Parametric Analysis of Compliant End Face Gas Film Seals Considering Slip Flow Effects
Abstract
:1. Introduction
2. Analytical Model
2.1. Physical Model
2.2. Mathematical Model
2.2.1. Reynolds Equation without Slip Flow Effects
- (1)
- The fluid inside the gas film conforms to the isothermal ideal gas model;
- (2)
- The flow state is laminar;
- (3)
- The pressure of the gas film does not change in the direction of the gas film thickness;
- (4)
- The surface of the sealing vice is smooth, and the dynamic ring has a rigid end face;
- (5)
- Neglect the influence of volume force and inertia force;
- (6)
- There is no misalignment in the assembly.
2.2.2. Reynolds Equation Considering Slip Flow Effects
2.2.3. Control Equations for Gas Film Thickness
2.2.4. Boundary Conditions
2.2.5. Seal Performance Parameters
2.2.6. Differential Format of the Gas Film Pressure Control Equation
2.2.7. Convergence Conditions and Iteration Error
3. Computational Validation
3.1. Irrelevance Verification of the Mesh
3.2. Validation of the Validity of the Computational Program
4. Results and Discussion
4.1. Pressure Distribution and End Face Deformation
4.2. Influence Law of Inlet and Outlet Pressure Ratio
4.3. Influence Law of Structural Parameters
4.3.1. Influence Law of Wave Foil Thickness
4.3.2. Influence Law of Wave Foil Chord Length
4.3.3. Influence Law of Wave Foil Pitch
5. Conclusions
- (1)
- The slip flow effect is most significant at the radius of 59.87 mm near the low-pressure side, and from this position, the closer to the inner and outer radii of the seal ring, the weaker the influence of the slip flow effect.
- (2)
- The slip flow effect reduces the gas film opening force and viscous friction power consumption, increasing the mass leakage rate. As the thickness of the gas film increases and the ambient pressure decreases, the role of the slip flow effect will gradually come to the fore.
- (3)
- The opening force of the compliant end face gas film seal will be strengthened with an increase in the inlet and outlet pressure ratio, wave foil chord length, and pitch and weakened with an increase in the wave foil thickness, and the trend is nearly linear, in which the inlet and outlet pressure ratio has the greatest influence.
- (4)
- The thickness of wave foil increases, the stiffness of the compliant end face increases, and it is not easy to deform in the axial direction. The decreasing trend of the mass leakage and the increasing trend of the stiffness leakage ratio show strong nonlinear characteristics, indicating that the increasing thickness of wave foil makes the compliant end face evolve gradually to the stiff end face.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameters | Numerical | Unit |
---|---|---|
outer radius | 77.78 | mm |
inner radius | 58.42 | mm |
minimum gas film thickness | 1.25–2.50 | μm |
wave foil thickness | 0.20–0.38 | mm |
flat foil thickness | 0.13–0.24 | mm |
half of the chord length | 1.50–2.50 | mm |
Poisson’s ratio of wave foil | 0.30 | - |
Poisson’s ratio of flat foil | 0.30 | - |
elastic modulus of wave foil | 2.00 × 1011 | Pa |
elastic modulus of flat foil | 2.00 × 1011 | Pa |
pitch | 3.20–5.00 | mm |
Parameters | Numerical | Unit |
---|---|---|
Inlet and outlet pressure ratio | 1.50–3.30 | - |
outlet pressure | 101,325 | Pa |
rotation speed | 50,000 | r·min−1 |
absolute temperature | 303.15 | K |
Parameters | Numerical | Unit |
---|---|---|
medium | air | - |
density | 1.1425 | kg·m−3 |
viscosity | 1.8 × 10−5 | Pa·s |
gas constant | 287.03 | - |
Parameters | Validation Model I | Validation Model II |
---|---|---|
geometric model | ||
spiral equation | ||
77.78 mm | 77.78 mm | |
58.42 mm | 58.42 mm | |
69 mm | 66.16 mm | |
spiral angle | 75° | 75° |
spiral-to-dam ratio | 1 | 1 |
number of grooves N | 12 | 12 |
4 μm | 5 μm | |
minimum gas film thickness | 3.05 μm | 3.05 μm |
4.5852 MPa | 0.405 MPa | |
0.1013 MPa | 0.101 MPa | |
10,380 r·min−1 | 500 r·min−1 | |
medium | air | air |
temperature | 300 K | 300 K |
dynamic viscosity | 1.8 g·m·s−1 | 1.79 g·m·s−1 |
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Jiang, H.; Yu, S.; Ding, X. Parametric Analysis of Compliant End Face Gas Film Seals Considering Slip Flow Effects. Appl. Sci. 2024, 14, 6953. https://doi.org/10.3390/app14166953
Jiang H, Yu S, Ding X. Parametric Analysis of Compliant End Face Gas Film Seals Considering Slip Flow Effects. Applied Sciences. 2024; 14(16):6953. https://doi.org/10.3390/app14166953
Chicago/Turabian StyleJiang, Haitao, Shurong Yu, and Xuexing Ding. 2024. "Parametric Analysis of Compliant End Face Gas Film Seals Considering Slip Flow Effects" Applied Sciences 14, no. 16: 6953. https://doi.org/10.3390/app14166953