Academic Journal

Numerical optimization of planar nozzle shapes for fused deposition modeling.

Bibliographic Details
Title: Numerical optimization of planar nozzle shapes for fused deposition modeling.
Authors: Tillmann, Steffen, González, Felipe A., Elgeti, Stefanie
Source: International Journal of Numerical Methods for Heat & Fluid Flow; 2026, Vol. 36 Issue 7, p2827-2848, 22p
Subject Terms: Pressure drop (Fluid dynamics), Mathematical optimization, Viscoelasticity, Fused deposition modeling, Multidisciplinary design optimization, Fluid flow, Spline theory
Abstract: Purpose: In fused deposition modeling (FDM), the nozzle plays a critical role in enabling high printing speeds while maintaining precision. Despite its importance, most applications still rely on standard nozzle designs. This paper aims to investigate the influence of nozzle geometry on pressure loss inside the nozzle, a key factor in high-speed printing performance. Design/methodology/approach: The authors focus on optimizing the nozzle shape to minimize the pressure loss and establish a framework that allows both simple angle-based optimization and more advanced spline-based parametrization. To model the polymer melt flow, the authors use a Giesekus model to account for viscoelastic effects. Findings: For angle-based optimization, the pressure-loss objective exhibits two local minima: one associated with smooth flow and another with pronounced recirculation regions inside the nozzle. While the latter yields a lower pressure drop, such flow patterns are generally undesirable due to increased residence times and the associated risk of material degradation and nozzle clogging. The spline-based parametrization results in only marginal additional reductions in pressure loss compared to angle optimization, while decreasing the manufacturability of the nozzle considerably. Originality/value: This paper presents a comparative study of FDM nozzle shape optimization using a Giesekus model. The authors introduce a flexible optimization framework that accommodates both simple and advanced geometric parametrizations. The main contribution is the systematic comparison between angle- and spline-based parametrizations across materials and extrusion velocities, showing that most of the achievable pressure-loss reduction is already captured by the simpler and more manufacture-ready angle optimization. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Numerical Methods for Heat & Fluid Flow is the property of Emerald Publishing Limited and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Numerical optimization of planar nozzle shapes for fused deposition modeling.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Tillmann%2C+Steffen%22">Tillmann, Steffen</searchLink><br /><searchLink fieldCode="AR" term="%22González%2C+Felipe+A%2E%22">González, Felipe A.</searchLink><br /><searchLink fieldCode="AR" term="%22Elgeti%2C+Stefanie%22">Elgeti, Stefanie</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: International Journal of Numerical Methods for Heat & Fluid Flow; 2026, Vol. 36 Issue 7, p2827-2848, 22p
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Pressure+drop+%28Fluid+dynamics%29%22">Pressure drop (Fluid dynamics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Viscoelasticity%22">Viscoelasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Fused+deposition+modeling%22">Fused deposition modeling</searchLink><br /><searchLink fieldCode="DE" term="%22Multidisciplinary+design+optimization%22">Multidisciplinary design optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid+flow%22">Fluid flow</searchLink><br /><searchLink fieldCode="DE" term="%22Spline+theory%22">Spline theory</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Purpose: In fused deposition modeling (FDM), the nozzle plays a critical role in enabling high printing speeds while maintaining precision. Despite its importance, most applications still rely on standard nozzle designs. This paper aims to investigate the influence of nozzle geometry on pressure loss inside the nozzle, a key factor in high-speed printing performance. Design/methodology/approach: The authors focus on optimizing the nozzle shape to minimize the pressure loss and establish a framework that allows both simple angle-based optimization and more advanced spline-based parametrization. To model the polymer melt flow, the authors use a Giesekus model to account for viscoelastic effects. Findings: For angle-based optimization, the pressure-loss objective exhibits two local minima: one associated with smooth flow and another with pronounced recirculation regions inside the nozzle. While the latter yields a lower pressure drop, such flow patterns are generally undesirable due to increased residence times and the associated risk of material degradation and nozzle clogging. The spline-based parametrization results in only marginal additional reductions in pressure loss compared to angle optimization, while decreasing the manufacturability of the nozzle considerably. Originality/value: This paper presents a comparative study of FDM nozzle shape optimization using a Giesekus model. The authors introduce a flexible optimization framework that accommodates both simple and advanced geometric parametrizations. The main contribution is the systematic comparison between angle- and spline-based parametrizations across materials and extrusion velocities, showing that most of the achievable pressure-loss reduction is already captured by the simpler and more manufacture-ready angle optimization. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Numerical Methods for Heat & Fluid Flow is the property of Emerald Publishing Limited and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 22
        StartPage: 2827
    Subjects:
      – SubjectFull: Pressure drop (Fluid dynamics)
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Viscoelasticity
        Type: general
      – SubjectFull: Fused deposition modeling
        Type: general
      – SubjectFull: Multidisciplinary design optimization
        Type: general
      – SubjectFull: Fluid flow
        Type: general
      – SubjectFull: Spline theory
        Type: general
    Titles:
      – TitleFull: Numerical optimization of planar nozzle shapes for fused deposition modeling.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Tillmann, Steffen
      – PersonEntity:
          Name:
            NameFull: González, Felipe A.
      – PersonEntity:
          Name:
            NameFull: Elgeti, Stefanie
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 07
              Text: 2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 09615539
          Numbering:
            – Type: volume
              Value: 36
            – Type: issue
              Value: 7
          Titles:
            – TitleFull: International Journal of Numerical Methods for Heat & Fluid Flow
              Type: main
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