Quantification of Reynolds-averaged-Navier-Stokes Model Structural Hypothesis Uncertainty in Transitional Boundary Layer and Airfoil Flows

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Chu, Minghan
Marker function , Model structural hypothesis uncertainty , Software tool development in OpenFOAM , Transitional airfoil flow
The Boussinesq turbulent-viscosity hypothesis is intrinsic to many Reynolds-averaged-Navier-Stokes (RANS)-based turbulence models and transition models. Although its drawback has been well acknowledged, the uncertainty it induces on RANS predictions of transitional flows has been ignored so far due to the conceptual complexity involved in the associated uncertainty quantification. This type of uncertainty is called the model structural hypothesis uncertainty. In this thesis, a systematic uncertainty quantification study was carried out to estimate the RANS model structural uncertainties in predicting transitional flat-plate boundary layer and transitional airfoil flows. An existing uncertainty quantification framework for turbulent flow predictions is extended to the transitional flow regime in conjunction with a widely adopted RANS transitional model. This framework is physics-based without external high-fidelity data as input, and it decomposes the Reynolds stress tensor and inject perturbations to the amplitude, shape (eigenvalue) and orientation (eigenvector) of the Reynolds stress tensor. Given that neither the open-source OpenFOAM code nor commercial software packages contain uncertainty quantification modules, a tremendous amount of efforts in this research was spent on software tool development and successfully integrated the uncertainty quantification framework into OpenFOAM. Our software module can be used by the computational fluid dynamics communities worldwide to access the model structural hypothesis uncertainties. This thesis reports the first contribution to the eigenvalue perturbations on a transitional boundary layer over a flat plate at three percent freestream turbulence intensity (T3A Case), and a transitional flow with separation bubble over the SD7003 airfoil at eight-degree of angle of attack. Eigenvalue perturbation was carried out through the barycentric map. For the T3A flow, most of the model structural hypothesis uncertainty was concentrated in the laminar-turbulent transition region. For the SD7003 flow, the reattachment point was well encompassed within the uncertainty bound. The thesis also concerns with the amplitude perturbation, and we developed a novel marker function to identify the doubtful regions where uncertainties should be assessed. The uncertainty bounds for the skin friction coefficient, wall pressure coefficient, mean velocity field and Reynolds shear stress distribution have been successfully identified. These bounds offer crucially important information for design engineers and these data were not available prior to this study.
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