An experimental and numerical investigation of a turbulent airfoil wake in a 90° curved duct

Abstract

A wake behind solid bodies subjected to extra rates of strain due to streamwise curvature and pressure gradient occurs in numerous engineering applications. The broad aim of this experimental and numerical study was to improve the present understanding of an airfoil wake subjected to simultaneous effects of streamwise curvature and pressure gradient. The experimental work was conducted using an open return type wind tunnel, which consisted of a square closed working test section incorporating a straight upstream tangent and a 90° bend with radius to height ratio of 1.17. A symmetrical NACA 0012 airfoil of 0.150 m chord length was used as the wake generating body, where the trailing edge of which was located at a distance of one chord length upstream of the bend entry plane. The measurement stations, 1 to 5, were located at one duct height upstream of the bend, at 0°, 45°, 90° and also at one duct height downstream of the bend. At each station, the mean and turbulence quantities were obtained in both normal (radial) and spanwise directions using hot-wire anemometry. The measured turbulence quantities were the normal intensities u'2(bar) , v'2(bar) , w'2(bar) and turbulence shear stresses -u'v'(bar) and - u'W'(bar). In addition, the static pressure distributions along the concave and convex walls of the test section, on the airfoil and in the normal (radial) direction at each station were measured. The measurements were carried out at three mainstream velocities, namely, 10, 15 and 20 m/s. In the numerical part of the work, the three-dimensional, incompressible, steady state and turbulent flow in the duct with the airfoil was computed using four different turbulence models, namely, the standard k-e model, Reynolds Stress Model, Realizable k-e model and RNG k-e model. The mean and turbulence quantities obtained experimentally at one duct height upstream of the bend were used as the inlet boundary conditions for the simulation. The discretisation of the governing equations was based on the finite volume technique where two discretisation schemes, namely, QUICK and upwind were used in conjunction with the above turbulence models. The modelling of the turbulent flow near the walls was achieved using the two-layer zonal model. The profiles obtained experimentally in the spanwise direction showed that the mean and turbulence quantities were symmetrical with respect to the central plane (z/H = 0.5) of the flow domain. The normal profiles at two spanwise locations, namely, z/H = 0.5 and 0.6 at each measuring station showed an asymmetric wake structure about the wake centreline due to the simultaneous effects of streamwise curvature and pressure gradient. The results showed that the turbulence intensities and shear stresses were affected strongly by the combined curvature and pressure gradient. The three-dimensional computation predicted the overall features of the flow satisfactorily. All turbulence models predicted the trends exhibited in the experimental static pressure distribution on the concave and convex walls closely. However, at each measuring station, the peak value and the shift of the wake region were over-predicted by all turbulence models. The predicted Reynolds stresses u'2(bar) , v'2(bar) , w'2(bar) and - u'v'(bar) showed good agreement with the experimental profiles at stations 2 to 4. The comparison with the standard k-c model confirmed that the additional terms and functions in the RNG and Realizable k-E models can significantly improve the prediction of complex flows. Also, the use of the two-layer zonal model on the airfoil was found to be superior to the standard wall functions method, which led to improved results, particularly in the wake region.