scholarly journals SENSITIVITY ANALYSIS FOR FORCED RESPONSE IN TURBOMACHINERY USING AN ADJOINT HARMONIC BALANCE METHOD

2016 ◽  
Author(s):  
Anna Engels-Putzka ◽  
Christian Frey
Keyword(s):  
Sensitivity Analysis ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Balance Method

Forced Response Prediction of Blades With Loosely Assembled Dovetail Attachment by HBM

2009 ◽  
Author(s):  
Shangguan Bo ◽  
Zili Xu ◽  
Qilin Wu ◽  
XianDing Zhou ◽  
ShouHong Cao
Keyword(s):  
Friction Force ◽  
Centrifugal Force ◽  
Dry Friction ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Balance Method ◽  
Force Model ◽  
Equivalent Stiffness ◽  
Equivalent Damping

To understand the mechanism of interfacial damping of axial loosely assembled dovetail to suppress blade vibration, a dry friction force model is presented by the Coulomb friction law and the macroslip model, and the mathematical expression of the friction force is derived. The nonlinear friction force is linearized as an equivalent stiffness and an equivalent damping through the one-term harmonic balance method. The effect of centrifugal force on the equivalent stiffness and the equivalent damping is studied. The forced response of one simplified blade with loosely assembled dovetail attachment is predicted by the harmonic balance method, in which the blade is described by the lumped mass and spring model, and the friction contact joints is simplified as a ideal friction damper. The results show that the equivalent stiffness of loosely assembled dovetail attachment increases with blade centrifugal force, gradually reaches a certain value, and there exists the maximum value for the equivalent stiffness. The equivalent damping increases at the beginning and then decreases with blade centrifugal force increasing, there exists a maximum too. The resonant frequency of blade rises with blade centrifugal force, but it no longer increases when the centrifugal force exceed a certain value. There exists a special centrifugal force on which the effect of dry friction damping is the best.

Forced Response Prediction of Constrained and Unconstrained Structures Coupled Through Frictional Contacts

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Ender Cigeroglu ◽  
Ning An ◽  
Chia-Hsiang Menq
Keyword(s):  
Harmonic Balance ◽  
Normal Load ◽  
Contact Point ◽  
Harmonic Balance Method ◽  
Response Prediction ◽  
Forced Response ◽  
Contact Forces ◽  
Balance Method ◽  
Frictional Contacts ◽  
Contact Points

In this paper, a forced response prediction method for the analysis of constrained and unconstrained structures coupled through frictional contacts is presented. This type of frictional contact problem arises in vibration damping of turbine blades, in which dampers and blades constitute the unconstrained and constrained structures, respectively. The model of the unconstrained/free structure includes six rigid body modes and several elastic modes, the number of which depends on the excitation frequency. In other words, the motion of the free structure is not artificially constrained. When modeling the contact surfaces between the constrained and free structure, discrete contact points along with contact stiffnesses are distributed on the friction interfaces. At each contact point, contact stiffness is determined and employed in order to take into account the effects of higher frequency modes that are omitted in the dynamic analysis. Depending on the normal force acting on the contact interfaces, quasistatic contact analysis is initially employed to determine the contact area as well as the initial preload or gap at each contact point due to the normal load. A friction model is employed to determine the three-dimensional nonlinear contact forces, and the relationship between the contact forces and the relative motion is utilized by the harmonic balance method. As the relative motion is expressed as a modal superposition, the unknown variables, and thus the resulting nonlinear algebraic equations in the harmonic balance method, are in proportion to the number of modes employed. Therefore the number of contact points used is irrelevant. The developed method is applied to a bladed-disk system with wedge dampers where the dampers constitute the unconstrained structure, and the effects of normal load on the rigid body motion of the damper are investigated. It is shown that the effect of rotational motion is significant, particularly for the in-phase vibration modes. Moreover, the effect of partial slip in the forced response analysis and the effect of the number of harmonics employed by the harmonic balance method are examined. Finally, the prediction for a test case is compared with the test data to verify the developed method.

scholarly journals Adjoint-Based Aeroelastic Design Optimization Using a Harmonic Balance Method

2020 ◽  
Author(s):  
Nitish Anand ◽  
Antonio Rubino ◽  
Piero Colonna ◽  
Matteo Pini
Keyword(s):  
Design Optimization ◽  
Harmonic Balance ◽  
Flow Analysis ◽  
Computational Cost ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Balance Method ◽  
Working Fluid ◽  
Compressor Cascade ◽  
Impulse Turbine

Abstract Turbomachinery blades characterized by highly-loaded, slender profiles and operating under unsteady flow may suffer from aeroelastic shortcomings, like forced response and flutter. One of the ways to mitigate these aeroelastic effects is to redesign the blade profiles, so as to increase aero-damping and decrease aero-forcing. Design optimization based on high-fidelity aeroelastic analysis methods is a formidable task due to the inherent computational cost. This work presents an adjoint-based aeroelastic shape-optimization framework based on reduced order methods for flow analysis and forced response computation. The flow analysis is carried out through a multi-frequency fully-turbulent harmonic balance method, while the forced response is computed by means of the energy method. The capability of the design framework is demonstrated by optimizing two candidate cascades, namely, i) a transonic compressor cascade and, ii) a supersonic impulse turbine rotor operating with toluene as working fluid, initially designed by means of the method of waves. The outcomes of the optimization show significant improvements in terms of forced-response in both cases as a consequence of aero-damping enhancement.

Computing Fluid Structure Interaction Coupling Time Spectral Method (TSM) and Harmonic Balance Method (HBM)

2017 ◽  
Author(s):  
Aude Cadel ◽  
Ghislaine Ngo Boum ◽  
Fabrice Thouverez ◽  
Alain Dugeai ◽  
Marie-Océane Parent
Keyword(s):  
Steady State ◽  
Flow Field ◽  
Spectral Method ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Balance Method ◽  
Integration Scheme ◽  
Fluid Structure ◽  
Time Spectral Method

This paper deals with fluid-structure interactions (FSI), involving a blade profile, submitted to different sources of excitations, as if it were included in a real engine. Two forces of excitation will be considered on the NACA 64A010 airfoil, described in : an external force, due to a forced rotation motion of the blade, and an aerodynamic force, induced by fluid flow around the structure. By using the Harmonic Balance Method, the airfoil’s motion equation becomes an algebraic problem. Then, this system is solved for each frequency of a chosen range. Therefore, the fluid effect on the translation motion of the profile is studied. To compute the time periodic aerodynamic field, the Time Spectral Method, implemented in the Onera’s elsA solver, is used for a fast and efficient resolution. This method relies on a time-integration scheme that turns the resolution of the turbulent Navier-Stokes problem into the resolution of several coupled steady state problems computed at different instants of the time period of the movement. The Theodorsen approach with several hypothesis exposed in allows an analytic estimation of the unsteady lift effort. The two approaches are compared for an imposed motion. In order to predict the dynamic behavior of the system, a fully coupled numerical methodology is developed. For each frequency and at each iteration, TSM supplies the flow field which is used by HBM as a nonlinear excitation on the structure to computate a periodic response and conversely, HBM supplies the new deformed mesh used by TSM to compute the flow field. This strategy has the advantage that all computations take place in the spectral domain, allowing thus to find the steady-state behavior of the fluid and the structure without computing any transient state. The analysis provides the Frequency Forced Response. Some frequencies in the range corresponding to a contribution change between structure and fluid damping are precisely highlighted.

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