Turbomachine Blades Research Articles

Numerical simulation of coupled aerothermal vibrations of the turbine blade

In the paper mathematic model and numerical method of simulation of coupled aerothermoelastic vibrations of turbomachine blade is presented. The results of the simulation of aerothermoelastic vibrations of turbine cooled blade are demonstrated

Vane Clocking Effects on the Resonant Response of an Embedded Rotor

st torsion mode resonant response of IBR-2 generated by the wakes from the upstream stators is quantified non-intrusively utilizing an Agilis NSMS for six vane clocking configurations at the design and high loading conditions. The forcing function to IBR-2 consists of the Stator1 wakes and the potential fields from Stators-1 and Stator-2, and their aerodynamic interactions. Thus, the IBR-2 resonant response experiments involve classic vane clocking, with the IGV, Stator-1 and Stator-2 each having identical vane counts. I. Introduction IGH Cycle Fatigue (HCF) and resonant response of turbomachine blading resulting from flow-induced vibrations continues to be a significant problem throughout the gas turbine industry. Design resonant response analyses consider a tuned blade row, i.e. a rotor with all blades having the same structural properties and thus, identical natural frequencies. In fact, there are small blade-to-blade structural property variations, termed mistuning, which are known to lead to significant increases in blade resonant response amplitude as compared to that of the tuned blade row, with mistuning often cited as an HCF source. Turbomachinery rotors have typically been bladed-disks, with individual blades inserted into a slotted disk and retained by means of a dove-tail or fir-tree attachment. Advances in manufacturing techniques have resulted in bladed-disks with increased uniformity, i.e. small mistuning. Unfortunately, smaller mistuning does not translate into lower amplitude blade vibrations. In addition, new manufacturing techniques have enabled integrally bladed rotors (IBRs) wherein the blades and disk are machined from a single piece of material. However, as compared to bladed-disks, IBRs have both much smaller mistuning and mechanical damping. As compared to bladed-disks, IBRs exacerbate the potential for large amplitude resonant response and HCF because of reduced mechanical damping and mistuning. The implementation of IBRs into engine designs also affects the development of acceptable rotors. When bladed-disks are found to have unacceptably high vibration amplitudes and vibratory stress during development or in the field, a traditional approach is to incorporate friction dampers. However, resonant response problems in IBRs may not be able to be solved with friction dampers because they cannot be easily implemented. Hence, new solutions are required to address IBR resonant response problems. In this regard, vane clocking is a potential technique for the control of the resonant response of embedded rotors. A particular embedded rotor is subjected to the periodic passing of the wakes from the upstream airfoil row and the potential disturbances from both the upstream and the downstream airfoils rows, i.e. an embedded rotor is subjected to three forcing functions, Figure 1. With airfoil rows having similar vane counts, the stationary vane rows can be indexed relative to one another to affect the airfoil row unsteady aerodynamic interactions. This circumferential indexing of vanes in adjacent rows with similar vane counts is termed vane clocking. Experimental research has shown that vane clocking can be an effective tool to increase turbine performance 1-4 , increase compressor

Mathematical model of aeroelastic vibrations of cascades of axial turbomachine blades, caused by circumferential nonuniformity of the flow

A system of linear differential equations with time-dependent coefficients, which describes aeroelastic vibrations of blade cascades in a nonuniform flow, is derived. With the use of the model of an ideal incompressible fluid and the hypothesis of cylindrical sections, determination of aerodynamic forces acting on the blades is reduced to solving problems by methods fairly well developed in the theory of cascades in unsteady flow. The possibility of the emergence of a parametric resonance is analyzed. It is demonstrated that circumferential nonuniformity of the flow in the turbomachine duct can substantially reduce the critical velocity of the cascade flutter.

On the Development of Turbomachine Blade Aerodynamic Design System

A turbomachine blade aerodynamic design process is proposed to design turbomachine blades. The design system, including a global optimization of through flow for whole machine and a local optimization of the airfoil design and airfoil section, stacks up. The airfoil generator code employs Bezier polynomial curves to produce smooth airfoil shapes. A meanline program combined with an optimizer was used to perform the global optimization. In the airfoil section design, for fast calculations of the airfoil pressure distributions a discrete vortex method is developed. A novel Navier-Stokes (N-S) solver is developed for further examination of the airfoil performance for final section design. The N-S code is used to obtain the blade-to-blade quasi-three-dimensional, turbulent, and viscous flow characteristics. The time-dependent N-S equations are discretized and integrated in a coupled manner based on a finite-volume formulation, as well as a flux-difference splitting. The flux-difference splitting method enables us to compute with a rapid convergence. The present N-S code can handle computations of both subsonic and supersonic flows and can be connected to an external optimizer code with the airfoil generator. After optimized airfoil was designed, a three-dimensional code was used for final tuning of the design.

Investigation of resonant modes and frequencies of plate vibrations as applied to turbomachine blades

The results of experimental and numerical investigations of resonant vibration frequencies and modes for rectangular cantilever plates of constant thickness are presented. The investigations are carried out using the methods of interference holography and finite elements, and the results may serve as basic references in determining resonant frequencies and modes of compressor and turbine blade vibrations.

Synchronization of four coupled van der Pol oscillators

It is possible that self-excited vibrations in turbomachine blades synchronize due to elastic coupling through the shaft. The synchronization of four coupled van der Pol oscillators is presented here as a simplified model. For quasilinear oscillations, a stability condition is derived from an analysis based on linearizing the original equation around an unperturbed limit cycle and transforming it into Hill’s equation. For the nonlinear case, numerical simulations show the existence of two well-defined regions of phase relationships in parameter space in which a multiplicity of periodic attractors is embedded. The size of these regions strongly depends on the values of the oscillator and coupling constants. For the coupling constant below a critical value, there exists a region in which a diversity of phase-shift attractors is present, whereas for values above the critical value an in-phase attractor is predominant. It is observed that the presence of an anti-phase attractor in the subcritical region is associated with sudden changes in the period of the coupled oscillators. The convergence of the coupled system to a particular periodic attractor is explored using several initial conditions. The study is extended to non-identical oscillators, and it is found that there is synchronization even over a wide range of difference among the oscillator constants.

Finite Element Simulation of Blade Row Viscous Interactions: Vane Vibratory Stress Prediction

DOI: 10.2514/1.17187 A fluid-structure interaction analysis is developed to study wake-generated turbomachine blade row unsteady aerodynamics and to predict the resulting vibratory stress. This is accomplished by incorporating the Baldwin– Lomax turbulence model into TAM-ALE3D, a 3-D multimaterial finite element code employing an arbitrary LagrangianEuleriansolver.ThisviscousTAM-ALE3Dmodelisthenutilizedtosimulate fluid-structureinteractions inthe PurdueTransonicCompressor. First, theviscousanalysis isexperimentally validated bysimulating therotorstator interaction unsteady aerodynamics at the part-speed condition at which detailed experimental data are available. The resonant response of the stator vanes to the unsteady aerodynamic excitation is then predicted by performing a full fluid-structure interaction simulation.

Nonintrusive turbomachine blade vibration measurement system

Conventional measurement systems for monitoring blade vibration generally use strain gauges attached to the surface of blades. Alternative noncontact measurement techniques are investigated in order to minimise the adverse effects of this method. In this paper, a new method based on groups of regularly spaced optical sensors and on apposite treatments is presented. An analytical model of the proposed monitoring system is introduced and some properties are studied. A general upper bound of the dynamic range is proposed. Some examples are presented and discussed. They assess the efficiency of this technique. Some specific situations are commented. The main advantage of the new system is its ability to analyse multicomponent blade vibrational signals on a large dynamic range with a reduced number of probes. Another interesting feature is that it enables the monitoring of all blades in a row.

Aerodynamic Damping Predictions in Turbomachines Using a Coupled Fluid-Structure Model

Flow-induced vibration of turbomachine blade rows is a coupled fluid-structure problem. Thus, rather than separate fluid and structural models, a coupled interacting fluid-structures analysis is needed. This need is addressed by extending the finite element code ALE3D that solves the three-dimensional Euler equations to model the unsteady aerodynamics of turbomachine blade rows. The same finite element model is applied to both the blading and the fluid, which results in consistency between the fluid and structure. Such a coupled interacting fluid-structure analysis enables the aerodynamic damping of multiple vibration modes to be predicted from two time-domain simulations: one with the blading in a vacuum and one with the blading in flow. This novel approach to predict aerodynamic damping is demonstrated by the consideration of a modern transonic compressor blade row. The blading is first impulsed in its first bending and first torsion modes in a vacuum. It is then immersed in the design-point flowfield and impulsed in its first bending and first torsion modes again. Signal processing tools applied to the predicted blade response time history extract the difference in the decay rate of both modes.

Wake Behavior behind Turbine Cascades in Compressible Two‐Dimensional Flows

The goal of the paper is to describe wake parameters of wakes from turbine cascades in compressible flows especially in planes where the leading edge of the following blade row would be located. Data from experiments with turbine cascades in compressible flow will be used to derive a theoretical approach which describes the wake growth and the recovery of the velocity deficit. The theory is based on similarity assumptions. The derived equations depend on simple and readily available parameters such as overall losses, exit angle, and Mach or Laval number. In compressible turbine flows, the influence of the inviscid flow field is of great importance. In this paper, an approach to take this influence into account when determining the behavior of the wake is presented. Correlations for basic characteristics of wakes in compressible flows are not readily available. Such correlations are necessary as input to unsteady flow and heat transfer calculation procedures for turbomachine blades. Based on available data on wake behavior in the compressible flow behind turbine blades, the correlations presented describe the wake behavior from the trailing edge to the confluence of the wakes of adjacent blades.

An Experimental and Computational Study of the Formation of a Streamwise Shed Vortex in a Turbine Stage

Shear layers shed by aircraft wings roll up into vortices. A similar, though far less common, phenomenon can occur in the wake of a turbomachine blade. This paper presents experimental data from a new single-stage turbine that has been commissioned at the Whittle Laboratory. Two low-aspect ratio stators have been tested with the same rotor row. Surface flow visualization illustrates the extremely strong secondary flows present in both NGV designs. These secondary flows lead to conventional passage vortices, but also to an intense vortex sheet which is shed from the trailing edge of the blades. Pneumatic probe traverses show how this sheet rolls up into a concentrated vortex in the second stator design, but not in the first. A simple numerical experiment is used to model the shear layer instability and the effects of trailing edge shape and exit yaw angle distribution are investigated. It is found that the latter has a strong influence on shear layer rollup: inhibiting the formation of a vortex downstream of NGV 1 but encouraging it behind NGV 2.

Wake-Induced Boundary Layer Transition in a Low-Speed Axial Compressor

The boundary layer on the blades of turbomachines substantially influences the loss production of the machine as well as the heat transfer between the blade surface and the fluid. For this reason the knowledge of the boundary layer structure and development plays an important role for the understanding and further improvement of turbomachines. The incoming wakes of the upstream blade rows strongly periodically influences the boundary layer on turbomachine blades. For this reason an unsteady, highly complex boundary layer behaviour can be observed. This paper presents experimental results of the unsteady boundary layer behaviour on the first stage stator blades of the four-stage Dresden Low-Speed Research Compressor. Different operating points of the compressor are investigated. Special consideration is taken on the analysis of the time-resolved structure of the incoming flow field and the unsteady boundary layer response. The wake passing triggers a periodic transition of the boundary layer starting already at the leading edge of the blade. The wake-induced transitional regions limit the extension of the laminar boundary layer in the front part of the blade. An improved description of the complex boundary layer structure is given.

Euler-Based Inverse Method for Turbomachine Blades, Part 2: Three-Dimensional Flows

The aerodynamic design method for turbomachine blades reported in part 1 is extended to three dimensions. In this inverse method, the blade pressure loading (i.e., pressure difference between blade upper and lower surfaces) and the blade thickness distributions are prescribed, and the corresponding blade camber surface is sought. The inverse problem is formulated using a pressure-loading boundary condition across the blade surfaces, and modification of the blade geometry is achieved using the flow-tangency conditions along the blade surfaces. The method is demonstrated for the design of axial-flow machines ranging from the subsonic to the supersonic flow regimes

Separation Bubbles Under Steady and Periodic-Unsteady Main Flow Conditions

Based on an experimental investigation carried out in a low-speed test facility at the Berlin University of Technology, this paper describes the formation of separation bubbles under steady and periodic-unsteady main flow conditions. The aim of the investigation was to understand the mechanism of separation, transition, and reattachment, and the effect of main flow unsteadiness on it. Separation bubbles for various main flow conditions were generated over a large flat plate, which experienced a similar pressure distribution to that on the suction surface of blades in turbomachines. The pressure distribution was generated by a contoured wall opposite the plate. Aimed at separating the effect of the velocity and the turbulence wake, this paper considers only the influence of the velocity wake. To this effect, a rotating flap was mounted downstream of the test section to produce periodic oscillations of the main flow. The overall flow field under steady main flow conditions was obtained by hot-wire measurements. Pressure taps were used to measure the pressure distribution over the plate. The Reynolds number effects were determined and compared to the measurement results in the literature. Results for periodic-unsteady separation bubbles are shown using different Strouhal numbers, oscillation amplitudes, and Reynolds numbers. Ensemble-averaged mean velocity profiles and the ensemble-averaged rms velocity profiles are used to demonstrate the development of the periodic boundary layer. Time–space diagrams are plotted to show the development of the periodic-unsteady boundary layers. The characteristic instability frequencies in the free shear layer are identified. The impact of the major parameters, Strouhal number and amplitude, on the bubble formation are discussed. [S0889-504X(00)01204-6]

Natural Transition Phenomena on an Axial Compressor Blade

Data from a surface hot-film array on the outlet stator of a 1.5-stage axial compressor are analyzed to look for direct evidence of natural transition phenomena. An algorithm is developed to identify instability waves within the Tollmien–Schlichting (T–S) frequency range. The algorithm is combined with a turbulent intermittency detection routine to produce space-time diagrams showing the probability of instability wave occurrence prior to regions of turbulent flow. The paper compares these plots for a range of blade loading, with free-stream conditions corresponding to the maximum and minimum inflow disturbance periodicity produced by inlet guide vane clocking. Extensive regions of amplifying instability waves are identified in nearly all cases. The implications for transition prediction in decelerating flow regions on axial turbomachine blades are discussed.

Euler-based inverse method for turbomachine blades. II - Three-Dimensional flows

Euler-based inverse method for turbomachine blades. II - Three-Dimensional flows

Issues of Simulation of Turbomachine Blade Vibration

Theoretical and experimental investigations confirm that the theory of beams can be used, within its applicability range, for express-analysis of the frequency spectrum of turbomachine blades. A detailed analysis of the displacement and stress fields in the vibration of blades requires using three-dimensional models.

Simulation of Vortex Shedding in a Turbine Stage

Vortex shedding in a turbomachine blade row is affected by the passing of blades in the adjacent downstream blade row, but these effects have not been examined in the literature. A series of flow simulations has been performed to study vortex shedding in a turbine stage, and to quantify the blade interaction effects on the unsteady pressure response. The numerical issues of spatial order of accuracy and the use of Newton subiterations were investigated first. Second-order spatial accuracy was shown to be inadequate to model the shedding frequency response and time-averaged base pressure accurately. For the small time step employed for temporal accuracy, Newton iterations were shown to be unnecessary. The effects of the adjacent blade row were examined by comparing the shedding frequency response for the stage simulations to the response for isolated cascades. The vane shedding was shown to occur exactly on a series of harmonics of the blade passing frequency for the stage case, compared to a single predominant frequency for the isolated cascade. Losses were also examined in the wake region. It was shown that close to the trailing edge, losses were mainly due to wake mixing. Farther downstream of the trailing edge, losses were predominantly due to the trailing edge shock wave.

Identification of Mistuning Characteristics of Bladed Disks From Free Response Data—Part I

The focus of the present two-part investigation is on the estimation of the dynamic properties, i.e., masses, stiffnesses, natural frequencies, mode shapes and their statistical distributions, of turbomachine blades to be used in the accurate prediction of the forced response of mistuned bladed disks. As input to this process, it is assumed that the lowest natural frequencies of the blades alone have been experimentally measured, for example, in a broach block test. Since the number of measurements is always less than the number of unknowns, this problem is indeterminate in nature. In this first part of the investigation, two distinct approaches will be investigated to resolve the shortfall of data. The first one relies on the imposition of as many constraints as needed to ensure a unique solution to this identification problem. Specifically, the mode shapes and modal masses of the blades are set to their design/tuned counterparts while the modal stiffnesses are varied from blade to blade to match the measured natural frequencies. The second approach, based on the maximum likelihood principle, yields estimates of all the structural parameters of the blades through the minimization of a specified “cost function.” The accuracy of these two techniques in predicting the forced response of mistuned bladed disks will be assessed on simple dynamic models of the blades.

Identification of Mistuning Characteristics of Bladed Disks From Free Response Data— Part II

The focus of the present two-part investigation is on the estimation of the dynamic properties, i.e., masses, stiffnesses, natural frequencies, mode shapes and their statistical distributions, of turbomachine blades to be used in the accurate prediction of the forced response of mistuned bladed disks. As input to this process, it is assumed that the lowest natural frequencies of the blades alone have been experimentally measured, for example in a broach block test. Since the number of measurements is always less than the number of unknowns, this problem is indeterminate in nature. In this second part of the investigation, the maximum likelihood method (ML) will first be revisited and a thorough assessment of its reliability in a wide variety of conditions, including the presence of measurement noise, different distributions of blade structural properties, etc., will be conducted. Then, a technique that provides a bridge between the two identification methods introduced in Part I, i.e., the random modal stiffnesses (RMS) and maximum likelihood (ML) approaches, will be presented. This technique, termed the improved random modal stiffnesses (IRMS) method is based on the maximum likelihood concepts but yields a mistuning model similar to that of the random modal stiffnesses technique. Finally, the accuracy of the RMS, ML, and IRMS methods in predicting the forced response statistics of mistuned bladed disks will be investigated in the presence of close blade alone natural frequencies.