Modification of the unsteady flow field predicted by transonic small distrubance equations using a NavierStokes solution of the steady flow field
Abstract
The first part of this report describes a numerical solution of the NavierStokes equations for flow over a thick supercritical airfoil with strong shockinduced separation on upper and lower surfaces. The separated flow region extends from the shock (approx 50 pct chord) to the trailing edge on both surfaces. The solution algorithm employed was an explicit predictorcorrector method. An algebraic turbulence model was used to describe the turbulent Reynolds stresses. The treatment of the eddyviscosity behavior through the shock, in the separated regions over the airfoil and in the near wake was the critical step for a successful solution. Many approaches have been used to extend the useful range of 2D, unsteady transonic small disturbances (TSD) procedures. The second part of the report describes another such procedure. Modifications to the TSD procedure, LTRAN2, that allow the procedure to determine the geometry corresponding to the prescibed pressure distribution from experimental data or as predicted by a NavierStokes solver are described. The new geometry accounts for compressible and viscous effects and is a much improved starting point for unsteady calculations. The TSD governing equations and boundary equations are reviewed, and then the modifications required for the inverse geometry definition are described. Results for three different airfoils (NACA 0012, NACA 64A010 and NLR 7301) are presented and discussed. A summary of the results, and recommendations for additional work are provided.
 Publication:

Ph.D. Thesis
 Pub Date:
 1987
 Bibcode:
 1987PhDT........43K
 Keywords:

 Flow Distribution;
 NavierStokes Equation;
 Small Perturbation Flow;
 Steady Flow;
 Transonic Flow;
 Unsteady Flow;
 Algorithms;
 Separated Flow;
 Supercritical Airfoils;
 Thickness;
 Turbulence Models;
 Fluid Mechanics and Heat Transfer