Leading-edge Suction Force Research Articles

Leading-edge Suction Behavior of Unsteady Airfoils in Forward And Reverse Flows

To model unsteady airfoil aerodynamics in forward and reverse flows in a simple and robust manner requires a strong understanding of the complex flow dynamics and their relation to first-order concepts. The current work explores the relation between the leading-edge suction force, represented nondimensionally by the leading-edge suction parameter (LESP), and the flow physics of forward and reverse dynamic stall as a function of freestream Reynolds number, airfoil thickness, and motion kinematics for the NACA 0012, 0015, and 0018 airfoils using computational tools. The relation between the LESP and critical events associated with leading-edge vortex (LEV) shedding was found to be independent of flow direction barring the signature to identify LEV initiation. Leading-edge suction was observed to continue to increase after LEV initiation in reverse flow and could be attributed to the combined effect of a weak LEV and strong trailing-edge vortice. While LESP, forces, and moments were found to be moderately dependent on airfoil thickness and strongly dependent on the Reynolds number in forward flow conditions and the critical LESP, in addition, was weakly dependent on motion kinematics, the aerodynamics were observed to be largely independent of said parameters in reverse flow. This allows for a single critical LESP value to be used for symmetric airfoils to indicate LEV initiation when the blunt edge is experiencing reversed flow, a finding which serves to largely reduce the empirical dependencies while modeling unsteady reverse dynamic stall in low-order methods.

Leading-edge flow sensing for detection of vortex shedding from airfoils in unsteady flows

Sensing of vortex shedding in unsteady airfoil flows can be beneficial in controlling and positively harnessing their effects for increased aerodynamic performance. The time variation of the leading-edge suction parameter (LESP), which is a non-dimensional measure of the leading-edge suction force, is shown to be useful in deducing the various events related to vortex shedding from unsteady airfoils. The recently developed leading-edge flow sensing (LEFS) technique, which uses a few pressures in the airfoil leading-edge region for deducing the aerodynamic state of an airfoil, is adapted to deduce the variation of LESP during an unsteady motion in incompressible flow. For this purpose, the flow over the airfoil is divided into an outer-region flow over the chord, modeled using thin airfoil theory, and an inner-region flow over the leading edge, modeled as a flow past a parabola. By matching these two flows, relations are derived for calculating the LESP from a few pressures at the leading edge. By studying the variations of the LEFS outputs and the calculated LESP for various unsteady motions, guidelines are presented for detecting events related to vortex shedding: initiation, pinch-off, and termination. Computational and experimental results for additional unsteady motions confirm the effectiveness of the LEFS as a sensing technique for events associated with vortex shedding on unsteady airfoils.

Dynamic modeling of a CPG-governed multijoint robotic fish

This paper is devoted to the formulation of a dynamic model of a serially connected multijoint robotic fish with a pair of wing-like pectoral fins, in which the whole robot is treated as a moving multilink rigid body in fluids. Considering that the thrust of fish mainly results from the force of trailing vortex, added lateral pressure, and leading edge suction force, the dynamic equations of the swimming fish have been derived by summing up the longitudinal force, lateral force, and yaw moment on each propulsive component in the context of Lagrangian mechanics. Along with the bio-inspired central pattern generators (CPGs) as the locomotor controller, the overall dynamic propulsive characteristics of the swimming robot are then estimated in a mathematical environment (i.e. Mathematica). Finally, simulations and experiments are carried out to validate the effectiveness of the built dynamic model. Results demonstrate that the CPG-coupled dynamic model provides a fairly good guide to seeking pragmatic backward swimming patterns for a carangiform robotic fish.

The optimal motion of two-dimensional undulating plate swimming in fluid flow

The optimum shape of a two-dimensional undulatory plate in its motion in fluid flow is analyzed and the physical parameters (the thrust and the power) are calculated by the boundary element method. With the commonly used Lagrange multiplier method, only a saddle point of the optimum solution can be obtained, but not the solution itself due to the singularity of the problem. To eliminate the singularity, a method is proposed by adding an amplitude constraint. The new method is a generalization of that proposed by Wu, and it can be applied to more complex cases. The optimum shape of the linearly varying amplitude motion is studied in detail. It is shown that both the maximum and the minimum solutions exist when the frequency is higher than a critical value. For a high frequency, the maximum efficient motion with a large amplitude at the leading edge and a small amplitude at the trailing edge induces a large leading edge suction force. As the frequency decreases, the leading edge suction force decreases to a minimum and then increases. For high wavenumbers, there exists an optimum frequency with the maximum efficiency. High efficiency holds over a large range of frequency. The optimum efficiency increases as the wavenumber increases. The increase of the wavenumber can also reduce the leading edge suction force. The optimization method can also be applied to a quadratically varying amplitude motion. It is found that the optimum efficiency is larger than that for the linearly varying amplitude motion. However, the additional efficiency is relatively small, especially as the original efficiency is already high enough.

Propulsive Force of a Flexible Flapping Thin Airfoil

The propulsive force generated by the leading-edge suction of a flapping thin airfoil can be obtained using unsteady aerodynamic notions based on the potential flow theory. Because the potential theory fails to predict the viscous forces, for flapping airfoils, in general there exists a net propulsive force generation. For low Reynolds numbers and for oscillations at low reduced frequencies, however, the viscous forces overcome the propulsive forces to give a net force against the flight direction. In the case of higher Reynolds numbers, flappings with large amplitudes, and high frequencies, the leading-edge suction force generated by the airfoil overcomes the viscous forces. In this study, the critical Reynolds number, the amplitude, and the reduced frequency values that yield the net propulsive force for an oscillating airfoil are predicted with unsteady viscous-inviscid interaction. The airfoil motions are modeled as 1) a thin rigid plate in vertical oscillation, that is, a heaving-plunging motion; 2) a flexibly cambered airfoil whose camber is changing periodically; and 3) the heaving-plunging motion of a flexibly cambered airfoil. The leading-edge suction force for all cases is predicted by means of the well-known Blasius theorem, and the time dependent surface velocity distribution of the airfoil is determined by unsteady aerodynamic considerations. This surface velocity distribution is used as the edge velocity of the unsteady boundary layer to predict the viscous effects. The coefficient of the propulsive force predicted with the present method agrees well with the values given in the literature up to the effective angle of attack at which the dynamic stall takes place.

Prediction of Steady Propeller Performance with a Nonlinear Slipstream and Boundary-Layer Effect

Both slipstream deformation and viscous effects are factors that affect the performance of a rotating marine propeller but neither of them has been properly treated in most of the current lifting-surface methods and surface panel theories. With the introduction of a partial roll-up wake model that is flexible to various cases of propeller geometry and loading condition, this paper presents a vortex-lattice method that can improve propeller performance prediction especially at heavy loading conditions. Some observations on the calculation of the blade leading-edge suction force and how to deduct it to account for the viscous drag increasing are given. The scale effect of propeller performance can be readily predicted by the quasi-three-dimensional boundary-layer calculation presented in this paper. Some patterns of the limiting streamlines on blade surfaces are also illustrated and compared with experimental results.

Airfoil leading-edge suction and energy conservation for compressible flow

When a flat-plate airfoil at zero angle of attack encounters a vertical gust in an otherwise uniform flow, it experiences a force along the chord. This leading-edge suction force is examined for compressible flow with a time-dependent gust. A simple derivation of the thrust force is based on the fact that the leading edge is a singular point so that the flow here is dominated by the leading-edge dipole strength. From the viewpoint of a fluid-fixed observer the fluid does work on the airfoil, and this energy must come from the incident gust. Demonstrating energy conservation is not surprising, but it gives a better understanding of the relationship between the individual energy terms. The derivation shows that the acoustic energy can be calculated using compact assumptions at low frequency, but that it must be calculated non-compactly at high frequency. For a general gust the work done on the airfoil is shown to equal the energy taken from the fluid, the energy transfer occurring at the leading edge. For a sinusoidal gust the energy contained in the incident gust is shown to equal the sum of the energy remaining in the wake, the work done on the airfoil and the acoustic energy radiated away. The relative proportions of the incident energy going to these three energy types depends on the gust frequency, the acoustic radiation becoming more efficient as the frequency increases. For a fixed gust frequency, the thrust force goes to zero at a Mach number of one, and for an incident gust consisting of vorticity on the airfoil axis, the entire energy of the gust is radiated as acoustic energy at this Mach number.

Aeroelastic characteristics of a highly flexible aircraft

This paper describes an aeroelastic analysis performed on a human-powered aircraft. The structural characteristics of this aircraft (namely, very flexible wings, high aspect ratio, and low wing loadings) are typical of proposed high-altitude long-endurance aircraft. Because of these unique features, the aircraft exhibits uncommon aeroelastic characteristics. The structural dynamics of the airplane are obtained from a finite element model. In an assumed mode approach, a subset of the natural mode shapes is used to calculate the quasisteady and unsteady generalized modal forces using a two-dimensional strip model, which includes unsteady drag and leading-edge suction forces. The aeroelastic model predicts the airplane to be stable (at both sea level and high altitude), except for a mildly unstable phugoid mode. The results indicate that unsteady aerodynamics are significant for this type of aircraft and that the flexibility of the aircraft must be included to correctly model the dynamics for control purposes. A final conclusion is that the aircraft dynamics are highly dependent on the flight conditions (flight speed and altitude). d,D e J k,K Nomenclature = area of span station i • parasite drag coefficient = slope of lift curve = aerodynamic moment about the aerodynamic center at zero angle of attack = half chord (ct/2) at span station i - damping, damping matrix = Oswald's efficiency factor

Static aeroelastic analysis of a three-dimensional oblique wing

Requirements for the aeroelastic analyses of an oblique-wing aircraft have posed serious problems because available analysis programs cannot be applied to asymmetric configurations in the subsonic through the low supersonic speed range and the effects of the wing leading edge suction forces are completely disregarded. Therefore, a capability to perform static aeroelastic analyses of an oblique wing at arbitrary skew positions was developed based on the framework of the MSC/NASTRAN static aeroelastic analysis. By the means of DMAP alterations, a portion of the subsonic static aeroelastic analysis scheme was modified to insert an aerodynamic influence coefficient matrix created externally by the NASA Ames Research Center aerodynamic panel codes. The modified scheme can cover the subsonic as well as the supersonic range for both symmetric and asymmetric configurations. Static aeroelastic responses of the oblique wing are studied at two skew angles and, in particular, the capability to calculate three-dimensional camber effects on the aerodynamic properties of the wing is investigated. Various aerodynamic coefficients of the rigid oblique wing are computed for two Mach numbers, 0.7 and 1.4, and the angle of attack is varied from −5 through 15°. Also, the wing flexibility effects on the aerodynamic coefficients and the displacement are examined at a Mach number of 0.7 for a 45° swept wing.

揚力面理論による誘導抵抗の予測能力

Methods for calculating induced drag are divided into two main categories, “Near Field Method (NFM)” and “Far Field Method (FFM).” “Conventional Vortex Lattice Method (VLM)” gives not-so-good results when NFM is used, because of its poor prediction of leading-edge suction forces. Some patch-works for it have been published, all of those results however are more or less unsatisfactory; only method holding consistency and rationality may be the Quasi-VLM by C. E. Lan. This paper reports the results of the induced drag calculated by BIS (Box-In-Strip), a new numerical lifting surface method developed by the present authors. Both leading-edge suction forces in NFM and Manglertype singular integral in FFM are evaluated satisfactorily. Analytical evaluation of the induced drag for elliptical wings, in steady incompressible flow, is devised referring to the Kida's theory. BIS yields excellent correlation with analytical solutions for both of NFM and FFM on elliptic planform wings. Besides BIS gives closer agreement between the calculated results by NFM and FFM than Quasi-VLM for the general wing planforms.

Energetics and optimum motion of oscillating lifting surfaces of finite span

The energetics of an unswept wing of finite span oscillating harmonically in combined pitch and heave in in viscid incompressible flow are determined in closed form. The calculations are based on a recently developed low-frequency unsteady lifting-line theory. The energetic calculations for the wing consist of sectional and total values of thrust, leading-edge suction force, power required to maintain the wing oscillations, and energy-loss rate due to vortex shedding in the wake, where the latter quantity is only defined for the entire wing. These results are used to analyse the optimum motion of a wing oscillating harmonically: optimum motion minimizes the power input for fixed average total thrust. The optimum solution is found to be unique (at least for low reduced frequencies), in contrast to the two-dimensional optimum, which is non-unique. Numerical results are presented for the energetics and optimum motion of an elliptic wing.To understand better the structure of the known solution for the optimum motion of an oscillating two-dimensional airfoil, the solution is recast in terms of the normal modes of the energy-loss-rate matrix. It is found that one of the modes, termed here the ‘invisible mode’, plays a central role in the optimum solution and is responsible for its non-uniqueness. The three-dimensional optimum, which is unique, does not have an invisible mode.

Comment on "Analytical Prediction of Vortex Lift"

S comments are warranted concerning the paper by J.W. Purvis entitled Analytical Prediction of Vortex Lift, which appears in the April 1981 issue of the Journal of Aircraft. The first comment is relative to the use of singular loadings in the design of mean camber shapes for wings experiencing leading-edge-vortex separated flow. By comparison, Ref. 1 outlines a low-drag, separated-flow design procedure which uses a more appropriate attached-flow initial loading that is nonsingular. There the final solution for the mean camber surface is obtained by iterating to find the shape-yielding minimum separated-flow drag at the required lift coefficient. The second comment is that the section-induced drag, see Eq. (12), does not have an elliptical distribution over the wing as proposed, but only in the Trefftz plane. This is well known (e.g., Ref. 2), and means that for most wings of interest the section-induced drag has to be determined in the near field. The consequence of this wrong assumption leads to an error in Eq. (26) and, hence, in the magnitude of the leading-edge suction force and vortex flow aerodynamics for wings with varying leading-edge sweep. The third comment deals with the missing multiplication by 2 in Eqs. (27), (30), (33), and (34), the missing division by 2 in Eqs. (28) and (37), and the typographical error in Eq. (32). Equation (32) should read

Flow near the leading edge of a rectangular wing of small aspect ratio with applications to the bow of a ship

A local solution is developed for the square-root singularity at the leading edge of a rectangular flat plate of small aspect ratio. The analysis is based on the assumption that the spanwise load distribution is elliptical, and it follows that the two-dimensional lifting-surface integral equation can be reduced to a one-dimensional integral equation of the Wiener-Hopf form. A solution is then obtained, valid near the leading edge, which yields the strength of the square-root singularity. This solution is used to compute the leading-edge suction force, which differs by 15% from the known value based on the total lift and drag expressions. The local solution is applied to study the flow around the stem of a ship's bow, as a result of a yawing motion, using Lighthill's rule to correct for the finite radius of curvature at the bow.