Comparison of Parabolized Vorticity and Navier-Stokes Solutions in a Mildly Nonorthogonal Coordinate System.

Abstract

Two-dimensional, steady, incompressible, laminar flow in a diffuser and nozzle is considered as a model problem. A sheared mapping is used to provide a rectangular, wall-fitted, computational domain. This transformation produces a mildly nonorthogonal coordinate system in which the Navier-Stokes equations and parabolized vorticity approximation are solved. The discretization uses fourth-order accurate polynomial splines to resolve the wall boundary layer with a relatively sparse grid and standard finite differences in the main stream direction. The spline-finite difference equations are solved by line relaxation and Newton-Raphson iteration. Comparison of Navier-Stokes and parabolized vorticity results are presented for two diffusers (both with separation and reattachment of the boundary layer) and one nozzle flow. The parabolized and Navier-Stokes solutions are found to be in excellent agreement. Comparisons with a published parabolized result are also given. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Feb 17, 1982
Accession Number
ADA113912

Entities

People

  • G. H. Hoffman

Organizations

  • Pennsylvania State University

Tags

Communities of Interest

  • Materials and Manufacturing Processes
  • Weapons Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Layer
  • Classification
  • Coordinate Systems
  • Difference Equations
  • Diffusers
  • Equations
  • Equations Of Motion
  • Flow
  • Geometry
  • Grids
  • Iterations
  • Laminar Flow
  • Layers
  • Navier Stokes Equations
  • Navy
  • Two Dimensional

Fields of Study

  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Mechanics and Fluid Dynamics.