CUG 1996 Spring Proceedings 65 Numerical Calculation and Visualization of Three-dimensional Flows of Engineering Interest I. Cuesta, J. Pallares, F.X. Grau, and Francesc Giralt, SEECAT, Universitat Rovira i Virgili, Tarragona, Spain. ABSTRACT: The FORTRAN CFD code 3DINAMICS has been developed to simulate momentum, mass, and heat transfer in laminar and turbulent unsteady three-dimensional flows. The code has been successfully applied to the simulation of several engineering flows, particu- larly we present four different ones: lid-driven cavity, natural convection in a cubical cavity, hydrodynamics in shallow ponds and three-dimensional transient flow in a dump combustor. Once this results have been obtained they have been interpreted converting the numerical files into pictures. In addition to the classical flow visualizations the current work explores two alter- native magnitudes to describe the structural characteristics of flows. Introduction Visualization of complex flow fields has become indispens- able for computational and experimental fluid flow researches, providing insights into data that would otherwise be impossible. Scientific visualization is therefore one of the fastest growing and most important areas of high performance computing. The visualization of three dimensional dynamic fields is still a challenge in CFD, mainly because of their vectorial character. The objective of such visualization is to portray an image of the flow structure in order to allow the identification and analysis of complex flow patterns. Several flow visualization techniques have been developed for analyzing flow fields. Such techniques may be classified into two groups according the nature of the variable of flow that is to be represent. The first group correspond to de vector vari- ables (for instance velocity) and the second contains de repre- sentation of scalar variables (pressure, temperature, etc.). The most classical way to show flow patterns has been the representation of the direction and magnitude of the velocity vectors and the lagrangian representation of the dynamic field by particle tracing: streamlines, pathlines, streaklines, etc. The purpose of this study is to characterize numerically four different flows; the lid-driven cavity, the natural convection in a cubical cavity, the hydrodynamics in shallow ponds and the transient flow in a dump combustor. The topology of the different types of structures is examined incorporating the representation of the second invariant of the velocity gradient into the previously standard plotting techniques. Governing equations In all of the four cases the flow is considered incompressible and the variation of fluid properties with temperature has been neglected, with the only exception of the buoyancy term for natural convection flow, for which the Boussinesq approxima- tion has been adopted. As a result, the Navier-Stokes and the energy transport equations are coupled only by the body force term, where linear dependence of density with temperature is assumed. All flows evolve in time t and are described in terms of the velocity u i at any position x i , pressure P, and temperature T (for non-isothermal calculations). The set of elliptic partial differen- tial equations governing a single-phase, constant property incompressible flow in cartesian coordinates may be written as: Continuity equation (1) Momentum (2) Energy (3) where v is the fuid kinematic viscosity, g i the gravitational acceleration and α the thermal diffusivity. i ∂u i ∂x = 0 ∂ i u ∂t + ∂ j u i u ( 29 j ∂x =- 1 ρ ∂P ∂ i x + ν 2 ∂ i u j ∂x j ∂x + i g ∂T ∂t + ∂ j uT ( 29 j ∂x =α 2 ∂ T j ∂x j ∂x