Simulation of Mold Filling for Non-Newtonian Fluids - Part 2

2006 ◽  
Vol 3 (2) ◽  
pp. 52-60
Author(s):  
Venkatesh M. Kulkarni ◽  
Chu Wee Liang ◽  
C.W. Tan ◽  
P.A. Aswatha Narayana ◽  
K.N. Seetharamu
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Molding Process ◽  
Algebraic Form ◽  
Design Guideline ◽  
Navier Stokes Equations ◽  
Transfer Molding ◽  
Encapsulation Process ◽  
Parametric Studies

This paper deals with the flow in the resin transfer molding process commonly used for IC chip encapsulation in the electronic packaging industry. A solution algorithm is presented for modeling the flow of a non-Newtonian fluid obeying a Power-Law model and the algorithm is used to conduct parametric studies in transfer molding. The flow model uses the Hele-Shaw approximation to solve the Navier-Stokes Equations and a pseudo-concentration algorithm for tracking the interface between the resin and the air. The Finite Element Method is employed to reduce the governing partial differential equations to algebraic form. The model is used to study the flow from the transfer ram into the cavity for different dimensions of transfer molding tools. Parametric studies are carried out to obtain balanced filling for transfer molding configuration. Parametric studies could provide a design guideline to optimize the encapsulation process prior to the setting up of an actual manufacturing set.

Flow in Cavities With Curved Boundaries

2009 ◽  
Author(s):  
Guillermo E. Ovando ◽  
Juan C. Prince ◽  
Sandy L. Ovando
Keyword(s):  
Stokes Equations ◽  
Operator Splitting ◽  
Vortex Formation ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Curved Boundaries ◽  
Navier Stokes Equations ◽  
Vertical Walls ◽  
Curved Walls

Fluid dynamics for a Newtonian fluid in the absence of body forces in a two-dimensional cavity with top and bottom curved walls was studied numerically. The vertical walls are fixed and the curved walls are in motion. The Navier-Stokes equations were solved using the finite element method combined with the operator splitting scheme. We analyzed the behaviour of the velocity fields, the vorticity fields and the velocity profiles of the fluid inside the cavity. The analysis was carried out for two different Reynolds numbers of 50 and 500 with two ratios (R = 1, −1) of the top to the bottom curved lid speed. For these values of parameters the flow is characterized by vortex formation inside the cavity. The spatial symmetry on the flow patterns are also investigated. We found that when the velocities of the top and bottom walls have opposite direction only one cell is formed in the central part of the cavity; however when the velocities of the top and bottom walls have the same direction the vortex formation inside the cavity is more complex.

A parallel partition of unity method for the nonstationary Navier-Stokes equations

2017 ◽  
Vol 27 (8) ◽  
pp. 1675-1686 ◽  
Author(s):  
Guangzhi Du ◽  
Liyun Zuo
Keyword(s):  
Stokes Equations ◽  
Partition Of Unity ◽  
Navier Stokes ◽  
Computational Time ◽  
The Finite Element Method ◽  
Partition Of Unity Method ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Standard Galerkin Method

Purpose The purpose of this paper is to propose a parallel partition of unity method (PPUM) to solve the nonstationary Navier-Stokes equations. Design/methodology/approach This paper opted for the nonstationary Navier-Stokes equations by using the finite element method and the partition of unity method. Findings This paper provides one efficient parallel algorithm which reaches the same accuracy as the standard Galerkin method but saves a lot of computational time. Originality/value In this paper, a PPUM is proposed for nonstationary Navier-Stokes. At each time step, the authors only need to solve a series of independent local sub-problems in parallel instead of one global problem.

Flow in Rectangular Cavities With Two Vertical Oscillating Walls

2008 ◽  
Author(s):  
Guillermo E. Ovando ◽  
Alberto Beltran ◽  
Sandy L. Ovando
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Navier Stokes Equations ◽  
Cell Structures ◽  
Lower Reynolds Number ◽  
Constant Displacement ◽  
Vertical Walls

Fluid dynamics in a two-dimensional rectangular cavity with vertical oscillatory walls out of phase was studied numerically. The Navier-Stokes equations were solved using the finite element method. We analyzed the behaviour of the velocity fields, the vorticity fields and we also obtained the streaklines of the fluid at the bottom left corner of the domain for one and two cycles, which is associated with the mixing of the fluid. The analysis was carried out for three different Reynolds numbers of 50, 500 and 1000 with constant displacement amplitude of the moving boundaries of 0.2. For this range of parameters the flow is characterized by two kind of symmetries. We found that for lower Reynolds number there is a good local mixing given by cell structures and the smooth behavior of the fluid inside the cavity; however for higher Reynolds number these structures disappear due to the fluid near the vertical walls impinges against the corner of the cavity, then this fluid is dispersed through the whole cavity during the cycle, increasing the global mixing of the fluid.

A Finite Element Analysis of the Navier-Stokes Equations Applied to High Speed Thin Film Lubrication

1987 ◽  
Vol 109 (1) ◽  
pp. 71-76 ◽  
Author(s):  
J. O. Medwell ◽  
D. T. Gethin ◽  
C. Taylor
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Thin Film Lubrication ◽  
Element Analysis ◽  
Navier Stokes Equations ◽  
Film Lubrication

The performance of a cylindrical bore bearing fed by two axial grooves orthogonal to the load line is analyzed by solving the Navier-Stokes equations using the finite element method. This produces detailed information about the three-dimensional velocity and pressure field within the hydrodynamic film. It is also shown that the method may be applied to long bearing geometries where recirculatory flows occur and in which the governing equations are elliptic. As expected the analysis confirms that lubricant inertia does not affect bearing performance significantly.

Simulation of Balanced Mold Filling in Transfer Molding for Newtonian Fluids

2004 ◽  
Vol 1 (4) ◽  
pp. 200-205
Author(s):  
Chu Wee Liang ◽  
Venkatesh M. Kulkarni ◽  
P.A.A. Aswataha Narayana ◽  
K.N. Seetharamu
Keyword(s):  
Newtonian Fluids ◽  
Partial Slip ◽  
Molding Process ◽  
Algebraic Form ◽  
Diffusion Term ◽  
Transfer Molding ◽  
Parametric Studies ◽  
Artificial Diffusion ◽  
Packaging Industry ◽  
The One

This paper presents the study of flow encapsulation processes as carried out in electronic packaging industry. A two dimensional Hele-Shaw model has been adopted to study the flow of Newtonian fluids into cavities at various distances from transfer ram in the transfer molding process. Velocity field obtained from Hele-Shaw is used in pseudo-concentration algorithm for front tracking with an artificial diffusion term added to allow partial slip at the fluid-wall interface and to damp numerical oscillation to a minimum level. Finite Element Method is employed to reduce the governing partial differential equations to algebraic form. Parametric studies have shown that by altering the dimensions and parameters of the mold tool, which will introduce different hydraulic resistances at the runner, gate and cavity, will lead to balanced filling in transfer molding. All the model dimensions or parameters remain constant except the one which is altered accordingly to allow different hydraulic resistances that will effectively enhance the filling and achieve balanced filling.

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