Unsteady Panel Method Research Articles

Unsteady Aerodynamics of Delta Kites for Airborne Wind Energy Under Dynamic Stall Conditions

ABSTRACTThree unsteady aerodynamic tools at different levels of fidelity and computational cost were used to investigate the unsteady aerodynamic behavior of a delta kite applied to airborne wind energy. The first tool is an in‐house unsteady panel method that is fast but delivers low to mid fidelity predictions. The second tool uses the open‐source CFD code SU2 to solve the unsteady Reynolds‐averaged Navier–Stokes equations with the SST turbulence model. At an intermediate level of fidelity, a semiempirical dynamic stall model that combines the panel method with a phenomenological dynamic stall module is proposed. The latter has free parameters that are fine‐tuned with CFD results from the second tool. The research on the dynamic stall model has been inspired by two flight test campaigns suggesting dynamic stall phenomena possibly driven by the periodic variation of the angle of attack (aerodynamic pitching motion) during crosswind maneuvers. The recorded inflow along the flight path was prescribed in the three aerodynamic tools. As expected, the price to pay for the low computational cost of the panel method is its inability to capture the dynamic stall phenomenon. The results from unsteady CFD qualitatively matched the experimental data identifying a leading‐edge vortex that forms and detaches cyclically during the pitching motion. Using RANS data, the semiempirical tool was fined‐tuned to reproduce the dynamic stall behavior, becoming an accurate and fast aerodynamic tool for coupling with any kite flight simulator. Further discussions on the effects of kite aerostructural deflections are included.

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 Torsional and Bending Stiffness on the Aerodynamic Performance of Flapping Wing

For large bird-like flapping wing aircraft, the fluid–structure coupling problem is very important. Through the passive torsional deformation of the wing, sufficient thrust is generated and propulsion efficiency is ensured. Moreover, spanwise bending deformation will affect lift and thrust. The flow field on the surface of the wing and the geometric nonlinearity caused by the large deformation of the wing should be considered during the design process. Existing research methods do not solve this problem accurately and efficiently. This paper provides a method to analyze the fluid–structure coupling problem of the flapping wing which adopts the three-dimensional unsteady panel method to solve the aerodynamic force, and adopts the linear beam element model combined with the corotational formulation method to consider the geometric nonlinear deformation of the wing beam. This article compares the performance of the flapping wing with different torsional and bending stiffness, and analyzes the airfoil surface pressure coefficients at different portions of the wing during the period. The results show that torsional stiffness has a large influence on the lift coefficient, thrust coefficient and propulsion efficiency. Meanwhile, the torsional stiffness of the wing beam and the initial geometric twist angle of the wing need to be well coordinated to achieve high efficiency. Moreover, appropriate bending stiffness of the wing is conducive to improving propulsion efficiency.

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.

Transition Flight Trajectory Optimization for a Flapping-Wing Micro Air Vehicle with Unsteady Vortex-Lattice Method

Flapping-wing micro air vehicles (FWMAVs) have the capability of performing various flight modes like birds and insects. Therefore, it is necessary to understand the various flight modes of FWMAVs in order to fully utilize the capability of the vehicle. The unique flight modes of FWMAVs can be studied through the trajectory optimization. This paper proposes a trajectory optimization framework of an FWMAV. A high-fidelity simulation model is included in the framework to sufficiently consider the complicated dynamics of the FWMAV. The unsteady aerodynamics are modeled with the unsteady panel method (UPM) and the unsteady vortex-lattice method (UVLM). The effect of wing inertia is also considered in the simulation model. In this study, transition flight trajectories are searched with the proposed framework. An optimal control problem is formulated for the transition flight from hovering to forward flight and transcribed to the parameter optimization problem with the direct shooting method. The cost function is defined as energy consumption. The same converged solution can be obtained with different initial guesses. The optimization results show that the FWMAV utilizes the pitch-up maneuver to increase altitude, although the forward speed is reduced. This pitch-up maneuver is performed more actively when the target velocity of transition is low, or the wind condition is favorable to acceleration.

Numerical simulation of aquatic animals locomotion using unsteady panel method

Investigation of aquatic animals' locomotion is of great importance due to their high propulsion efficiency. An efficient algorithm considering all effective parameters is needed to understand the hydrodynamic behavior and their propulsive efficiency. In this paper, a robust three-dimensional unsteady panel method in form of a computer software Panel3D® is presented. Since, in the fish propulsion problems, the contribution of pressure forces is mostly dominant rather than viscous effects, using potential methods are often good choice. Implementation of a wake sheet with a time marching algorithm enables us to simulate burst starting problems such as sudden fish swimming or wing movements. Furthermore, to simulate the flexible oscillation of deforming bodies, it is needed to implement three-dimensional flexible panel movements in the solver. The accuracy of the solver was examined with vorticity generation pattern and estimation of propulsion forces of three kinds of fishes. The effect of frequency and phase angle of oscillating motions has been investigated in different cases.

Three-Dimensional Unsteady Aerodynamic Analysis of a Rigid-Framed Delta Kite Applied to Airborne Wind Energy

The validity of using a low-computational-cost model for the aerodynamic characterization of Airborne Wind Energy Systems was studied by benchmarking a three-dimensional Unsteady Panel Method (UnPaM) with experimental data from a flight test campaign of a two-line Rigid-Framed Delta kite. The latter, and a subsequent analysis of the experimental data, provided the evolution of the tether tensions, the full kinematic state of the kite (aerodynamic velocity and angular velocity vectors, among others), and its aerodynamic coefficients. The history of the kinematic state was used as input for UnPaM that provided a set of theoretical aerodynamic coefficients. Disparate conclusions were found when comparing the experimental and theoretical aerodynamic coefficients. For a wide range of angles of attack and sideslip angles, the agreement in the lift and lateral force coefficients was good and moderate, respectively, considering UnPaM is a potential flow tool. As expected, UnPaM predicts a much lower drag because it ignores viscous effects. The comparison of the aerodynamic torque coefficients is more delicate due to uncertainties on the experimental data. Besides fully non-stationary simulations, the lift coefficient was also studied with UnPaM by assuming quasi-steady and steady conditions. It was found that for a typical figure-of-eight trajectory there are no significant differences between unsteady and quasi-steady approaches allowing for fast simulations.

SIMULATION OF A MANEUVERING AIRCRAFT USING A PANEL METHOD

We present a method for numerical simulations of a maneuvering aircraft, which uses a first-order unsteady panel method as the only source of aerodynamic forces and moments. By using the proposed method, it is possible to simulate a motion of an aircraft, while the only required inputs are geometry and inertia characteristics, which significantly reduces the time required to start the simulation. We validated the method by a comparison of recordings of flight parameters (position, velocities, accelerations) from an actual aerobatic flight of a glider and the results obtained from the simulations. The simulation was controlled by deflections of control surfaces recorded during the actual flight. We found a reasonable agreement between the experimental data and the simulation. The design of our method allows to evaluate not only the integral kinematic quantities but also instant local pressure and inertia loads. This makes our method useful also for a load evaluation of an aircraft. A significant advantage of the proposed method is that only an ordinary workstation computer is requiredto perform the simulation.

Propulsion Performance of Spanwise Flexible Wing Using Unsteady Panel Method

In this paper, the propulsion performance of a spanwise flexible oscillating wing, which is broadly similar to the undulation of a fin fluke, is investigated. The geometry of the fluke underwent three prescribed harmonic oscillating motions simultaneously while surging with constant velocity. The effect of deflection phase angle, flexibility parameter, and wing tip deflection amplitude on thrust coefficient and swimming efficiency was studied. A low-order unsteady panel method coupled with a time stepping algorithm for free wake alignment is implemented in a computer program to estimate the propulsion efficiency of lifting bodies. A novel approach is introduced to evaluate the singular integrals of line vortices by using an adaptive mollifier function. This method is an efficient way to accelerate computational speed by reducing the order of problem from R 3 to body boundaries. Results present the significant effect of phase angle on the propulsion characteristics of oscillating fluke.

Flapping flight in the wake of a leading insect

This study explores the wake effects of an upstream leading insect on the flight performance of a following one. The potential-flow based aerodynamic model, which combines the unsteady panel and unsteady vortex-lattice methods, is used to compute aerodynamic loads and simulate wake structures. The accuracy of the current aerodynamic model was confirmed in this study. The paper shows that the following insect does not cause any noticeable impact on the leading insect aerodynamics, while unfavorable effects due to the presence of the leading insect were found on the following counterpart. Nonetheless, by choosing a proper wing kinematic phase, the following insect may absorb the energy of the leading insect’s trailing wake, and therefore mitigate these negative effects. The variations of the required mechanical power of the following insect against the wing kinematic phase difference were shown to be related to the travel of the leading insect’s downstroke starting vortex.

Investigation of Rotor Noise Shielding Effects by the Helicopter Fuselage in Forward Flight

This paper presents a numerical study on the rotor noise shielding effects by the helicopter fuselage. The method used to assess acoustic shielding is based on a fast multipole boundary element method, which includes the forward flight effect. A free-wake unsteady panel method, in combination with a Ffowcs Williams–Hawkings (FW-H) integral formulation, is used to compute the rotor noise sources for the blade vortex interaction flight condition. The prediction methodologies are described. Validation of boundary element method and the forward flight effect by means of Taylor’s transformation are conducted by using analytic solutions. The error estimation for the case without mean flow indicates that for sufficient grid resolution the maximum error occurring in the shadow region is less than 0.06 dB. The error estimation for the Taylor transformation shows that the error can be up to 6% for . In addition, a Kirchhoff source surface model used to treat the real rotor noise is described. Finally, the method is applied to a BO105 wind tunnel model to understand the noise shielding features of the main and tail rotors.

Effect of sudden change in free stream velocity on the wind turbine airfoil performance based on boundary element method

In this study, the aerodynamic effects of sudden change in magnitude of incident velocity are investigated in detail for wind turbine airfoils. For this purpose, the unsteady panel method which is based on two-dimensional singularity approach has been developed. The model is first validated via using both the analytical functions and experimental data. The jump in free-stream velocity has been supposed to be applied in two different cases. The first is the airfoil at initially steady state and the second is the airfoil experiencing sinusoidal free-stream velocity. For both cases, the parametric study has been performed consequently investigating the effects of velocity difference magnitude, phase angle, airfoil characteristic and relative velocity oscillation amplitude. The response pattern of lift coefficient is shown to be a combination of three distinct behaviors: an initial jump, a secondary fall and a damped like envelope. The results showed that when the sudden velocity change is being applied on steady case, the time constant of recovery is finite and limited, while for the oscillatory case, the recovery time scale is considerably increased. Moreover, the local change in the normalized lift coefficient seems to be less than 0.3 for the steady case, while it can rise to 0.9 in dynamic oscillatory case. The magnitude of overshoot and undershoot has meaningful correlation with both relative velocity change and the initial phase in which the change occurs.

Energy Generation Efficiency and Strength Coupled Design and Optimization of Wind Turbine Rotor Blades

Wind turbine rotor failures have been reported that resulted in substantial damage and cost for maintenance and recovery. This work developed a wind turbine rotor blade design and optimization method to address a coupled energy generation efficiency and blade structural strength design issue, as a generic procedure applicable to both turbine rotors and propellers, in air and water. The optimization procedure was developed for optimum radial blade sectional thickness distribution with a prescribed constant safety factor across the span. While maintaining the required structural strength and integrity of the rotor blades, this procedure is to achieve the following objectives: (1) reduce material use to minimum and (2) obtain the optimum power generation efficiency with the optimum structural strength. A propeller-turbine rotor code coupling aerodynamic and structural properties was developed. For a given blade geometry and chosen material, performance prediction of the instantaneous loading acting on all blade sections and the strength of a local blade section was performed and optimized. A time-domain, three-dimensional unsteady panel method was implemented, developed, and used to perform the optimization. A wind turbine 10 m in diameter from the National Renewable Energy Laboratory (NREL) (Golden, Colorado) was used as a base design example and for optimization based on an extreme wind speed of 100 km/h. The final result achieved a total savings of 18.72% in blade material.

From flapping to heaving: A numerical study of wings in forward flight

Direct Numerical Simulations of the flow around a pair of flapping wings are presented. The wings are flying in forward flight at a Reynolds number Re=500, flapping at a reduced frequency k=1. Several values of the radius of flapping motion are considered, resulting in a database that shows a smooth transition from the wing rotating with respect to its inboard wingtip (flapping), to a vertical oscillation of the wing (heaving). In this transition from flapping to heaving, the spanwise-averaged effective angle of attack of the wing increases while the effect of the Coriolis and centripetal accelerations becomes weaker. The present database is analyzed in terms of the value and surface distribution of the aerodynamic forces, and in terms of 2D and 3D flow visualizations. While the former allows a decomposition of the force in pressure (i.e., the component of the force normal to the surface of the wing) and skin friction (i.e., tangential to the surface of the wing), the latter allows the identification of specific flow structures with the corresponding forces on the wing. It is found that the aerodynamic forces in the vertical direction (lift) tend to increase for wings moving with larger radius of flapping motion, becoming maximum for the heaving configuration. This is mostly due to the increase of the spanwise-averaged effective angle of attack of the wing with the radius of the flapping motion. Also, the local changes in the effective angle of attack have a strong effect on the structure of the leading edge vortex, resulting in changes in the distribution of suction along the span near the leading edge of the wing. The effect of the apparent accelerations is mostly felt on the spanwise position where the separation of the LEV occurs. On the other hand, the differences in the force in the streamwise direction (thrust/drag) between the configurations with different radius of flapping motion seems to be linked to the position of the stagnation point dividing the suction and pressure side boundary layers, which seems to be controlled by the local effective angle of attack. Finally, the results of the DNS are used to evaluate the performance of an unsteady panel method, and to explain its deficiencies.

Wing flexibility effects on the flight performance of an insect-like flapping-wing micro-air vehicle

This study explores the effects of wing flexibility on several characteristics of flight, in this case the trim conditions, power requirements and dynamic stability of an insect-like flapping-wing micro-air vehicle (FWMAV) based on the hawkmoth Manduca sexta. The wing structure is analyzed by the finite-element method. A potential-based aerodynamic model which encompasses the unsteady panel method and the extended unsteady vortex-lattice method is employed to compute the aerodynamic forces. The motions of the FWMAV are obtained using a flexible multibody dynamics program coupled with the potential-based aerodynamic model. The results of this study show that the trim conditions of insect-like flexible and rigid FWMAVs may differ significantly from each other. When the flight speed is less than 3.0 m/s, using flexible wings is favorable, as they help the FWMAV reduce the power requirement and stabilize the lateral dynamics. However, at 3.0 m/s, these advantages are almost unnoticeable, while at 4.0 m/s, the flexible insect-like FWMAV requires even more mechanical power than its rigid counterpart.

Simulation of the flow past a circular cylinder using an unsteady panel method

In the present work, an in-house UnSteady Double Wake Model (USDWM) is developed for simulating general flow problems behind bodies. The model is presented and used to simulate flows past a circular cylinder at subcritical, supercritical, and transcritical flows. The flow model is a two-dimensional panel method which uses the unsteady double wake technique to model flow separation and its dynamics. In the present work the separation location is obtained from experimental data and fixed in time. The highly unsteady flow field behind the cylinder is analyzed in detail. The results are compared with experiments and Unsteady Reynolds-Averaged Navier Stokes (URANS) simulations and show good agreement in terms of the vortex shedding characteristics, drag, and pressure coefficients for the different flow regimes.

Unsteady Aerodynamic Model Based on the Leading-Edge Stagnation Point

The significance of the leading-edge stagnation point as an unsteady aerodynamic observable is investigated. Using first-order unsteady potential flow theory, a simple model relating the stagnation point to the unsteady lift is derived for an airfoil undergoing arbitrary unsteady maneuvers. In particular, the dynamic circulatory effects are shown to be accounted for by tracking the stagnation point. Linearization permits the superposition of solutions for thickness and camber. The model is validated using numerical simulations, employing both steady and unsteady panel methods. In addition, its validity is investigated experimentally through steady and unsteady wind-tunnel tests of a wing section. The stagnation point is estimated in real time from the convective heat transfer distribution measured using a hot-film sensor array instrumented around the wing’s leading edge. Applications of these findings to flutter suppression and gust-load alleviation are experimentally demonstrated.

Aerodynamics and mechanisms of elementary morphing models for flapping wing in forward flight of bat

The large active wing deformation is a significant way to generate high aerodynamic forces required in bat flapping flight. Besides the twisting, the elementary morphing models of a bat wing are proposed, such as wing-bending in the spanwise direction, wing-cambering in the chordwise direction, and wing area-changing. A plate of aspect ratio 3 is used to model a bat wing and a three dimensional unsteady panel method is applied to predict the aerodynamic forces. It is found that the cambering model has a great positive influence on the lift, followed by area-changing model and then the bending model. The further study indicates that the vortex control is a main mechanism to produce high aerodynamic forces, and the mechanisms for the aerodynamic force enhancement are the asymmetry of the cambered wing and the amplifier effects of wing area-changing and wing bending. The lift and thrust are mainly generated during the downstroke and almost negligible forces during the upstroke by the integrated morphing model-wing.

Evaluation, design and optimization for strength and integrity of polar class propellers

An advanced 3D unsteady panel method was developed for the design and optimization of the strength and integrity of polar class propellers. Blade ice loading specification in both milling and impact cases, under the Unified Polar Class Rules (URI3), by the International Association of Classification Societies (IACS), was implemented. An optimization example and analysis were given for an R-class propeller. The strength of the R-class propeller was assessed for all 7 polar classes and 5 loading cases. Comparison was also made for all polar classes and ice loading cases. As the blade has little skew with a wide chord, both the spindle torque and the in-plane bending moment are small, so only out-of-plane bending failure is the key factor for strength. It was also found that by URI3, there is little difference in strength requirement between polar classes 1 (strongest requirement) and 7 (the weakest). An integrity design and optimization example showed a saving of 1.4tonnes of blade material (22% saving) by decreasing the safety factor to 1.51 (the minimum safety factor under URI3 is 1.5), for which case the blade thickness is about 80% of the existing design.

Aerodynamic mechanism of forces generated by twisting model-wing in bat flapping flight

The aerodynamic mechanism of the bat wing membrane along the lateral border of its body is studied. The twist-morphing that alters the angle of attack (AOA) along the span-wise direction is observed widely during bat flapping flight. An assumption is made that the linearly distributed AOA is along the span-wise direction. The plate with the aspect ratio of 3 is used to model a bat wing. A three-dimensional (3D) unsteady panel method is used to predict the aerodynamic forces generated by the flapping plate with leading edge separation. It is found that, relative to the rigid wing flapping, twisting motion can increase the averaged lift by as much as 25% and produce thrust instead of drag. Furthermore, the aerodynamic forces (lift/drag) generated by a twisting plate-wing are similar to those of a pitching rigid-wing, meaning that the twisting in bat flight has the same function as the supination/pronation motion in insect flight.