Higher-order Turbulence Products of Velocity and Temperature for Adverse Pressure Gradient Boundary Layer Flows

Higher-order turbulent products of momentum and temperature are experimentally presented for heated boundary layers subjected to adverse pressure gradient (APG) and zero pressure gradient (ZPG) flows. Clauser’s equilibrium parameter, b, was set to 1.8 for APG case and 0 for ZPG case. The temperature difference between the heated wall and free stream was held constant at 12°C. Triple wire measurements were conducted to acquire simultaneous fluctuations of the two turbulent velocity components (u’ and v’) and the fluctuation of temperature (T’). Findings in this study show pressure gradient effect on the higher-order products, which tend to be dependent on large scale coherent structure of the boundary layer turbulence, to enhance vertical diffusion of stress, suppress stream-wise transport of stress, and increase structure sizes. INTRODUCTION It is known that local Reynolds number, wall-shear stress, surface roughness, and boundary layer thickness are important parameters of structure for turbulent boundary layers. Pressure gradient has been also noted as one of the parameters affecting on the coherent structure in turbulent boundary layers. Generally, decelerating flows subjected to an adverse pressure gradient (APG) thicken the boundary layer and complicate the flow characteristics; whereas, accelerating flows stabilize the boundary layer. The adverse pressure gradient often occurs in fluid flow along solid surface and may become an important issue for machinery design and maintenance due to its effect on separation and deceleration of flow. Additionally, complete structure measurements of APG flows can provide benchmark data for development of numerical turbulent models. Kline et al. (1967) and Lian (1990) observed the coherent structures of TBL in the presence of APG and compared the shapes and movement of the streaks formed near the wall for zeropressure-gradient flows. Valuable quantitative experiments on TBL subjected to APG condition have been conducted by Simpson et al. (1981), Watmuff and Westphal (1989), Nagano et al. (1991), Mislevy and Wang (1994), Ayala et al. (1997), Nagano et al. (1998), and others. In the findings presented in the above studies, the validity of law-of-the-wall was shown to be questionable under APG conditions. Measurement techniques of coherent structures in boundary layers have improved with development of testing equipment and computer hardware. However, simultaneous measurement of instantaneous velocity and temperature close to the wall is still problematic. Strong intermittence of flow regimes in a boundary layer causes additional difficulty for both measurement and analysis. Therefore, different types of approach, such as conditional sampling (Murlis et al.; 1982), have been used to filter meaningful information out of massive amounts of data. In the present investigation, statistical analysis of higher order products (triple and quadrant momentum and temperature products) were measured to study APG effect on turbulent coherent structures in the boundary layer. EXPERIMENTAL APPARATUS AND CONDITION An open-circuit low-speed boundary-layer wind tunnel was used in the present study. The overall length of the wind tunnel is 7.5 m, which include 3 m long by 0.3 m wide test-section. The ceiling of the wind tunnel consists of thirty-six individual Plexiglas sheets, which are used to adjust the test-section geometry for a specific APG configuration. Free-stream turbulence intensities for ZPG and APG were about 1 % and 1.5 %, respectively. A further detail description of the wind-tunnel facility can be found in Ayala et al. (1997). A triple wire probe (TSI 1295BH-T1.5) was used to perform simultaneous measurements of turbulence fluctuations in normal and stream-wise flow directions including temperature fluctuations. This custom-made triple wire probe consists of a tungsten X probe and a platinum temperature wire. Detailed specifications of this sensor and its application are presented in Ayala et al. (1997). For all turbulent measurements, the sensor real-time sampling frequency was set to 10 kHz per channel where 60,000 data points were collected at each acquisition. Wall temperature distribution was monitored with a series of thermocouples embedded in the surface and a digital thermometer. These thermocouples were calibrated against a platinum-resistance thermometer (PRT). In the present investigation, the adverse-pressure-gradient parameter, b, was set to 1.8 which corresponded to Clauser’s (1954) data. The corresponding Reynolds number value based on the momentum-deficit thickness was about 3,800. The zero-pressure-gradient boundary layer was also measured to compare its data with APG measurements. DATA REUDUCTION Analog voltage outputs from two Constant Temperature Anemometer (CTA) and a Constant Current Anemometer (CCA), for velocity and temperature measurements, were descritized to digital signals by a 12-bit A/D converter. A linear calibration equation was used for the voltage signal from the CCA to reduce instantaneous temperature fluctuations (with 2% uncertainty). Because the wall surface was heated and the boundary layer was under non-isothermal condition, a correction factor had to be considered for data reduction of the CTA signal. In the present study, the general correction equation,