Control Volume Finite Element Method Research Articles

Numerical prediction of flow and heat transfer of power-law fluids in a plane channel with a built-in heated square cylinder

Structure of unsteady laminar flow and heat transfer of power-law fluids in two-dimensional horizontal plane channel with a built-in heated square cylinder is studied numerically. The governing equations are solved using a control volume finite element method (CVFEM) adapted to the staggered grid. Computations are performed over a range of Reynolds and Richardson numbers from Re = 20 to 200 and from Ri = 0 to 8, respectively at fixed Prandtl number Pr = 50 and blockage ratio value β′ = 1/8. Three different values of the power-law index ( n = 0.5, 1 and 1.4) are considered in this study to show its effect on the value of the critical Reynolds number defining the transition between two different flow regimes (symmetrical and periodic flows), the variations of Strouhal number, drag and lift coefficients and the heat transfer from the square cylinder as function of Reynolds number. Heat transfer correlations are obtained through forced convection. A discussion about the buoyancy effect on the flow pattern and the heat transfer for different power-law index is also presented.

NUMERICAL SOLUTION FOR THE PARAMETER ESTIMATION OF THE MOISTURE TRANSFER COEFFICIENT

We investigate the estimation of the moisture transfer coefficients in porous media by optimization technique which minimizes the functional defined by the squares error of the numerical solution of an inverse diffusion problem from their experimental values of the moisture content at the some time-steps. In this paper, we solve a diffusion equation numerically by the control volume finite element methods.

Periodically Fully-Developed Flow and Heat Transfer Over Flat and Oval Tubes Using a Control Volume Finite-Element Method

A Control Volume Finite-Element Method in conjunction with imposed periodically fully-developed flow conditions was used to perform a two-dimensional, laminar, steady-flow numerical study comparing the performance of a flat tube and an oval tube to that of a round tube in a simulated heat exchanger device for the case of specified heat flux along the tube walls. The Reynolds number range for the study was 50 to 350. Fluids of Prandtl number 0.7 and 7.0 were considered. For the cases studied, the heat transfer enhancement ratio was less than one indicating that the round tube outperformed both the flat tube and the oval tube based on heat transfer considerations alone. However, for all cases studied, the heat transfer performance ratio was greater than one indicating that if both heat transfer performance and required pumping power are considered, both the flat tube and oval tube outperformed the round tube.

Evanescent magnetic field effects on entropy generation at the onset of natural convection

This paper numerically investigates the effect of an externally evanescent magnetic field on total entropy generation in a fluid enclosed in a square cavity by using a control volume finite element method to solve the conservation equations at Prandtl number of 0·71. The values of relaxation time of the magnetic field are chosen, so that the Lorentz force acts only in the transient state of entropy generation in natural convection. The total entropy generation was calculated for, fixed value of irreversibility distribution ratio, different relaxation time varying from 0 to 1/5 and Grashof number varying from 104 to 105. The effects of the Hartman number and the magnetic field inclination angle on the evolution of total entropy generation throughout the transient regime were investigated. Results show that the application of evanescent magnetic field not only suppresses the fluctuation of the total entropy generation in the transient state, but also reduces the gap for magnetic field relaxation time less than 1/10.

Numerical analysis of heat transfer and flow field around cross-flow heat exchanger tube with fouling

Fouling is one of the main problems of heat transfer which can be described as the accumulation on the heat exchanger tubes, i.e.; ash deposits on the heat exchanger unit of the boiler. A decrease in heat transfer rate by this deposition causes loss in system efficiency and leads to increasing in operating and maintenance costs. This problem concerns with the coupling among conduction heat transfer mode between solid of different types, conjugate heat transfer at the interface of solid and fluid, and the conduction/convection heat transfer mode in the fluid which can not be solved analytically. In this paper, fouling effect on heat transfer around a cylinder in cross flow has been studied numerically by using conjugate heat transfer approach. Unlike other numerical techniques in existing literatures, an unstructured control volume finite element method (CVFEM) has been developed in this present work. The study deals with laminar flow where the Reynolds number is limited in the range that the flow field over the cylinder is laminar and steady. We concern the fouling shape as an eccentric annulus with constant thermal properties. The local heat transfer coefficient, temperature distribution and mean heat transfer coefficient along the fouling surface are given for concentric and eccentric cases. From the results, we have found that the heat transfer rate of cross-flow heat exchanger depends on the eccentricity and thermal conductivity ratio between the fouling material and fluid. The effect of eccentric is dominant in the region near the front stagnation point due to high temperature and velocity gradients. The mean Nusselt number varies in asymptotic fashion with the thermal conductivity ratio. Fluid Prandtl number has a prominent effect on the distribution of local Nusselt number and the temperature along the fouling surface.

Solution of the inverse radiation problem for anisotropically scattering medium using the control volume finite element method

In this paper, an inverse analysis is performed for the estimation of radiative parameters from the measured temperature profile in an absorbing, emitting, and anisotropically scattering medium. The control volume finite element method is employed to solve the direct problem in a 3-D rectangular furnace. The inverse problem is formulated as an optimization problem between the calculated and the experimental data and the Levenberg-Marquardt method is used for its solution. The sensitivity analysis is made in order to determine whether it is possible to identify the parameters. Also, the effects of angular and spatial grid numbers and the initial guesses on the accuracy of the inverse problem are investigated. This method combination, which is applied for the first time to solve 3-D inverse radiation problem, has been found to accurately predict the unknown parameters.

Numerical analysis of natural convection in a prismatic enclosure

Natural convection heat transfer and fluid flow have been examined numerically using the control-volume finite-element method in an isosceles prismatic cavity, submitted to a uniform heat flux from below when inclined sides are maintained isothermal and vertical walls are assumed to be perfect thermal insulators, without symmetry assumptions for the flow structure. The aim of the study is to examine a pitchfork bifurcation occurrence. Governing parameters on heat transfer and flow fields are the Rayleigh number and the aspect ratio of the enclosure. It has been found that the heated wall is not isothermal and the flow structure is sensitive to the aspect ratio. It is also found that heat transfer increases with increasing of Rayleigh number and decreases with increasing aspect ratio. The effects of aspect ratio become significant especially for higher values of Rayleigh number. Eventually the obtained results show that a pitchfork bifurcation occurs at a critical Rayleigh number, above which the symmetric solutions becomes unstable and asymmetric solutions are instead obtained.

Prediction of radiative heat transfer in 3D complex geometries using the unstructured control volume finite element method

In this paper, a 3D algorithm for the treatment of radiative heat transfer in emitting, absorbing, and scattering media is developed. The numerical approach is based on the utilization of the unstructured control volume finite element method (CVFEM) which, to the knowledge of the authors, is applied for the first time to simulate radiative heat transfer in participated media confined in 3D complex geometries. This simulation makes simultaneously the use of the merits of both the finite element method and the control volume method. Unstructured 3D triangular element grids are employed in the spatial discretization and azimuthal discretization strategy is employed in the angular discretization. The general discretization equation is presented and solved by the conditioned conjugate gradient squared method (CCGS). In order to test the efficiency of the developed method, several 3D complex geometries including a hexahedral enclosure, a 3D equilateral triangular enclosure, a 3D L-shaped enclosure and 3D elliptical enclosure are examined. The results are compared with the exact solutions or published references and the accuracy obtained in each case is shown to be highly satisfactory. Moreover, this approach required a less CPU time and iterations compared with those of even parity formulation of the discrete ordinates method.

Three‐dimensional flow simulation of resin transfer molding utilizing multilayered fiber preform

AbstractImpregnation of the multi‐layered fiber preform with injected resin was analyzed by using the control volume finite element method for three‐dimensional mold filling simulation of the resin transfer molding (RTM). Numerically predicted flow fronts were compared with experimental data to validate accuracy of the numerical results and applicability of the numerical code developed in this study. Since isothermal Newtonian flow was assumed, Darcy's law and continuity equation were used as governing equations and permeability tensors employed for each layer. Flow simulation was conducted for the two types of mold geometries, i.e., rectangular plate and hollow cylinder. It was proven by comparing numerical results with experimental data that the simulation code is accurate enough to predict the flow patterns, especially when multi‐layered preforms were placed in the cylindrical mold. It was also found that the filling time was reduced by using outer gates compared with the case of inner gates. Three‐dimensional numerical simulation provided useful information for mold filling and can be used to design an optimum mold and make the RTM process efficient. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Modeling of lifting‐device aerodynamics using the actuator surface concept

AbstractThe actuator surface (AS) concept and its implementation within a differential, Navier–Stokes control volume finite‐element method (CVFEM) are presented in this article. Inspired by vortex and actuator disk methods, the AS concept consists of using porous surfaces carrying velocity and pressure discontinuities to model the action of lifting surfaces on the flow. The underlying principles and mathematics associated with AS are first reviewed, as well as their implementation in a CVFEM. Results are presented for idealized 2D cases with analytical solutions, as well as for the 3D cases of a finite wing and an experimental wind turbine. In the case of the finite wing, wake induction is well handled by the model with accurate predictions of induced angles and drag when compared with the Prandtl lifting line model. Comparisons with volume force approaches, often used to model the action of propellers or wind turbine blades in a simplified analysis, show that the AS concept has some interesting advantages in terms of accuracy and respect of flow physics. This new approach is easy and rapid to embed in most computational fluid dynamics (CFD) methods. It is applicable to a wide range of problems involving thin lifting devices like finite wings, propellers, helicopter or wind turbine blades. Copyright © 2009 John Wiley & Sons, Ltd.

A control-volume finite-element method for three-dimensional multiphase basin modeling

In this paper we describe a 3D control-volume finite-element method to solve numerically the coupled partial differential equations (PDEs) governing geological processes involved in the evolution of sedimentary basins. These processes include sediment deposition and deformation, hydrocarbon generation, multiphase fluid flow, and heat transfer in deforming porous media. These integrated processes possess a wide range of time-scales, indicating the need for implicit methods. In addition, sedimentary basins are geometrically complex environments, requiring unstructured tetrahedral meshes to adequately represent the problem realistically without the need for an excessive number of mesh elements. Here, we also present a general formulation for problems involving back-oil, thermal, or compositional models using overall component mass concentrations, and an arbitrary Lagrangian–Eulerian (ALE) formulation to deal with salt motion conservatively. The Newton method is used to solve the sparse Jacobian systems resulting from the linearization of the coupled non-linear PDEs for multiphase flow and energy transfer. These systems are solved with the generalized minimal residual method (GMRES) method with an incomplete lower–upper (ILU) preconditioner for faster inner iteration convergence rates. We applied this model to a sedimentary basin and we describe the results for this basin.

Two-dimensional control volume modeling of the resin infiltration of a porous medium with a heterogeneous permeability tensor

Resin Transfer Molding (RTM) is a polymer composite processing technique widely used in the aeronautics and automotive sectors. This paper describes the numerical simulation of the RTM process where Darcy's law was used for the mathematical formulation of the problem. A control volume finite element method was used for the determination of pressure gradients inside the mold, and a geometric reconstruction algorithm is used for the resin flow-front determination. Permeability of the medium was considered either a constant or a two dimensional tensor. The application was validated by direct comparison with literature data and good qualitative and quantitative agreement was obtained. The finite volume method was built to be used with a two-dimensional unstructured grid, hence allowing the analysis of complex geometries. The results showed that the proposed methodology is fully capable of predicting resin flow advancement in a multi-layer (with distinct physical properties) reinforced media.

A modified rule of mixture for the vacuum-assisted resin transfer moulding process simulation

The vacuum-assisted resin transfer moulding process (VARTM) offers many advantages over the traditional resin transfer moulding such as lower tooling cost, room temperature processing. Computer simulation has become a powerful tool for liquid composite moulding process design and optimisation. In the VARTM process simulation, due to the presence of HPM and flow channels, the conventional simulation will require 3-D geometric model and mesh generation. The extensive computation load and complexity of pre-processing limit the usage of simulation in the process design and optimisation. In this paper, a two-step method for improving the efficiency of VARTM process simulation is presented. First, a design of experiment approach was coupled with 2-D CVFEM (control volume finite element method) simulation to calculate the equivalent permeability and porosity for various process variable combinations. Based on the data from DOE, a modified rule of mixture for calculating the equivalent permeability and porosity was developed, with which the mould filling can be simulated in 2-D. Second, the algorithm for the through-thickness flow front construction was developed. The presented method was validated by comparing the result against that from the 3-D simulation. It shows that the accuracy is within 5% while the computation time saving is over 99%.

Implementation of the Stress Jump Condition in a Control-Volume Finite-Element Method for the Simulation of Laminar Coupled Flows in Adjacent Open and Porous Domains

Laminar coupled flow of a Newtonian fluid in adjacent open and fluid-saturated porous domains is modeled using the continuity and the Navier-Stokes equations in the open domain, and a continuity equation and the Brinkman-Forchheimer equations in the porous domain. At the interface, a jump condition is used with two adjustable coefficients: one related to an excess viscous stress and the other to an excess inertial stress. This mathematical model is solved using a control-volume finite-element method and a novel procedure for incorporating the interfacial stress jump condition. The solutions of two illustrative example problems are also presented and discussed.

Optimal discontinuous finite element methods for the Boltzmann transport equation with arbitrary discretisation in angle

This paper describes the development of two optimal discontinuous finite element (FE) Riemann methods and their application to the one-speed Boltzmann transport equation in the steady-state. The proposed methods optimise the amount of dissipation applied in the streamline direction. This dissipation is applied within an element using a novel Riemann FE method, which is based on an analogy between control volume discretisation methods and finite element methods when integration by parts is applied to the transport terms. In one-dimension the optimal finite element solutions match the analytical solution exactly at each outlet node. Both schemes couple elements in space via a Riemann approach. The first of the two schemes is a Petrov–Galerkin (PG) method which introduces dissipation via the equation residual. The second scheme uses a streamline diffusion stabilisation term in the discretisation. These two methods provide a discontinuous Petrov–Galerkin (DPG) scheme that can stabilise an element across the full range of radiation regimes, obtaining robust solutions with suppressed oscillation. Three basis functions in angle of particle travel have been implemented in an optimal DPG Riemann solver, which include the PN (spherical harmonic), SN (discrete ordinate) and LWN (linear octahedral wavelet) angular expansions. These methods are applied to a series of demanding two-dimensional radiation transport problems.

Analysis for optimal gate design of thin-walled injection molding

Abstract The 3C (Computer, Communication and Consumer) product has the properties of being light, thin, short and small. In this study, numerical simulations of three-dimensional injection molding are used for thin-walled product. The governing differential equations are discredited by using control volume finite element method. This research points out the processing phenomenon of electronic dictionary battery covers in thin-walled injection molding. This research emphasizes the gate design of thin-walled injection molding for PC+ABS materials. The results show that the gate for single point of two sides is suitable on thin-walled injection molding by numerical simulation. The results also show that the processing is very well for thin-walled injection molding by numerical simulation.

A FLUX-BASED CONSERVATION APPROACH FOR ACOUSTIC PROBLEMS

In this paper a Control Volume Finite Element Method for harmonic acoustic problems is presented. A dispersion analysis for control volume constructed on Q1 finite elements is compared to Galerkin FEM. The spatial convergence is also given in an eigenfrequency determination process for a cavity. The application for exterior acoustic problems is also studied by dividing the whole field into inner and outer domains using a fictitious boundary. A control volume formulation is used to compute the inner field of the truncated problem, and several approaches are combined to describe the outer field behavior on the outside of the fictitious boundary. The task of coupling is easily implemented through the balance of local flux through polygonal volumes. A two-dimensional configuration with a circular interface demonstrates the validity of this approach.

Numerical model for the prediction of dilute, three‐dimensional, turbulent fluid–particle flows, using a Lagrangian approach for particle tracking and a CVFEM for the carrier phase

AbstractA numerical model for dilute, three‐dimensional, turbulent, incompressible fluid–solid particle flows and its application to a demonstration problem are presented. An Eulerian description is used to model the flow of the fluid (carrier) phase, and the governing equations are solved using a control‐volume finite element method (CVFEM). The motion of the solid (particulate) phase is simulated using a Lagrangian approach. An efficient algorithm is proposed for locating the particles in the finite element mesh. In the demonstration problem, which involves a particle‐laden axisymmetric jet, a modified k–ε turbulence model is used to characterize the velocity and length scales of the turbulent flow of the fluid phase. The effect of turbulence on the particle trajectories is accounted for through a stochastic model. The effect of the particles on the fluid time–mean velocity and turbulence (two‐way coupling) is also addressed. Comparisons between predictions and available experimental data for the demonstration problem are presented. Satisfactory agreement is obtained. Copyright © 2008 John Wiley & Sons, Ltd.

Numerical Simulation of Passive Control on Vortex Shedding Behind Square Cylinder Using Splitter Plate

Passive control on vortex shedding behind a square cylinder in a laminar channel flow using a splitter plate is conducted numerically. Computations are carried out for different Reynolds numbers ranging from 110 to 200 at a fixed blockage ratio β=h/H = 1/4. The governing equations are solved with a control volume finite element method adapted to a staggered grid. In examining the instantaneous flow fields, it is found that the critical length of the splitter plate Lc, characterizing the disappearance of vortex shedding, can be correlated by a linear relationship: Lc = 0.0373 Re–3.4373. The effect of the splitter plate length and its location in the wake region on the Strouhal number, and the drag and lift coefficients are also analyzed.

The study of injection/compression liquid composite molding

Abstract Liquid composite molding (LCM) is one of the most important processes to produce reinforced plastics. To reduce the injection pressure and improve the part quality, injection/compression liquid composite molding (I/CLCM) was applied in this study. The research was conducted through modeling, numerical simulation, and experimental analysis. Control-volume finite-element method (CVFEM) has been widely used in LCM simulation. This research applied this numerical approach to simulate the I/CLCM processes. The simulation results were verified through experimental analysis. An analytical solution was derived to calculate the required injection pressure and filling time. A three-point bending test was also conducted to compare the mechanical properties of LCM parts and I/CLCM parts.