Effects of aspect ratio and sidewall boundary-layer in airfoil testing

Abstract

A correction to account for the sidewall boundary-layer effects in two-dimensional airfoil testing is presented by taking into consideration the nonlinear variation of the crossflow velocity across the width of the tunnel. The crossflow effects in the wind tunnel are represented in an empirical manner by considering the inviscid, compressible flow between a straight and a wavy wall. The analysis shows significant reduction in sidewall boundary-layer effects on airfoil midspan measurements with increasing aspect ratio of the model. Application of the correction to wind-tunnel data on airfoils demonstrated the method to be satisfactory in correlating shock location and also in giving good agreement between the measured pressure distribution and computed free air predictions. shed due to loss of lift in the boundary layer and a consequent change in the effective angle of incidence. The second approach, proposed independently by Barn well2 and Winter and Smith,3 assumes the changes in the boundary-layer thickness due to model-induced pressure field to have a significant effect on the flow over the airfoil. Using the small disturbance equation and accounting for the changes in the width of the flow passage, Barnwell presented a simplified correction for the measured forces in the form of a modified Prandtl-Glauret rule to account for the attached sidewall boundary-layer effects. Barn well's correction gave good agreement with the experiments of Bernard-Guell e4 at low Mach numbers. Sewall5 extended Barn well's approach to transonic speeds using the von Karman similarity parameter. Recently, an alternative simpler form of the correction encompassing both the Barnwell and Sewall methods has been proposed by Murthy.6 The Barnwell-Sewall correction appears to be effective in giving a satisfactory comparison between the measured and calculated pressure distributions on several airfoils tested in the NASA Langley 0.3-m Transonic Cryo- genic Tunnel.79 These studies suggest that the change in the sidewall boundary-layer thickness due to the airfoil pressure field can be a significant source of blockage correction, particularly at transonic speeds. The Barnwell-Sewall correction has been derived under certain assumptions of simplified boundary-layer treatment and linear variation of the crossflow velocity across the width of the tunnel. These assumptions imply that the airfoil chord is sufficiently large so that the effect of the sidewall boundary layers can be considered to be quasi-one-dimensional. Barn- well10 has shown recently that the linear crossflow assumption is justified provided (4d*/b)(b/c)2 is small. Hence, this assumption is likely to become less accurate when the width of the tunnel is much larger than the airfoil chord (i.e., for high- aspect-ratio models).