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Description
Monte Carlo simulations are traditionally carried out for the determination of the amplification of forced vibration response of turbomachine/jet engine blades to mistuning. However, this effort can be computationally time consuming even when using the various reduced order modeling techniques. Accordingly, some investigations in the past have focused on obtaining simple approximate estimates for this amplification. In particular, two of these have proposed the use of harmonic patterns of the blade properties around the disk as an approximate alternative to the many random patterns of Monte Carlo analyses. These investigations, while quite encouraging, have relied solely on single degree of freedom per sector models of the rotor.
In this light, the overall focus of the present effort is a revisit of harmonic
mistuning of rotors focusing first the confirmation of the previously obtained findings with a more detailed model of the blisk in both conditions of an isolated blade-dominated resonance and of a veering between blade and disk dominated modes. The latter condition cannot be simulated by a single degree of freedom per sector model. Further, the analysis will consider the distinct cases of mistuning due to variations of material properties (Young's modulus) and geometric properties (geometric mistuning). In the single degree of freedom model, both mistuning types are equivalent but they are not, as demonstrated here, in more realistic models. The difference arises because changes in geometry induce not only changes in natural frequencies of the blades alone but of their modes and the importance of these two sources of variability is discussed with both Monte Carlo simulation and harmonic mistuning results.
The present investigation focuses also on the possible extension of the harmonic mistuning concept and of its quantitative information that can be derived from such analyses. From it, a novel measure of blade-disk coupling is introduced and assessed in comparison with the coupling index introduced in the past. In conclusions, the low cost of harmonic mistuning computations in comparison with full Monte Carlo simulations is
demonstrated to be worthwhile to elucidate the basic behavior of the mistuned rotor in a random setting.
In this light, the overall focus of the present effort is a revisit of harmonic
mistuning of rotors focusing first the confirmation of the previously obtained findings with a more detailed model of the blisk in both conditions of an isolated blade-dominated resonance and of a veering between blade and disk dominated modes. The latter condition cannot be simulated by a single degree of freedom per sector model. Further, the analysis will consider the distinct cases of mistuning due to variations of material properties (Young's modulus) and geometric properties (geometric mistuning). In the single degree of freedom model, both mistuning types are equivalent but they are not, as demonstrated here, in more realistic models. The difference arises because changes in geometry induce not only changes in natural frequencies of the blades alone but of their modes and the importance of these two sources of variability is discussed with both Monte Carlo simulation and harmonic mistuning results.
The present investigation focuses also on the possible extension of the harmonic mistuning concept and of its quantitative information that can be derived from such analyses. From it, a novel measure of blade-disk coupling is introduced and assessed in comparison with the coupling index introduced in the past. In conclusions, the low cost of harmonic mistuning computations in comparison with full Monte Carlo simulations is
demonstrated to be worthwhile to elucidate the basic behavior of the mistuned rotor in a random setting.
ContributorsSahoo, Saurav (Author) / Mignolet, Marc Paul (Thesis advisor) / Chattopadhyay, Aditi (Committee member) / Oswald, Jay (Committee member) / Arizona State University (Publisher)
Created2014
Description
The focus of this investigation is on the development of a surrogate model of hypersonic aerodynamic forces on structures to reduce the computational effort involved in the determination of the structural response. The application is more precisely focused on uncertain structures. Then, following an uncertainty management strategy, the surrogate may exhibit an error with respect to Computational Fluid Dynamics (CFD) reference data as long as that error does not significantly affect the uncertainty band of the structural response. Moreover, this error will be treated as an epistemic uncertainty introduced in the model thereby generating an uncertain surrogate. Given this second step, the aerodynamic surrogate is limited to those exhibiting simple analytic forms with parameters that can be identified from CFD data.
The first phase of the investigation focuses on the selection of an appropriate form for the surrogate for the 1-dimensional flow over a flat clamped-clamped. Following piston theory, the model search started with purely local models, linear and nonlinear of the local slope. A second set of models was considered that involve also the local displacement, curvature, and integral of displacement and an improvement was observed that can be attributed to a global effect of the pressure distribution. Various ways to involve such a global effect were next investigated eventually leading to a two-level composite model based on the sum of a local component represented as a cubic polynomial of the downwash and a global component represented by an auto-regressive moving average (ARMA) model driven nonlinearly by the local downwash. This composite model is applicable to both steady pressure distributions with the downwash equal to the slope and to unsteady cases with the downwash as partial derivative with time in addition to steady.
The second part of the investigation focused on the introduction of the epistemic uncertainty in the aerodynamic surrogate and it was recognized that it could be achieved by randomizing the coefficients of the local and/or the auto-regressive components of the model. In fact, the combination of the two effects provided an applicable strategy.
The first phase of the investigation focuses on the selection of an appropriate form for the surrogate for the 1-dimensional flow over a flat clamped-clamped. Following piston theory, the model search started with purely local models, linear and nonlinear of the local slope. A second set of models was considered that involve also the local displacement, curvature, and integral of displacement and an improvement was observed that can be attributed to a global effect of the pressure distribution. Various ways to involve such a global effect were next investigated eventually leading to a two-level composite model based on the sum of a local component represented as a cubic polynomial of the downwash and a global component represented by an auto-regressive moving average (ARMA) model driven nonlinearly by the local downwash. This composite model is applicable to both steady pressure distributions with the downwash equal to the slope and to unsteady cases with the downwash as partial derivative with time in addition to steady.
The second part of the investigation focused on the introduction of the epistemic uncertainty in the aerodynamic surrogate and it was recognized that it could be achieved by randomizing the coefficients of the local and/or the auto-regressive components of the model. In fact, the combination of the two effects provided an applicable strategy.
ContributorsSharma, Pulkit (Author) / Mignolet, Marc Paul (Thesis advisor) / Liu, Yongming (Committee member) / McNamara, Jack (Committee member) / Arizona State University (Publisher)
Created2017