Andreas Fischersworring-Bunk

Finite element modeling of the residual stress evolution in forged and direct-aged alloy 718 turbine disks during manufacturing and its experimental validation

In this work the evolution of the residual stress field in a forged and heat treated turbine disk of Alloy 718 and its subsequent relaxation during machining was simulated and measured. After forging at around 1000 °C the disks were natural air cooled to room temperature and direct aged in a furnace at 720 °C for 8 hours and at 620 °C for 8 hours. The machining of the Alloy 718 turbine disk was performed in two steps: The machining of the Alloy 718 turbine disk was performed in two steps: First, from the forging contour to a contour used for ultra-sonic testing. Second, from the latter to the final contour. The thermal boundary conditions in the finite element model for air cooling and furnace heating were estimated based on analytical equations from literature. A constitutive model developed for the unified description of rate dependent and rate independent mechanical material behavior of Alloy 718 under in-service conditions up to temperatures of 1000 °C was extended and parametrized to meet the manufacturing conditions with temperatures up to 1000 °C. The results of the finite element model were validated with measurements on real-scale turbine disks. The thermal boundary conditions were validated in-field with measured cooling curves. For that purpose holes were drilled at different positions into the turbine disk and thermocouples were mounted in these holes to record the time-temperature curves during natural cooling and heating. The simulated residual stresses were validated by using the hole drilling method and the neutron diffraction technique. The accuracy of the finite element model for the final manufacturing step investigated was ±50 MPa.In this work the evolution of the residual stress field in a forged and heat treated turbine disk of Alloy 718 and its subsequent relaxation during machining was simulated and measured. After forging at around 1000 °C the disks were natural air cooled to room temperature and direct aged in a furnace at 720 °C for 8 hours and at 620 °C for 8 hours. The machining of the Alloy 718 turbine disk was performed in two steps: The machining of the Alloy 718 turbine disk was performed in two steps: First, from the forging contour to a contour used for ultra-sonic testing. Second, from the latter to the final contour. The thermal boundary conditions in the finite element model for air cooling and furnace heating were estimated based on analytical equations from literature. A constitutive model developed for the unified description of rate dependent and rate independent mechanical material behavior of Alloy 718 under in-service conditions up to temperatures of 1000 °C was extended and parametrized to meet the manufac...

Moving Least Squares Metamodels—Hyperparameter, Variable Reduction and Model Selection

The objective of metamodel applications is to obtain a large amount of system information from a small data set. Areas of application within the Computer-aided engineering are e.g. optimization problems, robust design engineering or sensitivity analysis. This paper deals with the metamodel techniques Least Squares (LS) regression and Moving Least Squares (MLS) as well as with their application in case of multivariate and nonlinear system behavior. In this context, LS regression represents a widely used method, which is limited in application due to the fixed polynomial order and the resulting relationship between existing support points and necessary polynomial coefficients. A more flexible metamodel technique regarding the description of nonlinearities is the MLS approach. In this procedure, the support points are weighted to build a local polynomial. The multivariate MLS-application is implemented by an anisotropic distance measure and a variable reduction. The selection of the most appropriate metamodel is tested for a deterministic model framework of mathematical test functions regarding the polynomial order, variable reduction and metamodel technique.

Adaptive Surrogate-Based Multi-Disciplinary Optimization for Vane Clusters

The presented work is part of a research project aimed towards multi-disciplinary robust shape optimization of low pressure turbine (LPT) vane clusters. Multi-disciplinary analysis for vane cluster optimization is used to evaluate design constraints, involving 3D aerodynamic Navier-Stokes simulation, transient thermal analysis, structural analysis and life prediction. The expense of these simulations combined with high-dimensional design space, makes the application of gradient-based or stochastic optimizers inefficient. To overcome these issues, a surrogate-based optimization approach is proposed here. High quality surrogate models are required for accurate description of the constraints with life prediction. Adaptive Global Surrogate-Based Optimizer, based on Gaussian-Process (GP) surrogate models and Expected Improvement infill criteria is employed, which allows to efficiently increase the surrogate quality while approaching the optimal solution at the same time. Additional techniques are introduced to deal with the geometry rebuild failure, as some combinations of the design parameters may produce infeasible geometry. The adaptive optimization method is successfully applied to the multi-disciplinary problem for the vane cluster shape optimization. The comparison of the method performance with a gradient-based optimizer indicates that a much lower number of true simulations is needed by the proposed method to find an optimal design. Successful optimization results shows the ability of the method to handle simulation crashes, caused by geometry rebuild failure.Copyright

Statistical Methods for a Stochastic Analysis of the Secondary Air System of a Jet Engine Low Pressure Turbine

In this paper several stochastic methods are evaluated with respect to their applicability for the analysis of fluid networks. The methods are applied for the analysis of a 1D flow model of the Secondary Air System (SAS) of a three stages low pressure turbine (LPT) of a jet engine. The stochastic analysis is comprised of a sensitivity analysis followed by an uncertainty analysis. The sensitivity analysis is performed to gain a better understanding of the SAS physics and robustness, to identify the important variables and to reduce the number of parameters involved in the simulations for the uncertainty analysis. The uncertainty analysis, using probability distributions derived from the manufacturing process, allows to determine the effect of the input uncertainties on responses such as pressures, fluid temperatures and mass flow rates. A review of the most common and relevant sampling methods is performed. A comparison of the respective computational cost and of the sample points distribution is proposed with the aim of finding the most suited method. The study shows that some of the sampling methods can not be recommended since they produce spurious correlations between independent input variables. With regards to the sensitivity analysis, many literature sources state that the Pearson correlation method is only valid for linear models when assessing the importance of input variables. As the SAS is highly non-linear, non-parametric variance based methods are introduced here to make up for the limitations of the correlation method. Following the results of the study, it is recommended to combine the sampling method with a non-parametric variance based method. Thus, the main effects as well as all the interactions among variables are captured.

Sensitivity Analysis and Uncertainty Quantification for a Coupled Secondary Air System Thermo-Mechanical Model of a Jet Engine Low Pressure Turbine Rotor

In this paper, several statistical methods are evaluated with respect to their applicability for the probabilistic analysis of a coupled flow-thermo-mechanical model of a low pressure turbine rotor. The probabilistic analysis is comprised of a sensitivity analysis followed by an uncertainty analysis. The sensitivity analysis is performed to gain a better understanding of the coupled flow-thermo-mechanical system. The uncertainty analysis, using probability distributions derived from the manufacturing process, allows the effect of the input uncertainties on the life duration of the rotor to be predicted.

Global sensitivity analysis for multidisciplinary studies of vane clusters

This work is part of the research aimed towards the multidisciplinary robust shape optimization of low pressure turbine (LPT) vane clusters. Here we focus on the global sensitivity analysis needed to identify the most important design variables and reduce the design parameter space for further optimization. Identifying shared important vari- ables for different disciplines will help to find a suitable multidisciplinary optimization architecture. To deal with high computational costs associated to the multidisciplinary analysis chain, a surrogate-based approach for sensitivity analysis is proposed here. Two well known high-dimensional test functions are used to validate the accuracy of the surrogate-based sensitivity analysis. Finally the process is successfully applied to the multidisciplinary analysis of the vane cluster. The results obtained show clearly the importance of performing advanced non-linear sensitivity analysis in addition to the computation of linear correlations.

Probabilistic Structure-Mechanical Assessment of Rotor Discs Considering Geometry Variations

For rotating critical parts, like compressor or turbine discs of aero engines, it is essential to perform reliable life predictions. Probabilistic methods are ideal to investigate these life predictions with regard to their sensitivities and robustness. Beside other system properties, the variation of geometrical disc parameters has a strong influence on the physical system behavior.Within this paper, the system behavior of a turbine disc is assessed with regard to its sensitivities, to enable the continuous optimization of the disc and to verify a new post-processing method. To suit this purpose, a process chain was developed from CAD-model to lifing analysis and embedded into a Monte Carlo Simulation (MCS). As input parameters geometrical parameters and their optimization ranges are used. The statistical evaluation of an MCS with regard to sensitivities is based on comparison of topologically similar locations. Similarity is achieved by the standard operation of “mesh morphing”, in which the original mesh of the initial geometry is deformed onto the new geometry. This method is limited to small variations. Another method is remeshing of the new geometry. This makes direct comparison at identical FE-nodes impossible and post-processing is done based on significant local features. The post-processing method described in this paper is a combination of aforementioned approaches. Based on this new method, the result variables von-Mises stress and life cycles are investigated for their sensitivities to geometrical parameters within the disc bore.Copyright