An experimental and computational investigation of the steady and unsteady transonic flowfields about a thick airfoil is described. An operational computer code for solving the two-dimensional, compressible Navier-Stokes equations for flow over airfoils was modified to include solid-wall, slip-flow boundary conditions to properly assess the code and help guide the development of improved turbulence models. Steady and unsteady fiowfieids about an 18% thick circular arc airfoil at Mach numbers of 0.720, 0.754, and 0.783 and a chord Reynolds number of 11 x 10 6 are predicted and compared with experiment. Results from comparisons with experimental pressure and skin-friction distributions show improved agreement when including test-section wall boundaries in the computations. Steady-flow results were in good quantitative agreement with experimental data for flow conditions which result in relatively small regions of separated flow. For flows with larger regions of separated flow, improvements in turbulence modeling are required before good agreement with experiment will be obtained. For the first time, computed results for unsteady turbulent flows with separation caused by a shock wave were obtained which qualitatively reproduce the time-dependent aspects of experiments. Features such as the intensity and reduced frequency of airfoil surface-pressure fluctuations, oscillatory regions of trailing-edge and shock-induced separation, and the Mach number range for unsteady flows were all qualitatively reproduced.
Conditionally sampled, ensemble-averaged velocity measurements, made with a laser velocimeter, were taken in the flowfield over the rear half of an 18°70thick circular arc airfoil at zero incidence tested at M= 0.76 and at a Reynolds number based on chord of !1 × 10 6. Data for one cycle of periodic unsteady flow having a reduced frequency f of 0.49 are analyzed. A series of compression waves, which develop in the early stages of the cycle, strengthen and coalesce into a strong shock wave that moves toward the airfoil leading edge. A thick shear layer forms downstream of the shock wave. The kinetic energy and shear stresses increase dramatically, reach a maximum when dissipation and diffusion of the turbulence exceed production, and then decrease substantially. The response time of the turbulence to the changes brought about by the shock-wave passage upstream depends on the shock-wave strength and position in the boundary layer. The cycle completes itself when the shock wave passes the midchord, weakens, and the shear layer collapses. Remarkably good comparisons are found with computations that employ the time-dependent Reynolds averaged form of the Navier-Stokes equations using an algebraic eddy viscosity model, developed for steady flows.
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