Calculation of flows in two-and three-dimensional nozzles by the approximate factorization method

1985 ◽  
Vol 25 (5) ◽  
pp. 56-67
Author(s):  
M.Ya. Ivanov ◽  
V.V. Koretskii
Keyword(s):  
Three Dimensional ◽  
Factorization Method ◽  
Approximate Factorization

Numerical Simulation of Viscous Flow-Field in Cascade Using Thin-Layer Equations and AF Method

1999 ◽  
Author(s):  
Yumin Xiao ◽  
R. S. Amano
Keyword(s):  
Flow Field ◽  
Boundary Conditions ◽  
Viscous Flow ◽  
Secondary Flow ◽  
Three Dimensional ◽  
Factorization Method ◽  
Computational Domain ◽  
Approximate Factorization ◽  
Calculation Results ◽  
Transonic Cascade

Abstract In this paper an implicit 3-D solver for computations of a viscous flow has been developed and the computations of the flow between blade passage are presented. This method employs an AF (Approximate Factorization) method in which four techniques are incorporated to speed up convergence to the steady-state solutions: (1) body-fitted H-grid; (2) artificial viscosity; (3) implicit residual smoothing; and (4) local time-stepping. The two-dimensional pseudo-characteristic method was used to determine the inlet and outlet boundary conditions of the computational domain and the periodic boundary conditions were used at inter-boards. The validation cases include subsonic and transonic viscous flows in C3X cascade. Results for these turbine cascade flows are presented and compared with experiments at corresponding conditions. Computed pressure distributions on blade surfaces show good agreement with the published experimental data. This method was further applied to a three-dimensional case and demonstrated the code capability for predicting the secondary flow in a 3-D transonic flow-field. From these computations it was found that the proposed method possesses superior convergence characteristics and can be extended to unsteady flow calculations. Finally, it was observed that the three-dimensional calculation results show that the secondary flow mechanism in a transonic cascade seems to be quit different from those, in a subsonic case.

An Implicit Algorithm for Stator-Rotor Interaction Analysis

1996 ◽  
Author(s):  
V. Michelassi ◽  
P. Adami ◽  
F. Martelli
Keyword(s):  
Interaction Analysis ◽  
Experimental Testing ◽  
Three Dimensional ◽  
Factorization Method ◽  
Steady Flows ◽  
Turbine Stage ◽  
Approximate Factorization ◽  
Time Step ◽  
Physical Time ◽  
Speed And Accuracy

A simple time-accurate algorithm is presented for the computation of the unsteady stator-rotor interaction. The algorithm is based on the scalar approximate factorization method originally developed for the computation of complex three-dimensional steady flows. The method introduces a physical time step, used to march in time, and a numerical time step to iterate in between physical time steps. The method is formulated so as to take full advantage of the implicit formulation and provide an implicit treatment of the unsteady terms. A set of preliminary tests on a turbine stage, still in the experimental testing phase, proved the speed and accuracy of the method which was able to capture the essential features of a transonic stage.

scholarly journals Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Trung Truong
Keyword(s):  
Inverse Scattering ◽  
Maxwell Equations ◽  
Field Data ◽  
Periodic Structures ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Unique Determination

AbstractThis paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

scholarly journals Implicit Euler Method for Three-Dimensional Turbomachinery Flow Calculation

1993 ◽  
Author(s):  
Shih H. Chen ◽  
Anthony H. Eastland
Keyword(s):  
Three Dimensional ◽  
Prediction Method ◽  
Minimum Cost ◽  
Inviscid Flow ◽  
Turnaround Time ◽  
Euler Method ◽  
Second Order ◽  
Approximate Factorization ◽  
Implicit Euler Method ◽  
Numerical Instabilities

A compressible three-dimensional implicit Euler solution method for turbomachinery flows has been developed. The goal of the present study is to develop an efficient and reliable method that can be used to replace the semi-empirical, semi-analytical quasi-three-dimensional turbomachinery flow prediction method currently being used for multi-stage turbomachinery design at early design stages. Currently, a methodology has been developed based on an inviscid flow model (Euler solver) and tested on single blade rows for validation. The method presented here is derived from the Beam and Warming implicit approximate factorization (AF) finite difference algorithm. To avoid high frequency numerical instabilities associated with the use of central differencing schemes to obtain a spatial second order accuracy, a combined explicit and implicit artificial dissipation model is adopted. This model consists of a second order implicit dissipation and mixed second/fourth order explicit dissipation terms. A Cartesian coordinate H-grid generated by a three-dimensional interactive grid generator developed by Beach is used. Results for SSME High Pressure Fuel Turbine are presented and the comparison with experimental data is discussed. The use of the present implicit Euler method and the three-dimensional turbomachinery interactive grid generator shows that turnaround time could be as short as one day using a workstation. This allows the designers to explore optimal design configurations at minimum cost.

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