing models in both condensation and boiling regimes.

The successful fulfillment of all the initial objectives—designing a fully instrumented experimental setup, generating a large and high-quality dataset, critically assessing current models, and proposing a new validated correlation—demonstrates the robustness and relevance of this research. It provides valuable tools for engineers and researchers working in the fields of refrigeration, thermal management, and compact heat exchanger design.

Looking forward, future work should extend this experimental framework to include additional refrigerants, including natural and low-GWP alternatives, and to investigate other minichannel geometries and orientations. Such efforts will help to broaden the applicability of the proposed model and pave the way toward the development of generalized predictive tools for advanced thermal systems using minichannels. The findings of this study thus represent an important step toward the realization of more compact, efficient, and environmentally sustainable thermal energy transfer technologies.