Steady and unsteady internal flow computations via the solution of the compressible Navier Stokes equations for low Mach numbers
Abstract
The objective is to approximate imcompressible flow fields by low Mach number compressible solutions in order to solve unsteady internal flow problems. The advantage of this approach is that certain difficulties associated with the numerical solution of incompressible interal flows, such as the treatment of the pressure terms, are overcome. The full unsteady compressible NavierStokes equations are solved numerically for axisymmetric flows. The conservation law form of the governing equation is used and the calculations performed on a curvilinear coordinates system. The numerical integration is achieved with an implicit finite difference scheme using approximate factorization and alternate direction implicit techniques. Steady state solutions were obtained first for a variety of internal flow problems: flows in ducts with smooth constrictions, suddenly expanding ducts and dusts with a step constriction. The low Mach number compressible results are compared with available experimental data and incompressible solutions. The first test for the unsteady calculations was to approximate the classical incompressible Womersley flow by a low Mach number unsteady compressible solution. The agreement of the numerical results with the analytical solution was satisfactory.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1987
 Bibcode:
 1987PhDT........13E
 Keywords:

 Computational Fluid Dynamics;
 Ducts;
 Incompressible Flow;
 NavierStokes Equation;
 Numerical Analysis;
 Conservation Laws;
 Finite Difference Theory;
 Mach Number;
 Fluid Mechanics and Heat Transfer