Keywords

1 Introduction

Hydrogen fuel cell is considered as a promising option in replacement of traditional fossil energy systems with high efficiency, low emission, and short refueling time. In the automotive industry, polymer electrolyte membrane fuel cell (PEMFC) is used widely. To ensure the operation stability and the duration of membrane, adequate hydrogen is critical for the anode, and same to the cathode with air. The hydrogen ratio defines the ratio of hydrogen inlet mole flow and mole flow consumed by fuel cell stack and it is usually greater than 1. Therefore, hydrogen recirculation system is required to reuse the excess hydrogen from anode exhaust gas, which improves the total efficiency of PEMFC and minimizes environmental pollution [1]. There are many researchers [2, 3] focusing the control strategy and control system simulation of hydrogen recirculation system.

Vortex blower is the key device in hydrogen recirculation system, which inputs work to anode exhaust hydrogen, and it is one of the most energy-consuming devices in PEMFC. Hence, a high efficiency vortex blower is desired for a superior performance PEMFC. Many researchers analyze vortex blower through experimental analysis, theoretical analysis, and simulation analysis. Song [4] discussed about the experimental characteristics of forward and backward bending impeller, which showed little difference in large flow condition. Badami [5] proposed a theoretical model with the consideration of clearance to study leakage. Han [6] analyzed the effect of different blade thickness and blade number, and also predicted fatigue life of blade through simulation. Cai and Zhang [7, 8] studied the influence of blade bending direction and bending angle on flow characteristic of vortex blower with simulation method. In addition, many researchers focus on aero-acoustic and noise simulation [9,10,11]. This study simulated the flow characteristic of a compact hydrogen vortex blower with experimental data.

2 Numerical Simulation

2.1 Geometry Modelling

As shown in Figs. 1 and 2, the vortex blower consists of two main parts, stational flow path with inlet and outlet, and impeller with rotational flow path. The rotational speed of impeller is 10,000–23,000 rpm. The diameter of inlet and outlet is 5 mm. The impeller inner diameter is 27 mm and outer diameter is 76 mm. The impeller has 36 blades. The thickness of blade is 0.8 mm. The fluid domain was calculated by interference operation. To ensure the full development of the flow, extension is added to both inlet and outlet, with length as same as the impeller outer diameter of 76 mm.

Fig. 1.
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Stator of vortex blower.

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Fig. 2.
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Impeller of vortex blower.

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2.2 Mesh Generation

Poly-Hexcore meshes were generated separately on stational flow domain and impeller domain by Fluent Meshing 2020 R1, Fig. 3 shows the Poly-Hexcore meshes of impeller domain and stational flow domain. Mesh independency was checked by refining the impeller domain and checking the pressure difference between inlet and outlet. The inlet flow of mesh independency checking state was set as 12.60 m3/h with rotational speed 17,000 rpm. Four groups of impeller domain mesh were generated with 921,221, 1,228,781, 3,872,419, and 5,853,783. The static pressure differences between inlet and outlet were simulated, and compared with the result from experiment (see Table 1). By consideration of both accuracy and computational resource, mesh group 1 was finally chosen for following numerical simulation.

Table 1. Mesh independency checking results.
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Fig. 3.
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Poly-hexcore meshes of impeller domain and stational flow domain.

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2.3 Solver Setup

In this study, all numerical simulations were conducted by Fluent 2020 R1. To achieve temporal accuracy and numerical stability in transient simulation, Courant number \(Co\) is required less than 1. The Courant number is defined as:

$$Co=\frac{\delta t\left|\mathbf{U}\right|}{\delta x}$$
(1)

where \(\delta t\) is the where is the time step, \(\left|\mathbf{U}\right|\) is the magnitude of the velocity and \(\delta x\) is the cell size. Because the rotational speed of the vortex blower is at the scale of ten thousand, according to \(Co\), the time step should be chosen little than \({10}^{-5}\) s, which will cause enormous computational effort. Therefore, in this study, simulations were completed with MRF method. The interface between the stator and the impeller is not conformal. In Fluent, there are several methods dealing with non-conformal interface, periodic boundary condition, periodic repeats, coupled wall, matching, and mapped. Because the couple wall interface has no flow exchange between two sides of interface, it is not suitable for the simulation in this study, and neither is mapped method, which is always combined with coupled wall.

The viscous model was selected as realizable k-ε two equation model, which is suitable for high Reynolds number flow. With k-ε model, near-wall treatment method should be selected. Scalable wall functions, non-equilibrium wall functions, and enhanced wall treatment are all suitable for this kind of simulation. By comparison with experimental data, enhanced wall treatment was finally chosen. Coupled scheme was used for pressure velocity coupling, with all velocity-relative terms in second order upwind scheme. For better convergence, pseudo transient option was chosen. As to boundary conditions, mass flow inlet and pressure outlet were selected.

3 Results and Discussion

3.1 Internal Flow Simulation

The flow characteristic of the vortex blower was obtained by four groups experiments on a standard blower test rig. In every group of experiments, the valve opening was set as a constant, and by increasing impeller revolution speed from 10,000 to 23,000 rpm, the mass flow and pressure difference were recorded.

The internal flow simulation was conducted based on the experiments. The rotational speed and inlet mass flow were set as same as experimental data, and the pressure difference was computed numerically. The error was acceptable in engineering with less than 20%. Hence the validation of internal flow simulation was checked. In Fig. 4, four groups of simulation results and experimental data were plotted. From group 1 to group 4, the valve opening was increased. Black squares represent experimental data and red circles are simulation results. From left to right on x axis, the rotational speed is increased from 10,000 to 23,000 rpm.

From Fig. 4(a)–(d), the deviation between simulation results and experimental data is growing. The reason for this deviation is that the mass flow was increasing from group 1 to group 4, and the vortex blower was operated with over inlet flow outside the design region, which caused choking condition. This is also a characteristic phenomenon of vortex blower, that it is more sensitive to choking condition than surging condition.

Fig. 4.
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Experimental data and simulation results of the vortex blower. Black squares represent experimental data. Red circles represent simulation results. The rotational speed is increased from 10,000 to 23,000 rpm from left to right on x axis.

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In Fig. 5, the pressure contours of interface between stator and rotator was plotted. The fluid is pressured sequentially by blades with the high-speed rotation of impeller, and the blade structure has influence of the flow pattern on the interface. The flow pathlines were shown in Fig. 6 and a series complex eddy structures near inlet were observed with low velocity. The low-energy flow was gathered around the inner circle of impeller, which will cause flow separation. Because of the centrifugal force, the flow separation near outer circle region was depressed. In the Fig. 7, the pressure contour of impeller also showed pressure gradient both from inlet to outlet and inner circle to outer circle.

Fig. 5.
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Pressure contours of interface between stator and rotator.

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Fig. 6.
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Pathlines colored by velocity magnitude.

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Fig. 7.
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Pressure contour of impeller.

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3.2 Influence of Blade Parameters

In following simulation, the operation point with rotational speed of 17,000 rpm and inlet mass flow of 12.60 m3/h was selected to study the influence of blade parameters to the performance of the vortex blower.

Firstly, the effect of blade number was studied. With the blade number changing evenly from 34 to 42 by 2, six new impeller models were generated. Under the selected operation point, the pressure difference between inlet and outlet was simulated as shown in Fig. 8. With the decrease of blade number, the pressure rise of the vortex blower is increasing. With the same revolution speed, the more blade number means the more friction between fluid flow and blades, which explain the tendency. Besides, the more blade number makes choking condition more easily to happen. So, higher blade number does not benefit the internal flow of vortex blower.

Fig. 8.
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The pressure rises of vortex blower with different blade number at rotational speed of 17,000 rpm and mass flow of 12.60 m3/h.

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The pressure contours of the interface between stator and rotator are shown in Fig. 9. Blade number is 34 on the left. Blade number is 42 on the right. The main flow patterns with blade structure are observed on both sides. However, the pressure contour of 34-blade-number impeller is much more uneven compared with 42-blade-number impeller, though the pressure rise is higher.

Fig. 9.
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Pressure contours of interface between stator and rotator. Blade number is 34 on the left. Blade number is 42 on the right.

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Figure 10 shows that, in the 34-blade-number impeller, there is a large low-pressure region at the suction surface near inlet, which means sever flow separation. With flow separation, larger secondary flow and other eddy structures will lead to higher energy loss. To ensure the performance of vortex blower with less blade number, further experiments should be done, and there will be an optimal number of blades for specific vortex blower structure.

Fig. 10.
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Pressure contours of suction surface near the inlet. Blade number is 34 on the left. Blade number is 42 on the right.

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Secondly, the influence of blade flapping angle was simulated. Blade flapping angle is defined as the space angle between rotation axis and blade plate. In addition, the blade flapping angle is positive when the flapping direction is the same as the rotational direction. In the baseline impeller, all blade plates are parallel to rotation axis, and the blade flapping angle is 0°. New impeller models with blade flapping angle of 5° and − 5° were shown in Fig. 11 left and right. The rotational direction of impeller is counterclockwise face to the paper.

Fig. 11.
figure 11

Impeller models with blade flapping angle. Left: 5°. Right: − 5°.

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These two impeller models were simulated and compared with baseline impeller as shown in Table 2. The positive flapping angle got higher pressure rise than baseline, and the negative flapping angle got lower pressure rise than baseline. By observing the pressure distribution on interface in Fig. 12, the positive blade flapping angle impeller has similar flow structure as low blade number, and the negative blade flapping angle influences flow like high blade number. The reason for negative flapping angle impeller has more smooth pressure contour is that the structure of the suction surface depressed the flow separation relatively. For further optimization of vortex blower, the optimal blade number combined with proper blade flapping angle is worth to discuss.

Table 2. Simulation results of impellers with different blade flapping angle.
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Fig. 12.
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Pressure contours of interface between stator and rotator.

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4 Conclusions

In this paper, a simulation method of the steady internal flow in a vortex blower for hydrogen recirculation system was detailly illustrated. Multiple reference frame method was used to dealing with the relative motion between rotor and stator. The energy characteristic of the vortex blower was recorded through experiments. With the validated simulation method, the influence of blade number and blade flapping angle was discussed. The following conclusions can be drawn:

  • The simulation of operation states within design condition region agreed well with experimental data. When the mass flow over the design region, choking condition will happen.

  • Higher blade number causes more friction loss between fluid flow and blade because of the higher blade frequency. Lower blade number will get higher pressure rise.

  • Positive blade flapping angle improves the pressure rise of the vortex blower. Negative blade flapping angle has the influence of depressing the flow separation at the impeller and make pressure field more even.