Unsteady Aerodynamic Forces Research Articles

An improved neural network for modeling airfoil's unsteady aerodynamics in transonic flow

Understanding the aerodynamic hysteresis loop phenomenon is essential when assessing aerodynamic performance and designing aircraft control systems. This phenomenon is a result of time delay effects in unsteady flow. Traditional methods of predicting unsteady aerodynamic forces using computational fluid dynamics have drawbacks, such as long cycles and low efficiency. In this paper, we focus on predicting the aerodynamic hysteresis loop of the NACA (National Advisory Committee for Aeronautics) 0012 airfoil in transonic flow using a new model called LIDNN (Latin hypercube sample input deep neural network). This model integrates input signals and optimization methods to improve upon traditional neural network models. Based on the example validation, the LIDNN model is authenticated as an accurate and efficient method in predicting the unsteady aerodynamic hysteresis loop of the NACA 0012 airfoil in transonic flow, and another significant advantage of the proposed model is its ability to solve multivariable problems effectively, even under varying Mach numbers.

Identification of Compressor Vibration Aerodynamic Forcing Mechanisms by Spectral Characteristics

Abstract Nonsynchronous vibration (NSV) in axial compressors can be caused either by (1) unsteady aerodynamic forces that are not related to motion of the blades or (2) motion-dependent aerodynamic forcing (e.g., flutter). Aerodynamic forcing mechanisms can be challenging to identify in experimental observations of NSV because the temporal vibration characteristics for both forcing mechanisms can appear similar. This work proposes a method for distinguishing between the two mechanisms using spectral characteristics. The method provides an interpretation of experimental data explicitly consistent with the analytical models used to differentiate between forced response and flutter. Two cases of NSV were observed in a 1.5-stage axial compressor at near-stall conditions. The circumferential wavenumber-dependent unsteady pressure spectra and nonintrusive stress measurement system (NSMS) spectra were observed to have distinct characteristics for the two NSV cases. Based on these distinct spectral characteristics, the first case was identified as blade-row aerodynamic forcing, while the second was identified as motion-dependent (flutter). Numerical simulations confirmed low aerodynamic damping at the conditions where flutter was observed.

Experimental and numerical studies on unsteady galloping driving mechanism of a truss beam with solid barriers

The long-span bridges with truss beam are widely recognized as typical wind-sensitive structures, and its wind-induced divergence events may become a very predominant issue. This work evaluates the galloping performance of a typical truss beam with wind barriers, which is detected to be susceptible to the infrequent vertical instability at specific attack angles, as evidenced by experimentation and numerical analysis. Since the truss beam constitutes a complex cross section, this study employs energy analysis to distinguish the crucial parts affected by vibration and discovers that the galloping vibration is mostly caused by the surfaces of the deck. Rather than relying on conventional quasi-steady theory, this study explores the unsteady aerodynamic forces to identify the underlying galloping driving mechanism. Our findings reveal that the instigator of galloping instability is the phase rising of lift with increasing wind speed. Additionally, the nonlinear mechanical damping is not a decisive parameter. Furthermore, we have investigated the impact of an essential ancillary facility, the wind barrier, and discovered that its galloping stability can be enhanced by increasing its porousness and decreasing its height. However, the underlying mechanisms behind this improvement are distinct.

Study on Lateral Vibration of Tail Coach for High-Speed Train under Unsteady Aerodynamic Loads

As the speed of high-speed trains increases, the vehicle’s lateral stability steadily deteriorates. There have been observations of abnormal vibrations in the tail car, particularly on certain sections of the railway line. This study built a high-speed train aerodynamic simulation model for a three-car consist, and a multibody dynamics simulation model for an eight-car consist based on numerical simulations of train aerodynamics and multibody dynamics. It investigated both steady and unsteady aerodynamic loads, flow field characteristics, and the dynamic performance of vehicles under varied aerodynamic loads at 400 km/h. The results indicate that the aerodynamic loads generated during high-speed train operation exhibit highly unsteady characteristics. Steady aerodynamic loads have a relatively minor impact on the vehicle’s dynamic performance, whereas unsteady loads exert a more significant influence. Under unsteady aerodynamic forces, the tail car experiences severe lateral vibrations. The lateral stability index, displacement, velocity, and acceleration of the tail car under unsteady conditions were measured at 2.26, 7.54 mm, and 0.53 m/s2, respectively. These values represent increases of over 17.71%, 148.84%, and 111.24%, respectively, compared to the steady loads. Large oscillation amplitudes result in more significant lateral displacements and accelerations of the vehicle. This phenomenon is a crucial factor contributing to the “tail swing” effect observed in high-speed trains. This study emphasizes the importance of considering unsteady aerodynamic effects in assessing the lateral stability of high-speed trains and highlights the significance of mitigating the adverse impacts of such dynamic responses, particularly in the tail car.

Numerical Investigation of Unsteady Rotor–Stator Interaction Mechanism and Wake Transportation Characteristics in a Compressor with Non-Uniform Tip Clearance Rotor

This study aims to numerically investigate a transonic compressor by solving the unsteady Reynolds-averaged Navier–Stokes equations. The flow mechanisms related to unsteady flow were carefully examined and compared between rotors with non-uniform tip clearance (D1) and small-value tip clearance (P1). The unsteady flow field near the 50% and 95% blade span characterized by unsteady rotor–stator interaction was analyzed in detail for near-stall (NS) conditions. According to the findings, the perturbation of unsteady aerodynamic force for the stator is much bigger than that of the rotor. At the mid-gap between the rotor and stator, the perturbation of tangential velocity of the D1 scheme in the rotor and stator frame is reduced. At the rotor’s outlet region, the perturbation intensity is divided into three main perturbation regions, which are respectively concentrated in the TLV near the upper endwall, the corner separation at the blade root, and the wake of the whole blade span. Through the analysis of the wake transportation characteristics, it was found that when the wake passes through the stator blade surface, the wake exerts a substantial influence on the flow within the stator passage. It further leads to notable pressure perturbations on the stator’s surface, as well as affecting the development and flow loss of the boundary layer. The negative jet effect induces opposite secondary flow velocity on both sides of the wake near the stator’s surfaces. Therefore, the velocity at a specific point on the stator’s suction surface will decrease and then increase. Conversely, the velocity at a particular point on the pressure surface will increase and then decrease.

Fluid-structure interaction behaviors of tension membrane roofs by fully-coupled numerical simulation

This study aims to investigate fluid-structure interaction (FSI) behaviors of an enclosed-type tension membrane flat roof. The roof with rectangular shape is chosen as the object because of its relatively idealized geometry for FSI analysis, which is a simplified shape compared to typical membrane roofs. Fully-coupled numerical simulations are performed to obtain the wind induced vibration, aerodynamic forces and surrounding flow field of the tension membrane roof structure, where large-eddy simulation (LES) is used for solving of the flow field, non-linear membrane elements are adopted for the structure field and partitioned algorithm is applied for the coupling between the flow and membrane vibration. The numerical simulations are validated by the aero-elastic experimental results. The characteristics of the wind-induced displacements and aerodynamic forces of the tension membrane roof are investigated in both time and frequency domains. The energy transfer characteristics between wind and the vibrating roof are investigated based on the phase analysis between the generalized forces and displacements of the membrane roof. The underlying mechanism of the modal-jump phenomena that the vibration mode of the membrane jumps from the first mode to the second mode with increasing wind velocity, as well as the instability mechanism of the tension membrane roof, are revealed by flow visualizations and unsteady aerodynamic forces identifications. It is found that the aero-elastic instability of the flat membrane roof is a kind of vortex-induced vibration (VIV), where the modal-jump phenomena and unstable vibration of the membrane roof occur with the occurrence of negative aerodynamic damping, induced by the interaction between the vortex transporting and the roof motion.

Numerical investigation of the dynamic stall reduction on the UAS-S45 aerofoil using the optimised aerofoil method

AbstractThis paper investigates the effect of the optimised morphing leading edge (MLE) and the morphing trailing edge (MTE) on dynamic stall vortices (DSV) for a pitching aerofoil through numerical simulations. In the first stage of the methodology, the optimisation of the UAS-S45 aerofoil was performed using a morphing optimisation framework. The mathematical model used Bezier-Parsec parametrisation, and the particle swarm optimisation algorithm was coupled with a pattern search with the aim of designing an aerodynamically efficient UAS-45 aerofoil. The $\gamma - R{e_\theta }$ transition turbulence model was firstly applied to predict the laminar to turbulent flow transition. The morphing aerofoil increased the overall aerodynamic performances while delaying boundary layer separation. Secondly, the unsteady analysis of the UAS-S45 aerofoil and its morphing configurations was carried out and the unsteady flow field and aerodynamic forces were analysed at the Reynolds number of 2.4 × 106 and five different reduced frequencies of k = 0.05, 0.08, 1.2, 1.6 and 2.0. The lift ( ${C_L})$ , drag ( ${C_D})$ and moment ( ${C_M})\;$ coefficients variations with the angle-of-attack of the reference and morphing aerofoils were compared. It was found that a higher reduced frequencies of 1.2 to 2 stabilised the leading-edge vortex that provided its lift variation in the dynamic stall phase. The maximum lift $\left( {{C_{L,max}}} \right)$ and drag $\left( {{C_{D,max}}} \right)\;$ coefficients and the stall angles of attack are evaluated for all studied reduced frequencies. The numerical results have shown that the new radius of curvature of the MLE aerofoil can minimise the streamwise adverse pressure gradient and prevent significant flow separation and suppress the formation of the DSV. Furthermore, it was shown that the morphing aerofoil delayed the stall angle-of-attack by 14.26% with respect to the reference aerofoil, and that the ${C_{L,max}}\;$ of the aerofoil increased from 2.49 to 3.04. However, while the MTE aerofoil was found to increase the overall lift coefficient and the ${C_{L,max}}$ , it did not control the dynamic stall. Vorticity behaviour during DSV generation and detachment has shown that the MTE can change the vortices’ evolution and increase vorticity flux from the leading-edge shear layer, thus increasing DSV circulation. The conclusion that can be drawn from this study is that the fixed drooped morphing leading edge aerofoils have the potential to control the dynamic stall. These findings contribute to a better understanding of the flow analysis of morphing aerofoils in an unsteady flow.

Efficient numerical prediction of blade forced response under inlet distortion

The compressor blade in an aircraft gas turbine engine may suffer from forced vibration problems under the unsteady aerodynamic force due to inlet distortion. This paper develops an efficient numerical method combination to predict the forced response. The computational fluid dynamics (CFD) method is combined with the Fourier transform method to simulate the unsteady flow field under inlet distortion. Then, the forced response of the blade is obtained by the frequency-domain method based on the modal force. The results show that the developed method combination improves the unsteady flow calculation efficiency by 20 times and the response calculation efficiency by 48 times at the cost of less than 5% accuracy compared with the traditional method combination, including the unsteady flow field calculation method based on the three-row full-annulus model and the transient analysis method for calculating the forced response. Finally, the developed method combination is used to analyze the forced response of the blade under different inlet total pressure distributions. The results indicate that the forced response can be effectively decreased by decreasing the total pressure difference and increasing the sector angle difference between the high-pressure and low-pressure areas.

Assessment of Turbulence Models for Unsteady Separated Flows Past an Oscillating NACA 0015 Airfoil in Deep Stall

This paper provides 2D Computational Fluid Dynamics (CFD) investigations, using OpenFOAM package, of the unsteady separated fully turbulent flows past a NACA 0015 airfoil undergoing sinusoidal pitching motion about its quarter-chord axis in deep stall regime at a reduced frequency of 0.1, a free stream Mach number of 0.278, and at a Reynolds number, based on the airfoil chord length, , of . First, eighteen 2D steady-state computations coupled with the SST model were carried out at various angles of attack to investigate the static stall. Then, the 2D Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations of the flow around the oscillating airfoil about its quarter-chord axis were carried out. Three eddy viscosity turbulence models, namely the Spalart-Allmaras, Launder-Sharma , and SST were considered for turbulence closure. The results are compared with the experimental data where the boundary layer has been tripped at the airfoil’s leading-edge. The findings suggest that the SST performs best among the other two models to predict the unsteady aerodynamic forces and the main flow features characteristic of the deep stall regime. The influence of moving the pitching axis downstream at mid chord was also investigated using URANS simulations coupled with the SST model. It was found that this induces higher peaks in the nose-down pitching moment and delays the stall onset. However, the qualitative behavior of the unsteady flow in post-stall remains unchanged. The details of the flow development associated with dynamic stall were discussed

Unsteady Aeroelastic Characterization and Scaling Relations of Flexible Membrane Wings

We present a numerical study to characterize nonlinear unsteady aeroelastic interactions of two-dimensional flexible wings at high angles of attack. The coupled fluid–flexible wing system is solved by a body-fitted variational aeroelastic solver based on the fully coupled Navier–Stokes and nonlinear structural equations. Using the coupled fluid–structure analysis, this study is aimed to provide physical insight and correlations for the aeroelastic behavior of flexible wings in the parameter space of the angle of attack and the aeroelastic number. The phase diagrams of the aerodynamic performance are established to obtain the envelope curves of the optimal performance and determine the transition line of the drag variation. The effects of the angle of attack and the aeroelastic number on the aeroelastic behaviors are systematically examined. The time-averaged membrane deformation is positively correlated with a nondimensional number, the so-called Weber number. A new scaling relation is proposed based on the dynamic equilibrium between the aerodynamic force fluctuation and the combined inertia–elastic fluctuation. The unsteady aerodynamic force can be adjusted by manipulating the membrane vibration, the mass ratio, the Strouhal number, and the aeroelastic number. The numerical investigations provide design guidelines and have the potential to enhance the maneuverability and flight agility of micro air vehicles with flexible wing structures.

On the distributed blowing control of flow around a square cylinder at a low Reynolds number

This paper numerically investigates the distributed blowing control of the flow around a square cylinder at a low Reynolds number of Re=200. The air holes are placed at the windward or leeward stagnation points. The control effect of the unsteady aerodynamic forces is notably different with different spanwise distributions of air holes, which is represented by the dimensionless air hole area ratio G. The simulation results indicate that the windward blowing control (WBC) shows better control effect than the leeward blowing control (LBC) in reducing the time-averaged drag coefficient Cd¯ of the square cylinder while the fluctuating lift coefficient Cl′ can be significantly suppressed by the LBC. Besides, the surface pressure distribution, the turbulence kinetic energy (TKE) and Reynolds shear stress (RSS) distributions and the shedding vortices in the wake are analysed and compared in detail under different control conditions. Finally, through the instantaneous 3D vortex structures and the spanwise fluctuating velocity w′ distribution in the flow field, the suppression of the unsteady aerodynamic forces is mainly related to the 3D vortex pairs induced by the blowing jet.

Aerodynamic stability and vibration mechanism of long-span flat roofs with various span to eaves-height ratios

Computational fluid dynamics (CFD) based on large eddy simulation (LES) is used to investigate the aerodynamic stability of long-span flat roofs with various span/eaves-height ratios (L/H) in this study. Forced vibration tests, where vibrations are induced in the first antisymmetric mode with various frequencies, are conducted on vibrating as well as rigid roofs with L/H = 3, 6, and 9 to obtain distributions of the wind pressure coefficients. The primary focus is the effect of L/H and that of the approach flow turbulence on the aerodynamic stability of the roof, which is quantified using energy consumption. The work done by the unsteady aerodynamic forces on the vibrating roof during the period of vibration was computed using the time histories of the wind pressures at various points on the roof. Furthermore, fluctuating wind pressures and energy consumption are characterized using complex proper orthogonal decomposition (CPOD) analysis. Finally, the vibration mechanism is discussed based on the energy consumption and convection of the wind pressures obtained from CPOD analysis. The results indicate that smooth flow has a higher probability of inducing aerodynamically unstable vibration than turbulent flow because of the phase excitation.

Effects of inertia on the time-averaged propulsive performance of a pitching and heaving foil

The inertia may play an important role in the unsteady behavior of a flapping foil. Of particular relevance in forward flapping locomotion is how the foil inertia may affect its time-averaged propulsive performance. This is the question addressed by the present study from a general, nonlinear formulation of the unsteady interaction with the surrounding fluid of a thin, flexible, two-dimensional and non-uniform foil undergoing prescribed pitching and heaving motion of any amplitude about an arbitrary pivot axis. For a rigid foil it is shown that, although the unsteady inertial forces and moments may be much larger than the unsteady aerodynamic forces and moments if the fluid density is much smaller than the foil density, the inertia does not affect the cycle-averaged propulsive performance for harmonic pitching and heaving motion, independently of their amplitude. Inertia may affect only the cycle-averaged moment if the mean angle of attack is not zero, but without affecting the cycle-averaged power input, and therefore the propulsive efficiency. When a small flexural deflection of the foil is considered, although the cycle-averaged inertial thrust and lift also vanish for any amplitude of the pitching and heaving harmonic motion, the cycle-averaged power input does not. Thus, the foil inertia contributes through the moment and power to the time-averaged propulsive performance for any flexural deflection of the foil, obtained her e analytically in terms of the trailing edge location for general pitching and heaving motion of any amplitude and phase and small flexural deflection amplitude. Simple analytical results are also provided for inertia dominated deflection, characterizing the conditions that minimize the power consumption. The results are valid for arbitrary chord-wise distribution of mass, thickness and (sufficiently large) stiffness of the foil.

Aeroelastic Stability of an Aerial Refueling Hose–Drogue System with Aerodynamic Grid Fins

In this work, the aeroelastic stability of an aerial refueling system is investigated. The system is formed by a classical hose and drogue, and the novelty of our work is the inclusion of a grid fin configuration to improve its stability. The unsteady aerodynamic forces on the grid fins are determined using the concept of a unit grid fin (UGF). For each UGF, the unsteady aerodynamic forces are computed using the Doublet-Lattice Method, and the forces on the complete grid fins are calculated using interfering factors obtained from wind tunnel measurements for the steady case. The static equilibrium position of the system influences the linearized perturbed unsteady motion of the ensemble. This effect, together with the phase lag angle introduced to account for the unsteady aerodynamic forces in the hose, makes the flutter computation of the complete system a non-typical one. The results show that, by adding the grid fins, the stability of the refueling system is improved, delaying or annulling flutter occurrence.

Forced response analysis of the rotor blade rows with the ROM-based aeroelastic model

Forced response is one of the aeroelastic problems which lead to the blade damage. The energy method based on the hypothesis of a conventional travelling wave model and direct numerical simulation are used usually to analyze the problem. However, energy method cannot cover the fluid-structure coupling effect, while numerical simulation needs large computational cost. A rapid method, based on the reduced order model (ROM), is developed to analyze the forced response of the rotor blades. The unsteady aerodynamic force acting on blades is divided into two parts according to the source. One part is due to the blade vibration. An unsteady aerodynamic force model is built to simulate it and then an aeroelastic model is built by coupling the structural equation. The other part is due to rotor-stator interaction (RSI), which is regarded as the excitation of the aeroelastic model. Then the forced response of the rotor blade rows is transferred to calculate the response of the aeroelastic model under the RSI excitation, which requires one to two orders of magnitude less computational time than direct numerical method and could study the effect of the structural parameters conveniently. Results show that the effect of fluid-structure coupling is crucial to the low-mass-ratio structure. Besides, the structural frequency is not exactly coincident with the excitation frequency when the response amplitude reaches its peak.

Deep learning predictions of unsteady aerodynamic loads on an airfoil model pitched over the entire operating range

For the design and certification of wind turbines, it is essential to provide fast and accurate unsteady aerodynamic load prediction models for the whole operational range of angle of attack, up to 180° for vertical-axis and 90° for horizontal-axis wind turbines. This work describes a computationally efficient unsteady forces prediction model based on a deep learning approach, namely the bidirectional long short-term memory (BiLSTM) algorithm, for an airfoil pitched over the full operational range of angles of attack up to 180°. No model has been developed to capture the unsteady forces at high angles of attack. Novel features based on operating conditions and the steady polars of the airfoil are used as inputs for the BiLSTM model. Direct measurements of steady and unsteady forces on a NACA 0021 airfoil model were conducted at reduced frequencies up to 0.075 and a Reynolds number of 120 000 in an open-jet wind tunnel for model learning and testing. The unsteady forces vary significantly from the steady values at high pitching amplitudes and post-stall angles, which, if not accounted for when simulating wind turbine performance, would result in inaccurate predictions. Furthermore, measurements revealed the effect of unsteady vorticity development and shedding on aerodynamic forces under forward and reverse flow conditions. The BiLSTM model is capable of capturing the underlying physics of unsteady aerodynamic forces under extreme operating conditions.

An Analytical Solution for Unsteady Aerodynamic Forces on Streamlined Box Girders with Coupled Vibration

This paper is a contribution to analyzing the aerodynamic forces on a streamlined box girder (SBG) with coupled vibration in a potential flow. The key enabling step was to assume that the normal velocity of the airflow at an arbitrary point on the surface of the SBG was equal to the normal velocity of the surface motion. The aerodynamic drag force, lift force, and pitching moment were expressed as functions of the motion state of the SBG and the SBG’s shape-related parameters. To investigate the applicability of this force model, the analytical solution at various angles of attack was compared with a numerical simulation in a viscous flow. The results imply that the amplitude of the analytical lift force and pitching moment agree well with the numerical results under the angles of attack of 0° and ±3°. Furthermore, the analytical drag force effectively predicts the second-order phenomenon resulting from the multiplication of the vertical and torsional vibration velocities. As a consequence, the present analytical solution provides an effective method for analyzing the aerodynamic forces acting on SBGs with coupled vibration.

Forced response in a multi-stage aeroderivative axial compressor with acoustic excitations: Method validation with field data

This paper presents the application of a forced response prediction process to an industrial aeroderivative axial compressor and its validation against experimental data. The forced response process is based on a dedicated strategy to decompose the overall unsteady aerodynamic forcing coming from URANS analyses, and an improved use of the interference diagram to detect additional acoustic forcing in the entire operating range. The identification of potential resonance conditions, or crossings, in the interference diagram is based on the assumptions of a cyclic symmetry tuned structure and a forcing function having an aliased engine order driven only by the airfoil count of the rotor/stator interactions of interest. Despite this, it is not rare that unexpected resonances appear during compressor validation tests, often calling for painful and time-consuming redesigns. This is witnessed by the unsteady analysis of an 11-stage axial compressor in which the spatial content of engine order forcing is influenced also by further rotor/stator interactions by means of Tyler-Sofrin acoustic modes that cause the onset of additional crossing conditions.The theory based on time and space decomposition is validated with full 3D unsteady forced response simulations of the entire multistage compressor. Numerical results, obtained by an in-house modal work approach, are compared with experimental data focusing on two resonances, the first of which can be detected by the classical interference diagram, while the second one is justified only by the improved use that considers the acoustic excitations. In both cases, the predicted blade responses are in good agreement with measurements.The theory associated with the generation mechanism of the additional nodal diameters is further explained using the results of dedicated numerical experiments conducted by changing the relative stator and rotor airfoil count on a reduced compressor domain.

Effect of microfibres placed at the front stagnation point of a circular cylinder on aerodynamics and wake flow

We experimentally investigated the control effectiveness of circular cylinder flow and the mechanism of self-adaptive microfibres inspired by bird feathers. The nylon wires were placed at the front stagnation point of a circular cylinder at a Reynolds number of Re = 2.67×104. Surface pressure measurement was employed to analyse the unsteady aerodynamic forces around the circular cylinder, and a high-speed particle image velocimetry measurement system was used to visualise and analyse the wake flow structures. The results indicate that the nylon wires at a high length ratio L/D evidently suppress the Reynolds stress and turbulent kinetic energy, thus suppressing the fluctuating lift and mean drag forces of a circular cylinder. In addition, the nylon-induced vortex at high L/D values can inhibit the interaction of the original shear layers to moderate the von Kármán vortex street behind the cylinder. However, the control effect is limited at low L/D values because the nylon-induced vortex structures cannot reach the wake field and interact with the shear layer.

Aeroelastic Characteristics of Rotor Blades of Last Stage of a Powerful Steam Turbine

Blades of powerful steam turbines are subjected to significant unsteady loads, which, in some cases, can lead to the appearance of self-excited oscillations or auto-oscillations. These fluctuations are extremely dangerous and negatively affect the life time of the blading. When developing new or upgrading existing turbine stages, it is necessary to carry out research on the aeroelastic behavior of the rotor blades. As a result of the modernization of a low-pressure cylinder of a 1000 MW steam turbine, the length of the rotor blades of the last stage increased to 1650 mm. In this regard, a numerical analysis of the aeroelastic characteristics of the last-stage rotor blades in the nominal operation mode was carried out. The analysis used the method of solving the coupled problem of unsteady aerodynamics and elastic blade vibrations, which allows the prediction of the amplitude-frequency spectrum of unsteady loads and blade vibrations in a viscous gas flow. The paper presents the results of numerical analysis of aeroelastic characteristics of the last stage rotor blades both for the mode of controlled harmonic oscillations with a given amplitude and inter-blade phase shift, and for the mode of coupled oscillations of the blades under influence of unsteady aerodynamic forces. The results of the simulation of coupled oscillations of blades for the first five natural forms are presented in the form of the time distribution of displacement of the blade peripheral cross-section, as well as the time distribution of forces and moments acting on the peripheral cross-section. The corresponding amplitude-frequency spectra of displacements and loads in the peripheral section are also given. The results of the calculations showed a positive damping of oscillations, the absence of flutter and auto-oscillations for the first five natural forms of oscillations of the blades in the nominal operation mode of the steam turbine