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Unsteady
Terms modified by Unsteady Selected AbstractsNumerical study of an inviscid incompressible flow through a channel of finite lengthINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009Vasily N. Govorukhin Abstract A two-dimensional inviscid incompressible flow in a rectilinear channel of finite length is studied numerically. Both the normal velocity and the vorticity are given at the inlet, and only the normal velocity is specified at the outlet. The flow is described in terms of the stream function and vorticity. To solve the unsteady problem numerically, we propose a version of the vortex particle method. The vorticity field is approximated using its values at a set of fluid particles. A pseudo-symplectic integrator is employed to solve the system of ordinary differential equations governing the motion of fluid particles. The stream function is computed using the Galerkin method. Unsteady flows developing from an initial perturbation in the form of an elliptical patch of vorticity are calculated for various values of the volume flux of fluid through the channel. It is shown that if the flux of fluid is large, the initial vortex patch is washed out of the channel, and when the flux is reduced, the initial perturbation evolves to a steady flow with stagnation regions. Copyright © 2008 John Wiley & Sons, Ltd. [source] New supplying evaporation precursor method with CVDHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 5 2009Motohiro Oshima Abstract We propose a novel system of chemical vapor deposition (CVD), i.e., flash boiling spray CVD (SF-CVD) to eliminate several kinds of problems, such as the decomposition of precursors in the supply line and evaporator. In this method, liquid precursors are supplied directly to the vacuum chamber through an injector, just like fuel for an automobile engine, without any vaporizers, so as to induce an unsteady and intermittent flash boiling spray in the chamber. However, it is necessary to keep the lowest ambient pressure possible because the saturated vapor pressure of the precursors is very low. Thus, this is very useful for modifying the saturated vapor pressure of the precursors. A technique of lowering the vaporization pressure is proposed by mixing a more saturated vapor-pressure organic solvent with a precursor. To determine the principles underlying FS-CVD, we first formed SiO2 film on the Si substrate. A mixed solution of tetraethylorthosilicate (TEOS) and n-pentane was used as the mixing solution. The film thickness distribution of SiO2 film on a 100-mm-diameter Si wafer was ±4% using this method. Furthermore, this method enabled us to control film with various thicknesses by optimizing the injection duration, cycle, and injection cycle per second. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20235 [source] FOIST: Fluid,object interaction subcomputation techniqueINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2009V. Udoewa Abstract Our target is to develop computational techniques for studying aerodynamic interactions between multiple objects. The computational challenge is to predict the dynamic behavior and path of the object, so that separation (the process of objects relatively falling or moving away from each other) is safe and effective. This is a very complex problem because it has an unsteady, 3D nature and requires the solution of complex equations that govern the fluid dynamics (FD) of the object and the aircraft together, with their relative positions changing in time. Large-scale 3D FD simulations require a high computational cost. Not only must one solve the time-dependent Navier,Stokes equations governing the fluid flow, but also one must handle the equations of motion of the object as well as the treatment of the moving domain usually treated as a type of pseudo-solid. These costs include mesh update methods, distortion-limiting techniques, and remeshing and projection tactics. To save computational costs, point force calculations have been performed in the past. This paper presents a hybrid between full mesh-moving simulations and the point force calculation. This mesh-moving alternative is called FOIST: fluid,object subcomputation interaction technique. Copyright © 2009 John Wiley & Sons, Ltd. [source] Parallel simulation of unsteady hovering rotor wakesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2006C. B. Allen Abstract Numerical simulation using low diffusion schemes, for example free-vortex or vorticity transport methods, and theoretical stability analyses have shown the wakes of rotors in hover to be unsteady. This has also been observed in experiments, although the instabilities are not always repeatable. Hovering rotor wake stability is considered here using a finite-volume compressible CFD code. An implicit unsteady, multiblock, multigrid, upwind solver, and structured multiblock grid generator are presented, and applied to lifting rotors in hover. To allow the use of very fine meshes and, hence, better representation of the flow physics, a parallel version of the code has been developed, and parallel performance using upto 1024 CPUs is presented. A four-bladed rotor is considered, and it is demonstrated that once the grid density is sufficient to capture enough turns of the tip vortices, hover exhibits oscillatory behaviour of the wake, even using a steady formulation. An unsteady simulation is then performed, and also shows an unsteady wake. Detailed analysis of the time-accurate wake history shows that three dominant unsteady modes are captured, for this four-bladed case, with frequencies of one, four, and eight times the rotational frequency. A comparison with theoretical stability analysis is also presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] Steady and unsteady incompressible flow in a double driven cavity using the artificial compressibility (AC)-based characteristic-based split (CBS) schemeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005P. Nithiarasu Abstract In this paper, the explicit characteristic-based split (CBS) scheme has been employed to solve both steady and unsteady flows inside a non-rectangular double driven cavity. This problem is recently suggested as a benchmark problem for incompressible flows. Both unstructured and structured meshes have been employed in the present study to make sure that the predicted results are as close to reality as possible. The results obtained show the existence of steady state at lower Reynolds numbers (,1000) and transient states at higher Reynolds numbers. The flow approaches a turbulent state as the Reynolds number is increased to 10 000. Copyright © 2005 John Wiley & Sons, Ltd. [source] Adaptive embedded unstructured grid methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004Rainald Löhner Abstract A simple embedded domain method for node-based unstructured grid solvers is presented. The key modification of the original, edge-based solver is to remove all geometry-parameters (essentially the normals) belonging to edges cut by embedded surface faces. Several techniques to improve the treatment of boundary points close to the immersed surfaces are explored. Alternatively, higher-order boundary conditions are achieved by duplicating crossed edges and their endpoints. Adaptive mesh refinement based on proximity to or the curvature of the embedded CSD surfaces is used to enhance the accuracy of the solution. User-defined or automatic deactivation for the regions inside immersed solid bodies is employed to avoid unnecessary work. Several examples are included that show the viability of this approach for inviscid and viscous, compressible and incompressible, steady and unsteady flows, as well as coupled fluid,structure problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] CFD analysis of an oscillating wing at various reduced frequenciesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2009Farooq Umar Abstract The effect of various reduced frequencies has been examined for an oscillating aspect ratio 10 NACA 0015 wing. An unsteady, compressible three-dimensional (3D) Navier,Stokes code based on Beam and Warming algorithm with the Baldwin,Lomax turbulence model has been used. The code is validated for the study against published experimental data. The 3D unsteady flow field is simulated for reduced frequency values of 0.1, 0.2 and 0.3 for a fixed mean angle of attack position and fixed amplitude. The type of motion is sinusoidal harmonic. The force coefficients, pressure distributions and flow visualization show that at the given conditions the flow remains attached to the wing surface even at high angles of attack with no clear separation or typical light-to-deep category of dynamic stall. Increased magnitude of hysteresis and higher gradients are seen at higher reduced frequencies. The 3D effects are even found at midspan locations. In addition, the rate of decrease in lift near the wing tips compared with the wing root is not much like in the static cases. Copyright © 2008 John Wiley & Sons, Ltd. [source] Application of local DFD method to simulate unsteady flows around an oscillating circular cylinderINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2008Y. L. Wu Abstract In this paper, the recently proposed local domain-free discretization (DFD) method is applied to simulate incompressible flows around an oscillating circular cylinder. It is found that it is very easy for the local DFD method to handle such moving boundary flow problems. This is because it does not need to move the mesh, which is indeed needed in traditional methods. Numerical experiments show that the present numerical results agree very well with the available data in the literature, and that the local DFD method is an effective tool for the computation of moving boundary flow problems. Copyright © 2008 John Wiley & Sons, Ltd. [source] A hybrid immersed boundary and material point method for simulating 3D fluid,structure interaction problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008Anvar Gilmanov Abstract A numerical method is developed for solving the 3D, unsteady, incompressible Navier,Stokes equations in curvilinear coordinates containing immersed boundaries (IBs) of arbitrary geometrical complexity moving and deforming under forces acting on the body. Since simulations of flow in complex geometries with deformable surfaces require special treatment, the present approach combines a hybrid immersed boundary method (HIBM) for handling complex moving boundaries and a material point method (MPM) for resolving structural stresses and movement. This combined HIBM & MPM approach is presented as an effective approach for solving fluid,structure interaction (FSI) problems. In the HIBM, a curvilinear grid is defined and the variable values at grid points adjacent to a boundary are forced or interpolated to satisfy the boundary conditions. The MPM is used for solving the equations of solid structure and communicates with the fluid through appropriate interface-boundary conditions. The governing flow equations are discretized on a non-staggered grid layout using second-order accurate finite-difference formulas. The discrete equations are integrated in time via a second-order accurate dual time stepping, artificial compressibility scheme. Unstructured, triangular meshes are employed to discretize the complex surface of the IBs. The nodes of the surface mesh constitute a set of Lagrangian control points used for tracking the motion of the flexible body. The equations of the solid body are integrated in time via the MPM. At every instant in time, the influence of the body on the flow is accounted for by applying boundary conditions at stationary curvilinear grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface. The influence of the fluid on the body is defined through pressure and shear stresses acting on the surface of the body. The HIBM & MPM approach is validated for FSI problems by solving for a falling rigid and flexible sphere in a fluid-filled channel. The behavior of a capsule in a shear flow was also examined. Agreement with the published results is excellent. Copyright © 2007 John Wiley & Sons, Ltd. [source] Developing implicit pressure-weighted upwinding scheme to calculate steady and unsteady flows on unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2008M. Darbandi Abstract The finite-volume methods normally utilize either simple or complicated mathematical expressions to interpolate the fluxes at the cell faces of their unstructured volumes. Alternatively, we benefit from the advantages of both finite-volume and finite-element methods and estimate the advection terms on the cell faces using an inclusive pressure-weighted upwinding scheme extended on unstructured grids. The present pressure-based method treats the steady and unsteady flows on a collocated grid arrangement. However, to avoid a non-physical spurious pressure field pattern, two mass flux per volume expressions are derived at the cell interfaces. The dual advantages of using an unstructured-based discretization and a pressure-weighted upwinding scheme result in obtaining high accurate solutions with noticeable progress in the performance of the primitive method extended on the structured grids. The accuracy and performance of the extended formulations are demonstrated by solving different standard and benchmark problems. The results show that there are excellent agreements with both benchmark and analytical solutions as well as experimental data. Copyright © 2007 John Wiley & Sons, Ltd. [source] Parallel solution of lifting rotors in hover and forward flightINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2007C. B. Allen Abstract An implicit unsteady, multiblock, multigrid, upwind solver including mesh deformation capability, and structured multiblock grid generator, are presented and applied to lifting rotors in both hover and forward flight. To allow the use of very fine meshes and, hence, better representation of the flow physics, a parallel version of the code has been developed. It is demonstrated that once the grid density is sufficient to capture enough turns of the tip vortices, hover exhibits oscillatory behaviour of the wake, even using a steady formulation. An unsteady simulation is then presented, and detailed analysis of the time-accurate wake history is performed and compared to theoretical predictions. Forward flight simulations are also presented and, again, grid density effects on the wake formation investigated. Parallel performance of the code using up to 1024 CPU's is also presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] Tracking accuracy of a semi-Lagrangian method for advection,dispersion modelling in riversINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2007S. Néelz Abstract There is an increasing need to improve the computational efficiency of river water quality models because: (1) Monte-Carlo-type multi-simulation methods, that return solutions with statistical distributions or confidence intervals, are becoming the norm, and (2) the systems modelled are increasingly large and complex. So far, most models are based on Eulerian numerical schemes for advection, but these do not meet the requirement of efficiency, being restricted to Courant numbers below unity. The alternative of using semi-Lagrangian methods, consisting of modelling advection by the method of characteristics, is free from any inherent Courant number restriction. However, it is subject to errors of tracking that result in potential phase errors in the solutions. The aim of this article is primarily to understand and estimate these tracking errors, assuming the use of a cell-based backward method of characteristics, and considering conditions that would prevail in practical applications in rivers. This is achieved separately for non-uniform flows and unsteady flows, either via theoretical considerations or using numerical experiments. The main conclusion is that, tracking errors are expected to be negligible in practical applications in both unsteady flows and non-uniform flows. Also, a very significant computational time saving compared to Eulerian schemes is achievable. Copyright © 2006 John Wiley & Sons, Ltd. [source] Comparative study of the continuous phase flow in a cyclone separator using different turbulence models,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2005H. Shalaby Abstract Numerical calculations were carried out at the apex cone and various axial positions of a gas cyclone separator for industrial applications. Two different NS-solvers (a commercial one (CFX 4.4 ANSYS GmbH, Munich, Germany, CFX Solver Documentation, 1998), and a research code (Post-doctoral Thesis, Technical University of Chemnitz, Germany, September, 2002)) based on a pressure correction algorithm of the SIMPLE method have been applied to predict the flow behaviour. The flow was assumed as unsteady, incompressible and isothermal. A k,, turbulence model has been applied first using the commercial code to investigate the gas flow. Due to the nature of cyclone flows, which exhibit highly curved streamlines and anisotropic turbulence, advanced turbulence models such as Reynolds stress model (RSM) and large eddy simulation (LES) have been used as well. The RSM simulation was performed using the commercial package activating the Launder et al.'s (J. Fluid. Mech. 1975; 68(3):537,566) approach, while for the LES calculations the research code has been applied utilizing the Smagorinsky model. It was found that the k,, model cannot predict flow phenomena inside the cyclone properly due to the strong curvature of the streamlines. The RSM results are comparable with LES results in the area of the apex cone plane. However, the application of the LES reveals qualitative agreement with the experimental data, but requires higher computer capacity and longer running times than RSM. This paper is organized into five sections. The first section consists of an introduction and a summary of previous work. Section 2 deals with turbulence modelling including the governing equations and the three turbulence models used. In Section 3, computational parameters are discussed such as computational grids, boundary conditions and the solution algorithm with respect to the use of MISTRAL/PartFlow-3D. In Section 4, prediction profiles of the gas flow at axial and apex cone positions are presented and discussed. Section 5 summarizes and concludes the paper. Copyright © 2005 John Wiley & Sons, Ltd. [source] Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfacesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2005Anton Smolianski Abstract The present work is devoted to the study on unsteady flows of two immiscible viscous fluids separated by free moving interface. Our goal is to elaborate a unified strategy for numerical modelling of two-fluid interfacial flows, having in mind possible interface topology changes (like merger or break-up) and realistically wide ranges for physical parameters of the problem. The proposed computational approach essentially relies on three basic components: the finite element method for spatial approximation, the operator-splitting for temporal discretization and the level-set method for interface representation. We show that the finite element implementation of the level-set approach brings some additional benefits as compared to the standard, finite difference level-set realizations. In particular, the use of finite elements permits to localize the interface precisely, without introducing any artificial parameters like the interface thickness; it also allows to maintain the second-order accuracy of the interface normal, curvature and mass conservation. The operator-splitting makes it possible to separate all major difficulties of the problem and enables us to implement the equal-order interpolation for the velocity and pressure. Diverse numerical examples including simulations of bubble dynamics, bifurcating jet flow and Rayleigh,Taylor instability are presented to validate the computational method. Copyright © 2004 John Wiley & Sons, Ltd. [source] A new symmetry-preserving Cartesian-grid method for computing flow past arbitrarily shaped objectsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8-9 2005Marc Dröge Abstract This paper deals with a numerical method for solving the unsteady, incompressible Navier,Stokes equations in domains of arbitrarily shaped boundaries, where the boundary is represented using the Cartesian-grid approach. We introduce a novel cut-cell discretization, which preserves the symmetry of convection and diffusion. That is, convection is discretized by a skew-symmetric operator and diffusion is approximated by a symmetric, positive-definite coefficient matrix. The resulting semi-discrete (continuous in time) system conserves the kinetic energy if the dissipation is turned off; the energy decreases if dissipation is turned on. The method is successfully tested for an incompressible, unsteady flow around a circular cylinder at Re=100. Copyright © 2005 John Wiley & Sons, Ltd. [source] A promising boundary element formulation for three-dimensional viscous flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005Xiao-Wei Gao Abstract In this paper, a new set of boundary-domain integral equations is derived from the continuity and momentum equations for three-dimensional viscous flows. The primary variables involved in these integral equations are velocity, traction, and pressure. The final system of equations entering the iteration procedure only involves velocities and tractions as unknowns. In the use of the continuity equation, a complex-variable technique is used to compute the divergence of velocity for internal points, while the traction-recovery method is adopted for boundary points. Although the derived equations are valid for steady, unsteady, compressible, and incompressible problems, the numerical implementation is only focused on steady incompressible flows. Two commonly cited numerical examples and one practical pipe flow problem are presented to validate the derived equations. Copyright © 2004 John Wiley & Sons, Ltd. [source] Prediction of unsteady, separated boundary layer over a blunt body for laminar, turbulent, and transitional flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2004D. Scott Holloway Abstract The focus of this paper is to study the ability of unsteady RANS-based CFD to predict separation over a blunt body for a wide range of Reynolds numbers particularly the ability to capture laminar-to-turbulent transition. A perfect test case to demonstrate this point is the cylinder-in-crossflow for which a comparison between experimental results from the open literature and a series of unsteady simulations is made. Reynolds number based on cylinder diameter is varied from 104 to 107 (subcritical through supercritical flow). Two methods are used to account for the turbulence in the simulations: currently available eddy,viscosity models, including standard and realizable forms of the k,, model; and a newly developed eddy,viscosity model capable of resolving boundary layer transition, which is absolutely necessary for the type and range of flow under consideration. The new model does not require user input or ,empirical' fixes to force transition. For the first time in the open literature, three distinct flow regimes and the drag crisis due to the downstream shift of the separation point are predicted using an eddy,viscosity based model with transition effects. Discrepancies between experimental and computational results are discussed, and difficulties for CFD prediction are highlighted. Copyright © 2004 John Wiley & Sons, Ltd. [source] Numerical approximation of optimal control of unsteady flows using SQP and time decompositionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2004S. S. RavindranArticle first published online: 1 APR 200 Abstract In this paper, we present numerical approximations of optimal control of unsteady flow problems using sequential quadratic programming method (SQP) and time domain decomposition. The SQP method is considered superior due to its fast convergence and its ability to take advantage of existing numerical techniques for fluid flow problems. It iteratively solves a sequence of linear quadratic optimal control problems converging to the solution of the non-linear optimal control problem. The solution to the linear quadratic problem is characterized by the Karush,Kuhn,Tucker (KKT) optimality system which in the present context is a formidable system to solve. As a remedy various time domain decompositions, inexact SQP implementations and block iterative methods to solve the KKT systems are examined. Numerical results are presented showing the efficiency and feasibility of the algorithms. Copyright © 2004 John Wiley & Sons, Ltd. [source] Computations of two passing-by high-speed trains by a relaxation overset-grid algorithmINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2004Jenn-Long Liu Abstract This paper presents a relaxation algorithm, which is based on the overset grid technology, an unsteady three-dimensional Navier,Stokes flow solver, and an inner- and outer-relaxation method, for simulation of the unsteady flows of moving high-speed trains. The flow solutions on the overlapped grids can be accurately updated by introducing a grid tracking technique and the inner- and outer-relaxation method. To evaluate the capability and solution accuracy of the present algorithm, the computational static pressure distribution of a single stationary TGV high-speed train inside a long tunnel is investigated numerically, and is compared with the experimental data from low-speed wind tunnel test. Further, the unsteady flows of two TGV high-speed trains passing by each other inside a long tunnel and at the tunnel entrance are simulated. A series of time histories of pressure distributions and aerodynamic loads acting on the train and tunnel surfaces are depicted for detailed discussions. Copyright © 2004 John Wiley & Sons, Ltd. [source] Indirect boundary element method for unsteady linearized flow over prolate and oblate spheroids and hemispheroidal protuberancesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2004Lisa F. Shatz Abstract The indirect boundary element method was used to study the hydrodynamics of oscillatory viscous flow over prolate and oblate spheroids, and over hemispheroidal bodies hinged to a plate. Analytic techniques, such as spheroidal coordinates, method of images, and series representations, were used to make the numerical methods more efficient. A novel method for computing the hydrodynamic torque was used, since for oscillatory flow the torque cannot be computed directly from the weightings. Instead, a Green's function for torque was derived to compute the torque indirectly from the weightings. For full spheroids, the method was checked by comparing the results to exact solutions at low and high frequencies, and to results computed using the singularity method. For hemispheroids hinged to a plate, the method for low frequencies was checked by comparing the results to previous results, and to exact solutions at high frequencies. Copyright © 2004 John Wiley & Sons, Ltd. [source] Linearized and non-linear acoustic/viscous splitting techniques for low Mach number flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2003Mohammad Farshchi Abstract Computation of the acoustic disturbances generated by unsteady low-speed flow fields including vortices and shear layers is considered. The equations governing the generation and propagation of acoustic fluctuations are derived from a two-step acoustic/viscous splitting technique. An optimized high order dispersion,relation,preserving scheme is used for the solution of the acoustic field. The acoustic field generated by a corotating vortex pair is obtained using the above technique. The computed sound field is compared with the existing analytic solution. Results are in good agreement with the analytic solution except near the centre of the vortices where the acoustic pressure becomes singular. The governing equations for acoustic fluctuations are then linearized and solved for the same model problem. The difference between non-linear and linearized solutions falls below the numerical error of the simulation. However, a considerable saving in CPU time usage is achieved in solving the linearized equations. The results indicate that the linearized acoustic/viscous splitting technique for the simulation of acoustic fluctuations generation and propagation by low Mach number flow fields seems to be very promising for three-dimensional problems involving complex geometries. Copyright © 2003 John Wiley & Sons, Ltd. [source] Reduced order state-space models from the pulse responses of a linearized CFD schemeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003Ann L. Gaitonde This paper describes a method for obtaining a time continuous reduced order model (ROM) from a system of time continuous linear differential equations. These equations are first put into a time discrete form using a finite difference approximation. The unit sample responses of the discrete system are calculated for each system input and these provide the Markov parameters of the system. An eigenvalue realization algorithm (ERA) is used to construct a discrete ROM. This ROM is then used to obtain a continuous ROM of the original continuous system. The focus of this paper is on the application of this method to the calculation of unsteady flows using the linearized Euler equations on moving meshes for aerofoils undergoing heave or linearized pitch motions. Applying a standard cell-centre spatial discretization and taking account of mesh movement a continuous system of differential equations is obtained which are continuous in time. These are put into discrete time form using an implicit finite difference approximation. Results are presented demonstrating the efficiency of the system reduction method for this system. Copyright © 2003 John Wiley & Sons, Ltd. [source] Computation of unsteady viscous incompressible flows in generalized non-inertial co-ordinate system using Godunov-projection method and overlapping meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002H. Pan Abstract Time-dependent incompressible Navier,Stokes equations are formulated in generalized non-inertial co-ordinate system and numerically solved by using a modified second-order Godunov-projection method on a system of overlapped body-fitted structured grids. The projection method uses a second-order fractional step scheme in which the momentum equation is solved to obtain the intermediate velocity field which is then projected on to the space of divergence-free vector fields. The second-order Godunov method is applied for numerically approximating the non-linear convection terms in order to provide a robust discretization for simulating flows at high Reynolds number. In order to obtain the pressure field, the pressure Poisson equation is solved. Overlapping grids are used to discretize the flow domain so that the moving-boundary problem can be solved economically. Numerical results are then presented to demonstrate the performance of this projection method for a variety of unsteady two- and three-dimensional flow problems formulated in the non-inertial co-ordinate systems. Copyright © 2002 John Wiley & Sons, Ltd. [source] Performance of finite volume solutions to the shallow water equations with shock-capturing schemesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2002K. S. Erduran Abstract Numerical methods have become well established as tools for solving problems in hydraulic engineering. In recent years the finite volume method (FVM) with shock capturing capabilities has come to the fore because of its suitability for modelling a variety of types of flow; subcritical and supercritical; steady and unsteady; continuous and discontinuous and its ability to handle complex topography easily. This paper is an assessment and comparison of the performance of finite volume solutions to the shallow water equations with the Riemann solvers; the Osher, HLL, HLLC, flux difference splitting (Roe) and flux vector splitting. In this paper implementation of the FVM including the Riemann solvers, slope limiters and methods used for achieving second order accuracy are described explicitly step by step. The performance of the numerical methods has been investigated by applying them to a number of examples from the literature, providing both comparison of the schemes with each other and with published results. The assessment of each method is based on five criteria; ease of implementation, accuracy, applicability, numerical stability and simulation time. Finally, results, discussion, conclusions and recommendations for further work are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source] Computational predictability of time-dependent natural convection flows in enclosures (including a benchmark solution)INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2002Mark A. Christon Abstract This paper summarizes the results from a special session dedicated to understanding the fluid dynamics of the 8:1 thermally driven cavity which was held at the First MIT Conference on Computational Fluid and Solid Dynamics in June, 2001. The primary objectives for the special session were to: (1) determine the most accurate estimate of the critical Rayleigh number above which the flow is unsteady, (2) identify the correct, i.e. best time-dependent benchmark solution for the 8: 1 differentially heated cavity at particular values of the Rayleigh and Prandtl numbers, and (3) identify those methods that can reliably provide these results. Copyright © 2002 John Wiley & Sons, Ltd. [source] A numerical model for the flooding and drying of irregular domainsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2002P. Brufau Abstract A numerical technique for the modelling of shallow water flow in one and two dimensions is presented in this work along with the results obtained in different applications involving unsteady flows in complex geometries. A cell-centred finite volume method based on Roe's approximate Riemann solver across the edges of both structured and unstructured cells is presented. The discretization of the bed slope source terms is done following an upwind approach. In some applications a problem arises when the flow propagates over adverse dry bed slopes, so a special procedure has been introduced to model the advancing front. It is shown that this modification reproduces exactly steady state of still water in configurations with strong variations in bed slope and contour. The applications presented are mainly related with unsteady flow problems. The scheme is capable of handling complex flow domains as will be shown in the simulations corresponding to the test cases that are going to be presented. Comparisons of experimental and numerical results are shown for some of the tests. Copyright © 2002 John Wiley & Sons, Ltd. [source] The transient nature of maximum maleic anhydride grafting of polypropylene: A mechanistic approach based on a consecutive reaction model.JOURNAL OF APPLIED POLYMER SCIENCE, Issue 1 2007Abstract This article compares the batch solution and molten state chemical modification of an atactic polypropylene to yield a grafted polypropylene. Short reaction times appear to be sufficient and indeed necessary for the highest graft yields to be obtained if degradative processes occurring in both reaction media are to be avoided. The consecutive reactions for the optimized grafting reaction pathway were proposed for the solution process in an earlier article. The present work attempts to correlate this pathway with that of the molten state process. Grafted succinic anhydride groups react with two resorcine molecules to yield grafted succinyl-fluorescein groups. This work considers the resorcine units as true molecular probes, to be able to stabilize and activate the complexes formed between the succinic anhydride groups and the propylene sequence. This work shows the unsteady and later dynamic character of the process. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 345,351, 2007 [source] CFD simulations of hydrodynamic/thermal coupling phenomena in a bubble column with internalsAICHE JOURNAL, Issue 9 2010Cédric Laborde-Boutet Abstract CFD simulations have been carried out in a full three-dimensional, unsteady, Eulerian framework to simulate hydrodynamic/thermal coupling in a bubble column with internals. A first part of the study, dedicated to the hydrodynamic/thermal coupling in liquid single-phase flows, showed that assuming constant wall temperature on the internals constitutes a reasonable approximation in lieu of comprehensive simulations encompassing shell flow and coolant flow together. A second part dealing with the hydrodynamics of gas,liquid flows in a bubble column with internals showed that a RNG k,, turbulence model formulation accounting for gas-induced turbulence was a relevant choice. The last part used these conclusions to build a hydrodynamic/thermal coupling model of a gas,liquid flow in a bubble column with internals. With a per-phase RNG k,, turbulence model and assuming constant wall temperature, it was possible to simulate heat transfer phenomena consistent with experimentally measured heat transfer coefficients. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source] Hydrogen separation of methyltriethoxysilane templating silica membraneAICHE JOURNAL, Issue 12 2007Jong-Ho Moon Abstract Hydrogen separation on microporous methyltriethoxysilane-templating silica composite/,-alumina membranes (below MTES membrane) was studied using three binary gas mixtures: H2/N2, H2/CO2, and H2/CH4. The characteristics of unsteady and steady-state permeation/separation on the MTES membrane were compared to each other. Although permeation flux in the H2/N2 mixture was comparatively low, H2 selectivity was high (H2/N2 SF , 30,60). On the contrary, the H2/CO2 mixture showed high permeation flux but low H2 selectivity (H2/CO2 SF , 1.5,6.5). The H2/CH4 mixture showed a large difference between permselectivity (28,48) and separation factor (10,22). Results from this study revealed that it was difficult to predict the separation factor using the one-component permeation ratio (permselectivity) over the experimental range tested. These separation characteristics could be primarily ascribed to the molecular size and structure of each gas, which likely contributed to steric hindrance or molecular sieving within the membrane pore. In addition, the adsorption affinity of each molecule on the membrane surface acted as a key factor in separation performance because it significantly influenced surface diffusion. The generalized Maxwell-Stefan model incorporating the dust gas model, and the Langmuir model could successfully predict the transient and steady-state permeation/separation. © 2007 American Institute of Chemical Engineers AIChE J, 2007 [source] Exact boundary observability of unsteady flows in a tree-like network of open canalsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2009Qilong Gu Abstract In this paper we establish the exact boundary observability of unsteady flows in a tree-like network of open canals with general topology. Copyright © 2008 John Wiley & Sons, Ltd. [source] | ||||||||||||||||||||||