Research on Aerodynamic Damping of Bladed Disk With Random Mistuning

2017 ◽  
Author(s):  
Lin Li ◽  
Xiaoping Yu ◽  
Peiyi Wang
Keyword(s):  
Travelling Waves ◽  
Elastic Stability ◽  
Travelling Wave ◽  
Wave Mode ◽  
Analysis Model ◽  
Aerodynamic Damping ◽  
Bladed Disk ◽  
Random Mistuning ◽  
Value Of It ◽  
Wave Modes

This paper presents an investigation on the aerodynamic damping of bladed disk (also called ‘blisk’) with mistuning. The study focuses mainly on the mechanism of the effect of random and intentional mistuning on the aero-elastic stability of blisk. For the purpose, aero-elastic stability equations of tuned and mistuned blisk in the frequency domain are established. NASA-Rotor37 is taken as the analysis model. In order to obtain the aerodynamic damping, the unsteady aero-elastic forces are calculated by the double channel harmonic method based on phase correction with aid of the general software CFX. Considering the stochastic characteristics of random mistuning, statistical analysis on the aerodynamic damping of mistuned blisk is performed. The effects of mistuning with different levels are compared. The mechanism of the effects of mistuning on the aero-elastic stability of blisk is found that mistuning couples the modes of different travelling waves and it concentrates the aerodynamic damping in a travelling wave-mode-family by increasing the aerodynamic damping ratios in forward travelling wave modes and decreasing the aerodynamic damping ratios in backward travelling wave modes. And the higher the mistuning level, the more obvious the trend. Furthermore, the following result is obtained: Whatever the mistuning level, in a traveling wave-mode-family, the aerodynamic damping of mistuned blisk is greater than the minimum aerodynamic damping of corresponding tuned blisk and less than the maximum value of it. Besides, the harmonic order of intentional mistuning that can be used to raise the aero-elastic stability of blisk is proposed.

Comparison of the Influence Coefficient Method and Travelling Wave Mode Approach for the Calculation of Aerodynamic Damping of Centrifugal Compressors and Axial Turbines

2017 ◽  
Author(s):  
K. Vogel ◽  
A. D. Naidu ◽  
M. Fischer
Keyword(s):  
Centrifugal Compressor ◽  
Travelling Wave ◽  
Wave Mode ◽  
Forced Response ◽  
Computational Time ◽  
Influence Coefficient ◽  
Average Deviation ◽  
Aerodynamic Damping ◽  
Influence Coefficients ◽  
Periodic Boundaries

The prediction of aerodynamic damping is a key step towards high fidelity forced response calculations. Without the knowledge of absolute damping values, the resulting stresses from forced response calculations are often afflicted with large uncertainties. In addition, with the knowledge of the aerodynamic damping the aeroelastic contribution to mistuning can be considered. The first section of this paper compares two methods of one-way-coupled aerodynamic damping computations on an axial turbine. Those methods are: the aerodynamic influence coefficient, and the travelling wave mode method. Excellent agreement between the two methods is found with significant differences in required computational time. The average deviation between all methods for the transonic turbine is 4%. Additionally, the use of transient blade row methods with phase lagged periodic boundaries are investigated and the influence of periodic boundaries on the aerodynamic influence coefficients are assessed. A total of 23 out of 33 passages are needed to remove all influence from the periodic boundaries for the present configuration. The second part of the paper presents the aerodynamic damping calculations for a centrifugal compressor. Simulations are predominantly performed using the aerodynamic influence coefficient approach. The influence of the periodic boundaries and the recirculation channel is investigated. All simulations are performed on a modern turbocharger turbine and centrifugal compressor using ANSYS CFX V17.0 with an inhouse pre- and post-processing procedure at ABB Turbocharging. The comparison to experimental results concludes the paper.

scholarly journals Mistuning Effects on the Nonlinear Friction Saturation of Flutter Vibration Amplitude

2020 ◽  
Author(s):  
Carlos Martel ◽  
Salvador Rodríguez
Keyword(s):  
Vibration Amplitude ◽  
Gas Flow ◽  
Travelling Waves ◽  
Computational Cost ◽  
Travelling Wave ◽  
Nonlinear Friction ◽  
Blade Vibration ◽  
Bladed Disk ◽  
Spring System ◽  
Mass Spring

Abstract The blade vibration level of an aerodynamically unstable rotor is a quantity of crucial importance to correctly estimate the blade fatigue life. This amplitude is the result of the balance between the energy pumped into the blades by the gas flow, and the nonlinear dissipation at the blade-disk contact interfaces. In a tuned configuration, the blade displacements can be described as a travelling wave consisting of one fundamental nodal diameter and frequency and its higher harmonics, and the problem can be reduced to the computation of a time periodic solution in just one sector. This simplification is no longer valid for a mistuned bladed disk. The resulting nonlinear vibration of the mistuned system is a combination of several travelling waves with different number of nodal diameters, coupled through mistuning. In this case, the complete bladed disk has to be considered, which requires an extremely high computational cost, and, for this reason, reduced order models (ROM) are required to analyze this situation. In this work, we use a 3 DOF/sector mass-spring system to describe the nonlinear friction saturation of the flutter vibration amplitude of a realistic mistuned bladed disk. The convergence of the solution of the mass-spring system is still quite slow because of the presence of many unstable modes with very similar growth rates. In order to speed-up the simulations a simpler asymptotic ROM is derived from the mass-spring model, which allows for much faster integration times. The simulations of the asymptotic ROM are compared with the measurements obtained in the European project FUTURE, where an aerodynamically unstable LPT rotor was tested with different intentional mistuning patterns.

Maximum Mistuned Vibration Amplitude With Aerodynamic Damping

2016 ◽  
Author(s):  
Carlos Martel ◽  
Luo Cuiping
Keyword(s):  
Vibration Amplitude ◽  
Travelling Wave ◽  
Forced Response ◽  
Dynamical Model ◽  
Reduced Model ◽  
Fem Model ◽  
Precise Information ◽  
Aerodynamic Damping ◽  
Bladed Disk ◽  
Maximum Amplification

Mistuning can dramatically increase the forced response of a bladed disk. In the case of damping coming from aerodynamic effects the situation is more complicated because the value of the damping is typically different for the different travelling wave modes of the system. This damping variability changes the effect of mistuning, and it can even result in a reduction of the maximum mistuned forced response amplitude below that of the tuned case (this was not possible in the usual case of constant material damping). In this paper the Asymptotic Mistuning Model (AMM) methodology is used to analyze this situation. The AMM is a reduced model that is systematically derived from the complete mistuned bladed disk dynamical model using a perturbative procedure based on the small size of the mistuning and the damping. Several different forcing cases are analyzed, and the results from the AMM are quantitatively compared with those from a FEM model of a mistuned bladed disk. The AMM gives also precise information about the key mechanisms involved in the forced response of mistuned cyclic structures, and about the maximum amplification of the vibration amplitude that the system can experience.

Travelling Wave Control of Rotating Discs and Analysis of its Spillover Effect

1988 ◽  
Vol 202 (2) ◽  
pp. 119-127 ◽  
Author(s):  
C-S Kim ◽  
C-W Lee
Keyword(s):  
Travelling Waves ◽  
Spillover Effect ◽  
Polynomial Equation ◽  
Travelling Wave ◽  
Rotating Disc ◽  
System A ◽  
Finite Dimensional ◽  
Control Scheme ◽  
Actuator System ◽  
Wave Control

A modal control scheme for rotating disc systems is developed based upon the finite-dimensional sub-system model including a few lower backward travelling waves important to the disc response. For the single discrete sensor and actuator system, a polynomial equation, which determines the closed-loop system poles, is derived and the spillover effect is analysed, providing a sufficient condition for stability. Finally, simulation studies are performed to show the effectiveness of the travelling wave control scheme proposed.

TRAVELLING WAVES AND OSCILLATIONS IN SAL’NIKOV’S COMBUSTION REACTION IN A COMPRESSIBLE GAS

2015 ◽  
Vol 56 (3) ◽  
pp. 233-247 ◽  
Author(s):  
RHYS A. PAUL ◽  
LAWRENCE K. FORBES
Keyword(s):  
Asymptotic Solution ◽  
Multiple Scales ◽  
Travelling Waves ◽  
Method Of Lines ◽  
Travelling Wave ◽  
Reaction Scheme ◽  
Compressible Viscous Gas ◽  
The Method Of Lines ◽  
Temperature Waves ◽  
Parameter Values

We consider a two-step Sal’nikov reaction scheme occurring within a compressible viscous gas. The first step of the reaction may be either endothermic or exothermic, while the second step is strictly exothermic. Energy may also be lost from the system due to Newtonian cooling. An asymptotic solution for temperature perturbations of small amplitude is presented using the methods of strained coordinates and multiple scales, and a travelling wave solution with a sech-squared profile is derived. The method of lines is then used to approximate the full system with a set of ordinary differential equations, which are integrated numerically to track accurately the evolution of the reaction front. This numerical method is used to verify the asymptotic solution and investigate behaviours under different conditions. Using this method, temperature waves progressing as pulsatile fronts are detected at appropriate parameter values.

Slip waves along the interface between two anisotropic elastic half-spaces in sliding contact

1988 ◽  
Vol 415 (1849) ◽  
pp. 389-419 ◽  
Keyword(s):  
Anisotropic Media ◽  
Wave Mode ◽  
Sliding Contact ◽  
Stoneley Wave ◽  
Shear Stresses ◽  
Wave Problem ◽  
Numerical Computations ◽  
Cubic Symmetry ◽  
Anisotropic Elastic ◽  
Wave Modes

A variant of the Stoneley-wave problem, namely slip waves between two homogeneous elastic half-spaces whose interface is incapable of supporting shear stresses, is studied. For two isotropic half-spaces there is either no or one slip-wave mode. In the case of anisotropic half-spaces, the possibility of a new slip-wave mode, called the second slip-wave mode, arises. The case of two identical anisotropic half-spaces of the same orientation is discussed in detail; criteria for the existence of a second slip-wave mode in terms of the nature of the transonic state are developed. It is concluded that for many anisotropic media a second slip-wave mode will exist within certain ranges of orientation of the slip-wave geometry. Numerical computations for iron (cubic symmetry) demonstrate that second slip-wave modes indeed exist in this material.

Nonlinear travelling internal waves with piecewise-linear shear profiles

2018 ◽  
Vol 856 ◽  
pp. 984-1013 ◽  
Author(s):  
K. L. Oliveras ◽  
C. W. Curtis
Keyword(s):  
Piecewise Linear ◽  
Travelling Waves ◽  
Tangential Velocity ◽  
Travelling Wave ◽  
Numerical Continuation ◽  
Travelling Wave Solutions ◽  
Water Wave Problem ◽  
Two Fluids ◽  
Wave Solutions ◽  
Linear Shear

In this work, we study the nonlinear travelling waves in density stratified fluids with piecewise-linear shear currents. Beginning with the formulation of the water-wave problem due to Ablowitz et al. (J. Fluid Mech., vol. 562, 2006, pp. 313–343), we extend the work of Ashton & Fokas (J. Fluid Mech., vol. 689, 2011, pp. 129–148) and Haut & Ablowitz (J. Fluid Mech., vol. 631, 2009, pp. 375–396) to examine the interface between two fluids of differing densities and varying linear shear. We derive a systems of equations depending only on variables at the interface, and numerically solve for periodic travelling wave solutions using numerical continuation. Here, we consider only branches which bifurcate from solutions where there is no slip in the tangential velocity at the interface for the trivial flow. The spectral stability of these solutions is then determined using a numerical Fourier–Floquet technique. We find that the strength of the linear shear in each fluid impacts the stability of the corresponding travelling wave solutions. Specifically, opposing shears may amplify or suppress instabilities.

Vibration Suppression of Mistuned Coupled-Blade-Disk Systems Using Piezoelectric Circuitry Network

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Hongbiao Yu ◽  
K. W. Wang
Keyword(s):  
Piezoelectric Transducer ◽  
Vibration Suppression ◽  
Structural Vibration ◽  
Bladed Disks ◽  
Disk Model ◽  
Bladed Disk ◽  
Engine Order ◽  
Optimal Network ◽  
Random Mistuning ◽  
Engine Components

For bladed-disk assemblies in turbomachinery, the elements are often exposed to aerodynamic loadings, the so-called engine order excitations. It has been reported that such excitations could cause significant structural vibration. The vibration level could become even more excessive when the bladed disk is mistuned, and may cause fatigue damage to the engine components. To effectively suppress vibration in bladed disks, a piezoelectric transducer networking concept has been explored previously by the authors. While promising, the idea was developed based on a simplified bladed-disk model without considering the disk dynamics. To advance the state of the art, this research further extends the investigation with focus on new circuitry designs for a more sophisticated and realistic system model with the consideration of coupled-blade-disk dynamics. A novel multicircuit piezoelectric transducer network is synthesized and analyzed for multiple-harmonic vibration suppression of bladed disks. An optimal network is derived analytically. The performance of the network for bladed disks with random mistuning is examined through Monte Carlo simulation. The effects of variations (mistuning and detuning) in circuit parameters are also studied. A method to improve the system performance and robustness utilizing negative capacitance is discussed. Finally, experiments are carried out to demonstrate the vibration suppression capability of the proposed piezoelectric circuitry network.

scholarly journals Nonuniform Continuity of the Osmosis K(2, 2) Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Aiyong Chen ◽  
Yong Ding ◽  
Wentao Huang
Keyword(s):  
Differential Equations ◽  
Small Amplitude ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Qualitative Theory ◽  
Travelling Wave Solutions ◽  
Solution Map ◽  
Wave Solutions ◽  
Periodic Travelling Wave ◽  
Uniformly Continuous

The qualitative theory of differential equations is applied to the osmosis K(2, 2) equation. The parametric conditions of existence of the smooth periodic travelling wave solutions are given. We show that the solution map is not uniformly continuous by using the theory of Himonas and Misiolek. The proof relies on a construction of smooth periodic travelling waves with small amplitude.

scholarly journals FKPP equation with impulses on unbounded domain

2017 ◽  
Vol 1 ◽  
pp. 1 ◽  
Author(s):  
Valaire Yatat ◽  
Yves Dumont
Keyword(s):  
Travelling Waves ◽  
Reaction Diffusion ◽  
Bare Soil ◽  
Travelling Wave ◽  
Reaction Diffusion Equations ◽  
Spreading Speed ◽  
Systems Dynamics ◽  
Travelling Wave Solutions ◽  
Minimal Speed ◽  
Wave Solutions

This paper deals with the problem of travelling wave solutions in a scalar impulsive FKPP-like equation. It is a first step of a more general study that aims to address existence of travelling wave solutions for systems of impulsive reaction-diffusion equations that model ecological systems dynamics such as fire-prone savannas. Using results on scalar recursion equations, we show existence of populated vs. extinction travelling waves invasion and compute an explicit expression of their spreading speed (characterized as the minimal speed of such travelling waves). In particular, we find that the spreading speed explicitly depends on the time between two successive impulses. In addition, we carry out a comparison with the case of time-continuous events. We also show that depending on the time between two successive impulses, the spreading speed with pulse events could be lower, equal or greater than the spreading speed in the case of time-continuous events. Finally, we apply our results to a model of fire-prone grasslands and show that pulse fires event may slow down the grassland vs. bare soil invasion speed.

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