Katherine J. Asztalos

We propose a technique for performing spectral (in time) analysis of spatially-resolved flowfield data, without needing any temporal resolution or information. This is achieved by combining projection-based reduced-order modeling with spectral proper orthogonal decomposition. In this method, space-only proper orthogonal decomposition is first performed on velocity data to identify a subspace onto which the known equations of motion are projected, following standard Galerkin projection techniques. The resulting reduced-order model is then utilized to generate time-resolved trajectories of data. Spectral proper orthogonal decomposition (SPOD) is then applied to this model-generated data to obtain a prediction of the spectral content of the system, while predicted SPOD modes can be obtained by lifting back to the original velocity field domain. This method is first demonstrated on a forced, randomly generated linear system, before being applied to study and reconstruct the spectral content of two-dimensional flow over two collinear flat plates perpendicular to an oncoming flow. At the range of Reynolds numbers considered, this configuration features an unsteady wake characterized by the formation and interaction of vortical structures in the wake. Depending on the Reynolds number, the wake can be periodic or feature broadband behavior, making it an insightful test case to assess the performance of the proposed method. In particular, we show that this method can accurately recover the spectral content of periodic, quasi-periodic, and broadband flows without utilizing any temporal information in the original data. To emphasize that temporal resolution is not required, we show that the predictive accuracy of the proposed method is robust to using temporally-subsampled data.

Proper thermal management of an electric motor for vehicle applications extends its operating range. One cooling approach is to impinge Automatic Transmission Fluid (ATF) onto the rotor end ring. Increased ATF coverage correlates to enhanced heat transfer. Computational Fluid Dynamics (CFD) analytical tools provide a mechanism to assess motor thermal management prior to hardware fabrication. The complexity of the fluid flow (e.g., jet atomization, interface tracking, wall impingement) and heat transfer makes these simulations challenging. Computational costs are high when solving these flows on high-speed rotating meshes. Typically, a Volume-of Fluid (VOF) technique (i.e., two-fluid system) is used to resolve ATF dynamics within this rotating framework. Suitable numerical resolution of the relevant physics for thin films under strong inertial forces at high rotor speeds is computationally expensive, further increasing the run times. In this work, a numerical study of rotor-ring cooling by ATF is presented using a patent automated Cartesian cut-cell based method coupled with Automatic Mesh Refinement (AMR). This approach automatically creates the Cartesian mesh on-the-fly and can effectively handle complex rotating geometries by adaptively refining the mesh based on local gradients in the flow field which results in better resolution of the air-ATF interface. A Single non-inertial Reference Frame (SRF) approach is used to account for the rotating geometry and to further improve the overall computational efficiency. Quasi-steady state conditions are targeted in the analysis of the results. Important physics such as ATF jet structure, velocity detail near the air-jet interface, ATF coverage/accumulation on the ring surface, and cooling capacity are presented for a low-resolution Reynolds averaged Navier-Stokes (RANS), high-resolution RANS, and high-resolution Large-Eddy Simulation (LES) models. Computations are scaled over hundreds of cores on a supercomputer to maximize turnaround time. Each numerical approach is shown to capture the general trajectory of the oil jet prior to surface impingement. The high-resolution LES simulation, however, is superior in capturing small scale details and heat transfer between the free jet and surrounding air.