Anderson, PD Patrick

Bie, VG  de

Hulsen, MA Martien

de Bie, Vincent

Hulsen, Martien A.

Anderson, Patrick D.

Pure OAI Repository

 The flow of a viscous fluid through an external gear pumpCitation for published version (APA):de Bie, V., Hulsen, M. A., & Anderson, P. D. (2019). The flow of a viscous fluid through an external gear pump.Document status and date:Published: 01/01/2019Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 17. Nov. 2023Stokes flowFrom numerical simulations, the flow rate over time isobtained (Fig. 3a), which shows that a fluctuation is present.The frequency of this fluctuation is related to the number ofteeth of the gears.Figure 3: The flow of a viscous fluid through a gear pump with a rotation speed of1 rad/s: (a) flow rate over time, and (b) mean efficiency versus the fluid viscosity.The ratio of the flow rate and the theoretically achievable flowrate results in an efficiency of the pump (Fig. 3b). For lowviscosities, the efficiency of the pump drops due to fluidleaking backwards (Fig. 4).Figure 4: The horizontal velocity of a fluid with a viscosity of 102 Pa⋅s flowingthrough an external gear pump with a rotation speed of 1 rad/s.ConclusionsA 2D numerical model of the external gear pump has beendeveloped to study the effect of processing conditions andmaterial properties on the flow of the fluid. The viscosityfunction in the model can be easily extended to account forthe effect of deformation rate, temperature and/or pressure.MethodThe flow of a fluid through a gear pump (Fig. 1) is described using the massand the momentum balance. The fluid behavior is represented by a viscousconstitutive model, which assumes a constant viscosity. The pressures at theentry and the exit are prescribed, resulting in a constant pressure differenceover the pump.Figure 1: Schematic overview of the working principle of the external gear pump.The domain of the pump is filled with triangular elements (Fig. 2). Adaptivelocal mesh refinement is needed due to the moving boundary and therelatively narrow gaps.Figure 2: The finite element mesh with local refinements in the narrow regions, which is generated usingGmsh and consists of triangular elements.The flow of a viscous fluid through an external gear pumpVincent G. de Bie, Martien A. Hulsen , and Patrick D. Anderson/ department of mechanical engineering www.tue.nl/ptIntake Transport DischargeGear pumps are often used for the transport of highviscosity fluids, for example in the production of car tires.In the extrusion process of the tire compounds, the flowrate is controlled by an external gear pump. The flow of afluid through the pump is numerically studied using thefinite element method.

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The flow of a viscous fluid through an external gear pump

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 The flow of a viscous fluid through an external gear pumpCitation for published version (APA):de Bie, V., Hulsen, M. A., & Anderson, P. D. (2019). The flow of a viscous fluid through an external gear pump.Document status and date:Published: 01/01/2019Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 16. Nov. 2023Stokes flowFrom numerical simulations, the flow rate over time isobtained (Fig. 3a), which shows that a fluctuation is present.The frequency of this fluctuation is related to the number ofteeth of the gears.Figure 3: The flow of a viscous fluid through a gear pump with a rotation speed of1 rad/s: (a) flow rate over time, and (b) mean efficiency versus the fluid viscosity.The ratio of the flow rate and the theoretically achievable flowrate results in an efficiency of the pump (Fig. 3b). For lowviscosities, the efficiency of the pump drops due to fluidleaking backwards (Fig. 4).Figure 4: The horizontal velocity of a fluid with a viscosity of 102 Pa⋅s flowingthrough an external gear pump with a rotation speed of 1 rad/s.ConclusionsA 2D numerical model of the external gear pump has beendeveloped to study the effect of processing conditions andmaterial properties on the flow of the fluid. The viscosityfunction in the model can be easily extended to account forthe effect of deformation rate, temperature and/or pressure.MethodThe flow of a fluid through a gear pump (Fig. 1) is described using the massand the momentum balance. The fluid behavior is represented by a viscousconstitutive model, which assumes a constant viscosity. The pressures at theentry and the exit are prescribed, resulting in a constant pressure differenceover the pump.Figure 1: Schematic overview of the working principle of the external gear pump.The domain of the pump is filled with triangular elements (Fig. 2). Adaptivelocal mesh refinement is needed due to the moving boundary and therelatively narrow gaps.Figure 2: The finite element mesh with local refinements in the narrow regions, which is generated usingGmsh and consists of triangular elements.The flow of a viscous fluid through an external gear pumpVincent G. de Bie, Martien A. Hulsen , and Patrick D. Anderson/ department of mechanical engineering www.tue.nl/ptIntake Transport DischargeGear pumps are often used for the transport of highviscosity fluids, for example in the production of car tires.In the extrusion process of the tire compounds, the flowrate is controlled by an external gear pump. The flow of afluid through the pump is numerically studied using thefinite element method.

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The flow of a viscous fluid through an external gear pump

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