On turbulence modeling for unsteady transonic flows

Abstract

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.

Numerical investigation of the compressible flow past an aerofoil

“…The selected parameters are the same as those performed in experiments (e.g. McDevitt et al 1976;Levy 1978;Marvin et al 1980). The relevant experimental data will thus be employed to validate the present calculation.…”

“…To validate the present simulation, we compare numerical results and experimental data (McDevitt et al 1976;McDevitt 1979;Marvin et al 1980) in terms of the frequency of shock motion, averaged pressure coefficient, mean velocity and turbulent shear stress, as well as some quantities related to the shock wave motion, which will be shown in the following section. Assessments of the effect of time step are performed on the calculated solutions.…”

“…As the flow considered here has a high Reynolds number Re ∼ O(10 7 ) (McDevitt et al 1976;Levy 1978;Marvin et al 1980), the methodology used is a significant issue in numerical simulations. Recent advances in the DES have provided a powerful tool for studying high-Reynolds-number flows and have comprehensively been surveyed by Spalart (2009).…”

“…Tijdeman & Seebass (1980) have classified the shock wave motions as being of three types, i.e. type A, B and C. Previous experimental studies of transonic flow over an 18 % thick circular-arc aerofoil at zero incidence have indicated that upstream-propagating shock waves occur alternately on the upper and lower surfaces for a certain range of the free-stream Mach number (McDevitt, Levy & Deiwert 1976;Levy 1978;McDevitt 1979;Marvin, Levy & Seegmiller 1980), which belongs to type C. Moreover, some numerical simulations have been performed using the time-dependent twodimensional Reynolds-averaged Navier-Stokes (RANS) equations with turbulence models (e.g. Marvin et al 1980;Rumsey et al 1996;Xiao, Tsai & Liu 2003).…”

“…The present work investigates the compressible flow past an 18 % thick circular-arc aerofoil for a free-stream Mach number M ∞ = 0.76 and a Reynolds number Re = 1.1 × 10 7 , corresponding to experiments (McDevitt et al 1976;Levy 1978;McDevitt 1979;Marvin et al 1980). The three-dimensional Favre-averaged compressible Navier-Stokes equations are solved numerically by means of a finitevolume approach (Lu et al 2005) combined with shock capture technique (Hill, Pantano & Pullin 2006).…”