Unsteady Aerodynamics Research Articles

A comprehensive CFD investigation of tip vortex trajectory in shrouded wind turbines using compressible RANS solver

It is well known that a shroud placed around a wind turbine can increase its power coefficient, but it brings complex mechanisms by which the shroud alters the flow passing through the rotor. Such mechanisms impose numerical challenges, as the shrouded turbines present nonlinear behavior in the wake. This paper deals with a comprehensive analysis of tip vortex trajectory in shrouded wind turbines using Reynolds Averaged Navier–Stokes numerical solutions. The analysis includes aerodynamic performance and vortex characteristics of the whole wind turbine. The Multiple Reference Frame is used on a high-order unstructured compressible solver to study both, isolated and shrouded rotor. The NREL Phase VI Unsteady Aerodynamic Experiment rotor is used as a test case. The accuracy of results for wind speeds between 7 and 25 ms−1 is discussed. Overall, good agreement is achieved between the computed pressure distributions and the experimental reference values. At stalled blade, more efforts are needed to improve numerical solutions, especially for integrated load quantities. The vortex structure is examined, showing that shroud impacts tip vortex trajectory by the increase of the axial induced velocity at the rotor plane. This result, demonstrates that the classical Prandtl tip loss is not accurate for shrouded turbine analysis, and modern finite blade functions are needed. The influence of the flow conditions on the tip vortex trajectory, flow separation and shroud interaction are also discussed.

Geometric control analysis of the unsteady aerodynamics of a pitching–plunging airfoil in dynamic stall

Geometric control theory is the application of differential geometry to the study of nonlinear dynamical systems. This control theory permits an analytical study of nonlinear interactions between control inputs, such as symmetry breaking or force and motion generation in unactuated directions. This paper studies the unsteady aerodynamics of a harmonically pitching–plunging airfoil in a geometric control framework. The problem is formulated using the Beddoes–Leishman model, a semi-empirical state space model that characterizes the unsteady lift and drag forces of a two-dimensional airfoil. In combination with the averaging theorem, the application of a geometric control formulation to the problem enables an analytical study of the nonlinear dynamics behind the unsteady aerodynamic forces. The results show lift enhancement when oscillating near stall and thrust generation in the post-stall flight regime, with the magnitude of these force generation mechanisms depending on the parameters of motion. These findings demonstrate the potential of geometric control theory as a heuristic tool for the identification and discovery of unconventional phenomena in unsteady flows.

Active Flutter Suppression of a Wing Section in the Subsonic, Sonic and Supersonic Regimes by the H∞ Control Method

This paper compares various procedures for determining the optimal control law for a wing section in compressible flow. The flow regime includes subsonic, sonic and supersonic flows. For the evolution of the system in the Laplace plane, the present method makes use of the exact unsteady aerodynamic forces in this plane once the control law is established. This is a great advantage over other results previously published, where the unsteady aerodynamics in the Laplace plane are merely approximations of the curve-fitted values in the frequency domain (imaginary axis). A comparison of different control techniques like pole placement, LQR and H-infinity control demonstrates that the H-infinity controller is the optimal choice, exhibiting an H-infinity norm approximately two orders of magnitude lower than the LQR case. Furthermore, the H-infinity controller demonstrates lower pole values than those of the pole placement and LQR compensator, showing the advantage of the H-infinity controller in terms of economic efficiency.

Mechanism of single-mode panel flutter in low supersonic flow

Supersonic panel flutter can be of two possible types: single-mode flutter and coupled-mode flutter. Compared to coupled-mode flutter, the physical mechanism of single-mode flutter is less studied at present. In order to reveal the inducing mechanism of single-mode flutter, the present paper constructed a reduced-order fluid model by using the system identification and the Auto Regressive with eXogenous input (ARX) model. Coupling the reduced-order model (ROM) for unsteady aerodynamics in low supersonic flow with the structural equation, a highly efficient ROM-based aeroelastic model in state space is formulated, then the flutter boundaries are obtained and the stability of aeroelastic modes are investigated by the complex eigenvalue analysis. According to the physical meaning of relevant parameters in unsteady aerodynamic reduced order model ARX, it is found that the unsteady characteristic of the flow, specifically the history effects of the unsteady aerodynamic forces, plays a dominant role in causing the single-mode panel flutter at low supersonic speeds. It is also shown that the higher modes are indeed weakly unstable in the absence of any structural damping or a viscous boundary layer.

Modeling of the Unsteady Aerodynamic Characteristics of the NACA 0015 Airfoil from the Data of Numerical Calculations of the Flow

Modeling of the Unsteady Aerodynamic Characteristics of the NACA 0015 Airfoil from the Data of Numerical Calculations of the Flow

Comparison of Unsteady Low- and Mid-Fidelity Propeller Aerodynamic Methods for Whirl Flutter Applications

Aircraft configurations with propellers have been drawing more attention in recent times, partly due to new propulsion concepts based on hydrogen fuel cells and electric motors. These configurations are prone to whirl flutter, which is an aeroelastic instability affecting airframes with elastically supported propellers. It commonly needs to be mitigated already during the design phase of such configurations, requiring, among other things, unsteady aerodynamic transfer functions for the propeller. However, no comprehensive assessment of unsteady propeller aerodynamics for aeroelastic analysis is available in the literature. This paper provides a detailed comparison of nine different low- to mid-fidelity aerodynamic methods, demonstrating their impact on linear, unsteady aerodynamics, as well as whirl flutter stability prediction. Quasi-steady and unsteady methods for blade lift with or without coupling to blade element momentum theory are evaluated and compared to mid-fidelity potential flow solvers (UPM and DUST) and classical, derivative-based methods. Time-domain identification of frequency-domain transfer functions for the unsteady propeller hub loads is used to compare the different methods. Predictions of the minimum required pylon stiffness for stability show good agreement among the mid-fidelity methods. The differences in the stability predictions for the low-fidelity methods are higher. Most methods studied yield a more unstable system than classical, derivative-based whirl flutter analysis, indicating that the use of more sophisticated aerodynamic modeling techniques might be required for accurate whirl flutter prediction.

Reduced-order prediction of unsteady spatial-temporal aerodynamics in a turbine cascade

A low-cost prediction method that effectively captures the detailed dynamics of unsteady motions is necessary for turbomachinery design. This paper applies two data-driven methods for unsteady cascade flow of a T106 low-pressure turbine with periodic incoming wakes under unknown conditions and unknown instants, respectively. For the prediction under unknown conditions, the dominant coherent structures of the unsteady flows are obtained using sparsity-promoting dynamic mode decomposition. An arbitrary case's sparse promoting modes serve as a basis for prediction and polynomial interpolation is employed to predict the characteristic parameters, including the amplitude and frequency. Based on the predicted characteristic parameters and sparse promoting modes, the flow fields within a range of Reynolds numbers can be reconstructed. The results show that the large-scale flow structure at different Reynolds numbers can be predicted with reasonable error. The detailed flow structure of cascade flow fields also agrees well with simulation results, demonstrating the method's excellent applicability. For the prediction under unknown instants, the dominant coherent structures of the unsteady flows are obtained using proper order decomposition. The extreme gradient boosting method is utilized to construct a surrogate model and predict the time coefficients at unknown times. Based on the dominating modes and predicted time coefficients, the flow fields within a range of unknown instants can be reconstructed. The cascade flow fields can be recovered with a relative error of less than 3 %. The vortex structures and blade surface pressure agree well with simulation results. The present work provides a promising approach for turbomachinery design and investigating underlying mechanisms with low data requirements.

Aeroelasticity Analysis of Folding Wing with Structural Nonlinearity Using Modified DLM

The structural nonlinear aeroelastic analysis of folding wings is conducted by integrating the modified Doublet Lattice Method in this paper. Firstly, a modified Doublet Lattice Method is investigated to relax the aspect ratio limitation of aerodynamic elements, and its correctness is verified through numerical examples. Secondly, the rational function approximation method is discussed, and the modified Doublet Lattice Method is approximated using the minimum state method to obtain the unsteady aerodynamic forces in the time domain. Finally, the aeroelastic characteristics of a folding wing with free-play and friction nonlinearity are studied by integrating time-domain unsteady aerodynamics with the nonlinear structural dynamics model. The results show that the modified Doublet Lattice Method, which relaxes the aspect ratio limitation of aerodynamic grid elements, is feasible and effective; Friction can suppress the influence of free-play nonlinearity on aeroelastic response.

Experimental and numerical investigation on the unsteady interaction in longitudinal stage separation for parallel-staged two-body configuration

Hypersonic stage separation is a significant process, probably involving complex aerodynamic interaction, which determines the survival of two-stage-to-orbit (TSTO) vehicles. The longitudinal stage separation (LSS) scheme is proposed to improve the safety of the parallel-staged TSTO vehicle, where a small interstage gap may result in weak interference. Therefore, an experimental and numerical study of LSS for the parallel-staged TSTO vehicle at Mach 7 with different angles of attack (AoA) is carried out. The dynamic interaction, including variations in the shock structure, wall pressure distribution, and unsteady aerodynamics, is investigated by testing and numerical simulation. The LSS experiments for the TSTO vehicle were performed using a high-speed pneumatic ejection launch system in the JF-12 shock tunnel, and the method was developed using high-speed visualization and image processing techniques to capture the separating trajectory. The numerical simulations were carried out using the overset grid method and solving the Navier–Stokes equations coupled with the rigid body dynamics equations to obtain the laminar flows over the TSTO vehicle during LSS. The qualitative and quantitative comparison of the test and numerical results showed good agreement in terms of aerodynamic performance, flowfield pattern, wall pressure, and separation trajectory. They show that the small interstage gap of the LSS leads to weak type I and VI shock–shock interactions, with short-duration weak shock reflection at a higher AoA. Furthermore, no shock reflection or interstage gap is observed at lower AoA. Moreover, no stage recontact is observed, and the safety and feasibility of LSS for parallel-staged TSTO vehicles are demonstrated.

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.

The effects of dynamic stalls on the aerodynamics and performance of a Darrieus rotor during self-start

Darrieus turbines face difficulty to self-start, especially in environments with fluctuating inflows that cause them to deviate repeatedly from their designed operating parameters. To elucidate the self-starting process in this study, a three-bladed Darrieus rotor was simulated numerically with vector diagrams to facilitate visualizations on the rotor behaviors. Based on segments of the average rotor torque coefficients (Cτ), the self-starting process consisted of linear and accelerated phases, with the first two segments in the linear phase and the next two segments in the accelerated phase. The simulation showed that the self-starting process was largely influenced by dynamic stalls. The rotor experienced difficulty to self-start in the first segment as it encountered a region of “dead band” with a negative mean cyclical caused by a reverse dynamic stall. This dynamic stall and its corresponding dead band disappeared in the second segment, which initiated the transition into the accelerated phase. In the third segment, forward dynamic stalls that formed boosted the generation and accelerated the angular speed of the rotor toward its peak. Finally, without any dynamic stalls formed in the fourth segment due to reduced values of the inflow angles on the blades, they reduced drastically until the rotor reached its steady phase. Outcomes from this work demonstrate that understanding the effects of unsteady aerodynamics is vital to improving the self-starting process. Potential design improvements on the rotor that address this aspect include static and dynamic pitching, blade flaps, intracyclical control, and flow controls using blowing and suction mechanisms.

Adaptive Internal Model Control for a Flexible Wing With Unsteady Aerodynamic Loads.

This article proposes adaptive internal model controls for the collocated output regulation of a flexible wing, where distributed disturbances, boundary disturbances, and references are from an exactly unknown exosystem. Observer-based tracking error feedback controls are first designed to address the robust output regulation in case of a known exosystem matrix. If the exosystem has an unknown matrix, an adaptive observer is further proposed with the observer error system converging to zero exponentially. Then, we can obtain adaptive observer-based controls by combining adaptive observers and observer-based controls, which are able to regulate the tracking errors toward zero in case of the exactly unknown disturbances and references. The corresponding closed-loop system is proved to be internally asymptotically stable. A simulation example is further provided for adaptive internal model control of the wing system.

Calculation and Selection of Airfoil for Flapping-Wing Aircraft Based on Integral Boundary Layer Equations

The flight of a migratory bird-like flapping-wing aircraft is characterized by a low Reynolds number and unsteadiness. The selection of airfoil profiles is critical to designing an efficient flapping-wing aircraft. To choose the suitable airfoil for various wing sections, it is necessary to calculate the aerodynamic forces of the unsteady two-dimensional airfoil with a Reynolds number in the range of 105. While accurate, calculating this by solving the Navier–Stokes equations is impractical for early design stages due to its high consumption of computing resources and time. The computational demands for extending it to 3D aerodynamic calculations are even more prohibitive. In this paper, a relatively simple method is proposed. The two-dimensional unsteady panel method is utilized to derive the inviscid flow field, the unsteady integral boundary layer method is utilized to solve the boundary layer viscous flow, and the eN transition model is adopted to predict the position of the transition. These models are coupled with the semi-inverse interaction method to solve the aerodynamics of the unsteady low-Reynolds-number two-dimensional airfoil. The unsteady aerodynamics of the symmetric and cambered airfoils at different wing sections are calculated respectively by the proposed method. Mechanism analysis of the calculation results is conducted, and a symmetrical airfoil or a slightly cambered airfoil is recommended for the wing tip, a moderately cambered airfoil is suggested for the outer-wing section, and a highly cambered airfoil is suggested for the inner-wing section.

Research of Unsteady Aerodynamic Characteristics of Electrically Controlled Rotor Airfoils with Trailing-Edge Flaps

An electrically controlled rotor (ECR), also known as a swashplateless rotor, eliminates the swashplate system to implement the primary control via the trailing-edge flaps (TEFs), which can result in enhancements in rotor performance, as well as substantial reductions in weight, drag, and cost. In this paper, the unsteady aerodynamic characteristics of the airfoil with TEF of a sample ECR under unsteady freestream condition are investigated. The CFD results are obtained with sliding and overset grid techniques that simulate the airfoil pitching and flap deflection. Comparative analysis of the aerodynamic characteristics under steady and unsteady freestream conditions at different advance ratios is conducted. At various advance ratios, the lift and drag coefficients are higher at a small angle of attack under unsteady freestream condition; however, it is the opposite at a large angle of attack. The peak values of the lift and drag coefficients show an increased trend with the increase in the advance ratio. On the contrary, the pitch moment and flap hinge moment coefficients demonstrate minor variation under unsteady freestream condition. Furthermore, the aerodynamic characteristics of airfoils become more unsteady with variation in the freestream. Therefore, the lift and drag coefficients of the ECR airfoil with TEF show significant differences between steady and unsteady freestream conditions; however, the pitch moment and the flap hinge moment coefficients show little difference.

Performance characterization of a slotted wind turbine airfoil featuring passive blowing

Renewable energy is crucial for a sustainable future, and wind energy holds significant potential as a viable solution to meet global demands. The current study employs high-fidelity Computational Fluid Dynamics (CFD) simulations to investigate the unsteady aerodynamics of an S809 wind turbine airfoil carved with an inclined contracting curved slot at the mid-chord location. The numerical analyses cover a wide range of angles of attack, α = 0°− 20°, at a chord-based Reynolds number of Rec = 5 × 105. The slotted airfoil exhibits superior aerodynamic performance over moderate-to-high angles of attack (α > 6°), with increased lift, reduced drag, and enhanced glide ratio of up to 1.3×, 0.5×, and 3.7× respectively, compared to the baseline. The slot-induced flow control significantly suppresses flow transition and separation across the airfoil surfaces. The attached-flow regime impedes the formation of flow anomalies, resulting in enhanced aerodynamic performance. Comparative analyses reveal significant reductions in velocity fluctuations, Reynolds shear, vorticity, and turbulent kinetic energy, across the slotted airfoil surface and wake region. The aeroacoustic analysis of the slotted airfoil exhibits substantial reduction in the far-field noise over moderate-high angles of attack, with an overall noise level reduction of approximately 14 decibels recorded at α = 17°. Overall, this study highlights the potential of slot-induced flow control as an effective strategy for enhancing the aerodynamic performance of wind turbines.

A lightweight vortex model for unsteady motion of airfoils

A low-order vortex model has been developed for analysing the unsteady aerodynamics of airfoils. The model employs an infinitely thin vortex sheet in place of the attached boundary layer and a sheet of point vortices for the shed shear layer. The strength and direction of the vortex sheet shed at the airfoil trailing edge are determined by an unsteady Kutta condition. The roll-up of the ambient shear layer is represented by a unique point vortex, which is consistently fed circulation by the last point vortex of the free vortex sheet. The model's dimensionality is reduced by using three tuning parameters to balance representational accuracy and computational efficiency. The performance of the model is evaluated through experiments involving impulsively started and heaving and pitching airfoils. The model accurately captures the dynamics of the development and evolution of the shed vortical structure while requiring minimal computational resources. The validity of the model is confirmed through comparison with experimental force measurements and a baseline unsteady panel method that does not transfer circulation in the free vortex sheet.

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.

Comparative analysis of fixed-pitch and variable-pitch control systems for multirotor drones: Acoustic characteristics and rotor phase control

In this study, the aerodynamic and aeroacoustic characteristics of multirotor electric vertical take-off and landing aircraft in hovering and forward flight are compared using two representative control methods: fixed-pitch control and variable-pitch control (i.e., revolution per minute (RPM) control and collective pitch control). To this end, a comprehensive multirotor noise assessment framework is used to predict the aerodynamics and noise of multirotors controlled by RPM and collective pitch. High-resolution time–frequency analysis is used to clarify the differences in noise spectral characteristics. The findings indicate that blade passage frequency characteristics vary significantly depending on the control method. The phase differences between the rotors of variable-pitch control remain constant irrespective of disturbances or attitude control. In other words, the frequencies of the tone noise do not exhibit short-periodic modulation, unlike those of RPM-controlled multirotor. Additionally, the aeroacoustic characteristics of fixed-pitch and variable-pitch controlled multirotor in response to wind velocity fluctuation are investigated by considering the direction of noise radiation and interference effects. The impact of the turbulent kinetic energy of wind on the noise characteristics is examined by quantifying the noise components associated with aerodynamic unsteadiness in flight. Furthermore, the rotor phase control method can be applied to reduce noise in both control methods. The optimization of rotor phases reduces tone noise significantly at the target observer point without causing aerodynamic losses in variable-pitch controlled multirotor. In contrast, the reduction in tone noise remains relatively limited for fixed-pitch controlled multirotor, as the rotor phase differences are not maintained.

Computational fluid–structure interaction framework for passive feathering and cambering in flapping insect wings

AbstractIn flapping insect wings, veins support flexible wing membranes such that the wings form feathering and cambering motions passively from large elastic deformations. These motions are essentially important in unsteady aerodynamics of insect flapping flight. Hence, the underlying mechanism of this phenomenon is an important issue in studies on insect flight. Systematic parametric studies on strong coupling between a model wing describing these elastic deformations and the surrounding fluid, which is a direct formulation of this phenomenon, will be effective for solving this issue. The purpose of this study is to develop a robust numerical framework for these systematic parametric studies. The proposed framework consists of two novel numerical methods: (1) A fully parallelized solution method using both algebraic splitting and semi‐implicit scheme for monolithic fluid–structure interaction (FSI) equation systems, which is numerically stable for a wide range of properties such as solid‐to‐fluid mass ratios and large body motions, and large elastic deformations. (2) A structural mechanics model for insect flapping wings using pixel modeling (pixel model wing), which is combined with explicit node‐positioning to reduce computational costs significantly in controlling fluid meshes. The validity of the proposed framework is demonstrated for some benchmark problems and a dynamically scaled model incorporating actual insect data. Finally, from a parametric study for the pixel model wing flapped in fluid with a wide range of solid‐to‐fluid mass ratios, we find a FSI mechanism of feathering and cambering motions in flapping insect wings.

Breaking Boundaries in Wind Engineering: LSU WISE Open-Jet Facility Revolutionizes Solar Panel and Building Design

Experimental wind engineering is crucial for global structural design. This paper addresses limitations in aerodynamic testing, particularly in wall-bounded and small-scale scenarios. Open-jet testing, introduced as an advanced tool, overcomes turbulence modelling constraints, providing a more accurate representation of real-world conditions. The LSU WISE open-jet facility produces complete turbulence at a large scale, eliminating the need for corrections accompanied by partial turbulence simulation. This discovery holds significant implications in wind engineering and unsteady aerodynamics. Integrating photovoltaic panels with gable-roofed buildings may not require additional structural reinforcement, with a reduction in wind uplift forces by 45–63%. Building-integrated photovoltaics (BIPV) offer design flexibility and aesthetic appeal despite potential higher upfront costs. Strategic interventions, such as design optimization and cost-effective installation methods, can enhance the economic viability of BIPV systems. Contrary to long-held beliefs, the findings challenge the notion that wind loads on structures with sharp corners are insensitive to Reynolds number. Open-jet testing produces higher peak pressures, providing real-world justification for actual damage in high-rise buildings. These results validate the author’s hypothesis regarding the underestimation of peak loads (in small-scale testing) leading to cladding failure in high-rise buildings. They emphasize the superiority of large-scale open-jet testing, underscoring its critical role in designing resilient structures. The LSU WISE open-jet facility’s unique capabilities hold immense promise for revolutionizing wind engineering, addressing grand challenges, and creating more resilient and sustainable infrastructure. Its applications span critical infrastructure, promising significant economic, societal, and educational impacts in STEM fields.