3.1 Pressure field and velocity field analysis
Three moments of t = 0.001, t = 0.006 and t = 0.009 are selected, and the simulated pressure and velocity distribution cloud map is shown in Fig. 3 below.
During the exhaust process, a significant pressure exceeding the gas pressure in the exhaust chamber is generated due to the force exerted on the valve disc. By using pressure cloud imagery and flow diagrams, the cause of this elevated pressure can be traced to the impact of gas escaping from the cylinder onto the lower section of the reed valve, which compresses the gas and leads to elevated pressure. The impact pressure of the gas helps maintain the pressure differential between the top and bottom of the reed valve, a crucial aspect of keeping it in an open state. The movement of the valve disc in the exhaust chamber has a profound effect on pressure distribution, resembling the lift curve of the reed valve during fluctuations in flow rate. When gas passes through the spring valve, uneven pressure distribution and significant changes in gas pressure gradients occur within a confined area. As the gas exits the exhaust chamber, the pressure gradient shifts downward, indicating a decrease in pressure. Consistent with Bernoulli's principle, low pressure prevails within the gas as it emerges from the exhaust chamber. The pressure at the valve port is significantly lower than the cylinder pressure.
As evident from the velocity flow diagram, when the reed valve opening is minimal, the valve outlet exhibits maximum velocity, and there is also a high velocity region at the outlet of the exhaust chamber. Since the valve port area is significantly smaller than the piston's cross-sectional area, it is explicitly clear that the velocity in the valve port is much higher than that in the cylinder throughout the entire exhaust process. The gas generates a vortex above the valve disc, and the closer the flow path in the vortex to the valve disc, the higher the gas flow velocity. It can be inferred that the energy of the vortex primarily derives from the viscous forces of the exiting gas.
3.2 Simulation of exhaust process under different valve thickness
The structural characteristics of the reed valve have a significant impact on the maximum stress and spring stiffness experienced by the valve during its opening phase. Among these parameters, the spring stiffness plays a fundamental role in determining the overall performance of the valve. Any unreasonable deviation from the optimal spring stiffness can lead to various complications, such as delayed opening/closing, valve vibration, and reduced fatigue life. According to the valve deformation theory, the valve thickness is a crucial parameter that affects its performance. Conventionally, reed valves are available in two thicknesses: 0.2mm and 0.3mm. In this comparative study, we have selected the superior thickness of the valve and simulated the valve's performance for both thicknesses. The results of the comparison are depicted in Fig. 4.6, which illustrates the relative pressure loss and valve disc lift for each thickness.
Table 1
Maximum lift and maximum relative pressure loss of valve
Valve plate thickness(mm) | Valve lift(mm) | Relative pressure loss(MPa) |
0.2 | 0.59 | 0.04 |
0.3 | 1.43 | 0.17 |
Based on simulation results, the pressure drop at a thickness of 0.2mm is 17,000 Pa, and at a thickness of 0.3mm, the pressure drop increases to 26,700 Pa, representing 33% and 20% of the exhaust pressure, respectively. The maximum valve lift for these thicknesses are 1.9mm and 0.86mm, respectively, and there were no incidents of valve double opening. As the thickness of the exhaust valve increases, the maximum pressure in the cylinder flow field also increases due to the increase in spring force. However, excessive valve spring force may cause failure of the valve to open normally. Therefore, additional gas thrust is needed to overcome the valve spring force in order to complete the compressor exhaust process. As a result, the peak pressure in the cylinder flow field increases with valve thickness. Comparison shows that the relative pressure drop under the two thicknesses reaches its maximum prior to the valve lift. For example, the time difference between the two is 0.0004s for a valve thickness of 0.2mm and less than 0.0008s for a valve thickness of 0.3mm. In summary, a valve disc with a thickness of 0.3mm has a stronger gas-blocking effect.
3.3 Simulation results under different valve width
Three different width sections of reed valves were selected: 3.7mm, 3.6mm, and 3.5mm. This enables a comparative analysis of the differences between these thicknesses, ultimately leading to the selection of the optimal valve disc thickness. The simulation results for the valve disc were then assessed, taking into consideration the relative pressure loss and valve lift, as illustrated in Fig. 4 below.
Based on the simulation results, the pressure drop across the three valve plates' section widths is 18500Pa, 18000Pa, and 17000Pa, respectively. The maximum lift of the discs is almost identical, measuring at 1.90mm, 1.88mm, and 1.97mm. Considering the fundamental concept of valve plate deformation, as the exhaust valve plate's section width increases, its spring stiffness also increases, resulting in greater pressure loss. These curves exhibit similarity because the valve disc's section width remains relatively constant. The valve lift curve indicates that wider section widths lead to more pronounced tremors, with the curve displaying two extreme values at 3.7mm. This valve disc tremor condition causes frequent expansions, reducing valve lifespan, and increases pressure loss. After comprehensive simulation results review, a 3.5mm valve slice section width is selected.
3.4 Simulation results under different valve width
Electromagnetic direct-drive air compressors must function within a specified range of exhaust pressures. Variations in exhaust pressure cause differences in pressure loss and valve lift during the exhaust process. To accurately simulate diverse exhaust pressures, this study utilized the gas compression model to calculate the cylinder volume for a specific exhaust pressure. By adjusting the initial calculation conditions and the fluid region's geometric model, we successfully simulated varied exhaust pressures. Specifically, we examined load and no-load conditions for exhaust pressures of 0.1 MPa and 0.5 MPa, respectively. See Table 2 for the initial conditions.
Table 2
Initial conditions under load and no load
| Initial pressure(MPa) | Total time(s) | Initial piston position(mm) |
no-load | 0.0 | 0.01 | 16 |
load | 0.4 | 0.0036 | 4.6 |
Set the model according to the above initial conditions, simulate the model under load and no-load conditions, and getValve lift and relative pressure loss curves are shown in Fig. 5:
The maximum pressure loss and maximum valve disc lift in the exhaust process are shown in Table 3:
Table 3
Maximum lift and maximum relative pressure loss of valve disc
Exhaust pressure(MPa) | Valve lift(mm) | Relative pressure loss(MPa) |
0.1 | 1.8 | 0.017 |
0.5 | 5.6 | 0.054 |
The simulation results demonstrate that the valve disc exerts a more robust obstructive effect on the gas during loading, resulting in greater pressure loss. Specifically, the maximum pressure loss is 54KPa, while the pressure loss under no load is 17KPa. These values represent 10.8% and 17% of the exhaust pressure, respectively.
Under no load conditions, the relative pressure loss varies proportionally with the displacement of valve disc. Conversely, during loading, the valve plate's displacement curve lags behind the relative pressure loss curve. With no load present, the relative pressure loss curve and valve lift curve change gradually and essentially align with the mass flow curve of the air inlet. However, during loading, both the relative pressure loss and valve lift exhibit irregular fluctuations throughout the exhaust process, with the former experiencing more intense fluctuations in particular.
Further analysis indicates that in no-load conditions, the gas inlet's mass flow rate is minimal and changes gradually, giving the valve disc ample time to deform. This is demonstrated by the fact that the valve disc's displacement essentially changes synchronously with the relative pressure drop. Under load conditions, during the initial exhaust process, the gas inlet's mass flow rate is high, and the valve plate lacks sufficient time to deform, leading to notable obstruction of the gas flow and a significant relative pressure loss. As the valve lift increases and the mass flow rate at the inlet decreases, the relative pressure loss decreases quickly. Due to its elasticity, during the latter half of the exhaust process, as the gas inlet's mass flow rate decreases, the valve lift and relative pressure loss increase, resulting in the valve disc opening twice. The valve disc's lift during the second opening is lesser than during the first and does not close in time during the final exhaust process. When there is no load, the valve disc has little impact on obstructing gas flow and can open and close promptly. However, under a load, due to the limited exhaust process time, the valve disc's deformation is not immediate, resulting in substantial pressure loss when the valve disc opens twice. Additionally, the valve disc cannot close promptly, leading to a minor backflow phenomenon. The valve disc blocks gas to some degree, mainly when there is significant exhaust pressure.