Comparison of supercritical airfoil flow calculations with wind tunnel results
Navier-Stokes calculations are performed for a supercritical airfoil at transonic design and subsonic condi- tions. Wind tunnel pressure-rail measurements are employed as boundary data in the calculations to account for wall-interference effects. A fine mesh is used so that most details of the flows were resolved, with particular at- tention given to the trailing-edge region. Detailed comparisons are made with the experimental data. Good agreement was obtained on the airfoil except at the trailing edge where separation occurred. Flow details in the trailing-edge region are examined and differences are shown to be attributable to the turbulence model employed. UPERCRITICAL airfoils are characterized by a nearly flat upper surface over a large midchord distance and a pronounced camber near the trailing edge. These character- istics combine to make the performance of these airfoils very sensitive to wind tunnel wall interference effects, viscous ef- fects, and small changes in Mach number and angle of at- tack. Because of the relatively flat upper surface, shock posi- tion is quite sensitive to wall interference. Because of the aft camber, there exists a strong adverse pressure gradient near the trailing edge. This leads to a thickening and, often, to a separation of the upper-surface boundary layer. Also, because of the aft camber, significant static-pressure dif- ferences exist across the near wake. Inter ferometric measurements by Spaid and Bachalo1 and the laser- velocimeter results of Johnson and Spaid2 have verified the existence of these pressure differences. The pressure dif- ference across the wake is, of course, related to wake cur- vature, and it has been suggested that curvature effects are important in the prediction of surface-pressure distri- butions.3'4 A supercritical airfoil section thus presents a predictive method with many difficulties. To date, predictions have not compared well with wind tunnel data, as evidenced by the results presented in Ref. 5. Since the numerical solutions were for free-air flows, wall-interference effects in the data could be a factor in the poor comparison. Other possible contributors are improper turbulence closure models and in- adequate spatial resolution. Thus, questions arise as to the validity of such comparisons. The present effort will attempt to resolve some of these questions. Navier-Stokes calculations are performed on a fine mesh. Wind tunnel wall effects are simulated by using measured pressures as boundary data along the upper and lower computational boundaries. Johnson and Spaid2 have obtained extensive measurements for the DSMA 671 super- critical section. Turbulence properties and mean velocities were measured in the boundary layer and wake. These data thus offer an excellent opportunity for detailed comparison with calculated results. Because a fine mesh is used and the wall effects are accounted for, any substantial differences be- tween experimental results and calculations should be at- tributable primarily to inadequacies in the turbulence model. Since experimental data are imposed on the outer computa- tional boundary, such an approach falls short of being an in- dependent predictive tool. Nevertheless, the method is useful in that: 1) direct comparisons between numerical and ex- perimental results may be made; 2) by also performing free- air calculations, differences between interference-free and confined flows may be illustrated; and 3) turbulence researchers are provided with a tool to enable valid com- parisons of measured and modeled turbulence properties on an airfoil. Other methods have been developed to eliminate or reduce wall-interference effects in transonic flow. Of particular in- terest here are the correction methods developed by Kemp 6"8 and Murman.9 In these methods, flowfield and surface- pressure measurements are employed to calculate either an effective airfoil shape or velocity jumps between the upper and lower surfaces. These are then used in free-air inviscid calculations to determine the angle of attack and Mach number that best fit the surface measurements. Through use of the measured pressures, these methods accommodate wall effects without recourse to modeling the wall-flow processes. They also account, at least partially, for viscous effects. However, interference and viscous effects may render the measured pressures on the airfoil incompatible with any in- viscid free-air solution, in which case correction methods are not applicable. If corrected values of Mach number and angle of attack can be found, an equivalent free-air solution can be computed using the Navier-Stokes code. Comparison of this solution with experiment and the pressure-boundary- condition solution provides insight into the correctability of these supercritical airfoil flows.