Estimating parameter and discretization uncertainties using a laminar–turbulent transition model

For computational fluid dynamic (CFD) simulations at intermediate Reynolds numbers, laminar-to-turbulent transition plays an important role in the flow physics. While this phenomenon is difficult to simulate, current state-of-the-art transition models provide viable means to do so without resorting to expensive scale-resolving simulations. Previous studies of these methods show that, as in reality, the results are sensitive to the inlet turbulence characteristics and their decay upstream of the studied body. The lack of understanding of the exact effect of these boundary condition values may contribute, together with the discretization uncertainties, to an increase of uncertainty in the output quantities of interest, such as force or torque values. Using the γ−R̃e_θt transition model, this work estimates the parameter and discretization uncertainties and combines them into a single value. Three input uncertainties related to turbulence are chosen: turbulence intensity, eddy viscosity, and a parameter used to define a turbulence decay-free zone upstream. Sobol indices are also obtained in order to quantify the relative importance of input and discretization uncertainties. Two cases are tested: a flat plate, focusing on the local skin friction; and a practical case of the Duisburg Propeller Test Case (DPTC), where surface-integral quantities of thrust and torque coefficients are assessed. Both cases show that the turbulence intensity and eddy viscosity have significant values of total-effect Sobol indices, showing a considerable contribution of these factors to the output variation of quantity of interests, making them key factors affecting the sensitivity of the final result. Results suggest that performing grid refinement studies alone is not sufficient to estimate the numerical uncertainties for this category of problems. It is therefore recommended to assess parameter and discretization uncertainties together for the presented and other similar applications with epistemic uncertainties related to turbulent kinetic energy.