Aerodynamic Torque Research Articles

Numerical modeling and analysis of multistage gear transmission system in wind turbine gearbox under load uncertainty

A multistage gear transmission system (MGTS) is widely used in wind turbine gearboxes. Its dynamic responses are closely related to stochastic aerodynamic torque that has a wide interval range between cut-in and cut-out wind speeds. However, most of the dynamic models of MGTS lack attention to dynamic responses caused by uncertainties of multiple parameters under varied input torque. In this study, a dynamic modeling method in conjunction with interval uncertain analysis of MGTS caused by multiple load-related parameters due to varied input torques is proposed. A comprehensive dynamic model of MGTS is developed considering time-varying gear mesh transmission error, load-related gear mesh stiffness and bearing stiffness as well as flexible shafts. The reasonability of simulation is validated, and then the effects of multiple load-related parameters on uncertain dynamic responses are discussed in-depth. Results show that both gear mesh stiffness and bearing stiffness are enlarged with increasing input torque to cause uncertain dynamic responses. These uncertainties would propagate along the flexible shaft and be suppressed by system rigidity. The dominant transverse vibration modes of shafts are sensitive to bearing stiffness, thus, uncertain bearing stiffness has remarkable effects on dynamic responses than gear mesh stiffness.

Modelling aerodynamic forces and torques of spheroid particles in compressible flows

In the present study, we conduct numerical simulations of compressible flows around spheroid particles, for the purpose of refining empirical formulas for drag force, lift force, and pitching torque acting on them. Through an analysis of approximately a thousand numerical simulation cases spanning a wide range of Mach numbers, Reynolds numbers and particle aspect ratios, we first identify the crucial parameters that are strongly correlated with the forces and torques via Spearman correlation analysis, based on which the empirical formulas for the drag force, lift force and pitching torque coefficients are refined. The novel formulas developed for compressible flows exhibit consistency with their incompressible counterparts at low Mach number limits and, moreover, yield accurate predictions with average relative errors of less than 5%. This underscores their robustness and reliability in predicting aerodynamic loads on spheroidal particles under various flow conditions.

Rapid attitude stabilization of ultra-low orbit satellites using movable masses and reaction wheels

This paper proposes a combination of movable masses and reaction wheels for the attitude control of ultra-low-orbit satellites. During the attitude control of ultra-low-orbit satellites, the satellite’s attitude is significantly influenced by the aerodynamic torque. Therefore, this paper proposes a combined control method using movable masses and reaction wheels. By adjusting the position of the movable masses to modify the relative distance between the center of mass (CM) and the center of pressure (CP), the aerodynamic torque is effectively reduced. Additionally, a finite-time terminal sliding mode extended state observer (TSMESO) is incorporated to estimate the reduced aerodynamic torque. Then, a finite-time non-singular terminal sliding mode control (NTSMC) method is introduced to achieve rapid attitude stabilization. Simulations demonstrate that under the proposed control system, the aerodynamic torque acting on the ultra-low-orbit spacecraft can be significantly reduced in a short time, and the response and high precision attitude stability can be effectively achieved.

Data-driven control of wind turbine under online power strategy via deep learning and reinforcement learning

This study proposes a data-driven wind turbine (WT) model predictive control (MPC) enhanced by a deep-learning (DL) radial basis function network (RBFN) and a reinforcement-learning (RL) deep Q-learning network (DQN). The RBFN provides comprehensive aerodynamic predictions, including thrust, torque, and power. Besides, the MPC linearization relies on the RBFN prediction to estimate force sensitivities. The DQN achieves an online power strategy (OPS) that solves the 2-degree-of-freedom (2-DOF) optimization of rotor speed and pitch angle, which can actively adjust power capture to meet different power requirements. The DQN adopts a novel bisection algorithm with a first-in-first-out (FIFO) queue for high-precision 2-DOF results. The MPC coordinates the permanent magnet synchronous generator (PMSG) and pitch servo, considering shaft rotation and tower movement. Compared with the maximum power point tracking (MPPT) and power reference point tracking (PRPT) based controls, the proposed RBFN-DQN-MPC reduces power fluctuation and ensures constant output. This study also compares the DQN with the categorical DQN (C51), which indicates that the DQN is more effective in the 2-DOF optimization. Hence, WTs enhanced by the DL-RL-MPC are intelligent and reliable for flexible wind generation.

Sliding mode control based on maximum power point tracking for dynamics of wind turbine system

This article presents a proportional-integral sliding mode control (PI-SMC) approach for a two-mass variable speed wind turbine (VSWT) system. Most studies on wind turbines typically focus mainly on the electromagnetic part of the generators, or even on the high-speed part, considering the shaft stiffness as negligible. However, the generator torque is actually driven by the aerodynamic torque, and a two-mass system like the one studied here plays the role of a transmission element for this power. To address this challenge, the problem of low power generation resulting from wind speed variability is tackled by designing a PI-SMC control law, capable of controlling the mechanical turbine model that optimizes power and torque by tracking the maximum power point (MPPT) for rotational speed and aerodynamic power. To validate the developed theoretical results, an application of the wind turbine system is simulated in Matlab/Simulink, for a particular case. The control used is capable of satisfying the dynamic performance of the systems.

Prediction model of aircraft hinge moment: Compressed sensing based on proper orthogonal decomposition

By hinge moment, we mean the aerodynamic torque exerted on the rudder shaft by the airflow passing through the aircraft control surface, with obtaining high-precision results often relying on wind tunnel tests. Due to the complex aerodynamic balance insulation and installation errors that must be considered in cryogenic wind tunnels, the main method for calculating hinge moments is to directly integrate surface pressure distribution information. However, it is usually difficult to arrange enough pressure taps, resulting in the accuracy failing to meet expectations. Combining the sparse wind tunnel test data and low-precision computational fluid dynamics results, this paper introduces the compressed sensing based on proper orthogonal decomposition (CS-POD) method and presents the sub-Ma model and the full-Ma model for predicting hinge moments. The number of sensors and sensor positions are determined based on the sparsity of the numerical simulations and basis functions. Then, the CS algorithm solves the basis coefficients. Finally, the hinge moments are obtained by integrating the reconstruction pressure distribution which is calculated by linearly combining the basis functions and basis coefficients. The result shows that the full-Ma model exhibits higher prediction accuracy with approximately five sensors under subsonic and transonic cases, reducing the relative error of the sub-Ma model by 2–10 times, even at high angles of attack. The mean reconstruction accuracy for the hinge moments is 97.6%, and for the normal forces, it is 94.3%. Therefore, adding relevant terms when the number of samples is small can effectively improve modeling accuracy.

Model predictive direct torque algorithm for coordinated electrical grid operation of wind energy conversion system-based doubly fed induction generator

ABSTRACT In this paper, robust predictive control (RPC) based on direct torque control space vector modulation (DTC-SVM) of the doubly fed induction generator wind turbine system (DFIG-WTS) is investigated to improve energy capture effectiveness. A novel cost function is introduced for the predictive speed regulator where the aerodynamic torque is considered as an unknown perturbation. This technique is designed to improve dynamic performance such as reference tracking, disturbance rejection, and robustness to parameter variations. The use of the DTC-SVM technique enhances performance in terms of constant switching frequency and reduced torque-flux ripples. The simulation results using real-time MATLAB/Simulink demonstrate the feasibility and validity of the proposed strategy, where very satisfactory performance has been achieved.

Wind turbine power extraction under partial wake operations, a CFD study using ALM.

This study focuses on the intricate interplay between large wind turbines and their wake effects on neighboring turbines. We specifically investigate the influence in power production and aerodynamic loads when a turbine operates under the influence of upstream turbine wakes. The analysis has been performed by means of Computational Fluid Dynamic simulations using OpenFOAM, while wind turbines are modelled with an Actuator Line Model approach. Two large IEA 15 MW reference wind turbines, with one turbine partially affected by the other’s wake, are analyzed. The research assesses the influence of turbine spacing on aerodynamic torque and blade loads. The study shows that the CP may suffer oscillations 2 orders of magnitude greater than the ones observed at the reference cases. For the most affected case, the torque experiences oscillations of a 5.46 % w.r.t. to the averaged torque over the last ten revolutions. The influence of operating in partial wake conditions is specially relevant on the blade root loads that are found to suffer an increase of ∼ 20 % and a decrease of ∼ 30 % over one revolution as the blade is affected by the highly sheared flow resulting from the upstream wake.

Numerical investigation of effects of riblets on wind turbine performance

In this study, systematically designed wind tunnel experiments were conducted to characterize the aerodynamic performance of a DU91-W2-250 airfoil with a riblet film. To quantify the impact of the riblet film on wind turbine performance, experimental results were used as input data for numerical simulations. Large-eddy simulations were conducted for the smooth and modified airfoils under uniform and turbulent inflow conditions. For the turbulent inflow simulations, staggered cubes were introduced upstream of the wind turbine to generate velocity fluctuations in the flow. Results from the numerical simulations show that improvements in the aerodynamic performance of the airfoil with riblets enhance the aerodynamic torque that drives the wind turbine, thereby increasing the power output. The improvement in the power coefficient with the use of the riblet film is higher for turbulent incoming wind compared to uniform flow conditions.

The Weis-Fogh Number Describes Resonant Performance Tradeoffs in Flapping Insects.

Dimensionless numbers have long been used in comparative biomechanics to quantify competing scaling relationships and connect morphology to animal performance. While common in aerodynamics, few relate the biomechanics of the organism to the forces produced on the environment during flight. We discuss the Weis-Fogh number, N, as a dimensionless number specific to flapping flight, which describes the resonant properties of an insect and resulting tradeoffs between energetics and control. Originally defined by Torkel Weis-Fogh in his seminal 1973 paper, N measures the ratio of peak inertial to aerodynamic torque generated by an insect over a wingbeat. In this perspectives piece, we define N for comparative biologists and describe its interpretations as a ratio of torques and as the width of an insect's resonance curve. We then discuss the range of N realized by insects and explain the fundamental tradeoffs between an insect's aerodynamic efficiency, stability, and responsiveness that arise as a consequence of variation in N, both across and within species. N is therefore an especially useful quantity for comparative approaches to the role of mechanics and aerodynamics in insect flight.

Aggressive flight control of quadrotors using incremental nonlinear dynamic inversion with a high-fidelity thrust unit model

The application of quadrotors has been expanded into aggressive tasks such as military confrontation and aerobatics shows, making it crucial to enhance flight maneuverability to adapt to rapid and large-scale command changes. Unlike hovering or low-speed modes, aggressive flight exacerbates quadrotor model uncertainty, making it challenging for controllers to balance response speed and robustness. This paper proposes an INDI control method that integrates a high-fidelity thrust model unit to address this practical need. First, based on the pole distribution theory and the application of INDI on quadrotors, it is concluded that the dynamic response of quadrotor flight is impacted by the accuracy of the thrust model. Second, consider the airflow velocity and angles, the high-fidelity modeling approach, and the aerodynamic forces and torque expression validated through wind tunnel experiments are provided. Then the flight controller for the quadrotor is designed with the established high-fidelity thrust unit model. Finally, aggressive trajectory-tracking flight tests are set to evaluate the improvement of our work. The results demonstrate that our proposed method indeed enhances the response speed and tracking accuracy, as well as the flight stability of the quadrotor.

Optimal attitude planning along torque equilibrium points using aerodynamic database for deorbiting large space debris

Currently, considerable attention is being directed toward active debris removal (ADR) using small, cost-effective satellites. From high altitude to re-entry, ADR missions use thrusters that consume significant amounts of fuel. The volume of the propulsion system in these satellites can be quite large, and it is difficult for a small satellite to accommodate a large-scale propulsion system. Thus, active utilization of atmospheric drag is being considered for small satellites with low capability. However, the principal challenge for small satellites to remove large debris is to deal with the large disturbance torque caused by strong atmospheric drag on the debris. This paper proposes attitude guidance around an equilibrium (balance) point in attitude dynamics acted on by gravity gradient and aerodynamic torques. The desired attitude is set to optimize two conflicting objectives: maximizing the projection area to generate large aerodynamic force and minimizing the disturbance torque. In this paper, we develop an aerodynamic database (ADDB) by rigorously calculating the aerodynamic torque for each altitude and solar array paddle (SAP) rotation based on an aerodynamic characteristic model of free molecular flow. Using the ADDB, the SAP angle and orbit altitude effects on the torque equilibrium attitude (TEA) are clarified. Then, the mean disturbance torque map at each orbit altitude is introduced to obtain the candidate TEA paths. The effectiveness of the proposed paths for debris descent is demonstrated through numerical simulations.

Wind turbine rotors in surge motion: new insights into unsteady aerodynamics of floating offshore wind turbines (FOWTs) from experiments and simulations

Abstract. An accurate prediction of the unsteady loads acting on floating offshore wind turbines (FOWTs) under consideration of wave excitation is crucial for a resource-efficient turbine design. Despite a considerable number of simulation studies in this area, it is still not fully understood which unsteady aerodynamic phenomena have a notable influence on the loads acting on a wind turbine rotor in motion. In the present study, investigations are carried out to evaluate the most relevant unsteady aerodynamic phenomena for a wind turbine rotor in surge motion. As a result, inflow conditions are determined for which a significant influence of these phenomena on the rotor loads can be expected. The experimental and numerical investigations are conducted on a two-bladed wind turbine rotor subjected to a tower-top surge motion. A specialised wind tunnel test rig has been developed to measure the aerodynamic torque response of the rotor subjected to surge motions with moderate frequencies. The torque measurements are compared to two free-vortex-wake (FVW) methods, namely a panel method and a lifting-line method. Unsteady contributions that cannot be captured using quasi-steady modelling have not been detected in either the measurements or the simulations in the covered region of motions ranging from a rotor reduced frequency of 0.55 to 1.09 and with motion velocity amplitudes of up to 9 % of the wind speed. The surge motion frequencies were limited to a moderate range (5 to 10 Hz) due to vibrations occurring in the experiments. Therefore, a numerical study with an extended range of motion frequencies using the panel and the lifting-line method was performed. The results from both FVW methods reveal significant unsteady contributions of the surge motions to the torque and thrust response that have not been reported in the recent literature. Furthermore, the results show the presence of the returning wake effect, which is known from helicopter aerodynamics. Additional simulations of the UNAFLOW scale model and the IEA 15 MW rotor demonstrate that the occurrence of the returning wake effect is independent from the turbine but determined by the ratio of 3P and surge motion frequency. In the case of the IEA 15 MW rotor, a notable impact of the returning wake effect was found at surge motion frequencies in the range of typical wave periods. Finally, a comparison with OpenFAST simulations reveals notable differences in the modelling of the unsteady aerodynamic behaviour in comparison to the FVW methods.

On the Variation of Cup Anemometer Performance Due to Changes in the Air Density

In the present paper, the effect of air density variations on cup anemometer performance is analyzed. The effect on the sensor’s performance is mainly due to the difference between the altitude at which the cup anemometer is working and the altitude at which this instrument was calibrated. Data from the available literature are thoroughly analyzed, focusing on explaining the coupled effect of the air temperature on both the rotor’s friction torque and the air density (that is, related to the aerodynamic torque on the rotor). As a result, the effect of air density variation at constant temperature (that is, leaving aside any variation of friction forces at the anemometer rotor shaft) on the sensor transfer function (i.e., on the calibration constants) is evaluated. The analysis carried out revealed a trend change in the variation with air density of the transfer function of the cup anemometer. For densities greater than 0.65, the calibration constants of the instrument have a variation with density that must necessarily change suddenly as the start-up speed, represented by the calibration constant B, becomes zero around this value of air density. To highlight the relevance of the present research, some estimations of the effect of wind speed measurement errors associated with air density changes on the Annual Energy Production (AEP) of wind turbines are included. A 1.5% decrease in the AEP forecast at air density corresponding to 2917 m above sea level is estimated for 3000–4500 kW wind turbines.

Using STAR-CCM+ Software in Aerodynamic Performance of Bogies under Crosswind Conditions

INTRODUCTION: STAR-CCM+ is a CFD software that uses continuum mechanics numerical techniques and is a tool for thermodynamic and fluid dynamics analysis. STAR-CCM+has expanded the functions of surface treatment, such as surface wrapper, surface remesh, and volume mesh generation.With the increase of train speed, the aerodynamic phenomena become more prominent, and the aerodynamic phenomena of high-speed trains in crosswind environment become more complicated. OBJECTIVES: Bogie is an important part of high-speed train. It is of great significance to study the aerodynamic performance Three groups of trains operating in a strong wind environment are modeled, and the surface pressure distribution characteristics of the car body and bogie, as well as the aerodynamic and aerodynamic torque distribution characteristics of each car and bogie, are analyzed when the train operates at 350km/h under a Class 12 crosswind condition. RESULTS: The results of the study show the variation rules of surface pressure, aerodynamic force and aerodynamic moment of the car body and bogie with wind speed. CONCLUSION: The windward surface pressure of the vehicle body increases linearly with the increase of wind speed, and the surface pressure of the roof and leeward side decreases linearly with the increase of wind speed.

Numerical and Experimental Analysis of the Aerodynamic Torque for Axle-Mounted Train Brake Discs

Numerical and Experimental Analysis of the Aerodynamic Torque for Axle-Mounted Train Brake Discs

Design and Integration of a Flapping Wing Apparatus

Abstract In this paper, we presented the design, integration, and experimental verification of a flapping wing apparatus. The purpose for this apparatus is to provide a framework to study the applicability of various types of sensors on flapping wings in the presence of forward speed. This work is inspired by the discoveries of mechanosensory hairs on insect wings that perform like strain-gauge sensors. To design the apparatus, we started by kinematic analysis of a crank-slider mechanism to actuate the wings. After that, we constructed the equations of motion of the entire system to find the proper gear ratio, motor properties, and other geometric dimensions. For the aerodynamic modeling, we used a quasi-steady formulation and presented a closed-form solution for the aerodynamic torque. Then, we explained the integration process and manufacturing of the main parts and presented two prototypes for the apparatus. At the end, we showed the final constructed versions of the apparatus and presented the experimental response and compared them with the simulation.

Design Methodology of Wind Turbine Rotor Models Based on Aerodynamic Thrust and Torque Equivalence

Limited by scaling effects, the physical model tests of FOWTs (floating offshore wind turbines) cannot simulate the aerodynamic loads on rotors correctly. To solve this problem, the real-time hybrid model tests in wind tunnels were developed and provided a feasible solution for the aerodynamic simulation. To perform the wind tunnel tests, the design of aerodynamic equivalent rotor models is most critical. In this study, an innovative methodology of aerodynamic equivalent design for the wind turbine rotors is developed based on GA (genetic algorithm). The NREL (National Renewable Energy Laboratory) 5 MW and DTU (Technical University of Denmark) 10 MW rotors are employed for the case studies to validate the proposed methodology. According to the results, the model-scale aerodynamic thrust performance can be accurately matched with the prototype in the entire region between cut-in and cut-out wind speeds, which allows the rotor model to provide correct thrust at different wind speeds. The variance of the aerodynamic torque with the wind speeds for the developed model is also in good agreement with the prototype, which could be beneficial for the design of the model-scale active pitch control strategy. Moreover, the applicability of the fitness functions of GA is discussed.

Comparison of Single and Dual Coherent Blades for a Vertical Axis Carousel Wind Rotor Using CFD and Wind Tunnel Testing

This paper focused on the investigation of the blades for a carousel rotor of a wind turbine with a vertical axis. Cross sections of the single coherent (SC) and the dual coherent (DC) blades were compared in terms of the aerodynamic forces and aerodynamic torque generated during rotor operation for various wind attack angles. The design of the DC blade is novelty proposed by the authors. The main objective of the study was to determine the influence of the blade cross-section on the propelling torque of a wind turbine with three blades, which is an important parameter for rotor starting. First, experimental studies were carried out in a wind tunnel for real-size blade models. A CFD analysis of the airflow around the blades was then conducted. The obtained results were used to evaluate the suitability of applying the studied blade types in the design of the carousel wind rotor. The assessment compared the drag force and the lift force as well as aerodynamic torque as a function of a wind attack angle. It was concluded that the rotor with three DC blades involved mainly the drag force in contrast to the rotor with three SC blades that also involved the lift force to a greater extent. Despite the rotor with DC blades obtained greater values of the drag forces on the blades, the rotor with SC blades obtained a greater starting torque.

Time characteristics of microsatellite attitude control at intervals between reac-tion wheels desaturations

The article is devoted to the processes study of changing the microsatellite reaction wheels angular velocities during its stabilization, turn and detumbling. Satellite control is considered under conditions of constant and harmonic external torques, as well as under gravitational, aerodynamic and magnetic disturbing torques. Expressions that describe the change in the reaction wheels angular velocities during satellite stabilization under the action of constant and harmonic torques at a frequency equal to the orbital angular velocity are given. The influence of the magnetic disturbing torque caused by the constant component of the satellite's dipole moment on the accumulation of the reaction wheels angular momentum has been studied. The formula for determining the magnitude of the reaction wheels angular velocities oscillations was obtained using a model of the Earth's magnetic field in the form of the straight dipole and taking into account a circular orbit. Moreover, its use for calculating the maximum values of angular velocities gives results that are very close to the results of modeling taking into account accurate models of the Earth’s magnetic field and the satellite’s center of mass trajectory. The maximum possible operating time intervals of the control system without forced desaturation of its controls are estimated.