Computation of flow around wings based on the Euler equations

TLDR

Inviscid transonic flows with strong shocks or complex vortices require the Euler equations as a realistic model. The study introduces WINGA2, a computational procedure that solves the Euler equations for transonic aircraft flow on a 0–0 mesh generated by transfinite interpolation. WINGA2 employs an explicit time‑marching finite‑volume scheme with a non‑reflecting far‑field boundary, temporal damping, artificial viscosity, and is validated on the CYBER 205 vector processor for steady‑state convergence. The method converges to a steady state and, on the ONERA M6 wing, the Euler model predicts a tip vortex arising from flow separation at the tip where curvature vanishes.

Abstract

Inviscid transonic flows containing either strong shock waves or complex vortex structure call for the Euler equations as a realistic model. We present here a computational procedure, termed WINGA2, for solving the Euler equations for transonic flow around aircraft upon a 0–0 mesh generated by transfinite interpolation. An explicit time-marching finite-volume technique solves the flow equations and features a non-reflecting far-field boundary condition and an internal mechanism for temporal damping together with a model for artificial viscosity. The method's convergence to a steady state is studied, and results computed on the CYBER 205 vector processor are presented. The Euler equation model is found to predict the existence of a tip vortex created by flow separating from the downstream region of the tip of the ONERA M6 wing where the radius of curvature approaches zero.