Suction Analogy Research Articles

Development and Fidelity Assessment of Potential Flow based Framework for Aerodynamic Modeling of High Lift Devices

High lift devices play a vital role in dictating the accelerated performance of an aircraft for different flight phases such as takeoff, landing, and aerobatic maneuvers. The aerodynamic design of high lift devices for any particular aircraft is an iterative process and is achieved through extensive aerodynamic Analysis of the aircraft for various flap configurations. Computational Fluid Dynamics (CFD) and Wind tunnel testing are highly effective techniques for performing the required Analysis, yet they have high computational costs and time. To overcome this shortcoming, a robust framework based on potential flow solver (PFS) and geometry parameterization is required without compromising the fidelity of the Analysis. This research aims to develop a highly robust aerodynamic analysis framework based on the Vortex Lattice Method (VLM) coupled with Polhamus Suction Analogy and parametric modeling of high lift devices. The fidelity of the framework is validated through experimental testing and is quantified by developing a fidelity assessment matrix. It is established that the computational cost of CFD has been reduced three times with only a 10% to 20% loss in accuracy when the developed framework is used. The developed PFS framework gives results from 80% to 90%. The framework results for a reference aircraft are thoroughly compared with CFD analyses. The framework provides values that agree with corresponding CFD analyses in a fraction of the time.

Comparative study on analytical and computational aerodynamic models for flapping wings MAVs

ABSTRACTA range of quasi-steady and unsteady aerodynamic models are used to predict the aerodynamic forces experienced by a flapping wing and a detailed comparison amongst these predictions in provided. The complexity of the models ranges from the analytical potential flow model to the computational Unsteady Vortex Lattice Method (UVLM), which allows one to describe the motion of the wake and account for its influence on the fluid loads. The novelty of this effort lies in a modification of the predicted forces as a generalisation of the leading edge suction analogy. This modification is introduced to account for the delayed stall mechanism due to leading edge flow separation. The model predictions are compared with two sets of independent experimental data and with computational fluid dynamics (CFD) simulation data available in the literature. It is found that both, the modified analytical model and the UVLM model can be used to describe the time history of the lift force, in some cases with better results than a high-fidelity CFD model. The models presented here constitute a useful basis for the aerodynamic design of bioinspired flapping-wings micro-air vehicles.

Instability and the post-critical behaviour of two-dimensional inverted flags in axial flow

Inverted flags – clamped–free elastic thin plates subjected to a fluid flowing axially and directed from the free end towards the clamped end – have been observed experimentally and computationally to exhibit large-amplitude flapping beyond a critical flow velocity. The motivation for further research on the dynamics of this system is partly due to its presence in some engineering and biological systems, and partly because of the very rich dynamics it displays. In the present paper, the goal is to develop a nonlinear analytical model for the dynamics and stability of high aspect ratio (i.e. height to length ratio) flags. The inviscid fluid flow is modelled via the quasi-steady version of Theodorsen’s unsteady aerodynamic theory, and the Polhamus leading-edge suction analogy is utilized to model flow separation effects from the free end (leading edge) at moderate angles of attack. Gear’s backward differentiation formula and a pseudo-arclength continuation technique are employed to solve the governing equations. Numerical results suggest that fluidelastic instability may be the underlying mechanism for the flapping motion of high aspect ratio heavy inverted flags. In other words, flapping may be viewed as a self-excited vibration. It was found from numerical results that the undeflected static equilibrium of the inverted flag is stable at low flow velocities, prior to the occurrence of a supercritical pitchfork bifurcation. The pitchfork bifurcation is associated with static divergence (buckling) of the flag. At higher flow velocities, past the pitchfork bifurcation, a supercritical Hopf bifurcation materializes, generating a flapping motion around the deflected static equilibrium. At even higher flow velocities, flapping motion becomes symmetric around the undeflected static equilibrium. Interestingly, it was also found that heavy flags may exhibit large-amplitude flapping right after the initial static equilibrium, provided that they are subjected to a sufficiently large disturbance. Moreover, inverted flags with a non-zero initial angle of attack were found to be less stable than their perfectly flow-aligned counterparts.

Experimental Investigation of the Effect of Trailing-Edge Flaps on Delta Wings

A low-speed wind-tunnel investigation is presented, characterizing the effect of plain trailing-edge flaps on 65 and 70 deg sweep delta wings. Four flap angles and three hinge locations were evaluated. The leading-edge suction analogy was extended to allow estimation of the effect of flaps on both the attached flow and vortex lift components. Additionally, expressions to estimate the drag and pitching moment coefficient were also developed. Comparisons of theory and experiment showed close accord. Flap deflection was observed to cause a notable reduction in the drag coefficient for a given lift coefficient. Wing stall, however, was observed at lower angles of attack than without the flap, caused by an earlier onset of vortex breakdown.

An aerodynamic model for insect flapping wings in forward flight

This paper proposes a semi-empirical quasi-steady aerodynamic model of a flapping wing in forward flight. A total of 147 individual cases, which consisted of advance ratios J of 0 (hovering), 0.125, 0.25, 0.5, 0.75, 1 and ∞, and angles of attack α of −5 to 95° at intervals of 5°, were examined to extract the aerodynamic coefficients. The Polhamus leading-edge suction analogy and power functions were then employed to establish the aerodynamic model. In order to preserve the existing level of simplicity, KP and KV, the correction factors of the potential and vortex force models, were rebuilt as functions of J and α. The estimations were nearly identical to direct force/moment measurements which were obtained from both artificial and practical wingbeat motions of a hawkmoth. The model effectively compensated for the influences of J, particularly showing outstanding moment estimation capabilities. With this model, we found that using a lower value of α during the downstroke would be an effective strategy for generating adequate lift in forward flight. The rotational force and moment components had noticeable portions generating both thrust and counteract pitching moment during pronation. In the upstroke phase, the added mass component played a major role in generating thrust in forward flight. The proposed model would be useful for a better understanding of flight stability, control, and the dynamic characteristics of flapping wing flyers, and for designing flapping-wing micro air vehicles.

Extended Unsteady Vortex-Lattice Method for Insect Flapping Wings

An extended unsteady vortex-lattice method is developed to study the aerodynamics of insect flapping wings while hovering and during forward flight. Leading-edge suction analogy and vortex-core growth models are used as an extension, which is incorporated into a conventional unsteady vortex-lattice method in an effort to overcome the challenges that arise when simulating insect aerodynamics such as wing–wake interaction and leading-edge effects. A convergence analysis was carried out to derive an optimal aerodynamic mesh and a time-step size for flapping-wing models. A parallel computing technique was used to reduce computational time. The aerodynamics of hawkmoth (Manduca sexta) wing models was simulated, and the results were validated against previous numerical and experimental data.

An improved quasi-steady aerodynamic model for insect wings that considers movement of the center of pressure

A quasi-steady aerodynamic model in consideration of the center of pressure (C.P.) was developed for insect flight. A dynamically scaled-up robotic hawkmoth wing was used to obtain the translational lift, drag, moment and rotational force coefficients. The translational force coefficients were curve-fitted with respect to the angles of attack such that two coefficients in the Polhamus leading-edge suction analogy model were obtained. The rotational force coefficient was also compared to that derived by the standard Kutta–Joukowski theory. In order to build the accurate pitching moment model, the locations of the C.Ps. and its movements depending on the pitching velocity were investigated in detail. We found that the aerodynamic moment model became suitable when the rotational force component was assumed to act on the half-chord. This implies that the approximation borrowed from the conventional airfoil concept, i.e., the ‘C.P. at the quarter-chord’ may lead to an incorrect moment prediction. In the validation process, the model showed excellent time-course force and moment estimations in comparison with the robotic wing measurement results. A fully nonlinear multibody flight dynamic simulation was conducted to check the effect of the traveling C.P. on the overall flight dynamics. This clearly showed the importance of an accurate aerodynamic moment model.

On the quasi-steady aerodynamics of normal hovering flight part II: model implementation and evaluation

This paper introduces a generic, transparent and compact model for the evaluation of the aerodynamic performance of insect-like flapping wings in hovering flight. The model is generic in that it can be applied to wings of arbitrary morphology and kinematics without the use of experimental data, is transparent in that the aerodynamic components of the model are linked directly to morphology and kinematics via physical relationships and is compact in the sense that it can be efficiently evaluated for use within a design optimization environment. An important aspect of the model is the method by which translational force coefficients for the aerodynamic model are obtained from first principles; however important insights are also provided for the morphological and kinematic treatments that improve the clarity and efficiency of the overall model. A thorough analysis of the leading-edge suction analogy model is provided and comparison of the aerodynamic model with results from application of the leading-edge suction analogy shows good agreement. The full model is evaluated against experimental data for revolving wings and good agreement is obtained for lift and drag up to 90° incidence. Comparison of the model output with data from computational fluid dynamics studies on a range of different insect species also shows good agreement with predicted weight support ratio and specific power. The validated model is used to evaluate the relative impact of different contributors to the induced power factor for the hoverfly and fruitfly. It is shown that the assumption of an ideal induced power factor (k = 1) for a normal hovering hoverfly leads to a 23% overestimation of the generated force owing to flapping.

Aerodynamic design of flat delta kite based on polhamus concept of leading edge suction analogy

The primary objective of this paper is to design an aerodynamically efficient delta kite that can balance a given load when subjected to aerodynamic loads at a specific angle of attack (α) and altitude (h). The aerodynamic forces calculated based on the potential theory heavily underestimate the forces because of the formation of leading edge vortices on the delta shaped kite. The leading edge vortices are the flow separations caused at the sharp leading edge even for very small angles of attack, which remain attached to the leading edge while the kutta condition is still satisfied at the trailing edge.Vortex lift and induced drag due to the leading edge vortices are calculated using the Polhamus method. Aerodynamic loads (L and D) have been computed by determining proportionality constants (kp, kv) using the standard Multhopp lifting surface theory (MLST). The variation of (CL) and (ΔCD) for delta kites with aspect ratio A=1, 1.5 and 2 has been examined and validated by comparing the computed CL and ΔCD values to experimental measurements. A set of vertical and horizontal loads (WT,HT) that can be balanced by delta kite at operational heights h=140, 150 and 160 m and α=8° has been successfully determined using this method. The method will be applied for the design and control of a delta kite, which will be used to harvest wind energy at high altitudes.© 2014 ASME

A career in vortices and edge forces

AbstractThis lecture recognises the background and distinguished work of Frederick William Lanchester, and notes that my background has a few similarities with his. These include a shared interest in wings, lift and vortices. My career at the NASA Langley Research Center spans the time-frame from America’s Super Sonic Transport through 2009. An early emphasis involved wind-tunnel testing of research aircraft models and the development of computer codes for subsonic aerodynamics of wing planforms. These attached-flow codes were applied to various configurations, including those with variable-sweep, dihedral, and more than one planform in both the analysis- and design-modes. These codes were used to provide a connection between leading-edge-forces and the associated additional lift on delta-wings with shed-vortex systems through the leading-edge suction analogy of Edward C. Polhamus. Subsequently, I extended the suction analogy to configurations with side-edges to predict the vortical-flow aerodynamics on complex configurations, including wing-strake combinations. These analysis codes could also be used in a design-by-analysis mode for configurations with leading-edge shed vortices. Later, I was involved in vortical-flow flight research with the F-106B and the F-16XL aircraft at cruise and maneuver conditions. Associated CFD predictions, generated by me and other members of the RTO/AVT-113 task group, have increased our understanding of the flight flow-physics measured on the F-16XL aircraft.

Theoretical study on two-dimensional aerodynamic characteristics of unsteady wings

A simple computing method based on a potential theory is developed for two-dimensional steady and unsteady deflected wings. This method of theoretical analysis is essentially related to thin and angular airfoils. Thus, the method is very simple but is effective to forecast aerodynamic forces for deflected or angular airfoils with a small camber operating in high Reynolds number flow, specifically in unsteady motion. The suction force acting on the leading edge of steady airfoils is theoretically obtained by using the Blasius formula. By Polhamus's leading edge suction analogy, the suction force is considered to be directed upward in partially separated flow for real thin airfoil with sharp leading edge. The theory can also be applied to obtain the aerodynamic characteristics of thin airfoils operating on low Reynolds number flow under some degree of approximation. This is very useful for the unsteady aerodynamic analysis because the Navier–Stokes equation can be solved by neither analytical nor numerical method for the thin and angular airfoils, which are common in the insect wing.

Analysis and Estimation of the Lift Components of Hovering Insects

An analysis is undertaken to provide a simple analytic expression to estimate the stroke averaged lift of a hovering insect based on geometric and kinematic data. The expression should prove useful in the conceptual design of biologically inspired microaerial vehicles. The study includes estimation of the average vortex lift developed. The leading-edge suction analogy in conjunction with actuator disk theory is invoked to establish the relationship between axial force on the wing and vortex lift. The expression allows decomposition of the total loading into its attached flow and vortex lift components. For the insects investigated the estimated vortex lift typically constituted 27‐50% of the attached flow lift and approximately 23‐34% of the total lift.

On aerodynamic modelling of an insect–like flapping wing in hover for micro air vehicles

This theoretical paper discusses recent advances in the fluid dynamics of insect and micro air vehicle (MAV) flight and considers theoretical analyses necessary for their future development. The main purpose is to propose a new conceptual framework and, within this framework, two analytic approaches to aerodynamic modelling of an insect-like flapping wing in hover in the context of MAVs. The motion involved is periodic and is composed of two half-cycles (downstroke and upstroke) which, in hover, are mirror images of each other. The downstroke begins with the wing in the uppermost and rearmost position and then sweeps forward while pitching up and plunging down. At the end of the half-cycle, the wing flips, so that the leading edge points backwards and the wing's lower surface becomes its upper side. The upstroke then follows by mirroring the downstroke kinematics and executing them in the opposite direction. Phenomenologically, the interpretation of the flow dynamics involved, and adopted here, is based on recent experimental evidence obtained by biologists from insect flight and related mechanical models. It is assumed that the flow is incompressible, has low Reynolds number and is laminar, and that two factors dominate: (i) forces generated by the bound leading-edge vortex, which models flow separation; and (ii) forces due to the attached part of the flow generated by the periodic pitching, plunging and sweeping. The first of these resembles the analogous phenomenon observed on sharp-edged delta wings and is treated as such. The second contribution is similar to the unsteady aerodynamics of attached flow on helicopter rotor blades and is interpreted accordingly. Theoretically, the fluid dynamic description is based on: (i) the superposition of the unsteady contributions of wing pitching, plunging and sweeping; and (ii) adding corrections due to the bound leading-edge vortex and wake distortion. Viscosity is accounted for indirectly by imposing the Kutta condition on the trailing edge and including the influence of the vortical structure on the leading edge. Mathematically, two analytic approaches are proposed. The first derives all the quantities of interest from the notion of circulation and leads to tractable integral equations. This is an application of the von Kármán-Sears unsteady wing theory and its nonlinear extensions due to McCune and Tavares; the latter can account for the bound leading-edge vortex and wake distortion. The second approach uses the velocity potential as the central concept and leads to relatively simple ordinary differential equations. It is a combination of two techniques: (i) unsteady aerodynamic modelling of attached flow on helicopter rotor blades; and (ii) Polhamus's leading-edge suction analogy. The first of these involves both frequency-domain (Theodorsen style) and time-domain (indicial) methods, including the effects of wing sweeping and returning wake. The second is a nonlinear correction accounting for the bound leading-edge vortex. Connections of the proposed framework with control engineering and aeroelasticity are pointed out.

Theoretical and Experimental Investigation of Biplane Delta Wings

Recent interest in micro aerial vehicles has resulted in the evaluation of innovative aerodynamic cone gurations and propulsive mechanisms to meettherequirements ofthesemachines. It is proposed that a biplaneformed using delta wings may proveto be an efe cient cone guration. Accordingly, a theoretical and experimental investigation to determine thecharacteristicsof delta wings in a biplanecone guration wasundertaken. Thewind-tunnel study was performed using 75-deg delta wings. The biplane wing’ s gap (separation) and stagger were varied. A theoretical method was developed that coupled Prandtl’ s biplane theory (Prandtl, L., and Tietjens, O. G., Applied Hydro and Aeromechanics , Dover, New York, 1934, pp. 211 ‐222) with Polhamus’ leading-edge suction analogy (Polhamus, E. C., “ Prediction of Vortex-Lift Characteristics by a Leading-Edge Suction Analogy,”Journal of Aircraft , Vol. 8, No. 4, 1971, pp. 193 ‐199). The experimental results showed that the separation between the wings has a signie cant effect on lift, the lift reducing with closer wing proximity. The biplane cone guration shows far less sensitivity to stagger, with effects only manifesting for angles of attack greater than 15 deg. Positive stagger (upper wing forward)increased lift whereas negative stagger decreased lift relative to an unstaggered cone guration. Similarly, positive stagger increased the maximum recorded lift coefe cient with negative stagger having the opposite effect. The theoretical method showed close accord with the experimental data and correctly predicted the effect of gap and stagger on lift. Theoretical analysis showed that for a dimensionally constrained planform, the delta wing biplane is an effective cone guration for moderate to large wing separation.

Lift Prediction of Spanwise Cambered Delta Wings

An analytic prediction method is derived to estimate the lift of delta wings with constant anhedral or dihedral, i.e., a V wing. The method is based on the leading-edge suction analogy, with expressions for leading-edge suction being developed that account for anhedral and dihedral. An empirical correction is combined with the resulting expression to incorporate an effective leading-edge sweep interpretation of wing roll. This approach allows an estimation of the disparate effects of anhedral and dihedral. The attached e ow lift component is estimated using a Trefftz plane expression for the apparent mass of a V wing. Comparisons are made with a variety of planforms, with encouraging agreement between theory and experiment being demonstrated.

Studies of vortex flaps for different sweepback angle delta wings

AbstractLow speed windtunnel measurements were made on a 50° delta wing with leading edge vortex flaps. Improvements in the lift/drag ratio were obtained by deflecting the leading edge vortex flap. Comparisons were made between the previously measured 60° and 70° delta wing results and the present 50° wing results. Improvements in the lift/drag ratio of the 50° delta wing were attained over a wider lift coefficient range than for the 70° delta wing. The highest lift/drag ratio for the 50° delta wing is achieved when the flow attaches to the flap surface without any large area of separation. Estimations of the aerodynamic forces were also made using a quasi-vortex lattice method coupled with the leading edge suction analogy for the 50°, 60° and 70° delta wings. The results obtained from this analysis agree qualitatively with the experimental results.

Prediction of Vortex Breakdown and Longitudinal Characteristics of Swept Slender Planforms

A method is presented to predict high-angle-of-attack, longitudinal aerodynamic characteristics of slender wing planforms in incompressible e ow. A semiempirical approach is used to predict the location of vortex breakdown and its variation with incidence. Breakdown predictions are then coupled to vortex lift expressions based on the leading-edge suction analogy. A correction is used to account for the attenuation of vortex suction after vortex breakdown, allowing prediction of lift, drag, and pitching moment at high angles of attack. Comparisons are made with a variety of planforms, with encouraging agreement between theory and experiment being demonstrated.

Advanced propeller performance calculation by a lifting surface method

The application of a lifting surface theory to compute the aerodynamics of advanced propellers is studied. Starting from the inviscid, compressible flow equations for a perturbed, axially subsonic flow, expressions are derived for the velocity field of a propeller. By using a representation of Green's function in separated, cylindrical coordinates, the radial boundary condition at the hub is naturally incorporated in the velocity field. Application of the boundary condition at the blade surfaces yields an integral equation for the unknown pressure jump distribution over the blades. A Galerkin projection transforms this integral equation into a set of linear equations, which is solved numerically. Comparison with experimental data shows that the gradients of thrust and power coefficients vs the advance ratio at the windmilling point are accurately predicted. By taking into account some higher-order effects in the geometry description of the blades, and by application of the so-called leading-edge suction analogy, a good agreement between theory and experiment is maintained up to high aerodynamic loading.

Connection between leading-edge sweep, vortex lift, and vortex strength for delta wings

An effort is made to clarify the effect of leading-edge sweep on the vortex lift and leading-edge vortex strength of a slender wing; while it is often assumed that increasing sweep enhances vortex lift and strength, the opposite is the case. The suction analogy is used in association with numerical and experimental data to derive simple formulas yielding the actual relationship for delta wings. The difference between vortex lift and nonlinear lift is highlighted.

Similarity for high-angle-of-attack subsonic/transonic slender-body aerodynamics

The work of Sychev (1960) is extended to sharp-edged wings and smooth bodies. A simple fit to the correlations based on the Polhamus (1966) suction analogy is shown for several affine families of bodies with elliptical cross sections. The results suggest that simple models for nonlinear subsonic/transonic flows over not-so-slender wings and bodies can be obtained from a combination of well-known linear-theory models for the attached flow and slender-body concepts for the vortical flow.