EXPERIMENTAL INVESTIGATION OF GOERTLER VORTICES AND BOUNDARY LAYER TRANSITION ON CONCAVE SURFACE

Abstract

Laminar and transitional boundary layer flows in the presence of longitudinal counter-rotating Goertler vortices were experimentally investigated on a concave surface of 2.0m radius of curvature in a perspex curved rectangular duct using hotwire anemometers. To accurately determine intermittency factor in the transitional boundary layer flows, three intermittency measurement methods, namely ? method, TERA (Turbulent Energy Recognition Algorithm) and M-TERA (Modified Turbulent Energy Recognition Algorithm) methods were rigorously tested and compared using the data obtained from hot-wire anemometer in concave surface and flat-plate boundary layer flows. Comparisons show that the M-TERA method is better than the other two as a turbulent detector under the same flow conditions. With the purpose of studying the characteristics of the laminar and transitional boundary layer flows on concave surface, extensive quantitative measurements of streamwise mean and fluctuating velocities were made. From the measurements, the turbulent intermittency factors, statistical calculations of the turbulent events and the longitudinal and normal space-time correlations were obtained. The results show that the initial Blasius boundary layer flow formed on the concave surface becomes three-dimensional as a system of counter-rotating streamwise vortices is established. These vortices grow continuously downstream producing regions of low- and high-speed fluid ( or downwash and upwash regions) in the spanwise direction. This results in inflexional streamwise velocity profile and a defect in normal profiles from the Blasius value at the upwash region. After reaching a saturation state where transition starts, the vortices cease to grow, and begin to attenuate with the streamwise positions. The streamwise development of turbulence intensity at the upwash and downwash regions show a strong link with that of mean velocity. In the laminar boundary layer, the maximum value of the Reynolds normal stress across the boundary layer increases with the streamwise location at both spanwise positions. In the early transitional region, two peaks were found in the upwash profiles. The comparisons between the u'rms/U0 profiles at the two regions indicate that their streamwise development processes are different. The intermittency profiles across the boundary layer in two different spanwise transitional regions for different free stream velocities exhibit similar behaviours. The intermittency does not decrease monotonically with increasing y from the wall to the outer flow. Instead, a fairly constant maximum value midway across the boundary layer at upwash, and a peak near the wall at downwash were respectively observed. The difference between the upwash and downwash intermittency profiles decreases with increasing velocity. For different free-stream velocities, transition starts and ends first at the upwash regions, and then downstream at the downwash regions. The transition lengths at the upwash region are longer than those at downwash region. In terms of transition start position, the present results agree well with other available data obtained on the concave surfaces. The comparison with the widely used flat-plate criterion of Abu-Ghannam and Shaw ( 1980) shows that the boundary layer momentum-thickness Reynolds numbers at the start of transition obtained on the concave surface are much lower than that on flat-plates. This indicates that the established correlations for start of transition on flat plates can not be applied to the Goertler vortex flows. The statistical results of intermittent turbulent events measured at two free-stream velocities show that the maximum number of the turbulent events occurs at intermittency of about 0.6. For nearly the same intermittency value, the number of turbulent events obtained at low free-stream velocity (U0 = 6m/s) is higher than that obtained at high free-stream velocity ( U0 = 15m/s). The mean streamwise length of the turbulent events and its rms-value at both upwash and downwash regions increase with increasing stage of transition. In the early stages of transition, the short turbulent events are always predominant in the total events. For both free-stream velocities and the upwash and downwash regions, the mean zero-crossing frequency of the joint fluctuating velocities of the turbulent events in the u-fluctuations increases gradually with increasing intermittency in the streamwise direction for two free-stream velocities, especially for the higher velocity. However, the zero-crossing frequency of turbulent velocities across the boundary layers are not significantly affected by the cross-stream intermittency values and local velocity for both free-stream velocities. Applying two single sensor hot wire probes, the longitudinal and normal spacetime correlations of streamwise velocities were measured in the transitional boundary layer flows. The influence of the disturbances caused by the upstream wire on the measurements of the downstream wire was checked. The space-time correlation changes with delay time and reaches a maximum value at an optimum delay time. The maximum correlation coefficient and optimum delay time vary considerably with the distance and angle between the two points at which the two hot wire probes were placed.