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In this study, the stationary flow of a polymeric fluid governed by the upper convected Maxwell law is computed in a 2‐D convergent geometry. A finite element method is…
In this study, the stationary flow of a polymeric fluid governed by the upper convected Maxwell law is computed in a 2‐D convergent geometry. A finite element method is used to obtain non‐linear discretized equations, solved by an iterative Picard (fixed point) algorithm. At each step, two sub‐systems are successively solved. The first one represents a Newtonian fluid flow (Stokes equations) perturbed by known pseudo‐body forces expressing fluid elasticity. It is solved by minimization of a functional of the velocity field, while the pressure is eliminated by penalization. The second sub‐system reduces to the tensorial differential evolution equation of the extra‐stress tensor for a given velocity field. It is solved by the so‐called ‘non‐consistent Petrov‐Galerkin streamline upwind’ method. As with other decoupled techniques applied to this problem, our simulation fails for relatively low values of the Weissenberg viscoelastic number. The value of the numerical limit point depends on the mesh refinement. When convergence is reached, the numerical solutions for velocity, pressure and stress fields are similar to those obtained by other authors with very costly mixed methods.
This paper presents a boundary element method (BEM) based on a subdomain approach for the solution of non‐Newtonian fluid flow problems which include thermal effects and…
This paper presents a boundary element method (BEM) based on a subdomain approach for the solution of non‐Newtonian fluid flow problems which include thermal effects and viscous dissipation. The volume integral arising from non‐linear terms is converted into equivalent boundary integrals by the multi‐domain dual reciprocity method (MD‐DRM) in each subdomain. Augmented thin plate splines interpolation functions are used for the approximation of field variables. The iterative numerical formulation is achieved by viewing the material as divided into small elements and on each of them the integral representation formulae for the velocity and temperature are applied and discretised using linear boundary elements. The final system of non‐linear algebraic equations is solved by a modified Newton's method. The numerical examples include non‐Newtonian problems with viscous dissipation, temperature‐dependent viscosity and natural convection due to bouyancy forces.
This paper gives a review of the finite element techniques (FE)applied in the area of material processing. The latest trends in metalforming, non‐metal forming and powder…
This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming and powder metallurgy are briefly discussed. The range of applications of finite elements on the subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for the last five years, and more than 1100 references are listed.
This paper presents the results of the simulation of the forging of a connecting rod. The calculation has been carried out by the code FORGE3 developed at the CEMEF…
This paper presents the results of the simulation of the forging of a connecting rod. The calculation has been carried out by the code FORGE3 developed at the CEMEF laboratory. FORGE3 is a three‐dimensional finite element computer program that can simulate hot forging of industrial parts. The flow problem is solved using a thermomechanical analysis. The mechanical resolution and the thermal one are coupled by the way of the consistency K which is thermodependent, the plastic deformation in the volume of the material and the friction heat flux on the surface. The material behaviour is assumed to be incompressible and viscoplastic (Norton—Hoff law) with the associated friction law. The thermal resolution includes the case of non‐linear physical properties and boundary conditions. An explicit Euler scheme is used for the mechanical resolution and two‐step schemes for the thermal one. For the computation of other parameters, it is necessary to have a good approximation for the strain rate tensor. The Orkisz method has been used to determine the deviatoric stress tensor and p is calculated by an original smoothing method. The results show that it is possible to get good information on the flow and on the physical properties during forging of automotive parts. Comparisons have been made with experimental measurements with a reasonably good agreement.
Numerical modelling and simulation of metal forming is rapidly gaining prominence in many industries all over the world due to its effective saving of production time…
Numerical modelling and simulation of metal forming is rapidly gaining prominence in many industries all over the world due to its effective saving of production time, effort and economy. In order to meet this need a special finite element code FORGE2 has been developed at CEMEF. In this work the theoretical basis of the FORGE2 along with its features such as thermo‐viscoplastic coupling, material compressibility and automatic mesh regeneration is reviewed and an attempt is made to simulate a few industrial forming processes taking into account the complex friction phenomena and thermal environment.
The design of vacuum calibrators for the cooling of complex PVC profilesis central to the production of high quality extrudates. One importantparameter governing cooling…
The design of vacuum calibrators for the cooling of complex PVC profiles is central to the production of high quality extrudates. One important parameter governing cooling efficiency is the heat transfer coefficient at the interface between the stainless steel calibrator and the PVC extrudate, whose value is often taken as constant regardless of the extrusion velocity and the applied pressure vacuum. In this paper, a method is proposed to evaluate the variation of the heat transfer coefficient over the entire calibrator length. The idea is to use temperature measurements together with heat transfer simulation to derive a heat transfer correlation that can be used in practical design cases.
This paper presents a study on implementing design of experiments for optimizing the extrusion blow molding process. The effect of screw speed, melting temperature…
This paper presents a study on implementing design of experiments for optimizing the extrusion blow molding process. The effect of screw speed, melting temperature, cooling time, pressure, mold temperature, and ambient temperatures on the outcome of the process is investigated. The significant factors affecting the volume and mass of the blow molded bottles are identified. The results show that melting temperature, pressure, and ambient temperature have a significant impact on the variation of produced bottle quality. An optimization technique is implemented to identify the best operating conditions to meet the required product output.
This paper sets out to show the feasibility of the genetic algorithm inverse method for the determination of the parameters of crystallization kinetics laws in isothermal…
This paper sets out to show the feasibility of the genetic algorithm inverse method for the determination of the parameters of crystallization kinetics laws in isothermal and non‐isothermal conditions, using multiple experiments.
The mathematical model for crystallization kinetics determination and the numerical methods of its resolution are introduced. Crystallization kinetic parameters determined by approximate physical analysis and the inverse genetic algorithm method are presented. Injection molding simulations taking into account crystallization are performed using the finite element method.
It is necessary to perform the optimization on two parameters, transformed volume fraction and number of spherulites to obtain correct results. It is possible to use results from different samples, in spite of the dispersion of some values.
Experimental data for isothermal and non‐isothermal conditions were used and obtained good results for the parameters of crystallization kinetics laws from which the evolutions of overall crystallization kinetics and crystalline microstructure were deduced. Nevertheless, the dispersion of the experimental data concerning the number of spherulites obtained with different samples is important. The evolution of the number of spherulites is required for the optimization to get correct results.
An important result of this work is that the genetic algorithm optimization can be applied to this problem where the experiments cannot be performed with a single sample and the experimental data for the number of spherulites have low precision. Even if only the crystallization kinetics was considered, the feasibility in molding simulation has been shown.
Simulation of crystallization in injection molding is very important for a later prediction of the end‐use properties.
– The purpose of this paper is to study numerically the rheological properties of fiber suspensions flowing through turbulent pipe flows.
The purpose of this paper is to study numerically the rheological properties of fiber suspensions flowing through turbulent pipe flows.
The work presented in this paper is derived the fluctuating equation for fiber orientation distribution function (FODF) in turbulent flows and solved using the method of characteristics. The FODF is predicted numerically. The numerical results of root-mean-square velocities generated by kinetic simulation sweeping model and are compared with the experimental data.
The fiber orientation distribution becomes wider with increasing Re. The components of the fourth-order orientation tensor increase with the increase of Re, and also increase along the radial direction and reach the maximum at the center line. The first normal stress difference is much less than the shear stress. For different Re the shear stress increases rapidly in the region far from the pipe center, and reaches its maximums at center, while the first normal stress difference decreases rapidly in the region far from the pipe center, and reaches its minimum at center finally.
By solving numerically the equation in a turbulent pipe flow with Reynolds number ranging from 2,500 to 1,000, the authors obtain the mean FODF which is in agreement with the experimental one qualitatively. Then the shear stress and first normal stress difference of suspensions are calculated based on the mean FODF.
Modelling of fiber suspension in injection molding cavities is very complex, with fluid flow, fiber orientation, and heat transfer effects taking place at the same time. Moreover, the flow is modified by the presence of fibers and vice versa. Therefore, the aim of the paper is to develop a Computational Fluid Dynamics (CFD) model to simulate and characterise the fiber suspension flow in two dimensional mold cavities. The model is intended to describe the fluid flow and heat transfer aspects of the suspension, and to predict the fiber orientation. The Navier-Stokes equations and the Jeffery (1922) equation are the governing equations for the velocity field and fiber motion respectively. The flow is considered to be two-dimensional incompressible, non-isothermal, transient and behave as non-Newtonian fluid containing suspension of short-fibers. The Finite Volume Method (FVM) combined with Control Volume Method is used to simulate the flow field by solving the momentum, energy and fiber orientation equations. To validate the numerical model, the numerical results are compared with available experimental findings. A good agreement between the numerical results and the experimental data is achieved. Since the behaviour of fiber suspension has great significance on the quality of the final product, this study has wide background of engineering application.