A Numerical Method for Solving Momentum Equations in Generalized Coordinates (Its Application to Three-Dimensional Separated Flows)

1985 ◽  
Vol 107 (1) ◽  
pp. 49-54 ◽  
Author(s):  
A. Nakayama
Keyword(s):  
Finite Difference ◽  
Control Volume ◽  
Three Dimensional ◽  
Separated Flow ◽  
Complex Nature ◽  
Tensor Calculus ◽  
Generalized System ◽  
Finite Difference Equations ◽  
Calculation Results ◽  
Difference Calculation

A finite difference calculation procedure has been developed for the calculations of the three-dimensional fully elliptic flows over irregular boundaries. A simple control volume analysis is introduced to reformulate the momentum equations in the generalized velocity and coordinate system, without resorting to any extensive tensor calculus. The finite difference equations are obtained by discretizing the conservation equations in this generalized system. For a practical application of the present finite difference calculation scheme, calculations are carried out on the three-dimensional separated flow in a converging-diverging rectangular duct. The calculation results reveal an extremely complex nature of the three-dimensional separated flow.

LES of Turbulent Separated Flow and Heat Transfer in a Symmetric Expansion Plane Channel

2005 ◽  
Vol 127 (5) ◽  
pp. 865-871 ◽  
Author(s):  
Kazuaki Sugawara ◽  
Hiroyuki Yoshikawa ◽  
Terukazu Ota
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Plane Channel ◽  
Separated Flow ◽  
Expansion Ratio ◽  
Vortical Flow ◽  
Flow And Heat Transfer ◽  
Finite Difference Equations ◽  
Separated And Reattached Flow ◽  
Fundamental Equations

The LES method was applied to analyze numerically an unsteady turbulent separated and reattached flow and heat transfer in a symmetric expansion plane channel of expansion ratio 2.0. The Smagorinsky model was used in the analysis and fundamental equations were discretized by means of the finite difference method, and their resulting finite difference equations were solved using the SMAC method. The calculations were conducted for Re=15,000. It is found that the present numerical results, in general, agree well with the previous experimental ones. The complicated vortical flow structures in the channel and their correlations with heat transfer characteristics are visualized through various fields of flow quantities.

LES of Turbulent Separated Flow and Heat Transfer in a Symmetric Expansion Plane Channel

2004 ◽  
Author(s):  
Kazuaki Sugawara ◽  
Hiroyuki Yoshikawa ◽  
Terukazu Ota
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Plane Channel ◽  
Separated Flow ◽  
Expansion Ratio ◽  
Vortical Flow ◽  
Flow And Heat Transfer ◽  
Finite Difference Equations ◽  
Separated And Reattached Flow ◽  
Fundamental Equations

LES method is applied to simulate numerically a turbulent separated and reattached flow and heat transfer in a symmetric expansion plane channel of expansion ratio 2.0. Smagorinsky model is used in the analysis and fundamental equations are discretized by means of the finite difference method, and their resulting finite difference equations are solved using SMAC method. The calculations are conducted for Re = 15000. It is found that the present numerical results, in general, agree well with the previous experimental ones. The complicated vortical flow structures in the channel and their correlations with heat transfer characteristics are visualized through various fields of flow quantities.

Calculation of External and Internal Transonic Flow Field of a Three-Dimensional S-Shaped Inlet

1985 ◽  
Author(s):  
Shen Huili ◽  
Luo Shijun ◽  
Ji Minggang ◽  
Xing Zongwen ◽  
Zhu Xin ◽  
...  
Keyword(s):  
Finite Difference ◽  
Flow Field ◽  
Transonic Flow ◽  
Present Method ◽  
Velocity Potential ◽  
Free Stream ◽  
Three Dimensional ◽  
Finite Difference Schemes ◽  
Finite Difference Equations ◽  
Free Stream Mach Number

A mixed finite difference method for calculating the external and internal transonic flow field around an s-shaped inlet is presented. Starting from the velocity potential equation and using Cartesian mesh and mixed finite difference schemes, the authors have obtained a system of finite difference equations and solved them with the aid of alternating line relaxations along two directions. Computations have been made for an s-shaped inlet with free stream Mach number M=0.8 at different angles of attack. Computed results are compared with those computed by perturbation method and with experimental results. Such a comparison shows that the present method is promising.

Evaluation of Selective Coolant Application for the Control of Work Roll Thermal Expansion

1985 ◽  
Vol 107 (2) ◽  
pp. 146-152 ◽  
Author(s):  
W. D. Bennon
Keyword(s):  
Thermal Expansion ◽  
Finite Difference ◽  
Control Volume ◽  
Three Dimensional ◽  
Work Roll ◽  
Cylindrical Domain ◽  
Model Formulation ◽  
Axial Distribution ◽  
Fully Implicit ◽  
Hot And Cold Rolling

A fully implicit three-dimensional, control-volume-based, finite difference model has been developed for predicting temperature distributions and thermal expansion in a rotating variable section cylindrical domain. Included in the model formulation is a technique for accommodating boundary conditions that are geometrically nonorthogonal with respect to the surface finite difference grid. Steady-state results applicable to hot and cold rolling processes are presented, with emphasis placed on the evaluation of selective coolant application as a means for controlling the axial distribution of radial roll thermal expansion.

Finite Difference Modeling of Anisotropic Flows

1995 ◽  
Vol 117 (2) ◽  
pp. 458-464 ◽  
Author(s):  
M. Keyhani ◽  
R. A. Polehn
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Taylor Expansion ◽  
Control Volume ◽  
Element Formulation ◽  
Solution Stability ◽  
The Finite Element Method ◽  
Finite Difference Equations ◽  
Anisotropic Heat Conduction ◽  
Limiting Case

A modification to the finite difference equations is proposed in modeling multidimensional flows in an anisotropic material. The method is compared to the control volume version of the Taylor expansion and the finite element formulation derived from the Galerkin weak statement. For the same number of nodes, the proposed finite difference formulation approaches the accuracy of the finite element method. For the two-dimensional case, the effect on accuracy and solution stability is approximately the same as quadrupling the number of nodes for the Taylor expansion with only a proportionately small increase in the number of computations. Excellent comparisons are made with a new limiting case exact solution modeling anisotropic heat conduction and a transient, anisotropic conduction experiment from the literature.

Finite‐difference calculation of traveltimes in three dimensions

Geophysics ◽  
1990 ◽  
Vol 55 (5) ◽  
pp. 521-526 ◽  
Author(s):  
John E. Vidale
Keyword(s):  
Finite Difference ◽  
Ray Tracing ◽  
Three Dimensional ◽  
Forward Modeling ◽  
Three Dimensions ◽  
Earthquake Location ◽  
Head Waves ◽  
Smooth Model ◽  
Numerical Grid ◽  
Difference Calculation

The traveltimes of first arriving seismic rays through most velocity structures can be computed rapidly on a three‐dimensional numerical grid by finite‐difference extrapolation. Head waves are properly treated and shadow zones are filled by the appropriate diffractions. Differences of less than 0.11 percent are found between the results of this technique and ray tracing for a complex but smooth model. This scheme has proven useful for earthquake location and shows promise as an inexpensive, well‐behaved substitute for ray tracing in forward‐modeling and Kirchhoff inversion applications.

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