A SOLUTION FOR THREE-DIMENSIONAL VORTEX FLOWS WITH STRONG CIRCULATION

Abstract

The Navier-Stokes equations for a viscous, incompressible fluid are considered for a steady, axisymmetric flow composed of a strong rotation combined with radial sink flow which exhausts axially inside a finite radius. The equations are reduced to two coupled partial differential equations in terms of the stream function and circulation. The equations contain three dimensionless parameters: the radial Reynolds number, a characteristic ratio of mass flow per unit length to circulation, and a characteristic ratio of an axial dimension to a radial dimension. The product of these last two dimensionless parameters is used as a new expansion parameter for generating an asymptotic series solution. To zeroth order in this parameter, the solution for the stream function is a linear distribution between two axial boundary values. First-order correction terms are calculated for a specific example. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 20, 1962
Accession Number
AD0276097

Entities

People

  • W.s. Lewellen

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Axisymmetric Flow
  • Differential Equations
  • Equations
  • Flow
  • Mass Flow
  • Navier Stokes Equations
  • Partial Differential Equations
  • Reynolds Number
  • Three Dimensional

Fields of Study

  • Mathematics
  • Physics

Readers

  • Aerodynamics.
  • Combustion and Flow Dynamics.
  • Structural Dynamics.