Kunio Kuwahara

Three-dimensional computation of unsteady flows around a square cylinder

Tetsuro Tamura ORI, Shimizu Corporation, 2-2-2 Uchisaiwai-cho, Chiyoda-ku, Tokyo 100, Japan Egon Krause Aerodynarnisches Institut, RWTH Aachen, WOllnerstraBe zw, 5. u. 7, Aachen, West Germany Susumu Shirayarna and Katsuya Ishii Institute of Computational Fluid Dynamics, 1-22-3 Haramachi, Meguro-ku, Tokyo 152, Japan Kunio Kuwahara The Institute of Space and Astronautical Science, 3-I-1 Yoshinodai, Sagamihara-shi, Kanagawa 229, Japan

Flow visualization in computational fluid dynamics

Several flow visualization techniques using the Lagran gian approach are proposed for analyzing the numerical solutions of unsteady flow fields computed by the Eu lerian approach. We show how these methods can be used to assess the validity of solutions and to extract the nature of the flow fields. The numerical algorithms for the flow solver and the flow visualization are introduced. The incompressible Navier-Stokes equations are solved using the extended MAC method and the compressible Euler equations are solved using the TVD MacCormack method. Most of the flow visualization methods are conventional. For vector fields, however, we introduce a particle tracing algorithm that is suitable for large amounts of numerical data. We present four flow visu alizations using these methods: flow past a circular cyl inder in two dimensions, shock wave propagation over a circular cylinder, flow past a sphere, and flow around an entire automobile.

Computational Study of Three-Dimensional Wake Structure

Three-dimensional wake structure is studied by numerically solving the incompressible Navier-Stokes equations. Results are visualized by a three-dimensional color graphic system. It was found that a pair of vortex tubes separated from a body plays the most important role in the wake. Near the body vortex tubes are rather stable, however, they gradually become unsteady as they flow down.

Computational study of flow in a curved pipe with circular cross section

Laminar imcompressible flows in a circular sectioned pipe were investigated by seeking numerical solutions to the Navier-Stokes equations. Three semi-circular pipes of radius ratios 0.05, 0.143 and 0.148 were studied. These calculations covered the Dean number ranging from 183 to 3847. In the range of low and medium Dean numbers, a steady-state solution was obtained; when the Dean number was high, a three-dimensional separation and the associated secondary flow were clearly observed far downstream near the outlet. Extensive flow visualizations were made to depict the computed results.

Direct Simulation of High-Reynolds-Number Flows by Finite-Difference Methods

At high Reynolds numbers, it is very difficult to solve the Navier-Stokes equations because of its numerical instability. This difficulty is due to the very small viscous diffusion. The eddy viscosity moEnl introduces a rather large diffusion into the system, which stabilizes the computation. It is natural to ask whether the high-Reynoldsnumber flow fields can be obtained without introducing a turbulence moEnl or sub-grid moEnling.

An Algorithm for Searching Points on Generalized Curvilinear Coordinate System and its Application to Flow Visualization

This paper describes a useful algorithm for searching points on generalized curvilinear coordinate systems, which are used in finite difference methods. With this algorithm one can compute computational coordinates of arbitrary points, whose physical coordinates are given, very fast and precisely. Once the computational coordinates are known, physical quantities at those points can be interpolated from the data of surrounding grid points. Then, this algorithm is applicable to any stage of simulations; integration of Navier-Stokes equation and pre/post processing of the data.