Abstract
Monocrystalline blades used in gas turbines exhibit material anisotropy, and the orientation of the anisotropy axis affects the deformation of the bladed disk. Considering the orientation of the anisotropy axis as a random design parameter, the uncertainty and sensitivity analysis for static blade deformations are presented for the first time. The following two cases are analyzed using a realistic bladed disk model with friction contacts: (i) deformation of the tuned bladed disks considering the uncertainty in anisotropy orientation and variations in fir tree root geometry and (ii) deformation of mistuned bladed disks with uncertain blade crystal orientations. For efficient uncertainty and sensitivity analysis, the applicability of the following surrogate models are explored: (i) an ensemble of regression trees (random forest) and (ii) gradient‐based polynomial chaos expansion. Faster convergence in statistical characteristics has been obtained using a surrogate model compared to that obtained from finite element model based Monte Carlo simulation. From sensitivity analysis, it has been inferred that the uncertainty in static displacements of a blade in a bladed disk is primarily due to the uncertainty in anisotropy angles of that blade itself and secondarily due to the interaction of different blade anisotropy angles.
Highlights
For efficient uncertainty analysis of deformation of high-fidelity bladed disk models, the usefulness of surrogate models based on random forest and polynomial chaos expansion has been studied
For mistuned bladed disks with numerous random parameters, in the form of blade anisotropy angles, gradient enhanced polynomial chaos expansion has been used to reduce the computational cost involved in building PCE approximation
For tuned bladed disk under static centrifugal load, the effect of variation in anisotropy orientation on blade displacements has been investigated taking into consideration some of the possible variations in fir tree root geometry
Summary
While performing uncertainty analysis of a coupled flow-thermo-mechanical model of a low-pressure turbine rotor of gas turbine engines, Antinori et al [47] used Sobol indices to reduce the dimensionality of the input parameter space by identifying most influential design parameters in the secondary air system of the aero-engine. Using a random forest-based surrogate model, the uncertainty in static deformation of tuned bladed disks caused by scattering in anisotropy orientation and root geometry variation is quantified. On the other hand, when the design parameter space is composed of only continuous variables, anisotropy angles in the case of mistuned bladed disk, the choice is mainly between polynomial chaos expansion and kriging. The blade anisotropic material properties and the friction coefficient values at the contact interfaces of blade-disk joints correspond to the temperatures at the operating regime of the analyzed bladed disk
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