Investigations on the Effect of Inclination Angle on the Aerodynamic Performance of a Two-Stage Centrifugal Compressor of a Proton Exchange Membrane Fuel Cell System

Abstract

This study examines how leading-edge inclination angles affect a two-stage centrifugal compressor’s aerodynamic performance using numerical and experimental methods. Five impellers with varied inclination configurations were designed for both stages. The results show that negative inclination improves the pressure ratio and efficiency under near-choke conditions, with greater enhancements in the low-pressure stage. Positive inclination significantly boosts the pressure ratio and efficiency under near-stall conditions, particularly in the low-pressure stage. Negative inclinations optimize blade loading and choke flow capacity, while effectively reducing incidence angle deviations induced by interstage pipeline distortion and decreasing outlet pressure fluctuation amplitude in the high-pressure stage. Positive inclinations delay flow separation, suppress tip leakage vortices, and extend the stall margin.

1. Introduction

Proton exchange membrane fuel cells (PEMFCs) can be started up rapidly at room temperature and have the characteristics of high energy conversion efficiency and high specific power output, and are widely used in vehicles and stationary power generation systems [1,2,3]. Proton exchange membrane fuel cells for automobiles usually require an air supply system to provide about 280 kilopascals of air (considering about 20 kilopascals of pipeline loss) to ensure the efficient operation of the battery stack [4,5]. As shown in Figure 1, the proton exchange membrane fuel cell system includes an air circuit (air filter, compressor, intercooler, humidifier) and a hydrogen circuit (hydrogen tank, pressure reducing valve, hydrogen circulation pump). In the air circuit, ambient air first passes through the filter, enters the compressor, is cooled to 80 to 85 degrees Celsius by the intercooler, and finally flows into the cathode side of the fuel cell stack after humidification. During this process, the compressor is the core power transmission component [6,7,8,9].

Owing to their broad flow range and high pressure ratio, two-stage centrifugal compressors have become the standard air supply solution for PEMFC systems exceeding 30 kW since 2021. Current research focuses on centrifugal compressors integrated with turbine energy recovery devices. The fuel cell exhaust (approximately 85 °C with residual pressure) can drive such turbines to assist motor operation, achieving 28–32% higher efficiency compared with conventional two-stage centrifugal compressors. However, challenges including water corrosion and system sealing reliability have hindered practical implementation of this technology. Consequently, two-stage centrifugal compressors remain the primary air supply solution for PEMFC systems [10,11].

A two-stage centrifugal compressor is generally composed of three core components: aerodynamic pressure bearings, high-frequency controllers, and high-speed permanent magnet motors. The high-frequency controllers drive the high-speed permanent magnet motor, which subsequently rotates two impellers with unequal pressure ratios to compress air. These impellers correspond to the compressor’s low-pressure and high-pressure stages, respectively. A pneumatically optimized interstage pipe connects the two stages, enabling airflow to transition from the low-pressure stage to the high-pressure stage, thereby completing the compression process [12,13].

As the sole component performing work on the gas, the impeller determines the energy transferred to the gas and directly influences the compressor’s pressure ratio [14,15]. The leading-edge inclination angle of the impeller significantly affects its power capacity. Clarifying the influence mechanism of the leading-edge inclination angle on two-stage centrifugal compressors holds substantial engineering value for optimizing compressors’ performance.

Smith [16] proposed the curved sweep blade design for axial flow impellers. Howard [17] conducted numerical studies on centrifugal impellers’ blade curvature, demonstrating that curved blades reduce low-energy fluid accumulation near the shroud and moderately enhance impellers’ turbocharging capacity. Van den Yang [18] investigated secondary flow control using curved blades in centrifugal compressors, revealing that curved blades regulate the internal secondary flow intensity by modifying the blade surface pressure gradients.

Significant research has been conducted on the working characteristics of centrifugal compressor impellers with tilted blade configurations under varying operating conditions. Harrison [19] demonstrated that blade tilt significantly affects blade surface loading, internal energy loss distribution, and boundary layer development. Harada [20] introduced blade skew for closed impellers, showing that this design reduces the hub-to-shroud pressure gradient, suppresses secondary flow generation, and enhances compressor efficiency. Ganesh et al. [21] and Wadia et al. [22] concluded that leading-edge inclination reduces blade tip sensitivity and elucidated its operational mechanisms. Oh et al. [23] provided geometric definitions for blade tip curvature variations, revealing distinct flow pattern changes at different blade development positions. Erdmenger et al. [24] studied compressors with diffuser blades, finding that moderate main blade sweep improves the pressure ratio at the expense of operating range, while splitter blade sweep expands the operating range by 16%. Wang et al. [25] calculated that forward curved blades enable stable low-power operation while improving the system’s efficiency. Zhang et al. [26] investigated manufacturing tolerance effects, demonstrating that efficiency losses from blade thickness errors can be offset by optimized blade angle reduction. Ding et al. [27] analyzed compressor cascade flow fields, showing that a positive cascade inclination reduces angular losses through spanwise pressure gradient adjustment. Increasing inclination angles elevates the airflow incidence angles and redistributes boundary layer flow, thereby expanding the compressor’s operational range.

To date, few studies have focused on the mechanism by which leading-edge inclination variations in two-stage centrifugal compressor impellers influence internal flow dynamics. The interstage pipeline between the low-pressure and high-pressure stages induces inlet flow distortion in the high-pressure stage [28], resulting in non-uniform flow field distribution. As airflow is pre-compressed by the low-pressure stage, it enters the high-pressure stage with elevated pressure and kinetic energy, enhancing its resistance to adverse pressure gradients—a distinct contrast to the flow characteristics at the low-pressure stage inlet. Consequently, variations in the impeller’s leading-edge inclination significantly alter the flow behavior throughout the two-stage compressor.

Although the coupling of multiple parameters in the design of centrifugal compressors is very complex, the inclination angle of the leading edge of the impeller has a profound impact on PEMFC compressors, especially in the internal flow control and inlet distortion caused by interstage pipelines. The literature [16,17,19,20,23] indicates the control of the blade inclination angle on the internal flow conditions of the impeller. Reference [28] also elaborates on the reasons for the distortion at the inlet of the high-pressure stage caused by the interstage pipeline. Therefore, before conducting complex multi-parametric optimization, it is necessary to clarify the specific influence of the leading-edge inclination angle of the impeller on the two-stage centrifugal compressor.

In this study, five centrifugal impellers with distinct leading-edge inclination angles were designed for both stages of a 120 kW PEMFC system compressor. Numerical simulations and experimental investigations were conducted to analyze the internal flow patterns, energy losses, and load distributions under diverse operating conditions, providing foundational insights for optimizing the aerodynamic design of two-stage centrifugal compressors.

2. Research Method

2.1. Research Model

The two-stage compressor, which incorporates a dynamic pressure air bearing and a high-speed frequency converter as its driving system, is schematically illustrated in Figure 2. Its core components include a low-pressure stage impeller, a high-pressure stage impeller, a vaneless diffuser, an interstage flow passage, and the corresponding low-pressure and high-pressure stage volutes. The design operating parameters are specified as follows: a rotational speed of 80,000 rpm, a mass flow rate of 0.19 kg/s, a pressure ratio of 2.8, and a maximum allowable speed of 100,000 rpm. The initial geometric configuration parameters of the compressor are detailed in

Table 1. Parameters of the base model.

Parameters	Low-Pressure Stage	High-Pressure Stage
Number of main blades	8	8
Number of splitter blades	8	8
Inlet diameter of impeller (mm)	55	50
Diffuser inlet diameter (mm)	80	74
Volute outlet diameter (mm)	41	41
Tip leading-edge clearance (mm)	0.3	0.3
Tip trailing edge clearance (mm)	0.3	0.3

.

2.2. Numerical Method

In this study, the leading-edge inclination of the impeller is defined as follows. The positive inclination is aligned with the impeller’s rotational direction. Negative inclination is oriented opposite to the rotational direction. Distinct models with varying leading-edge inclination angles were developed for both the low-pressure stage (LPS) and high-pressure stage (HPS) impellers. The baseline model features a leading-edge perpendicular to the hub. Five additional configurations with leading-edge inclination angles of −15°, −5°, 0°, +5°, and +15° were generated (Figure 3), with the nomenclature and geometric specifications detailed in

Table 2. Nomenclature of impeller models with varied leading-edge inclination angles.

Model Set Name		Negative Leading Edge	Positive Leading Edge
Low-pressure stage impeller	Model A1	−15°	——
	Model A2	−5°	——
	Model A3	0°	0°
	Model A4	——	+5
	Model A5	——	+15°
High-pressure stage impeller	Model B1	−15°	——
	Model B2	−5°	——
	Model B3	0°	0°
	Model B4	——	+5
	Model B5	——	+15°

.

2.2.1. Mesh Generation

This study employs the IGG/AutoGrid module of NUMECA 9.0 software for structured mesh generation for the compressor. Considering the significant blade curvature of the centrifugal impeller, an O–H hybrid topology is adopted: O-type grids are applied around the blade, while H-type grids are used in the leading-edge, trailing-edge, tip clearance, and flow passage regions. For stationary components (diffuser, volute, and interstage pipe), manual meshing is performed using the IGG module. The diffuser–volute interface is connected through perfect matching to form a complete computational domain, whereas the asymmetric structures of the volute and interstage pipe utilize a butterfly topology to enhance mesh accuracy. The overall mesh distribution is shown in Figure 4.

To ensure computational accuracy and minimize mesh dependency, four grid systems with varying densities were established for both stages. As demonstrated in

Table 3. Verification of mesh independence.

Mesh Set Name		Number of Elements	Design Condition Pressure Ratio	Near-Stall Condition Pressure Ratio	Near-Clogging Operating Condition Pressure Ratio
Low-pressure stage	Mesh-A1	2,057,103	1.807	1.836	1.605
	Mesh-B1	2,260,417	1.800	1.842	1.597
	Mesh-C1	2,463,661	1.801	1.840	1.599
	Mesh-D1	2,666,905	1.801	1.840	1.600
High-pressure stage	Mesh-A2	1,931,984	1.525	1.576	1.453
	Mesh-B2	2,123,516	1.520	1.569	1.446
	Mesh-C2	2,315,048	1.521	1.570	1.450
	Mesh-D2	2,506,580	1.519	1.570	1.451

, which compares pressure ratio variations under design conditions across mesh resolutions, a grid count exceeding 2 million cells (while satisfying quality criteria of no negative volumes, orthogonality > 10°, aspect ratio < 1000, skewness < 5) limits pressure ratio errors to within 0.2%, with further refinement showing negligible impact. Consequently, the single-passage computational mesh comprises 2,463,661 cells for the low-pressure stage and 2,315,048 cells for the high-pressure stage. The full annulus simulations utilize 11,344,470 cells (low-pressure stage) and 10,716,273 cells (high-pressure stage).

2.2.2. CFD Method

The numerical simulation in this study was completed using the FINE/Turbo platform of NUMECA 9.0. The boundary conditions at the compressor inlet were set as an axial intake with the specified total pressure and total temperature. The inlet of the low-pressure stage was set at 101,325 Pa and 298.15 K. The inlet of the high-pressure stage was set as the outlet parameters of the low-pressure stage. The outlet boundary conditions were defined by the specified mass flow rate. All wall boundary conditions adopted the adiabatic no-slip condition. For steady-state single-channel calculations, the stator–rotor interface was processed by the mixed plane method, while the full-loop simulation used the frozen rotor method. In non-steady-state calculations, the boundary conditions were matched with the steady-state settings, and the stator–rotor interface was regarded as a “sliding grid surface”, with the initial conditions coming from the steady-state results. The rotor rotation period was divided into 160 time steps, with each step corresponding to a 2.25° rotation of the impeller.

The governing equations were solved using the three-dimensional Reynolds-Averaged Navier–Stokes (RANS) equations with the Spalart–Allmaras (S-A) turbulence model [29]. Spatial discretization utilized a second-order central difference scheme, while temporal integration was achieved via a fourth-order Runge–Kutta method. For unsteady simulations, Jameson’s dual time stepping method was implemented. This approach introduces a pseudo-time derivative term into the steady-state equations, enabling iterative computation through dual time advancement. A large physical time step was selected, with convergence acceleration achieved by integrating multigrid techniques, local time stepping, and implicit residual smoothing. The pseudo-time derivative term is expressed as

$${\displaystyle \frac{\partial }{\partial t}}{\displaystyle \underset{V}{\iiint }UdV+{\displaystyle \underset{V}{\iiint }\frac{\partial U}{\partial \tau }}}dV+{\displaystyle \underset{S}{\iint }\overrightarrow{F}·d\overrightarrow{S}={\displaystyle \underset{V}{\iiint }QdV}}$$

(1)

where $t$ and $\tau$ represent the physical time steps and virtual time steps, respectively; $U$ is the vector solution of conserved variables; $V$ is the volume of the control body; $\overrightarrow{F}$ is the flux form of a conserved variable; and $Q$ is the source term. When performing each physical time step in the steady calculation involving virtual time steps, a Taylor expansion of the flux $U·V$ is required, as follows:

$${\left(U·V\right)}^{n+1}={\left(U·V\right)}^n+{\displaystyle \frac{\partial {\left(U·V\right)}^n}{\partial t}}\Delta t+o\left(\Delta t^2\right)$$

(2)

In the next time step (n + 1) in physical calculations, the formula above can be expressed further as:

$$U_{initial}^{n+1}{V}^{n+1}={\left(U·V\right)}^n+{\beta }_1{\left(U·V\right)}^n+{\beta }_0{\left(U·V\right)}^n+{\beta }_{-1}{\left(U·V\right)}^n$$

(3)

2.3. CFD Method Validation

In the collaborative laboratory of Northeast University, experimental tests were conducted on a two-stage centrifugal compressor to validate the accuracy of the computational fluid dynamics (CFD) method. The test bench comprised two main circuits: the working gas circuit and the cooling water circuit. By collecting the performance parameters at multiple rotational speeds, comprehensive aerodynamic performance data under various operating conditions were systematically obtained. Designed to simulate the compressor’s operating state within a proton exchange membrane fuel cell (PEMFC) system, the bench was driven by a permanent magnet motor. Pressure and temperature sensors installed at the compressor’s inlet and outlet collected real-time data, which were then standardized to reference conditions. Schematic diagrams of the test bench and compressor installation are provided in Figure 5a and b, respectively.

Table 4. Experimental instruments.

Test Instrumentation	Manufacturer	Range
High-speed motor	Syco Tec (Germany)	0~120,000 rpm
Pressure and temperature integrated sensor	SANTANA (Germany)	0~4 MPa
Self-priming pump (RJm-70-600)		0–3 m3/h
Air filter assembly (AF005)	Beijing SinoHytec Co., Ltd. (China)
Flow sensor (0281006196)	SHENAN (China)	8–500 kg/h
Intake air cooler (SN2107050015)	TOYOTA (Japan)

lists the sensors, controllers, and other components used. During testing, the motor was started and adjusted to 40,000 rpm for preheating. Once the parameters stabilized, the rotational speed was incrementally increased to the rated speed while monitoring the pressure transmission. Flow rate was adjusted by controlling the valve opening. Upon detection of a distinct rumbling noise from the compressor, indicating entry into the surge zone, data collection at the reduced flow point was halted. After completing all the data acquisition, the compressor’s speed was gradually reduced and shut down following a cooldown period, concluding the experiment. In this study, efficiency refers to the overall compressor efficiency, defined as the ratio of the actual output power to the theoretical input power, expressed by the following formula

$$\eta ={\displaystyle \frac{m·C_p·T_{in}·\left(P{r}^{\left(\kappa -1\right)/\kappa }-1\right)}{P_{inv}}}$$

(4)

where $P_r$ is the pressure ratio; $C_p$ is the specific heat at constant pressure, $C_p=1004 \mathrm{J}/\left(\mathrm{k}\mathrm{g}·\mathrm{K}\right)$; $\kappa$ is the specific heat ratio $\left(\kappa =1.4\right)$; and $P_{inv}$ indicates the power input to the controller.

Figure 5c compares the CFD and experimental data at the rated speed of 80 revolutions per minute. As shown in the figure, the CFD results are highly consistent with the experimental measurements. However, as the mass flow rate increases, the differences between the CFD and experimental data gradually increase but remain within 2%. Under the design conditions, the pressure ratio and efficiency differences between the CFD and the experiment are 1% and 3%, respectively, and the experimental values are always higher than the numerical predictions. These deviations mainly result from the experimental cooling system, where the metal components (such as the volute) dissipate heat, reducing the isentropic compression work and improving the overall efficiency, and the thermal expansion effect, where the reduction in the gap between the impeller and diffuser reduces the tip leakage loss. The strong correlation between the experimental results and the numerical results verifies the reliability of the adopted CFD method. To verify the repeatability of the experiment, comparative experiments at different speeds of 60,000 rpm and 100,000 rpm were conducted, as shown in Figure 5d, and the same experimental results were obtained, further verifying the feasibility of the model.

3. Results and Discussion

3.1. Compressor Performance Analysis

In this work, isentropic efficiency is used as a metric to measure the performance of the compressor. It is defined as

$${\eta }_s={\displaystyle \frac{{h_2}^s-h_1}{h_2-h_1}}$$

(5)

where $h_2^s$ is the enthalpy value of the isentropic process at the exit, $h_2$ is the enthalpy value at the exit of the actual process, and $h_1$ is the enthalpy value at the entrance.

Figure 6 presents CFD results of five compressor models with leading-edge inclination angles ranging from −15° to 15°. Comparative analysis shows that the high-pressure stage exhibits a slower rate of isentropic efficiency variation compared with the low-pressure stage. The low-pressure stage demonstrates a slower pressure ratio enhancement than the high-pressure stage for equivalent mass flow increments. These performance differences primarily result from inlet flow distortion effects. Furthermore, the pre-compressed airflow entering the high-pressure stage contributes to its consistently lower efficiency relative to the low-pressure stage. The efficiency characteristics follow a parabolic trend with mass flow rate, peaking near the design point for the base model. Positive inclination angles shift the peak efficiency toward lower mass flow rates, while negative angles extend it to higher flow regions.

Compared to the base model, the pressure ratio and efficiency of LP-A1 model increase 1.5% and 2.5% under near-stall conditions; while the values are 0.25% and 0.6% for the HP-B1 model. Under near-choke conditions, the pressure ratio and efficiency of LP-A5 model increase 2.8% and 9.2%; for the HP-B5 model, the values are 1.1% and 3.3%. Compared with the base model, positive inclination angles enhance the pressure ratio and efficiency in low-flow regions, improving the stall margin. Conversely, negative angles increase the choking flow capacity in high-flow regions. However, positive inclinations beyond 5° accelerate pressure ratio decay. This aerodynamic performance degradation correlates directly with leading-edge flow separation intensity, which is particularly pronounced in the high-pressure stage.

3.2. Flow Characteristic Analysis

3.2.1. Internal Flow Field Analysis

Figure 7 and Figure 8 illustrate the meridional circumferential relative velocity streamlines and entropy distribution characteristics of the compressor under low-flow conditions. It can be seen that under low-flow conditions, two distinct recirculation zones of different sizes form at the leading edge and tip clearance of the main blade in the low-pressure stage, with the vortex core intensity gradually strengthening as the leading-edge inclination angle increases. In contrast, a larger recirculation zone forms at the leading edge of the main blade in the high-pressure stage, but the vortex core intensity is weaker than that in the low-pressure stage and decreases as the leading-edge inclination angle increases.

According to the streamline characteristics in Figure 7a, the recirculation vortex at the leading edge of the low-pressure stage main blade is primarily formed by the combined effects of the adverse pressure gradient and tip clearance flow. Under low-flow conditions, the lower inlet velocity of the impeller exacerbates the adverse pressure gradient in the diffuser section, causing the boundary layer to lack sufficient kinetic energy to maintain attached flow, thereby triggering separation. This separation phenomenon is reflected in the high-entropy regions in Figure 9, indicating concentrated flow losses. Additionally, the interaction between the tip clearance leakage flow and the main flow forms a secondary vortex structure, with the intensity increasing as the leading-edge inclination angle enlarges.

The entropy distribution in Figure 8 further reveals the spatial characteristics of flow losses. In the low-pressure stage, the high-entropy regions corresponding to the leading-edge recirculation vortex indicate significant flow losses in this area. In contrast, the entropy distribution in the high-pressure stage is more uniform, demonstrating that the pressurization effect from the preceding stages effectively suppresses separation losses. This difference mainly stems from the increased inlet pressure in the high-pressure stage, which enhances the kinetic energy of the airflow, enabling it to better overcome the adverse pressure gradient.

The flow characteristics of the low-pressure and high-pressure stages exhibit notable differences. In the low-pressure stage, the lower inlet pressure makes the airflow prone to separation under the adverse pressure gradient, forming a dual vortex structure. As the leading-edge inclination angle increases, the vortex core intensity gradually strengthens, further exacerbating flow losses. In the high-pressure stage, however, the pressurization effect from the preceding stages increases the inlet pressure, enhancing the airflow’s kinetic energy and suppressing the development of recirculation vortices. As a result, the vortex core intensity in the high-pressure stage is weaker than that in the low-pressure stage and decreases with an increasing leading-edge inclination angle.

Figure 9 and Figure 10 present the velocity distribution contours at the inlet of the compressor under design point conditions. It can be seen that the low-velocity region near the pressure surface gradually expands with an increasing leading-edge inclination angle. During high-speed rotation, centrifugal forces and wall adhesion effects drive airflow accumulation near the pressure surface, forming a low-momentum zone. The increased leading-edge inclination angle elevates the incidence angle at the impeller’s inlet, generating localized vortices and recirculation zones that induce flow deceleration, exacerbate separation, and further enlarge the low-velocity region. Notably, in Region A of Figure 10, an extensive low-velocity zone emerges at the tip of the high-pressure stage impeller. This phenomenon arises from the inlet velocity distortion caused by the flow’s non-uniformity in the interstage pipeline, which leads to flow discrepancies within the impeller’s passage and degrades its performance.

Figure 11 and Figure 12 show the radial velocity distribution at the circumferential exit section of the impeller. In these figures, the transverse velocity cloud image represents the division of the circumferential angle of the impeller, while the longitudinal velocity cloud image shows the distribution from the hub to the shroud side. For the low-pressure stage model, the radial velocity distribution at the outlet is relatively uniform, and the influence of low velocity caused by blockage at the tongue is relatively minor. Compared with the A3 model, the other two models with leading-edge inclination modifications exhibit increased exit flow velocities. The change in the blade’s leading-edge inclination angle causes the incident direction of the airflow to deviate from the radial direction. This alteration increases the radial component of the fluid velocity vector as it passes through the blade, resulting in an increase in the radial velocity at the impeller’s exit position.

In the A5 model, regions of low flow velocity appear at the outlet. As shown in Figure 11, the positive increase in the leading-edge inclination of the impeller leads to an expansion of the flow separation area near the blade tip, intensifying the tip leakage vortex and causing low flow velocity near the hub. For the high-pressure stage model, due to the blocking effect of the spiral tongue and the inlet distortion of the interstage pipes, a large area of velocity deficit exists between 0° and 120° along the impeller’s circumference. The positive increase in the leading-edge inclination of the blade increases the attack angle, thereby mitigating the influence of inlet distortion. Similar to the low-pressure stage model, changes in the leading-edge inclination angle also enhance the radial velocity distribution. In the B5 model, a positive increase in the leading-edge inclination of the impeller results in a low flow velocity area near the shroud side.

The blade passage diffusion degree is typically defined as the ratio of the outlet’s cross-sectional area to the inlet’s cross-sectional area of the blade passage. It can be expressed by the following formula

$$D={\displaystyle \frac{A_{out}}{A_{in}}}$$

(6)

where $A_{in}$ and $A_{out}$ represent the cross-sectional areas of the inlet and outlet of the blade channel, respectively. A higher diffusion degree indicates a more significant change in the cross-sectional area of the blade passage, leading to a greater reduction in flow velocity within the passage and a higher conversion efficiency from kinetic energy to pressure energy, thereby improving the compressor’s pressure ratio. However, an excessively high diffusion degree may induce flow separation, degrading the compressor’s performance.

As shown in Figure 13, as the leading-edge inclination angle of the low-pressure impeller decreases, both the inlet cross-sectional area of the blade passage and the diffusion degree increase. Consequently, the flow loss within the passage decreases, and the airflow stabilizes, enhancing the impeller’s energy transfer capacity and improving the compressor’s efficiency. However, the reduced inclination angle causes the leading edge of the main blade to rotate in a direction that obstructs the main blade’s flow path. This results in increased airflow deflection at the main blade’s leading edge, disturbing the downstream flow field. The disturbed airflow enters the diverter blade at an inappropriate angle, impacting its leading edge and triggering flow separation, which deteriorates the flow conditions near the diverter blade’s leading edge.

Additionally, due to the change in the leading-edge inclination angle, secondary flow emerges near the shroud side of the high-pressure stage impeller, with a more pronounced secondary flow structure observed at the 50% span position. In contrast, the circumferential extent of secondary flow in the baseline model is minimal. However, adjusting the leading-edge inclination angle positively influences the flow direction, diminishing the secondary flow and promoting a more uniform velocity distribution within the flow channel.

In the flow section of the impeller, a pressure gradient forms between the pressure surface and the adjacent suction surface, as well as from the blade root to the tip regions. Under the combined influence of these two gradients, a positive pressure gradient is established from the hub region of the pressure surface to the cascade region of the suction surface. As shown in Figure 14, with an increase in the leading-edge inclination angle, the positive pressure gradient area on the pressure surface expands and shifts toward the suction surface. This phenomenon enhances airflow migration from the blade surface adhesion layer to the blade tip, causing low-energy fluid accumulation in the tip region and promoting the growth of low-energy vortices.

Compared with the low-pressure stage, a distinct pressure reduction zone exists in the local flow channel region of the high-pressure stage impeller, specifically near the spiral tongue. Due to the circumferential non-uniformity of the volute, the blocking effect of the spiral tongue disrupts the airflow along the flow channel in the reverse direction. Simultaneously, inlet distortion caused by the interstage pipelines results in an uneven airflow distribution, leading to localized pressure reduction.

When the impeller’s leading-edge inclination angle is oriented opposite to the direction of rotation, the air inlet angle decreases. Under the assumptions of a constant impeller speed and relative velocity, the velocity triangle principle indicates that both the absolute velocity and its axial component increase as the leading-edge angle orientation opposes the rotation direction. This configuration enhances the flow rate while stabilizing the internal flow, thereby improving the pressure load distribution across the impeller, reducing low-velocity cluster accumulation on the blade surface, and ultimately enhancing the working capacity of the impeller.

A comparison of tip leakage flow variations in impellers with different leading-edge inclination angles reveals that under high-flow-rate conditions, tip leakage flow primarily consists of two components. The first component is the mainstream leakage flow from the pressure surface to the suction surface through the blade tip clearance. The second component arises from the influence of the attack angle at the impeller inlet, which generates a low-energy flow region near the blade tip, forming a strong tip leakage vortex. Under high flow rate conditions, the leakage vortex intensifies, its structure becomes more complex, and it significantly disrupts the normal airflow state.

When the leading-edge inclination angle increases in the opposite direction, the reduction in the inlet air attack angle decreases the low-energy flow region near the blade tip, suppressing the leakage vortex and reducing leakage flow. As shown in Figure 15, increasing the leading-edge inclination angle in the opposite direction elevates the axial velocity, mitigates the effects of pressure load redistribution on the impeller, and shifts the low-velocity flow region away from the suction surface, thereby improving the flow conditions.

3.2.2. Impeller Blade Load Analysis

Figure 16 presents the spatiotemporal distribution of static pressure at the 50% span position under design point conditions. The horizontal axis represents the normalized position from the impeller’s inlet to the outlet flow channel, while the vertical axis shows the normalized results over a complete time period. The total number of time steps is 160, with a total period count of $2\pi$. For the low-pressure stage model, the outlet static pressure decreases as the leading-edge inclination angle increases, accompanied by localized pressure fluctuations. In the A5 model, a uniformly distributed low-pressure zone emerges within the 0.2–0.4 chord length range, a phenomenon attributed to the combined effects of airflow separation and localized adverse pressure gradients within the flow channel.

For the high-pressure stage model, a significant low-pressure area forms at the impeller inlet, extending to the 0.4 chord length position. Compared with the low-pressure stage model, the high-pressure stage model exhibits a larger pressure fluctuation region at the outlet, caused by the coupling effect of intake distortion from the interstage pipeline and the reverse-propagating pressure wave from the volute. As the leading-edge inclination angle increases, the static pressure at the outlet of the high-pressure stage model decreases monotonically.

The spatiotemporal evolution characteristics of the B1 model closely align with those of the B3 model. In contrast, although the B5 model shows an extensive low-pressure zone at the inlet, its outlet pressure pulsation is significantly reduced. Specifically, for the B5 model, the inlet’s low-pressure area occupies a wide distribution range, while the outlet’s pressure fluctuations are attenuated compared with other configurations.

To investigate blade load fluctuations, the concept of the root mean square (RMS) of the blade load is introduced. The formula for calculating the RMS of load fluctuations is as follows

$$RMS=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{t=0}^{N-1}{(P_t-\overline{P})}^2}}$$

(7)

where $P_t$ is the load value at the time step $t$ and $\overline{P}$ is the average load value at all time steps.

As shown in Figure 17, for the low-pressure stage model, high load fluctuations are primarily concentrated near the leading-edge tip and trailing edge of the blade. Compared with the A3 model, the A1 model exhibits a reduced high-load fluctuation area in the blade tip region, while the overall blade load fluctuation gradually increases, with outlet load fluctuations exceeding those of the A3 model. In contrast, the A5 model shows a decreased high-load fluctuation area at the blade tip but increased load fluctuations within the blade interior and trailing edge. This behavior arises because a positive increase in the blade’s leading-edge angle aligns the airflow more closely with the centrifugal force direction during entry, promoting flow separation and thereby intensifying load fluctuations.

The load fluctuation in the blade tip region is primarily caused by tip leakage vortex-induced losses. As shown in the figure, increasing the leading-edge inclination angle of the blade effectively suppresses tip leakage. For the low-pressure stage model, the overall load fluctuation range is significantly larger than that of the high-pressure stage model, with concentrated fluctuations near the blade leading and trailing edges. In the high-pressure stage model, the higher airflow pressure reduces tip leakage compared with the low-pressure stage.

A comparison with the B3 model reveals no significant difference in load fluctuation near the leading edge of the B1 model, but the trailing edge exhibits higher load fluctuation. In contrast, the B5 model shows a notable reduction in internal blade load fluctuation and a slight increase in outlet region fluctuation; however, the overall load distribution becomes more uniform, enhancing the blade’s operational reliability. A negative inclination can reduce the deviation of the inlet’s attack angle, especially in the case of interstage distortion; at the same time, it can change the pressure gradient from the hub to the casing, suppressing the secondary flow at the end walls. Structurally, it involves the reconstruction of the load distribution, transferring the load towards the blade core by tilting the leading edge inward, thereby reducing the stress concentration at both ends.

4. Conclusions

This study, through a combination of numerical simulation and experimental verification, systematically investigated the influence of variation of the inclination angle from 15° to 15° on the two stages of the PEMFC centrifugal compressor for the geometric parameter of the leading-edge inclination angle, especially in terms of internal flow control and the distortion of the inlet of the interstage pipeline. The key findings are summarized as follows:

(1)

The +15° inclined impeller exhibits superior stability under near-stall conditions. For the low-pressure stage (LP-A5 model), the impeller’s work capacity improves, the pressure ratio increases, and the stall margin expands by approximately 5%. These enhancements are attributed to optimized incidence angle alignment, which suppresses tip leakage vortices and delays flow separation.

(2)

The −15° inclined impeller demonstrates excellent performance under high-flow conditions. Geometrically constrained channels formed between the main and splitter blades reduce streamwise pressure gradients. Enhanced kinetic energy at high flow rates overcomes boundary layer resistance, suppresses secondary flow development, and ensures smoother internal airflow.

(3)

The negative inclination effectively reduces the incidence angle deviations induced by interstage pipeline distortion. Compared with the baseline model (B3), the B1 model shows reduced outlet pressure fluctuation amplitude and significantly improved flow uniformity in the high-pressure stage passages. In contrast, the +15° configuration (B5 model) increases local entropy due to expanded tip separation zones, potentially compromising operational stability. Additionally, the −15° impeller reduces blade load fluctuations, thereby extending the operational lifespan.

These findings provide critical theoretical insights for the aerodynamic optimization of two-stage centrifugal compressors, particularly for fuel cell systems requiring wide operational ranges.