Analysis of Two-Dimensional Incompressible Flow Past Airfoils Using Unsteady Navier-Stokes Equations

Abstract

The conservative form of the unsteady NavierStokes equations in terms of vorticity and stream function in generalized curvilinear coordinates are used to analyze the flow structure of steady separation and unsteady flow with massive separation. The numerical method solves the discretized equations using an ADI-BGE method. The method.is applied to a symmetric 12 percent thick Joukowski airfoil. A conformal clustered grid is generated; several 1-D stretching transformations are used to obtain a grid that attempts to resolve many of the multiple scales of the unsteady flow with massive separation, while maintaining the transformation metrics to be smooth and continuous in the entire flow field. Detailed numerical results are obtained for three flow configurations (1) Re = 1000, a = 5°, (ii) Re = 1000, a -15°, (iii) Re -10,000, a = 5°.Ho artificial dissipation was added; however, lack of a fine grid in the normal direction has presently led to results which are considered qualitative, especially for case (iii).

An Improved Navier-Stokes Procedure for Analysis of Two-Dimensional Aerofoils in Laminar and Turbulent Flows

“…65 6 30 and 120 6 60, give identical results. The excellent agreement with the results of Ghia et al 18 con®rms that the present method is accurate and ef®cient. For turbulent¯ows, three different aerofoil sections, namely an NACA 4412 and two models of Nakayama, 19 have been chosen for comparison, mainly because they provide extensive data both on the aerofoil and in the wake.…”

Physics of forced unsteady flow for a NACA 0015 airfoil undergoing constant-rate pitch-up motion

“…In the earlier studies (Ghia et al, 1992;Osswald et al, 1990) by the authors, all spatial derivatives were approximated using central differences. In the present study, the convective derivatives in the vorticity transport equation ( 10) are approximated using a third-order biased UDS, with all other spatial derivatives stilI being approximated using CDS.…”

“…In light of the review article by Carr (1988), no attempt has been made in the present paper to review some of the noteworthy contributions made to this subject in the past. Ghia et al (1992) recently presented some preliminary results of their unsteady NS analysis using the vorticity stream function formulation. A brief discussion of their analysis is given in the next two sections.…”

“…(3) To determine the physical mechanism involved in moment stall, with the ultimate goal of revealing aerodynamic mechanisms to delay or mediate its effect. Osswald et al (1990) modified their earlier analyses (Ghia et al, 1985;Osswald et aI., 1985) for fixed body flows to now permit arbitrary six degree-of-freedom maneuvers. The general 3D analysis of Osswald et al (1990) is in terms of velocity and vorticity variables.…”

Simulation of Self-Induced Unsteady Motion in the Near Wake of a Joukowski Airfoil

“…Ghia, Osswald and U. Ghia (1985a) analyzed massively separated flow past a 12 percent thick Joukowski airfoil using a symmetric C-grid. The Reynolds number 3 H ranged from 10 to 10 and the angle of attack a was varied up to 10°.…”