Development of schlieren-image based flow diagnostics and analysis for supersonic jet flows - Lim, Desmond Haoxiang (Nanyang Technological University, 2020)
The primary focus of this thesis is on the developments of image-based flow diagnostics for supersonic jet flow and noise control. Three different in-house techniques are presented: (1) 3D shock wave reconstruction technique based on schlieren imaging and visual hull concepts, (2) schlieren image velocimetry based on the optical flow algorithm (SIVOF), and (3) a data-driven approach to identify and characterize intermittent jet screech based on proper orthogonal decomposition (POD) of time-resolved schlieren images. The secondary focus is to provide experimental data and improve understanding on problems associated with the supersonic jet. To this end, the in-house techniques are applied in conjunction with conventional experimental techniques to Mach number 1.45 supersonic cold jets produced from convergent-divergent circular nozzles. In order to achieve flow and noise control, modifications to the nozzle exit are introduced through bevelling, and four different designs are investigated; baseline, 30° bevelled, 30° double-bevelled and 60° bevelled circular nozzles. The 3D shock wave reconstruction technique was developed to accurately reconstruct the first shock cell of an over-expanded baseline jet, which consists of a 0.9 mm diameter Mach disk imaged at a focal distance of over 700 mm. This is a scenario typically encountered during scaled-down testing in laboratories and represents a significant challenge in the context of 3D image reconstruction. To mitigate this issue, an in-house semi-synthetic camera calibration procedure was developed to provide highly precise camera parameters. In addition, multi-view schlieren image post-processing and the volume carving visual hull approach were used to digitally reconstruct the shock wave. The nominal cubic voxel resolution of the reconstructed shock wave was 0.044 mm, and the key parameters of under-expanded baseline and 30° bevelled jet shock structures have a 2.5% average error when compared to traditional schlieren visualization techniques. These results attest the accuracy and high-fidelity of the technique. Furthermore, since the technique directly reconstructs the shock structures without measuring a prior fluid property such as the 3D density or velocity field, it benefits from experimental simplicity and requires little resources in both experimental setup and image post-processing. In an extended study, the 3D shock wave reconstruction technique was applied in conjunction with traditional schlieren visualization to study the effects of bevelled nozzles on standoff shocks in supersonic impinging jets. The properties of the standoff shock are known to be a strong function of the nozzle-pressure-ratio and separation distance based on the existing literature. In the study, the 3D geometry, position and stability properties of the standoff shock at three different flow configurations were investigated, and the results indicate that the standoff shock is also sensitive to the nozzle exit geometry. This was attributed to changes in the jet shock structures and the reflection point as a result of the nozzle exit modifications. Since the reflection point is a region of low pressure on the top side of the standoff shock, a localized suction effect is created which influences the standoff shock. The strength and location of the reflection point were identified as the major contributing factors leading to the observed changes in the standoff shock properties. The schlieren image velocimetry technique based on an in-house optical flow algorithm is proposed as an alternative velocimetry technique that has the advantage of offering a dense velocity field, is totally non-intrusive, avoids seeding challenges, and allows flow physics to be incorporated into the objective function. The optical flow algorithm incorporated modern minimization methods with second order div-curl regularizer and robust penalty functions. As a result, it outperformed a competitive open source optical flow algorithm in a synthetic validation test, with an average endpoint error of 0.701. The technique was applied to over-expanded baseline and 30° bevelled jets with the results agreeing well with earlier studies. When compared against PIV results, the much higher spatial and temporal resolution of SIVOF resulted in sharper and clearer vortical structures that can be tracked across several time-resolved frames. An embedded shear layer resulting from subsonic flow downstream of a 0.9 mm diameter Mach disk was also observed, which is testament to the high-fidelity flow field offered by SIVOF. A new image-based technique that can identify and characterize intermittent jet screech is proposed. Short-time POD was performed on time-resolved schlieren images of under-expanded baseline and bevelled jets. Spectral analyses were performed on the time coefficients of the first POD modes, and the frequencies associated with the peak amplitudes were recorded and organized into a histogram with a bin width of St=0.01. The frequency of occurrence of the statistical mode was proposed as a parameter that can robustly identify the presence and characterize the type of jet screech, with the jet screech frequency revealed by the statistical mode. The baseline and 30° bevelled jet results revealed a peak amplitude at precisely the acoustically-validated screech frequency of St=0.25, indicating a correlation between the turbulent flow structures and the screech tone.