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doi: 10.1002/fld.1650120302pmid: N/A
Predictions were performed for two different confined swirling flows with internal recirculation zones. The convection terms in the elliptic governing equations were discretized using three different finite differencing schemes: hybrid, quadratic upwind interpolation and skew upwind differencing. For each flow case, calculations were carried out with these schemes and successively refined grids were employed. For the turbulent flow case the k‐ε turbulence model was used. The predicted cases were a laminar swirling flow investigated by Bornstein and Escudier, and a turbulent low‐swirl case studied by Roback and Johnson. In both cases an internal recirculation zone was present. The laminar case is well predicted when account is taken of the estimated radial velocity component at the chosen inlet plane. The quadratic upwind interpolation and skew upwind schemes predict the main features of the internal recirculation zone also with a coarse grid. The turbulent case is well predicted with the coarse as well as the finer grids, the skew upwind and quadratic upwind interpolation schemes yielding results very close to the measurements. It is concluded that the skew upwind scheme reaches grid independence slightly before the quadratic upwind scheme, both considerably earlier than the hybrid scheme.
Yang, Jinn‐Chuang; Hsu, Euan‐Lung
doi: 10.1002/fld.1650120303pmid: N/A
The Holly‐Preissmann two‐point finite difference scheme (HP method) has been popularly used for solving the advection equation. The key idea of this scheme is to solve the dependent variable (i.e. the concentration for the pollutant transport problem) by the method of characteristics with the use of cubic interpolation on the spatial axis. The interpolating polynomials of higher order are constructed by use of the dependent variable and its derivatives at two adjacent grid points. In this paper a new interpolating technique is introduced for incorporation with the Holly‐Preissmann two‐point method. The new method is denoted herein as the Holly‐Preissmann reach‐back method (HPRB) and allows the characteristics to project back several time steps beyond the present time level. Through stability analyses it has been observed that the increase of the reach‐back time step numbers for the characteristics indeed reduces the numerical damping and dispersive phenomena. A schematic model has been constructed to demonstrate the merits of this new technique for the calculation of the pure advection and dispersion equations. Numerical experiments and comparisons with analytical solutions which support and demonstrate this new technique are presented.
Martins, Luis‐Filipe; Ǵhoniem, Ahmed F.
doi: 10.1002/fld.1650120304pmid: N/A
A numerical scheme based on the application of the vortex method to update the vorticity field and the implementation of the finite element method to satisfy the normal velocity boundary condition inside a complex time‐dependent geometry is applied to simulate the flow produced by a piston sliding out of a chamber equipped with single or multiple intakes. This unsteady confined vortex flow is of interest in many applications. We use the idealization that the flow is incompressible, two‐dimensional and planar and we analyse the results to study the flow during the intake process inside a model of an engine cylinder. The chamber top is fitted with an inlet channel, an inlet port or an inlet valve. In all cases when the intake channel axis coincides with that of the chamber, the flow in each side of the chamber consists essentially of two large counter‐rotating eddies of almost the same size. The computed structures of these flows resemble qualitatively those which have been observed experimentally. The fluid motion is also computed for the case of a chamber equipped with an intake whose axis is not aligned with the chamber axis. In this case the flow at the end of the stroke is dominated by a single large eddy produced by the merging of the two eddies forming on the sides of the port.
doi: 10.1002/fld.1650120305pmid: N/A
A numerical method based on the boundary‐fitted finite difference method (BFDM) is presented in this paper. The boundaries are external (the boundary of the physical domain) and internal (which corresponds to the fracture network). The difference between this approach and the usual one lies in the inclusion of discrete fractures in the volume that represents the porous medium. The numerical model has been used in the prediction of the flow pattern in several internationally recognized verification cases and applied to the solution of hypothetical problems of interest to us in the field of nuclear waste repository modelling. The results obtained show that the numerical approach considered gives accurate and reliable predictions of the hydrodynamics of fractured‐porous media, thus justifying its use for the above‐mentioned studies.
Mouzakis, F. N.; Bergels, G. C.
doi: 10.1002/fld.1650120306pmid: N/A
Predictions are presented of the two‐dimensional turbulent flow over a triangular ridge. The time‐averaged Reynolds equations are written in an orthogonal curvilinear co‐ordinate system and transformed to finite difference form after discretization in physical space. Turbulence is simulated by the two‐equation κ‐ε model of turbulence. In the first part of the paper the basics of the numerical method are presented and in the second part comparisons are made between predictions and available laboratory data. Therefore the validity and reliability of the method as well as its flexibility in treating complex recirculating flows are assessed. Results of engineering significance are presented of the effect of the ridge slope on the length of the recirculation region and on the overspeed factor on top of the ridge.
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