Effects of Laminar, Turbulent, and Slip Conditions in a Fluid Film on a Dry Gas Seal
Abstract
:1. Introduction
2. Method of Analysis
2.1. Governing Equations According to Laminar, Turbulent and Slip Conditions of Fluid Film
2.2. Derivation of a Finite-Element Equation
3. Numerical Verification
3.1. Verification of the Turbulent Condition of the Developed Program with Prior Research
3.2. Verification of Slip Conditions of the Developed Program Using Prior Research
4. Experimental Verification
5. Effect of Laminar, Turbulent, and Slip Conditions of a Fluid Film on a Dry Gas Seal
5.1. Pressure of the Fluid Film in a Dry Gas Seal Due to Laminar, Turbulent, and Slip Conditions of Fluid Film
5.2. Opening Force of the Fluid Film in a Dry Gas Seal Due to Laminar, Turbulent and Slip Conditions of Fluid Film
5.3. Leakage Rate of a Fluid Film of a Dry Gas Seal Due to Laminar, Turbulent, and Slip Conditions of a Fluid Film
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Turbulent coefficient for radial flow; | |
Turbulent coefficient for circumferential flow; | |
Film thickness [mm] | |
Knudsen number | |
Shape function vector | |
Element pressure vector [Pa] | |
Pressure [Pa] | |
Flow rate for laminar flow [g/s] | |
Flow rate for slip flow [g/s] | |
Flow rate for turbulent flow [g/s] | |
Slip coefficient; | |
Reynolds number | |
Gas constant [J/(kg·K)] (: 287 J/(kg·K)) | |
Temperature [K] | |
Rotating velocity [rad/s] | |
Fluid velocity [m/s] | |
weighting function | |
Greek symbols | |
Density [kg/m3] | |
arbitrary vector | |
Viscosity [Pa∙s] |
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Range of Inverse Kn | c0 | c1 | c2 | c3 |
---|---|---|---|---|
5 < 1/Kn ≤ 1000 | 1.000 | 6.097 | 6.391 | −12.812 |
0.15 < 1/Kn ≤ 5 | 0.831 | 7.505 | 0.939 | −0.058 |
1/Kn ≤ 0.15 | −13.375 | 12.640 | 0.099 | 0.0004 |
Fluid Condition | Cr | Cθ |
---|---|---|
Laminar | 1/12 | 1/12 |
Turbulent | 1/Gr | 1/Gθ |
Slip | qp/12 | qp/12 |
Parameter | Value |
---|---|
Outer radius, ro [mm] | 69.5 |
Groove radius, rg [mm] | 62.4 |
Inner radius, ri [mm] | 55.7 |
Groove number, ng | 12 |
Groove depth, hg [mm] | 0.007 (average) |
Taper depth, ht [mm] | 0.003 |
Spring force [N] | 36 |
Outer Pressure [bar] | Leakage Rate [g/s] | Difference [%] | |||||
---|---|---|---|---|---|---|---|
Experiment | L_Method | LT_Method | LTS_Method | Experiment − L_Method | Experiment − LT_Method | Experiment − LTS_Method | |
10 | 0.36 | 0.68 | 0.47 | 0.45 | −92.5 | −31.5 | −27.7 |
20 | 0.57 | 0.94 | 0.55 | 0.54 | −65.3 | 4.3 | 6.2 |
30 | 0.80 | 1.51 | 0.77 | 0.76 | −88.9 | 3.1 | 4.5 |
40 | 0.95 | 2.06 | 0.94 | 0.93 | −115.8 | 1.1 | 2.2 |
50 | 1.12 | 2.73 | 1.08 | 1.07 | −144.6 | 3.1 | 4.1 |
60 | 1.31 | 3.49 | 1.22 | 1.21 | −166.8 | 6.4 | 7.3 |
Clearance [μm] | Opening Force [N] | Difference [%] | ||||
---|---|---|---|---|---|---|
L_Method | LT_Method | LTS_Method | L_Method − LT_Method | L_Method − LTS_Method | LT_Method − LTS_Method | |
2.5 | 27,372 | 28,462 | 28,432 | 4.0 | 3.9 | −0.1 |
3 | 27,152 | 27,477 | 27,451 | 1.2 | 1.1 | −0.1 |
3.5 | 26,948 | 26,704 | 26,681 | −0.9 | −1.0 | −0.1 |
4 | 26,758 | 26,087 | 26,067 | −2.5 | −2.6 | −0.1 |
Clearance [μm] | Opening Force [N] | Difference [%] | ||||
---|---|---|---|---|---|---|
L_Method | LT_Method | LTS_Method | L_Method − LT_method | L_Method − LTS_Method | LT_Method − LTS_Method | |
2.5 | 3372 | 3564 | 3544 | 5.7 | 5.1 | −0.6 |
3 | 3231 | 3376 | 3358 | 4.5 | 3.9 | −0.5 |
3.5 | 3115 | 3228 | 3213 | 3.6 | 3.1 | −0.5 |
4 | 3017 | 3111 | 3098 | 3.1 | 2.7 | −0.4 |
Clearance [μm] | Leakage Rate [mg/s] | Difference [%] | ||||
---|---|---|---|---|---|---|
L_Method | LT_Method | LTS_Method | L_Method − LT_Method | L_Method − LTS_Method | LT_Method − LTS_Method | |
2.5 | 458.4 | 381.3 | 384.3 | −16.8 | −16.2 | 0.8 |
3 | 963.0 | 761.3 | 764.7 | −20.9 | −20.6 | 0.4 |
3.5 | 1643.0 | 1230.3 | 1234.6 | −25.1 | −24.9 | 0.3 |
4 | 2527.4 | 1794.5 | 1800.6 | −29.0 | −28.8 | 0.3 |
Clearance [μm] | Leakage Rate [mg/s] | Difference [%] | ||||
---|---|---|---|---|---|---|
L_Method | LT_Method | LTS_Method | L_Method − LT_Method | L_Method − LTS_Method | LT_Method − LTS_Method | |
2.5 | 11.1 | 12.6 | 13.0 | 12.7 | 16.1 | 3.0 |
3 | 15.5 | 17.1 | 17.5 | 10.5 | 12.9 | 2.2 |
3.5 | 22.0 | 23.9 | 24.3 | 8.8 | 10.7 | 1.7 |
4 | 30.7 | 33.0 | 33.5 | 7.6 | 9.1 | 1.5 |
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Hahn, M.; Park, Y.; Kang, M.; Jun, S.; Jang, G. Effects of Laminar, Turbulent, and Slip Conditions in a Fluid Film on a Dry Gas Seal. Machines 2022, 10, 954. https://doi.org/10.3390/machines10100954
Hahn M, Park Y, Kang M, Jun S, Jang G. Effects of Laminar, Turbulent, and Slip Conditions in a Fluid Film on a Dry Gas Seal. Machines. 2022; 10(10):954. https://doi.org/10.3390/machines10100954
Chicago/Turabian StyleHahn, Mibbeum, Youngjun Park, Minsoo Kang, Sanghyun Jun, and Gunhee Jang. 2022. "Effects of Laminar, Turbulent, and Slip Conditions in a Fluid Film on a Dry Gas Seal" Machines 10, no. 10: 954. https://doi.org/10.3390/machines10100954