Tip Shroud Research Articles

Strength analysis method of CMCs tip shroud structure considering random distribution of preform properties

This paper considers the impact of the random distribution of yarn properties on the mechanical and failure behavior of ceramic matrix composites (CMCs) structures and proposes an integrated analysis method based on preform-structure. Tensile tests of CMCs tip shroud specimens were carried out, and the digital image correlation technique was used to record the deformation of the specimens in real-time during loading. Based on the actual structure, a preform model of the CMCs tip shroud was established, and the kernel density estimation method was used to obtain the distribution of the yarn cross-sectional area. The random distribution of the cross-sectional area is equivalent to material properties, simulating the dispersion of the performance of CMCs. The progressive damage method simulates the failure mode during the specimen's loading process. The peak load error is 1.5 %, and the failure modes such as transverse shear damage, stitching yarn fracture, and interlaminar separation were successfully predicted.

Experimental Study and 3D Optimization of Small-Scale Solar-Powered Radial Turbine Using 3D Printing Technology

Small-Scale Turbines (SSTs) are among the most important energy-extraction-enabling technologies in domestic power production systems. However, owing to centrifugal forces, the high rotating speed of SSTs causes excessive strains in the aerofoil portions of the turbine blades. In this paper, a structural performance analysis is provided by combining Finite Element Methods (FEM) with Computational Fluid Dynamics (CFD). The primary objective was to examine the mechanical stresses of a Small-Scale Radial Turbine (SSRT) constructed utilizing 3D printing technology and a novel plastic material, RGD 525, to construct a SSRT model experimentally. After introducing a suitable turbine aerodynamics model, the turbine assembly and related loads were translated to a structural model. Subsequently, a structural analysis was conducted under various loading situations to determine the influence of different rotational speed values and blade shapes on the stress distribution and displacement. Maximum von Mises and maximum main stresses are significantly affected by both the rotor rotational speed and the working fluid input temperature, according to the findings of this research. The maximum permitted deformation, on the other hand, was more influenced by rotational speed, while the maximum allowable fatigue life was more influenced by rotating speed and fluid intake temperature. Also, the region of the tip shroud in the rotor had greater deflection values of 21% of the blade tip width.

Fully Coupled Analysis of Flutter Induced Limit Cycles: Frequency Versus Time Domain Methods

Abstract To save resources and reduce emissions, it is crucial to reduce weight of aircraft engines and further increase aerodynamic efficiency of gas and steam turbines. For turbine blades, these goals often lead to flutter. Thus, innovative flutter-tolerant designs are explored, where flutter induces limit cycle oscillations (LCOs) of tolerable yet nonzero levels. Flutter represents a self-excitation mechanism and, in the linear case, would lead to exponential divergence. Flutter-induced LCOs are therefore an inherently nonlinear phenomenon. The saturation of flutter-induced vibrations can be caused by nonlinear frictional contact interactions, e.g., in tip shroud interfaces. To develop flutter-tolerant designs, efficient methods are required which compute LCOs based on an appropriate modeling of elastic, inertia, aerodynamic, and contact forces. We recently developed a Frequency Domain Fluid-Structure Interaction (FD-FSI) solver for flutter-induced LCOs. The solver relies on the Harmonic Balance method applied to the structure as well as the fluid domain. It was shown that especially for long and slender blades with friction in shroud interfaces and strong aerodynamic influence, a coupled analysis can significantly increase the accuracy of predicted LCOs compared to the current state-of-the-art methods. Conventional methods do not properly account for the nonlinear change of frequency and deflection shape, and the effect of these changes on the aerodynamic damping, and thus fail in predicting certain LCOs at all. In the current work, the FD-FSI solver is numerically validated against Time Domain Fluid-Structure Interaction (TD-FSI) simulations. As a test case, a shrouded low-pressure turbine with friction in the shroud interfaces is considered. The point of operation is highly loaded and transonic in order to make the test case challenging. Apart from a successful validation of the FD-FSI solver, we shed light on important advantages and disadvantages of both solvers. Due to the lack of robust phase-lag boundary conditions for time domain solvers, a full blade row must be simulated. Thus, the FD-FSI solver typically requires only a fraction of the computational costs. Moreover, the FD-FSI solver contributes to an increased physical understanding of the coupled vibrations: By analyzing the contribution of individual harmonics, we analyze why unexpected even harmonics appear in a certain LCO. On the other hand, the FD-FSI solver does not provide information on the asymptotic stability of the LCOs and is strictly limited to periodic oscillations. Indeed, quasi-periodic limit torus oscillations (LTOs) appear in our test case. Using the TD-FSI solver, we confirm the internal combination resonance, postulated recently as necessary condition for LTOs, for the first time, in a fully coupled analysis.

Experimental Studies of the Discharge Characteristics of Variable-Pitch Multifinned Seals

Variable-pitch multifinned seals (VPMS) have not hitherto found wide use in the steam turbines produced in Russia, although they are quite often used outside of Russia. In modernizing the existing and designing new steam turbines, rotor blades with an integrally machined shroud are used, which opens the possibility to manufacture multirow peripheral seals. In this connection, the question about selecting the optimal VPMS configuration becomes of important practical significance. The results obtained in this study made it possible to experimentally estimate the extent to which different combination of fin pitches on the rotor and stator influence the VPMS discharge characteristics and to elaborate practical recommendations on using them. The minimal leak flow was recorded for the VPMS models with a 2-mm-wide pitch on the rotor. Comparative experimental investigations of VPMS models with 3- and 4-mm-wide spacers on the rotor and 4- and 5-mm-wide spacers on the stator were carried out as applied to the shroud seals of large-capacity steam turbines. The model pair with the 4- and 5-mm-wide spacers on the rotor and stator, i.e., with the pitches equal to 4.8 and 5.8 mm on the rotor and stator, respectively, can be regarded as the most optimal of those investigated in this work. It has been shown experimentally that, with all other things being equal, the leak in VPMSs is by 22–25% smaller than it is in straight-flow seals. By using VPMS, it becomes possible to avoid rubbing of the rotor against the stator under the conditions of relative radial and axial rotor displacements in transient modes of operation. In addition, the aerodynamic forces in VPMS able to excite a low-frequency shaft line self-oscillation are approximately equal to 60% of the similar forces occurring in the conventional radial clearance seals. In view of this circumstance, VPMS can be recommended for use instead of the standard tip shroud seals in the high- and intermediate-pressure cylinders in new and modernized steam turbines.

Development of a fully-coupled harmonic balance method and a refined energy method for the computation of flutter-induced Limit Cycle Oscillations of bladed disks with nonlinear friction contacts

Flutter stability is a dominant design constraint of modern gas and steam turbines. To further increase the feasible design space, flutter-tolerant designs are currently explored, which may undergo Limit Cycle Oscillations (LCOs) of acceptable, yet not vanishing, level. Bounded self-excited oscillations are a priori a nonlinear phenomenon, and can thus only be explained by nonlinear interactions such as dry stick–slip friction in mechanical joints. The currently available simulation methods for blade flutter account for nonlinear interactions, at most, in only one domain, the structure or the fluid, and assume the behavior in the other domain as linear. In this work, we develop a fully-coupled nonlinear frequency domain method which is capable of resolving nonlinear flow and structural effects. We demonstrate the computational performance of this method for a state-of-the-art aeroelastic model of a shrouded turbine blade row. Besides simulating limit cycles, we predict, for the first time, the phenomenon of nonlinear instability, i.e., a situation where the equilibrium point is locally stable, but for sufficiently strong perturbation (caused e.g.by an impact), the dry frictional dissipation cannot bound the flutter vibrations. This implies that linearized theory does not necessary lead to a conservative design of turbine blades. We show that this phenomenon is due to the nonlinear contact interactions at the tip shrouds, which cause a change of the vibrational deflection shape and frequency, which in turn leads to a loss of aeroelastic stability. Finally, we extend the well-known energy method to capture these effects, and conclude that it provides a good approximation and is useful for initializing the fully-coupled solver.

Analysis of Friction-Saturated Flutter Vibrations With a Fully Coupled Frequency Domain Method

Abstract Flutter stability is a dominant design constraint of modern turbines. Thus, flutter-tolerant designs are currently explored, where the resulting vibrations remain within acceptable bounds. In particular, friction damping has the potential to yield limit cycle oscillations (LCOs) in the presence of a flutter instability. To predict such LCOs, it is the current practice to model the aerodynamic forces in terms of aerodynamic influence coefficients for a linearized structural model with fixed oscillation frequency. This approach neglects that both the nonlinear contact interactions and the aerodynamic stiffness cause a change in the deflection shape and the frequency of the LCO. This, in turn, may have a substantial effect on the aerodynamic damping. The goal of this paper is to assess the importance of these neglected interactions. To this end, a state-of-the-art aero-elastic model of a low pressure turbine blade row is considered, undergoing nonlinear frictional contact interactions in the tip shroud interfaces. The LCOs are computed with a fully coupled harmonic balance method, which iteratively computes the Fourier coefficients of structural deformation and conservative flow variables, as well as the a priori unknown frequency. The coupled algorithm was found to provide excellent computational robustness and efficiency. Moreover, a refinement of the conventional energy method is developed and assessed, which accounts for both the nonlinear contact boundary conditions and the linearized aerodynamic influence. It is found that the conventional energy method may not predict a limit cycle oscillation at all while the novel approach presented here can.

Application of blade tip shroud brush seal to improve the aerodynamic performance of turbine stage

The blade tip shroud brush seal is applied to replace the labyrinth seal for the aerodynamic performance improvement of turbine stage. The leakage flow characteristics of the brush seal are numerically predicted by using the Reynolds-Averaged Navier–Stokes equations and non-linear Darcian porous medium model. The numerical leakage flow rate of the brush seal is in well agreement with the experimental data. The last and first long teeth of the labyrinth seal were designed to bristle pack named as the postposed and preposed brush seals based on the 1.5 turbine stage. The leakage flow rate and aerodynamic performance of the turbine stage with blade tip shroud labyrinth seal and brush seal are numerically investigated. The effect of the sealing clearance between bristle pack and tip shroud on the aerodynamic performance of turbine stage is conducted which ranged from 0 mm to 0.4 mm. The axial deflection of the bristle pack is analyzed with consideration of the aerodynamic forces and contact frictional force. The obtained results show that the leakage flow rate of the tip shroud brush seals with bristle tip 0.4 mm clearance which decreases by up to 18% in comparison with the labyrinth seal, and the aerodynamic efficiency increases by 0.6%. Compared to the tip labyrinth seal, tip shroud brush seals can decrease the relative deflection angle of exit flow. This flow behavior results in reducing the mixing loss between the tip leakage flow and mainstream. The similar axial deflection of the bristle pack for two kinds of brush seals is observed at the same sealing clearance. The deflection of the bristle pack under the function of the aerodynamic forces is protected by the backing plate. This work provides the theoretical basis and technical support for the brush seal application in the turbine industries.

Computational Fluid Dynamics-Based Throughflow Analysis of Transonic Flows in Steam Turbines

Abstract A computational fluid dynamics (CFD)-based throughflow solver is applied to the meridional analysis of low-pressure steam turbine modules. The throughflow code inherits its numerical scheme from a state-of-the-art CFD solver (TRAF code) and incorporates real gas capabilities, three-dimensional flow features, and spanwise mixing models. Secondary flow effects are introduced via a concentrated vortex model. Tip gap and shroud leakage effects are modeled in terms of source vectors in the system of governing equations. The impact of part-span shrouds and snubbers are accounted for, on a local basis, through suitable body force fields. The advection upstream splitting method (AUSM+-up) upwind strategy has been adopted as a basis to construct a numerical flux scheme explicitly suited for throughflow applications. The original formulation has been adapted to handle real gas flows and to embed the treatment of body force fields in a fully consistent framework. The capability of the procedure is assessed by analyzing the low-pressure modules of two large steam turbines designed and manufactured by Ansaldo Energia. These modules include rotor tip shrouds and part-span snubbers and feature supersonic flow and large blade twist. Throughflow predictions in terms of main performance figures and radial distributions of flow quantities are compared with experimental data and 3D steady viscous analyses. It will be shown how the proposed CFD-based throughflow model can be fruitfully used in the early stages of the design as it delivers predictions of comparable accuracy with 3D CFD analyses at a fraction of the computational time.

Tip-Shroud Labyrinth Seal Effect on the Flutter Stability of Turbine Rotor Blades

Abstract The effect of the tip-shroud seal on the flutter onset of a shrouded turbine rotor blade, representative of a modern gas turbine, is numerically tested, and the contributions to the work per cycle of the aerofoil and the tip shroud are clearly identified. The numerical simulations are conducted using a linearized frequency-domain solver. The flutter stability of the shrouded rotor blade is evaluated for an edgewise mode and compared with the standard industrial approach of not including the tip-shroud cavity. It turns out that including the tip shroud significantly changes the stability prediction of the rotor blade. This is due to two facts. First, the amplitude of the unsteady pressure created in the inter-fin cavity due to the motion of the airfoil is much greater than that of the airfoil. The impact of this contribution increases with the frequency. Second, the effect of the outer shroud of the rotor blade, which usually is not included either in the simulations, has an opposite trend with the nodal diameter than the airfoil reducing the maximum and minimum damping. It is concluded that the combined effect of the seal and its platform tends to stabilize the edgewise mode of the rotor blade for all the examined nodal diameters and reduced frequencies. Finally, the numerical results are shown to be consistent with those obtained using an analytical simplified model to account for the effect of the labyrinth seals.

Features of the Vortex Flow Structure around a One Fin Shroud

Modern gas turbines have high efficiency. A further increase in their economic efficiency can be achieved, on the one hand, by enhancing the accuracy of the parameter prediction at the design stage and, on the other hand, by the possibility of improving the design for different components of the flow path based on the results of calculating the complicated viscous spatial structure of the flow. One of the tools for enhancing the efficiency of gas turbines is the minimization of the rotor-tip leakage, the rate of which is reduced by shrouding the rotor blades. In particular, using numerical methods and software tools based on the former, one can perform thorough computational analysis of the vortex structure of the flow in the vicinity of the tip shroud and sufficiently accurately determine the rotor-tip leakage rates and other parameters of the stage. Such an approach allows a more accurate assessment of the leakage than semiempirical approaches used in practice. In particular, the assessment by the correlation dependence showed that the leakage rate for the tip shroud design in question with a tip clearance of 5 mm exceeded the leakage rate calculated using the method that considers the specific features of the tip shroud design and the vortex structure of the flow in the vicinity of it by 8.65%. As exemplified by the last-stage rotor blade of a stationary gas turbine, the possibility of controlling the leakage of the main flow through the tip clearance is demonstrated based on results of a numerical experiment.

Numerical analysis of multiple friction contacts in bladed disks

The damping potential of multiple friction contacts in a bladed disk is investigated. Friction contacts at tip shrouds and strip dampers are considered. It is shown that friction damping effectiveness can be potentially increased by using multiple friction contact interfaces. Friction damping depends on many parameters such as rotational speed, engine excitation order and mode family and therefore it is not possible to damp all the critical resonances using a single kind of friction contact interface. For example, a strip damper is more effective for the low nodal diameters, where blade/disk coupling is strong. The equations of motion of the bladed disk with multiple friction contacts are derived in the frequency domain for a cyclic structure with rotating excitations. A highly accurate method is used to generate the frequency response function (FRF) matrix. Furthermore, a finite element contact analysis is performed to compute the normal contact load and the contact area of the shroud interface at operating rotational speed. The multiharmonic balance method is employed in combination with the alternate frequency time domain method to find the steady state periodic solution. A low-pressure turbine bladed disk is considered and the effect of the engine excitation level, strip mass, thickness and the accuracy of FRF matrix on the nonlinear response curve are investigated in detail.

Turbine Aerodynamic Low-Frequency Oscillation and Noise Reduction Using Partial Shrouds

The design of highly efficient low-pressure gas turbines in compliance with strict emission regulations for pollutants and noise, as well as long component lifetime, requires the detailed knowledge of potential excitations in the flow. The analysis of fast response measurement data from a 1.5-stage low-pressure axial turbine in the frequency domain shows multiple relevant excitation and noise sources in the flowfield, in addition to the primary rotor–stator interaction. Especially nonsynchronous low-frequency modes at 10% of the blade-passing frequency, occurring in the tip shroud exit cavity, are found to communicate with the main flow and are amplified through the downstream stator row by a flow instability in the interaction area of the passage vortex and boundary layer. Full-annular unsteady computational fluid dynamics simulations are carried out in addition to the experiments to probe the origin of the cavity modes. They predict the rotor–stator interaction well, but they struggle to resolve low-frequency oscillations in the cavities. Out of the four tested configurations, a shroud trailing-edge cutback is the most efficient option to prevent the formation of the cavity modes. The tradeoff for a low-frequency fluctuation reduction of 12 dB using a trailing-edge partial shroud is a total–total stage efficiency drop of 0.7%.

Quantifying Loss Mechanisms in Turbine Tip Shroud Cavity Flows

Numerical calculations, steady as well as unsteady, of flow in a turbine stage with a tip shroud cavity elucidate that the loss-generating flow features consist of tip seal leakage jet, the interaction of cavity exit flow with main flow, the partially recirculating cavity inlet flow interaction with vane wakes, and injection of leakage flow into the shroud cavity. The first two flow features, namely, the tip seal leakage flow and mixing of cavity exit flow with main flow, dominate while the injection of leakage flow plays an indirect role in affecting the loss generation associated with cavity exit flow. The tip shroud cavity flow essentially consists of a system of toroidal vortices, the configuration of which is set by the cavity geometry and changes when subject to unsteady vane–rotor interaction. The role which the toroidal vortices play in setting the cavity inlet recirculating flow pattern and loss generation is delineated. It is suggested that there exists a link between the inlet cavity sizing and the toroidal vortical structure. The computed results appear to indicate that the main flow path approximately perceives the presence of the tip shroud cavity as a sink–source pair; as such a flow model based on this approximation is formulated. Loss variations with tip gap height and leakage flow injection are assessed. Results show that the expected loss due to mixing has a functional dependence on the square of the difference in their velocity magnitude and swirl. The tip seal leakage jet loss scales approximately linearly with the corrected mass flow rate per unit area over the range of tip gaps investigated.

Effects of blade surface treatments in tip–shroud abradable contacts

In aero engines a thermally sprayed abradable lining is applied to the inside of the casing in order to provide a seal around the tips of the compressor blades. As engines become more efficient the materials used must be able to endure higher temperatures and moving parts must be made lighter. This combination is not currently possible in late stages of the compressor as hard abradable materials can cause titanium blades to wear excessively. One solution to this is to add a surface treatment to the blade tips.Two surface treatments have been investigated, firstly cubic boron nitride (cBN) grits are bonded to the tip of the blade by electroplating. Secondly blades are coated in Cr(Al)N by cathodic arc deposition. The performance of these surface treatments is investigated on a test rig capable of monitoring the blade length, rub forces and abradable temperature during the test. Additional tests are performed against stepped coatings giving insight into the condition of the blade and abradable during the test. S.E.M., E.D.S., X.R.F., profilometry and wear debris have been used to characterise the wear mechanisms produced during the tests.Grit (cBN) tipped blades load with abradable material after a period of efficient cutting causing grit pull out and fracture. Flat Cr(Al)N coated blades failed due to thermal damage to the coating caused by adhesion of abradable material onto the Cr(Al)N coating, while chamfered blades cut efficiently at low incursion rates.

The Effect of Shell Thickness, Insulation and Casting Temperature on Defects Formation During Investment Casting of Ni-base Turbine Blades

Abstract Turbine blades have complex geometries with free form surface. Blades have different thickness at the trailing and leading edges as well as sharp bends at the chord-tip shroud junction and sharp fins at the tip shroud. In investment casting of blades, shrinkage at the tip-shroud and cord junction is a common casting problem. Because of high temperature applications, grain structure is also critical in these castings in order to avoid creep. The aim of this work is to evaluate the effect of different process parameters, such as, shell thickness, insulation and casting temperature on shrinkage porosity and grain size. The test geometry used in this study was a thin-walled air-foil structure which is representative of a typical hot-gas-path rotating turbine component. It was observed that, in thin sections, increased shell thickness helps to increase the feeding distance and thus avoid interdendritic shrinkage. It was also observed that grain size is not significantly affected by shell thickness in thin sections. Slower cooling rate due to the added insulation and steeper thermal gradient at metal mold interface induced by the thicker shell not only helps to avoid shrinkage porosity but also increases fill-ability in thinner sections.

Numerical Investigation of the Interaction between Mainstream and Tip Shroud Leakage Flow in a 2-Stage Low Pressure Turbine

The pressing demand for future advanced gas turbine requires to identify the losses in a turbine and to understand the physical mechanisms producing them. In low pressure turbines with shrouded blades, a large portion of these losses is generated by tip shroud leakage flow and associated interaction. For this reason, shroud leakage losses are generally grouped into the losses of leakage flow itself and the losses caused by the interaction between leakage flow and mainstream. In order to evaluate the influence of shroud leakage flow and related losses on turbine performance, computational investigations for a 2-stage low pressure turbine is presented and discussed in this paper. Three dimensional steady multistage calculations using mixing plane approach were performed including detailed tip shroud geometry. Results showed that turbines with shrouded blades have an obvious advantage over unshrouded ones in terms of aerodynamic performance. A loss mechanism breakdown analysis demonstrated that the leakage loss is the main contributor in the first stage while mixing loss dominates in the second stage. Due to the blade-to-blade pressure gradient, both inlet and exit cavity present non-uniform leakage injection and extraction. The flow in the exit cavity is filled with cavity vortex, leakage jet attached to the cavity wall and recirculation zone induced by main flow ingestion. Furthermore, radial gap and exit cavity size of tip shroud have a major effect on the yaw angle near the tip region in the main flow. Therefore, a full calculation of shroud leakage flow is necessary in turbine performance analysis and the shroud geometric features need to be considered during turbine design process.

Computational study of the effects of shroud geometric variation on turbine performance in a 1.5-stage high-loaded turbine

Generally speaking, main flow path of gas turbine is assumed to be perfect for standard 3D computation. But in real engine, the turbine annulus geometry is not completely smooth for the presence of the shroud and associated cavity near the end wall. Besides, shroud leakage flow is one of the dominant sources of secondary flow in turbomachinery, which not only causes a deterioration of useful work but also a penalty on turbine efficiency. It has been found that neglect shroud leakage flow makes the computed velocity profiles and loss distribution significantly different to those measured. Even so, the influence of shroud leakage flow is seldom taken into consideration during the routine of turbine design due to insufficient understanding of its impact on end wall flows and turbine performance. In order to evaluate the impact of tip shroud geometry on turbine performance, a 3D computational investigation for 1.5-stage turbine with shrouded blades was performed in this paper. The following geometry parameters were varied respectively: The aim of this paper is to isolate the influence of shroud and cavity geometry modifications on turbine aerodynamicnamic performance and to obtain clear trends of efficiency changes caused by different tip shroud geometry. Moreover, interaction between leakage flow and mainstream for different shroud configuration is also highlighted in order to penetrate into the physical mechanisms producing them. Due to the limitations of the model selected in this paper, the aim of research is not to put forward the design rules of turbine shroud. However, the results obtained from this work will be useful to the integrated design and optimization of turbine with shrouded blades.

Design of a high-precision, flat-on-flat fretting test apparatus with high temperature capability

In jet engines the blade resonant vibration amplitude is normally reduced by increasing the structural damping by using, for example, tip shrouds. These devices dissipate the energy generated at the contact surfaces between the relative motion and the friction force. Contact parameters, principally the friction coefficient and contact stiffness, are required to characterize the dynamics of shrouded blade system. Moreover, if at these contact surfaces severe wear occurs, a loss of interference takes place and the energy dissipated by the shroud decreases. Consequently the blade vibration amplitude increases and a catastrophic blade failure could take place. In this work a test rig for the contact parameter measurements and micro wear characterization of flat-on-flat contact surfaces has been developed. The test rig works at high temperatures of up to 1000°C, by means of induction heating. One of the specimens was attached to the rig frame, basically an inertial mass and four springs, and subsequently excited by an electromagnetic shaker. The second specimen was allowed to approach the first specimen and to rotate in such a way that the geometric contact between the two surfaces occurred at three points. In this way a real “flat to flat” contact was obtained. The two surfaces were kept in contact by means of a constant normal load. The tangential contact force was measured by a force sensor while the relative displacements between the contact surfaces were measured by two laser vibrometers. The relative displacement was kept under control by acting on the shaker force. Tangential force and relative displacement were used to describe the hysteresis loop and, consequently, to obtain the friction coefficient and contact stiffness during the wear process. The temperature is feedback controlled by using two thermocouples placed within the specimens near the contact surfaces. The main results are the characterization of the contact parameters and the wear behavior of real flat-on-flat contact surfaces, and the possibility of measuring easily the wear volume history of the same pair of specimens with a negligible perturbation to the wear processes from volume measurements.

The Radial Displacement of the HPT Blade under the Effects of the Temperature Field and the Centrifugal

The blade temperature field is computed using the finite element software of ANSYS and Hypermesh. The radial displacement response under the temperature field and centrifugal is analyzed. And a new method of plotting the grid and loading the boundary for complicated three-dimensional model in the finite element software is advanced. The heat transfer coefficients at different parts of the blade are introduced. The results show that for the temperature circumference distribution of the blade profile, the temperature is the highest at the leading and trailing edges and low at the middle. For the radial distribution the temperature is low at the blade root, and high at the blade profile and the integral tip shroud. The effect of temperature field is the main reason of the blade radial displacement while the centrifugal effect accounts for little.

Multiharmonic Forced Response Analysis of a Turbine Blading Coupled by Nonlinear Contact Forces

Abstract In turbomachinery applications, the rotating turbine blades are subjected to high static and dynamic loads. The static loads are due to centrifugal stresses and thermal strains whereas the dynamic loads are caused by the fluctuating gas forces resulting in high vibration amplitudes, which can lead to high cycle fatigue failures. Hence, one of the main tasks in the design of turbomachinery blading is the reduction in the blade vibration amplitudes to avoid high dynamic stresses. Thus, coupling devices like underplatform dampers and tip shrouds are applied to the blading to reduce the vibration amplitudes and, therefore, the dynamic stresses by introducing nonlinear contact forces to the system. In order to predict the resulting vibration amplitudes, a reduced order model of a shrouded turbine blading is presented including a contact model to determine the nonlinear contact forces. To compute the forced response, the resulting nonlinear equations of motion are solved in the frequency domain using the multiharmonic balance method because of the high computational efficiency of this approach. The transformation from the time domain into the frequency domain is done by applying Galerkin’s method in combination with a multiharmonic approximation function for the unknown vibration response. This results in an algebraic system of nonlinear equations in the frequency domain, which has to be solved iteratively in order to compute the vibration response. The presented methodology is applied to the calculation of the forced response of a nonlinear coupled turbine blading in the frequency domain.