A method for modifying two-dimensional adaptive wind-tunnel walls including analytical and experimental verification

The theoretical development of a simple and consistent method for removing the interference in adaptive-wall wind tunnels is reported. A Cauchy integral formulation of the velocities in an imaginary infinite extension of the real wind-tunnel flow is obtained and evaluated on a closed contour dividing the real and imaginary flow. The contour consists of the upper and lower effective wind-tunnel walls (wall plus boundary-layer displacement thickness) and upstream and downstream boundaries perpendicular to the axial tunnel flow. The resulting integral expressions for the streamwise and normal perturbation velocities on the contour are integrated by assuming a linear variation of the velocities between data-measurement stations along the contour. In an iterative process, the velocity components calculated on the upper and lower boundaries are then used to correct the shape of the wall to remove the interference. Convergence of the technique is shown numerically for the cases of a circular cylinder and a lifting and nonlifting NACA 0012 airfoil in incompressible flow. Experimental convergence at a transonic Mach number is demonstrated by using an NACA 0012 airfoil at zero lift.