Control Volume Finite Element Research Articles

A study on fiber orientation in the compression molding of fiber reinforced polymer composite material

It is important to predict the fiber orientation state in controlling the mechanical and physical properties of the final parts in the compression molding process. A computer simulation has been performed to predict the fiber orientation state during compression molding. In the flow analysis, the generalized Hele–Shaw (GHS) model and the control volume finite element method (CVFEM) were employed, and second order tensor representation was used in the fiber orientation analysis. The conventional fiber orientation model has been based on the assumption of homogeneous suspension, i.e. the fiber content is uniform everywhere in the charge. However, in the actual compression molding process where long fibers are used and the fiber content is high, the homogeneous suspension assumption is violated since the fiber separation phenomenon occurs and a fiber concentration gradient is developed. In this study, a new fiber orientation model considering the fiber separation effect is suggested. The results of the analysis are compared with those of experiment and they show good agreement.

MIXED CONVECTION IN A PLANE CHANNEL WITH A BUILT-IN TRIANGULAR PRISM

The superposition of Von Karman street and convective cells in a horizontal plane channel containing a triangular prism and heated from below constitute the principal subject of this numerical investigation. The numerical scheme is based on the control volume finite element method (CVFEM) adapted to the standard staggered grid with the SIM PLER algorithm for pressure-velocity coupling and an Alternating Direction Implicit (ADI) scheme for the time integration. Many standard test flows are simulated successfully. Results are obtained for a Grashof number ranging from 0 to 1.5 10 4 at Pr 0.71 and Re 100 with constant physical properties. At the outlet of the computational domain a convective boundary condition (CBC) is used. Results are presented to show the effect of development of convective cells on the flow pattern and on the Strouhal number. Regarding the heat transfer rate, we focus on the effect of the presence of the triangular prism on the heat flux transferred from the hot wall to the flow.

UPF: two-dimensional finite-element groundwater flow model for saturated–unsaturated soils

A finite-element program for modeling water flow in saturated–unsaturated soils is presented. The program can handle non-uniform flow regions having irregular boundaries and local anisotropy. The flow domain can be either in a vertical or in a horizontal plane, or in a three dimensional system with radial symmetry. The flow equation is solved by using either a Galerkin finite-element (GFE), or a control-volume finite-element (CVFE) method. The discretization of the flow domain is obtained by using triangular finite elements and linear shape functions; the integration in time is performed by a finite-difference (FD) Picard scheme. Different schemes of the ‘upstream’ and ‘lumping’ procedures in computing, respectively, the conductivity and capacity matrices are compared, taking as evaluation parameters the global mass balance errors and the stability of the solutions. The listing of the FORTRAN 77 source code, along with the user manual, the description of the subroutines used in the code, and four input files for four test cases are available by anonymous FTP from ftp.iamg.org site or may be downloaded by Internet from http://www.iamg.org/CGEditor/index.htm.

Aerodynamic analysis of HAWTs operating in unsteady conditions

AbstractThis article presents a numerical method for predicting unsteady aerodynamics of horizontal axis wind turbines (HAWTs). In this method the flow field is described by the unsteady incompressible Navier–Stokes equations. The rotor and tower are idealized respectively as actuator disc and flat plate permeable surfaces on which external normal surficial forces are balanced by fluid pressure discontinuities. The external forces exerted by the rotor and tower on the flow are prescribed according to blade element theory. Dynamic behaviour of the rotor aerodynamic characteristics is simulated using either the Gormont or the Beddoes–Leishman model. The resulting mathematical formulation is solved using a control volume finite element method. The fully implicit scheme is used for time discretization. In general, the proposed method has demonstrated its capability to adequately represent the field data. It has been demonstrated that the accuracy of the predicted results depends primarily on the dynamic stall model as well as on the turbulence model employed. Copyright © 2001 John Wiley & Sons, Ltd.

Mass conservation in numerical simulation of resin flow

Abstract The finite element/control volume (FE/CV) approach is commonly used for numerical simulation of resin flow in many composites manufacturing processes. The law of mass conservation is sometimes violated with the use of this approach. Especially, when the Galerkin formulation is used with isoparametric finite elements to obtain the pressure field, the balance of resin mass cannot be achieved. In this paper, reasons leading to such mass imbalance are investigated. A numerical model based on material incompressibility is developed to eliminate the problem. A few isothermal flow simulation examples are presented to demonstrate the application of the model. The results obtained are in excellent agreement with the analytical solutions.

A novel first-order scheme for numerical two-dimensional radiative transfer analysis

This paper presents a skewed upwinding procedure for application to the Control Volume Finite Element Method (CVFEM) in the context of radiation heat transfer problems involving participating media. The proposed first order scheme is stable, economical, accurate and it inherently precludes the possibility of computing negative coefficients in the discretized algebraic equations while accounting for the direction of radiant propagation. The suggested first-order skew positive coefficients upwind scheme (SPCUS) is validated by application to several basic two-dimensional test problems, acknowledged by the radiative heat transfer community: its performance has proven to be excellent.

An analysis of the three-dimensional resin-transfer mold filling process

Resin-transfer molding (RTM) is a process in which thermosetting resin is injected into a mold cavity pre-loaded with a porous fibrous preform. For parts with small thickness, the mold-filling process can be modeled as two-dimensional by neglecting the resin flow in the thickness direction. However thicker parts require extensive resin flow through the thickness and thus the three-dimensional effect in the resin flow must be considered. In this study, numerical simulations of three-dimensional mold filling during RTM were performed. The governing differential equations were discretized by using the control volume finite element method (CVFEM). The CVFEM technique was employed bacause of its simplicity in handling the moving boundary problems. The temperature and the degree of cure were also calculated. In order to evaluate the validity of the numerical results, they were compared with exact solutions for simple geometries, and close agreement was observed. Experiments were also performed. To check the three-dimensional resin front location as a function of time inside the preform, an optical fiber was used as a sensing element. The agreements between the experimental data and the numerical results were found to be satisfactory. Numerical calculations for complicated geometries were also performed to illustrate the effectiveness of the computer code developed in this study.

Analysis of resin transfer moulding process with controlled multiple gates resin injection

Abstract In resin transfer moulding, increase of fibre volume fraction decelerates the resin flow. For fast resin flow without increasing injection pressure, resin can be injected using multiple injection gates. However, with improper injection schemes, the resin front becomes complicated and numerous air bubbles may form where the flow fronts merge. In this study, two different multiple gate injection schemes were investigated. One is to open the gates in a sequential manner as the resin front advances. The other is to control the resin injection pressure as a function of time. Mould filling was simulated numerically using the Control Volume Finite Element Method (CVFEM). Experiments were performed to verify the simulation results. The resin front shapes observed from the experiments were compared with the numerical results. Close agreements were found. The controlled multiple gate injection methods were proven to reduce the injection time by a big margin as well as to prevent the formation of air bubbles due to air entrapment.

Numerical predictions of two-dimensional conduction, convection, and radiation heat transfer. I. Formulation

The research presented in this paper involves the detailed formulation of a Control-Volume Finite Element Method (CVFEM) for the solution of combined-mode heat transfer in participating media. The proposed numerical method accounts for emitting, absorbing, and scattering media in regularly- and irregularly-shaped geometries. In the proposed CVFEM, the calculation domain is divided into three-node triangular finite elements: the geometrical flexibility associated with finite element methods is preserved. Each element is further subdivided in such a way that upon assembly of all elements, complete control volumes are formed around each node in the calculation domain. To account for the directional nature of radiation heat transfer, a spherical envelope, surrounding each node in the calculation domain, is discretized in adjacent non-overlapping solid angles (or control angles). Element-based interpolation functions for the dependent variables, and the subdomain-type method of weighted residuals are used to derive algebraic approximations to the governing equations. Interpolation schemes that guarantee positive contributions to the coefficients in the algebraic discretization equations are used to approximate the convective and radiative fluxes across control-volume surfaces.

Computational and experimental investigation of flow and fluid mixing in the roller bottle bioreactor.

The fully three-dimensional velocity field in a roller bottle bioreactor is simulated for two systems (creeping flow and inertial flow conditions) using a control volume-finite element method, and validated experimentally using particle imaging velocimetry. The velocity fields and flow patterns are described in detail using velocity contour plots and tracer particle pathline computations. Bulk fluid mixing in the roller bottle is then examined using a computational fluid tracer program and flow visualization experiments. It is shown that the velocity fields and flow patterns are substantially different for each of these flow cases. For creeping flow conditions the flow streamlines consist of symmetric, closed three-dimensional loops; and for inertial flow conditions, streamlines consist of asymmetric toroidal surfaces. Fluid tracers remain trapped on these streamlines and are unable to contact other regions of the flow domain. As a result, fluid mixing is greatly hindered, especially in the axial direction. The lack of efficient axial mixing is verified computationally and experimentally. Such mixing limitations, however, are readily overcome by introducing a small-amplitude vertical rocking motion that disrupts both symmetry and recirculation, leading to much faster and complete axial mixing. The frequency of such motion is shown to have a significant effect on mixing rate, which is a critical parameter in the overall performance of roller bottles.

Control-Volume Finite Element Analysis of Phase Change During Direct Chill Casting

A fully implicit control-volume finite element method is used to analyze the phase change during DC casting of aluminum alloy. The mathematical model is based on the integral form of the enthalpy equation. A Eulerian-Lagrangian transformation, together with a deforming grid technique, is introduced to efficiently track the evolution of the physical domain. The temperature distribution predicted by the numerical model is in good agreement with that measured in previous experiments. [S0022-1481(00)00502-8]

HIGHLY SCALABLE PARALLEL COMPUTATIONAL MODELS FOR LARGE-SCALE RTM PROCESS MODELING SIMULATIONS, PART 1: THEORETICAL FORMULATIONS AND GENERIC DESIGN

This article reports the recent development of a highly scalable parallel computational model for process modeling and manufacturing applications of large-scale composite structures with particular emphasis on resin transfer molding (RTM). Fundamental concepts and characteristic features of the proposed scalable parallel algorithms are described and developed in technical detail. The approaches for simulating process modeling and manufacturing applications of composites includes: (1) the traditional, explicit control-volume finite-element (CV-FE) approach, and (2) a recently developed and new, implicit pure finite-element pure (pure FE) approach. SGI Power Challenge and SGI Origin 2000, which are symmetric multiprocessor (SMP) computing platforms, are employed in this study. The issues of implementation and software development of these manufacturing process simulations are parallel algorithm development, data structures, and interprocessor communication strategies, with emphasis on performance and scalability on these symmetric multiprocessors. W ith the motivation for providing effective computational procedures suitable for practical process modeling and manufacturing applications of large-scale composite structures and general finite-element simulations, the proposed developments not only provide a sound theoretical basis but also serve to be ideally portable to a wide range of parallel architectures. W hereas the theoretical formulations and generic design are described in Part 1, the parallel formulation of the theory and implementation will be presented in Part 2, and the techniques developed are applied to large-scale problems using Power Challenge and SGI Origin to demonstrate the effectiveness and the practical applicability, which will be presented in Part 3 of this work.

CONTROL VOLUME FINITE ELEMENT NUMERICAL SIMULATION OF MIXED CONVECTION IN AN AIR-COOLED CAVITY

This paper presents a numerical study of transient mixed convection of laminar flows in an air-cooled cavity in which a fluid is injected at a temperature lower than the initial temperature of the cavity. A control volume finite element method (CVFEM) using triangular elements is employed to discretize the governing equations. The performance of the numerical algorithm is first tested. In order to investigate the quality of the ventilation and cooling, the dynamic and thermal fields are numerically determined for a large range of Reynolds and Richardson numbers and for different inlet-outlet locations. Cooling efficiency is examined at transient and at steady regimes.

HIGHLY SCALABLE PARALLEL COMPUTATIONAL MODELS FOR LARGE-SCALE RTM PROCESS MODELING SIMULATIONS, PART 2: PARALLEL FORMULATION THEORY AND IMPLEMENTATION

We highlight some key elements of the parallel formulation theory and implementational aspect of process modeling and manufacturing applications of composites with particular emphasis on resin transfer molding (RTM). The approaches for simulating process modeling and manufacturing applications of composites include (1) the traditional explicit control-volume finite-element (CV-FE) approach, and (2) a recently developed and new, implicit, pure finite-element (pure FE) approach. SGI Power Challenge and SGI Origin 2000, which are symmetric multiprocessor (SMP) computing platforms, are employed in this study. The issues in implementation and software development of these manufacturing process simulations are parallel algorithm development, data structures, and interprocessor communication strategies, with emphasis on performance and scalability on these symmetric multiprocessors. Fundamental concepts and characteristic features of the proposed scalable parallel algorithms are described and developed with theoretical analysis

TRANSPORE : A GENERIC HEAT AND MASS TRANSFER COMPUTATIONAL MODEL FOR UNDERSTANDING AND VISUALISING THE DRYING OF POROUS MEDIA

ABSTRACT In this work a sophisticated numerical model is presented that describes the drying of porous media. This model, which is known as TransPore, has evolved over the years through the direct inputs of both authors. Nowadays, TransPore can be used to analyse the drying of media that are of completely arbitrary shape and size, under a variety of drying conditions. The engine of the computational model uses a number of state-of-the-art numerical methods that ensure the simulation results describe the particular drying process accurately, whilst guaranteeing the most efficient and effective usage of computer resources. For example, the numerical discretisation method is based on a completely conservative hybrid finite element control volume technique that uses a finite element mesh for its background gradient interpolation. Furthermore, flux limiting is used to reduce numerical dispersion in the drying kinetics and the generated non-linear system is resolved using the full Newton method for the outer iteration coupled together with a preconditioned conjugate gradient technique for the inner iteration. A graphical interface has been linked to the model to enable online visualisation of the drying process. The mathematical model allows both homogeneous and heterogeneous porous media to be simulated. The resultant software is an extremely powerful and effective tool for investigating existing dryer designs and for proposing new and innovative drying schedules that provide optimal drying quality in minimal drying time.

Turbulent heat transfer to near-critical water in a heated curved pipe under the conditions of mixed convection

Numerical modeling was performed to investigate the developing turbulent flow and heat transfer characteristics of water near the critical point in a curved pipe. The renormalization group (RNG) κ– ϵ model was used to account for the turbulent flow and heat transfer in the curved pipe at a constant wall temperature with or without buoyancy force effect. A control volume finite element method (CVFEM) was used to solve the three-dimensional full elliptic governing equations for the problem numerically. Due to the great variation in physical properties of water near the critical point, the turbulent flow heat transfer can be significantly altered compared with the pure forced convection in the curved pipe. This study explored the influence of the near-critical pressure and wall temperature on the development of fluid flow and heat transfer along the pipe. The numerical results for forced convective flow and heat transfer were compared with experiments available in the literature. Based on the results of this research, the velocity, temperature, heat transfer coefficient, friction factor distribution, and effective viscosity are presented graphically and analyzed.

THREE-DIMENSIONAL RESIN TRANSFER MOLDING: ISOTHERMAL PROCESS MODELING AND IMPLICIT TRACKING OF MOVING FRONTS FOR THICK, GEOMETRICALLY COMPLEX COMPOSITES MANUFACTURING APPLICATIONS - PART 2

In the manufacture of complex thick composite structures, isothermal process modeling simulation tools analyzing the three-dimensional flow of resin impregnating the thick fiber preform are instrumental in initial process optimizations. We present a new implicit formulation based on accurately taking into account the transient nature of the time-dependent conservation of resin mass and employing the pure finite element method to implicitly solve for the pressure field and to track the flow front progression of the resin inside the mold cavity. Our emphasis is on thick composites. Our previous efforts involved two-dimensional thin sections [1] and the implicit type approach. The present method is an extension of that effort to three-dimensional thick composites. The numerical developments involving the present implicit methodology and tracking of the resin progression flow fronts provide an improved and physically accurate representation of the physical problem. They do not involve the time step restrictions based on the Courant condition as in the traditional explicit finite element-control volume (FE-CV) associated formulation discussed in Part 1 in this issue. Instead, we treat the transient process as a series of quasi-steady-state processes. For illustrative purposes, the present developments are first validated with simple geometries, then extended to practical applications for isothermal conditions, and finally, contrasted to part 1 in this issue of this study.

THREE-DIMENSIONAL RESIN TRANSFER MOLDING: ISOTHERMAL PROCESS MODELING AND EXPLICIT TRACKING OF MOVING FRONTS FOR THICK GEOMETRICALLY COMPLEX COMPOSITES MANUFACTURING APPLICATIONS - PART 1

In resin transfer molding (RTM) process modeling, current practices involved in the simulation of resin impregnation through porous media have been generally restricted to two-dimensional formulations based on Darcy's law for flow through thin cavities due to the increased computational demand and stringent stability restrictions of the traditionally employed explicit finite element-control volume (FE-CV) type approaches. The presence of multiple fiber layers in thick composites, or the notion of introducing impermeable inserts inside the fiber bundles to serve as protective armor, causes the resin impregnation to be a three-dimensional flow. This paper describes full three-dimensional simulations based on an explicit FE-CV technique to assess the practicality and suitability of the approach. Though viable, the technique treats the transient mold filling problem as a series of quasi-steady state problems. Additionally, an effective alternate form and discretization of the field variables based on a flux-based finite element representation is presented in conjunction with the above primarily to illustrate the theoretical developments for general situations. For linear situations, they readily revert exactly to the traditional finite element representations. In part 2 of this paper a transient computational methodology based on a pure implicit finite element method for applicability to three-dimensional RTM flow modeling is presented to demonstrate the improved effectiveness of the approach. The objectives of the efforts (part 1 here and part 2 in this issue), besides providing a clear understanding for flow in thick composites under isothermal conditions, are simply to (1) describe and investigate the traditional developments for practical geometrically complex three-dimensional composite sections, (2) describe extensions of our previous efforts and provide effective avenues for handling three-dimensional thick composites, and (3) contrast the two approaches and explore the pros and cons for practical three-dimensional composites process modeling.

Analysis of resin transfer/compression molding process

AbstractResin transfer/compression molding (RT/CM) is a two‐step process in which resin injection is followed by mold closing. This process can enhance the resin flow speed and the fiber volume fraction, as well as reducing the mold filling time. In this study, a simulation program for the mold filling process during RT/CM was developed using the modified control volume finite element method (CVFEM) along with the fixed grid method. The developed numerical code can predict the resin flow, temperature, pressure, and degree of cure distribution during RT/CM. The compression force required for squeezing the impregnated preform can also be calculated. Experiments were performed for a complicated three‐dimensional shell to verify the feasibility of the RT/CM process and the numerical scheme. The compression force and the compression speed were measured. A close agreement was found between the experimental data and the numerical results. The resin front location obtained from a short shot experiment was compared with the numerical prediction. Again, a close agreement was observed. In order to demonstrate the effectiveness of the numerical code, simulations were performed for more complicated process conditions with anisotropic permeability of the preform at higher fiber volume fractions.

The effects of inlet turbulence on the development of fluid flow and heat transfer in a helically coiled pipe

In this paper, the effects of inlet turbulence level on the development of three-dimensional turbulent flow and heat transfer in the entrance region of a helically coiled pipe are investigated by means of a fully elliptic numerical study. The k– ε standard two-equation turbulence model is used to simulate turbulent flow and heat transfer, which are assumed to develop from the inlet to the outlet simultaneously. Constant wall temperature and uniform inlet conditions are applied. The governing equations are solved by a Control-Volume Finite Element Method with an unstructured nonuniform grid system. Numerical results presented in this paper cover a Reynolds number range of 10 4–10 5, a Prandtl number range of 0.02–100, and an inlet turbulence intensity range of 2–40%. The development of the main velocity field, the secondary velocity field, the temperature field, bulk turbulent kinetic energy, the average friction factor, and average Nusselt numbers are discussed. It is found that bulk turbulent kinetic energy far from the entrance is not affected by the inlet turbulence level. Significant effects of the inlet turbulence level on the development of the friction factor and Nusselt number occur within a short axial distance from the entrance only.