Numerical computations were conducted to simulate flash deposition experiments on gas turbine disk samples with internal impingement and film cooling using a computational fluid dynamics (CFD) code ( FLUENT ). The standard k- ω turbulence model and Reynolds-averaged Navier–Stokes were employed to compute the flow field and heat transfer. The boundary conditions were specified to be in agreement with the conditions measured in experiments performed in the BYU turbine accelerated deposition facility (TADF). A Lagrangian particle method was utilized to predict the ash particulate deposition. User-defined subroutines were linked with FLUENT to build the deposition model. The model includes particle sticking/rebounding and particle detachment, which are applied to the interaction of particles with the impinged wall surface to describe the particle behavior. Conjugate heat transfer calculations were performed to determine the temperature distribution and heat transfer coefficient in the region close to the film cooling hole and in the regions further downstream of a row of film cooling holes. Computational and experimental results were compared to understand the effect of film hole spacing, hole size, and TBC on surface heat transfer. Calculated capture efficiencies compare well with experimental results.

Integral bladed disks (also known as blisks) are more widely used in modern aeroengine compressor designs because of the potential weight savings, but there are challenges in controlling the extreme vibration response levels in mistuned blisks, which are blisks with blades slightly different from each other. As blisks lack the uncertainty and variability of friction properties related to joints, the maximum vibration response level of a blisk test piece in operation can be predicted prior to installation. A previously proposed response-level prediction procedure for mistuned blisks is outlined, and its robustness is studied. A method of improving the results, given noisy experimental data, is proposed. Some of the issues discussed are validated by using experimental data.

Reliable design of a secondary air system is one of the main tasks for the safety and unfailing performance of gas turbine engines. To meet the increasing demands of gas turbine designs, improved tools in the prediction of secondary air system behavior over a wide range of operating conditions are needed. A real gas turbine secondary air system includes several components, therefore, its analysis is not carried out through a complete computational fluid dynamics (CFD) approach. Usually, those predictions are performed using codes based on simplified approach, which allows to evaluate the flow characteristics in each branch of the air system requiring very poor computational resources and few calculation time. Generally, the available simplified commercial packages allow to correctly solve only some of the components of a real air system, and often, the elements with a more complex flow structure cannot be studied; among such elements, the analysis of rotating cavities is very hard. This paper deals with a design tool developed at the University of Florence for the simulation of rotating cavities. This simplified in-house code solves the governing equations for steady one-dimensional axisymmetric flow using experimental correlations, both to incorporate the flow phenomena caused by multidimensional effects such as heat transfer and flow field losses, and to evaluate the circumferential component of velocity. Although this calculation approach does not enable a correct modeling of the turbulent flow within a wheel space cavity, the authors tried to create an accurate model, taking into account the effects of inner and outer flow extraction, rotor and stator drag, leakages, injection momentum, and finally, the shroud/rim seal effects on cavity ingestion. The simplified calculation tool was designed to simulate the flow in a rotating cavity with radial outflow, both with the Batchelor and/or Stewartson flow structures. A primary 1D-code testing campaign is available in the literature ( 2008, “Analysis of Gas Turbine Rotating Cavities by a One-Dimensional Model,” ISROMAC Paper No. 12-2008-20161 ). In the present paper, the authors developed, using CFD tools, reliable correlations for both stator and rotor friction coefficients and provided a full 1D-code validation, due to the lack of experimental data, comparing the in-house design-code predictions with those evaluated by CFD.

Existence of large scale unsteady flow structures manifested in contrarotating vortex pairs has been previously identified in rotor disk cavities. The nonaxisymmetric nature with an unknown number of vortices presents a computational challenge, as a full 360 deg circumferential domain will be needed, requiring significant computational resources. A novel circumferential spatial Fourier spectral technique is adopted in the present work to facilitate efficient computational predictions of the nonaxisymmetric flows. Given that the flow nonuniformities in the circumferential direction are of large length scales, only a few circumferential Fourier harmonics would be needed, resulting in a drastic reduction in number of circumferential mesh points to be required. The modeling formulations and implementation aspects will be described. Computational examples will be presented to demonstrate the validity and effectiveness of the present modeling approach. The computational results show that the nonaxisymmetric flow patterns, in terms of the number of vortex pairs, are sensitive to small scale external disturbances. It is also indicated that the occurrence of a nonaxisymmetric flow might be captured by the present Fourier solution with even one harmonic.

Nonaxisymmetric endwall profiling is a promising method to reduce secondary losses in axial turbines. However, in high-pressure turbines, a small amount of air is ejected at the hub rim seal to prevent the ingestion of hot gases into the cavity between the stator and the rotor disk. This rim seal purge flow has a strong influence on the development of the hub secondary flow structures. This paper presents time-resolved experimental and computational data for a one-and-1/2-stage high work axial turbine, showing the influence of purge flow on the performance of two different nonaxisymmetric endwalls and the axisymmetric baseline case. The experimental total-to-total efficiency assessment reveals that the nonaxisymmetric endwalls lose some of their benefit relative to the baseline case when purge is increased. The first endwall design loses 50% of the efficiency improvement seen with low suction, while the second endwall design exhibits a 34% deterioration. The time-resolved computations show that the rotor dominates the static pressure field at the rim seal exit when purge flow is present. Therefore, the purge flow establishes itself as jets emerging at the blade suction side corner. The jet strength is modulated by the first vane pressure field. The jets introduce circumferential vorticity as they enter the annulus. As the injected fluid is turned around the rotor leading edge, a streamwise vortex component is created. The dominating leakage vortex has the same sense of rotation as the rotor hub passage vortex. The first endwall design causes the strongest circumferential variation in the rim seal exit static pressure field. Therefore, the jets are stronger with this geometry and introduce more vorticity than the other two cases. As a consequence the experimental data at the rotor exit shows the greatest unsteadiness within the rotor hub passage with the first endwall design.

This paper deals with the computation of eigenvalues and eigenvectors of a mistuned bladed disk. First, the existence of derivatives of repeated eigenvalues and corresponding eigenvectors is discussed. Next, an algorithm is developed to compute these derivatives. It is shown how a Taylor series expansion can be used to efficiently compute eigenvalues and eigenvectors of a mistuned system. Numerical examples are presented to corroborate the validity of theoretical analysis.

Buoyancy-induced flow occurs in the rotating cavities between the adjacent disks of a gas-turbine compressor rotor. In some cases, the cavity is sealed, creating a closed system; in others, there is an axial throughflow of cooling air at the center of the cavity, creating an open system. For the closed system, Rayleigh–Bénard (RB) flow can occur in which a series of counter-rotating vortices, with cyclonic and anticyclonic circulation, form in the r - ϕ plane of the cavity. For the open system, the RB flow can occur in the outer part of the cavity, and the core of the fluid containing the vortices rotates at a slower speed than the disks: that is, the rotating core “slips” relative to the disks. These flows are examples of self-organizing systems, which are found in the world of far-from-equilibrium thermodynamics and which are associated with the maximum entropy production (MEP) principle. In this paper, these thermodynamic concepts are used to explain the phenomena that were observed in rotating cavities, and expressions for the entropy production were derived for both open and closed systems. For the closed system, MEP corresponds to the maximization of the heat transfer to the cavity; for the open system, it corresponds to the maximization of the sum of the rates of heat and work transfer. Some suggestions, as yet untested, are made to show how the MEP principle could be used to simplify the computation of buoyancy-induced flows.

In high-pressure turbines, a small amount of air is ejected at the hub rim seal to cool and prevent the ingestion of hot gases into the cavity between the stator and the disk. This paper presents an experimental study of the flow mechanisms that are associated with injection through the hub rim seal at the rotor inlet. Two different injection rates are investigated: nominal sucking of −0.14% of the main massflow and nominal blowing of 0.9%. This investigation is executed on a one-and-1/2-stage axial turbine. The results shown here come from unsteady and steady measurements, which have been acquired upstream and downstream of the rotor. The paper gives a detailed analysis of the changing secondary flow field, as well as unsteady interactions associated with the injection. The injection of fluid causes a very different and generally more unsteady flow field at the rotor exit near the hub. The injection causes the turbine efficiency to deteriorate by about 0.6%.

Most of the existing mistuning research assumes that the aerodynamic forces on each of the blades are identical except for an interblade phase angle shift. In reality, blades also undergo asymmetric steady and unsteady aerodynamic forces due to manufacturing variations, blending, mis-staggered, or in-service wear or damage, which cause aerodynamically asymmetric systems. This paper presents the results of sensitivity studies on forced response due to aerodynamic asymmetry perturbations. The focus is only on the asymmetries due to blade motions. Hence, no asymmetric forcing functions are considered. Aerodynamic coupling due to blade motions in the equation of motion is represented using the single family of modes approach. The unsteady aerodynamic forces are computed using computational fluid dynamics (CFD) methods assuming aerodynamic symmetry. Then, the aerodynamic asymmetry is applied by perturbing the influence coefficient matrix in the physical coordinates such that the matrix is no longer circulant. Therefore, the resulting aerodynamic modal forces in the traveling wave coordinates become a full matrix. These aerodynamic perturbations influence both stiffness and damping while traditional frequency mistuning analysis only perturbs the stiffness. It was found that maximum blade amplitudes are significantly influenced by the perturbation of the imaginary part (damping) of unsteady aerodynamic modal forces. This is contrary to blade frequency mistuning where the stiffness perturbation dominates.

This paper deals with the development of an accurate reduced-order model of a bladed disk with geometric mistuning. The method is based on vibratory modes of various tuned systems and proper orthogonal decomposition of coordinate measurement machine data on blade geometries. Results for an academic rotor are presented to establish the validity of the technique.

Blade-to-blade variations of bladed disk assemblies result in local zoning of vibration modes as well as amplitude magnifications, which primarily reduces the high cycle fatigue life of aeroengines. Criteria were introduced to determine the level of these mode localization effects depending on various parameters of a real high pressure compressor blisk rotor. The investigations show that blade vibration modes with lower interblade coupling, e.g., torsion modes or modes with high numbers of nodal diameter lines, have a significantly higher sensitivity to blade mistuning, which can be characterized by the higher percentage of blades on the total blisk strain energy.

A method of estimating the turbine rim seal ingestion rates was developed using the time-dependent pressure distributions on the hub of turbines and a simple-orifice model. Previous methods use the time-averaged pressure distribution downstream of the vanes to estimate seal ingestion. The present model uses the pressure distribution near the turbine hub, obtained from 2D time-dependent stage calculations, and a simple-orifice model to estimate the pressure-driven ingress of gas-path fluid into the turbine disk cavity and the egress of cavity fluid to the gas path. The time-dependent pressure distribution provides the influence of both the vane wakes and the bow wave from the blade on the pressure difference between the hub pressure at an azimuthal location and the cavity pressure. Results from the simple-orifice model are used to determine the effective Cd that matches the cooling effectiveness at radii near the rim seal with the amount of gas-path-ingested flow required to mix with the coolant flow. Cavity ingestion data from rim seal ingestion experiments in a 1.5-stage turbine and numerical simulations for a 1 vane, 2-blade sector of the 16-vane, 32-blade turbine were used to evaluate the method. The experiments and simulations were performed for close-spaced and wide-spaced half stages between both the vane and blade and between the blade and a trailing teardrop-shaped strut. The comparison of the model with a single Cd for axial gap seals and the experiments showed a reasonable agreement for both close- and wide-spaced stages.

A new reduced-order aeroelastic model using the principal shapes (AMPSs) of modes is presented. Rotors with flexible disks and alternate blade mistuning can challenge the fidelity of flutter prediction techniques that assume uniform blade-to-blade geometry and mode shape invariance with nodal diameter pattern. The AMPS method, however, accounts for alternating blade geometry as well as varying blade mode shapes, providing accurate flutter predictions for a large number of modes from a small number of computational fluid dynamics simulations. AMPS calculations on rotors with alternate blade mistuning are presented and compared to other prediction techniques. The results provide insight into how alternate blade mistuning affects aerodynamic coupling and the flutter characteristics of a rotor.

Amplitude magnification is defined as the maximum forced response amplitude of any blade on a mistuned bladed disk divided by the maximum response amplitude of any blade on a tuned bladed disk over a range of engine order excitation frequencies. This paper shows that amplitude magnification can be approximated as the maximum ratio of modal force divided by modal vector magnitude in an isolated family of turbine engine bladed disk modes. An infinite linear mistuning pattern, defined by a constant interblade stiffness increment between an infinite number of blades, is found to minimize the maximum modal force when subjected to engine order N/4 excitation. Linear mistuning, an approximation of the infinite linear mistuning pattern, approximately minimizes the maximum modal force for bladed disks with a finite number of blades when subjected to engine order N/4 excitation. From this theory, 2 / N is proposed to be a lower boundary for amplitude magnification. The linear mistuning method is demonstrated to produce very low amplitude magnifications numerically and experimentally. The numerical examples suggest that linear mistuning may produce amplitude magnifications near the absolute minimum possible.

The problem of estimating the mutual interaction of the effects of Coriolis forces and of blade mistuning on the vibration characteristics of bladed disks is addressed in this paper. The influence of different degrees of mistuning on forced response and amplification factors are studied in the presence of Coriolis forces and then compared to their non-Coriolis counterparts using a computationally inexpensive, yet representative, model of a bladed disk. The primary objective of the study reported in this paper is to establish whether current mistuned bladed disk analyses should incorporate Coriolis effects in order to represent accurately all the significant factors that affect the forced response levels.

A method has been developed to calculate directly resonance frequencies and resonance amplitudes as functions of design parameters or as a function of excitation levels. The method provides, for the first time, this capability for analysis of strongly nonlinear periodic vibrations of bladed disks and other structures with nonlinear interaction at contact interfaces. A criterion for determination of major, sub-, and superharmonic resonance peaks has been formulated. Analytical expressions have been derived for accurate evaluation of the criterion and for tracing resonance regimes as function of such contact interface parameters as gap and interference values, friction and contact stiffness coefficients, and normal stresses. High accuracy and efficiency of the new method have been demonstrated on numerical examples including a large-scale nonlinear bladed disk model and major types of contact interfaces including friction contact interfaces, gaps, and cubic nonlinearities.

Advanced structural dynamic models for both wedge and split underplatform dampers have been developed. The new damper models take into account inertia forces and the effects of normal load variation on stick-slip transitions at the contact interfaces. The damper models are formulated for the general case of multiharmonic forced response analysis. An approach for using the new damper models in the dynamic analysis of large-scale finite element models of bladed disks is proposed and realized. Numerical investigations of bladed disks are performed to demonstrate the capabilities of the new models and an analysis of the influence of the damper parameters on the forced response of bladed disks is made.

An approach is developed to analyze the multiharmonic forced response of large-scale finite element models of bladed disks taking account of the nonlinear forces acting at the contact interfaces of blade roots. Area contact interaction is modeled by area friction contact elements which allow for friction stresses under variable normal load, unilateral contacts, clearances, and interferences. Examples of application of the new approach to the analysis of root damping and forced response levels are given and numerical investigations of effects of contact conditions at root joints and excitation levels are explored for practical bladed disks.

The forced vibration response of bladed disks can increase dramatically due to blade mistuning, which can cause major durability and reliability problems in turbine engines. To predict the mistuned forced response efficiently, several reduced-order modeling techniques have been developed. However, for mistuned bladed disks, increases in blade amplitude levels do not always correlate well with increases in blade stress levels. The stress levels may be computed by postprocessing the reduced-order model results with finite element analysis, but this is cumbersome and expensive. In this work, three indicators that can be calculated directly from reduced-order models are proposed as a way to estimate blade stress levels in a straightforward, systematic, and inexpensive manner. It is shown that these indicators can be used to predict stress values with good accuracy relative to finite element results, even for a case in which the displacement and stress levels show different frequency response trends.

An efficient method for analysis of nonlinear vibrations of mistuned bladed disk assemblies has been developed. This development has facilitated the use of large-scale finite element models for realistic bladed disks, used hitherto in analysis of linear vibration, to be extended for the analysis of nonlinear multiharmonic vibration. The new method is based on a technique for the exact condensation of nonlinear finite element models of mistuned bladed disks. The model condensation allows the size of the nonlinear equations to be reduced to the number of degrees of freedom where nonlinear interaction forces are applied. The analysis of nonlinear forced response for simplified and realistic models of mistuned bladed disks has been performed. For a practical high-pressure bladed turbine disk, several types of nonlinear forced response have been considered, including mistuning by (i) scatter of underplatform dampers, (ii) shroud gap scatter, and (iii) blade frequency scatter in the presence of nonlinear shroud interactions.