scholarly journals A three-dimensional iterative scheme for an electromagnetic capacitive applicator

1990 ◽  
Vol 37 (10) ◽  
pp. 975-986 ◽  
Author(s):  
M.J. Sowinski ◽  
P.M. van den Berg
Keyword(s):  
Iterative Scheme ◽  
Three Dimensional

Numerical Analysis of Turbine Coolant Passage Flows

1998 ◽  
Author(s):  
Meng-Sing Liou ◽  
K. P. Singh
Keyword(s):  
Iterative Scheme ◽  
Three Dimensional ◽  
Nasa Lewis Research ◽  
Reynolds Stresses ◽  
Complex Flow ◽  
Internal Flows ◽  
The Matrix ◽  
Turbine Component ◽  
Unstructured Tetrahedral Meshes ◽  
Matrix Bandwidth

We report in this paper a project undertaken at NASA Lewis Research Center with an aim at achieving a timely, reliable, and high-fidelity CFD prediction of aeropropulsion systems. The present paper specifically addresses issues relevant to internal flows in a turbine component. The flows are three dimensional, highly viscous and turbulent and the geometry is complex. We choose to discretize the computation domain with unstructured tetrahedral meshes and approximate the inviscid fluxes with the recent upwind scheme, AUSM+. An implicit discrete system of unknowns is solved by the Gauss-Seidel Jacobi iterative scheme with a coloring strategy to reduce the matrix bandwidth. A one-equation turbulence model is used to represent the Reynolds stresses. To calculate the complex flow in a turbine coolant passage, we first validate the code for unit problems that contain some subset features. The calculations show excellent results for the backward-facing step and the 180-degree-turn duct. Finally we provide a detailed analysis of the flow in the simulated geometry of th turbine coolant passage.

Identification of nonlinear B–H curves based on magnetic field computations and multigrid methods for ill-posed problems

2003 ◽  
Vol 14 (1) ◽  
pp. 15-38 ◽  
Author(s):  
BARBARA KALTENBACHER ◽  
MANFRED KALTENBACHER ◽  
STEFAN REITZINGER
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Numerical Solutions ◽  
Iterative Scheme ◽  
Three Dimensional ◽  
Multigrid Methods ◽  
Stopping Criterion ◽  
Nonlinear Inverse Problem ◽  
Field Problem ◽  
Ill Posed

Our task is the identification of the reluctivity $\nu\,{=}\,\nu(B)$ in $\vec{H}\,{=}\,\nu(B) \vec{B}$, ($B\,{=}\,|\vec{B}|$) from measurements of the magnetic flux for different excitation currents in a driving coil, in the context of a nonuniform magnetic field distribution. This is a nonlinear inverse problem and ill-posed in the sense of unstable data dependence, whose solution is done numerically by a Newton type iterative scheme, regularized by an appropriate stopping criterion. The computational complexity of this method is determined by the number of necessary forward evaluations, i.e. the number of numerical solutions to the three-dimensional magnetic field problem. We keep the effort minimal by applying a special discretization strategy to the inverse problem, based on multigrid methods for ill-posed problems. Numerical results demonstrate the efficiency of the proposed method.

Study on Hydrodynamic Torque of a Butterfly Valve

2005 ◽  
Vol 128 (1) ◽  
pp. 190-195 ◽  
Author(s):  
Ju Yeop Park ◽  
Myung Kyoon Chung
Keyword(s):  
Iterative Scheme ◽  
Three Dimensional ◽  
Physical Reality ◽  
Two Dimensional ◽  
Butterfly Valve ◽  
Valve Design ◽  
Conventional Model ◽  
Torque Coefficient ◽  
Theoretical Results ◽  
Valve Model

Since knowledge on hydrodynamic torque of a butterfly valve is very important for butterfly valve design, its hydrodynamic torque is investigated theoretically. For this, a recently developed two-dimensional butterfly valve model is solved through the free-streamline theory with a newly devised iterative scheme and the resulting two-and three-dimensional torque coefficients are compared with previous theoretical results based on the conventional butterfly valve model and experiments. Comparison shows that the improvement due to the new butterfly valve model is marginal. That is, the three-dimensional torque coefficient is well represented by the new model. Otherwise, the two-dimensional torque coefficient is well predicted by the conventional model. In spite this fact, the present results can be used in further researches on butterfly valves because the improved butterfly valve model is mathematically correct and reflects physical reality more correctly than the conventional valve model.

A Three-Dimensional Rigid-Lid Model for Closed Basins

1977 ◽  
Vol 99 (4) ◽  
pp. 656-662 ◽  
Author(s):  
S. Sengupta
Keyword(s):  
Poisson Equation ◽  
Energy Equation ◽  
Iterative Scheme ◽  
Three Dimensional ◽  
Neumann Boundary ◽  
Temperature Fields ◽  
The Poisson Equation ◽  
Horizontal Momentum ◽  
Wind Driven Circulation ◽  
Closed Basins

A numerical rigid-lid model for wind driven circulation and temperature fields in closed basins has been developed. The horizontal momentum equations each include the non-steady, non-linear inertia, Coriolis, pressure gradient and all three viscous terms. The energy equation includes the non-steady, convective and all three diffusion terms. The hydrostatic and Boussinesq approximations have been used. A Poisson equation derived from the vertically integrated horizontal momentum equations has been used as the predictive equation for surface pressure. An iterative scheme with normalization has been developed to solve the Poisson equation for pressure with Neumann boundary conditions. A vertically normalized system of equations which maps variable depth domains to a constant depth has been used. The model has been applied to a pond located near Cleveland, Ohio. The effect of topography and buoyancy on wind driven circulation has been investigated. The relative importance of the terms in the transport equations has been analyzed.

A Viscous/Inviscid Interactive Approach for the Prediction of Performance of Hydrofoils and Propellers with Nonzero Trailing Edge Thickness

2011 ◽  
Vol 55 (01) ◽  
pp. 45-63
Author(s):  
Yulin Pan ◽  
Yulin Pan
Keyword(s):  
Degrees Of Freedom ◽  
Iterative Scheme ◽  
Three Dimensional ◽  
Current Method ◽  
3D Models ◽  
Cavity Surface ◽  
Two Dimensional ◽  
Cavity Pressure ◽  
Interactive Approach ◽  
Trailing Edge

A viscous/inviscid interactive (VII) approach is applied to predict the performance of hydrofoils and propellers with nonzero trailing edge thickness. The emphasis has been put on developing VII models for flow separation. The investigation starts from a two-dimensional (2D) hydrofoil. The current method uses an iterative scheme to find a nonlifting closing extension behind the trailing edge. Two kinds of schemes are applied for the iteration process:a non-lifting extension with 1 or 2 degrees of freedom, in fully wetted condition andan extension which is treated like a cavity surface, but with a nonconstant cavity pressure distribution. The results from these schemes are compared with those from a commercial RANS Solver (Fluent). Next, the current schemes using flap extensions are extended to three-dimensional (3D) propeller flows. The 3D models are developed so that all the span-wise strips of the propeller satisfy similar conditions to those used in 2D. A propeller with significant nonzero trailing edge thickness is analyzed, using several 3D models, and the results are compared with existing experimental data.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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