Control Volume Finite Element Method Research Articles

Thermofluid Optimization of a Heated Helicopter Engine Cooling-Bay Surface

In this paper, a global optimization technique based on the Adaptive Response Surface Method (ARSM) is integrated with a Control Volume Finite-Element Method (CVFEM) for thermofluid optimization. T...

Determination of three-dimensional permeability of fiber preforms by the inverse parameter estimation technique

A method is presented for measuring the permeability of three-dimensional orthotropic fiber preforms using the inverse parameter estimation technique. The method is based on an optimization procedure that minimizes differences between computed and measured times of arrival of the flow front at various locations in the mold during resin transfer molding. The arrival time is computed by numerical simulation using the control volume finite element method. The validity of this method was examined experimentally. It was shown that the proposed method can be implemented in a straightforward manner and yields reliable results.

Entropy generation at the onset of natural convection

The entropy generation due to heat transfer and friction has been determined in transient state for laminar natural convection by solving numerically the mass, momentum and energy balance equations, using a control volume finite-element method. The variations of the total entropy generation as function of time for Rayleigh number and irreversibility distribution ratio set at 10 3⩽ Ra⩽10 5 and 10 −4⩽ ϕ⩽10 −1 were investigated. The evolution of the maximum of entropy generation with the Rayleigh number is studied. The effect of the irreversibility distribution ratio on the maximum entropy generation and the entropy generation in steady state are analyzed. The irreversibility maps for Rayleigh number set at 10 3⩽ Ra⩽10 5 and irreversibility distribution ratio ϕ=10 −4 are plotted.

An investigation of spatial and temporal weighting schemes for use in unstructured mesh control volume finite element methods

In this work the control volume finite element (CVFE) method is used to discretise a two-dimensional non-linear transport model on an unstructured mesh. First and second order temporal weighting, combined with various flux limiting techniques (spatial weighting) are analysed in order to identify the most accurate and efficient numerical scheme. An inexact Newton method is used to resolve the underlying discrete non-linear system. In computing the Newton step the performance of the preconditioned iterative solvers BiCGSTAB and GMRES, in conjunction with a two-node Jacobian approximation is also examined. A linear benchmark problem that admits an analytical solution is used to assess the accuracy and computational efficiency of the numerical model. The results show that the flux limited second order temporal scheme substantially reduce numerical diffusion on relatively coarse meshes. The low temperature wood drying non-linear case study highlights that the first order temporal scheme combined with flux limiting achieves good accuracy on a relatively coarse mesh and improves the overall computational efficiency.

Interpolation functions in control volume finite element method

The main contribution of this paper is the study of interpolation functions in control volume finite element method used in equal order and applied to an incompressible two-dimensional fluid flow. Especially, the exponential interpolation function expressed in the elemental local coordinate system is compared to the classic linear interpolation function expressed in the global coordinate system. A quantitative comparison is achieved by the application of these two schemes to four flows that we know the analytical solutions. These flows are classified in two groups: flows with privileged direction and flows without. The two interpolation functions are applied to a triangular element of the domain then; a direct comparison of the results given by each interpolation function to the exact value is easily realized. The two functions are also compared when used to solve the discretized equations over the entire domain. Stability of the numerical process and accuracy of solutions are compared.

Control volume function approximation methods and their applications to modeling porous media flow

In this paper we introduce a new control volume method for the discretization of a partial differential equation. The interpolation in this method utilizes ‘bilinear’, spline, or weighted distance functions. We call this new method the control volume function approximation (CVFA) method. It can accurately approximate both the pressure and velocity in the simulation of multiphase flow in porous media, effectively reduce grid orientation effects, and be easily applied to arbitrarily shaped control volumes. It is suitable for hybrid grid porous media simulations. In this paper we focus on its development, numerical study, and comparison with a standard control volume finite element method. A two-phase incompressible flow problem is used to show the efficiency and accuracy of the CVFA.

Determination of in‐plane permeability of fiber preforms by the gas flow method using pressure measurements

AbstractA method is described for measuring the in‐plane permeability of orthotropic fibrous preforms using gas flow. The method is based on an optimization process between computed and measured pressures at various locations in the mold during steady state gas flow through the enclosed preform. The computed pressure is obtained by the control volume finite element method (CVFEM). This method was demonstrated by using a specially designed mold with multiple ports for gas injection and pressure measurement and it was shown that it can be implemented easily and yields consistent and reliable results.

Control-volume finite-element method for the solution-of 2d Euler equations on unstructured moving grids

In this paper, Euler equations are solved to simulate compressible flow on unstructured moving grids. Solution domain is discretized using control-volume finite-element method. This method is benefited from the power of finite element in discretizing solution domain, and the capability of finite volume in conserving physical quantities. For the evaluation of flux vector components at the control-volume surfaces, we employed the flux-difference scheme of Roe, modified for moving grids. Geometric conservation laws are implemented carefully to prevent solution errors produced by grid movement. To demonstrate the accuracy of the algorithm in solving fluid flow problems on moving grids, a number of test problems have been carried out.

Processing of polyurethane/polystyrene hybrid foam and numerical simulation

Polyurethane foams were produced by using a homogenizer as a mixing equipment. Effects of stirring speed on the foam structure were investigated with SEM observations. Variation of the bubble size, density of the foam, compressive strength, and thermal conductivity were studied. A hybrid foam consisting of polyurethane foam and commercial polystyrene foam is produced. Mechanical and thermal properties of the hybrid foam were compared with those of pure polyurethane foam. Advancement of flow front during mold filling was observed by using a digital camcorder. Four types of mold geometry were used for mold filling experiments. Flow during mold filling was analyzed by using a two-dimensional control volume finite element method. Variation of foam density with respect to time was experimentally measured. Creeping flow, uniform density, uniform conversion, and uniform temperature were assumed for the numerical simulation. It was assumed for the numerical analysis that the cavity has thin planar geometry and the viscosity is constant. The theoretical predictions were compared with the experimental results and showed good agreement.

A Viscous Three-Dimensional Differential/Actuator-Disk Method for the Aerodynamic Analysis of Wind Farms

Computational Fluid Dynamics (CFD) is a promising tool for the analysis and optimization of wind turbine positioning inside wind parks (also known as wind farms) in order to maximize power production. In this paper, 3-D, time-averaged, steady-state, incompressible Navier-Stokes equations, in which wind turbines are represented by surficial forces, are solved using a Control-Volume Finite Element Method (CVFEM). The fundamentals of developing a practical 3-D method are discussed in this paper, with an emphasis on some of the challenges that arose during their implementation. For isolated turbines, results have indicated that the proposed 3-D method attains the same level of accuracy, in terms of performance predictions, as the previously developed 2-D axisymmetric method and the well-known momentum-strip theory. Furthermore, the capability of the proposed method to predict wind turbine wake characteristics is also illustrated. Satisfactory agreement with experimental measurements has been achieved. The analysis of a two-row periodic wind farm in neutral atmospheric boundary layers demonstrate the existence of positive interference effects (venturi effects) as well as the dominant influence of mutual interference on the performance of dense wind turbine clusters.

DETERMINATION OF PERMEABILITY OF FIBROUS MEDIUM CONSIDERING INERTIAL EFFECTS

A method is described for measuring the Reynolds number dependent permeability in order to consider the inertial effects of the flow through porous media. A nonlinear correction term is introduced and the corresponding coefficients are determined by inverse analysis. The method is based on an optimization process between computed and measured pressures at various locations in the mold and flow rates at the gate during steady state gas flow through the enclosed fiber preform. The computed pressure is obtained by the control volume finite element method (CVFEM). The proposed method was demonstrated by using a specially designed mold with multiple ports for gas injection and pressure measurement

A Lagrangian–Eulerian model of particle dispersion in a turbulent plane mixing layer

AbstractA Lagrangian–Eulerian model for the dispersion of solid particles in a two‐dimensional, incompressible, turbulent flow is reported and validated. Prediction of the continuous phase is done by solving an Eulerian model using a control‐volume finite element method (CVFEM). A Lagrangian model is also applied, using a Runge–Kutta method to obtain the particle trajectories. The effect of fluid turbulence upon particle dispersion is taken into consideration through a simple stochastic approach. Validation tests are performed by comparing predictions for both phases in a particle‐laden, plane mixing layer airflow with corresponding measurements formerly reported by other authors. Even though some limitations are detected in the calculation of particle dispersion, on the whole the validation results are rather successful. Copyright © 2002 John Wiley & Sons, Ltd.

THREE-DIMENSIONAL NON-NEWTONIAN COMPUTATIONS OF MICRO-INJECTION MOLDING WITH THE FINITE ELEMENT METHOD

Micro-injection molding is a branch of micro-electromechanical system (MEMS) technology. Actually, the research of micro-injection molding is just beginning in the world. In this study, three-dimensional non-Newtonian computations of micro-injection molding were performed. The governing differential equations were discredited by using control volume finite element method (CVFEM). The analysis with different polymers (such as PS, PC, PMMA), process parameters (injection time mold temperature injection temperature and injection pressure) uses to simulate the micro-house for example. In order to obtain optimum result, the simulation introduces Taguchi method to discuss the influence of each parameter in micro-injection molding. In this study, the results show that the mold temperature is the most important factor on process parameters. The mold temperature on micro-injection molding is higher than the glass transition temperature of plastic material. The best suitable material is PMMA.

Simulation of Liquid Composite Molding Based on Control-Volume Finite Element Method

The control-volume finite element method (CVFEM) is a widely used numerical tool for modeling the polymer molding process because it is more user friendly and more robust than the conventional finite element or finite difference methods. This work compares the accuracy and stability of five upwind schemes of CVFEM for simulating the non-isothermal flow in the reactive liquid composite molding (LCM) processes. The results show that the mass weighted skew upwind (MAW) and the one-point upwind schemes are the most robust for simulating non-isothermal reactive flow in complicated flow domains and mesh shape. The streamline upwind control-volume (SUCV) scheme provides better numerical accuracy for simulating isothermal reactive flow. However, it tends to give unrealistic solutions at nodes close to the inlet region when simulating non-isothermal reactive flow in complicated geometry with obtuse triangular mesh. The two-point upwind scheme is inferior to MAW, the one-point upwind, and the SUCV schemes. The exponential and linear shape functions are not suitable for simulating the reactive LCM processes.

AN ANALYSIS OF THE THREE-DIMENSIONAL MICRO-INJECTION MOLDING

Micro system technology (MST) is including Optic, Mechanism, Electricity, Material, Control and Chemistry, etc. It can miniaturize product and increase its function, quality, reliability and add-value. The size of micro product is closing to nanometer. Micro-injection molding is a branch of micro system technology. Actually, the research of micro-injection molding is just beginning on the world. In this study, numerical simulations of three-dimensional micro-injection molding are performed. The governing differential equations are discredited by using control volume finite element method. The analysis with different polymers (such as PP PA POM) process parameters (injection time mold temperature injection temperature and injection pressure) uses to simulate the micro-gear for example. In order to obtain optimum result, the simulation introduces Taguchi method to discuss the influence of each parameter in micro-injection molding. In this study, the results show that the mold temperature is the most important factor on process parameters. The mold temperature on micro-injection molding is higher than the glass transition temperature of plastic material.

Numerical simulation of three-dimensional mold filling process in resin transfer molding using quasi-steady state and partial saturation formulations

This paper presents numerical simulations of a three-dimensional isothermal mold filling process based on the concept of control volume finite element method. Two numerical schemes are employed to track the flow front: one is based on the quasi-steady state formulation and the other is based on the formulation of partial saturation at flow front. The resulting codes named RTMS and RAPFIL, respectively, allow the prediction of flow front and pressure field in the three-dimensional molds with complex geometries. Since the preform permeability may be a function of fluid velocity, the proposed numerical schemes have accounted for velocity-dependency of permeability. This introduces complexity in the numerical schemes due to the correlation between the preform permeability and the fluid velocity during the mold filling. The validity of the two schemes is evaluated by comparison with analytical solutions for simple geometries, and excellent agreements are observed. To illustrate the applicability of the developed codes, the mold filling process of some mold geometries is simulated. A close agreement is observed between the results obtained by both codes in all cases. The CPU time required for the RAPFIL is significantly less than the RTMS as a conventional method on a personal computer and hence, the RAPFIL shows to be quite CPU time-effective for the simulation of complicated three-dimensional geometries.

Optimization of filling process in RTM using a genetic algorithm and experimental design method

AbstractIn the resin transfer molding (RTM) process, preplaced fiber mat is set up in a mold and thermoset resin is injected into the mold. An important issue in RTM processing is minimizing the cycle time without sacrificing part quality or increasing the cost. In this study, a numerical simulation and optimization process for the filling stage was conducted in order to determine the optimum gate locations. The control volume finite element method (CVFEM), modeled as a 2‐dimensional flow, was used in this numerical analysis along with the coordinate transformation method to analyze a complex 3‐dimensional structure. Experiments were performed to monitor the flow front to validate the simulation results. The results of the numerical simulation corresponded with that of the experimental quite well for every single, simultaneous, and sequential injection procedure. The optimization analysis of the sequential injection procedure was performed to minimize fill time. The complex geometry of an automobile bumper core was chosen. A genetic algorithm was used to determine the optimum gate locations in the 3‐step sequential injection case. Taguchi's experimental design method was also used for determining the pressure contribution of each gate. These results could provide the information on the optimum gate locations and injection pressure in each injection step and predict the filling time and flow front.

Méthode couplée CVFE/BE pour les calculs acoustiques en domaine non borné

A new method based on the flux conservation for acoustic computations in unbounded domain is presented. The domain is divided in outer and inner regions by a fictitious boundary. The inner problem is solved by a control volume finite element method while the outer flow is treated with a boundary element method. The coupling of the two sub-domains is performed using an appropriate expression for the outgoing fluxes satisfying the Sommerfeld condition. A two-dimensional configuration with a circular interface is considered to show that the method is effective. Results of this method are compared to an analytical solution and to results from the literature.

Numerical investigation of forced convection in a plane channel with a built-in triangular prism

Structure of laminar flow and heat transfer, in a two-dimensional horizontal channel differentially heated, with a built-in triangular prism is investigated from the numerical solutions of complete Navier–Stokes and energy equations. The numerical scheme is based on Control Volume Finite-Element Method with the SIMPLER algorithm for pressure-velocity coupling. Many standard test flows are successfully simulated. Results are obtained for Reynolds number ranging from 20 to 250 at Pr= 0.71 with constant physical properties. The flow is especially studied in details for two Reynolds numbers, Re= 30 as a sample of the symmetric flow, and Re= 100 as a sample for the periodic flow. Results are presented to show how the presence of such bluff body affects the flow pattern and the heat transfer from the hot bottom plate to the flow in both cases, symmetric and periodic flows.

A CONTROL-VOLUME FINITE-ELEMENT METHOD (CVFEM) FOR UNSTEADY, INCOMPRESSIBLE, VISCOUS FLUID FLOWS

A control-volume finite-element method (CVFEM), to simulate unsteady, incompressible, and viscous fluid flows, using nine-noded quadrilateral elements, has been developed. The Navier-Stokes equations in primitive variables u-v-p are the mathematical model of the flows. A technique of upwind, known as MAW, Mass-Weighted Interpolation, was extended for the finite element employed in this work. The set of nonlinear partial differential equations was integrated, and after using interpolation functions and time discretization, the algebraic system of equations was solved by using the frontal method of solution. Results obtained for some benchmark problems compared favorably with available results from the literature.