Estimating Turbulence Modeling Uncertainty for Turbomachinery Flows Using Physics-Constrained Eigenspace Perturbations of the Reynolds Stress Tensor

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Abstract

The synthesis of RANS (Reynolds-averaged Navier-Stokes) equations and the required modeling of turbulence entails certain uncertainties in CFD (Computational Fluid Dynamics). Currently, engineers employ safety factors to address these uncertainties in turbomachinery design processes, which lead to overly conservative designs and result in missed opportunities to optimize the performance. Therefore, understanding the uncertainties in CFD and establishing methods to analyze the credibility of numerical simulations is crucial to achieve robust designs for future turbomachinery components and to create virtual certification processes. This cumulative dissertation investigates a framework to account for the uncertainty stemming from the turbulence closure model, a primary source of the overall uncertainty in RANS simulations. Although there are a variety of approaches to assess the uncertainty associated with turbulence models, the appropriate estimation of the epistemic uncertainty inherent in turbulence models is demanding. Therefore, the establishment of a methodology capable of reasonably assessing this model-form uncertainty in the context of RANS-based design of turbomachinery components is a major objective of the present thesis. The EPF (Eigenspace Perturbation Framework), designed to add physics-constrained perturbations to the eigenspace of the Reynolds stress tensor and provide a systematic approach to quantifying its inherent uncertainty, is implemented in the CFD solver TRACE and evaluated in the scope of this thesis. The current research includes an extensive verification of the numerical implementation as well as a scrutiny of the conceptual idea of the EPF. This thesis proposes enhancements related to the consistency and applicability of the methodology, while exploring its general capabilities and limitations. Additionally, the introduction of machine learning to reduce user-defined input and prevent overly conservative estimations of the turbulence modeling uncertainty is discussed and results are presented. Moreover, the eigenvalue perturbation is applied to the TUDa compressor stage, presenting the first application of the EPF to multi-row turbomachinery flows. Finally, the ability to quantify, analyze and interpret the uncertainties associated with turbulence closure models, provides a valuable starting point for next-generation enhancements in modeling turbulent effects for complex configurations and flow phenomena. Overall, by refining the EPF and critically assessing its capabilities, this dissertation contributes to the development of reliable methods to consider the uncertainties in CFD.

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