Computation of Three-Dimensional Time-Dependent Flow Using the Euler Equations


Book Description

The development of a computer program to solve the three-dimensional, unsteady Euler equations is described. A finite volume method in Cartesian coordinates is used with the MacCormack predictor-corrector algorithm. The grid imposed on the computational domain is topologically equivalent to a regular grid on a cube. The resulting control volumes are hexahedrones with quadrilateral faces. Solutions are presented to show the accuracy of the computer program and to demonstrate the degree of flexibility with respect to complex model geometry. (Author).




Computation of Three-Dimensional Transonic Internal Flow in Cylindrical Coordinates


Book Description

The Euler equations for the inviscid rotational flow of a perfect gas are solved for three-dimensional subsonic-transonic internal flow by use of a time-dependent numerical technique. The numerical approach, which is an extension and modification of that of Cline for two-dimensional flows, is based on the use of the MacCormack finite-difference method for the interior field points. The reference-plane method of characteristics is used for coupling the interior field solution to the boundary points. Both the basic equations and the numerical procedures are described, as is the computer program which was written in FORTRAN IV language for either the Cray-1 or the IBM 370/165 computer. As presently written, the program is applicable to the computation of three-dimensional flow in both axisymmetric and relatively simple three-dimensional nozzle geometries. The validity of the computer program was established by computing, in various ways, an axisymmetric nozzle flow as a three-dimensional flow; the numerical results are in good agreement with the results from a well-established computer program for axisymmetric flow. (Author).







Three-dimensional, Time-dependent, Compressible, Turbulent, Integral Boundary-layer Equations in General Curvilinear Coordinates and Their Numerical Solution


Book Description

A method is presented for computing three-dimensional, time-dependent, compressible, turbulent boundary layers in nonorthogonal curvilinear coordinates. An integral method is employed in the interest of computational speed and because the three-dimensional method is an extension of an existing two-dimensional method. After presenting a detailed derivation of the integral form of the boundary-layer equations, the necessary auxiliary relations are given along with the relationships between integral lengths expressed in streamline and nonorthogonal coordinates. A time dependent approach is used to account for time accuracy (if desired) and to provide a method that is compatible with the surface grid used by an inviscid solver for use in viscous-inviscid interaction calculations. The equations are solved using a Runge-Kutta scheme with local time stepping to accelerate convergence. Stability and convergence of the numerical scheme are examined for various space differences compared with measurements and with computations of previous investigators.




Computation of Three-Dimensional Complex Flows


Book Description

Der Sammelband enthält Beiträge einer Tagung über die Simulation von dreidimensionalen Flüssigkeiten. Sie geben einen Überblick über den Stand des Wissens auf dem Gebiet der numerischen Simulation der Turbulenz, angewandt auf eine weite Spanne von Problemen wie Aerodynamik, Nicht-Newtonsche Flüssigkeiten, Konvektion.This volume contains the material presented at the IMACS-COST Conference on CFD, Three-Dimensional Complex Flows, held in Lausanne (Switzerland), September 13 - 15, 1995. It gives an overview of the current state of numerical simulation and turbulence modelling applied to a wide range of fluid flow problems such as an example aerodynamics, non-Newtonian flows, transition, thermal convection.










A 3-Dimensional Navier-Stokes-Euler Code for Blunt-Body Flow Computations


Book Description

The shock-layer flowfield is obtained with or without viscous and heat-conducting dissipations from the conservative laws of fluid dynamics equations using a shock-fitting implicity finite-difference technique. The governing equations are cast in curvilinear-orthogonal coordinates and transformed to the domain between the shock and the body. Another set of equations is used for the singular coordinate axis, which, together with a cone generator away from the stagnation point, encloses the computation domain. A time-dependent alternating direction implicit factorization technique is applied to integrate the equations with local-time increment until a steady solution is reached. The shock location is updated after the flowfield computation, but the wall conditions are implemented into the implicit procedure. Innovative procedures are introduced to define the initial flowfield, to treat both perfect and equilibrium gases, to advance the solution on a coarse-to-fine grid sequence, and to start viscous flow computations from their corresponding inviscid solutions. The results are obtained from a grid no greater than 28 by 18 by 7 and converged within 300 integration steps. They are of sufficient accuracy to start parabolized Navier-Stokes or Euler calculations beyond the nose region, to compare with flight and wind-tunnel data, and to evaluate conceptual designs of reentry spacecraft. Li, C. P. Johnson Space Center NASA-TM-58266, S-546, NAS 1.15:58266 RTOP 506-51-17-00-72...