Two-dimensional Airfoil Research Articles

A multi-task learning framework for aerodynamic computation of two-dimensional airfoils

Accurate and efficient prediction of airfoil aerodynamic coefficients is essential for improving aircraft performance. However, current research often encounters significant challenges in balancing accuracy with computational efficiency when predicting complex aerodynamic coefficients. In this paper, a Multi-Task Learning framework for Aerodynamic parameters Computation (MTL4AC) of two-dimensional (2D) airfoils is proposed. The MTL4AC processes two key subtasks: flow field prediction and pressure coefficient prediction. These two subtasks complement each other to reveal both global and local aerodynamic changes around the airfoil. The flow field prediction provides a coarse-grained global perspective, which focuses on the pressure and velocity variations on and around the airfoil surface. The pressure coefficient prediction offers a fine-grained local perspective, which concentrates on the pressure distribution on the airfoil surface to accurately calculate lift and drag coefficients. The MTL4AC demonstrated substantial improvements in the experiments conducted on the public dataset, achieving significant enhancements in accuracy and stability. This research contributes an accurate and efficient framework for aerodynamic computation, integrating geometric features and advanced multi-task learning techniques to achieve superior performance in predicting aerodynamic coefficients.

Sensor placement for optimal aerodynamic data fusion

Aircraft design is recently evolving towards a digital twin representation that involves many heterogeneous data sources. The aerodynamic development of aircraft usually incorporates data from computational fluid dynamics simulations, wind tunnel testing, and flight tests. All of these data sources have their advantages and disadvantages, which can optimally be combined using data fusion methods. However, the quality of the data fusion result strongly depends on the experimental design, i.e. the placement of discrete sensors. Therefore, an optimized sensor placement is essential for data fusion applications, as the number of sensors is limited. This work presents a sensor placement strategy for the widely used Gappy proper orthogonal decomposition data fusion methodology. The sensor placement relies on a Bayesian formulation of the data fusion, allowing accurate error estimates. Based on the Bayesian posterior, a utility function characterizes the quality of the fused result by quantifying the expected information gain for the proper orthogonal decomposition coefficients. As the optimization of the sensor locations involves a complex combinatorial problem, we introduce an efficient genetic algorithm for this task. The method is demonstrated on a two-dimensional airfoil and the NASA Common Research Model with synthetic measurement errors. For both test cases, an optimal sensor placement results in smaller reconstruction errors than a conventional layout. The Bayesian approach leads, in most cases, to more accurate reconstructions and is more versatile than other well-established sensor placement methods. The proposed genetic algorithm finds better optima with significantly fewer function evaluations than the widely used greedy algorithms.

Separation and reattachment fixed Reynolds-stress model for iced airfoil and wing simulations

Differential Reynolds-stress models (RSMs) are the higher level of Reynolds-averaged Navier-Stokes (RANS) modeling and generally considered to have more potential than eddy viscosity models (EVMs) when applied to separated flows. Nevertheless, some peculiarities have been observed in simulating flows over iced wings. The first is the numerical stability problem caused by non-streamlined wall surfaces. To weaken this, a wall-boundary-natural scale λ=ω−1/8 is introduced into SSG/LRR RSM in this paper. The second is to remedy the problem of the unsatisfactory non-equilibrium characteristic in separating shear layer (SSL), a correction determined by anisotropy of Reynolds normal stresses is developed. The last focuses on the unphysical backbending of the streamlines near stagnation/reattachment (SR) points. Since the SSL correction will worsen this defect, a SR correction is carried out to blended with it. Four two-dimensional iced airfoils and a three-dimensional iced wing are simulated and then the above measures are confirmed to be the positive.

تعزيز الخصائص الديناميكية الهوائية عن طريق تعديالت سطح الجنيح

The enhancement of the aerodynamic characteristics of the NACA0012 airfoil is studied numerically. ANSYS Fluent is used to simulate the airfoil's performance by applying certain surface modifications in the form of dimples and protrusions. Different shapes were used, namely, semicircular, v-shaped and square. Analysis has been done on an airfoil of 1m chord length with these modifications, which were implemented on the upper surface of a twodimensional airfoil model and placed at 75% of chord length. A comparative study of surfacemodified airfoil models was done to investigate lift and drag for a constant at Re = 3.0E6 at various angles of attack and compare them with smooth airfoils. The results reveal that the aerodynamic characteristics were improved by applying surface modifications, and the flow separation on the airfoil can be delayed by using dimples and protrusions on the upper surface. It was found that the semicircular dimples and v-shaped bumps have the best aerodynamic enhancement, where the lift coefficient was improved by 11% and 9% compared to smooth airfoils, respectively, while the drag coefficients were reduced by 3% for both shapes. Also, based on these surface-modified airfoil analyses, the stall angle was increased by two degrees. In comparison, the semicircular dimples are more suitable for enhancing the performance characteristics of airfoils.

On the Generalization Capability of a Data-Driven Turbulence Model by Field Inversion and Machine Learning

This paper discusses the generalizability of a data-augmented turbulence model with a focus on the field inversion and machine learning approach. It is highlighted that the augmented model based on two-dimensional (2D) separated airfoil flows gives poor predictive capability for a different class of separated flows (NASA wall-mounted hump) compared to the baseline model due to extrapolation. We demonstrate a sensor-based approach to localize the data-driven model correction to tackle this generalizability issue. Furthermore, the applicability of the augmented model to a more complex aeronautical three-dimensional case, the NASA Common Research Model configuration, is studied. Observations on the pressure coefficient predictions and the model correction field suggest that the present 2D-based augmentation is to some extent applicable to a three-dimensional aircraft flow.

Utilizing global-local neural networks for the analysis of non-linear aerodynamics

In addressing the computational challenges pervasive in engineering where time and cost limitations are key concerns, particularly within the Computational Fluid Dynamics (CFD) domain, Reduced Order Models (ROMs) have emerged as instrumental tools. Focused on reducing computational complexity without intrusively modifying the computational model, this study centres on the strategic application of aerodynamic ROMs, which provide efficient computation of distributed quantities and aerodynamic forces. This work presents ROMs for non-linear aerodynamic applications, integrating principal component analysis (PCA) with Global Local Neural Networks (GLNN). The effectiveness of the proposed methodology is demonstrated by leveraging dependency on the parameter space created with non-linear high-fidelity CFD data, incorporating viscous simulation for a comprehensive approach. Results are first presented for a two-dimensional airfoil case and then for a three-dimensional test case featuring a transonic wing-body-tail transport aircraft configuration (NASA Common Research Model). In transonic flows, the proposed ROMs demonstrate the ability to accurately capture both the location and strength of shocks, as well as forces and moments for unseen prediction points. This highlights the efficiency of the proposed method in navigating complex aerodynamic scenarios, achieving comparable accuracy to full-order modelling but at orders of magnitude less computational time, for unseen parameters outside the ROM training set within the parameter space.

Design and Validation of the Trailing Edge of a Variable Camber Wing Based on a Two-Dimensional Airfoil.

Variable camber wing technology stands out as the most promising morphing technology currently available in green aviation. Despite the ongoing advancements in smart materials and compliant structures, they still fall short in terms of driving force, power, and speed, rendering mechanical structures based on kinematics the preferred choice for large long-range civilian aircraft. In line with this principle, this paper introduces a linkage-based variable camber trailing edge design approach. Covering coordinated design, internal skeleton design, flexible skin design, and drive structure design, the method leverages a two-dimensional supercritical airfoil to craft a seamless, continuous two-dimensional wing full-size variable camber trailing edge structure, boasting a 2.7 m span and 4.3 m chord. Given the significant changes in aerodynamic load direction, ground tests under cruise load utilize a tracking-loading system based on tape and lever. Results indicate that the designed single-degree-of-freedom Watt I mechanism and Stephenson III drive mechanism adeptly accommodate the slender trailing edge of the supercritical airfoil. Under a maximum cruise vertical aerodynamic load of 17,072 N, the structure meets strength requirements when deflected to 5°. The research in this paper can provide some insights into the engineering design of variable camber wings.

Laminar separation bubble formation and bursting on a finite wing

The transient processes of laminar separation bubble (LSB) formation and bursting on a rectangular NACA 0018 wing are studied experimentally. A two-dimensional airfoil model is used as a baseline for the assessment of finite wing effects. The models are subjected to ramp changes in free-stream velocity causing the flow to switch between a state where an LSB forms and a state without reattachment. Lift force and particle image velocimetry measurements are used to relate the flow development to the aerodynamic loading. The lift coefficient of the airfoil exhibits substantial hysteresis, and the duration of the lift transients range from $10$ to $22$ convective time scales for bubble formation and $22$ to $30$ convective time scales for bursting. In contrast, the transient lift coefficients of the wing change gradually, with less hysteresis. The wing tip causes greater three-dimensionality in the separation bubble, whose thickness increases near the midspan where bursting is initiated. During bubble formation, the region of separated flow contracts towards the midspan. The gradual change in lift of the wing is linked to slower spanwise expansion and contraction of the separated flow region relative to the airfoil. On both models, the wavenumbers and amplitudes of disturbances in the separated shear layer rapidly change when reattachment initiates or ceases. Applying the bursting criterion of Gaster (Tech. Rep. Reports and Memoranda 3595. Aeronautical Research Council, London, 1967) to the bubble on the wing shows that bursting of the bubble at a single spanwise location is insufficient to cause complete spanwise failure of reattachment, and that the relationship between bursting parameters depends on spanwise position.

Combined Theodorsen and Sears theory: experimental validation and modification

The response of airfoils to unsteady disturbances is a classic problem in the aerodynamics field. Many theoretical models have been proposed in the past to predict the unsteady aerodynamic forces of airfoils. However, these theories focused on individual airfoil motions or incoming flow disturbances, while the theoretical models for multiple disturbances still need to be developed. In this study, a theoretical model to predict the aerodynamic force of an oscillating airfoil encountering vertical gust is derived from a linear combination of Theodorsen's and Sears’ theories. Experimental investigations involving a two-dimensional pitching airfoil encountering a sinusoidal vertical gust are carried out to examine the proposed theory. It is found that the theory effectively captures the trends in the unsteady lift of airfoils subjected to dual disturbances. However, it tends to overestimate the lift amplitude. Notably, when a quasi-steady correction is applied to the theory, the prediction accuracy is greatly improved. The theory correction agrees well with experiment at small pitching frequencies, while deviations exist at higher pitching frequencies. The temporal evolution of the flow velocity reveals that the velocity disturbance induced by the coupled disturbance around the airfoil conforms to the linear superposition of the velocities induced by each individual disturbance, consistent with the prediction of the vortex sheet model. As the pitching frequency increases, significant nonlinear effects appear near the trailing edge of the airfoil, which may be one key factor for the disparities between the theoretical predictions and the experimental lift at higher pitching frequencies.

Coupling of Eddy-Viscosity-Scale Reynolds-Stress Model with an Algebraic Transition Model

Attempts to extend a Reynolds-stress model (RSM) for transition flow simulations have begun to cause concern in recent years based on the fact that the RSM has more potential than an eddy viscosity model when applied to complex three-dimensional flowfields. In terms of the RSM, however, coupling more transport equations will further increase its complexity (may worsen robustness and convergence rate). In this paper, a γ-based algebraic transition model originating from the SA-BC model is coupled with an νt-scale RSM (EV-RSM) to form a new transition/turbulence model, called tEV-RSM. Some numerical tests are conducted with a fifth-order scheme, WCNS, including the well-known T3 flat plate series, a two-dimensional airfoil (S809), a two-dimensional three-element airfoil (30P-30N), a three-dimensional prolate-spheroid, and a three-dimensional circular cylinder. The proposed model is compared with the SA-BC and γ-Reθt SST models, which indicates that it can predict the flows primarily governed by Tollmien–Schlichting transition or bypass transition well and has an advantage in predicting the flows with detached separation. Meanwhile, the iteration convergence rate of the tEV-RSM is fast enough considering it as a seven-equation model.

On the study of the pitch angular offset effects at various flapping frequencies for a two-dimensional asymmetric flapping airfoil in forward flight

This article explores the aerodynamic performance of a two-dimensional elliptical airfoil undergoing sinusoidal heaving and asymmetric pitching motions in forward-flight conditions for the Strouhal number (St) range of 0.1–0.6. The study employs numerical simulations and water tunnel experiments to investigate the effects of non-zero pitch angular offset angles (θoffset) while maintaining a fixed Reynolds number of 5000 and an effective angle of attack amplitude of 15° at the pivot location. The θoffset is varied from −15° to +15° at 5° intervals. The present research shows that these parameters significantly impact the leading-edge effective angle of attack, flow velocity, and the formation of high-pressure regions, which are crucial factors in thrust and lift generation throughout the flapping cycle. Moreover, the pitch angle determines whether the resultant force favors thrust or lift. It is observed that the cyclic time-averaged lift consistently increases with θoffset, surpassing symmetric cases (θoffset = 0°). Conversely, the cyclic time-averaged thrust is lower for non-zero θoffset values. Increasing St enhances both cyclic time-averaged thrust and lift up to the respective critical Sts, after which their performance declines. Notably, the critical St of cyclic time-averaged lift exceeds that of cyclic time-averaged thrust; interestingly, their values are invariant with θoffset. Moreover, in the conditions where thrust efficiency maximizes, lift efficiency attains a minimum value and vice versa. So, depending upon the application, one needs to suitably select the pitch angular offset and flapping frequency to maximize thrust or lift performance.

Control of linear instabilities in two-dimensional airfoil boundary layers

The present study deals with the control of linear, modal and non-modal growth of perturbations in a trapezoidal wing boundary layer. The asymmetric NACA 2515 airfoil is chosen for the analysis. The boundary layer velocity profiles, at different locations on the airfoil, are obtained using the Falkner–Skan equations. The non-modal linear stability theory is used to obtain the amplification of the initial perturbations, for which the state-space approach is adopted. The control is brought about using a Linear Quadratic Regulator (LQR) controller by the means of addition of fluid momentum in the wall-normal direction from the wing surface. Maximum transient energy growth is calculated across a range of wavenumber pairs, and control is applied to the pair with the highest energy growth. In this numerical analysis, we show that the transient growth is higher towards the trailing edge because of the adverse pressure gradient of the flow. Upon control actuation, the reduction in the transient energy growth of perturbations is achieved up to a maximum of 54.6%.

Enhanced Aerodynamic Performance of a Two-Dimensional Airfoil Using Moving Boundaries

The effects of moving boundary conditions on the aerodynamic performance of a two-dimensional NACA 0012 airfoil at different angles of attack (α) in a uniform freestream at a Reynolds number of 10,000 are numerically studied. The moving boundary conditions are motivated by inviscid potential flow around the airfoil, which also satisfies the viscous equations of motion. In this study, the wall is moved at the slip velocity of the inviscid flow, or a fraction of it. These prescribed moving boundary conditions are shown to suppress vortex shedding, thus allowing the drag to go toward zero and the lift coefficient toward 2πα over a wide range of angles of attack (α≤20°) even in the separated flow regime. It is shown that moving boundary conditions are effective over a wide range of their strengths with respect to the overall power required (required to overcome aerodynamic drag and move the airfoil boundary). This power is shown to attain a minimum near the inviscid flow moving boundary condition, which is around 10% or less of the power required for the stationary boundary condition. Finally, the effectiveness of the moving boundary conditions is demonstrated for fully turbulent flow regimes at Re=6 million as well.

Neural-Network-Based Model for Trailing-Edge Flap Loads in Preliminary Aircraft Design

Accurately predicting the forces and moments acting on trailing-edge devices under different flight conditions is a critical aspect in the design of the kinematics and actuation for high-lift or variable-camber applications. However, accurate modeling without elaborated computational fluid dynamics (CFD) analyses in the subsonic and transonic regimes needs a sophisticated model. Thus, the objective of this paper is to create such a model that accurately predicts the forces and moments acting on flaps during different flight conditions while remaining applicable to the preliminary aircraft design. The target values in this model are the three-dimensional (3D) forces and moments on the flap, which were obtained through 3D CFD simulations. The chosen input values required for the model include two-dimensional airfoil data, and wing geometry data for three different aircraft types: short-, medium-, and long-range, including a high-aspect-ratio configuration. Among several potential approaches, a neural network was deemed to be the most promising for predicting the target values. The neural network was used as a regression tool to accelerate the model development process in the preliminary aircraft design. Consequently, multiple studies were conducted on how the setup of the neural network, including the number of neurons, activation functions, and initialization, influences the results. The results reveal that the developed neural network accurately predicts the flap forces and moments with a mean deviation of under 2% for the vertical force Fz and the lateral force Fx and under 4% for the moment My.

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.

An immersed boundary method for the thermo–fluid–structure interaction in rarefied gas flows

An immersed boundary method for the thermo–fluid–structure interaction in rarefied gas flows is presented. In this method, the slip model is incorporated with the penalty feedback immersed boundary method to address the velocity and temperature jump conditions at the fluid–structure interface in rarefied gas flows within the slip-flow regime. In addition, the compressible flows governed by the Navier–Stokes equations are solved by using a high-order finite difference method; the elastic solid is solved by using the finite element method; the fluid and solid dynamics are solved independently, and the thermo–fluid–structure interaction is achieved by using a penalty feedback method in a partitioned way. To model the local rarefaction in the supersonic flow, an artificial viscosity is proposed by introducing the local Knudsen number to diffuse the sharp transition at the shock wave front. Several validations are conducted: the Poiseuille flow in a channel, the flow around a two-dimensional airfoil, a moving square cylinder in a channel, the flow around a sphere, and a moving sphere in quiescent flow. The numerical results from the present method show very good agreements with the previous published data obtained by other methods, confirming the good ability of the proposed method in handling the thermo–fluid–structure interaction in both weakly and highly compressible rarefied gas flows. Inspired by the micro/unmanned aerial vehicles in Martian exploration, the proposed method is applied to the aerodynamics of a flapping wing in rarefied gas flows in both two-dimensional and three-dimensional spaces to demonstrate the versatility of the proposed method for modeling flows involving large deformation and fluid–structure interaction.

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.

THE EFFECT OF THE SPLIT NACA 0015 AIRFOIL ON VARIATIONS IN REYNOLDS NUMBER

This research will discuss the advantages of a NACA 0015 airfoil with a split configuration under varying Reynolds numbers. Computational Fluid Dynamics (CFD) simulations with a K-epsilon turbulence model were conducted on a two-dimensional split airfoil to achieve this goal. Initially, simulations were carried out for the unsplit airfoil geometry at different Reynolds numbers within an angle of attack (AoA) range of 00 to 250. Subsequently, simulations were performed for the split airfoil geometry at various Reynolds numbers within the same AoA range. The unsplit airfoil experiences stall at AoA greater than 110 degrees, while the split airfoil experiences stall at AoA greater than 130 degrees. Additionally, using a split airfoil enhances Cl, with an average increase of approximately 7-8% across different Reynolds numbers. In addition to the Cl improvement, the split airfoil exhibits lower Cd values than the unsplit airfoil, with an average reduction of about 26-28% across all Reynolds number variations. Overall, using separate airfoils improves the aerodynamic performance of the airfoil, with an average increase in Cl/Cd of approximately 33-37% across all Reynolds number variations. In conclusion, the split airfoil performs better than the unsplit airfoil.

Aerodynamics of finite wings with leading-edge flags

Post-stall lift enhancement on rectangular and tapered wing planforms by means of attached leading-edge flags has been investigated at a Reynolds number of 100,000. The study has aimed to investigate the fluid-flag interactions in the presence of a wing tip and variable chord-length, and also compares the results with those for the two-dimensional airfoil case. For the rectangular wing, the characteristics of the interaction of the wake, flag, and vortex as well as the frequency of flag oscillations reveal no noticeable differences from those of the nominally two-dimensional airfoil. For the aspect ratio tested, this suggests that the wake three-dimensionality does not have much effect. However, the magnitude of the lift enhancement is lower due to the existence of the tip vortex. For both the airfoil and rectangular wing, the flag oscillations are nearly two-dimensional and occur in the first beam mode. For the tapered wing tested (with the taper ratio of 0.33 and semi-aspect ratio of 4), the frequency of the flag oscillations and the lift enhancement are almost identical to those of the rectangular wing. However, there is a significant phase lag of the flag oscillations towards the wing tip for the tapered wing. Phase-averaged velocity measurements suggest oblique vortex shedding from the flag.

An adaptive machine learning-based optimization method in the aerodynamic analysis of a finite wing under various cruise conditions

Conventional wing aerodynamic optimization processes can be time-consuming and imprecise due to the complexity of versatile flight missions. Plenty of existing literature has considered two-dimensional infinite airfoil optimization, while three-dimensional finite wing optimizations are subject to limited study because of high computational costs. Here we create an adaptive optimization methodology built upon digitized wing shape deformation and deep learning algorithms, which enable the rapid formulation of finite wing designs for specific aerodynamic performance demands under different cruise conditions. This methodology unfolds in three stages: radial basis function interpolated wing generation, collection of inputs from computational fluid dynamics simulations, and deep neural network that constructs the surrogate model for the optimal wing configuration. It has been demonstrated that the proposed methodology can significantly reduce the computational cost of numerical simulations. It also has the potential to optimize various aerial vehicles undergoing different mission environments, loading conditions, and safety requirements.