Stability, LES, and Resolvent Analysis of Thermally Non-uniform Supersonic Jet Noise

For decades noise-induced hearing loss has been a concern of the Department of Defense (DoD). My research investigates noise generation and dispersion in supersonic jets and focuses on the fluid-dynamic regime typical of high-performance turbojet and turbofan engines. The goal of my research is to understand how dispersion and propagation of wavepackets can be modified by noise reduction strategies based on secondary injections of fluid with a different temperature from the main jet. The research is organized into three studies that focus on instability, large eddy simulations, and resolvent modes.

The first study is a computational investigation of the role of thermal non-uniformity on the development of instability modes in the shear-layer of a supersonic $M=1.5$, $Re=850,000$ jet. Cold fluid is injected at the axis of a heated jet to introduce radial non-uniformity and control the spatial development of the shear layer. The mean flow is analyzed with an efficient 2D and 3D Reynolds-averaged Navier-Stokes (RANS) approach using the SU2 code platform for 3 different cases -baseline, centered, and offset injection. Different turbulence models are tested and compared with the experiments. The coherent perturbation is analyzed using linear parallel and parabolized stability equations (PSEs).

The second study investigates novel formulations of large eddy simulation models using an arbitrary high order discontinuous Galerkin scheme. The LES analysis focuses on both numerical issues (such as convergence against the polynomial order of the mesh), modeling issues (such as the choice of subgrid model), and underlying physics (such as vortex stretching and noise generation). Wall models are used to capture the viscous sublayer at the nozzle. The Ffowcs Williams-Hawkings (FW-H) method is used for far-field noise predictions for all cases. Three-dimensionality is studied to investigate how injection in the shear layer acts to create a rotational inviscid core and affects the mixing of the cold fluid and noise dispersion.

The third study extends the (first) instability study by considering (global) resolvent modes. Such optimally forced modes of the turbulent mean flow field will identify the turbulent coherent structures (wavepackets) for different turbulence models at $M=1.5$. The LES simulations performed in the second study will be used to extract the mean flow and the dynamic modes for comparison. My research plan is to perform the resolvent analysis of the axisymmetric mean flow fields for the thermally activated case (i.e., the centered injection) and compare it to the baseline jet case. Different turbulence models will be investigated to determine the correct alignment of dynamic and resolvent modes. Finally, I will consider the three-dimensional, non-axisymmetric mean flow created by offset injection described in the second study, which requires evaluating the convolution products of resolvent modes and base flow. Such three-dimensional resolvent compressible modes have never been identified in the context of supersonic jets.