Structured Grid System Research Articles

Automatic elliptic grid generation by an approximate factorisation

A procedure for automatic numerical generation of a structured grid system with coordinate lines coinciding with all boundaries of a general two-dimensional region containing a body of arbitrary shape is presented. The solution procedure incorporated the method of false transients and the approximate factorisation algorithm, where a sequence of time steps is cycled in a geometric fashion with repeated endpoints, and has a capability for clustering grid lines close to the body. The procedure requires significantly much less computational effort to obtain a converged solution than a point or line successive over-relaxation iterative scheme. Although, the superiority of the presented algorithm has been demonstrated for the grid generation problem, it can be utilised for other problems requiring the solution of a set of elliptic partial differential equations of similar nature.

401 構造格子SuperCartesian法による複雑形状に対する熱流体解析技法(OS04.流体の数値計算手法と数値シミュレーション(1))

401 構造格子SuperCartesian法による複雑形状に対する熱流体解析技法(OS04.流体の数値計算手法と数値シミュレーション(1))

On coupling the Reynolds‐averaged Navier–Stokes equations with two‐equation turbulence model equations

AbstractTwo methods for coupling the Reynolds‐averaged Navier–Stokes equations with the q–ω turbulence model equations on structured grid systems have been studied; namely a loosely coupled method and a strongly coupled method. The loosely coupled method first solves the Navier–Stokes equations with the turbulent viscosity fixed. In a subsequent step, the turbulence model equations are solved with all flow quantities fixed. On the other hand, the strongly coupled method solves the Reynolds‐averaged Navier–Stokes equations and the turbulence model equations simultaneously. In this paper, numerical stabilities of both methods in conjunction with the approximated factorization‐alternative direction implicit method are analysed. The effect of the turbulent kinetic energy terms in the governing equations on the convergence characteristics is also studied. The performance of the two methods is compared for several two‐ and three‐dimensional problems. Copyright © 2005 John Wiley & Sons, Ltd.

Prevalence of Pubococcygeus Muscle Detachment from the Pubic Bone in Women with Symptomatic Anterior Vaginal Compartment Prolapse

Objective This study, part of a larger investigation into the outcome of surgery for female pelvic organ prolapse, was performed to determine the prevalence of pubococcygeus muscle detachment from the pubic bone on magnetic resonance imaging (MRI) in women with symptomatic anterior vaginal compartment prolapse. Methods Axial T2 weighted pelvic MRI was performed on 70 women with symptomatic anterior vaginal compartment prolapse and 18 continent nulliparous normal references. The images were analyzed by 2 observers using a structured grid system to record the attachment of the pubococcygeus muscle (PCM) to the pubic bone, and continuity of the muscle from its origin. Results Pubococcygeus muscle detachment from the pubic bone was seen in 39 (56%) of the women with anterior vaginal compartment pelvic organ prolapse. PCM detachment appears more common on the right compared with the left side (49% versus 32% respectively). All the asymptomatic continent nulliparous women had intact muscles. Conclusion Pubococcygeal muscle detachment from the pubic bone on MRI is common, and occurs more often on the right side in women with symptomatic anterior vaginal compartment pelvic organ prolapse. The high prevalence of pubococcygeal muscle detachment in women with anterior vaginal compartment prolapse shown in this study may provide an explanation for the high recurrence of anterior vaginal compartment prolapse following anterior vaginal repair.

Numerical simulation of unsteady compressible flows induced by a high-speed train passing through a tunnel

The unsteady flow fields induced by a high-speed train travelling through a tunnel have been numerically simulated. In order to present the relative motion between a train and a tunnel, a modified patched-grid scheme based on the structured grid system has been developed and employed for an axisymmetric unsteady Euler solver using Roe's flux difference splitting method. In this paper, the innovative zonal method, named the hybrid dimension method, is proposed and applied to the train-tunnel interaction problems. The basic idea of this method is to maximize the efficiency of numerical calculations by minimal assumption of spatial dimensions. The numerical results from the modified patched-grid scheme showed good agreement with the inviscid compressible phenomena of the experimental result, i.e. the entry compression wave and the micropressure wave. The hybrid dimension method is successfully applied to the present modified patched-grid method, hardly losing the numerical accuracy. Moreover, the hybrid dimension method is expected to reduce the huge computation time of the train-tunnel interaction problems especially for the cases of long tunnels.

Numerical and Experimental Study of Offshore Pipeline Stability in Trench

Offshore pipelines are to be stabilized against external loading caused mainly by wave and currents. When pipelines are placed in a trench, the forces acting on them are reduced considerably. To investigate the stability in various trench sections, the flow over the pipeline is numerically simulated and compared with experimental results obtained from particle image velocimetry measurement. This paper consists of two parts: single pipe and dual pipe in various trench sections. Each part compares numerical results with experimental results, which include mean flow pattern, drag-force coefficient, and lift-force coefficient. For a single pipe, Smagainsky's eddy viscosity model combined with a truncated deductive model is applied to represent the stress field in a quadrilateral structured grid system. In the numerical simulation for dual pipes, the Navier-Stokes equation and elliptic mesh generation method are used. The stability of various trench conditions is addressed in terms of mean amplitudes of oscillating lift and drag and reduction factors for each case. The results can be effectively applied to pipeline design.

Computation of Subsonic Inviscid Flow past a Cone Using High-Order Schemes

A wake-dominated unsteady flow of Mach number 0.2 past a cone of vertex angle 60 deg is calculated numerically using high-order finite difference schemes on structured grids. The three-dimensional compressible Euler equations are solved to simulated an inviscid flow that exhibits large fluctuations of pressure and velocity as a result of the shedding of vortices behind the cone. An axisymmetric structured grid system is used. It is generated by rotating a two-dimensional grid plane around a centerline. The grid singularity at the centerline, where the Jacobian and some grid metrics approach infinity, is avoided by changing the form of the flux vectors in the Euler equations without any asympotic assumption or simplification. Fourth-and sixth-order finite difference schemes are used for the evaluation of spatial derivatives, and a fourth order Runge-Kutta scheme is used for marching the solution in time. The complex wake structures and motions behind the cone are investigated by visualizing the vorticity field. The mean flow pattern and periodic phenomena are analyzed and compared with experimental data. This demostrates the accuracy of the present approach to further analyses of wake-dominated flows past axisymmetric blunt-based bodies.

Discrete Ordinates Interpolation Method Applied to Irregular Three-Dimensional Geometries

[S0022-1481(00)00304-2]

Numerical Analysis of Three-Dimensional Flow in a Forward Curved Centrifugal Fan

Numerical study of three-dimensional turbulent flow in a forward curved centrifugal fan is presented. Standard turbulence model and non-orthogonal curvilinear coordinates arc used to consider the turbulent flow field and complex geometry. Finite Volume approach is adopted for discretization scheme and structured grid system is used to help convergence. Multiblock grid system is used for flow field and divided into five domains that are inlet, outlet, impeller, tip clearance and scroll. It is assumed that the flow field is steady and incompressible. These numerical results are compared with the experimental data inside a rotor and at the fan outlet. Most important flow features are captured through this numerical approach. Finally details of flow field inside a fan are described and analyzed.

Modeling of kraft recovery boilers

The subject of this work is the modeling of recovery boilers. A three-dimensional, steady-state computer simulation of the flow and combustion process in a recovery boiler is presented here. The numerical algorithm of the original code was modified and extended to cater for certain special aspects of recovery boilers, such as the in-flight combustion of black liquor droplets and char bed burning. To represent the fine structure of numerous air ports, a higher level of grid topology than in the conventional, structured grid system is required. In this work, a highly flexible, unstructured and mixed cell topology grid with local mesh refinement was employed. A number of computations were carried out using various firing arrangements including the ROTAFIRE system. The results show considerable potential and reliability in the use of computer simulations for the improvements and optimization of recovery boilers.

三角形要素を用いたダイバージェンス・フォーミュレーション法による流体潤滑数値解析法

The formulation of a general numerical method for fluid film lubrication of irregular bearing shapes in the high bearing number region is presented. We expand the formulation of the divergence formulation method to the triangular element used in the finite element method. Here, the pressure function is not an element-interpolation function but a node-interpolation function. The mass flux is evaluated along the sides of the triangular elements, so that several calculation schemes, which are commonly used in the divergence formulation method on structured grid systems, can be introduced for unstructured grid systems easily. The formulation is suitable not only for acute-angled triangu-lar elements but also for obtuse-angled triangular elements. Numerical examples demonstrate the applicability and accuracy of the method.

A Divergence Formulation-Finite Element Method with Use of Triangular Elements for the Dynamic Characteristics of a Fluid Lubrication Analysis.

A general numerical method of calculation of the dynamic characteristics of fluid film lubrication in irregular bearing shapes and a high bearing number region is described. The method represents an expansion of the formulation of the divergence formulation method to the triangular element used in the finite element method. Weighted upstream schemes which are commonly used in the divergence formulation method on structured grid systems can be introduced in unstructured grid systems very easily. Numerical results for stiffness and damping coefficients of oil and gasjournal bearings show the usefulness and accuracy of the method.

Interactive grid generation and NURBS applications

This paper addresses recent developments of grid generation techniques employing nonuniform rational B-spline formulations (NURBS). Grid refinement algorithms for arbitrary curves and surfaces with NURBS maintain high fidelity of the geometry, and allow time-efficient interactive grid generation. Bezier curve formulations are utilized to subdivide surface patches to accomplish a smooth and near orthogonal zonal grid. A CAD/Grid interface code based on NURBS formulations has been developed which converts CAD data from IGES files into the format accepted by the structured grid system. Two interactive grid generation codes, a general-purpose code and a customized one for turbomachinery configurations, have been developed on the basis of NURBS' definition.

Three-dimensional adaptive grid-embedding Euler technique

A new three-dimensional adaptive-grid Euler procedure is presented that automatically detects high-gradient regions in the flow and locally subdivides the computational grid in these regions to provide a uniform, high level of accuracy over the entire domain. A tunable, semistructured data system is utilized that provides global, topological unstructured-grid flexibility along with the efficiency of a local, structured-grid system. In addition, this data structure allows for the flow solution algorithm to be executed on a wide variety of parallel/vector computing platforms. An explicit, lime-marching, control volume procedure is used to integrate the Euler equations to steady state

Numerical study of mixing in supersonic combustors with hypermixing injectors

A numerical study was conducted to evaluate the performance of wall mounted fuel-injectors designed for potential Supersonic Combustion Ramjet (SCRAM-jet) engine applications. The focus of this investigation was to numerically simulate existing combustor designs for the purpose of validating the numerical technique and the physical models developed. Three different injector designs of varying complexity were studied to fully understand the computational implications involved in accurate predictions. A dual transverse injection system and two streamwise injector designs were studied. The streamwise injectors were designed with swept ramps to enhance fuel-air mixing and combustion characteristics at supersonic speeds without the large flow blockage and drag contribution of the transverse injection system. For this study, the Mass-Averaged Navier-Stokes equations and the chemical species continuity equations were solved. The computations were performed using a finite-volume implicit numerical technique and multiple block structured grid system. The interfaces of the multiple block structured grid systems were numerically resolved using the flux-conservative technique. Detailed comparisons between the computations and existing experimental data are presented. These comparisons show that numerical predictions are in agreement with the experimental data. These comparisons also show that a number of turbulence model improvements are needed for accurate combustor flowfield predictions.

Finite Analytic Numerical Solutions for Unsaturated Flow with Irregular Boundaries

This study illustrates the development of the finite‐analytic (FA) numerical solutions associated with an optimal (variable) time‐weighting factor for water flow in unsaturated porous media with irregular boundaries. This method entails the nine‐point and five‐point elements such that it can simulate quite well the irregular flow domain without using boundary‐fitted transformation. For an element near the irregular boundaries, a five‐point FA algebraic solution is derived; for a regular element, the nine‐point FA algebraic equation is used. In execution of numerical computation, the irregular five‐point boundary element is recasted into the nine‐point element, allowing a regular structured grid system to be used to solve for the water flow in an irregular domain. Two problems are solved in this study. The first is a transient, two‐dimensional flow of water under a strip source infiltration of constant flux with regular boundaries. Uniform clay loam, uniform coarse sand, and layered system of soil are used...

Finite volume method on the unstructured grid system

Applying the Voronoi diagram to the cell system for the finite volume method, a new method on the unstructured grid system is devised for the simulation of incompressible steady flow. In this method, the SIMPLE algorithm can be applied with little expansion. The turbulent flow around the two-dimensional vehicle model is simulated with the k - ϵ turbulence model by this method. Comparing the calculation result with another result obtained using the structured grid system and the experimental data, the new method is shown to be suitable for the simulation of complex flow fields.