title: Pressure Sensor-based Estimation of the Velocity Field in Bluff Body Wake-flows
Creators: name: Popinhak, Andre Ricardo
Publisher: name: Graduate Studies
Year: 2024
Subjects: subject: proper orthogonal decomposition
subject: stochastic estimation
subject: sensor-based estimation
subject: pressure-velocity correlations
subject: Engineering--Mechanical
subject: Engineering--Aerospace

description: This investigation introduces the Multiscale Proper Orthogonal Decomposition with Distribution-Based Parameter Optimization (mPOD DBPO) to a sensor-based flow estimation technique within the context of turbulent forward-facing step (FFS) flow. The FFS flow was selected because of its complex nature, which consisted of two unsteady recirculation bubbles, a pronounced separating shear layer, flow reattachments, and freestream interactions, making the FFS a suitable candidate to test advanced estimation techniques. Analysis revealed convergence within the first seven most energetic POD modes, which formed the basis for constructing a low-order model (LOM) utilized in subsequent estimations. The primary goal was to evaluate the advantages of employing velocity and pressure-sensor data within the Proper Orthogonal Decomposition (POD) subspace. This strategy improved computational efficiency but did not significantly enhance the quality of flow estimation. The secondary objective was to establish an objective method for the selection of the pressure POD coefficients for flows with a wide range of scales, including nonlinear terms. Stemming from this objective, the Probabilistic Approach is introduced, featuring dynamically adjustable statistical cutoff thresholds based on desired percentiles from the pressure-velocity correlation’s cumulative distribution function (CDF). This method enables adaptable pressure POD coefficient selection, integrating optimization methodologies to effectively retain the unique requirements of each flow estimation task. The third objective was to explore the mitigation of multicollinearity among pressure POD coefficients by incorporating quadratic terms formulated within an orthonormal (ON) basis function. This basis function was obtained via the algorithm Modified Gram-Schmidt (MGS). Adding quadratic terms to an orthonormal basis (quadratic-POD-POD-ON) made some small improvements to the reconstruction of the coherent shear layer and lowered the absolute energy errors over certain intervals, but it tended to overestimate the energy contributions across different spectral ranges. Thus, this formulation was not effective in integrating the nonlinear terms into the model. The mPOD DBPO method, consistent with contemporary frameworks, effectively separated both velocity and pressure data into distinct frequency bands via a frequency domain filtering operation. For each filtered frequency band, a tailored optimization methodology was employed. This optimization specifically aimed to select the pressure POD coefficients through the novel Probabilistic Approach, which significantly reduced subjectivity and improved the statistical significance of the selected coefficients. This tailored approach facilitated robust and accurate estimation of turbulent flow dynamics, proving particularly beneficial for the complex, high-dimensional nature of FFS flow, marked by its highly energetic separating shear layer and intricate recirculation zones. As a result, the mPOD DBPO outperformed other methods such as Linear Stochastic Estimation (LSE), LSE-POD, linear-POD-POD, and quadratic-POD-POD-ON. Additionally, it is recommended to empirically determine the system's complexity limits using mean Sample Entropy to identify the frequency bands where the mPOD DBPO method can predict accurately. To develop and validate these estimation methods, vortex shedding phenomena were simulated using analytical models such as synthetic signals and an adapted theoretical model for Kármán Vortex Street. The former approach validated the implementation of estimators like quadratic-POD-POD-ON and assessed the collinearity level using the average variance inflation factor (VIF), while the latter tested the efficacy of the Probabilistic Approach, before the estimators LSE, LSE-POD, linear-POD-POD, quadratic-POD-POD-ON, and mPOD DBPO are contrasted within the context of the FFS flow.