Influence of Non-Uniform Airflow on Two-Phase Parallel-Flow Heat Exchanger in Data Cabinet Cooling System

Abstract

The energy consumption of data center cooling systems is rapidly increasing, necessitating urgent improvements in cooling system performance. This study investigates a pump-driven two-phase cooling system (PTCS) utilizing a parallel-flow heat exchanger (PFHE) as an evaporator, positioned at the rear of server cabinets. The findings indicate that enhancing the vapor quality at the PFHE outlet improves the overall cooling performance. However, airflow non-uniformity induces premature localized overheating, restricting further increases in vapor quality. For PFHEs operating with a two-phase outlet condition, inlet air temperature non-uniformity has a relatively minor impact on the cooling capacity but significantly affects the drop in pressure. Specifically, higher upstream air temperatures increase the pressure drop by 7%, whereas higher downstream air temperatures reduce it by 7.7%. The implementation of multi-pass configurations effectively mitigates localized overheating caused by airflow non-uniformity, suppresses the decline in cooling capacity, and enhances the operational vapor quality of the cooling system.

1. Introduction

Data centers are crucial infrastructures that support a wide range of digital activities. As their size and capacity expand, so does their energy consumption, particularly in cooling systems. Efficient cooling is essential to maintain optimal operating conditions and prevent server cabinets overheating. Server cabinets, housing numerous servers and other equipment, are fundamental components of data centers. According to studies, cooling systems account for approximately 30–50% of the total energy consumption in data centers [1,2]. As data centers continue to grow in scale and capacity, improving the efficiency of cooling systems becomes increasingly essential to reduce overall energy consumption and operational costs [3,4].

Air cooling for data cabinets can be categorized into three levels based on spatial scale: room-level cooling, row-level cooling, and rack-level cooling [5,6]. Among these, room-level cooling systems utilizing underfloor air supply are widely adopted in conventional data centers. However, this approach is limited by the mixing of hot and cold air as well as the occurrence of local hot spots, which reduce cooling efficiency [7]. Row-level cooling addresses this issue by deploying cooling units near a row or column of racks, directly delivering cold air to the target area and minimizing the bypass of cold air around IT equipment back to the cooling units. Nevertheless, row-level cooling still struggles to completely eliminate local hot spots [8,9]. In contrast, rack-level cooling integrates cooling units directly into the IT racks, significantly shortening the airflow path of hot and cold air. This approach effectively avoids cooling capacity waste and air mixing, making it the most promising strategy for enhancing cooling efficiency [10,11].

Computational fluid dynamics (CFD) is a powerful tool that enables engineers to numerically simulate and predict fluid behavior under various conditions [12,13]. Many researchers have utilized CFD techniques to optimize airflow distribution within data cabinets, enhancing air thermal management and evaluating the thermal performance of cooling systems. For instance, a bidirectional synchronous coupled CFD-FNM (fluid network model) framework has been proposed to describe the overall flow and temperature distribution within data centers. Compared with experimental results, the maximum temperature error at the rack outlet is less than 3.5 °C, with 81.6% of the rack outlet areas exhibiting a relative temperature error of less than 5% [14]. Additionally, Lim et al. introduced a ventilation efficiency index to accurately identify hot spot locations and utilized CFD methods to optimize server exhaust angles to mitigate hot spot effects. Their research demonstrated that adjusting the exhaust angle to a 60° vertical angle significantly improves temperature distribution uniformity [3]. By comparing the DES turbulence model and the standard k-ε RANS model in rack-level air separation in data centers, Saiyad et al. found that both models can ensure that the cabinet inlet temperature is controlled within 1.4 °C compared with the experimental data. However, the K-ε model cannot predict the supply heat index (SHI), return temperature index (RTI), and beta index (β), while the DES model captures the recirculation region in the cold aisle very well [15]. Cui et al. proposed a multi-scale simulation method for data centers, integrating room-level, rack-level, and server-level models to optimize system performance. Their study demonstrated that aisle containment systems significantly enhance the thermal environment of servers, reducing the maximum server temperature from 87.5 °C to 73.1 °C. The multi-scale model allows for efficient optimization of air conditioning parameters, facilitating higher supply air temperatures and lower airflow rates while ensuring safe server operation. Additionally, the study validated the feasibility of using radial basis function (RBF) networks for fast and accurate chip temperature prediction, offering a practical approach for thermal management in data centers [16]. Rambo and Joshi introduced a multi-scale modeling approach specifically designed for data centers, aiming to establish a cohesive thermal management strategy that integrates seamlessly across different scales [17]. Their framework was further refined by Joshi and collaborators, who highlighted that data center length scales span four orders of magnitude, ranging from macro-scale components such as rooms and ducts to micro-scale elements including racks, servers, and chips. Given this complexity, precise temperature prediction requires a well-coordinated design strategy at each level. Expanding on this foundation, Joshi [18] applied the multi-scale method to simulate fluid flow and thermal behavior in data centers, analyzing the interaction between server-level heat generation and the overall temperature distribution by coupling the rack and server scales. Liu et al. conducted a systematic study on the application of open-source software, including OpenFOAM and ParaView, for geometry preparation, mesh generation, experimentally guided numerical setup, and result visualization. To streamline the process, a JAVA program was developed, enabling case preparation and simulation execution with a single command. Additionally, self-adaptive momentum sources were implemented to regulate the airflow through servers. The proposed strategy was validated using a pilot data center from Alibaba Cloud (Alibaba Group). The developed solver accurately predicted air temperature distributions in cold and hot aisles, achieving an average error of 0.7 K. This work lays the foundation for automated CFD simulations of data centers using open-source tools [19]. The parallel-flow heat exchanger (PFHE) is renowned for its high heat transfer area density, compact structure, exceptional operational efficiency, and superior temperature uniformity [20,21,22]. These characteristics have established it as an efficient heat exchange device, widely implemented in data center rack-level cooling systems. Typically, PFHEs are installed at the rear of racks, serving as evaporators that absorb the high-temperature air discharged by servers through the evaporation of the refrigerant, thereby reducing the discharge air temperature of the cabinet. A comprehensive model of the PFHE-separation heat pipe evaporator has been established, utilizing computational fluid dynamics (CFD) methods to analyze internal refrigerant flow and heat transfer characteristics in detail, and exploring the specific influence of fill ratio on system performance [23,24]. Additionally, researchers conducted an in-depth analysis of temperature and airflow distribution within the cabinet, revealing that the system’s cooling air demand is reduced by 50% compared to traditional computer room air conditioning (CRAC) systems [25]. By combining experimental and simulation methods, they further optimized the baffle design and found that a well-configured baffle arrangement could achieve a maximum temperature reduction of 0.7 °C in hotspot areas [26].

Heat pipe technology has been widely adopted in rack-level cooling systems, primarily classified into gravity-driven and pump-driven types. To address the high heat flux dissipation challenges within server cabinets, researchers have proposed multi-stage heat pipe loop systems, which effectively reduce air mixing and mitigate local hotspots while maximizing the utilization of natural cooling resources, leading to a cooling energy consumption reduction of up to 46% [27]. Furthermore, studies on heat pipe systems in data centers have shown that under non-uniform heat load conditions, the system can achieve self-regulation by operating multiple evaporators in parallel. Experimental results indicate that even when the maximum heat load is 15 times the minimum, the ratio of maximum to minimum flow rate remains only 1.67, highlighting its limited self-regulation capability [28]. Despite having some degree of self-adaptability, gravity-driven heat pipe systems still encounter challenges under low charge ratios and high input power conditions, particularly when multiple evaporators operate in parallel. Issues such as excessive flow resistance or insufficient refrigerant charge can result in localized overheating of the evaporator, significantly compromising overall heat transfer performance and potentially leading to system instability [29,30]. In contrast, pump-driven heat pipe systems have demonstrated superior performance in small-scale data center applications, particularly in low outdoor temperature conditions, where they efficiently leverage natural cooling sources, reduce system energy consumption, and enhance energy efficiency [31,32,33]. Additionally, an innovative study introduced a hybrid rack-level cooling system that integrates pump-driven heat pipes with vapor compression technology. This system utilizes a single refrigerant for both the refrigerant pump and the compressor, enabling highly efficient system integration. Research findings indicate that the system achieves an power usage effectiveness (PUE) of 1.23, demonstrating significant advantages in energy efficiency [34]. Moreover, researchers have explored the application of microchannel evaporators combining heat pipe and vapor compression technologies in rack-level cooling systems [35,36,37,38]. Specifically, PFHEs coupled with separated heat pipe technology have been applied in telecommunication room cooling systems, where experimental results show an EER of up to 23 [39]. To further enhance performance, researchers have developed a comprehensive model of PFHE-separated heat pipe evaporators, employing CFD simulations to analyze the internal refrigerant flow and heat transfer characteristics, while also investigating the impact of charge ratio on system performance [23,26].

Current research in rack-level cooling systems predominantly focuses on optimizing microchannel evaporators and enhancing overall performance, with relatively limited studies examining the impact of non-uniform airflow on heat exchanger performance. This complex issue involves multiple factors and mechanisms. Previous research has mainly concentrated on vehicle front end cooling modules (FECMs) under non-uniform airflow conditions, revealing that extreme non-uniform airflow can decrease thermal efficiency by up to 30% and increase pressure drops by 90% [40,41]. Studies on PFHE performance under non-uniform airflow have primarily addressed single-phase heat transfer and flow distribution, with a proposed principle of internal pressure balance (PIPB) used to evaluate flow distribution matching in vehicles. These studies indicate that a larger length–diameter ratio improves internal flow distribution uniformity and minimizes heat transfer rate deterioration across different airflow patterns [42]. Research on phase change heat transfer under non-uniform airflow has centered on fin-tube and corrugated-tube heat exchangers, with theoretical studies examining the influence of non-uniform air flow at the inlet on finned tube condensers [43,44,45]. Additionally, numerical, and experimental methods have been used to analyze the impact of uneven wind speed distribution on multi-loop tubular finned evaporators, finding a decrease in evaporator capacity of 7.78% compared to uniform airflow conditions [46].

Existing studies have shown that non-uniform airflow significantly affects heat exchanger performance, yet there is a notable lack of research on PFHE performance when used as evaporators under such conditions. This complexity arises from the superposition of velocity and temperature fields, with the evaporator experiencing liquid, two-phase, and vapor states. To address this gap, a pump-driven two-phase cooling system (PTCS) is constructed in this paper. Based on measured airflow velocity and temperature distribution within a server cabinet, a calculation model for two-phase heat transfer of a PFHE under non-uniform airflow conditions is established and validated experimentally. This research provides a comprehensive analysis of the impact of non-uniform airflow on PFHE cooling capacity and pressure drop and explores how structural optimization can mitigate its adverse effects.

2. Experiment Method

2.1. Experimental System Description

To investigate the impact of non-uniform air-side velocity and temperature on a PFHE, a data cabinet equipped with a pump-driven two-phase cooling system (PTCS) was selected as the subject of the study. As shown in Figure 1, the PTCS reduces the discharge air temperature of the cabinet through the evaporation of the refrigerant inside the PFHE installed at the rear of the cabinet, thereby maintaining a stable room temperature. The cabinet used is a standard 42U rack, with 25 1U servers installed from the 8U to the 32U position. Data transmission between servers is facilitated by a switch, and potential air leaks in areas outside the servers are prevented by placing dummy panels in the remaining upper and lower gaps. Five fans are evenly distributed behind the evaporator to regulate the airflow speed into the PFHE.

The two-phase gas–liquid or superheated vapor exiting the PFHE is transported outdoors, where it is condensed into a liquid state and then enters the reservoir. After being pressurized by the pump, the liquid refrigerant flows back into the PFHE. The PFHE’s air inlet is equipped with a grid of 3 columns by 4 rows, totaling twelve Pt100 temperature sensors, while its air outlet has five Pt100 temperature sensors placed uniformly from top to bottom. Figure 1 shows the distribution of air temperature measuring points at the inlet and outlet of PFHE prior to testing. These thermocouples are calibrated to ensure temperature accuracy within a margin of 0.1 °C under identical environmental conditions. Three pressure sensors are strategically placed at the evaporator inlet, outlet, and the reservoir to facilitate the measurement of evaporation pressure and pressure drop. A turbine volume flowmeter is arranged in the liquid-phase pipeline from the pump to the PFHE, with a measuring range of 0~5 L/min. The circulating medium in the pump-driven two-phase cooling loop is R134a. In the actual operation of the equipment room, according to the recommendations of ASHRAE, the air conditioner in the equipment room maintains the ambient temperature of the equipment room within 27 °C [47].

To assess the non-uniformity of inlet air temperature and velocity in the heat exchanger, a total of twelve temperature measurement points, arranged in a uniform 4-row by 3-column grid, were deployed at the inlet to capture the distribution of inlet air temperatures. A handheld anemometer was utilized to measure the velocity non-uniformity, with a total of twenty velocity measurement points arranged in a uniform 4-row by 5-column grid at the inlet. The average wind speed recorded over a stable one-minute period after velocity stabilization was considered the true inlet air speed at each measurement point, thereby obtaining the inlet air temperature distribution of the heat exchanger. At the outlet, five temperature measurement points were evenly distributed from top to bottom to measure the outlet air temperature distribution. The specific locations of the temperature measurement points are detailed in Figure 2. Prior to testing, these thermocouples were calibrated to ensure temperature accuracy within 0.1 °C under identical environmental conditions.

Table 1. Geometric parameters of parallel-flow heat exchanger.

Parameter	Value (Unit)	Parameter	Value (Unit)
Tube outer width Bbo	32 mm	Tube inner width Bbi	30.7 mm
Tube outer height Hbo	1.3 mm	Tube inner height Hbi	0.74 mm
Tube inner height Hbi	31	Wall thickness δw	0.31 mm
Fin width Bf	32 mm	Fin height Hf	8 mm
Fin spacing Pf	1.1 mm	Fin thickness δf	0.1 mm
Lover angle θ	30°	Louver pitch Pl	1 mm
Louver length Ll	8 mm	Header diameter D	38 mm
Tube length L	1400 mm	Number of flat pipes	46

shows the detailed specifications of the PFHE, which is designed with a single-pass structure. The key specifications are as follows: The inlet of the PFHE is located at the bottom, and the outlet is located at the top. It is connected to the lower pipeline through a 16 mm aluminum tube with a length of about 1700 mm. The collector pipe has a hydraulic diameter of 38 mm and there are 46 flat tubes each with a length of 1400 mm, a width of 32 mm, and a height of 1.3 mm; each tube contains 31 fins, with 32 ports per tube and there are 21 fins per inch, with each fin having a height of 8 mm and a thickness of 0.1 mm; the louvers are angled at 30 degrees, spaced 1 mm apart, and are 6 mm long.

2.2. Velocity and Temperature Distribution

Before exploring the impact of non-uniform airflow on the performance of heat exchangers, it is imperative to initially ascertain the exhaust temperatures and inlet air velocity distributions of the servers. This was achieved by manipulating the server loading positions to evaluate the thermal exhaust temperatures and airflow velocity distributions. The experiments were conducted under three scenarios: all 25 servers operating at full load; only the top 13 servers operating at full load with the remaining servers idle; and the bottom 12 servers operating at full load with the others idle. Linear interpolation of data from 12 temperature sensors was employed to obtain the air temperature distribution entering the evaporator. The experimental findings revealed a relatively uniform velocity distribution in the vertical direction, prompting this study to focus solely on the horizontal velocity distribution. The velocities measured using anemometers were fitted to derive the velocity distribution curves.

Figure 3 illustrates the inlet air temperature distribution within the heat exchanger under varying load distributions. The backplane’s central region maintains consistently lower temperatures, with high-temperature zones developing on both sides of the heat exchanger. In scenarios where the lower section is fully loaded, the high-temperature areas manifest in the lower-middle portions on both sides, with the highest temperature recorded at a modest 33.7 °C. The thermal airflow, under the suction of the fans, enters the heat exchanger before it can fully ascend, leading to a relatively even temperature distribution due to the unloaded upper section, which exhibits a minor variance between the highest and lowest temperatures. With the upper section fully loaded, the rising thermal currents cause the lower portion to cool, shifting the high-temperature zones to the upper-middle regions of the heat exchanger and significantly broadening the high-temperature range. Here, the temperature variance is the most significant among the conditions, reaching 6.2 °C and resulting in an uneven temperature spread. In the case of full server load, the peak temperature hits 35.8 °C, with the high-temperature regions on both sides noticeably exceeding those of other scenarios.

Figure 4 depicts the velocity distribution across the heat exchanger’s width, as determined through measurement and subsequent curve fitting. The airflow speed is clearly non-uniform, exhibiting a parabolic, yet asymmetrically distributed profile, regardless of the air volume. This trend is likely influenced by the transverse relative positioning of the PFHE and the fans. The maximum airflow occurs at the normalized width ranging from 0.4 to 0.5. With increasing airflow rate, from 0.336 m³/s to 0.884 m³/s, the distribution of velocity becomes more uniform, with the ratio of the minimum to maximum velocities increasing from 0.61 to 0.85. This suggests that increasing the fan speed could be a strategy to mitigate the non-uniformity of the inlet air temperature to the PFHE.

3. Mathematical Model

When a parallel-flow heat exchanger serves as an evaporator, the heat transfer process of the coolant inside involves three phases: liquid, two-phase, and superheated vapor. At the inlet header, the coolant is in the liquid phase, and an orifice plate is installed internally for liquid distribution, ensuring relatively uniform distribution. The heat transfer in each section of the heat exchanger is calculated using the effectiveness-NTU method. It is noteworthy that the air velocity and temperature distributions on the air side are obtained through linear interpolation based on experimental temperature measurement points. This study aims to investigate the flow and heat transfer performance of PFHE under non-uniform airflow conditions. To facilitate simulation calculations while accurately representing the actual evaporative heat transfer process, the microchannel evaporator model has undergone a certain degree of idealization, as detailed below:

• The convection heat transfer and flow of refrigerant in the flat tube are one-dimensional steady processes;
• The air side is a one-dimensional flow, but the velocity and temperature distribution are non-uniform;
• The heat transfer between the air and the refrigerant is crossflow, ignoring the heat transfer in the non-mainstream direction;
• Computation is considered to be a steady state process;
• The refrigerant is evenly divided in the flat tube.

3.1. Control Equations

Each flat tube is divided into 100 equal segments along its height to investigate the local characteristics of heat transfer. Additionally, on the air side, the heat exchanger is subdivided into 46 equal segments along its width, corresponding to 46 flat tubes, thereby constructing the heat transfer model for the PFHE. By determining the thermophysical properties of the refrigerant at the outlet of each micro-element and using these properties as the initial conditions for the subsequent micro-element, calculations are progressively performed from the inlet to the outlet of the PFHE. This method effectively computes the heat transfer performance of each micro-segment and provides insights into the overall efficiency of the PFHE. Figure 5 illustrates the inlet air temperature of the PFHE and a schematic diagram of heat transfer within a micro-element. In this figure, the temperatures and velocities on the air side are obtained by fitting and interpolation based on a finite number of measurement points. This process involves reading the temperature and velocity information for each segment; therefore, the velocity and temperature of the air entering each segment of the PFHE differ. The heat balance equation is as follows:

The heat balance equation for each element is as follows:

$$Q_i={\mathrm{m}}_{\mathrm{a}}c{p}_a\left(T_{a,in}-T_{a.o}\right),$$

(1)

$$Q_i=m_r\left(H_{ri+1}-H_{ri}\right),$$

(2)

$$Q_i=\epsilon C_{\min }\left(T_{ri}-T_{a,in}\right),$$

(3)

$$C_{\min }=\min \left(m_a{c}_{p,a},m_r{c}_{p,r}\right),$$

(4)

where in this equation, Q represents the heat transfer rate, T denotes temperature, m is the mass flow rate of the working fluid, C_p is the specific heat capacity of air, H stands for the enthalpy of the working fluid, i and i + 1, respectively, indicate the inlet and outlet; ε is for efficiency, the subscripts a and r, respectively, represent the working fluid air and the coolant.

When the working medium is single phase, the efficiency is:

$$\epsilon =1-exp\left\{{\displaystyle \frac{1}{C_r}}NT{U}^{0.22}\left[exp(-C_{r}NT{U}^{0.78})-1\right]\right\},$$

(5)

$$C_r={\displaystyle \frac{\min (m_a{c}_{p,a}{m}_r{c}_{p,r})}{\max (m_a{c}_{p,a}{m}_r{c}_{p,r})}},$$

(6)

When the working medium is single phase, the efficiency is:

$$\epsilon =1-e^{(-NTU)},$$

(7)

$$NTU={\displaystyle \frac{U{A}_0}{C_{\min }}},$$

(8)

$$U={\displaystyle \frac{1}{\frac{1}{h_r}\frac{A_o}{A_w}+\frac{{\delta }_w}{{\lambda }_w}\frac{A_o}{A_w}+\frac{1}{{\eta }_o{h}_a}}},$$

(9)

where NTU represents the number of heat transfer units, A_o is the total heat transfer area of the air side, U stands for the overall heat transfer coefficient, h_a and h_r are the heat transfer coefficients on the air side and refrigerant side, respectively, δ_w denotes the thickness of the edge wall, m, λ_w is the thermal conductivity of the flat tube, and η_o signifies the fin efficiency.

3.2. Heat Transfer and Pressure Drop Correlations of Refrigerant

The heat exchange on the refrigerant side involves three distinct phases: liquid, two-phase, and superheated vapor. It necessitates the application of different correlations for each state. Specifically, when the refrigerant is in the subcooled or superheated vapor states, the Gnielinski equation [48] is commonly used for refrigerant liquid or vapor, as detailed below:

$$Nu=\left\{\begin{array}{l}{\displaystyle \frac{(f/8)\left({\mathrm{Re}}_{D_b}-1000\right)\mathrm{Pr}}{1+12.7\sqrt{f/8}\left({\mathrm{Pr}}^{2/3}-1\right)}},2300<{\mathrm{Re}}_{D_b}<{10}^6\hfill \\ 4.36,{\mathrm{Re}}_{D_b}\le 2300\hfill \end{array}\right.,$$

(10)

$${\mathrm{Re}}_{D_b}={\displaystyle \frac{G_r{D}_b}{{\mu }_r}},$$

(11)

$$f={\left(1.82{\log }_{10}{\mathrm{Re}}_{D_b}-1.64\right)}^{-2},$$

(12)

$$h_r={\displaystyle \frac{{\lambda }_{r}Nu}{D_b}},$$

(13)

In this equation, Nu represents the Nusselt number, Re_Db is the Reynolds number, f denotes the friction factor, D_b is the hydraulic diameter, G_r indicates the refrigerant mass flux, μ_r is the dynamic viscosity of the refrigerant, h_r refers to the heat transfer coefficient on the refrigerant side, and λ_r is the thermal conductivity of the refrigerant.

The Gungor correlation [49] is applicable to subcooled boiling and saturated boiling, and it is also suitable for both horizontal and vertical flows. Consequently, this correlation model proposed by Gungor has been employed to calculate the two-phase heat exchange of refrigerant within microchannel evaporators, as shown below:

$$h_{tp}=E{h}_l+S{h}_{nb},$$

(14)

$$h_l=0.023{\mathrm{Re}}_l^{0.8}{\mathrm{Pr}}_l^{0.4}{\displaystyle \frac{{\lambda }_l}{D_b}},$$

(15)

$$h_{nb}=55p_r^{0.12}{\left(-{\log }_{10}{p}_r\right)}^{-0.55}{M}^{-0.5}{q}^{0.67},$$

(16)

$$E=1+24000B{o}^{1.16}+1.37X_{tt}^{-0.86},$$

(17)

$$S={\left(1+1.15\times {10}^{-6}{E}^2{\mathrm{Re}}_l^{1.17}\right)}^{-1},$$

(18)

$$X_{tt}={\left({\displaystyle \frac{1-x}{x}}\right)}^{0.9}{\left({\displaystyle \frac{{\rho }_g}{{\rho }_l}}\right)}^{0.5}{\left({\displaystyle \frac{{\mu }_l}{{\mu }_g}}\right)}^{0.1},$$

(19)

where h_tp, h_l, and h_nb, respectively, represent the two-phase heat transfer coefficient; the forced convection heat transfer coefficient, and the nucleate boiling heat transfer coefficient, E and S are enhancement and suppression factors for forced convection, respectively. D_b stands for hydraulic diameter, Pr_l, Re_l, respectively, represent the Prandtl number, and the Reynolds number of the liquid-phase refrigerant, M is molecular weight, X_tt is the Martinelli parameter, λ_l represents thermal conductivity of the liquid-phase refrigerant, ρ indicates density, μ_r is the dynamic viscosity, x is the vapor quality of the refrigerant, and the subscripts l and g represent liquid and vapor, respectively.

Regarding the pressure drop on the refrigerant side, it includes pressure drops across the liquid phase, two-phase, and superheated vapor phase. Specifically, the pressure drop for the refrigerant in the liquid and vapor phases is calculated using the Church correlation [50], while the pressure drop in the two-phase is determined using the Friedel correlation [51,52]. Details can be found in references.

3.3. Heat Transfer and Pressure Drop Correlations of Air

For the heat transfer and pressure drop model of the air-side louvered fins, the Kim and Bullard empirical correlation formula [20] is used, as follows:

$$j={\mathrm{Re}}_a^{-0.487}{\left({\displaystyle \frac{\theta }{90}}\right)}^{0.27}{\left({\displaystyle \frac{P_f}{P_l}}\right)}^{-0.14}{\left({\displaystyle \frac{H_f}{P_l}}\right)}^{-0.29}{\left({\displaystyle \frac{B_f}{P_l}}\right)}^{-0.23}{\left({\displaystyle \frac{L_l}{P_l}}\right)}^{0.68}{\left({\displaystyle \frac{P_l}{P_l}}\right)}^{-0.28}{\left({\displaystyle \frac{{\delta }_f}{P_l}}\right)}^{-0.05}$$

(20)

$$f={\mathrm{Re}}_a^{-0.781}{\left({\displaystyle \frac{\theta }{90}}\right)}^{0.444}{\left({\displaystyle \frac{P_f}{P_l}}\right)}^{-1.682}{\left({\displaystyle \frac{H_f}{P_l}}\right)}^{-1.22}{\left({\displaystyle \frac{B_f}{P_l}}\right)}^{0.818}{\left({\displaystyle \frac{L_l}{P_l}}\right)}^{1.97}$$

(21)

$${\mathrm{Re}}_a={\displaystyle \frac{G_a{P}_l}{A_{f_e}{\mu }_a}}$$

(22)

$$h_a=j{\mathrm{Re}}_a{\mathrm{Pr}}_a^{1/3}{\displaystyle \frac{{\lambda }_a}{P_l}}$$

(23)

$$\Delta P_a={\displaystyle \frac{f{A}_o}{2{\rho }_a{A}_{fe}}}{\left({\displaystyle \frac{G_a}{A_{fe}}}\right)}^2$$

(24)

where j and f, respectively, represent the heat transfer factor and friction factor, h_a denotes the air-side heat transfer coefficient, ΔP_a is the air side pressure drop, Pr_a and Re_a are the Prandtl and Reynolds numbers of air, respectively; A_fe and A_o, respectively, indicate the effective fin area and the total heat transfer area on the air side, μ_a is the dynamic viscosity of air, λ_a is the thermal conductivity of air, and ρ_a represents the density of air.

3.4. Model Verification

To validate the accuracy of the simulation results, this study employed a thermal imaging camera to record experimental observations and compared the captured images with the numerical predictions. To visualize the temperature distribution within the parallel-flow heat exchanger (PFHE), the backplate housing the cooling fan was removed during validation, allowing thermal imaging recordings while relying solely on the airflow generated by the internal server fans. Under these conditions, the air-flow velocity was considered uniform, with only the non-uniformity of the inlet air temperature taken into account, as illustrated in Figure 6. The computed temperature and vapor quality distributions of the refrigerant were compared with the thermal imaging results. The vapor quality distribution revealed that higher inlet air temperatures at the lateral sides led to significantly higher vapor quality near the edges compared to the central region. This caused overheating to occur first in the outermost flat tubes, while the two-phase region in the upstream section remained relatively uniform. As the refrigerant flowed downstream and overheating intensified, the flat tube temperature increased rapidly, reaching a maximum of 31 °C, which closely matched the thermal imaging observations. This consistency confirms that the proposed model can accurately predict the two-phase heat transfer process within the PFHE.

Figure 7 presents a comparative analysis between the experimental data and the numerical calculation of outlet air temperature and pressure drop at varying refrigerant flow rates. The results demonstrate a strong correlation between the measured and computed values. In Figure 7a, the distribution of outlet air temperature along the refrigerant flow direction is depicted. Initially, in the subcooled region, heat transfer occurs in a single-phase state, causing the outlet air temperature to gradually increase as the refrigerant flows downstream. At higher flow rates, the single-phase heat transfer region extends further due to the greater subcooling length. Upon entering the two-phase region, as the vapor quality increases, the convective heat transfer enhancement factor E exhibits a positive correlation with vapor quality, while the pool boiling suppression factor S shows a negative correlation, as described in Equations (17)–(19). In the downstream region, convective heat transfer becomes dominant, and the increasing vapor quality enhances the forced convection heat transfer coefficient, leading to a gradual decrease in outlet air temperature. Throughout the two-phase region, the difference between the experimental and computed temperatures remains within 0.2 °C, demonstrating the model’s accuracy in capturing the transition from subcooled to overheated states. In the superheated region, the mixing of cooling air with hot airflow introduces slight discrepancies, though the maximum temperature deviation remains within 1 °C. Overall, the predicted temperature trends align well with experimental measurements.

Figure 7b compares the total pressure drop under different refrigerant flow rates. When the flow rate decreases from 1.79 L/min to 1.52 L/min, the evaporator pressure drop slightly increases. This is primarily attributed to the reduced mass flow rate, which lowers the evaporation temperature within the parallel-flow heat exchanger. The enhanced cooling capability offsets the anticipated reduction in pressure drop. However, when the flow rate further decreases to 1.28 L/min, localized overheating occurs within the heat exchanger. Higher vapor quality contributes to a reduction in flow resistance within the flat tubes, which aligns with the findings of previous literature [53]. Additionally, low refrigerant flow rates inherently reduce the overall system pressure drop, leading to a significant decrease in evaporator pressure drop. The maximum discrepancy between the experimental and simulated pressure drops is within 5.3%, further validating the accuracy of the proposed model.

4. Results and Discussion

4.1. Effect of Refrigerant Flow Rate

Table 2. Distribution of refrigerant variables under different refrigerant flow rates.

Refrigerant Flow Rate (L/min)	Outlet Air Temperature (°C)	Vapor Quality	Refrigerant Local HTC (W/m2 °C)
Q = 1.79
Q = 1.52
Q = 1.28
Q = 1.05

presents the distribution of outlet air temperature, vapor quality, and heat transfer coefficient (HTC) under varying refrigerant flow rates. Due to the coupling effect of non-uniform airflow velocity and temperature on the air side, the outlet air temperature fluctuates at the same height within the heat exchanger, resulting in an irregular temperature distribution. At flow rates of 1.79 L/min and 1.52 L/min, the highest outlet temperature is observed near the saturation liquid boiling region at the upstream inlet of the PFHE. However, when the flow rate decreases to 1.28 L/min, localized overheating occurs at the downstream outlet, highlighting the impact of non-uniform airflow. Regions with higher inlet air velocity and temperature are the first to experience overheating, reducing the uniformity of the outlet temperature distribution. The maximum outlet temperature reaches 30.7 °C. As the refrigerant flow rate further decreases to 1.08 L/min, the high-temperature region expands downstream, and the outlet air temperature approaches the inlet air temperature, with the maximum temperature reaching 34.4 °C, forming an upward-opening parabolic high-temperature zone. This trend closely aligns with the airflow velocity distribution shown in Figure 4.

The vapor quality distribution further reveals the impact of airflow non-uniformity, leading to variations in the vapor profile. When the flow rate exceeds 1.55 L/min, no localized overheating is detected in any of the PFHE’s flat tubes. Due to the higher airflow velocity in the central region, the vapor quality at the center of the heat exchanger is higher than at the sides. However, at 1.28 L/min, overheating occurs at the outlet of 33 central flat tubes, despite the average vapor quality at these outlets being only 0.92. This indicates that non-uniform airflow can induce localized overheating within the heat exchanger. When the flow rate is further reduced to 1.05 L/min, the overheated region expands significantly, and 44 flat tubes, excluding those at the sides, exhibit extensive overheating.

The local HTC distribution of the refrigerant exhibits a strong correlation with the vapor quality distribution. A comparison of HTC under different flow rates reveals that both higher vapor quality and increased flow rate enhance the heat transfer coefficient in the two-phase region. However, the presence of an overheated region significantly reduces the local HTC. At 1.05 L/min, a large-scale overheating zone appears in the upper section of the heat exchanger, leading to a decline in PFHE performance. This condition should be avoided in practical system applications to maintain optimal cooling efficiency.

Figure 8 illustrates the cooling capacity and inlet/outlet pressure of the PFHE under varying refrigerant flow rates. Notably, as the refrigerant flow rate decreases, the evaporator’s cooling capacity initially increases and then declines. Before significant overheating occurs within the heat exchanger, reducing the flow rate enhances the system’s cooling performance, reaching its peak at 1.28 L/min. This trend is consistent with previous studies on pump-driven two-phase cooling systems, which indicate that the primary role of the liquid pump is to facilitate refrigerant circulation rather than directly enhance heat transfer. Excessively high flow rates increase the evaporation and condensation temperature differentials, which negatively impacts the overall heat transfer efficiency of the system [54]. It is important to note that in pump-driven two-phase cooling systems, if the pump provides insufficient flow, the resulting effect is similar to the low driving force in gravity-driven heat pipes, leading to the formation of extensive overheated regions within the heat exchanger. When the flow rate is further reduced to 1.05 L/min, the overheated zone expands significantly, resulting in a substantial decrease in cooling capacity. Relevant literature indicates that once the outlet quality of the flat tube is greater than one, the heat transfer of the channel will deteriorate, resulting in a sharp rise in wall temperature, and the greater the possibility of system heat transfer deterioration [22]. This results in a rapid decline in cooling capacity, thereby failing to fully exploit the advantages of pump-driven cooling [31,55].

As shown in Figure 8b, evaporator pressure decreases with a reduction in refrigerant flow rate, which is the primary reason for the decline in cooling capacity—a greater temperature difference between the air and evaporator surface enhances heat exchange efficiency. However, the increase in cooling capacity partially offsets the drop in evaporator pressure, explaining the slight rise in pressure drop at 1.52 L/min, as observed in Figure 7b. Once the flow rate decreases to 1.28 L/min, a notable reduction in both evaporator pressure and pressure drop occurs. A comprehensive analysis of the results suggests that the optimal operating condition for pump-driven two-phase cooling systems is achieved when the evaporator outlet vapor quality is relatively high or slightly superheated. However, non-uniform airflow can lead to premature localized overheating at the outlet, restricting further increases in vapor quality and ultimately limiting system performance improvements.

4.2. Effect of Inlet Air Temeprature Distribution on the PFHE Performance

Given the variability of experimental heat loads, this study defines four distinct inlet air temperature distribution patterns for the PFHE, as Figure 9 illustrates. These patterns represent non-uniform thermal load distributions, including higher temperatures in the upstream region, downstream region, and central region of the PFHE. Since the refrigerant flows upward from the bottom within the PFHE, the term “downstream hot section” refers to higher inlet air temperatures in the refrigerant outlet region, while “upstream hot section” indicates higher inlet air temperatures at the refrigerant inlet region. During the calculations, the airflow rate of the PFHE was set to 0.336 m³/s, with an average inlet air temperature of 35 °C. Additionally, the calculations ensured that the refrigerant vapor quality at the PFHE outlet did not result in overheating, and the refrigerant flow rate was maintained at 1.75 L/min.

Figure 10a,b illustrate the outlet pressure distribution, pressure drop, and cooling capacity of the PFHE under different inlet air temperature distributions. Due to the non-uniform airflow, the central region, which has a higher airflow velocity, exhibits greater heat transfer capacity, leading to a larger pressure drop. Consequently, the outlet pressure of the central flat tubes is significantly lower than that of the tubes located at the sides. While the overall outlet-pressure-distribution curves remain consistent across the four temperature distribution cases, the pressure differences among the flat tube outlets vary considerably. The upstream hot section results in the largest pressure difference at the outlet, reaching 2.71 kPa. For two-phase outlet heat exchangers, examining the effects of different temperature distributions on cooling capacity and pressure drop reveals that thermal load distribution has a limited impact on cooling capacity but a more pronounced effect on the drop in pressure. Previous studies on the effects of non-uniform heat loads on flow distribution have also indicated that the pressure drop in two-phase flow is highly sensitive to variations in heat flux [22]. However, this study reveals that the impact of different temperature distributions on pressure drop varies. Compared to a uniform temperature distribution, the pressure drop in the downstream hot section decreases by 7.7%, while it increases by 7.0% in the upstream hot section.

Figure 10c presents the outlet air temperature distribution at the 23rd flat tube under different temperature distribution scenarios. The outlet air temperature follows a consistent pattern across all cases: higher temperatures at the PFHE upstream and lower temperatures at the downstream. The upstream hot section results in the least uniform outlet air temperature, with a maximum temperature difference of 1.9 °C. This is attributed to the combination of high inlet air temperature and lower HTC in the upstream region. In contrast, the downstream hot section achieves the most uniform outlet temperature, with a temperature difference of only 0.3 °C, as the higher temperature airflow in the downstream region partially offsets HTC variations. In the centrally hot configuration, the outlet air temperature initially increases and then decreases, reflecting the influence of localized heating in the central PFHE region. Figure 10d depicts the vapor quality distribution within the flat tubes along the flow direction. Due to the higher inlet air temperature in the upstream hot section, the vapor quality increases more rapidly at the PFHE inlet compared to other cases, leading to higher vapor quality at the downstream section. This contributes to the excessive pressure drop observed in this configuration. Similarly, in the middle-hot and downstream-hot configurations, the regions of rapid vapor quality increase are concentrated in the central and downstream sections of the PFHE, respectively. In contrast, under a uniform temperature distribution, vapor quality increases more evenly across the entire heat exchanger.

From the above analysis, it can be concluded that for two-phase outlet parallel-flow heat exchangers, thermal load distribution has a minimal effect on cooling capacity but significantly influences pressure drop. Concentrating the thermal load in the downstream region reduces the overall pressure drop by 7.7% and enhances the uniformity of the outlet air temperature, making it a preferable design approach for optimizing system performance.

4.3. Effect of Non-Uniform Air Flow on the Multi-Pass PFHE

To investigate the effects of non-uniform air velocity and temperature on the multi-pass PFHE, it was first necessary to develop several multi-pass configurations. This study builds on previous comprehensive analyses of a single-pass heat exchanger, extending it to double-pass and triple-pass configurations. The double-pass PFHE consists of a first path flowing from the bottom to the top using 23 flat tubes, followed by a second path returning from the top to the bottom with another 23 flat tubes. The triple-pass PFHE has a first path moving from the bottom to the top with 15 flat tubes, a second path descending from the top to the bottom with 15 flat tubes, and a third path ascending from the bottom to the top with 16 flat tubes. Figure 11 shows detailed flow diagrams of these configurations, with the arrows in the diagram representing the direction of refrigerant flow

Table 3. Distribution of refrigerant variables with different pass configurations.

Parameter	Outlet Air Temperature (°C)	Vapor Quality	Refrigerant Local HTC (W/m2 °C)
Double-pass
Triple-pass

presents the distribution of outlet air temperature, vapor quality, and local HTC in the PFHE under different flow configurations. In the dual-pass PFHE, the outlet air temperature is strongly influenced by the higher airflow velocity in the central region, resulting in overheating in flat tubes numbered 24–42. At this point, the vapor quality at the PFHE outlet reaches 0.97. In the triple-pass PFHE, overheating is observed at the outlet of flat tubes numbered 31–46 in the third flow path, indicating that all refrigerant exiting the heat exchanger is in the superheated vapor state. Additionally, the impact of flow arrangement on heat transfer performance was examined. The results indicate that as the number of flow passes increases, the maximum outlet air temperature, the length of the single-phase heat transfer region, and the local HTC in the two-phase region all increase.

Figure 12 illustrates the cooling capacity and pressure drop of the PFHE under different pass configurations. As the number of passes increases, the cooling capacity gradually improves. However, compared to uniform airflow conditions, non-uniform airflow generally reduces the cooling performance of the PFHE, though this reduction diminishes as the number of passes increases. Under non-uniform airflow conditions, the cooling capacity of the single-pass, double-pass, and triple-pass PFHE configurations decreases by 7.6%, 5.7%, and 3.2%, respectively, compared to the uniform airflow case. This trend suggests that for a PFHE with a superheated outlet, a multi-pass configuration not only enhances cooling performance but also mitigates the negative effects of airflow non-uniformity. In contrast, the impact of airflow non-uniformity on PFHE pressure drop is relatively minor. However, increasing the number of passes significantly raises the pressure drop from 23.8 kPa in the single-pass configuration to 95.5 kPa in the triple-pass configuration.

4.4. Structural Optimization

Based on the vapor quality distribution from Table 3, certain regions of the outlet in the double-pass PFHE have already achieved superheating, and these superheated areas exhibit relatively lower cooling capacity. By modifying the dimensions of the flat tubes and the number of first pass flat tubes it is possible to reduce the overall pressure drop across the heat exchanger with a slight reduction in cooling capacity, while still maintaining a higher cooling capacity compared to the single-pass PFHE. The optimization should meet the following conditions: the structure of the fins and louvers on the air side must remain unchanged; the length and total number of flat tubes must be consistent; and the width of the flat tubes, typically correlated with fin width, should also remain unchanged.

Figure 13 demonstrates the impact of altering the number of flat tubes in the first pass of the double-pass PFHE on cooling capacity and pressure drop. As the number of tubes in the first pass increases, the number in the second pass correspondingly decreases, yet the cooling capacity remains relatively stable, exceeding 5000 W. This stability is primarily due to most of the flat tubes reaching a superheated state, with changes in the length of the superheated region having minimal impact on the cooling capacity. The cooling capacity of the double-pass PFHE is consistently more than 6% higher than that of the single-pass PFHE under uniform airflow. The pressure drop across the double-pass heat exchanger generally decreases as the number of tubes in the first pass is reduced. By reducing the number of tubes in the first pass, the pressure drop can be significantly lowered; however, even at its minimum, the pressure drop of the double-pass PFHE is still higher than that of the single-pass PFHE. Therefore, it is not possible to simultaneously optimize both cooling capacity and pressure drop of the PFHE by merely adjusting the number of flat tubes in the first pass.

Figure 14 presents a detailed analysis of the influence of flat tube height on the cooling capacity and pressure drop of a dual-pass PFHE under non-uniform airflow conditions. The results indicate that as the flat tube height increases, the cooling capacity gradually decreases. When the tube height increases from 1.3 mm to 3.1 mm, the cooling capacity decreases by 2.2%, which supports the hypothesis proposed earlier. This finding confirms that adjusting the flat tube height in a dual-pass PFHE can reduce the overheated area at the outlet region, shifting the heat transfer mode to primarily two-phase heat exchange. Although this results in a slight reduction in cooling capacity, the overall performance still exceeds that of the single-pass configuration by 4%. The impact of flat tube height on pressure drop is particularly significant. As the flat tube height increases, the pressure drop decreases rapidly. Once the tube height exceeds 1.5 mm, the pressure drop in the dual-pass PFHE falls below that of the single-pass configuration. In the context of pump-driven two-phase cooling systems for data center cabinets, local overheating caused by non-uniform airflow can suppress further increases in vapor quality at the PFHE outlet. However, adopting a dual-pass PFHE configuration can mitigate the impact of localized overheating, enabling the heat exchanger outlet to achieve a higher vapor quality. Furthermore, the increase in flow resistance associated with additional passes can be effectively managed by optimizing the flat tube height.

5. Conclusions

Based on a pump-driven two-phase cooling system (PTCS) for data cabinets and an analysis of the inlet airflow velocity and temperature of an existing server cabinet backplate evaporator, this study developed a two-phase heat transfer model for a parallel-flow heat exchanger (PFHE) under non-uniform airflow conditions. The influence of refrigerant flow rate on heat exchanger performance was investigated, and the PFHE structure was optimized to mitigate the adverse effects of non-uniform airflow on system performance. The main conclusions are as follows:

• Enhancing the vapor quality at the outlet improves system performance. The PTCS achieves optimal performance when the PFHE outlet reaches a vapor quality of one or exhibits slight superheating. However, non-uniform airflow induces localized overheating, which restricts further increases in outlet vapor quality, thereby limiting system performance improvements.
• For cooling systems where the PFHE outlet remains in a two-phase state, non-uniform temperature distributions have a limited impact on cooling capacity, with variations remaining within 3% compared to uniform airflow conditions. However, the influence on pressure drop is more pronounced: when the air temperature is higher in the upstream region, the pressure drop increases by 7%, whereas higher temperatures in the downstream region reduce the pressure drop by 7.7%. Therefore, in data center cooling applications where the PFHE outlet remains in a two-phase state, concentrating heat dissipation in the downstream section of the heat exchanger is preferred.
• Multi-pass configurations effectively alleviate localized overheating caused by airflow non-uniformity. Compared to uniform airflow conditions, the cooling capacity of single-pass, dual-pass, and triple-pass PFHEs decreases by 7.6%, 5.7%, and 3.2%, respectively. However, increasing the number of passes significantly raises the pressure drop, leading to a substantial increase in system resistance.
• Optimizing flat tube height effectively controls flow resistance associated with multi-pass configurations. By adjusting the flat tube height, dual-pass PFHEs demonstrate superior cooling performance and lower pressure drops under non-uniform airflow conditions, making them a more effective solution for pump-driven two-phase cooling systems in data center cabinets.

While this study provides valuable insights into the optimization of pump-driven two-phase cooling systems, further research is needed to address remaining challenges and enhance system performance. Future investigations should focus on the following key areas: 1. Developing adaptive control strategies for real-time regulation of refrigerant flow rates based on dynamic heat load variations in data centers; 2. Exploring advanced air distribution strategies to minimize airflow non-uniformity and reduce localized overheating. We hope that these insights will contribute to a deeper understanding of two-phase cooling system optimization and provide practical guidance for the implementation of high-performance data centers.