Keywords

1 Introduction

Hydrogen refueling station is a hub connecting the production, transportation and application of hydrogen, where the pressurization of hydrogen is a necessary step to improve the energy density and practicality of hydrogen as an energy source. In this process, hydrogen needs to be pressurized to an extremely high pressure of 45 MPa or 90MPa, while its high purity must be guaranteed [1]. Diaphragm compressor is widely used as the hydrogen compressor in hydrogen refueling stations due to its high compression ratio and superior sealing performance [2]. However, as the core component of diaphragm compressor, the diaphragm is also one of the vulnerable parts [3]. Due to the fact that the cost of compression devices can account for about half of installed capital cost of a hydrogen refueling station [4], and the failure of diaphragm will further increases the operating cost of the station, reasonable analysis of diaphragm failure is of great significance for reducing the cost of the hydrogen refueling station.

The diaphragm of the diaphragm compressor is generally composed of three plates, which are the process plate contacting with hydrogen, the hydraulic plate contacting with hydraulic oil, and the middle plate avoiding possible leaks while the diaphragm’s failure happens. Usually, the failure of the diaphragm occurs on the process plate, i.e., the hydrogen side plate, or hydraulic plate [5], while the former is more frequent. Furthermore, the fracture of the process plate can be found at the edge, the center and the middle area [5].

Most literature used static structure analysis of the diaphragm when it clings to the cavity of the cylinder head or the perforated plate and concluded that the stress at the edge or center of the process plate or the middle area of the hydraulic plate exceeds the allowable stress, which gave the reasons for the cracks at these locations [5,6,7,8]. However, little literature discussed the cracks appearing in the middle area of the process plate. The static structure analysis and dynamic analysis based finite element method (FEM) simulation are applied to the diaphragm respectively, and the results are compared and discussed in this paper. It is found that the result of dynamic analysis is more consistent with the failure mode of the diaphragm, which explain the reason for the failure in the middle area of the process plate.

2 Fault Cases

In some diaphragm failure events of the diaphragm compressors for hydrogen refueling station, cracks are found in the middle area of the process plates. Figure 1(a, b) display two fault cases of the diaphragm with the cracks of the process plates appearing in the middle area near the exhaust holes. The cases belonged to the diaphragm compressors with the same design parameters which are listed in Table 1.

Table 1. Parameters of diaphragm compressors with diaphragm failure.
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Fig. 1.
figure 1

Fault cases of the diaphragm

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3 Failure Analysis of the Diaphragm

In the diaphragm compressor, the diaphragm is clamped by the cylinder head and cylinder block at the edge, and the middle part undergoes reciprocating deformation. Since the diaphragm is constrained by the cavity of the cylinder head and the perforated plate, which means it is not free to deform, the deformation cannot be calculated with theoretical method of thin-plate large deflection theory neither small deflection theory, particularly for the state when the diaphragm has not yet fully fitted the cavity. Thus, the FEM simulations are used to analyze the failure of the diaphragm. In which, the process plate is subjected to the uniform pressure of hydrogen with the maximum of 45 MPa and the minimum of 15 MPa, while the hydraulic plate to the uniform pressure of hydraulic oil with the maximum of 55 MPa and the minimum of 5 MPa. Furthermore, the hydrogen pressure and the oil pressure are assumed to change according to the sinusoidal manners represented by Eqs. (1) and (2) respectively.

$${p}_{g}=30+15{\text{sin}}(\omega t)$$
(1)
$${p}_{o}=30+25{\text{sin}}(\omega t)$$
(2)

In addition, the cavity surface of the cylinder head is generated by the traditional generatrix Eq. (3) which is a single exponential polynomial with the exponential term \(z\) taking 3.

$$ w = \frac{4.2}{{z - 1}}\left[ {2\left( \frac{r}{165} \right)^{z + 1} - \left( {z + 1} \right)^{2} + \left( {z - 1} \right)} \right] $$
(3)

where \(r\) and \(w\) are the radius and the height of any point on the cavity. Considering the additional stress may be caused by the discharge holes and suction holes, the fine structure is added on the cylinder head model. To carry out the simulations, each plate of the diaphragm is divided into two layers with uniform thickness and 21,024 elements with 31,755 nodes in total. Particularly, the elements at the center area are refined to the size of 0.1 mm to capture the impact of discharge holes, and those in the edge where is clamped are refined to the size of 0.3 mm to capture the effect of clamping conditions on the deformation of the diaphragm. The modeling of the diaphragm and the mesh division are illustrated in Fig. 2(a) and (b) respectively. Besides, it is supposed that the deformation three plates always remain consistent and adhere tightly to each other, while the friction coefficient at the contact between the process plate and the cylinder head, as well as at the contact between the hydraulic plate and the cylinder block, is 0.15.

Fig. 2.
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Modeling of the diaphragm and its mesh division.

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3.1 Static Structure Analysis

In the traditional analysis of the diaphragm of diaphragm compressor, inertia effect and collision of the diaphragm and the cavity is ignored, the loads and the structure’s response are assumed to vary slowly with respect to time. And any state during the diaphragm’s deformation process is believed to be at static equilibrium. Thus, the analysis becomes a statics problem. In this section, static structural analysis is used to obtain the deformation and the stress of the diaphragm as the pressure difference between the oil and hydrogen varies.

Figure 3 shows the von-Mises stress distribution cloud map of the diaphragm while the maximum stress happens. Figure 4(a)–(f) illustrate some representative moments of the deflection distribution and the stress distribution of the process plate along the radius, from undeformed state to fitting the cylinder head. According to the static structure analysis, the maximal von-Mises stress of the diaphragm appears at the center of the process plate when the diaphragm clings to the cylinder head. In the beginning, the stress at the center of the process plate is smaller than that at the edge. As pressure difference rises, the stress at the center gradually increases and always occupies the maximum value of the entire plate. In addition, the deflection at the center of the process plate is the largest and those of other positions decrease as the radii increase. From the results, the value of the maximal von-Mises stress is 248 MPa which is lower than the allowable stress limit of the diaphragm material. Apparently, the results of the static structure analysis cannot explain the fault cases shown in Fig. 1.

Fig. 3.
figure 3

The von-Mises stress distribution cloud map of the diaphragm while the maximum happens obtained by static structure analysis.

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Fig. 4.
figure 4

The deflection and von-Mises stress of the process plate along the radius at different moments calculated by static structure analysis.

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3.2 Dynamic Analysis

As the deformation of the diaphragm is actually a dynamic process, the inertial effect of the diaphragm and the collision between the diaphragm and the cavity of cylinder head should be considered to obtain more accurate results. Explicit dynamics is used in the dynamic analysis to obtain the transient response of the diaphragm during deforming.

Figure 5 shows the von-Mises stress distribution cloud map of the diaphragm while the maximum happens. Figure 6(a)–(f) illustrate some representative moments of the deflection distribution and the stress distribution of the process plate along the radius during the deformation from the undeformed state to fitting the cylinder head. According to the dynamic analysis, the maximal von-Mises stress of the diaphragm appears at the process plate, particularly, at the center and the ring with a radius of about 60 mm before the diaphragm clings to the cylinder head. From the beginning, the stress near the edge is higher than that at the center. Though the stress on the entire diaphragm increases as pressure difference rises, the maximum stress is distributed on the ring near the edge of the process plate and the ring shrinks towards the center during the deformation process. On the other side, the stress at the center of the process plate oscillates in the deformation and reach the highest at t = 0.78 ms before the diaphragm clings to the cavity. Correspondingly, the deflection of the maximum stress ring is largest before t = 0.78 ms. After that, the largest deflection of the process plate occurs at the center during the oscillation of the center area which clings to the cavity finally. From the results, the value of the maximal von-Mises stress is 564 MPa which is higher than the allowable stress limit of the diaphragm material and is able to cause the diaphragm cracking at these regions. This conclusion is consistent with the fault cases shown in Fig. 1.

Fig. 5.
figure 5

The von-Mises stress distribution cloud map of the diaphragm while the maximum happens, which is obtained by dynamic analysis.

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Fig. 6.
figure 6

The deflection and von-Mises stress of the process plate along the radius at different moments calculated by dynamic analysis.

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4 Conclusions

By calculating the deformation and stress of the diaphragm, the fractures of the process plate of the diaphragms of the diaphragm compressor in the fault cases are analyzed. The results of statics structure analysis and dynamics analysis are compared with diaphragm fault cases respectively, in which the latter can explain well the cause of the diaphragm rupture. During the deformation, the center area of the diaphragm oscillates and collides with the cavity of the cylinder head as the pressure difference changes, which leads to the maximum stress at the center and on the ring nearby. The process of deformation is very different from the results of static structure analysis, which shows the inertial and the collision of the diaphragm cannot be ignored, as well as the necessity of dynamic analysis in the failure analysis of diaphragm.