Numerical studies on a proposed stepwise binarization method for the topology optimization analysis of the sloshing control problem
In this study, the effect of the proposed binarization method on the topology optimization analysis of two-fluid flows with free surfaces was investigated. The oscillation of the liquid content of a vessel, referred to as sloshing, was numerically analyzed, and density-based topology optimization an...
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| Format: | Article |
| Language: | English |
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The Japan Society of Mechanical Engineers
2024-01-01
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| Series: | Journal of Fluid Science and Technology |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/jfst/19/1/19_2024jfst0001/_pdf/-char/en |
| _version_ | 1797230097883725824 |
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| author | Masaya KOBAYASHI Takahiko KURAHASHI |
| author_facet | Masaya KOBAYASHI Takahiko KURAHASHI |
| author_sort | Masaya KOBAYASHI |
| collection | DOAJ |
| description | In this study, the effect of the proposed binarization method on the topology optimization analysis of two-fluid flows with free surfaces was investigated. The oscillation of the liquid content of a vessel, referred to as sloshing, was numerically analyzed, and density-based topology optimization analysis was performed to suppress sloshing. In density-based topology optimization, the emergence of grayscale, which is neither a structural nor a fluid domain, is problematic. Therefore, in this study, the hyperbolic tangent function used in the sigmoid transformation to represent the structural and fluid domains was improved. In the early stages of the topology update, grayscale is allowed and the curves of the sigmoid transformation are loosely connected; however, as the number of iterations increases, the curves become steeper to eliminate grayscale. The optimization analysis was performed using a grayscale elimination method previously described in the research by Aage et al. (2008) and the proposed stepwise binarization method. The governing equations for the flow field consisted of the Navier-Stokes equations for unsteady incompressible viscous flow and the continuity equation. The interface was determined using the density function method. When dealing with incompressible viscous flow, caution should be exercised during the discretization process owing to the numerical instabilities caused by advection dominance and incompressibility conditions. To eliminate numerical instabilities, the governing equations were discretized based on the Lagrange-Galerkin and penalty methods. The numerical results confirmed that the grayscale was eliminated when the stepwise binarization method was employed. |
| first_indexed | 2024-04-24T15:23:05Z |
| format | Article |
| id | doaj.art-0ab2539291d944f9816b290199a09412 |
| institution | Directory Open Access Journal |
| issn | 1880-5558 |
| language | English |
| last_indexed | 2024-04-24T15:23:05Z |
| publishDate | 2024-01-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Journal of Fluid Science and Technology |
| spelling | doaj.art-0ab2539291d944f9816b290199a094122024-04-02T07:08:39ZengThe Japan Society of Mechanical EngineersJournal of Fluid Science and Technology1880-55582024-01-01191JFST0001JFST000110.1299/jfst.2024jfst0001jfstNumerical studies on a proposed stepwise binarization method for the topology optimization analysis of the sloshing control problemMasaya KOBAYASHI0Takahiko KURAHASHI1Department of Mechanical Engineering, Graduate School of Nagaoka University of TechnologyDepartment of Mechanical Engineering, Institute of GIGAKU, Nagaoka University of TechnologyIn this study, the effect of the proposed binarization method on the topology optimization analysis of two-fluid flows with free surfaces was investigated. The oscillation of the liquid content of a vessel, referred to as sloshing, was numerically analyzed, and density-based topology optimization analysis was performed to suppress sloshing. In density-based topology optimization, the emergence of grayscale, which is neither a structural nor a fluid domain, is problematic. Therefore, in this study, the hyperbolic tangent function used in the sigmoid transformation to represent the structural and fluid domains was improved. In the early stages of the topology update, grayscale is allowed and the curves of the sigmoid transformation are loosely connected; however, as the number of iterations increases, the curves become steeper to eliminate grayscale. The optimization analysis was performed using a grayscale elimination method previously described in the research by Aage et al. (2008) and the proposed stepwise binarization method. The governing equations for the flow field consisted of the Navier-Stokes equations for unsteady incompressible viscous flow and the continuity equation. The interface was determined using the density function method. When dealing with incompressible viscous flow, caution should be exercised during the discretization process owing to the numerical instabilities caused by advection dominance and incompressibility conditions. To eliminate numerical instabilities, the governing equations were discretized based on the Lagrange-Galerkin and penalty methods. The numerical results confirmed that the grayscale was eliminated when the stepwise binarization method was employed.https://www.jstage.jst.go.jp/article/jfst/19/1/19_2024jfst0001/_pdf/-char/enstepwise binarization methodtwo-fluidtopology optimizationsloshing problemlagrange-galerkin methodadjoint variable method |
| spellingShingle | Masaya KOBAYASHI Takahiko KURAHASHI Numerical studies on a proposed stepwise binarization method for the topology optimization analysis of the sloshing control problem Journal of Fluid Science and Technology stepwise binarization method two-fluid topology optimization sloshing problem lagrange-galerkin method adjoint variable method |
| title | Numerical studies on a proposed stepwise binarization method for the topology optimization analysis of the sloshing control problem |
| title_full | Numerical studies on a proposed stepwise binarization method for the topology optimization analysis of the sloshing control problem |
| title_fullStr | Numerical studies on a proposed stepwise binarization method for the topology optimization analysis of the sloshing control problem |
| title_full_unstemmed | Numerical studies on a proposed stepwise binarization method for the topology optimization analysis of the sloshing control problem |
| title_short | Numerical studies on a proposed stepwise binarization method for the topology optimization analysis of the sloshing control problem |
| title_sort | numerical studies on a proposed stepwise binarization method for the topology optimization analysis of the sloshing control problem |
| topic | stepwise binarization method two-fluid topology optimization sloshing problem lagrange-galerkin method adjoint variable method |
| url | https://www.jstage.jst.go.jp/article/jfst/19/1/19_2024jfst0001/_pdf/-char/en |
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