Uncertainty Quantification Integrated with the Reduced-Dimensional Modeling of Supersonic Shear Flows

The development of reduced-order models as fast running models for the simulation of fluid flows has been a research topic for several years [1,2] and their widespread application to supersonic aerothermodynamics is a topic of continued research. Though Reynolds-Averaged solutions are generally considered computationally affordable numerical methods, real-time results for complex systems are not possible with such solvers. For applications such as digital twin framework, real-time results are paramount and reduced-dimensional and reduced-order models can be a solution.

The authors present a novel approach where reduced-dimensional modeling leveraging K-means clustering [3] and uncertainty quantification has been integrated with reduced-order modeling. The approach is demonstrated by modeling the supersonic flow over a double-fin-on-cylinder test article [4] where shock-boundary layer interactions are dominant. Heterogeneous experimental data for 20-degree and 5-degree fins was used as the so-called training data to develop a reduced-order model of the surface pressure distribution for a fin with a 10-degree incident angle. Further, Reynolds averaged Navier Stokes (RANS) computational fluid dynamics (CFD) calculations are conducted for the same 10-degree configuration, and the results are leveraged as additional training data. The experimental data obtained from various facilities can have different dimensionality and CFD data can have different dimensionality depending upon the grid density and numerical methods employed. If the dimensionality of each dataset is reduced to the same dimensionality, all data can be fused and the resulting large dataset can be used to build the reduced-order model. The research challenges in performing this dimensionality reduction are (1) maintaining an acceptably accurate representation of the relevant physical interactions and (2) quantifying both the contribution of the error and imprecision in dimensionality reduction and uncertainty inherent in the training data to the uncertainty of a reduced-order model’s predictions. This research will show the results from dimensionality reduction and reduced-order modeling, and implement existing uncertainty quantification (UQ) methods that address the above research challenges.