bluuebunny/crossref_metadata_2025_split huggingface dataset:
Performance of a multigrid calculation procedure in three‐dimensional sudden expansion flows
Authors: Vanka S. P. 
Published: August 2005

AbstractThe performance of a recently developed calculation procedure for steady incompressible flows is assessed in a variety of three‐dimensional sudden expansion type flows representative of those encountered in several types of industrial equipment. The calculation procedure, called here BLIMM (for block‐implicit multigrid method), is based on a coupled solution of the three‐dimensional momentum and continuity equations in primitive variables, using the multigrid technique. Different Reynolds numbers and finite difference grids are considered for each flow situation. The rates of convergence and the computational times are reported for each case.
A numerical method for the calculation of incompressible, steady, separated flows around aerofoils
Authors: Tzabiras G. , Dimas A. , Loukakis T. 
Published: August 2005

AbstractThe present work deals with the numerical calculation of the incompressible turbulent flow around aerofoils. An orthogonal curvilinear grid of ‘C’ type is used for the solution of the time averaged equations and Reynolds stresses are modelled according to the κ‐ε turbulence model. PISO and SIMPLE algorithms are used to solve the strongly coupled system of the derived finite volume equations and convergence is improved by applying the method of variable local underrelaxation factors. Comparisons between the calculated and measured pressure distributions are presented for NACA 0012 and NACA 4412 wing sections. The formation of separation bubbles according to calculations is also shown.
Porous aerofoil analysis using viscous‐inviscid coupling at transonic speeds
Authors: Olling Charles R. , Dulikravich George S. 
Published: August 2005

AbstractViscous‐inviscid interaction is used to compute steady two‐dimensional, transonic flows for solid and porous aerofoils. A full‐potential code was coupled with both a laminar/transition/turbulent integral boundary‐layer/turbulent wake code and the finite‐difference boundary‐layer code using the semi‐inverse methods of Carter and Wigton. The coupling was performed using the transpiration coupling concept, thus allowing for analysis of porous aerofoils with passive physical transpiration. The computations confirm experimental findings that passive physical transpiration can lead to a lower drag coefficient and a higher lift coefficient, a weaker shock and elimination of shock‐induced separation. Nevertheless, it is very important that the extent of the porous region and permeability factor distribution of the porous region are chosen carefully if these improvements are to be achieved.
A hodograph‐based method for the design of shock‐free cascades
Authors: Hassan A. A. , Dulikravich G. S. 
Published: August 2005

AbstractA hodograph‐based method, originally developed by the first author for the design of shock‐free aerofoils, has been modified and extended to allow for the design of shock‐free compressor blades. In the present procedure, the subsonic and supersonic regions of the flow are decoupled, allowing the solution of either an elliptic or a hyperbolic‐type partial differential equation for the stream function. The coupling of both regions of the flow is carried out along the sonic line which adjoins both regions. For the subcritical portion of the flow considered here, the pressure distribution is prescribed in addition to the upstream and downstream flow conditions. For the supercritical portion of the flow, the stream function on the sonic line is given instead of the supercritical pressure distribution which is found as part of the solution. In the special hodograph variables used, the equation for the stream function is solved iteratively using a second‐order accurate line relaxation procedure for the subsonic portion of the flow. For the supercritical portion of the flow, a characteristic marching procedure in the hodograph plane is used to solve for the supersonic flow. The results are then mapped back to the physical plane to determine the blade shape and the supercritical pressures. Examples of shock‐free compressor blade designs are presented. They show good agreement with the direct computation of the flow past the designed blade.
Computer‐extended series for a source/sink driven gas centrifuge
Authors: Berger M. H. 
Published: August 2005

AbstractWe have reformulated the general problem of internal flow in a modern, high speed gas centrifuge with sources and sinks in such a way as to obtain new, simple, rigorous closed form analytical solutions. Both symmetric and antisymmetric drives lead us to an ordinary differential equation in place of the usual inhomogeneous Onsager partial differential equation. Owing to the difficulties of exactly solving this sixth order, inhomogeneous, variable coefficient ordinary differential equation we appeal to the power of perturbation theory and techniques. Two extreme parameter regimes are identified, the so‐called semi‐long bowl approximation and a new short bowl approximation. Only the former class of problems is treated here. The long bowl solution for axial drive is the correct leading order term, just as for pure thermal drive. New O(1) results are derived for radial, drag and heat drives in two dimensions. Then regular asymptotic, even ordered power series expansions for the flow field are carried out on the computer to O(ε4) using MACSYMA. These approximations are valid for values of ε near unity. In the spirit of Van Dyke, one can carry out this expansion process, in theory, to apparently arbitrary order for arbitrary but finite decay length ratio. Curiously, the flows induced by axial and radial forces are proportional for asymptotically large source scale heights, x*. Corresponding isotope separation integral parameters will be given in a companion paper.
Flow simulation in channels with distorted geometry using a spectral code with co‐ordinate transformation
Authors: Fodemski T. R. , Voke P. R. , Collins M. W. 
Published: August 2005

AbstractTurbulence is essentially four‐dimensional in character, and requires the corresponding treatment of the well‐known Navier‐Stokes equations. However, this has only been possible over the past twenty years and then by using the largest computers available. Interest is now turning from the initial, mainly smooth channel, simulations to geometries of eventual engineering significance. This paper reports a new code using the spectral methods of Orszag, but also incorporating a novel generalized co‐ordinate transformation approach.Initial predictions for smooth channels agree well with published data. For distorted geometries, the initial velocity field has considerable influence on the success of the simulations. This is accommodated by gradual (step) changes towards the required distortion, so that the initial velocity field for the ‘new’ geometry is the final field from the previous step. Examples are given of different two‐dimensional channel geometries achieved, and these include the successful prediction of recirculating flows.
On the development of Taylor vortices in a vertical annulus with a heated rotating inner cylinder
Authors: Ball Kenneth S. , Farouk Bakhtier 
Published: August 2005

AbstractA numerical study has been conducted to determine the heat transfer characteristics and flow patterns which develop around a rotating, heated vertical cylinder enclosed within a stationary concentric cylinder. A tall annulus (aspect ratio of 10) with fixed, adiabatic horizontal end‐plates and a radius ratio of 0·5 has been considered. Furthermore, the effect that the introduction of buoyancy forces by heating the inner cylinder has on the development of the Taylor vortex flow is examined. It is observed that the formation of the Taylor vortices is delayed until the rotational parameter σ = Gr/Re2 has a value below unity for any given Reynolds number Re which is above the critical value Recrit for the formation of Taylor vortices in an isothermal flow. Also, the Taylor cells first appear at the top of the annulus. As σ is gradually decreased below unity, bifurcations to other states are observed. The final structure of the secondary flow is noticeably distorted in the mixed‐convection mode, with the size of the Taylor cells varying greatly along the height of the annulus. This distortion diminishes as σ is further decreased, until the isothermal flow pattern is nearly recovered below σ = 0·01.
On pressure boundary conditions for the incompressible Navier‐Stokes equations
Authors: Gresho Philip M. , Sani Robert L. 
Published: August 2005

AbstractThe pressure is a somewhat mysterious quantity in incompressible flows. It is not a thermodynamic variable as there is no ‘equation of state’ for an incompressible fluid. It is in one sense a mathematical artefact—a Lagrange multiplier that constrains the velocity field to remain divergence‐free; i.e., incompressible—yet its gradient is a relevant physical quantity: a force per unit volume. It propagates at infinite speed in order to keep the flow always and everywhere incompressible; i.e., it is always in equilibrium with a time‐varying divergence‐free velocity field. It is also often difficult and/or expensive to compute. While the pressure is perfectly well‐defined (at least up to an arbitrary additive constant) by the governing equations describing the conservation of mass and momentum, it is (ironically) less so when more directly expressed in terms of a Poisson equation that is both derivable from the original conservation equations and used (or misused) to replace the mass conservation equation. This is because in this latter form it is also necessary to address directly the subject of pressure boundary conditions, whose proper specification is crucial (in many ways) and forms the basis of this work. Herein we show that the same principles of mass and momentum conservation, combined with a continuity argument, lead to the correct boundary conditions for the pressure Poisson equation: viz., a Neumann condition that is derived simply by applying the normal component of the momentum equation at the boundary. It usually follows, but is not so crucial, that the tangential momentum equation is also satisfied at the boundary.
Finite‐element analysis of fluid flow and heat transfer for staggered bundles of cylinders in cross flow
Authors: Dhaubhadel M. N. , Reddy J. N. , Telionis D. P. 
Published: August 2005

AbstractThe two‐dimensional Navier‐Stokes equations and the energy equation governing steady laminar incompressible flow are solved by a penalty finite‐element model for flow across finite depth, five‐row deep, staggered bundles of cylinders. Pitch to diameter ratios of 1·5 and 2·0 are considered for cylinders in equilateral triangular and square arrangements. Reynolds numbers studied range from 100 to 400, and a Prandtl number of 0·7 is used. Velocity vector fields, streamline patterns, vorticity, pressure and temperature contours, local and average Nusselt numbers, pressure and shear stress distributions around the cylinder walls and drag coefficients are presented. The results obtained agree well with available experimental and numerical data.
Computation of three‐dimensional transonic flows using two stream functions
Authors: Sherif A. , Hafez M. 
Published: August 2005

AbstractA computational method for three‐dimensional flows is presented in terms of two stream functions, which may be considered as two components of a generalized vector potential. An iterative scheme is developed such that only a sequence of two‐dimensional‐like problems, for each function, is solved. The convergence of the iterative scheme is studied based on von Neumann linear analysis. For transonic flow calculation, numerical methods used for potential flows are readily applied, namely artificial density and Zebra relaxation. Results of transonic flow calculations around a wing are presented.
Numerical solution of a free surface problem by a boundary element method
Authors: Aitchison Joyce M. , Karageorghis Andreas 
Published: August 2005

AbstractThis paper describes a method for the numerical solution of a Riabouchinsky cavity flow. Application of a boundary element method leads to a system of non‐linear equations. The mild singularity appearing at the separation point is treated with the introduction of a curved boundary element, which satisfies the exact behaviour of the free boundary in that neighbourhood.
A method for generating irregular computational grids in multiply connected planar domains
Authors: Weatherill N. P. 
Published: August 2005

AbstractA method for generating irregular triangular computational grids in two‐dimensional multiply connected domains is described. A set of points around each body is defined using a simple grid generation technique appropriate to the geometry of each body. The Voronoi regions associated with the resulting global point distribution are constructed from which the Delaunay triangulation of the set of points is thus obtained. The definition of Voronoi regions ensures that the triangulation produces triangles of reasonable aspect ratios given a grid point distribution. The approach readily accommodates local clustering of grid points to facilitate variable resolution of the domain. The technique is generally applicable and has been used with success in computing triangular grids in multiply connected planar domains. The suitability of such grids for flow calculations is demonstrated using a finite element method for solution of the inviscid transonic flow over two‐ dimensional high‐lift aerofoil configurations.
A new fluid‐structure interaction analysis based on higher‐order boundary elements
Authors: Hearn Grant E. , Donati Edilio 
Published: August 2005

AbstractIn strip theory analysis the vessel is represented by a series of 2D transverse sections. For 2D arbitrary‐shaped sections either floating in the free surface or totally submerged, a higher‐order boundary element analysis has been developed to permit determination of the associated radiation and diffraction velocity potentials.In this paper the formulation of the cited interaction problems is reworked to reflect the new capability of permitting curved boundary elements to represent the geometry and a higher‐order functional behaviour of the unknown velocity potentials over that geometry. This is in direct contrast to the usual technique of using straight‐line geometric panels and invariant behaviour of the required potentials over these simple panels.Applications to representative sections of floating ships and the fully submerged pontoon section of a semi‐submersible are presented. Within these applications the results of the standard Frank close‐fit technique, of linear panels and constant behaviour, are compared with different combinations of higher‐order representations of the geometry and the determined velocity potentials.Conclusions regarding the advantages and limitations of the procedures developed are discussed.
A flux‐vector splitting method for steady Navier‐Stokes equations
Authors: Dick E. 
Published: August 2005

AbstractThe flux‐vector splitting method is applied to the convective part of the steady Navier‐Stokes equations for incompressible flow. By the use of partial upwind differences in the split first‐order part and central differences in the second‐order part, a set of discrete equations is obtained which can be solved by vector variants of classical relaxation schemes. It is shown that accurate results can be obtained on one of the GAMM backward‐facing step test problems.
Examination of pressure oscillations arising in the computation of cascade flow using a boundary‐fitted co‐ordinate system
Authors: Lapworth B. L. 
Published: August 2005

AbstractThe incompressible flow through a two‐dimensional cascade is computed using the SIMPLE algorithm in a boundary‐fitted co‐ordinate system. With the standard staggered grid arrangement the numerical solution was found to allow localized pressure oscillations to persist adjacent to the periodic boundaries. These oscillations were found to be a consequence of the extended momentum control volumes which are required in this region of the cascade. Such control volumes may be removed by the use of appropriately non‐staggered velocity storage locations, which are also desirable in the boundary‐fitted system since the Cartesian velocity components are no longer related to the grid line orientations. However, this storage permits the propagation of global pressure oscillations, which were previously suppressed by the staggered grid arrangement. This paper attempts to define a solution procedure which uses non‐staggered velocity locations and is able to eliminate the consequent global pressure oscillations. To achieve this aim, two forms of pressure correction scheme were considered. The first implemented the scheme proposed by Vanka et al. but was found to be inadequate in the open part of the cascade, whereas the second employed a modification of the scheme proposed by Rhie and Chow and was found to be successful in all regions of the flow. The results computed using this scheme were compared with the available experiment results.
A multigrid method for recirculating flows
Authors: Sivaloganathan S. , Shaw G. J. 
Published: August 2005

AbstractThe use of multigrid methods in complex fluid flow problems is recent and still under development. In this paper we present a multigrid method for the incompressible Navier‐Stokes equations. The distinctive features of the method are the use of a pressure‐correction method as a smoother and a novel continuity‐preserving manner of grid coarsening. The shear‐driven cavity problem is used as a test case to demonstrate the efficiency of the method.
Computation of complex fluid flows using an adaptive grid method
Authors: Shyy Wei 
Published: August 2005

AbstractRecently the concept of adaptive grid computation has received much attention in the computational fluid dynamics research community. This paper continues the previous efforts of multiple one‐dimensional procedures in developing and asessing the ideas of adaptive grid computation. The focus points here are the issue of numerical stability induced by the grid distribution and the accuracy comparison with previously reported work. Two two‐dimensional problems with complicated characteristics—namely, flow in a channel with a sudden expansion and natural convection in an enclosed square cavity—are used to demonstrate some salient features of the adaptive grid method. For the channel flow, by appropriate distribution of the grid points the numerical algorithm can more effectively dampen out the instabilities, especially those related to artificial boundary treatments, and hence can converge to a steady‐state solution more rapidly. For a more accurate finite difference operator, which contains less undesirable numerical diffusion, the present adaptive grid method can yield a steady‐state and convergent solution, while uniform grids produce non‐convergent and numerically oscillating solutions. Furthermore, the grid distribution resulting from the adaptive procedure is very responsive to the different characteristics of laminar and turbulent flows. For the problem of natural convection, a combination of a multiple one‐dimensional adaptive procedure and a variational formulation is found very useful. Comparisons of the solutions on uniform and adaptive grids with the reported benchmark calculations demonstrate the important role that the adaptive grid computation can play in resolving complicated flow characteristics.
Curvature‐compensated convective transport: SMART, A new boundedness‐ preserving transport algorithm
Authors: Gaskell P. H. , Lau A. K. C. 
Published: August 2005

AbstractThe paper describes a new approach to approximating the convection term found in typical steady‐state transport equations. A polynomial‐based discretization scheme is constructed around a technique called ‘curvature compensation’; the resultant curvature‐compensated convective transport approximation is essentially third‐order accurate in regions of the solution domain where the concept of order is meaningful. In addition, in linear scalar transport problems it preserves the boundedness of solutions. Sharp changes in gradient in the dependent variable are handled particularly well. But above all, the scheme, when used in conjunction with an ADI pentadiagonal solver, is easy to implement with relatively low computational cost, representing an effective algorithm for the simulation of multi‐dimensional fluid flows. Two linear test problems, for the case of transport by pure convection, are employed in order to assess the merit of the method.
On variable grids for modelling flow in reciprocating engines
Authors: Shah P. , Markatos N. C. , Glynn D. R. 
Published: August 2005

AbstractThe moving boundary (i.e. the piston) within a reciprocating engine poses the problem that as it moves towards the cylinder head it compresses the computational grid lines. Control cells that started with reasonable aspect ratios become so compressed that aspect ratios of 1000 are not unusual in some cases. This, of course, adversely affects numerical accuracy and convergence. It is the purpose of this paper to present a conservative scheme that allows for the removal and addition of grid cells, during simulation, so as to restore reasonable aspect ratios. Results of the computations are presented and compared with experimental data. It is concluded that with the proposed scheme convergence is obtained within fewer iterations, CPU time is reduced and the results are generally in better agreement with experimental data.
A simple numerical technique for transient creep flows with free surfaces
Authors: Golafshani Mehdi 
Published: August 2005

AbstractA simple, but powerful iterative technique is presented for the numerical solution of the time‐dependent flow of an incompressible viscous fluid with or without a free surface. The usual numerical stability restrictions related to the viscous acceleration terms are avoided using standard implicit differencing techniques. The properties and accuracy of the method are illustrated by several calculational examples.
Unsteady viscous flow over a grooved wall: A comparison of two numerical methods
Authors: Hung S. C. , Kinney R. B. 
Published: August 2005

AbstractA numerical study is made of the unsteady two‐dimensional laminar flow of an incompressible fluid over a periodically grooved wall. Two independent finite difference techniques are employed. One is based on the vorticity‐stream function and the other on the vorticity‐velocity (i.e. induction law) formulation. The fluid motion is initiated impulsively from rest and is assumed to be spatially periodic in the streamwise direction. The numerical formulations are derived in detail. The generation of vorticity at the solid surface is modelled differently in the two approaches, and this is found to play an important role in determining the surface pressure distribution and the drag coefficient. The flow field is examined during the early transient phase of development, during which the greatest changes occur. Results are presented for a moderate Reynolds number (based on groove depth) equal to 100. It is found that the vorticity‐stream function approach does not produce a spatially periodic wall pressure distribution, and therefore global conservation of total vorticity is not achieved. This results in substantial errors in the predictions for the drag coefficient. These deficiencies are not found in the results obtained by the vorticity‐velocity formulation.