Effects of uncertainties in positioning of PIV plane on validation of CFD results of a high-head Francis turbine model

Abstract

The use of Computational Fluid Dynamics (CFD) for the design of modern hydraulic turbines has increased and matured significantly in the last decades. More recently, CFD is also used to understand how to safely widen the hydraulic turbine operating ranges, and avoid hazardous conditions during transient operation. The accuracy of such CFD results relies on validation with experimental data which contains numerous sources of uncertainties. The present work is focusing on the effects of the uncertainties in the positioning of the experimental Particle Image Velocimetry (PIV) plane on the validation of CFD results of the high-head Francis-99 turbine model. A transient shutdown sequence is considered, where the available experimental and numerical data are considered accurate according to a conventional thorough validation procedure. A part of that validation procedure is the comparison of spatially and temporally varying velocity profiles along three lines of the experimental PIV plane. The positioning of this PIV plane is here considered uncertain, using three translational and three rotational stochastic parameters with uniform probability distribution functions. The validated CFD results are used to extract the data that depends on these uncertainties, while this is not possible for the experimental data. The polynomial chaos expansion method is employed for the Uncertainty Quantification (UQ) study while Sobol’ indices are utilized for the Sensitivity Analysis (SA). The UQ can be used to show how the considered uncertainties impact the extracted components of the velocity field, and the sensitivity analysis reveals the relative contribution of each uncertain parameter to the quantity of interest. For this particular case it is shown that the so-called horizontal velocity component is most sensitive to the plane-normal positioning of the PIV plane. This is also the velocity component where all the numerical results found in the literature differ most from the experimental results. It is also shown that the probability distribution function of the numerical horizontal velocity is covered by the experimental standard deviation bounds, which means that it is quantified that the numerical and experimental results are similar within the range of the uncertainties.