Mechanical Engineering - Theses
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ItemCharacteristics of energetic motions in turbulent boundary layers( 2019)In this dissertation, we present the first measurements of two-dimensional (2-D) energy spectra of the streamwise velocity component (u) in high Reynolds number turbulent boundary layers. The measurements in the logarithmic region of turbulent boundary layers give new evidence supporting the self-similarity arguments that are based on Townsend’s (1976) attached eddy hypothesis. The 2-D spectrum is found to be able to isolate the range of self-similar scales from the broadband turbulence, which is not possible with the measurement of a 1-D energy spectrum alone. High Reynolds number flows are characterized by large separation of scales. Therefore, to obtain converged 2-D statistics while resolving the broad spectrum of length and time scales, a novel experimental technique is required. To this end, we devise a technique employing multiple hot-wire probes to measure the 2-D energy spectra of u. Taylor’s frozen turbulence hypothesis is used to convert temporal-spanwise information into a 2-D spatial spectrum which shows the contribution of streamwise (λx) and spanwise (λy) length scales to the streamwise variance at a given wall height (z). The validation of the measurement technique is performed at low Reynolds number by comparing against the direct numerical simulation (DNS) data of Sillero et al. (2014). Based on these comparisons, a correction is introduced to account for the spatial resolution associated with the initial separation of the hot-wires. The proposed measurement technique is used to measure the 2-D spectra in the logarithmic region for friction Reynolds numbers ranging from 2400 to 26000. At low Reynolds numbers, the shape of the 2-D spectra at a constant energy level shows λy/z ∼ (λx/z)1/2 behaviour at large scales, which is in agreement with the existing literature. However, at high Reynolds numbers, it is observed that the square-root relationship tends towards a linear relationship (λy ∼ λx) as required for self-similarity and predicted by the attached eddy hypothesis. Finally, we present a model for the logarithmic region of turbulent boundary layers, which is based on the attached eddy framework and driven by the scaling of experimental 2-D spectra of u. The conventional attached eddy model (AEM), which comprises self-similar wall-attached eddies (Type A) alone, represent the large scale motions at high Reynolds numbers reasonably well. However, the scales that are not represented by the conventional AEM are observed to carry a significant proportion of the total kinetic energy. Therefore, in the present study we propose an extended AEM, where in addition to Type A eddies, we also incorporate Type CA and Type SS eddies. These represent the self-similar but wall-detached low-Reynolds number features and the non-self-similar wall-attached superstructures, respectively. The extended AEM is observed to predict a greater range of energetic length scales and capture the low- and high-Reynolds number scaling trends in the 2-D spectra of all three velocity components.