Non-Linear Dynamics of Steam Turbine Blades With Shroud: Numerical Analysis and Experiments

2012 ◽  
Author(s):  
Stefano Zucca ◽  
Muzio M. Gola ◽  
Francesco Piraccini
Keyword(s):  
Frequency Domain ◽  
Steam Turbine ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Low Pressure ◽  
Forced Response ◽  
Numerical Code ◽  
Accurate Information ◽  
Normal Contact ◽  
Non Linear

The prediction of the aeromechanical behavior of low-pressure blades represents one of the main challenges in the Steam Turbine Industry. The evaluation of forced response and damping is critical for the reliability of new designs and usually requires expensive validation campaigns such as Wheel Box Tests (WBT). A WBT consists of one or more blade rows assembled on a rotor and spun at the desired rotating speed in a vacuum cell, with synchronous excitation provided by various sources. The WBT provides accurate information about the blade modes frequency, the alternating response level, and allows the evaluation of the mechanical damping. Given the large effort in terms of costs and time associated to the experimental activity, the possibility to rely on the output of a numerical code either during the first steps of a new design or to investigate the effect of minor changes to a current design would be extremely beneficial to the development of future products. In order to compute the non-linear forced response of shrouded blades of steam turbines, custom numerical solvers must be developed, since commercial finite element (FE) solvers do not perform this kind of analysis in the frequency domain. In this paper, the forced response of a blade with shrouds of a low pressure steam turbine is computed and numerical results are compared with the experimental Wheel Box Tests performed at GE Oil & Gas. The calculations require a three-step procedure: in the first step, a non-linear static analysis is performed in ANSYS® in order to compute the actual contact area on the shroud surface and the distribution of static normal loads, then a reduced order model of the blade is generated in ANSYS® taking into account the stiffening effect on the blade of the pre-stress due to the centrifugal force, finally the reduced model is imported in a numerical code and the non-linear forced response of the blade is computed. The numerical code solves the balance equations of the system in the frequency domain, by means of the Harmonic Balance Method, imposing cyclic symmetry boundary conditions of the system. An interpolation procedure is implemented in order to manage the non-perfectly matching meshes of the shroud contact surfaces, while the tangential and normal contact stiffness is computed with a numerical model based on the contact mechanics principles. The numerical and the experimental results around some of the critical resonances of the system are compared in order to assess the reliability and accuracy of the numerical tool for its future implementation in the mechanical design practice of the blades.

A Contact Model for Nonlinear Forced Response Prediction of Turbine Blades: Calculation Techniques and Experimental Comparison

2008 ◽  
Author(s):  
Christian M. Firrone ◽  
Marco Allara ◽  
Muzio M. Gola
Keyword(s):  
Normal Load ◽  
Contact Stiffness ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Model ◽  
Experimental Comparison ◽  
Normal Contact ◽  
Contact Models

Dry friction damping produced by sliding surfaces is commonly used to reduce vibration amplitude of blade arrays in turbo-machinery. The dynamic behavior of turbine components is significantly affected by the forces acting at their contact interfaces. In order to perform accurate dynamic analysis of these components, contact models must be included in the numerical solvers. This paper presents a novel approach to compute the contact stiffness of cylindrical contacts, analytical and based on the continuous contact mechanics. This is done in order to overcome the known difficulties in simultaneously adjusting the values of both tangential and normal contact stiffness experimentally. Monotonic loading curves and hysteresis cycles of contact forces vs. relative displacement are evaluated as a function of the main contact parameters (i.e. the contact geometry, the material properties and the contact normal load). The new contact model is compared with other contact models already presented in literature in order to show advantages and limitations. The contact model is integrated in a numerical solver, based on the Harmonic Balance Method (HBM), for the calculation of the forced response of turbine components with friction contacts, in particular underplatform dampers. Results from the nonlinear numerical simulations are compared with those from validation experiments.

Forced Response of Interlocked Vane Segments: Numerical Predictions and Experimental Results

2006 ◽  
Author(s):  
Stefano Zucca ◽  
Sergio Filippi ◽  
Fabio Droetti ◽  
Muzio M. Gola
Keyword(s):  
Tangential Force ◽  
Harmonic Balance Method ◽  
Outer Radius ◽  
Forced Response ◽  
Experimental Results ◽  
Numerical Code ◽  
Friction Forces ◽  
Normal Contact ◽  
Numerical Predictions ◽  
Local Compliance

Resonant vibrations affect fatigue life of vane segments. Friction damping is employed to reduce vibration amplitude. When vane segments are assembled, they are twisted so that lower platforms are in contact. The sum of displacements of the two ends of the lower platform after twisting is defined ‘interlocking’. Different ‘interlocking’ values correspond to different values of normal contact force. When interlocked vanes vibrate under external force excitation, energy is dissipated by friction forces at lower platform contacts providing damping to the system. The aim of this paper is the experimental validation of a numerical code for forced response calculation of interlocked vane segments. Since friction forces depend on relative displacements of bodies in contact, the system is nonlinear. System force response is computed by means of Harmonic Balance Method (HBM). Contact model implemented in the code is characterised by tangential and normal stiffness to take into account local compliance of the contact area. Gross slip occurs when the instantaneous ratio of tangential force to normal force is equal to the friction coefficient. Also effect of microslip is taken in account. The experimental set-up used to validate the code is made of a vane segment fixed at the outer radius to an aluminium frame and in contact with two supports at the inner radius. Comparison between the numerical predictions and experimental results is performed for different values of interlocking (i.e. force normal to the contact).

Forced Response of Bladed Disks in Cyclic Symmetry With Underplatform Dampers

2006 ◽  
Author(s):  
Stefano Zucca ◽  
Juan Borrajo ◽  
Muzio M. Gola
Keyword(s):  
Contact Stiffness ◽  
Harmonic Balance Method ◽  
Rigid Bodies ◽  
Forced Response ◽  
Numerical Code ◽  
Algebraic Equations ◽  
Bladed Disks ◽  
Disk Model ◽  
Normal Contact ◽  
Linear Algebraic Equations

In this paper a methodology for forced response calculation of bladed disks with underplatform dampers is described. The FE disk model, supposed to be cyclically symmetric, is reduced by means of Component Mode Synthesis and then DOFs lying at interfaces are further reduced by means of interface modes. Underplatform dampers are modeled as rigid bodies translating both in the radial and in the tangential direction of the engine. Contacts between blade platforms and damper are simulated by means of contact elements characterized by both tangential and normal contact stiffness, allowing partial separation of contact surfaces. Differential equilibrium equations are turned in non-linear algebraic equations by means of the Harmonic Balance Method (HBM). The methodology is implemented in a numerical code for forced response calculation of frictionally damped bladed disks. Numerical calculations are performed to evaluate the effectiveness of both the reduced order model and the underplatform model in simulating the dynamic behavior of bladed disks in presence of underplatform dampers.

The Impact of Excitation and Mode Shape on Non-Linear Blade Vibrations

2020 ◽  
Author(s):  
Johannes Linhard ◽  
Andreas Hartung ◽  
Stefan Schwarz ◽  
Hans-Peter Hackenberg ◽  
Mateusz Sienko
Keyword(s):  
Mode Shape ◽  
Optical Measurement ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Vibration Measurement ◽  
Numerical Predictions ◽  
Non Linear ◽  
Strain Gauge Measurements ◽  
The Impact

Abstract Recently, reliable non-linear dynamic solvers for the analysis of frictionally coupled turbine blades have been developed which are based on either Higher Harmonic Balance Method or Non-linear Modal Analysis. One of these tools is OrAgL which was developed by Institute of Dynamics of Vibrations (Leibniz University of Hannover) and Institute of Aircraft Propulsion Systems (University of Stuttgart). In [1], the rig and engine validation results of with OrAgL performed forced response analyses have been published: The main aim of this paper was the comparison of non-linear numerical predictions (amplitude, frequencies) with the blade-to-blade averaged values of optical measurement results obtained using MTU’s non-contact vibration measurement system for shrouded turbine blades (BSSM-T). Detailed analyses and validations performed over the last two years showed several novel aspects of validation such as the comparison with strain gauge measurements. Moreover, a better understanding of the impact of excitation (magnitude and load distribution over the airfoil) as well as of the impact of the mode shape on the formation of saturation regimes is now possible. The results obtained from the analyses of real turbine blades are presented in this work.

Forced Response Sensitivity Analysis Using an Adjoint Harmonic Balance Solver

2018 ◽  
Author(s):  
Anna Engels-Putzka ◽  
Jan Backhaus ◽  
Christian Frey
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Unsteady Aerodynamics ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Algorithmic Differentiation ◽  
Design And Optimization ◽  
Initial Application ◽  
Reverse Mode ◽  
Geometric Changes

This paper describes the development and initial application of an adjoint harmonic balance solver. The harmonic balance method is a numerical method formulated in the frequency domain which is particularly suitable for the simulation of periodic unsteady flow phenomena in turbomachinery. Successful applications of this method include unsteady aerodynamics as well as aeroacoustics and aeroelasticity. Here we focus on forced response due to the interaction of neighboring blade rows. In the CFD-based design and optimization of turbomachinery components it is often helpful to be able to compute not only the objective values — e.g. performance data of a component — themselves, but also their sensitivities with respect to variations of the geometry. An efficient way to compute such sensitivities for a large number of geometric changes is the application of the adjoint method. While this is frequently used in the context of steady CFD, it becomes prohibitively expensive for unsteady simulations in the time domain. For unsteady methods in the frequency domain, the use of adjoint solvers is feasible, but still challenging. The present approach employs the reverse mode of algorithmic differentiation (AD) to construct a discrete adjoint of an existing harmonic balance solver in the framework of an industrially applied CFD code. The paper discusses implemen-tational issues as well as the performance of the adjoint solver, in particular regarding memory requirements. The presented method is applied to compute the sensitivities of aeroelastic objectives with respect to geometric changes in a turbine stage.

A Novel Method of Coupling the Steam Turbine Exhaust Hood and the Last Stage Blades Using the Non-Linear Harmonic Method

2013 ◽  
Author(s):  
Zoe Burton ◽  
Grant Ingram ◽  
Simon Hogg
Keyword(s):  
Steam Turbine ◽  
Turbine Blades ◽  
Computation Time ◽  
Computational Effort ◽  
Alternative Methods ◽  
Test Case ◽  
Exhaust Hood ◽  
Harmonic Method ◽  
Non Linear ◽  
Last Stage

The exhaust hood of a steam turbine is a vital area of turbomachinery research its performance strongly influences the power output of the last stage blades. It is well known that accurate CFD simulations are only achieved when the last stage blades are coupled to the exhaust hood to capture the strong interaction. This however presents challenges as the calculation size grows rapidly when the full annulus is calculated. The size of the simulation means researchers are constantly searching of methods to reduce the computational effort without compromising solution accuracy. This work uses a novel approach, by coupling the last stage blades and exhaust hood by the Non-Linear Harmonic Method, a technique widely used to reduce calculation size in high pressure turbine blades and axial compressors. This has been benchmarked against the widely adopted Mixing Plane method. The test case used is the Generic Geometry, a representative exhaust hood and last stage blade geometry that is free from confidentiality and IP restrictions and for which first calculations were presented at last year’s conference [1]. The results show that the non-uniform exhaust hood inlet flow can be captured using the non-liner harmonic method, an effect not previously achievable with single passage coupled calculations such as the mixing plane approach. This offers a significant computational saving, estimated to be a quarter of the computation time compared with alternative methods of capturing the asymmetry with full annulus frozen rotor calculations.

Advanced Water Droplet Erosion Protection for Modern Low Pressure Steam Turbine Steel Blades

2015 ◽  
Author(s):  
Joerg Schuerhoff ◽  
Andrei Ghicov ◽  
Karsten Sattler
Keyword(s):  
Steam Turbine ◽  
Water Droplet ◽  
Precipitation Hardening ◽  
Turbine Blades ◽  
Low Pressure ◽  
Steam Turbines ◽  
Treatment Facility ◽  
Material Loss ◽  
Pressure Steam ◽  
Steam Turbine Blades

Blades for low pressure steam turbines operate in flows of saturated steam containing water droplets. The water droplets can impact rotating last stage blades mainly on the leading edge suction sides with relative velocities up to several hundred meters per second. Especially on large blades the high impact energy of the droplets can lead to a material loss particularly at the inlet edges close to the blade tips. This effect is well known as “water droplet erosion”. The steam turbine manufacturer use several techniques, like welding or brazing of inlays made of erosion resistant materials to reduce the material loss. Selective, local hardening of the blade leading edges is the preferred solution for new apparatus Siemens steam turbines. A high protection effect combined with high process stability can be ensured with this Siemens hardening technique. Furthermore the heat input and therewith the geometrical change potential is relatively low. The process is flexible and can be adapted to different blade sizes and the required size of the hardened zones. Siemens collected many years of positive operational experience with this protection measure. State of the art turbine blades often have to be developed with precipitation hardening steels and/or a shroud design to fulfill the high operational requirements. A controlled hardening of the inlet edges of such steam turbine blades is difficult if not impossible with conventional methods like flame hardening. The Siemens steam turbine factory in Muelheim, Germany installed a fully automated laser treatment facility equipped with two co-operating robots and two 6 kW high power diode laser to enable the in-house hardening of such blades. Several blade designs from power generation and industrial turbines were successfully laser treated within the first year in operation. This paper describes generally the setup of the laser treatment facility and the application for low pressure steam turbine blades made of precipitation hardening steels and blades with shroud design, including the post laser heat treatments.

Powertrain Resilient Mounting Design Analysis

2018 ◽  
Author(s):  
Tigran Parikyan ◽  
Nikola Naranca ◽  
Jochen Neher
Keyword(s):  
Rigid Body ◽  
Modal Analysis ◽  
Frequency Domain ◽  
Static Analysis ◽  
Software Tool ◽  
Software Tools ◽  
Forced Response ◽  
Marine Engine ◽  
Linear Elastic ◽  
Non Linear

For efficient modeling of engine (or powertrain) supported by non-linear elastic mounts, a special methodology has been elaborated. Based on it, software tool has been developed to analyze the motion of rigid body and elastic mounts, which comprises of three modules: • Non-linear static analysis; • Modal analysis (undamped and damped); • Forced response (in frequency domain). Application example of a large V12 marine engine illustrates the suggested workflow. The results are verified against other software tools and validated by measurements.

Range of Variability in the Dynamics of Semi-Cylindrical Friction Dampers for Turbine Blades

2008 ◽  
Author(s):  
Stefano Zucca ◽  
Daniele Botto ◽  
Muzio M. Gola
Keyword(s):  
Degrees Of Freedom ◽  
Turbine Blades ◽  
Numerical Test ◽  
Forced Response ◽  
Numerical Code ◽  
Test Case ◽  
Force Coefficient ◽  
System A ◽  
Flat Side ◽  
Fatigue Failures

Under-platform dampers are used to reduce resonant stresses in turbine blades to avoid high cycle fatigue failures. In this paper a model of semi-cylindrical under-platform damper (i.e. with one flat side and one curved side) for turbine blades is described. The damper kinematics is characterized by three degrees of freedom (DOFs): in-plane translations and rotation. Static normal loads acting on the damper sides are computed using the three static balance equations of the damper. Non-uniqueness of normal pre-loads acting on the damper sides is highlighted. Implementation of the model in a numerical code for the forced response calculation of turbine blades with under-platform dampers shows that non-uniqueness of normal pre-loads leads to non-uniqueness of the forced response of the system. A numerical test case is presented to show the capabilities of the model and to analyze the effect of the main system parameters (damper mass, excitation force, coefficient of friction and damper rotation) on the damper behavior and on the system dynamics.

Simulations of Unsteady Blade Row Interactions Using Linear and Non-Linear Frequency Domain Methods

2015 ◽  
Author(s):  
Christian Frey ◽  
Graham Ashcroft ◽  
Hans-Peter Kersken
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Measurement Data ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Frequency Domain Methods ◽  
Blade Row ◽  
Non Linear ◽  
Rotor Stator Interaction ◽  
Unsteady Simulation

This paper compares various approaches to simulate unsteady blade row interactions in turbomachinery. Unsteady simulations of turbomachinery flows have gained importance over the last years since increasing computing power allows the user to consider 3D unsteady flows for industrially relevant configurations. Furthermore, for turbomachinery flows, the last two decades have seen considerable efforts in developing adequate CFD methods which exploit the rotational symmetries of blade rows and are therefore up to several orders of magnitude more efficient than the standard unsteady approach for full wheel configurations. This paper focusses on the harmonic balance method which has been developed recently by the authors. The system of equations as well as the iterative solver are formulated in the frequency domain. The aim of this paper is to compare the harmonic balance method with the time-linearized as well as the non-linear unsteady approach. For the latter the unsteady flow fields in a fan stage are compared to reference results obtained with a highly resolved unsteady simulation. Moreover the amplitudes of the acoustic modes which are due to the rotor stator interaction are compared to measurement data available for this fan stage. The harmonic balance results for different sets of harmonics in the blade rows are used to explain the minor discrepancies between the time-linearized and unsteady results published by the authors in previous publications. The results show that the differences are primarily due to the neglection of the two-way coupling in the time-linearized simulations.

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