Analysis of deformation of mistuned bladed disks with friction and random crystal anisotropy orientation using gradient-based polynomial chaos expansion

Single crystal blades used in high pressure turbine bladed disks of modern gas-turbine engines exhibit material anisotropy. In this paper the sensitivity analysis is performed to quantify the effects of blade material anisotropy orientation on deformation of a mistuned bladed disk under static centrifugal load. For a realistic, high fidelity model of a bladed disk both: (i) linear, and (ii) non-linear friction contact conditions at blade roots and shrouds are considered. The following two kinds of analysis are performed: (i) local sensitivity analysis, based on first order derivatives of system response w.r.t design parameters, and (ii) statistical analysis using polynomial chaos expansion. The polynomial chaos expansion is used to transfer the uncertainty in random input parameters to uncertainty in static deformation of the bladed disk. An effective strategy, using gradient information, is proposed to address the “curse of dimensionality” problem associated with statistical analysis of realistic bladed disk

Uncertainty quantification of coal seam gas production prediction using Polynomial Chaos

A surrogate model approximates a computationally expensive solver. Polynomial Chaos is a method to construct surrogate models by summing combinations of carefully chosen polynomials. The polynomials are chosen to respect the probability distributions of the uncertain input variables (parameters); this allows for both uncertainty quantification and global sensitivity analysis. In this paper we apply these techniques to a commercial solver for the estimation of peak gas rate and cumulative gas extraction from a coal seam gas well. The polynomial expansion is shown to honour the underlying geophysics with low error when compared to a much more complex and computationally slower commercial solver. We make use of advanced numerical integration techniques to achieve this accuracy using relatively small amounts of training data

Uncertainty Quantification and Global Sensitivity Analysis of a Lagrangian Acoustical-meteorological Coupled Simulation

This study focuses on the methods of Monte Carlo and the generalized polynomial chaos expansion, both of which make it possible to obtain the first statistical moment and the Sobol' sensitivity indices for uncertainty and sensitivity analysis, respectively. These methods are applied to acoustical-meteorological simulations with several hill topographies and also with several variations of meteorological parameters. The results are compared and it is observed that both methods can be applied. The generalized polynomial chaos expansion method produces similar results to the Monte Carlo method but with lower computational costs. The results also show the same pattern as other studies on the meteorological effects on sound propagation for specific test cases

Uncertainty Quantification of Turbulence Model Applied to a Cavitating Hydrofoil

This paper presents the Global Sensitivity Analysis of the coefficients of the standard k-ε turbulence model used in RANS (Reynolds Averaged Navier-Stokes) simulations aimed to predict the flow around a bi-dimensional hydrofoil operating at non-cavitating and cavitating flow regimes. The sensitivity analysis is treated by the Sobol Decomposition, where the Sobol Indices are computed through the Polynomial Chaos Expansion of the 2-nd order with a Point-Collocation Non-Intrusive approach. From the current results, it seems that the considered cavitating flow regime is less sensitive to the variability of the input parameters, at least for the prediction of lift and drag

Efficient Uncertainty Quantification Applied to the Aeroelastic Analysis of a Transonic Wing

The application of a Point-Collocation Non-Intrusive Polynomial Chaos method to the uncertainty quantification of a stochastic transonic aeroelastic wing problem has been demonstrated. The variation in the transient response of the first aeroelastic mode of a three-dimensional wing in transonic flow due to the uncertainty in free-stream Mach number and angle of attack was studied. A curve-fitting procedure was used to obtain time-independent parameterization of the transient aeroelastic responses. Among the uncertain parameters that characterize the time-dependent transients, the damping factor was chosen for uncertainty quantification, since this parameter can be thought as an indicator for flutter. Along with the mean and the standard deviation of the damping factor, the probability of having flutter for the given uncertainty in the Mach number and the angle of attack has been also calculated. Besides the Point-Collocation Non-Intrusive Polynomial Chaos method, 1000 Latin Hypercube Monte Carlo simulations were also performed to quantify the uncertainty in the damping factor. The results obtained for various statistics of the damping factor including the flutter probability showed that an 8th degree Point-Collocation Non-Intrusive Polynomial Chaos expansion is capable of estimating the statistics at an accuracy level of 1000 Latin Hypercube Monte Carlo simulation with a significantly lower computational cost. In addition to the uncertainty quantification, the response surface approximation, sensitivity analysis, and reconstruction of the transient response via Non-Intrusive Polynomial Chaos were also demonstrated