Turbomachinery Blade Research Articles

A novel approach to reduce fan rotor blades stress in case of resonance due to inlet flow distortion by means of piezoelectric actuators

Resonant vibration condition involves a drop in the life-cycle of the components and is one of the main causes of high cycle fatigue failure (HCF) in turbomachinery blades. As a consequence vibration damping techniques play a key role for turbomachinery designers. Even though resonant vibration conditions can be identified by means of the Singh’s Advanced Frequency Evaluation (SAFE) diagram at the design level, not all resonant conditions can be avoided. Among these methods, systems of piezoelectric (PZT) actuators can be tuned to actively damp the vibrations caused by resonant excitations. In this work, an analytical model was developed to identify the optimal voltage distribution that maximises the reduction in blade stress. The model considers the flexural–torsional–extensional deformations coupling due to the pre-twisting, non-constant cross-section and inertial loads of the rotating blades. A typical case was examined to demonstrate the effectiveness of the proposed method, which involved vibration induced by inlet flow distortion in an axial fan stage coupled with a three-strut front frame. A decoupled approach based on Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) simulations was used to evaluate the aerodynamic loads and to numerically validate the optimal voltage distribution on the PZT actuator pairs. The results show that the proposed method alleviates the effects of the resonant response to an inlet flow distortion on a fan integrally bladed disc (blisk) and the optimal voltage distribution predicted by the model is the one that achieves the highest blade stress mitigation.

On the Probabilistic Endurance Prediction Approach for Turbomachinery Blades and Vanes

Abstract The design and aeromechanical assessments of turbomachinery blades and vanes comprise a wide range of complex processes that tend to be based on conventional deterministic methods. These processes often provide a “snapshot” evaluation of the new component designs at the nominal operating conditions. While the deterministic methods can predict the high cycle fatigue (HCF) endurance with reasonable accuracy, they assume that the conservative safety factors applied to cover for the parametric variations, uncertainties, and unknowns will not change during the product life cycle. This approach is intended to be conservative and in some cases may overlook the lack of robustness. The present paper proposes a robust design analysis approach based on probabilistic methodology for the aeromechanical assessment of rotor blades and stator vanes of turbomachinery. The robust design approach can account explicitly for the effects of design and manufacturing variability. This methodology can reduce the levels of conservatism in the deterministic approach and can provide a more thorough risk assessment. This paper offers a generalized aeromechanical analysis formulation based on probabilistic methods to evaluate the HCF capability of turbomachinery components. Herein, this methodology is demonstrated using a typical stator vane of an aero engine compressor and it is based on Monte-Carlo and design of experiment (DOE) simulations. The methodology consists of parametric sensitivity studies and identification of the most influential parameters that control the HCF endurance. Future ideas and roadmap of the aeromechanical probabilistic analysis capability development are also discussed.

Experimental Determination of Blade Tip Rub Forces in a Multiblade System

Abstract As improved efficiency goals require ever smaller gaps between rotating turbomachinery blade tips and stationary outer casings, it becomes more important to understand the physics of what happens when a blade tip rubs against the casing. A key piece of information to be determined is the force exerted on the blade tip during the rub event. This paper presents a method of extracting the blade tip rub forces from experiments conducted at The Ohio State University Gas Turbine Laboratory. To identify the forces during the rub, three multi-axis load cells are mounted behind a segment of the casing to measure the forces exerted on the casing during the rub event. Recovering blade tip forcing from this load cell data requires creating an appropriate model that can relate the measured data at the load cells to the high-speed rotating blade loads. The continuous, repeated nature of the rubs in the experiment makes this a challenge. This paper discusses the creation and performance of a state-space realization model developed from stationary ping test data that is used to address these challenges. The model is augmented with information on the angular position of the blades from a rotary encoder and information on the angular span of the rub, which increases with rub depth. Challenges and solutions related to finding tangential frequency responses, simultaneous blade rubs, and irregularities in the experimental data are also discussed. This paper aims to summarize the process and effectiveness of this approach for finding blade tip forces, as well as lessons learned along the way.

High-Fidelity Simulation Study of the Unsteady Flow Effects on High-Pressure Turbine Blade Performance

Abstract Unsteadiness, in the form of both broadband background disturbances and discrete coherent wakes, can have a strong effect on the performance of turbomachinery blades. The influence of the incoming flow has received much interest as it inevitably affects the blade boundary layers and develops as it passes through the machine. In the present work, we investigate the effect of unsteady flow on high-pressure turbines (HPTs), using high-fidelity datasets produced by wall resolved large-eddy simulation of an HPT stage. The effects of incident wakes from an upstream stator, compounded by the presence of freestream turbulence, on the downstream rotor are investigated. Based on analyzing cases with different turbulence intensities and length scales prescribed at the inlet, we show that changing the freestream turbulence characteristics has a direct effect on the unsteady behavior of the stator wakes. As a result, the performance of the rotor is also significantly affected. By detailing the influence of the wake–turbulence interaction, we aim to distinguish driving forces on rotor performance, be it changes in the incident wakes or direct influence from the freestream turbulence. Furthermore, the aerothermal behaviors of the rotor blades have been extensively investigated, showing that the blade boundary layers on the suction and pressure sides respond differently to external disturbances. The insights gained can provide designers with guidelines in understanding the unsteady flow effects of a given flow state, and how the unsteadiness present, either broadband or deterministic, will affect the performance of downstream blades.

An Advanced Multifidelity Multidisciplinary Design Analysis Optimization Toolkit for General Turbomachinery

The MDAO framework has become an essential part of almost all fields, apart from mechanical, transportation, and aerospace industries, for efficient energy conversion or otherwise. It enables rapid iterative interaction among several engineering disciplines at various fidelities using automation tools for design improvement. An advanced framework from low to high fidelity is developed for ducted and unducted turbomachinery blade designs. The parametric blade geometry tool is a key feature which converts low-fidelity results into 3D blade shapes and can readily be used in high-fidelity multidisciplinary simulations as part of an optimization cycle. The geometry generator and physics solvers are connected to DAKOTA, an open-source optimizer with parallel computation capability. The entire cycle is automated and new design iterations are generated with input parameter variations controlled by DAKOTA. Single- and multi-objective genetic algorithm and gradient method-based optimization cases are demonstrated for various applications. B-splines are used to define smooth perturbation of parametric variables chordwise and spanwise of the blade. The ability to create parametric 3D blade shapes quickly from low-fidelity analyses with advanced control is demonstrated to be unique and enables a rapid 3D design cycle. Non-intuitive designs are feasible in this framework and designers can really benefit from parametric geometry manipulation. Optimization at each fidelity is realized through automation. As part of the multidisciplinary analysis, 3D structural analysis is also performed using the unidirectional fluid–structure interaction for a few cases with imported pressure loads from the 3D RANS solution. Examples of axial turbofans, compressor rotors, turbines, radial compressors, propellers, wind and hydrokinetic turbines are demonstrated to prove generality.

Multifidelity Optimization Under Uncertainty for Robust Design of a Micro-Turbofan Turbine Stage

Abstract This paper presents a multifidelity optimization strategy for efficient uncertainty quantification and robust optimization applicable to turbomachinery blade design. The proposed strategy leverages freeform parameterization technique for flexible geometric perturbation and multifidelity information to reduce the number of evaluations of the expensive information source needed for robust optimization. The multifidelity Monte Carlo method was used to construct and exploit a surrogate-based multifidelity model based on the combination of high and low-fidelity CFD simulations and cheap regression models. Uncertainty quantification and robust optimization considering manufacturing tolerances were performed at a single operating point. An improvement in mean isentropic expansion efficiency of 2.98% was achieved for the robust design compared with the baseline although the mean mass flow rate and total pressure ratio differed by 1.72% and 0.67%, respectively. Compared to a single high-fidelity model, the multifidelity model was able to estimate the mean with a maximum deviation of 0.28% and 2.9% for the standard deviation. Furthermore, the multifidelity model realized a percentage reduction in computational cost of 66.18% for a combination of high fidelity CFD and regression models and 17.87% for high and low CFD models. One key observation was that, for small sampled high-fidelity CFD datasets that are highly correlated, it is possible to use only the high-fidelity model combined with regression models for constructing the multifidelity model without the need for low-fidelity CFD dataset. This significantly reduces the computational cost and time for acquiring and constructing a reliable stochastic model whiles maintaining reasonable accuracy.

터빈 블레이드 주위 유동 해석을 위한 자동 정렬 격자 생성

A computational grid is a crucial component in computational fluid dynamics, that greatly affects the accuracy and the cost of a numerical analysis. However, generating a grid with high quality is challenging and time-consuming, for turbomachinery blades with various shapes and configurations. In addition, the user-dependency in grid generation deteriorates the reliability of the analysis. We develop an algorithm that can automatically generate a structured grid for simulations of flow over a turbomachinery blade. Using an elliptic grid generation method, a high-quality O-type grid with high grid orthogonality on the wall is generated. Users only need to specify basic grid specifications such as grid number and resolution. The efficacy of the developed algorithm is evaluated for various two-dimensional and three-dimensional blades.

A coupled CAD‐free parameterization‐morphing method for adjoint‐based shape optimization

AbstractThis article presents a fully differentiated CAD‐free shape parameterization coupled with a grid displacement method for performing adjoint‐based aerodynamic shape optimization efficiently. Both tools are integrated into an adjoint‐based aerodynamic shape optimization process, where the shape changes and the corresponding grid adaptation take place simultaneously, in a single step. The role of the proposed shape parameterization technique is to control the shape changes of the aerodynamic body under study during shape optimization, and to modify it according to the spatial distribution of the gradient. The latter frequently contains numerical noise, due to the limited resolution of spatial discretization schemes, which can result in irregular surfaces, if the raw gradient is used directly. The proposed parameterization undertakes the elimination of this noise, thus ensuring smooth surfaces during the shape optimization. More specifically, a subset of the nodes belonging to the design surface is selected as the design vector (handles) and is responsible for controlling the surface displacements. The analytical differentiation of the parameterization, considering the adjoint morphing technique for the computation of the grid sensitivities, allows for its integration within a gradient‐based optimization process, where the adjoint method is used to compute the gradient of the objective w.r.t. all nodal positions. The propagation of this gradient information to the handles is efficiently and accurately achieved through the inclusion of the differentiated parameterization expression. The developed CAD‐free process chain is successfully demonstrated in an automotive S‐section cooling duct and a serpentine‐like one, used for internal turbomachinery blade cooling.

Improved Body Force Model for Estimating Off-Design Axial Compressor Performance

Based on the COMSOL software, body forces substituted into the Reynolds-averaged Navier–Stokes (RANS) equations as the source terms instead of the actual blade rows were improved to better predict the compressor performance. Improvements in parallel body force modeling were implemented, central to which were the local flow quantities. This ensured accurate and reliable off-design performance prediction. The parallel force magnitude mainly depended on the meridional entropy gradient extracted from three-dimensional (3D) steady single-passage RANS solutions. The COMSOL software could easily and accurately translate the pitchwise-averaged entropy into the grid points of the body force domain. A NASA Rotor 37 was used to quantify the improved body force model to represent the compressor. Compared with the previous model, the improved body force model was more efficient for the numerical calculations, and it agreed well with the experimental data and computational fluid dynamics (CFD) results. The results indicate that the improved body force model could quickly and efficiently capture the flow field through a turbomachinery blade row.

Experimental validation of FEM-computed stress to tip deflection ratios of aero-engine compressor blade vibration modes and quantification of associated uncertainties

Blade Tip Timing (BTT) technology is concerned with the estimation of turbomachinery blade stresses. The stresses are determined from BTT data by relating the measured tip deflection to the stresses via Finite Element (FE) models. The correlation of BTT measurements with FE predictions involves a number of uncertainties. This paper presents the process for validating the FE stress and deflection predictions of aero-engine compressor blades under non-rotation conditions as a critical preliminary step towards the complete understanding of their dynamic behaviour under rotating conditions when using BTT measurements. The process steps are described in detail, including the FE modelling and analysis of the blades and the blade-disk assembly, and the measurements of the blade tip deflection and blade stress. Furthermore, the uncertainties associated with the FE modelling and the measurement processes are quantified. The results show that the FE model is valid considering the control of most uncertainties. The experimental validation of the FE-computed stress-to-tip deflection calibration factors in the present study provides the basis for the determination of the calibration factors under rotational conditions using a previously presented BTT data simulator, and for the design of corresponding rotating experiments using BTT.

Meshfree reduced order model for turbomachinery blade flutter analysis

The paper introduces a development and application of boundary element based meshfree reduced order model for subsonic flutter analysis of turbomachinery blade cascade. The prime objective of the present work is to demonstrate the efficient use of meshfree hybrid boundary element method for subsonic flutter analysis of low pressure stage steam turbine blades . The meshfree incompressible fluid solver is developed employing 3D inviscid panel method . To model the flow separation inviscid-PM is hybridized with integral boundary layer approach using inviscid-viscous coupling mechanism along with discrete vortex particle method. A 3D annular test cascade is modeled using proposed meshfree solver for the flutter analysis. The comparison of estimated pressure coefficient and aerodynamic damping highlights a good agreement with experimental data and mesh based CFD-model’s results. Moreover, it have observed that the computational time for flutter analysis using proposed method is significantly lower compared to traditionally used CFD based numerical models for subsonic flutter in 3D blade cascade.

Experimental approach of surface pressure measurements on additive manufactured nozzle guide vane in a turbocharger turbine

Obtaining the surface pressure measurement of the pneumatic blades in turbomachinery is beneficial in understanding the flow mechanism around the blades and designing of the blades to improve the turbomachinery performance. However, it is difficult for the turbocharger turbine due to the space limitation, high rotational speed, and small geometric size. The present study investigates a novel measuring approach of the surface pressure of the guide vane in a turbocharger turbine based on the additive manufacturing techniques, which is not reported in the previous literature. The static pressure on the pressure side and suction side of the guide vanes in the variable nozzle turbine was investigated using both the experimental and numerical methods. The results show that the majority of the measuring results generally agree with the numerical prediction at different operating points with the relative difference below 5%. Besides, the trends of the static pressure as the rotational speed and mass flow rate between the pressure side and suction side were also captured in the experimental methodology. The highest deviations between experimental and calculated models were found in the first and fifth pressure taps on the guide vanes with an averaged absolute relative difference of up to 11.61% and 16.1% for 20% opening and 60% opening, respectively. The ratio of the kinetic pressure to total pressure and the flow field in the guide vane passage were analyzed to estimate the influence on the static pressure measurement. Nevertheless, the preliminary comparison results still encourage and extend the bounds of the possibility in the use of additive manufacturing techniques for miniature pneumatic blade surface pressure measurement.

Multirow Adjoint-Based Optimization of NICFD Turbomachinery Using a Computer-Aided Design-Based Parametrization

Abstract Currently, most of the adjoint-based design systems documented in the open literature assume that the fluid behaves as an ideal gas, are restricted to the optimization of a single row of blades, or are not suited to impose geometric constraints. In response to these limitations, this paper presents a gradient-based shape optimization framework for the aerodynamic design of turbomachinery blades operating under nonideal thermodynamic conditions. The proposed design system supports the optimization of multiple blade rows, and it integrates a computer-aided design (CAD)-based parametrization with a Reynolds-averaged Navier–Stokes (RANS) flow solver and its discrete adjoint counterpart. The capabilities of the method were demonstrated by performing the design optimization of a single-stage axial turbine that employs isobutane (R600a) as working fluid. Notably, the aerodynamic optimization respected the minimum thickness constraint at the trailing edge of the stator and rotor blades and reduced the entropy generation within the turbine by 36%, relative to the baseline, which corresponds to a total-to-total isentropic efficiency increase of about 4 percentage points. The analysis of the flow field revealed that the performance improvement was achieved due to the reduction of the wake intensity downstream of the blades and the elimination of a shock-induced separation bubble at the suction side of the stator cascade.

Study on identification of modal parameters of mistuned bladed disks

To develop turbomachinery blades with high reliability, it is indispensable to verify the natural frequency, damping, resonant stress, etc. under operating condition, and utilize these data in the mechanical design of a new blade. BTT (Blade Tip Timing) and the telemetry system have been widely used to measure the modal parameters of turbomachinery blades. In measurement of the modal parameters of blades under rotation, it is pointed out that the mistuning phenomena make the identification of modal parameters difficult. Namely, because, in a mistuned bladed disk, responses of many vibration modes are superimposed, it becomes difficult to correctly identify the natural frequency and damping of an individual blade. This is one of the critical issues to be overcome for developing blades with high reliability. In this study, a novel identification method of modal parameters of a mistuned system is proposed, where the modal parameters of a mistuned bladed disk are identified using the frequency responses consisting of many vibration modes. To verify the validity of the identification method proposed, typical mistuned systems of a turbocharger are analyzed, and the modal parameters are identified. The effect of the noise included in the measured frequency response on the accuracy of the identification is examined in detail.

Turbulent flow around circular arcs

The flow around a circular arc is governed by the effect of the sharp leading edge and the arc's curvature. There is a range of incidences where a leading-edge separation bubble (LESB) is formed on the convex side of the arc, and the reattached boundary layer separates further downstream. Akin to foils and cylinders, for increasing values of the Reynolds number, the boundary layer turns from laminar to turbulent resulting in a step change in the forces, here termed force crisis. This phenomenon is characterized experimentally for an arc with a camber-to-chord ratio of 0.22 and for a range of the Reynolds number from 53 530 to 218 000. Forces are measured both in a towing tank and in a water tunnel, and particle image velocimetry is undertaken in the water tunnel. In stark contrast to cylinders, where the force crisis is associated with the laminar-to-turbulent transition of the boundary layer, here, it is found to be associated with the suppressed relaminarization of the boundary layer. In fact, the LESB is always turbulent at the tested conditions, and relaminarization occurs up to a combination of critical angles of attack and critical Reynolds numbers. The critical angle of attack varies linearly with the Reynolds number. These results may contribute to the design of thin cambered wings, sails, and blades at a transitional Reynolds number such as the wings of micro aerial vehicles, swept wings in subsonic flight, turbomachinery blades, and the sails of autonomous sailing vessels.

Analysis on Aerodynamic Stability of Blades by an Efficient Fluid–Structure Coupling Method

AbstractPoor calculation efficiency is a major issue in the investigation of time-domain aerodynamics of turbomachinery bladings by fluid–structure coupling. In this work, a numerical methodology f...

The High-Speed Cascade Wind Tunnel at the Bundeswehr University Munich after a Major Revision and Upgrade

Since its first operation in 1956 at DFL Braunschweig and after its movement to Munich, the High-Speed Cascade Wind Tunnel (HGK) at Bundeswehr University Munich is intensively used for fundamental and application-oriented research on aero-thermodynamics of turbomachinery bladings. Numerous systematic airfoil design studies were performed over the last decades. Thanks to the HGK facility, which enables thorough and detailed cascade testing at turbomachinery-relevant conditions, many of those airfoils for different purposes finally made it into turbomachinery applications. Nowadays, the HGK still provides very useful contributions to the understanding of the complicated flow in compressor and turbine bladings, and thereby extends the knowledge on relevant physical phenomena. As a consequence of the intense usage, this unique test facility was subject to a major revision and upgrade. The performed changes are presented within this paper including an overview on new capabilities in terms of the extended operating range, the data acquisition system, and the recently available measurement equipment.

An Efficient Approach for Predicting Resonant Response with the Utilization of the Time Transformation Method and the Harmonic Forced Response Method

Resonant response of turbomachinery blades can lead to high cycle fatigue (HCF) if the vibration amplitudes are significant. Therefore, the dangerousness assessment of the resonance crossing is important. It requires accurate predictions of the aerodynamic excitation, damping, and response, which will consume immense computational costs. The novel aspect of this study is the development of an efficient approach, which incorporates the time transformation (TT) method to predict the aerodynamic excitations and the harmonic forced response method to obtain the response levels. The efficiency and accuracy of this method were evaluated by comparing with traditional methods for the resonance crossing excited by upstream wake in a 1.5 multistage compressor. For the aerodynamic excitation, discrepancies of ±2% at the mean pressure and ±25% at the harmonic pressure in most areas expect for the blade root were observed, but the calculation time required by the TT method was only 5% of that by the time-marching method. Moreover, response levels with the same aerodynamic forces were compared between the harmonic forced-response and transient dynamic methods. Small differences in the displacement and stress variables were observed; the relative deviation was smaller than 2% with only 1% computing time compared with the transient method, indicating the high accuracy and efficiency of the efficient approach.

A gradient-based method assisted by surrogate model for robust optimization of turbomachinery blades

The design optimization taking into account the impact of uncertainties favors improving the robustness of the design. A Surrogate-Assisted Gradient-Based (SAGB) method for the robust aerodynamic design optimization of turbomachinery blades considering large-scale uncertainty is introduced, verified and validated in the study. The gradient-based method is employed due to its high optimization efficiency and any one surrogate model with sufficient response accuracy can be employed to quantify the nonlinear performance changes. The gradients of objective performance function to the design parameters are calculated first for all the training samples, from which the gradients of cost function can be fast determined. To reveal the high efficiency and high accuracy of SAGB on gradient calculation, the number of flow computations needed is evaluated and compared with three other methods. Through the aerodynamic design optimization of a transonic turbine cascade minimizing total pressure loss at the outlet, the SAGB-based gradients of the base and optimized blades are compared with those obtained by the Monte Carlo-assisted finite difference method. Moreover, the results of both the robust and deterministic aerodynamic design optimizations are presented and compared to demonstrate the practicability of SAGB on improving the aerodynamic robustness of turbomachinery blades.

EXTENDING A VAN DER POL BASED REDUCED-ORDER MODEL FOR FLUID-STRUCTURE INTERACTION APPLIED TO NON-SYNCHRONOUS VIBRATIONS IN TURBOMACHINERY

Abstract This paper expands upon a multi-degree-of-freedom, Van der Pol oscillator used to model buffet and Nonsynchronous Vibrations (NSV) in turbines. Two degrees-of-freedom are used, a fluid tracking variable incorporating a Van der Pol oscillator and a classic spring, mass, damper mounted cylinder variable; thus, this model is one of fluid-structure interaction. This model has been previously shown to exhibit the two main aspects of NSV. The first is the lock-in or entrainment phenomenon of the fluid shedding frequency jumping onto the natural frequency of the oscillator, while the second is a stable limit cycle oscillation (LCO) once the transient solution disappears. Improvements are made to the previous model to better understand this aeroelastic phenomenon. First, an error minimizing technique through a system identification method is used to tune the coefficients in the Reduced Order Model (ROM) to improve the accuracy in comparison to experimental data. Secondly, a cubic stiffness term is added to the fluid equation; this term is often seen in the Duffing Oscillator equation, which allows this ROM to capture the experimental behavior more accurately, seen in previous literature. The finalized model captures the experimental cylinder data found in literature much better than the previous model. These improvements also open the door for future models, such as that of a pitching airfoil or a turbomachinery blade, to create a preliminary design tool for studying NSV in turbomachinery.