Abstract
3D CFD simulations are performed to resolve the leakage rates, axial pressure drops, and dynamic force coefficients of smooth annular seals. Simulations are performed for several, simple annular seal geometries subject to water and gas flows in order to verify and validate the open-source CFD library OpenFOAM for such applications. Rotordynamic force coefficients are determined using the whirling-rotor method. Accuracy of CFD-predicted results is assessed through direct comparison with published experimental data and bulk-flow model predictions. For the three water seals analyzed, the open-source, CFD-predicted dynamic coefficients closely agree with their experimental counterparts. The k-\(\omega \) family of turbulence models is shown to outperform the k-\(\epsilon \) models. For the gas seals, the open-source CFD solver is shown to be unsatisfactory in predicting damping coefficients and simulations are alternatively performed with ANSYS Fluent.
Similar content being viewed by others
References
Hirs GG (190) Fundamentals of a bulk-flow theory for turbulent lubricant films. Ph.D. thesis, University of Technology Delft
Hirs GG (1973) A bulk-flow theory for turbulence in lubricant films. J Lubr Technol 95(2):137. https://doi.org/10.1115/1.3451752
Frêne J, Arghir M, Constantinescu V (2006) Combined thin-film and Navier-Stokes analysis in high Reynolds number lubrication. Tribol Int 39(8):734. https://doi.org/10.1016/j.triboint.2005.07.004
Black H (1969) Effects of hydraulic forces in annular pressure seals on the vibrations of centrifugal pump rotors. J Mech Eng Sci 11(2):206
Black H, Jenssen D (1970) Dynamic hybrid bearing characteristics of annular controlled leakage seals. Proc Inst Mech Eng 184:92
Childs DW (1983) Dynamic analysis of turbulent annular seals based on Hirs’ lubrication equation. J Lubr Technol 105(3):429. https://doi.org/10.1115/1.3254633
Childs DW (1983) Finite-length solutions for rotordynamic coefficients of turbulent annular seals. J Lubr Technol 105(3):437. https://doi.org/10.1115/1.3254636
Nelson C (1985) Rotordynamic coefficients for compressible flow in tapered annular seals. J Tribol 107(3):318. https://doi.org/10.1115/1.3261062
Launder B, Leschziner M (1978) Flow in finite-width, thrust bearings including inertial effects: I-laminar flow. J Lubr Technol 100(3):330. https://doi.org/10.1115/1.3453181
Launder B, Leschziner M (1978) Flow in Finite-Width Thrust Bearings Including Inertial Effects: II-Turbulent Flow. J Lubr Technol 100(3):339. https://doi.org/10.1115/1.3453182
San Andrés LA (1991) Analysis of variable fluid properties, turbulent annular seals. J Tribol 113(4):694. https://doi.org/10.1115/1.2920681
Arghir M, Frêne J (2001) Numerical solution of lubrication’s compressible bulk flow equations: applications to annular gas seals analysis. In: Turbo expo: power for land, sea, and air, vol 3. https://doi.org/10.1115/2001-GT-0117. V003T01A004
Przekwas AJ, Athavale MM (1992) Development of a CFD code for fluid dynamic forces in seals. In: Proceedings of the 1992 seals flow development workshop (CP-10124). NASA Lewis Research Center, Cleveland, pp 68–84
Nielsen KK, Jønck K, Underbakke H (2012) Hole-pattern and honeycomb seal rotordynamic forces: validation of CFD-based prediction techniques. J Eng Gas Turbines Power 134(12):122505. https://doi.org/10.1115/1.4007344
Dietzen F, Nordmann R (1987) Calculating rotordynamic coefficients of seals by finite-difference techniques. ASME J Tribol 109(3):388. https://doi.org/10.1115/1.3261453
Athavale M, Hendricks R (1996) A small perturbation CFD method for calculation of seal rotordynamic coefficients. Int J Rotating Mach 2(3):167. https://doi.org/10.1155/S1023621X96000048
Baskharone EA, Hensel SJ (1991) A finite-element perturbation approach to fluid/rotor interaction in turbomachinery elements. Part 1: Theory J Fluids Eng 113(3), 353. https://doi.org/10.1115/1.2909504
Baskharone EA, Hensel SJ (1991) A finite-element perturbation approach to fluid/rotor interaction in turbomachinery elements. Part 2: Appl J Fluids Eng 113(3):362. https://doi.org/10.1115/1.2909505
Arghir M, Frêne J (1997) Forces and moments due to misalignment vibrations in annular liquid seals using the averaged Navier-Stokes equations. J Tribol 119(2):279. https://doi.org/10.1115/1.2833194
Patankar SV, Spalding DB (1972) Numerical predictions of three-dimensional flows. Tech. Rep. MED Rep. EF/TN/A/46, Imperial College, London (1972)
Patankar SV (1980) Numerical heat transfer and fluid flow. CRC Press, Boca Raton
Tam LT, Przekwas AJ, Muszynska A, Hendricks RC, Braun MJ, Mullen RL (1988) Numerical and analytical study of fluid dynamic forces in seals and bearings. J Vib Acoustics Stress Reliab Design 110(3):315. https://doi.org/10.1115/1.3269519
Athavale M, Hendricks RC, Steinetz BM (1995) Numerical simulation of flow in a whirling annular seal and comparison with experiments. Tech. Rep. TM 106961, NASA (1995)
Moore JJ, Palazzolo AB (2001) Rotordynamic force prediction of whirling centrifugal impeller shroud passages using computational fluid dynamic techniques. J Eng Gas Turbines Power (Trans ASME) 123(4):910. https://doi.org/10.1115/1.2900958
Ha TW, Choe BS (2014) Numerical prediction of rotordynamic coefficients for an annular-type plain-gas seal using 3D CFD analysis. J Mech Sci Technol 28(2):505. https://doi.org/10.1007/s12206-011-0830-3
Moore JJ (2003) Three-dimensional CFD rotordynamic analysis of gas labyrinth seals. J Vib Acoust 125(4):427. https://doi.org/10.1115/1.1615248
Tsukuda T, Hirano T, Watson C, Morgan NR, Weaver BK, Wood HG (2018) A numerical investigation of the effect of inlet preswirl ratio on rotordynamic characteristics of labyrinth seal. J Eng Gas Turbines Power 140(8):082506. https://doi.org/10.1115/GT2017-64745
Ha TW, Choe BS (2012) Numerical simulation of rotordynamic coefficients for eccentric annular-type-plain-pump seal using CFD analysis. J Mech Sci Technol 26(4):1043. https://doi.org/10.1007/s12206-012-0217-x
Untaroiu A, Untaroiu CD, Wood HG, Allaire PE (2013) Numerical modeling of fluid-induced rotordynamic forces in seals with large aspect ratios. J Eng Gas Turbines Power 135(1):012501. https://doi.org/10.1115/1.4007341
Kim SH, Ha TW (2016) Prediction of leakage and rotordynamic coefficients for the circumferential-groove-pump seal using CFD analysis. J Mech Sci Technol 30(5):2037. https://doi.org/10.1007/s12206-016-0410-4
Chochua G, Soulas TA (2007) Numerical modeling of rotordynamic coefficients for deliberately roughened stator gas annular seals. J Tribol 129(2):424. https://doi.org/10.1115/1.2647531
Voigt AJ, Iudiciani P, Nielsen KK, Santos IF (2016) CFD applied for the identification of stiffness and damping properties for smooth annular turbomachinery seals in multiphase flow. In: ASME Turbo Expo 2016: turbomachinery technical conference and exposition (American Society of Mechanical Engineers, 2016), pp V07BT31A034–V07BT31A034. https://doi.org/10.1115/GT2016-57905
Weller HG, Tabor G, Jasak H, Fureby C (1998) A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput Phys 12(6):620. https://doi.org/10.1063/1.168744
OpenFOAM (2019) OpenFOAM ver. 5.x. https://doi.org/10.1115/1.29009580
OpenFOAM (2019) OpenFOAM-extend ver. 4.0. https://doi.org/10.1115/1.29009581
ANSYS®, Fluent Release Version 19.1, User Guide (2019)
ANSYS®, Fluent Release Version 19.1, Theory Guide (2019)
Wagner C, Sinzig S, Thümmel T, Rixen D (2018) Calculating rotordynamic coefficients of liquid annular seals by CFD for vibration analysis and validation at the Test Rig. In: International conference on rotor dynamics. Springer, New York, pp 397–410. https://doi.org/10.1007/978-3-319-99262-4_29
Wilcox DC et al (1998) Turbulence modeling for CFD, vol 2. DCW industries La Canada, CA
Swamee P, Jain A (1976) Explicit equations for pipe-flow problems. J Hydraulics Div 102(5):657
Spalding D (1961) A single formula for the “law of the wall”. J Appl Mech 28(3):455
Jasak H (1996) Error analysis and estimation for the finite volume method with applications to fluid flows. Ph.D. thesis, Imperial College, University of London (1996)
Ferziger JH, Perić M (2002) Computational methods for fluid dynamics, 3rd edn. Springer, New York
Elrod D, Nicks C, Childs D, Nelson C (1985) A comparison of experimental and theoretical results for rotordynamic coefficients of four annular gas seals. NASA Progress Report NASA-CR-176086, Texas A&M University, College Station
Childs D (1993) Turbomachinery rotordynamics: phenomena, modeling, and analysis. Wiley, Hoboken
Constantinescu VN, Galetuse S (1974) On the possibilities of improving the accuracy of the evaluation of inertia forces in laminar and turbulent films. J Tribol 96(1):69. https://doi.org/10.1115/1.3451912
White FM (1998) Fluid mechanics, 4th edn. McGraw-Hill, London
Nelson CC, Nguyen DT (1987) Comparison of Hirs’ equation with Moody’s equation for determining rotordynamic coefficients of annular pressure seals. J Tribol 109(1):144. https://doi.org/10.1115/1.3261306
Childs D, Nelson C, Nicks C, Scharrer J, Elrod D, Hale K (1986) Theory versus experiment for the rotordynamic coefficients of annular gas seals: Part 1-Test facility and apparatus. J Tribol 108(3):426. https://doi.org/10.1115/1.3261226
Kanki H, Kawakami T (1984) Experimental study on the dynamic characteristics of pump annular seals, IMechE, paper, pp 159–166
Celik IB, Ghia U, Roache PJ, Freitas CJ, Coleman H, Raad PE (2008) Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J Fluids Eng 130(7):78001. https://doi.org/10.1115/1.2960953
Menter FR (1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 32(8):1598. https://doi.org/10.2514/3.12149
Massmann H (1986) Ermittlung der dynamischen Parameter axial turbulent durchströmter Ringspalte bei inkompressiblen Medien. Ph.D. thesis, Universität Kaierslautern (1986)
Simon F, Frêne J (1989) Static and dynamic characteristics of turbulent annular eccentric seals: effect of convergent-tapered geometry and variable fluid properties. J Tribol 111(2):378. https://doi.org/10.1115/1.3261927
Simon F, Frêne J (1992) Analysis for incompressible flow in annular pressure seals. J Tribol 114(3):431. https://doi.org/10.1115/1.2920902
Simon J, Frêne J (1990) Rotordynamic coefficients for turbulent annular misaligned seals. In: 3rd International symposium on transport phenomena and dynamics of rotating machinery, vol 2. Honolulu, Hawaii
Dunn MS (1990) A comparison of experimental results and theoretical predictions for the rotordynamic coefficients of stepped annular gas seals. Master’s thesis, Texas A&M (1990)
Ransom DL, San Andrés L (1999) Identification of force coefficients from a gas annular seal-effect of transition flow regime to turbulence. Tribol Trans 42(3):487. https://doi.org/10.1080/10402009908982245
Nordmann R, Dietzen F, Weiser H (1989) Calculation of rotordynamic coefficients and leakage for annular gas seals by means of finite difference techniques. J Tribol 111(3):545. https://doi.org/10.1115/1.3261964
Funding
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754462.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Editorial responsibility: Samuel da Silva.
Appendix
Appendix
See Table 7.
Rights and permissions
About this article
Cite this article
Snyder, T., Santos, I. Rotordynamic force estimation of turbulent, annular seals using OpenFOAM®. J Braz. Soc. Mech. Sci. Eng. 43, 119 (2021). https://doi.org/10.1007/s40430-021-02814-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40430-021-02814-y