Numerical calculations for flows past an unconventional airfoil

Abstract

A computer program has been developed for both two-dimensional compressible and incompressible turbulent flows around airfoils. Numerical solutions have been obtained by solving the steady-state Reynolds-averaged Navier-Stokes equations in primitive variable form. The standard k-$\varepsilon$ turbulence model was employed and a compression turbulence model was also discussed. Based on a non-staggered arrangement on a body-fitted grid system, the discretized transport equations were solved either by a hybrid or a second-order upwind differencing scheme. A multiple pressure correction procedure with implicit density treatment has been used. The solutions were obtained through an under-relaxed iterative process.

Various cases of flow past NACA 0012 and 4412 airfoils were examined first. The experimental data available included cases with freestream Mach numbers varying from 0 to 0.799, the chord Reynolds number up to 9 $\times$ 10$\sp6$, and the angle of attack ranging from 0$\sp\circ$ to 13.87$\sp\circ$. The results were good when compared with experimental data. Many cases of incompressible and compressible flows past an unconventional airfoil were then computed. The freestream Mach number varied from 0 to 0.9 with the chord Reynolds number of 3.9 $\times$ 10$\sp6$. The general behavior of the unconventional airfoil is presented.