Comparisons of aeroelastic computer code predictions against measured rotor vibratory response data

Experimental investigations of the aerodynamic damping of compressor blades are usually performed by forcing the blades externally to a motion that is similar to a given mode shape and inter-blade phase angle (IBPA) while measuring the motion-induced unsteady pressure distribution. Evaluating this to an aerodynamic work entry from the fluid to the blade, at least a local contribution to the flutter (in-)stability can be determined. Test rigs are usually non-rotating linear or rotating annular cascade wind tunnels. In the latter case, besides measuring in and transmitting data out of the rotating system, the excitation of the blades themselves is still a challenge. In the present case a blisk rotor with realistic fan blade geometries and flow conditions was investigated aeroelastically. For the excitation of the 1st bending (1F) mode shape of the blading a sector of five blades was chosen. In this sector the natural vibration of the blading, represented by constant vibration amplitudes and a given IBPA should be simulated. Therefore the blades were equipped with Macro Fiber Composites (MFC). These foils of piezoelectric material expand and contract due to the applied high voltage. A control system was developed to adjust the amplitude and the IBPA of the blade vibration. For the transmission of the high voltage, a separate data transmission system on the base of liquid metals was chosen. The blade vibration was measured by strain gauges and additionally monitored by a specific rig system. The aeroelastic investigations were carried out in the compressor test facility M2VP of the DLR Institute of Propulsion Technology in Cologne. During the measurement, the MFCs were able to excite the blades to a certain extent. The paper will present the technique to excite the blades of a compressor blisk by means of MFCs as well as achieved vibration amplitudes and limitations under engine-like operating conditions.

Results of computing the aerodynamic stability limit for basic modes on supersonic turbines for LOX and LH2 turbo pumps in open cycles are presented and discussed. It is shown that it will be virtually impossible to design blades for supersonic turbines that satisfy the criterion that all modes be aerodynamically stable. An engineering approach based on total damping is subsequently suggested using a characteristic aerodynamic damping that can be used for modes that are aerodynamically unstable. Nomenclature c – chord Cw- aerodynamic work coefficient f – frequency IBPA- Inter blade phase angle k – reduced frequency L – blade span m – modal mass n- number of blades of the blade row ND- Nodal diameter P0 – inlet total pressure Uaero – aerodynamic work Ustruct Vrel - inlet relative flow velocity δ - vibration amplitude ω - circular frequency

The relationship between the tip clearance flow (TCF) and the blade vibration in the lock-in region was numerically investigated on a transonic rotor. Both the bending (1B) and torsional (8th) modes were analyzed under 0 ND. The time marching method and a single-passage model were used, which were verified by citing and comparing with the results in references. The phase of the TCF (referring to the phase difference between the unsteady pressure caused by the TCF and the blade vibration) changed with the frequency ratio in the lock-in region. The strength of the TCF was influenced slightly by the blade vibration amplitude. A separation method of the unsteady pressure caused by the TCF and the blade vibration was developed and verified at different conditions. The unsteady pressure of nonsynchronous vibration (NSV) was separated into the components of the TCF and the blade vibration under the 1B and 8th modes. The unsteady pressure component of the TCF changed little with the vibration amplitude and mainly existed in the tip area. The unsteady pressure component of the blade vibration was larger at part spans and its distribution depended on the modal shape and the vibration amplitude. The unsteady pressure components of the TCF and the blade vibration determined the aerodynamic work/damping in the lock-in region. The aerodynamic work components of the TCF and the blade vibration increased linearly and at a rate of the square with the vibration amplitude, respectively. TCF was dominant in the initial stage of vibration. With the vibration amplitude increasing, the aerodynamic work done by the unsteady pressure component of the blade vibration gradually caught up. The aerodynamic damping of the TCF changed with the phase of the TCF. TCF provided positive damping at some phases and negative damping at other phases. In the initial stage of vibration, the system was stable at the phases TCF providing positive damping and unstable at the phases of negative damping. NSV occurred only when TCF provided negative damping and the unsteady pressure component of the blade vibration provided positive damping. If the aerodynamic damping of the blade vibration was negative, the vibration would be enlarged until failure. Regardless of other damping forms, the maximum amplitude of NSV can be obtained by calculating the balance of the aerodynamic work. For the 8th mode, the limit amplitude under 0 ND was 0.0926%C, which corresponded to vibration stress of about 60 MPa.

The forced response of the first rotor of an E3E-type high pressure compressor blisk is analyzed with regard to varying mistuning, varying engine order excitations and the consideration of aeroelastic effects. For that purpose, SNM-based reduced order models are used in which the disk remains unchanged while the Young’s modulus of each blade is used to define experimentally adjusted as well as intentional mistuning patterns. The aerodynamic influence coefficient technique is employed to model aeroelastic interactions. Furthermore, based on optimization analyses and depending on the exciting EO and aerodynamic influences it is searched for the worst as well as the best mistuning distributions with respect to the maximum blade displacement. Genetic algorithms using blade stiffness variations as vector of design variables and the maximum blade displacement as objective function are applied. An allowed limit of the blades’ Young’s modulus standard deviation is formulated as secondary condition. In particular, the question is addressed if and how far the aeroelastic impact, mainly causing aerodynamic damping, combined with mistuning can even yield a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the inter-blade phase angle is the main driver for a possible response attenuation considering the fundamental blade mode. The results of the optimization analyses are compared to the forced response due to real, experimentally determined frequency mistuning as well as intentional mistuning.

This paper describes the development of the source-doublet-based potential paneling method for oscillating cascade unsteady aerodynamic load predictions. By using the integral influence coefficient method and by using the interblade phase angles, the unsteady loads on an oscillating cascade can be accurately predicted at a minimum cost. As the grids are placed only on the blade surfaces, the blades are allowed to vibrate without grid deformation problems. Four notable subsonic oscillating cascade test cases that cover most important parameters, e.g., blade geometry, interblade phase angle, flow coefficient, flow speed, frequency, etc., are studied in this paper. The agreement between the present solutions and other numerical/experimental results demonstrates the robustness of the present model. Applicability of the method for realistic compressible flow cascades is also discussed.

An energy balance technique is developed to predict the coupled bending-torsion mode aerodynamically forced response of an airfoil. In this technique, the energy input to the airfoil system per cycle of oscillation is generated by gust forces and moments and, under certain conditions, the self-induced aerodynamic forces and moments. The energy dissipation per cycle is associated with the structural damping, the static moment term for coupled motions, and under certain conditions, the self-induced aerodynamic forces and moments. The effects of the various aerodynamic parameters on the coupled forced response are then considered.In particular, the effects of the inlet Mach number, the interblade phase angle, the level of structural damping, and the cascade geometry on the coupled bending-torsion aerodynamically forced response of a flat plate airfoil cascade are demonstrated.

This is part two of a two-part paper. Part One describes the methodologies of a blade forced response prediction system. The emphasis of this part is to demonstrate the capability and computational efficiency of the system for predicting blade forced response. Part two firstly presents verification of the multistage time-linearized unsteady flow solver through comparison of predicted blade surface pressure distributions with data measured on a VKI transonic turbine stage. It concludes with presentation of the results of an analysis carried out on the last stage rotor blade of an ALSTOM three-stage transonic test compressor. In the analysis, strain gauge results together with Finite Element (FE) modal analysis identify the resonant crossings. The mode shape of the blade vibration is used in the CFD code to predict the blade aerodynamic damping. The aerodynamic damping is compared with the blade system damping obtained from the strain gauge tests. The variation is shown of aerodynamic and mechanical damping with blade mode shape. The blade unsteady modal forces induced by the upstream stators are derived from the calculated unsteady flows. The blade vibration at three resonant crossings is compared with those given by strain gauge measurements. Good comparisons and high computational efficiency demonstrate that the forced response methodologies described in Part One can be used in the blade design process to tackle blade aeromechanical issues.

Acoustic reflections and multiple blade-row effects have an impact on aeroelastic behavior, which can change the aerodynamic damping by a significant amount. However, conventional flutter analyses neglect these effects as they ignore any information about the multistage unsteady interaction. In order to capture them, the authors of this paper have developed a multistage coupling methodology for ITP’s in-house unsteady 3D frequency-domain linearized RANS solver. The current approach allows carrying out CFD simulations on a multistage environment built upon an arbitrary number of blade-rows; each one of them could also have an arbitrary number of frequencies and/or interblade phase angles. The coupling mechanism between consecutive blade-rows arises in a somewhat straightforward way after the solutions are decomposed as the sum of several spinning modes in the inter-row boundaries and the continuity of acoustic, vortical and entropic waves is enforced. This method is suitable for flutter and forced response computations, and also for tonal noise propagation. The focus of this paper is on the study of multiple blade-row effects on flutter stability margin. A brief analysis of results for a couple of simple test cases is presented to demonstrate the correctness of the method. Then, a detailed flutter analysis for a representative LPT geometry is performed and the results are compared with a single row conventional analysis. The impact of neighboring and further blade-rows, as well as spinning modes scattered from the fundamental circumferential mode, are accounted for in the unsteady aerodynamic loading of the excited blade.

A linearized unsteady incompressible aerodynamic model for airfoil cascades is developed that is not restricted to harmonic motion at a constant interblade phase angle. This is accomplished by starting with the unsteady aerodynamic coefe cients generated by LINSUB, a semianalyticunsteady cascadeaerodynamics codethat assumes linearity in both space and time. An inverse Fourier transform is then performed to predict the unsteady aerodynamic forces on the airfoils due to an impulsive acceleration. This result, termed the cascade indicial function, is then convolved with the arbitrary motion of the blades to obtain the unsteady aerodynamic forces on the airfoils in the time domain. The aerodynamic damping predicted by the time domain model is shown to compare well to LINSUB results when the interblade phase angle is constant. Results demonstrating the ability of the model to handle arbitrary airfoil motion are also presented. Nomenclature

This study is centered on the aeroelastic problem for axial compressors blisk airfoils in presence of geometrical variability. The combined problem of structural dynamics and unsteady aerodynamics is of interest for these machines due to the stress induced by blade vibration. The geometrical variability resulting from the manufacturing process of blisk airfoils and its impact on the aeroelastic problem is investigated, focusing on the aerodynamic damping. The manufacturing geometrical variability is analyzed in a probabilistic manner. A digital twin of the variability is created starting from a dataset of optical surface scans. The measured geometries are parameterized to describe the differences from the nominal geometry. An Autoencoder represents these deviations within a required accuracy, while using a minimal set of variables. The data reduction provided by the Autoencoder technique proved to be very efficient, especially if compared to linear methods as the principal components analysis, allowing to investigate multi-passage deviations from the nominal geometry. The aerodynamic damping is computed by an unsteady CFD solver, using the aerodynamic influence coefficients method. The manufacturing geometrical variability model is used to represent the real blisk airfoil geometries investigated. The uncertainty quantification evaluates the impact of the deviations from the nominal cyclic symmetrical design on the aerodynamic damping curve. The results can be combined in an aeroelastic reduced order model with the mistuning of the mechanical properties to represent the mistuned blisk vibrations.

In recent years the Harmonic Balance method has become a popular tool in the field of turbomachinery design. While it can efficiently capture nonlinear effects in time-periodic flows, its application to complex configurations such as cavities or casing treatments requires sophisticated domain coupling methods. To address this topic, in a series of two papers, we present and validate an algorithm for the coupling of non-conforming mesh topologies across domain boundaries. In this first paper the basic algorithm and its verification are presented in detail. In the second paper the method is applied to analyze the impact of a casing treatment on blade flutter in a compressor stage. It is shown in this paper that memory layout can have a strong impact on memory usage and CPU time. To handle indexed modes, i.e., modes with the same frequency but different inter-blade phase angles, we introduce virtual passage segments on which the required spatial Discrete Fourier Transform (DFT) is performed. Using Almost Periodic Fourier Transforms (APFT) to transfer the temporal solution harmonics we show that the computational overhead can be significantly reduced when compared to a standard temporal DFT ansatz. In this context a simple, but robust algorithm is proposed to determine the temporal sampling interval and distribution of the sampling points such that a bound on the condition number of the resulting APFT matrix is satisfied. The method is verified and analyzed using three academic test cases: the propagation of an entropy wave across moving interfaces in an empty duct with a rotating mean flow; the aerodynamic excitation of a simple rotor blade exposed to a time-periodic gust disturbance; and the flow in a duct with an attached cavity.

This paper investigates the acoustically induced rotor blade vibration that occurred in a state-of-the-art 1.5-stage transonic research compressor. The compressor was designed with the unconventional goal to encounter self-excited blade vibration within its regular operating domain. Despite the design target to have the rotor blades reach negative aerodamping in the near stall region for high speeds and open inlet guide vane, no vibration occurred in that area prior to the onset of rotating stall. Self-excited vibrations were finally initiated when the compressor was operated at part speed with fully open inlet guide vane along nominal and low operating line. The mechanism of the fluid–structure interaction behind the self-excited vibration is identified by means of unsteady compressor instrumentation data. Experimental findings point toward an acoustic resonance originating from separated flow in the variable inlet guide vanes (VIGV). A detailed investigation based on highly resolved wall-pressure data confirms this conclusion. This paper documents the spread in aerodynamic damping calculated by various partners with their respective aeroelastic tools for a single geometry and speed line. This significant spread proves the need for calibration of aeroelastic tools to reliably predict blade vibration. This paper contains a concise categorization of flow-induced blade vibration and defines criteria to quickly distinguish the different types of blade vibration. It further gives a detailed description of a novel test compressor and thoroughly investigates the encountered rotor blade vibration.

Separation of the contributions of aerodynamic and structural damping in vibrations of inclined cables

The present numerical study aims at examining the influence of intrarow interaction effects in aerodynamic damping predictions of an axial turbine rotor. The investigated operating point corresponds to a resonance crossing associated with the fundamental engine order of the stator blade row. Accordingly, the pressure perturbations induced by the vibration of the rotor at its modal frequency are found to be coincident in frequency and thus superimpose with the pressure perturbations resulting from intrarow interaction phenomena. A methodology for extracting vibration induced pressure perturbations for the subsequent calculation of the vibration induced modal aerodynamic damping is established and applied within the scope of the present study. Applying this methodology, both the influence of the underlying mean and transient flow field as well as the influence of acoustic wave reflections at the adjacent stator blade row is investigated on the predicted aerodynamic damping. In this context, the underlying mean flow field, which is found to be slightly altered in the presence of intrarow interaction phenomena, was proven to have a significant influence on vibration induced pressure perturbations. Moreover, acoustic wave reflections at the adjacent stator blade row are found to have the capability of influencing the aerodynamic damping depending on their actual phasing when impinging onto the turbine rotor.

The aeroelastic characteristics of a compressor stage were analyzed using a computational fluid dynamic (CFD) solver that uses the harmonic balance method to solve the governing equations. The three dimensional solver models the unsteady flow field due to blade vibration using the Reynolds-Averaged Navier-Stokes equations. The formulation enables the study of the effect of blade row interaction through the inclusion of coupling modes between blade rows. It also enables the study of nonlinear effects of high amplitude blade vibration by the inclusion of higher harmonics of the fundamental blade vibration frequency. In the present work, the solver is applied to study in detail the aeroelastic characteristics of a transonic compressor stage. Various parameters were included in the study: number of coupling modes, blade row axial spacing, and operating speeds. Only the first vibration mode is considered with amplitude of oscillation in the linear range. Both aeroelastic stability (flutter) of rotor blade and unsteady loading on the stator are calculated. The study showed that for the stage considered, the rotor aerodynamic damping is not influenced by the presence of the stator even when the axial spacing is reduced by nearly 25 percent. However, the study showed that blade row interaction effects become important for the unsteady loading on the stator when the axial spacing is reduced by the same amount.