Abstract
External gear pumps are used in fluid transport systems because of their tight clearances and accurate flow control. These tight clearances are a challenge for numerical studies in terms of spatial discretization. In earlier work, the flow of a viscous fluid in an external gear pump is computed using the finite element method (FEM). An element size based on the respective distance between boundaries is proposed. In this study, results based on the earlier work are compared to extrusion experiments of EPDM. The aim of this study is not only to validate the numerical simulations, but also to determine what material characteristics need to be taken into account for an accurate output prediction of the external gear pump. Especially the introduction of shear-thinning behavior results in an improvement of the amplitude of the pressure difference fluctuation. Taking into account compressibility, alters the torque fluctuation in such a way that it mimics the experiments. Unfortunately, the fluctuation in torque still has a too high amplitude. Eventually, simulations are performed including shear-thinning behavior, a temperature- and pressure-dependent viscosity, and compressibility. The effect of measuring the material behavior using oscillatory or shear experiments is shown. Furthermore, the simulations are applied to a second EPDM. Finally, different processing conditions are tested. For the simulations, only qualitative agreement is found, possibly as a result of the no slip boundary condition.
-
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
-
Research funding: None declared.
-
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
Borghi, M., Zardin, B., and Specchia, E. (2009). External gear pump volumetric efficiency: Numerical and experimental analysis. SAE Technical paper, 2009-01-2844.10.4271/2009-01-2844Search in Google Scholar
Battarra, M. and Mucchi, E. (2020). On the assessment of lumped parameter models for gear pump performance prediction. Simul. Model. Pract. Theory 99: 102008, https://doi.org/10.1016/j.simpat.2019.102008.Search in Google Scholar
Brooks, A.N. and Hughes, T.J.R. (1982). Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 32: 199–259, https://doi.org/10.1016/0045-7825(82)90071-8.Search in Google Scholar
Casoli, P., Vacca, A., and Franzoni, G. (2005). A numerical model for the simulation of external gear pumps. In: Proceedings of the JFPS International Symposium on Fluid Power, 2005. Tsubaka, pp. 705–710.10.5739/isfp.2005.705Search in Google Scholar
Casoli, P., Vacca, A., and Berta, G.L. (2008). Optimization of relevant design parameters of external gear pumps. In: Proceedings of the JFPS International Symposium on Fluid Power, 2008. Toyama, pp. 277–282.10.5739/isfp.2008.277Search in Google Scholar
Castilla, R., Gamez-Montero, P.J., Ertürk, N., Vernet, A., Coussirat, M., and Codina, E. (2010). Numerical simulation of turbulent flow in the suction chamber of a gearpump using deforming mesh and mesh replacement. Int. J. Mech. Sci. 52: 1334–1342, https://doi.org/10.1016/j.ijmecsci.2010.06.009.Search in Google Scholar
Cardinaels, R., van Puyvelde, P., and Moldenaers, P. (2007). Evaluation and comparison of routes to obtain pressure coefficients from high-capillary rheometry data. Rheol. Acta 46: 495–505, https://doi.org/10.1007/s00397-006-0148-5.Search in Google Scholar
de Bie, V.G., Hulsen, M.A., and Anderson, P.D. (2021). Finite element modeling of a viscous fluid flowing through an external gear pump. Macromol. Theory Simul. 30: 2000060, https://doi.org/10.1002/mats.202000060.Search in Google Scholar
de Bie, V.G., Luijten, L.S.D.P., Hulsen, M.A., and Anderson, P.D. (2022a). Three-dimensional finite element modeling of a viscous fluid flowing through an external gear pump. Macromol. Theory Simul. 31: 2100046, https://doi.org/10.1002/mats.202100046.Search in Google Scholar
de Bie, V.G., Hulsen, M.A., and Anderson, P.D. (2022b). The effect of non-Newtonian behavior on contact formation in an external gear pump. J. Non-Newtonian Fluid Mech., accepted for publication, https://doi.org/10.1016/j.jnnfm.2022.104818.Search in Google Scholar
del Campo, D., Castilla, R., Raush, G.A., Gamez Montero, P.J., and Codina, E. (2012). Numerical analysis of external gear pumps including cavitation. J. Fluids Eng. 134: 081105, https://doi.org/10.1115/1.4007106.Search in Google Scholar
Falfari, S. and Pelloni, P. (2007). Setup of a 1d model for simulating dynamic behaviour of external gear pumps. SAE Technical Paper, 2007-01-4228.10.4271/2007-01-4228Search in Google Scholar
Frosina, E., Senatore, A., Buono, D., and Stelson, K.A. (2017). A modeling approach to study the fluid-dynamic forces acting on the spool of a flow control valve. J. Fluids Eng. 139: 011103, https://doi.org/10.1115/1.4034418.Search in Google Scholar
Freudenberg Sealing Technologies (2019). Material 60 EPDM 290, Available at: https://www.fst.com/-/media/files/materialdatasheet/60\%20epdm\%20290-en.pdf.Search in Google Scholar
Gehrmann, O., Kröger, N.H., Erren, P., and Juhre, D. (2017). Estimation of compression modulus of a technical rubber via cyclic volumetric compression tests. Technische Mechanik 37: 28–36.Search in Google Scholar
Geiger, K. (1989). Rheologische Charakterisierung von EPDM-Kautschukmischungen mittels Kapillarrheometer-Systemen. Kautschuk Gummi Kunststoffe 42: 273–283.Search in Google Scholar
Huang, K.J. and Lian, W.C. (2009). Kinematic flowrate characteristics of external spur gear pumps using an exact closed solution. Mech. Mach. Theory 44: 1121–1131, https://doi.org/10.1016/j.mechmachtheory.2008.10.002.Search in Google Scholar
Houzeaux, G. and Codina, R. (2007). A finite element method for the solution of rotary pumps. Comput. Fluids 36: 667–679, https://doi.org/10.1016/j.compfluid.2006.02.005.Search in Google Scholar
Hu, H.H., Patankar, N.A., and Zhu, M.Y. (2001). Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique. J. Comput. Phys. 169: 427–462, https://doi.org/10.1006/jcph.2000.6592.Search in Google Scholar
Hughes, T.J.R., Mallet, M., and Mizukami, A. (1986). A new finite element formulation for computational fluid dynamics II: beyond SUPG. Comput. Methods Appl. Mech. Eng. 54: 341–355, https://doi.org/10.1016/0045-7825(86)90110-6.Search in Google Scholar
He, S., Lin, Y., Cao, S., Lin, J., and Du, X. (2015). Improvement in thermal conductivity and mechanical properties of ethylene-propylene-diene monomer rubber by expanded graphite. Polym. Compos. 38: 870–876, https://doi.org/10.1002/pc.23648.Search in Google Scholar
Jaensson, N.O., Hulsen, M.A., and Anderson, P.D. (2015). Stokes-Cahn-Hilliard formulations and simulations of two-phase flows with suspended rigid particles. Comput. Fluids 111: 131–144, https://doi.org/10.1016/j.compfluid.2014.12.023.Search in Google Scholar
Kumar, K.A. and Balamuralikrishnan, N. (2013). Performance evaluation of gear pump by 2D unsteady CFD analysis. In: ASME 2013 gas turbine India conference. Chennai.10.1115/GTINDIA2013-3607Search in Google Scholar
Laun, H.S. (2003). Pressure dependent viscosity and dissipative heating in capillary rheometry of polymer melts. Rheol. Acta 42: 295–308, https://doi.org/10.1007/s00397-002-0291-6.Search in Google Scholar
Manring, N.D. and Kasaragadda, S.B. (2003). The theoretical flow ripple of an external gear pump. J. Dyn. Syst., Meas. Control 125: 396–404, https://doi.org/10.1115/1.1592193.Search in Google Scholar
Mithun, M.G., Koukouvinis, P., Karathanassis, I.K., and Gavaises, M. (2019). Numerical simulation of three-phase flow in an external gear pump using immersed boundary approach. Appl. Math. Model. 72: 682–699, https://doi.org/10.1016/j.apm.2019.03.022.Search in Google Scholar
Mitrias, C., Egelmeers, T.R.N., Jaensson, N.O., Hulsen, M.A., and Anderson, P.D. (2019). Simulation of bubble growth during the foaming process and mechanics of the solid foam. Rheol. Acta 58: 131–144, https://doi.org/10.1007/s00397-018-01123-x.Search in Google Scholar
Matmatch (2021). Ethylene propylene diene rubber (EPDM), alternative and trade names Keltan, Nordel, Vistalon, Dutral, Available at: https://matmatch.com/materials/mbas121-ethylene-propylene-diene-rubber-epdm-.Search in Google Scholar
Pellegri, M. and Vacca, A (2015). A cfd-radial motion coupled model for the evaluation of the features of journal bearings in external gear machines. In: Proceedings of the ASME/BATH 2015 symposium on fluid power and motion control, FPMC2015. Chicago.10.1115/FPMC2015-9540Search in Google Scholar
Plachy, R., Scheiner, S., Luczynski, K.W., Holzner, A., and Hellmich, C. (2017). Compressibility of unvulcanized natural and EPDM rubber: new experimental protocol and data evaluation in the framework of large strain elasticity theory. Polymer 123: 334–344, https://doi.org/10.1016/j.polymer.2017.06.061.Search in Google Scholar
Riemslagh, K., Vierendeels, J., and Dick, E. (2000). An arbitrary Lagrangian-Eulerian finite-volume method for the simulation of rotary displacement pump flow. Appl. Numeric. Math. 32: 419–433, https://doi.org/10.1016/s0168-9274(99)00061-6.Search in Google Scholar
Spanjaards, M.M.A., Hulsen, M.A., and Anderson, P.D. (2021). Die shape optimization for extrudate swell using feedback control. J. Non-Newtonian Fluid Mech. 293: 104552, https://doi.org/10.1016/j.jnnfm.2021.104552.Search in Google Scholar
Spanjaards, M.M.A., Hulsen, M.A., and Anderson, P.D. (2022). Numerical study of residual stresses due to external cooling in extruded polymer profiles. Macromol. Theory Simul. 31: 2100074, https://doi.org/10.1002/mats.202100074.Search in Google Scholar
Spanjaards, M.M.A., Peters, G.W.M., Hulsen, M.A., and Anderson, P.D. (2021). Numerical study of the effect of thixotropy on extrudate swell. Polymers 13: 4383, https://doi.org/10.3390/polym13244383.Search in Google Scholar PubMed PubMed Central
Sedri, F. and Riasi, A. (2019). Investigation of leakage within an external gear pump with decompression slots: numerical and experimental study. J. Brazil. Soc. Mech. Sci. Eng. 41, https://doi.org/10.1007/s40430-019-1717-8.Search in Google Scholar
Tankasala, S. and Vacca, A. (2017). A solution for an electronically-controlled variable delivery external gear pump. In: Proceedings of the ASME/BATH 2017 symposium on fluid power and motion control, FPMC2017-4328. Sarasota.10.1115/FPMC2017-4328Search in Google Scholar
Tankasala, S. and Vacca, A. (2019). Theoretical analysis and design of a variable delivery external gear pump for low and medium pressure applications. J. Mech. Des. 141: 013401, https://doi.org/10.1115/1.4041351.Search in Google Scholar
Thiagarajan, D., Dhar, S., and Vacca, A. (2017). Improvement of lubrication performance in external gear machines through micro-surface wedged gears. Tribol. Trans. 60: 337–348, https://doi.org/10.1080/10402004.2016.1168898.Search in Google Scholar
Vacca, A. and Guidetti, M. (2011). Modelling and experimental validation of external spur gear machines for fluid power applications. Simul. Model. Pract. Theory 19: 2007–2031, https://doi.org/10.1016/j.simpat.2011.05.009.Search in Google Scholar
Vergnes, B., d’Halewyn, S., and Boube, M.F. (1992). Wall slip and instabilities in the flow of EPDM compounds. In: XIth international congress on rheology, Brussels.10.1016/B978-0-444-89007-8.50159-3Search in Google Scholar
Wang, S., Sakura, H., and Kasarekar, A. (2011). Numerical modelling and analysis of external gear pumps by applying generalized control volumes. Math. Comput. Model. Dyn. Syst. 17: 501–513, https://doi.org/10.1080/13873954.2011.577556.Search in Google Scholar
Yoon, Y., Park, B.H., Shim, J., Han, Y.O., Hong, B.J., and Yun, S.H. (2017). Numerical simulation of three-dimensional external gear pump using immersed solid method. Appl. Therm. Eng. 118: 539–550, https://doi.org/10.1016/j.applthermaleng.2017.03.014.Search in Google Scholar
Zhao, X. and Vacca, A. (2019). Theoretical investigation into the ripple source of external gear pumps. Energies 12: 535, https://doi.org/10.3390/en12030535.Search in Google Scholar
Zhou, J., Vacca, A., and Casoli, P. (2014). A novel approach for predicting the operation of external gear pumps under cavitating conditions. Simul. Model. Pract. Theory 45: 35–49, https://doi.org/10.1016/j.simpat.2014.03.009.Search in Google Scholar
Zhao, X. and Vacca, A. (2017). Numerical analysis of theoretical flow in external gear machines. Mech. Mach. Theory 108: 41–56, https://doi.org/10.1016/j.mechmachtheory.2016.10.010.Search in Google Scholar
Zhao, X. and Vacca, A. (2018). Analysis of continuous-contact helical gear pumps through numerical modeling and experimental validation. Mech. Syst. Signal Process. 109: 352–378, https://doi.org/10.1016/j.ymssp.2018.02.043.Search in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Editorial
- Special issue for John Vlachopoulos
- Review Article
- Calendering of thermoplastics: models and computations
- Special Issue Contributions
- Film casting of polycarbonate/multi-walled carbon nanotubes composites using ultrasound-assisted twin-screw extruder: experiment and simulation
- Effect of mixing conditions and polymer particle size on the properties of polypropylene/graphite nanoplatelets micromoldings
- Extrusion foaming of linear and branched polypropylenes – input of the thermomechanical analysis of pressure drop in the die
- Improving the thickness distribution of parts with hybrid thermoforming
- Synergistic material extrusion 3D-printing using core–shell filaments containing polycarbonate-based material with different glass transition temperatures and viscosities
- TPU-based porous heterostructures by combined techniques
- Surfactant-free oil-in-oil emulsion-templating of polyimide aerogel foams
- Factors determining the flow erosion/part deformation of film insert molded thermoplastic products
- The extrusion of EPDM using an external gear pump: experiments and simulations
- News
- PPS News
Articles in the same Issue
- Frontmatter
- Editorial
- Special issue for John Vlachopoulos
- Review Article
- Calendering of thermoplastics: models and computations
- Special Issue Contributions
- Film casting of polycarbonate/multi-walled carbon nanotubes composites using ultrasound-assisted twin-screw extruder: experiment and simulation
- Effect of mixing conditions and polymer particle size on the properties of polypropylene/graphite nanoplatelets micromoldings
- Extrusion foaming of linear and branched polypropylenes – input of the thermomechanical analysis of pressure drop in the die
- Improving the thickness distribution of parts with hybrid thermoforming
- Synergistic material extrusion 3D-printing using core–shell filaments containing polycarbonate-based material with different glass transition temperatures and viscosities
- TPU-based porous heterostructures by combined techniques
- Surfactant-free oil-in-oil emulsion-templating of polyimide aerogel foams
- Factors determining the flow erosion/part deformation of film insert molded thermoplastic products
- The extrusion of EPDM using an external gear pump: experiments and simulations
- News
- PPS News