Wall shear stress sensing, friction drag reduction, and the wake of two staggered cylinders

Abstract

This thesis is an experimental study of turbulence, covering three topics: (i) a carbon nanotube (CNT) sensor for wall shear stress (WSS) measurements in a turbulent boundary layer (TBL); (ii) the control of a TBL for drag reduction based on piezo-ceramic (PZT) actuator-generated wall oscillations; and (iii) the turbulent wake of two staggered square cylinders. Firstly, a CNT sensor has been developed to measure the mean and fluctuating WSS in a macroscopic TBL. The CNT WSS sensor is based on the thermal-principle and featured by a high spatial and temporal resolution (in the order of nm and kHz, respectively), a low power consumption (in the order of μW), and a compact fabrication process compared with traditional WSS sensors. The CNT WSS sensing element was characterized in detail before its calibration. The CNT sensor was operated under a constant temperature (CT) operation mode and an overheat ratio range of -0.15 ~ -0.19, and calibrated in a fully developed turbulent channel flow. It has been observed for the first time in a macroscopic flow that the sensor output power is approximately proportional to the 1/3-powered WSS, as expected for a thermal-principle-based WSS sensor, and the WSS measurement was demonstrated for a low Reynolds number flow. Secondly, the active control of a TBL has been experimentally investigated with a view to reduce the skin-friction drag and to improve our understanding of the flow. A PZT actuator array, aligned spanwise and flush-mounted with the wall surface, was employed to generate wall-normal oscillations and, given a phase shift between two adjacent actuators, a transverse travelling wave along the wall. A number of control parameters were examined, including the wavelength (41.6 ~ ∞ wall units), oscillation amplitude (0.83 ~ 2.77 wall units) and frequency (0.13 ~ 0.65 wall units). Local skin-friction drag, estimated from the slope of streamwise mean velocity profile in the linear region, exhibits a strong dependence on the control parameters. A maximum skin-friction drag reduction of 50% has been achieved at 17 wall units downstream of the actuator tip, given the wavelength, oscillation amplitude and frequency at 416, 1.94 and 0.39, respectively, all in wall units. The near-wall flow structures with and without perturbation were measured extensively using laser-illuminated smoke-wire flow visualization, hotwire, hot-film and particle image velocimetry (PIV) techniques, and were compared with each other. The data have been carefully examined and analysed using techniques such as space-time cross-correlation, proper orthogonal decomposition (POD) and conditional averaging based on the variable-interval time-averaging (VITA) detections. All the results point to a pronounced change in the coherent structures in the boundary layer under control. The physical picture behind the control is summarized in a conceptual model of the modified coherent structures. Thirdly, the turbulent wake of two staggered square cylinders has been studied based on the laser-induced fluorescence (LIF) flow visualization, hotwire, PIV and load cell measurements at Re (≡ U∞d/ν, where U∞ is the free-stream velocity and d is the cylinder width) = 300 ~ 1.3 × 10⁴. The configurations examined cover P/d = 1.5 ~ 5.0 with an interval of 0.5 and α = 0° ~ 90° with an increment of 5°, where P is the centre-to-centre distance between the cylinders and α is the incident angle between the streamwise direction and the line through the cylinder centres. Four distinct flow regimes were identified based on the Strouhal numbers (St) maps in the P/d-α plane and the downstream evolution of the flow structures at x/d = 4.0 ~ 15.0, where x is the downstream distance from the mid-point between the cylinders. Two flow regimes, i.e., S-I and S-II, are characterized by only one vortex street in the wake and the other two, i.e., T-I and T-II, by two streets of vortices. Regime S-I occurs largely at α < 20° and is further divided into two sub-regimes, i.e., S-Ia and S-Ib, in view of their distinct vortex strengths. Regime S-II is identified mainly at P/d < 3.0 and α > 45°, where vortex shedding from the different free-stream sides of the two-cylinder pair have distinct frequencies. Regime S-II is further categorized into S-IIa and S-IIb, depending on which cylinder the higher-frequency vortex sheds from; the higher-frequency vortices are from the upstream cylinder in the former, whilst they are from the downstream one in the latter. Regime T-I occurs mostly at P/d ≥ 3.0 and 40° ≤ α ≤ 75°, where two streets of vortices were detected with slightly different frequencies. A narrow street and a wide street occur behind the upstream and downstream cylinders, respectively. Regime T-II displays two coupled vortex streets. The two streets may exhibit different relations. Therefore, this regime is divided into two sub-regimes, i.e. T-IIa and T-IIb, with the former occurring largely at P/d ≥ 3.0 and α > 75° and the latter at P/d ≥ 4.0 and 20° ≤ α < 40°. The two streets are mostly anti-phased in sub-regime T-IIa but the vortices shedding from the downstream cylinder are always synchronized with that from the upstream one in T-IIb. Initial conditions, i.e. interactions between the four shear layers around the two cylinders, are connected with different flow regimes and are discussed in detail. Time-averaged and fluctuating drag and lift forces acting on the two square cylinders were measured for all the configurations. The forces are largely categorized into three, i.e. the small, the intermediate and the large α, and exhibit distinct characteristics in each group, corroborating the classification of the flow regimes.