Numerical Problems Related to Solving the Navier-Stokes Equations in Connection with the Heat Transfer with the Use of FEM

Dyja, R.; Gawrońska, Elżbieta; Grosser, A.

doi:10.1016/j.proeng.2017.02.187

Cited by 8 publications

(4 citation statements)

References 15 publications

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“…In calculations, it is assumed that small time step is used, hence in determination of actual values of material properties, when temperature was needed, temperature from previous time step was used. This strategy allows to treat solidification equation as linear and even solve it independently from Navier-Stokes equations, which gives better overall performance [11]. Moreover, such approach makes possible to use lumped mass matrix in solidification equation [11,12].…”

Section: Mathematical Modelmentioning

confidence: 99%

A computer simulation of solidification taking into account the movement of the liquid phase

2018

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In the paper, we present the results of solidification simulation taking into account the movement of the liquid phase. The results are obtained from an author software which is implemented on the base of a stabilized finite elements method (Petrov-Galerkin formulation). Using that formulation the Navier-Stokes equation is solved together with the convection term (Boussinesq approximation). The Finite Element Method (FEM) formulation is responsible for solidification, approximating the solution of the heat conduction equation (with the internal heat source term responsible for the heat released during the phase transition). The movement of the liquid phase in a solidifying cast that is caused by convection can significantly affect the process of heat transfer from the casting to the mold, which in turn has an influence on the temperature distribution in the cast and may cause a change in the location of the defects. The presented results allow to assess under what conditions the effect of convection on the solidification process is significant.

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Section: Mathematical Modelmentioning

confidence: 99%

A computer simulation of solidification taking into account the movement of the liquid phase

2018

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“…The temperature field and liquid material velocity field are determined on the basis of the solution of mass, momentum and energy conservation equations. The motion of melted material in the fusion zone is mainly generated by natural convection according to Boussinesq model [12][13][14][15]. Mathematical model assumes fuzzy solidification front between solidus and liquidus temperatures where liquid material motion is treated as a fluid flow through porous medium with respect to Darcy's model.…”

Section: Numerical Solutionsmentioning

confidence: 99%

Computer simulations of thermal phenomena in surface heating process using the real distribution of Yb:YAG laser power

et al. 2018

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This work concerns mathematical and numerical modelling of temperature field during Yb:YAG laser heating of sheets made of S355 steel with the motion of liquid steel in the fusion zone taken into account. Laser power distribution and the caustics are determined on the basis of the geostatistical kriging method. Temperature field and melted material velocity field in the fusion zone are obtained from the numerical solution of continuum mechanics equations using projection method and finite volume method. Numerical algorithms are implemented into computer solver using ObjectPascal programming language. Computer simulations of Yb:YAG laser heating process are performed for different process parameters. Characteristic zones of experimentally obtained cross sections of heated elements are compared to numerically predicted fusion zone and heat affected zone.

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“…It is critical to know how new materials, structures, or models behave under load. Therefore, many researchers, including us, study the obtained results of the finite element methods (FEM) analysis of stress and strain distributions in order to approximate the mechanical parameters of devices [ 21 , 22 , 23 ]. In this way, the models become useful for the comparative analysis of different geometries, which—together with appropriate empirical validation studies—allow functional structure development.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Study of Geometry’s Impact on the Thermal and Mechanical Properties of Periodic Surface Structures

Gawrońska

Dyja

2021

Materials

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The paper focuses on thermal and mechanical analysis of Periodic Surface Structure (PSS). PSS is a continuous surface with a specific topology that is mathematically formulated by geometric factors. Cubic P-surface (“primitive”), D-surface (“diamond”), and G-surface (“gyroid”) structures were simulated under load and heat transport using a numerical approach. We conducted our study by solving the stress and heat equations using the Finite Element Method (FEM). We achieved results using our software module, which generates PSS and simulates stress and temperature distribution. The stress model defined by dependence between stress and strain, gained from an experiment, and correlation of strain and displacement, gained from geometric conditions, was used in numerical experiments. The influence of geometric factors on the thermal and mechanical behavior of PSS was qualitatively determined. We showed decreasing effective stress values with an increased number of cells in the cubic domain for concerned PSS. It is important, because the increase in the number of cells does not increase the structure’s volume.

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Numerical Problems Related to Solving the Navier-Stokes Equations in Connection with the Heat Transfer with the Use of FEM

Cited by 8 publications

References 15 publications

A computer simulation of solidification taking into account the movement of the liquid phase

A computer simulation of solidification taking into account the movement of the liquid phase

Computer simulations of thermal phenomena in surface heating process using the real distribution of Yb:YAG laser power

A Numerical Study of Geometry’s Impact on the Thermal and Mechanical Properties of Periodic Surface Structures

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