Characteristic-based Split Research Articles

A numerical investigation of fluid flow over a rotating cylinder with cross flow oscillation

This paper studies a two-dimensional incompressible viscous flow past a rotating cylinder with cross flow oscillation using a finite element method based on the characteristic based split (CBS) algorithm to solve governing equations including full Navier–Stokes and continuity equations. Dynamic unstructured triangular grid is used employing lineal and torsional spring analogy which is coupled with the solver by an Arbitrary Lagrangian–Eulerian (ALE) formulation. After verifying the accuracy of the numerical code, simulations are conducted for the flow past a rotating cylinder with cross flow oscillation at moderate Reynolds numbers of 50, 100, and 200 considering different non-dimensional rotational speeds based on the free-stream velocity in the range 0–2.5, and various oscillating amplitudes and frequencies. Effects of the oscillation and rotation of the cylinder on the vortex shedding both in lock-on and non-lock-on regions, the mean drag and lift coefficients, and the Strouhal number are investigated in detail. It is found that similar to the fixed cylinder beyond a critical non-dimensional rotational speed the vortex shedding is highly suppressed. In addition, by increasing the rotational speed of the cylinder, the lift coefficient increases while decreasing the drag coefficient. However, in the vortex lock-on region both the lift and the drag coefficients increase significantly.

Micro‐scale synthetic‐jet actuator flow simulation with characteristic‐based‐split method

PurposeThe purpose of this paper is to present a computational study to investigate the effects of rectangular cavity design of a piezoelectrically driven micro‐synthetic‐jet actuator on generated flow.Design/methodology/approachFlow simulations were done using a compressible Navier‐Stokes solver, which is based on finite element method implementation of a characteristic‐based‐split (CBS) algorithm. The algorithm uses arbitrary Lagrangian‐Eulerian formulation, which allows to model oscillation of the synthetic jet's diaphragm in a realistic manner. Since all simulated flows are in the slip‐flow‐regime, a second order slip‐velocity boundary condition was applied along the cavity and orifice walls. Flow simulations were done for micro‐synthetic‐jet configurations with various diaphragm deflections amplitudes, cavity heights, and widths. All of the simulation results were compared with each other and evaluated in terms of the exit jet velocities, slip‐velocities on the orifice wall and instantaneous momentum fluxes at the jet exit.FindingsIt is shown that compressibility and rarefaction have important effects on the flow field generated by the micro‐synthetic‐jet actuator. The effect of the geometrical parameters of the cavity to important flow features such slip and phase lag are presented.Originality/valueThe paper reports results of a systematical study of the flow field inside a micro‐scale synthetic‐jet actuator, providing designers of such devices additional information for sizing the cavity within slip flow regime. Furthermore, it is demonstrated that the CBS, together with slip boundary conditions can be successfully used to compute such flows.

A two‐step Taylor‐characteristic‐based Galerkin method for incompressible flows and its application to flow over triangular cylinder with different incidence angles

AbstractAn alternative characteristic‐based scheme, the two‐step Taylor‐characteristic‐based Galerkin method is developed based on the introduction of multi‐step temporal Taylor series expansion up to second order along the characteristic of the momentum equation. Contrary to the classical characteristic‐based split (CBS) method, the current characteristic‐based method does not require splitting the momentum equation, and segregate the calculation of the pressure from that of the velocity by using the momentum–pressure Poisson equation method. Some benchmark problems are used to examine the effectiveness of the proposed algorithm and to compare with the original CBS method, and the results show that the proposed method has preferable accuracy with less numerical dissipation.We further applied the method to the numerical simulation of flow around equilateral triangular cylinder with different incidence angles in free stream. In this numerical investigation, the flow simulations are carried out in the low Reynolds number range. Instantaneous streamlines around the cylinder are used as a means to visualize the wake region behind, and they clearly show the flow pattern around the cylinder in time. The influence of incidence angle on flow characteristic parameters such as Strouhal number, Drag and Lift coefficients are discussed quantitatively. Copyright © 2009 John Wiley & Sons, Ltd.

Artificial Compressibility-Based CBS Scheme for the Solution of the Generalized Porous Medium Model

In this work, the authors present an artificial compressibility (AC) version of the characteristic-based split (CBS) algorithm for the numerical solution of flow through a fluid-saturated porous medium. In this study, a fully matrix-inversion-free version of the CBS algorithm is used for the first time to solve the generalized porous medium flow equations for forced-, free-, and mixed-convection problems. The efficiency, the accuracy, and the steady-state convergence of the AC-CBS algorithm are verified through comparison with numerical and analytical solutions available in the literature. The advantages of the proposed AC-CBS scheme include easy parallelization and implementation procedure.

An investigation of pulsatile flow in a model cavo‐pulmonary vascular system

AbstractThe complexities in the flow pattern in a cavo‐pulmonary vascular system—after application of the Fontan procedure in the vicinity of the superior vena cava, inferior vena cava, and the confluence at the T‐junction—are analysed. A characteristic‐based split (CBS) finite element scheme involving the artificial compressibility approach is employed to compute the resulting flow. Benchmarking of the CBS scheme is carried out using standard problems and with the flow features observed in an experimental model with the help of a dye visualization technique in model scale. The transient flow variations in a total cavo‐pulmonary connection (TCPC) under pulsatile conditions are investigated and compared with flow visualization studies. In addition to such qualitative flow investigations, quantitative analysis of energy loss and haemodynamic stresses have also been performed. The comparisons show good agreement between the numerical and experimental flow patterns. The numerically predicted shear stress values indicate that the pulsatile flow condition is likely to be more severe than steady flow, with regard to the long‐term health of the surgically corrected TCPC. Copyright © 2008 John Wiley & Sons, Ltd.

Numerical simulation of mass and energy transport phenomena in solid oxide fuel cells

Solid Oxide Fuel Cells (SOFCs) represent a very promising technology for near future energy conversion thanks to a number of advantages, including the possibility of using different fuels. In this paper, a detailed numerical model, based on a general mathematical description and on a finite element Characteristic based Split (CBS) algorithm code is employed to simulate mass and energy transport phenomena in SOFCs. The model predicts the thermodynamic quantity of interest in the fuel cell. Full details of the numerical solution obtained are presented both in terms of heat and mass transfer in the cell and in terms of electro-chemical reactions that occur in the system considered. The results obtained with the present algorithm is compared with the experimental data available in the literature for validation, showing an excellent agreement.

An artificial‐dissipation‐based fractional step scheme for upper‐convected Maxwell (UCM) fluid flow past a circular cylinder

AbstractThe fully explicit characteristic‐based split (CBS) scheme is employed to solve viscoelastic flow problems. The upper‐convected Maxwell (UCM) model is employed in the present study. In addition to allowing equal‐order interpolations for pressure and velocity, the proposed method along with an appropriate artificial damping scheme is able to produce stable solutions for different Deborah numbers (De). The higher‐order time terms introduced by the simplified characteristic Galerkin approximation are sufficient to obtain stable solution at very low De, but an additional damping is essential to maintain positive definitiveness of the conformation tensor at higher De. We demonstrate the need for an additional damping by analysing the basic forward time central space scheme applied to the constitutive equations. A second‐order artificial damping is employed to counteract the negative dissipation introduced by the explicit time discretization. The example studied in this paper is the widely used and difficult problem of flow past a circular cylinder. The results presented show that the velocity and extra stresses converge easily to a steady state at lower De values. At higher De values, the convergence to steady state is slow due to the incremental way in which the artificial damping is added. Copyright © 2008 John Wiley & Sons, Ltd.

Finite element modelling of electro‐osmotic flows on unstructured meshes

PurposeThis paper seeks to numerically model electro‐osmotic flow (EOF) through microchannels using a finite element‐based unstructured mesh solution methodology.Design/methodology/approachThe finite element method (FEM) combined with the characteristic‐based split (CBS) algorithm is used to solve the coupled Navier‐Stokes equations in order to simulate EOFs. The Laplace and Poisson‐Boltzmann equations are solved explicitly a priori to the solution of the fluid dynamic equations. The external electric field and internal potential values are then used to construct the source terms of the fluid dynamics equations.FindingsProposed methodology works excellently on unstructured meshes for both two‐ and three‐dimensional flow problems. The results obtained for benchmark channel flow problems show an excellent agreement with analytical and experimental data.Originality/valueThe idea of using the FEM and the CBS algorithm to solve the governing equations of EOFs is proposed. This particular method of solving these equations is unprecedented. In addition to benchmark examples, a problem of practical importance is also solved in this paper.

The locally conservative Galerkin (LCG) method for solving the incompressible Navier–Stokes equations

AbstractIn this paper, the locally conservative Galerkin (LCG) method (Numer. Heat Transfer B Fundam. 2004; 46:357–370; Int. J. Numer. Methods Eng. 2007) has been extended to solve the incompressible Navier–Stokes equations. A new correction term is also incorporated to make the formulation to give identical results to that of the continuous Galerkin (CG) method. In addition to ensuring element‐by‐element conservation, the method also allows solution of the governing equations over individual elements, independent of the neighbouring elements. This is achieved within the CG framework by breaking the domain into elemental sub‐domains. Although this allows discontinuous trial function field, we have carried out the formulation using the continuous trial function space as the basis. Thus, the changes in the existing CFD codes are kept to a minimum. The edge fluxes, establishing the continuity between neighbouring elements, are calculated via a post‐processing step during the time‐stepping operation. Therefore, the employed formulation needs to be carried out using either a time‐stepping or an equivalent iterative scheme that allows post‐processing of fluxes. The time‐stepping algorithm employed in this paper is based on the characteristic‐based split (CBS) scheme. Both steady‐ and unsteady‐state examples presented show that the element‐by‐element formulation employed is accurate and robust. Copyright © 2007 John Wiley & Sons, Ltd.

On the use of characteristic‐based split meshfree method for solving flow problems

AbstractThis study presents characteristic‐based split (CBS) algorithm in the meshfree context. This algorithm is the extension of general CBS method which was initially introduced in finite element framework. In this work, the general equations of flow have been represented in the meshfree context. A new finite element and MFree code is developed for solving flow problems. This computational code is capable of solving both time‐dependent and steady‐state flow problems. Numerical simulation of some known benchmark flow problems has been studied. Computational results of MFree method have been compared to those of finite element method. The results obtained have been verified by known numerical, analytical and experimental data in the literature. A number of shape functions are used for field variable interpolation. The performance of each interpolation method is discussed. It is concluded that the MFree method is more accurate than FEM if the same numbers of nodes are used for each solver. Meshfree CBS algorithm is completely stable even at high Reynolds numbers. Copyright © 2007 John Wiley & Sons, Ltd.

The characteristic‐based split (CBS) scheme for viscoelastic flow past a circular cylinder

AbstractA fully explicit, characteristic‐based split (CBS) method for viscoelastic flow past a circular cylinder, placed in a rectangular channel, is presented. The pressure equation in its explicit form is employed via an artificial compressibility parameter. The constitutive equations used here are based on the Oldroyd‐B model. No loss of convergence to steady state was observed in any of the results presented in this paper. Comparison of the present results with other available numerical data shows that the CBS algorithm is in excellent agreement with them at lower Deborah numbers. However, at higher Deborah numbers, the present results differ from other numerical solutions. This is due to the fact that the positive definitiveness of the conformation matrix is lost between a Deborah number of 0.6 and 0.7. However, the positive definitiveness is retained when an artificial diffusion is added to the discrete constitutive equations at higher Deborah numbers. It appears that the fractional solution stages used in the CBS scheme and the higher‐order time step‐based convection stabilization clearly reduce the instability at higher Deborah numbers. The Deborah number limit reached in the present work is three without artificial dissipation and two with artificial dissipation. Copyright © 2007 John Wiley & Sons, Ltd.

An ALE based iterative CBS algorithm for non-isothermal non-Newtonian flow with adaptive coupled finite element and meshfree method

This paper presents a generalized scheme of the fractional step algorithm using Characteristic Based Split (CBS) in ALE framework for the numerical simulation of incompressible non-isothermal non-Newtonian fluid flows and applies it, combined with the adaptive coupled finite element and meshfree method for spatial discretizations, to the polymer injection molding process. Based on the idea to discretize the material time derivative instead of the spatial time derivative, the characteristic Galerkin method is derived in a more general way and is used to discretize the non-Newtonian momentum and the energy conservation equations. An iterative procedure which makes the conservation equations satisfied in an implicit sense is introduced into the scheme to enhance its stability in the time domain. Numerical experiments with the power-law fluid model demonstrate and validate the performance and the capability of the proposed scheme.

Laminar and turbulent flow calculations through a model human upper airway using unstructured meshes

AbstractIn this paper, numerical investigation of airflow through a human upper airway is presented using an unstructured‐based characteristic‐based split (CBS) scheme. The CBS scheme used in the present study employs a fully explicit matrix‐free solution procedure along with artificial compressibility. A one equation Spalrat–Allmaras (SA) turbulence model is employed to study low and moderate Reynolds number flows. A detailed discussion of the qualitative and quantitative results is presented. The results show a strong influence of the Reynolds number on the flow pattern and quantities of interest, pressure drop and wall shear stress. It is also apparent that SA model can be employed on unstructured meshes to predict the steady flow with good accuracy. Thus, the novelties of the present paper are: use of the unstructured mesh‐based solution algorithm and the successful application of the SA model to a typical human upper airway. Copyright © 2006 John Wiley & Sons, Ltd.

Editorial

This special issue on the ‘Characteristic-Based Split (CBS)’ scheme was conceived from the experience of different people working in different areas of computational mechanics. The objective in the main is the presentation of the CBS scheme in its very general form to accommodate general engineering problems of interest to the engineering community. Thus, we have included papers on general fluid dynamics, shallow-water flows, solid dynamics, porous media and heat transfer. A total of eight papers have been included into this special issue. The first paper by Nithiarasu et al. describes the CBS scheme in detail with an explanation on the origin of the characteristic-based procedures and their extension to solve compressible and incompressible flows. This paper also describes the merger of the characteristic-based procedure with a fractional step algorithm to develop the CBS procedure. Several examples are also presented to demonstrate the robustness and accuracy of this unified approach to compressible and incompressible flows. Though only fluid dynamics examples are presented in the first paper, the suitability of the method to solve solid dynamic problems is demonstrated in the second paper by Rojek et al. This paper again demonstrates the novelty of the proposed approach. The presented idea immediately forms the basis for coupled fluid-solid problems using a single approach with different constitutive equations. The third paper is presented by Ortiz et al. which describe the CBS approach to shallow-water problems. Once again the versatility of the method is demonstrated for an entirely different kind of incompressible flow equations. The shallow-water equations presented in this paper resembles the inviscid compressible flows. Thus, it is obvious that the same methodology used to solve the compressible flows can be extended to the shallow-water equations. The next paper is a recent work on porous media problems using the CBS approach. The authors, Salomoni and Schrefler, have demonstrated the use of the CBS scheme to a complicated porous medium problem. Once again this proves that the application of the CBS scheme is not limited to fluid dynamics problems. The next three papers by Massarotti et al., Morandi Cecchi and Venturin and Kulkarni et al. are the applications of the CBS scheme to different engineering problems. In Massarotti et al., the method has been extensively used to steady and unsteady incompressible flows with heat transfer to make a general assessment of the method in its fully explicit and semi-implicit forms. This paper gives an in-depth comparison between the two variations. In Morandi Cecchi and Venturin, the method is applied to solve a practical shallow-water problem of the Venice Lagoon. The third paper in the application series by Kulkarni et al. deals with a practical application of under-fill simulation process in electronic packaging. All these three papers clearly demonstrate the flexibility of the CBS method for different applications of practical importance. This special issue is concluded by a paper on a comparative study between the CBS scheme and other recent methods. This last paper is presented by Codina et al. and compares the CBS method against the family of recent subgrid scale (SGS) methods. Finally, we would like to thank Prof. O. C. Zienkiewicz for supporting this special issue and writing a foreword. We are also grateful to Professor R. W. Lewis, editor of the International Journal for Numerical Methods in Engineering for permitting us to produce this special issue. We hope this special issue will be of great use to the readers to learn about the CBS scheme and its development over the last 10 years.

Explicit and semi‐implicit CBS procedures for incompressible viscous flows

AbstractThis paper presents a numerical comparison of two different numerical procedures based on the characteristic‐based split (CBS) algorithm for the solution of incompressible flows. The first procedure is based on the original semi‐implicit version of the CBS, introduced in the early days of the scheme development. The second was proposed more recently in order to have a fully explicit version of the scheme, and is based on the introduction of an artificial compressibility type of formulation. The interest in fully explicit schemes has increased because of the easy and efficient parallelization. The main differences between the two versions of the schemes are highlighted in this work, and a numerical comparison is presented on the basis of several benchmark solutions. Both steady and unsteady flows are considered. With the explicit version of the scheme a dual time stepping procedure is needed to recover unsteady solutions. Copyright © 2006 John Wiley & Sons, Ltd.

Numerical simulation of underfill encapsulation process based on characteritsic split method

AbstractElectronic packaging protects the integrated circuit chip from environmental and mechanical damages. Underfilling encapsulation is an electronic packaging technology used to reinforce the solder joints between chip and the substrate. For better mould design and optimization of the process, flow analysis during the encapsulation process is the first necessary step. This paper focuses on the study of fluid flow in underfilling encapsulation process as used in electronics industry. A two‐dimensional numerical model was developed to simulate the mould filling behaviour in underfilling encapsulation process. The analysis was carried out by writing down the conservation equations for mass, momentum and energy for a two‐dimensional flow in an underfilling area. The governing equations are solved using characteristic based split (CBS) method in conjunction with finite element method to get the velocity and pressure fields. The velocity field was used in pseudo‐concentration approach to track the flow front. Pseudo‐concentration is based on the volume of fluid (VOF) technique and was used to track fluid front for each time step.A particular value of the pseudo‐concentration variable was chosen to represent the free fluid surface which demarcates mould compound region and air region. Simulation has been carried out for a particular geometry of a flip‐chip package. The results obtained are in good agreement with the available numerical and experimental values and thus demonstrate the application of the present numerical model for practical underfilling encapsulation simulations. Copyright © 2006 John Wiley & Sons, Ltd.

The Characteristic‐Based Split (CBS) scheme—a unified approach to fluid dynamics

AbstractThis paper presents a comprehensive overview of the characteristic‐based methods and Characteristic‐Based Split (CBS) scheme. The practical difficulties of employing the original characteristic schemes are discussed. The important features of the CBS scheme are brought out by studying several problems of compressible and incompressible flows. All special consideration necessary for solving these problems are thoroughly discussed. The CBS scheme is presented in such a way that any interested researcher should be able to develop a code using the information provided. Several invicid and viscous flow examples are also provided to demonstrate the unified CBS approach. For sample two‐dimensional codes, input files and instructions, the readers are referred to ‘www.nithiarasu.co.uk’ Copyright © 2006 John Wiley & Sons, Ltd.

Analysis of fluid flow through micro‐fluidic devices using characteristic‐based‐split procedure

AbstractGas flow in micro‐electro‐mechanical systems can be considered as rarefied since the ratio of free molecular path length to the characteristic length of the device is high. It is possible to analyse these flows using a conventional Navier–Stokes solver with modified boundary conditions to account for temperature‐jump and slip‐velocity on solid walls. In this study, characteristic‐based‐split (CBS) algorithm is modified to account for slip‐velocity and temperature‐jump boundary conditions in order to perform compressible flow analysis for a micro sized geometry. The CBS algorithm is a split procedure which yields a unified solution method valid for both compressible and incompressible flows. To verify the modified CBS solver, straight micro channel and micro step duct geometries are selected as test cases. To reduce the size of the implicit part of the algorithm, pseudo‐quadratic velocity/linear pressure elements (pP2P1) are employed. The results obtained using CBS algorithm, are compared with other analytical and computational results available in the literature. It is shown that this implementation of the CBS algorithm is applicable and effective for micro gas flows. It is also shown that, increasing Knudsen number results in increased temperature‐jump and slip‐velocity. This effect, however, is limited, especially for high Mach number flows. Copyright © 2006 John Wiley & Sons, Ltd.

Characteristic‐based split (CBS) algorithm finite element modelling for shallow waters in the Venice lagoon

AbstractIn this paper, the characteristic‐based split (CBS) algorithm is presented to solve water motion problem due to tides in the Venice lagoon. The basic equations are the well‐known vertically integrated shallow‐water equations expressed in terms of total water depth and horizontal velocities. The approximation of any additional scalar variables, such as temperature, concentration or pollutant dispersion from the appropriate advection–diffusion governing equations is also outlined. Numerical results illustrate the performance of the proposed algorithm on both advection–diffusion and shallow‐water problems. Copyright © 2006 John Wiley & Sons, Ltd.

Numerical comparison of CBS and SGS as stabilization techniques for the incompressible Navier–Stokes equations

AbstractIn this work, we present numerical comparisons of some stabilization methods for the incompressible Navier–Stokes. The first is the characteristic‐based split (CBS). It combines the characteristic Galerkin method to deal with convection‐dominated flows with a classical splitting technique, which in some cases allows us to use equal velocity–pressure interpolations. The other two approaches are particular cases of the subgrid scale (SGS) method. The first, obtained after an algebraic approximation of the subgrid scales, is very similar to the popular Galerkin/least‐squares (GLS) method, whereas in the second, the subscales are assumed to be orthogonal to the finite element space. It is shown that all these formulations display similar stabilization mechanisms, provided the stabilization parameter of the SGS methods is identified with the time step of the CBS approach. This paper provides the numerical experiments for the comparison of formulations made by Codina and Zienkiewicz in a previous article. Copyright © 2006 John Wiley & Sons, Ltd.