Elliptic Airfoil Research Articles

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.

A Hermite-type collocation mesh-free approach for simulating incompressible viscous fluid flows

In this work, a novel Hermite-type mesh-free model for incompressible viscous fluid flows is proposed, as a way, to overcome the numerical difficulties experienced by solving under weak or strong formulation the pure stream-function Navier–Stokes equation. In this model a dimensionless virtual domain is utilized, in order to make an accurate dimensionless shape-functions of the recently developed Hermite-type collocation Weighted Least Square approximation, by using dimensionless scale parameters. Then, a Jacobian transformation matrix is built to express the shape-functions spatial derivatives from the virtual to the considered domain. The resolution of the obtained nonlinear algebraic system is performed by the High Order Continuation Method. Numerical tests were investigated on incompressible viscous isothermal fluid flows in lid-driven cavity, backward-facing step, sudden expansions and around various obstacle shapes. They show the advantages of the proposed model compared to the reference Hermite-type collocation models used for pure stream-function equation and the weak Galerkin procedures as Finite Element Method and Element Free Galerkin method, in term of computation accuracy, number of degree of freedom, implementation simplicity and computation time. The numerical and experimental results of literature confirm the validity and capability of the proposed dimensionless model to simulate fluid flows in a expended-lengths inflow–outflow geometry and around obstacles of circular, inclined elliptical and Joukowski airfoil shapes.

An Eulerian based geometry conforming grid-block dynamic mesh refinement for the lattice Boltzmann method

An algorithm for a three-dimensional fine-grid block encompassing a moving solid body using a multi-relaxation time model of the lattice Boltzmann method is proposed and developed. In this numerical framework, a geometry-conforming fine block shifts a coarse lattice unit as the object translates by same amount. The effective utilization of higher-order spatial interpolation has been demonstrated in place of the commonly used low-order temporal interpolation in traditional grid refinement techniques within the lattice Boltzmann method. The successful application of this method has been showcased through three distinct cases: the settling of a solid sphere in a fluid tank under the influence of gravity, hovering motion of an elliptic airfoil, and the “clap and fling” motion of an insect wing. In this regard, various interpolation schemes based on the location of nodes in the overlapping zones of fine and coarse block are discussed. In addition, two cases were evaluated, case 1 where distributions are interpolated and case 2 where macroscopic variables are directly interpolated. It was observed that both interpolations gave same computational accuracy for low Reynolds number [∼O(102)]. However, as Re is increased [∼O(103)], direct interpolation of macroscopic variables proved erroneous and resulted in a large deviation in fluid forces and is not recommended. The geometry-conforming dynamic mesh refinement results in a substantial decrease in computation time, approximately 90%, along with a memory reduction of about 80% compared to the fully refined counterpart.

Drag reducer design of wind turbine blade under flap-wise fatigue testing

Wind turbine blade fatigue testing is necessary to verify the reliability of the structure design. A large aerodynamic drag is experienced under flap-wise fatigue testing since the prototype blade under testing moves through the air as a bluff body. An ellipse-sectional drag reducer made of a thin-wall shell is usually installed near the blade tip to alleviate the aerodynamic drag resistance. However, the correlation between drag reducer profile shape and aerodynamic characteristics has not been studied. In addition, the mass and stiffness of the drag reducer also have an adverse influence on the fatigue testing quality. In this study, a shuttle-shaped airfoil is proposed and an optimization design framework is built by a high-efficient aero-structure integrated numerical method. Results indicate that, as compared to the elliptical airfoils, an optimized shuttle-shaped airfoil can more effectively reduce the aerodynamic drag and at the same time improve the prototype blade test reliability.

Vortex Identification and Quantification on Blunt Trailing-Edge Rotor Blades in Reverse Flow

An inherent aerodynamic limitation of high-advance-ratio high-speed helicopters is reverse flow on the retreating blades, which can be a source of several unsteady effects, like vortex formation, that reduce rotor performance. The current study is the first detailed comparison of a rotor with a conventional, sharp trailing-edge NACA 0012 airfoil section with one equipped with a blunt-edge elliptical airfoil section. The aim was to detect and quantify vortex formation in reverse flow using planar particle image velocimetry on a subscale, low-Reynolds-number rotor rig in a water tank. The investigated blade azimuth angles ranged from 240 to 300 deg for advance ratios between 0.40 and 1.00 at pitch angles from 13 to 25 deg. Four main vortex structures were detected. At the aerodynamic leading edge, a strong interference of the tip vortex with the reverse-flow dynamic stall vortex was identified when blade flapping was restricted. Dynamic stall vortices advect closer to the blade surface for the blunt elliptical airfoil, thus reducing the wake area in reverse flow. Blade pitch kinematics govern the reverse-flow entrance-vortex strength and coherency. A coherent vortex street or wake sheet forms at the aerodynamic trailing edge of either airfoil. Overall, the vortex structures that form on the ellipse are more coherent than those on the NACA 0012. The current study highlights the significance of airfoil geometry, specifically the trailing-edge curvature, of an airfoil on the resulting vortex structures in reverse flow, strongly affecting the rotor performance at high advance ratios.

Modelling of Flow Characteristics of Main Rotor with Elliptical Root Section in Hover Mode

The modelling of a helicopter main rotor flow field in hover regime is being considered. The aerodynamic and aeroacoustics characteristics of two rotor models with different blade root geometries are compared. The first rotor has the shape of NACA0012 air foil in the root section of the blades. The second rotor model has an elliptic air foil in the root of the rotor blade. The amplitude and temporal characteristics of the aeroacoustics emission in near-field are investigated using Computational Fluid Dynamics (CFD).

Numerical Simulation of Flow over Elliptical Airfoils with Different Curvature

Numerical Simulation of Flow over Elliptical Airfoils with Different Curvature

The Drag of an Elliptical Airfoil at a Reynolds Number of 1000

There have been many studies on the mechanisms of unsteady aerodynamics, such as leading-edge vortex (LEV) formation, wing-wake interaction, and spanwise flow. Spanwise flow can only be observed on three-dimensional wing models; however other phenomena such as LEV and wing-wake interaction can be captured using two-dimensional airfoil models. This study focuses on two-dimensional elliptical airfoil because this profile can generate counter-rotating vortices used by insects to generate aerodynamic forces. This research aims to analyze the drag production of two-dimensional elliptical airfoils flapping with bumblebee-inspired kinematics in asymmetrical normal-hovering mode at a typical Reynolds number range of . It is found that drag is generated during the downstroke while thrust during the upstroke. It is also found that the creation and shedding of counter-rotating vortices are closely related to the generation of thrust. The results also indicate that asymmetrical strokes can be used in normal hovering to minimize drag or produce thrust.

Simulation of Aerodynamic Performances of Flexible Flapping Wing Airfoils

Compared with fixed wings, the flapping wing has a significant aerodynamic performance advantage at low speeds and low Reynolds numbers, which draws more and more attentions. But most previous studies focus on rigid flapping airfoils, the aerodynamic performances of flexible flapping airfoils are still unclear. A fluid-solid coupling model for the flexible elliptical airfoils was developed to analyze the flow field around the airfoil, the airfoil deformation and the aerodynamic characteristics of airfoils, at different wind speeds and attack angles. Compared with the rigid airfoil, the flexible airfoil can delay the shedding time of the wake vortex and reduce the oscillation frequency of the disturbance on the lift force. The flexible airfoil significantly suppresses the disturbance of the wake flow and reduces the oscillation amplitude of disturbance. Even, the airfoil disturbance oscillation can be completely eliminated at an appropriate Young’s modulus of the airfoil. These results provide a theoretical guidance for the design of soft aircraft.

A new many-objective aerodynamic optimization method for symmetrical elliptic airfoils by PSO and direct-manipulation-based parametric mesh deformation

A new many-objective aerodynamic optimization method is proposed to design the distinctive symmetrical elliptic airfoil applied on the canard rotor wing aircraft with special requirements on both low drag in different Mach numbers and large drag divergence Mach number. A parameterized direct manipulation of free form deformation (DFFD) method is proposed to realize the one-step process on geometry parameterization and mesh deformation. Then an efficient multi and many-objective particle swarm optimization algorithm (LMPSO) is built to optimize the symmetrical elliptic airfoil to comprehensively improve its aerodynamics. The biobjective optimization of drag reductions at hover stage and at cruise flight shows that the new method can significantly reduce the drag of the elliptic airfoil but at the cost of drag increases at high angles of attack. The four-objective optimization results indicate that the consideration of the high angle of attack flight conditions can improve the aerodynamic performance of the airfoil over a large lift range, which is more practical in engineering application. The five-objective optimization presents that the maximization of the drag divergence Mach number of the elliptic airfoil can be significantly promoted when adding three more design conditions at high Mach number. In general, the optimization results demonstrate that the developed new method can effectively improve the aerodynamic performance of symmetrical elliptic airfoils and provide support on the development of the canard rotor wing aircraft.

Added-mass force on elliptic airfoils

Herein, exact algebraic expressions for the non-circulatory (added-mass) forces on elliptic airfoils are derived for any two-dimensional motion – including simultaneous rectilinear acceleration and rotation – embedded in a steady free-stream flow. Despite the lengthy history of the added-mass concept and its widespread application to cylinders of various cross-sections, such closed-form expressions for elliptic cylinders, in terms of kinematic and geometric parameters alone, have remained absent from the literature until now. Inspection of the derived equations reveals that for pure pitching about a point on the chord-line, increasing thickness always decreases the added-mass force magnitude. For any given motion of the chord-line, the difference in force between thick and thin airfoils is proportional to the square of the thickness, although this difference may be positive or negative for the general three-degree-of-freedom case. In the special case of zero thickness and small pitch angles, Theodorsen's added-mass lift force on rigid thin airfoils is recovered; for large pitch angles, an exact generalization of Theodorsen's expression, applicable to the chord-normal direction, is given.

Influence of the pivot location on the thrust and propulsive efficiency performance of a two-dimensional flapping elliptic airfoil in a forward flight

In this article, the effect of the pivot point location on the thrust performance of a two-dimensional sinusoidal flapping elliptic airfoil in a forward flight condition is investigated using numerical simulations and in-house water tunnel experiments. On the chord line, three different pivot locations at a distance of 0.25c, 0.5c, and 0.75c from the leading edge of the airfoil are considered, where c is the chord length of the airfoil. The flapping frequency and effective angle of attack are varied to investigate the propulsive performance of the airfoil at a Reynolds number of 5000. It is noticed that a modification in the pivot location significantly influences the linear velocity distribution, the evolution of the leading-edge vortex, and the near wake region on the airfoil. Consequently, both the transient and time-averaged thrust coefficient of the flapping airfoil is considerably affected. In addition, we have observed when the flapping frequency is increased, the time-averaged thrust coefficient of the airfoil tends to increase up to a critical Strouhal number and deteriorates thereafter. The same trend of time-averaged thrust coefficient is seen at all considered pivot locations and effective angle of attacks. Our finding suggests, at the high flapping frequency, the formation of rotation induced adverse suction region around the airfoil and delay in the shedding of the leading edge vortex developed in the previous flapping stroke are the primary sources, attributing to the thrust deterioration of the flapping airfoil with symmetric pivot location 0.5c. On the other hand, the thrust degrading effects at the two asymmetric pivot locations, 0.25c and 0.75c, are triggered by the adverse suction regions induced by asymmetric airfoil-surface velocity distribution as well as airfoil-wake vortices interaction. Moreover, the thrust degradation can be postponed to a higher critical Strouhal number if the airfoil pivot location is set near the leading edge and higher amplitude of effective angle of attack is followed. Besides, we found that the airfoil propulsive efficiency is affected due to a change in the aerodynamic power co-efficient with the modification of the pivot location. Furthermore, our observation concludes that the pivot location at 0.25c from the leading edge has maximum time-averaged thrust and propulsive efficiency performances at least for the range of pivot locations, flapping frequencies, and effective angle of attacks examined here.

Improvement of the power extraction performance of a semi-active flapping airfoil by employing two-sided symmetric slot airfoil

Low power extraction efficiency is considered as one of the significant drawbacks of the semi-active flapping airfoil power generator (FAPG). A novel two-sided symmetric slot airfoil was employed in this work to overcome this problem. A coupled numerical method was developed and validated to simulate the interaction between the wind and flapping airfoil. Moreover, the TAGUCHI method was employed to select candidate parameters of the slot and arrange the virtual design of the numerical experiment. It is shown that the power extraction performance of the semi-active FAPG can be improved by employed slot airfoil, compared to the generator with baseline elliptical airfoil, the maximum efficiency is increased 6.01% for the generator with optimized slot airfoil. The aerodynamic behavior analysis of the airfoil showed that due to the slot, the effect lift of the airfoil is increased, therefore improves the passive rotation velocity and power extraction performance of the FAPG.

On the Thrust Generation from an Elliptic Airfoil in Plunging and Translating Motion at Low Reynolds Numbers

In this paper, numerical simulation elliptic airfoil model, which mimics the biological locomotion, is studied. Elliptic airfoil undergoes a combined plunging and translating at low Reynolds number is simulated by using body fitted coordinate system. The moving mesh in the physical domain is mapped to a regular fixed mesh in the computational domain through a time dependent transformation between the physical and computational co-ordinates. The governing equations of laminar incompressible flow are transformed in the computational plane by incorporating the time dependent transformation, which naturally accounts for the mesh velocities. The transformed equations are discretized on the structured, collocated, o-type elliptic grid using the finite difference methodology. The unsteady equations are marched in time by using a semi-implicit pressure correction (projection) scheme. Along with the time marching of the governing equations, utilizing the mesh velocities and the forward Eulertime integration also moves the mesh points. The effect of Reynolds number (Re) is investigated on the flapping flight propulsion is investigated. It is found that there exists a critical Reynolds number (Rec) for every frequency after which there exists a thrust force. The effect of Rec is related to transformation of neutral wake to thrust generating wake. It is also found that the optimal frequency corresponds to a reduced frequency parameter of 0.7 where a lock in exists. It is also found that this Stc is independent of Re and the mode of vortex shedding is same at Re = 100 and 200 for Stc = 0.7. Further, it is shown that the mode of vortex shedding present is always helpful in thrust generation.

Role of synthetic jet control in energy harvesting capability of a semi-active flapping airfoil

The role of synthetic jet (SJ) control in the energy harvesting capability of a semi-active flapping airfoil is numerically investigated in this study. An elliptic airfoil with ratio of 8, which is placed in a two-dimensional laminar flow, is employed to harvest energy from the flow field. The airfoil undergoes an imposed pitching motion, and then an induced plunging motion can be achieved. A pair of SJs with the same frequency and strength is integrated into the upper and lower surfaces of flapping airfoil. As a result, the flow field around the airfoil would be modified by the SJs. At the Reynolds number of 1100 and the pitching axis location of one-third chord, the effects of the inclined angle between the jet direction and the chord line, the phase angle between the SJs and the pitching motion as well as the position of SJ slot on the energy harvesting capability are systematically examined. With the help of SJs, it is demonstrated that the enhancement of energy harvesting efficiency can be achieved. Based on the numerical analysis, it is indicated that the jet flow on the airfoil surfaces with suitable working parameters, which results in the obvious increase of lift force, can benefit the energy extraction performance of the flapping airfoil.

Numerical investigation of lift enhancement in flapping hover flight

The focus of this work is the study of lift enhancement in flapping hover flight using numerical simulations. An idealized set of kinematics for a NACA0012 airfoil consisting of sequential translations and rotations is considered for this purpose, such that the Cl response can be demarcated into translational and rotational parts, which facilitates comparison of forces attributed to translation and rotation. Additionally, comparisons with pure translation and pure rotation are done to isolate the effect of wing–wake interactions. The investigation reveals that the majority of lift is produced in the translational phase. The wing–wake interactions affect the translational phase of the response more than the rotational phase. However, the rotation rate determines the extent of influence of wing–wake interactions on the translational lift response. The effect of different durations of overlap between the translational and rotational motions is also assessed based on the Cl time histories and mean Cl, and the study reveals that an optimum duration of overlap can maximize the lift. An immersed-boundary method with integrated surface-load reconstruction capabilities is used for the computations presented here. The reconstruction of the surface stresses and their integration are carried out with the framework of a parallel solver. The method is validated for a flow past a NACA0012 airfoil executing a non-periodic plunge motion and a non-periodic pitch/plunge motion and a flow around an elliptic airfoil executing a flapping motion.

Use of synthetic jet to a fully-active flapping foil for power extraction enhancement

The power extraction performance of a fully-active flapping foil with synthetic jet is numerically investigated in this work. An elliptic airfoil with ratio of 8, which is placed in a two-dimensional laminar flow, is adopted to extract power from the flow. The foil implements the imposed translational and rotational motions synchronously. A pair of synthetic jets with the same frequency and strength is integrated into the upper and lower surfaces of flapping foil. As a result, the flow field around the foil could be affected by the synthetic jets greatly. At the Reynolds number of 1000 and the pitching axis location of half chord, the effects of the jet strength, the inclined angle between the jet direction and the chord line, as well as the phase angle between the synthetic jets and the flapping motion on the power extraction performance are systematically investigated. Compared with the traditional flapping foil, it is demonstrated that the enhancement of power extraction efficiency can be achieved with the help of synthetic jets. Based on the numerical analysis, it is indicated that the jet flow on the foil surfaces alters the vortex-shedding process and modifies the pressure distribution on the foil surface. As a result, the overall power extraction of the flapping foil can be benefitted.

Force generation of smooth and corrugated airfoil performing unsteady motions at low Reynolds number

Structurally, corrugated airfoil for flapping wing MAV applications is more desirable due to its increased strength. Therefore, any aerodynamic (penalty) effects due to corrugation on such airfoil have found considerable attention. The objective of the paper is to computationally examine the effects of corrugation on an elliptical airfoil performing translation and pitching motion at Re = 100 by comparing it with the performance of a smooth NACA 0012 airfoil. The forces and the flow structures generated over the airfoils during their unsteady motion are solved using Navier–Stokes equations. These unsteady motions include the airfoil accelerating from the rest position and quickly pitching up in a constant free stream. The two airfoils are considered in the study with 50 and 100 equally spaced perturbations on the upper and the lower surfaces, respectively. The surface of a standard ellipse has been modified with the regular perturbations or ‘corrugation’ of the order of 1% c on the upper and the lower surfaces. The current study reveals that during the airfoil acceleration from the rest to U and, subsequently, in a constant velocity translation, the corrugated airfoils (regular surface perturbations) have similar behavior of the force and the moment coefficients (also similar vorticity plots) in comparison with the smooth airfoil. However, it is also found that for the fast and the slow pitching motion in a free stream, the corrugated airfoil (after certain angle of attack) has slightly lower values of the lift and the moment coefficients in comparison with the smooth airfoil; which is due to the small effect of corrugation on the velocity profile. It is concluded that the unsteady effect dominates the geometric differences (smooth versus corrugated airfoil); therefore, corrugated airfoil can be utilized to provide structural strength for flapping wing MAV applications.

Exact solutions of boundary integral equation arising in vortex methods for incompressible flow simulation around elliptical and Zhukovsky airfoils

The problem of 2D incompressible flow simulation around airfoils using vortex methods is considered. An exact solution for the boundary integral equation with respect to a free vortex sheet intensity at the airfoil surface line that arises in such problems is obtained. The exact solution is constructed for flows around elliptical and Zhukovsky airfoils using the theory of complex potentials and conformal mappings technique. It is possible to take into account the influence of singularities in the flow domain — point vortices which simulate vortex wake. The obtained exact solutions can be used to verify and estimate the accuracy of numerical schemes for the boundary integral equation solution: such procedure is also described in details.

Hybrid inverse/optimization design method for rigid coaxial rotor airfoils considering reverse flow

Double-ended airfoils with round leading and trailing edges outperform conventional round-nose and sharp trailing-edge airfoils when used for the inboard part of a rigid coaxial rotor operating in forward flight, as reverse flow can occupy 80% surface of the retreating blade. However, aerodynamic design optimization for this kind of airfoils is challenging, since it is required to achieve drag reduction over a wider lift range in both forward and reverse flows but there is no method available currently. To address this problem, this article proposes an efficient hybrid inverse/optimization design method that combines inverse design and direct optimization within a surrogate-based optimization (SBO) framework. The weighted objective function consists of two components: prescribed pressure distributions and total drag. The resulting constrained optimization problem is solved by using kriging surrogate model and dedicated infill-sampling method. The proposed method is demonstrated by aerodynamic shape optimizations of a DBLN-526 airfoil and an elliptical airfoil and compared with direct optimization method. For DBLN-526 airfoil case, 7%–30% drag reduction is achieved in the range from zero lift to maximum lift and the optimum airfoil features better stall characteristics. For the case of elliptical airfoil of 40% thickness, significant drag reduction is achieved in both forward and reverse flows and the optimum airfoil features more robust aerodynamic performance at off-design Mach numbers. The results confirm that the proposed method outperforms the conventional direct optimization method and more practical for aerodynamic shape optimization of double-ended airfoils.