In this paper, optimization of the first blade of a new test rig is pursued using a hybrid model comprising the genetic algorithm, artificial neural networks and design of experiments. Blade tuning...

https://www.tandfonline.com/doi/pdf/10.1080/19942060.2019.1649196

Aeromechanical optimization of first row compressor test stand blades using a hybrid machine learning model of genetic algorithm, artificial neural networks and design of experiments

Torsional aeroelastic analysis of a turbomachinery cascade comprised of three-layered sandwich blades embedded with Magnetorheological Elastomer (MRE) core layer is carried out in this paper. The MRE material is used as a constrained damping layer between two elastic skins in order to investigate its effects on the aeroelastic stability of a blade cascade. To formulate the structural dynamic of the blades, torsional theory of rectangular laminated plates is used and the unsteady Whitehead's aerodynamic theory is employed to model the aerodynamic loadings. Assumed modes method and the Lagrange's equations are used to derive the governing equations of motion of the coupled aeroelastic system. Then, the effects of different parameters on flutter stability of the blades cascade are studied in details. It is found that the magnetic field and MRE layer thickness have significant influences on the flutter boundary of the system and the mistuning of the magnetic field intensity has beneficial effect on the flutter stability. Additionally, the results confirm that the concept of sandwich blades provided with MRE core has capability to utilize as a passive treatment in turbomachinery applications for improving the flutter characteristics of the blades.

Aeroelastic instability analysis of a turbomachinery cascade with magnetorheological elastomer based adaptive blades

Quasi-steady prediction of coupled bending–torsion flutter under rotating stall

In this paper, a quasi-steady method is developed for predicting the coupled bending-torsion flutter in a compressor cascade during classic surge. The classic surge is one of the major compressor flow field instabilities involving pulsation of the main flow through the compressor. The primary reason for the occurrence of the classic surge is the stalling of the blade rows and if the conditions are favorable this can trigger flutter, which is a self-excited aero elastic instability. The classic surge flow is modeled by using the well-established model of Moore and Greitzer and the obtained flow condition is used to determine the aerodynamic loads of the cascade using the linearized Whitehead's theory. The cascade stability is then examined by solving the two dimensional structural model by treating it as a complex eigenvalue problem. The structural stability is analyzed for a range of values of the frequency ratio and primary emphasis is given for the frequency ratio value of 0.9 as many interesting features could be revealed. The cascade shows a bifurcation from bending flutter to the torsional one signifying that only one of the flutter modes are favored at any instant in time. The torsional flutter is found to be the dominant flutter mode for a range of frequency ratios during classic surge whereas the bending flutter is found to occur only for some values of frequency ratio very close to unity as the torsional loads acting on the blades are found to be orders of magnitude higher than the bending loads. A rapid initiation of torsional flutter is seen to occur during classic surge for frequency ratio values very close to unity and it is perceived that during blade design, frequency ratios should be kept below 0.9 to prevent the flutter possibilities. An estimate of structural energy variation with time indicates that even if the total structural energy is negative one of the modes can go unstable during classic surge.

Quasi-Steady Prediction of Coupled Bending-Torsion Flutter Under Classic Surge

This paper studies the effects of bending-torsion coupling on the flutter stability boundaries of a turbomachinery cascade with Magnetorheological Elastomer (MRE) based sandwich blades. The blade structure is considered as a non-uniform sandwich beam with an embedded MRE core. The governing equations of bending and torsional motions are obtained based on the classical sandwich beam theory and the unsteady Whitehead aerodynamic theory is applied for modeling of the aerodynamic flow. The equations of motion governing on the coupled aeroelastic system have been derived in a discrete form by Lagrange's equations and using the assumed modes method. The stability analysis is performed and the effects of various parameters such as coupling, magnetic field, taper ratios and different mistuning patterns on the flutter characteristics have been investigated. The results indicate that the flutter stability is clearly affected by the interaction between the bending and torsional motions which is in agreement with the results previously obtained for a typical cascade. The results also indicate that the change of blade cross sectional area has a significant effect on the flutter boundaries.

Coupled bending-torsion flutter investigation of MRE tapered sandwich blades in a turbomachinery cascade

The development o f propulsion system technology over the last few decades has encountered and overcome several technological barriers. A large number o f problems were resolved resulting in considerably higher component efficiencies and reduced fuel consumption. These advances led to lighter overall designs and higher power densities compared to earlier designs. The accomplishment of lighter designs for the turbomachinery components also led to some drawbacks due to the reduced margins on the design factor-of-safety. Consequently, aeroelastic stability has become a major concern, and is often the limiting design constraint. So a careful and systematic study of coupled bending-torsion flutter o f a cascade in incompressible flow was carried out which requires estimation of unsteady aerodynamic loads, and a structural model o f the cascade. Unsteady aerodynamic loads were evaluated using Whitehead's solution for incompressible flow through a cascade of arbitrary geometry and interblade phase angle. The lift and moment coefficients calculated were found to match within the four decimal place accuracy with the results given by Whitehead and other literature. The blades were modeled as an equivalent 2-D section at 75% of span, and structural and inertial couplings were lumped into an effective CG-EA offset. Structural damping was included in the equations of motion. The resulting complex eigenvalue problem was solved recognizing the fact that there are two parameters in the eigenvalue problem, namely the reduced frequency k and the interblade phase angle β. The critical flutter speed was determined by minimizing it with respect to β, keeping the constraint on β as suggested by Lane. The solution provided the critical flutter speed with respect to both the torsion and the bending modes as a function of the interblade phase angle as well as dominant vibration frequencif s at flutter. Various structural and aerodynamic parameters of the cascade were varied and the effect of the variations on the coupled bending torsion flutter was studied. A jump was observed in the flutter boundary near frequency ratio of I, which was explained by the change in the mode shape of the vibration, which is represented by interblade phase angle. The developed technique can be used as a preliminary design tool for the aeroelastic flutter analysis of turbo-machinery blades.

H. Pathak

Papers

Effects of Geometric and Structural Parameters on Coupled Bending Torsion Flutter in Turbo Machinery Blades