Effects of a Cavity’s Fractal Boundary on the Free Front Interface of the Polymer Filling Stage

Abstract

The unsmooth boundary of a cavity for the stage of filling glass fiber-reinforced polymer melt affects the flow property and the shape of the free interface’s shape, as a result, it will affect greatly the process, the degree and the location of the front interface, and the weld lines’ property and product quality as well. Here, the two-scale fractal theory is adopted to figure out the basic property of the unsmooth boundary, and governing equations are established in a fractal space. The numerical results can provide insight into the filling process and reveal the main factors affecting the shape of the free interface. The fractal interface is illustrated by the least-square method in different fractal spaces based on numerical simulation results. The fractal cavity sheds a new light on controlling the interface.

Experimental Examination of Gas-liquid Two-phase Flow Patterns in an Inclined Rectangular Channel with 90° Bend for Various Vertical Lengths

“…Two-phase flows are of considerable interest to many industries such as power generation, thermal hydraulic reactor system, chemical plants and food production. The two-phase flow in a rectangular channel has attracted special research interest in recent decades owing to its numerous applications such as in plate type nuclear fuels [1][2][3], high performance micro-electronics [4,5] and polymer melt filling process [6][7][8].…”

Numerical studies on an accidental flashfire at a water fun park by FLACS software

“…The k- model is used to model turbulence in explosion whereas the beta model is used to model the change of combustion reaction rate, which can be confirmed for the simulation explosion process effectively. Note that the algebraic sub-grid scales-variational multi-scale (ASGS-VMS) finite element method [16,17] was used to solve the polymer melt filling process, the first time ever performed for the two-phase flow of polymer melt filling process.…”

“…There are many similar works on powder explosion with numerical studies [13][14][15]. An effective numerical algorithm was developed for a gas-melt two-phase flow and used to simulate a polymer melt filling process [16,17]. The suggested algorithm can deal with the moving interface and discontinuities of unknowns across the interface.…”

The variational iteration method for Whitham-Broer-Kaup system with local fractional derivatives

“…Many non-differentiable phenomena in applied sciences and engineering can be described by local fractional differential equations or fractal differential equations, especially for fractal media [1] including porous media like concrete [2], hierarchical structure [3], porous cells [4], crystals [5], and unsmooth boundaries [6,7]. In recent years, the study of initial value problems modeled by local fractional partial differential equations has attracted many mathematicians and physicists [8][9][10][11].…”