Nonlinear analysis of the dynamics of articulated composite rotor blades

The general nonlinear intrinsic equations of motion of an elastic composite beam are solved in order to obtain the elasto-dynamic response of a rotating articulated blade. The solution utilizes the linear Variational-Asymptotic Method (VAM) cross-sectional analysis, together with an improved damped nonlinear model for the rigid-body motion analysis of helicopter blades in coupled flap and lead-lag motions. The explicit (direct) integration algorithm implements the perturbation method in order to solve the transient form of the nonlinear intrinsic differential equations of motion and obtain the elasto-dynamic behavior of an accelerating composite blade. The specific problem considered is an accelerating articulated helicopter blade of which its motion is analyzed since it starts rotating from rest until it reaches the steady-state condition. It is observed that the steady-state solution obtained by this method compares very well with other available solutions. The resulting simulation code is a powerful tool for analyzing the nonlinear response of composite rotor blades; and for serving the ultimate aim of efficient noise and vibration control in helicopters.     

An aeroelastic model for composite rotor blades with straight and swept tips. Part I: Aeroelastic stability in hover

An analytical model for predicting the aeroelastic behavior of composite rotor blades with straight and swept tips is presented. The blade is modeled by beam type finite elements along the elastic axis. A single finite element is used to model the swept tip. The non-linear equations of motion for the finite element model are derived using Hamilton's principle and based on a moderate deflection theory and accounts for: arbitrary cross-sectional shape, pretwist, generally anisotropic material behavior, transverse shears and out-of-plane warping. Numerical results illustrating the effects of tip sweep, anhedral and composite ply orientation on blade aeroelastic behavior are presented. It is shown that composite ply orientation has a substantial effect on blade stability. At low thrust conditions, certain ply orientations can cause instability in the lag mode. The flap-torsion coupling associated with tip sweep can also induce aeroelastic instability in the blade. This instability can be removed by appropriate ply orientation in the composite construction.     

直升机旋翼/机体动稳定性研究进展

首先对直升机旋翼/机体动不稳定性问题的种类进行了简要概述,包括旋翼挥舞/变距、变距/摆振、挥舞/摆振和挥舞/摆振/变距耦合等孤立旋翼动不稳定性问题,以及直升机地面共振和空中共振等旋翼/机体耦合动不稳定性问题,然后分别从气动力与结构的高精度数值模型、动稳定性的计算分析方法和实验模型测试3 个方面详细介绍了直升机旋翼/机体动不稳定性问题的研究现状,并着重讨论了直升机旋翼/机体动稳定性分析技术最近的主要研究方向:耦合CFD(computational fluid dynamics)/CSD(computational structuraldynamics) 的直升机旋翼气弹动稳定性分析、复合材料旋翼动稳定性分析及其材料不确定性影响、带减摆器的旋翼/机体动稳定性分析和先进直升机构型的旋翼/机体动稳定性分析,最后对直升机旋翼/机体动稳定性研究的发展趋势进行了展望.     

Modelling and dynamic stability of a hingeless active fibre composite blade

The main focus of this investigation was to investigate dynamic stability of what is now commonly referred to as an active twist rotor blade. With the ultimate intention of controlling helicopter blade vibrations, active or smart materials embedded in the rotor blade in various arrangements as opposed to the conventional passive isolation devices and absorbers are used. Structurally integrated interdigitated piezoelectric fibre composite material is considered in this work. This active composite may be used in constructing the blade in place of or concurrent with, composite blades. This fibrous composite is able to twist the blade, when subjected to an electric field, due to its unique arrangement of active fibres. The paper begins with outlining the design for lay-up sequence of the active blade. This is followed by developing a complete structural and dynamic modelling of the equations of motion of the smart blades for hover flight. These equations are used to investigate dynamic stability of the steady state motion of the smart blades under parametric excitation. In closing, as a preliminary step to determine the actuation authority of the active fibres, the open-loop response of the blade to an impulsive type of actuation is also investigated.     

Vibratory load predictions of a high-advance-ratio coaxial rotor system validated by wind tunnel tests

To investigate the aeromechanics of coaxial counter-rotating lift-offset rotor systems, a comprehensive analysis model of a laboratory-scale torque-balanced rotor designed for high-advance-ratio forward flight was developed. Measured blade and control system geometries and structural properties were input to the model. Lower-order aerodynamics modeling with a free-vortex wake method was used. While previous analytical studies on this coaxial rotor test rig have focused on performance and control requirements, in this current work, vibratory hub and pitch link loads, the influence of rotor–rotor phasing and the effects on blade deflections and tip clearance were investigated. The analysis was validated by wind-tunnel tests at advance ratios of 0.21–0.52 and for a lift offset varying from zero to 25%. Coaxial rotor performance, pitch link loads, unsteady thrust and rolling moments correlated well with the measurements. Pitching and rolling moment 2/rev and 4/rev harmonics correlated well for all lift offsets and advance ratios, whereas the vibratory torque was significantly overpredicted. The correct trends for varying lift offset and advance ratio were predicted in drag, side force, and thrust harmonics. Corresponding magnitudes were also predicted well, although an underprediction of the side force 4/rev harmonics was observed. Good correlation was found for the predicted blade tip clearance between the rotors over the entire range of lift offset and rotor–rotor phase angles, showing that advance ratio had little effect and judicial use of rotor phasing can increase the critical tip clearance.     

A comprehensive PIV measurement campaign on a fully equipped helicopter model

The flow field around a helicopter is characterised by its inherent complexity including effects of fluid?Cstructure interference, shock?Cboundary layer interaction, and dynamic stall. Since the advancement of computational fluid dynamics and computing capabilities has led to an increasing demand for experimental validation data, a comprehensive wind tunnel test campaign of a fully equipped and motorised generic medium transport helicopter was conducted in the framework of the GOAHEAD project. Different model configurations (with or without main/tail rotor blades) and several flight conditions were investigated. In this paper, the results of the three-component velocity field measurements around the model are surveyed. The effect of the interaction between the main rotor wake and the fuselage for cruise/tail shake flight conditions was analysed based on the flow characteristics downstream from the rotor hub and the rear fuselage hatch. The results indicated a sensible increment of the intensity of the vortex shedding from the lower part of the fuselage and a strong interaction between the blade vortex filaments and the wakes shed by the rotor hub and by the engine exhaust areas. The pitch-up phenomenon was addressed, detecting the blade tip vortices impacting on the horizontal tail plane. For high-speed forward flight, the shock wave formation on the advancing blade was detected, measuring the location on the blade chord and the intensity. Furthermore, dynamic stall on the retreating main rotor blade in high-speed forward flight was observed at r/R?=?0.5 and 0.6. The analysis of the substructures forming the dynamic stall vortex revealed an unexpected spatial concentration suggesting a rotational stabilisation of large-scale structures on the blade.     

Euler solutions for self-generated rotor blade-vortex interactions

A finite-difference procedure has been developed for the prediction of three-dimensional rotor blade-vortex interactions. The interaction velocity field was obtained through a non-linear superposition of the rotor flow field, computed using the unsteady three-dimensional Euler equations, and the embedded vortex wake flow field, computed using the law of Biot-Savart. In the Euler model, near wake rotational effects were simulated using the surface velocity ‘transpiration’ approach. As a result, a modified surface boundary condition was prescribed and enforced at each time step of the computations to satisfy the tangency boundary condition. For supercritical interactions using an upstream-generated vortex, accuracy of the numerical results were found to rely on the user-specified vortex core radius and vortex strength. For the more general self-generated subcritical interactions, vortex wake trajectories were computed using the lifting-line helicopter/rotor trim code CAMRAD. For these interactions, accuracy of the results were found to rely heavily on the CAMRAD-predicted vortex strength, vortex orientation with respect to the blade, and to a large extent on the user-specified vortex core radius. Results for the one-seventh scale model OLS rotor and for a non-lifting rectangular blade having a NACA0012 section are presented. Comparisons with the experimental windtunnel data are also made.     

Numerical simulation of unsteady blade row interactions induced by passing wakes

A numerical study of the unsteady phenomena resulting of periodic passing wakes is presented. An unsteady passing wake boundary condition is implemented in a three-dimensional Navier–Stokes code. Unsteady computations are performed to evaluate the capability of the code to simulate the rotor–stator interaction flow. The analysis of the flow structures shows the vortical disturbances and the migration of the incoming wakes through the blade passage. This physical analysis allows to separate the main origins of the losses.     

Differential infrared thermography for boundary layer transition detection on pitching rotor blade models

Differential infrared thermography (DIT) was investigated and applied for the detection of unsteady boundary layer transition locations on a pitching airfoil and on a rotating blade under cyclic pitch. DIT is based on image intensity differences between two successively recorded infrared images. The images were recorded with a high framing rate infrared camera. A pitching NACA0012 airfoil served as the first test object. The recorded images were used in order to investigate and to further improve evaluation strategies for periodically moving boundary layer transition lines. The measurement results are compared with the results of unsteady CFD simulations based on the DLR-TAU code. DIT was then used for the first time for the optical measurement of unsteady transition locations on helicopter rotor blade models under cyclic pitch and rotation. Image de-rotation for tracking the blade was employed using a rotating mirror to increase exposure time without causing motion blur. The paper describes the challenges that occurred during the recording and evaluation of the data in detail. However, the results were found to be encouraging to further improve the method toward the measurement of unsteady boundary layer transition lines on helicopter rotor models in forward flight.     

Basic design scheme for wave rotors

Pressure wave devices use shock waves to transfer energy directly between fluids without additional mechanical components, thus having the potential for increased efficiency. The wave rotor is a promising technology which uses shock waves in a self-cooled dynamic pressure exchange between fluids. For high-pressure, high-temperature topping cycles, it results in increased engine overall pressure and temperature ratio, which in turn generates higher efficiency and lower specific fuel consumption. Designing a wave rotor mainly focuses on predicting the behavior of shock and expansion waves. The extant literature presents numerous examples of wave rotor designs, but most of them rely on complicated numerical analyses as well as computer code developed specifically for this application. This paper presents an initial scheme used for designing wave rotors employing thermodynamic and gasdynamic analysis as well as computational fluid dynamic analysis. Basic theory and a simplified model of the wave rotor are used to predict the travel time and strength of waves. The model is then refined using a more advanced numerical scheme on the basis of the Lax–Wendroff method and FLUENT, a commercial CFD code.

---

Research was conducted while F. Iancu was a Ph.D. candidate at Michigan State University.     

Nonlinear aeroelastic coupled trim and stability analysis of rotor-fuselage

Based on the Hamilton principle and the moderate deflection beam theory, discretizing the helicopter blade into a number of beam elements with 15 degrees of freedora, and using a quasi-steady aero-model, a nonlinear coupled rotor/fuselage equation is established. A periodic solution of blades and fuselage is obtained through aeroelastic coupled trim using the temporal finite element method （TEM）. The Peters dynamic inflow model is used for vehicle stability. A program for computation is developed, which produces the blade responses, hub loads, and rotor pitch controls. The correlation between the analytical results and related literature is good. The converged solution simultaneously satisfies the blade and the vehicle equilibrium equations.     

A framework for CFD analysis of helicopter rotors in hover and forward flight

A framework is described and demonstrated for CFD analysis of helicopter rotors in hover and forward flight. Starting from the Navier–Stokes equations, the paper describes the periodic rotor blade motions required to trim the rotor in forward flight (blade flapping, blade lead‐lag and blade pitching) as well as the required mesh deformation. Throughout, the rotor blades are assumed to be rigid and the rotor to be fully articulated with separate hinges for each blade. The employed method allows for rotors with different numbers of blades and with various rotor hub layouts to be analysed. This method is then combined with a novel grid deformation strategy which preserves the quality of multi‐block structured, body‐fitted grids around the blades. The coupling of the CFD method with a rotor trimming approach is also described and implemented. The complete framework is validated for hovering and forward flying rotors and comparisons are made against available experimental data. Finally, suggestions for further development are put forward. For all cases, results were in good agreement with experiments and rapid convergence has been obtained. Comparisons between the present grid deformation method and transfinite interpolation were made highlighting the advantages of the current approach. Copyright © 2006 John Wiley & Sons, Ltd.     

Operational Modal Analysis of a Helicopter Rotor Blade Using Digital Image Correlation

A novel procedure to perform operational modal analysis on a reduced-scale, 2 m diameter helicopter rotor blade is described. Images of the rotor blade rotating at 900 RPM are captured by a pair of high-speed digital cameras at a sampling rate of 1000 frames per second. From these images, the out-of-plane bending deformation of the rotor blade is measured using Digital Image Correlation, with a spatial resolution of 7.2 mm and an accuracy of 60 μm, or 0.006 % of the rotor radius. Modal parameters including natural frequencies and mode shapes are determined from the bending deformation through application of the Ibrahim Time Domain method. The first three out-of-plane bending modes were identified at each rotational speed and compared to an analytical finite element model of the rotor blade. The experimental and analytical natural frequencies agreed to within 0.2 % in the best case and 10.0 % in the worst case. The experimental mode shapes were also found to closely match the analytical predictions. The results of this study demonstrate the ability of this procedure to accurately determine the modal parameters of rotating helicopter rotor blades.     

Performance improvement of small-scale rotors by passive blade twist control

A passive twist control is proposed as an adaptive way to maximize the overall efficiency of the small-scale rotor blade for multifunctional aircrafts. Incorporated into a database of airfoil characteristics, Blade Element Momentum Theory is implemented to obtain the blade optimum twist rates for hover and forward flight. In order to realize the required torsion of blade between hover and forward flight, glass/epoxy laminate blade is proposed based on Centrifugal Force Induced Twist concept. Tip mass is used to improve the nose-down torsion and the stabilization of rotating flexible blade. The laminate blades are tested in hover and forward flight modes, with deformations measured by Laser Displacement Sensor. Two Laser Displacement Sensors are driven by the tracking systems to scan the rotating blade from root to tip. The distance from blade surface to a reference plane can be recorded section by section. Then, a polynomial surface fitting is applied to reconstruct the shape of rotating blade, including the analysis of measurement precision based on the Kline–McClintock method. The results from deformation testings show that nose-down torsion is generated in each flight mode. The data from a Fluid Structure Interaction model agrees well with experimental results at an acceptable level in terms of the trend predictions.     

Near-wake measurement in a rotor/stator axial compressor using slanted hot-wire technique

 Three-dimensional near-wake structure behind a rotor was measured using slanted hot-wire technique in a large-scale, low-speed, rotor/stator axial compressor. Unsteady flow interaction between blade rows was varied by setting the axial gap between rows at 10% and 30% of rotor chord. Results show that stronger flow interactions between blade rows, or closer axial gap, produce more pronounced time variation within the rotor wake. All parameters measured – three component velocities, yaw and pitch angles – varied strongly within the wake, and are quantified. Received: 8 July 1996/Accepted: 29 May 1997     

AN INTEGRATED NONLINEAR APPROACH FOR TURBOMACHINERY FORCED RESPONSE PREDICTION. PART II: CASE STUDIES

This paper discusses the application of an advanced turbomachinery forced prediction model to two representative turbomachinery cases: an HP turbine and a rig fan. The approach is based on an integrated nonlinear multi-passage analysis that includes both the stator and the rotor blade-rows. The numerical model has advanced features such as nonlinear friction damping for turbine blades, tip gap flows and blade vibratory motion. A series of inviscid and viscous computations were performed for an HP turbine with 36 stator and 92 rotor blades. The peak-to-peak maximum displacements were predicted with and without root friction dampers and the findings were compared with available experimental data. Good agreement was observed in most cases. It was found that most of the unsteady forcing was due to the potential effects. In a second phase of the turbine work, the response to low engine-order excitation was predicted using a multi-row whole-annulus model. The stator assembly was assumed to have blades with varying throat widths and the magnitude of the unsteady aerodynamic forcing was found to increase with increasing scatter in throat width variation. A second forced response study was conducted for a rig fan with 15 variable inlet guide vanes (VIGVs) and 20 rotor blades. For a 30° VIGV opening, a good match was observed between the predicted and measured wake profiles. Similarly, the measured and predicted rotor blade vibration levels were also found to be in good agreement. It is concluded that the proposed methodology can be applied, with reasonable confidence, to the study of industrial cases.     

伽辽金有限元素法对旋翼气弹稳定性的应用

采用伽辽金加权余数有限元素法发展了一种悬停状态下无铰旋翼桨叶气弹稳定性的分析方法。分析模型包括预锥角、下垂角、预掠角、总距角、桨根预安装角、桨叶预扭角、变距轴偏置、根部外伸量和操纵线系刚度等结构参数，对无铰旋翼桨叶气弹稳定性研究有普遍适用意义。试验证明该理论可行并能用于研究无铰旋翼结构参数对桨叶气弹稳定性的影响，也能用于直升机旋翼的型号设计。     

Local shrinkage and stress induced by thermo-oxidation in composite materials at high temperatures

The paper is concerned with the modelling, simulation and experimental characterisation of local shrinkage strains and stresses induced by thermo-oxidation phenomena in the IM7/977-2 carbon/epoxy composite material at elevated temperatures. The oxygen concentration and mechanical fields were established through a coupled model constructed from a unified multiphysical approach and the thermodynamics of irreversible processes. The model was implemented in the ABAQUS^® finite element commercial code. Simulations of thermo-oxidation-induced matrix shrinkage were run at a local scale, i.e., the scale of the elementary constituents of the composite, the fibre and the matrix. The experimental assessment was done at the same scale, and the local matrix shrinkage profiles were measured by confocal interferometric microscopy.A good agreement was found between the simulated and measured profiles, validating the unified model. The thermo-oxidation induced stress field was analysed to understand the influence of the environment on the onset of damage in composite materials at elevated temperature.     

A numerical modelling of stator–rotor interaction in a turbine stage with oscillating blades

In real flows unsteady phenomena connected with the circumferential non-uniformity of the main flow and those caused by oscillations of blades are observed only jointly. An understanding of the physics of the mutual interaction between gas flow and oscillating blades and the development of predictive capabilities are essential for improved overall efficiency, durability and reliability. In the study presented, the algorithm proposed involves the coupled solution of 3D unsteady flow through a turbine stage and the dynamics problem for rotor-blade motion by the action of aerodynamic forces, without separating the outer and inner flow fluctuations. The partially integrated method involves the solution of the fluid and structural equations separately, but information is exchanged at each time step, so that solution from one domain is used as a boundary condition for the other domain. 3-D transonic gas flow through the stator and rotor blades in relative motion with periodicity on the whole annulus is described by the unsteady Euler conservation equations, which are integrated using the explicit monotonous finite volume difference scheme of Godunov–Kolgan. The structural analysis uses the modal approach and a 3-D finite element model of a blade. The blade motion is assumed to be constituted as a linear combination of the first natural modes of blade oscillations, with the modal coefficients depending on time. A calculation has been done for the last stage of the steam turbine, under design and off-design regimes. The numerical results for unsteady aerodynamic forces due to stator–rotor interaction are compared with results obtained while taking into account blade oscillations. The mutual influence of both outer flow non-uniformity and blade oscillations has been investigated. It is shown that the amplitude-frequency spectrum of blade oscillations contains the high-frequency harmonics, corresponding to the rotor moving past one stator blade pitch, and low-frequency harmonics caused by blade oscillations and flow non-uniformity downstream from the blade row; moreover, the spectrum involves the harmonics which are not multiples of the rotation frequency.     

Materially and geometrically non-linear woven composite micro-mechanical model with failure for finite element simulations

A computational micro-mechanical material model of woven fabric composite material is developed to simulate failure. The material model is based on repeated unit cell approach. The fiber reorientation is accounted for in the effective stiffness calculation. Material non-linearity due to the shear stresses in the impregnated yarns and the matrix material is included in the model. Micro-mechanical failure criteria determine the stiffness degradation for the constituent materials. The developed material model with failure is programmed as user-defined sub-routine in the LS-DYNA finite element code with explicit time integration. The code is used to simulate the failure behavior of woven composite structures. The results of finite element simulations are compared with available test results. The model shows good agreement with the experimental results and good computational efficiency required for finite element simulations of woven composite structures.