@article{babu_narsipur_gopalarathnam_2024, title={Lift tailoring on unsteady airfoils with leading-edge vortex shedding using an inverse aerodynamic approach}, volume={36}, ISSN={["1089-7666"]}, DOI={10.1063/5.0208567}, abstractNote={In this paper, we present a physics-informed approach to tailor the lift profile of an unsteady airfoil through the execution of an appropriate maneuver. In previous research, a low-order aerodynamic model based on the unsteady thin airfoil theory was developed for predicting the flowfield and loads on airfoils undergoing arbitrary motions. The theory was phenomenologically augmented using the concept of leading edge suction parameter (LESP) to incorporate the capability to predict intermittent leading edge vortex (LEV) shedding. The criticality of LESP was used to predict the onset and termination of LEV shedding and thus model the effect of LEVs on the flowfield and loads for a prescribed motion. In the current work, an inverse aerodynamic formulation is developed based on this framework for tackling the inverse problem: to obtain the motion kinematics required for generating a prescribed lift profile for an airfoil operating in the dynamic-stall regime. The LEV-modeling capability of the aerodynamic model enables the motion-design algorithm to take into account the effect of complex phenomena, such as dynamic stall and LEV shedding, which are not taken into account in previous research approaches. Several case studies are presented to demonstrate various scenarios such as lift tracking using pitching and heaving motions, lift cancellation during unsteady motion, and the generation of a given lift profile using two equivalent motions. The kinematic profiles generated by the inverse formulation are also simulated using a high-fidelity unsteady computational fluid dynamics solver to validate the predictions.}, number={5}, journal={PHYSICS OF FLUIDS}, author={Babu, Arun Vishnu Suresh and Narsipur, Shreyas and Gopalarathnam, Ashok}, year={2024}, month={May} }
 @article{narsipur_ramesh_gopalarathnam_edwards_2023, title={Discrete vortex modeling of perching and hovering maneuvers}, volume={5}, ISSN={["1432-2250"]}, DOI={10.1007/s00162-023-00653-2}, journal={THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS}, author={Narsipur, Shreyas and Ramesh, Kiran and Gopalarathnam, Ashok and Edwards, Jack R.}, year={2023}, month={May} }
 @article{hughes_gopalarathnam_bryant_2023, title={Modulation and Annihilation of Aeroelastic Limit-Cycle Oscillations Using a Variable-Frequency Disturbance Generator}, ISSN={["1533-385X"]}, DOI={10.2514/1.J062295}, abstractNote={ Nonlinear aeroelastic limit-cycle oscillations (LCOs) have become an area of interest due to both detrimental effects on flying vehicles and use in renewable energy harvesting. Initial studies on the interaction between aeroelastic systems and incoming flow disturbances have shown that disturbances can have significant effects on LCO amplitude, with some cases resulting in spontaneous annihilation of the LCO. This paper explores this interaction through wind-tunnel experiments using a variable-frequency disturbance generator to produce flow disturbances at frequencies near the inherent LCO frequency of an aeroelastic system with pitching and heaving degrees of freedom. The results show that incoming disturbances produced at frequencies approaching the LCO frequency from below produce a cyclic growth-decay in LCO amplitude that resembles interference between multiple sine waves with slightly varying frequencies. An aeroelastic inverse technique is applied to the results to study the transfer of energy between the pitching and heaving degrees of freedom as well as the aerodynamic power moving into and out of the system. Finally, the growth-decay cycles are shown to both excite LCOs in an initially stationary wing and annihilate preexisting LCOs in the same wing by appropriately timing the initiation and termination of disturbance generator motion. }, journal={AIAA JOURNAL}, author={Hughes, Michael T. and Gopalarathnam, Ashok and Bryant, Matthew}, year={2023}, month={Feb} }
 @article{jenkins_babu_bryant_gopalarathnam_2023, title={Numerical Study of Circular-Cylinder Disturbance Generators with Rigid Splitter Plates}, ISSN={["1533-385X"]}, DOI={10.2514/1.J062729}, abstractNote={ This paper describes the numerical study of oscillating circular cylinders with rigid splitter plates of different lengths. These geometries may be used as disturbance generators for the study of unsteady airfoils and wings operating in highly vortical flowfields. It has been shown that cylinders undergoing forced rotational oscillations at their natural shedding frequency can produce wakes with minimal deviation in cycle-to-cycle vortex strength and position. Adding a splitter plate allows these deviations to be reduced even further. We present cases for oscillating cylinders having splitter-plate lengths up to [Formula: see text] at a Reynolds number of 7600. Frequencies are maintained at the natural shedding frequency, and a rotational amplitude of 45 deg is used. Numerical simulations are performed using a two-dimensional unsteady Reynolds-averaged Navier–Stokes (RANS) code. Results are presented in the form of vorticity contours and cycle-averaged velocity profiles, as well as the dominant frequencies of cylinder lift force and downstream velocity angles. The results show that splitter-plate lengths shorter than [Formula: see text] adversely affect the ability to generate a coherent vortex wake due to shear layer roll-up near the trailing edge of the plate. Splitter plates longer than [Formula: see text] produced a reverse von Kármán wake with consistent cycle-to-cycle vortex shedding. }, journal={AIAA JOURNAL}, author={Jenkins, Michael and Babu, Arun Vishnu Suresh and Bryant, Matthew and Gopalarathnam, Ashok}, year={2023}, month={Oct} }
 @article{ramanathan_gopalarathnam_2023, title={Prediction of leading-edge-vortex initiation using criticality of the boundary layer}, volume={5}, ISSN={["1432-2250"]}, DOI={10.1007/s00162-023-00648-z}, abstractNote={The initiation of leading-edge-vortex formation in unsteady airfoil flows is governed by flow criticality at the leading edge. While earlier works demonstrated the promise of criticality of leading-edge suction in governing LEV shedding, this criterion is airfoil and Reynolds number dependent. In this work, by examining results from Navier–Stokes computations for a large set of pitching airfoil cases at laminar flow conditions, we show that the onset of flow reversal at the leading edge always corresponds to the boundary-layer shape factor reaching the same critical value that governs laminar flow separation in steady airfoil flows. Further, we show that low-order prediction of this boundary-layer criticality is possible with an integral-boundary-layer calculation performed using potential-flow velocity distributions from an unsteady panel method. The low-order predictions agree well with the high-order computational results with a single empirical offset that is shown to work for multiple airfoils. This work shows that boundary-layer criticality governs LEV initiation, and that a low-order prediction approach is capable of predicting this boundary-layer criticality and LEV initiation.}, journal={THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS}, publisher={Springer Science and Business Media LLC}, author={Ramanathan, Hariharan and Gopalarathnam, Ashok}, year={2023}, month={May} }
 @article{narsipur_gopalarathnam_2023, title={Leading-Edge Suction Behavior of Unsteady Airfoils in Forward and Reverse Flows}, volume={68}, ISSN={["2161-6027"]}, DOI={10.4050/JAHS.68.022009}, abstractNote={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.}, number={2}, journal={JOURNAL OF THE AMERICAN HELICOPTER SOCIETY}, author={Narsipur, Shreyas and Gopalarathnam, Ashok}, year={2023}, month={Apr} }
 @article{suresh babu_narsipur_bryant_gopalarathnam_2022, title={Leading-edge-vortex tailoring on unsteady airfoils using an inverse aerodynamic approach}, volume={34}, ISSN={["1089-7666"]}, DOI={10.1063/5.0090328}, abstractNote={In this paper, we present an approach to obtain a desired leading-edge vortex (LEV) shedding pattern from unsteady airfoils through the execution of suitable motion kinematics. Previous research revealed that LEV shedding is associated with the leading-edge suction parameter (LESP) exceeding a maximum threshold. A low-order method called LESP-modulated discrete vortex method (LDVM) was also developed to predict the onset and termination of LEV shedding from an airfoil undergoing prescribed motion kinematics. In the current work, we present an inverse-aerodynamic formulation based on the LDVM to generate the appropriate motion kinematics to achieve a prescribed LESP variation, and thus, the desired LEV shedding characteristics from the airfoil. The algorithm identifies the kinematic state of the airfoil required to attain the target LESP value through an iterative procedure performed inside the LDVM simulation at each time step. Several case studies are presented to demonstrate design scenarios such as tailoring the duration and intensity of LEV shedding, inducing LEV shedding from the chosen surface of the airfoil, promoting or suppressing LEV shedding during an unsteady motion on demand, and achieving similar LEV shedding patterns using different maneuvers. The kinematic profiles generated by the low-order formulation are also simulated using a high-fidelity unsteady Reynolds-averaged Navier–Stokes method to confirm the accuracy of the low-order model.}, number={5}, journal={PHYSICS OF FLUIDS}, author={Suresh Babu, Arun Vishnu and Narsipur, Shreyas and Bryant, Matthew and Gopalarathnam, Ashok}, year={2022}, month={May} }
 @article{narsipur_gopalarathnam_edwards_2022, title={Low-Order Modeling of Dynamic Stall on Airfoils in Incompressible Flow}, volume={9}, ISSN={["1533-385X"]}, DOI={10.2514/1.J061595}, abstractNote={ Airfoil dynamic stall in incompressible flow is characterized by two interacting viscous flow phenomena: time-varying trailing-edge separation and the shedding of intermittent leading-edge-vortex structures. In the current work, a physics based low-order method capable of modeling the interactions between the two flow phenomena is developed with the aim of predicting dynamic stall with only a few empirical tuning parameters. Large computational datasets are used to understand the flow physics of unsteady airfoils so as to augment an inviscid, unsteady airfoil theory to model the time-dependent viscous effects. The resulting model requires only three empirical coefficients for a given airfoil and Reynolds number, which could be obtained from a single moderate-pitch-rate unsteady motion for that airfoil/Reynolds number combination. Results from the low-order model are shown to compare excellently with computational and experimental solutions, in terms of both aerodynamic loads and flow-pattern predictions. In addition to formulating a method with limited empirical dependencies, the current research provides valuable insights into the flow physics of unsteady airfoils and their connection to rapidly predictable theoretical parameters. }, journal={AIAA JOURNAL}, author={Narsipur, Shreyas and Gopalarathnam, Ashok and Edwards, Jack R.}, year={2022}, month={Sep} }
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TopicsAerodynamic PerformanceAerodynamicsAeronautical EngineeringAeronauticsAviationAviation SafetyAvionicsFlight TestGuidance, Navigation, and Control SystemsPressure SensorsSensorsSkin FrictionTransducersTurbulenceWind Tunnels KeywordsFlow SensorsAirfoilWind Tunnel TestsLift CoefficientBoundary Layer SeparationAdverse Pressure GradientAerodynamic CharacteristicsTwo Dimensional FlowShear StressStatic PressurePDF Received28 October 2021Accepted4 April 2022Published online15 May 2022}, journal={JOURNAL OF AIRCRAFT}, publisher={American Institute of Aeronautics and Astronautics (AIAA)}, author={Aleman, Maria A. and Gopalarathnam, Ashok and Granlund, Kenneth}, year={2022}, month={May} }
 @article{hirato_shen_gopalarathnam_edwards_2021, title={Flow criticality governs leading-edge-vortex initiation on finite wings in unsteady flow}, volume={910}, ISSN={["1469-7645"]}, DOI={10.1017/jfm.2020.896}, abstractNote={Abstract}, journal={JOURNAL OF FLUID MECHANICS}, author={Hirato, Yoshikazu and Shen, Minao and Gopalarathnam, Ashok and Edwards, Jack R.}, year={2021}, month={Jan} }
 @article{saini_narsipur_gopalarathnam_2021, title={Leading-edge flow sensing for detection of vortex shedding from airfoils in unsteady flows}, volume={33}, ISSN={["1089-7666"]}, DOI={10.1063/5.0060600}, abstractNote={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.}, number={8}, journal={PHYSICS OF FLUIDS}, author={Saini, Aditya and Narsipur, Shreyas and Gopalarathnam, Ashok}, year={2021}, month={Aug} }
 @article{loewenthal_gopalarathnam_2022, title={Low-Order Modeling of Wingtip Vortices in a Vortex Lattice Method}, volume={60}, ISSN={["1533-385X"]}, DOI={10.2514/1.J060654}, abstractNote={Wingtip-flow effects on the aerodynamic forces and moments of a wing become increasingly significant as the aspect ratio decreases. These effects are dominated by the tip vortex and an associated s...}, number={3}, journal={AIAA JOURNAL}, author={Loewenthal, Ethan and Gopalarathnam, Ashok}, year={2022}, month={Mar}, pages={1708–1720} }
 @article{sureshbabu_medina_rockwood_bryant_gopalarathnam_2021, title={Theoretical and experimental investigation of an unsteady airfoil in the presence of external flow disturbances}, volume={921}, ISSN={["1469-7645"]}, DOI={10.1017/jfm.2021.484}, abstractNote={Abstract
	  
	    
	      
	    
	  }, journal={JOURNAL OF FLUID MECHANICS}, author={SureshBabu, ArunVishnu and Medina, Albert and Rockwood, Matthew and Bryant, Matthew and Gopalarathnam, Ashok}, year={2021}, month={Jul} }
 @article{kirschmeier_pash_gianikos_medina_gopalarathnam_bryant_2020, title={Aeroelastic inverse: Estimation of aerodynamic loads during large amplitude limit cycle oscillations}, volume={98}, ISSN={["0889-9746"]}, DOI={10.1016/j.jfluidstructs.2020.103131}, abstractNote={This paper presents an algorithm to compute the aerodynamic forces and moments of an aeroelastic wing undergoing large amplitude heave and pitch limit cycle oscillations. The technique is based on inverting the equations of motion to solve for the lift and moment experienced by the wing. Bayesian inferencing is used to estimate the structural parameters of the system and generate credible intervals on the lift and moment calculations. The inversion technique is applied to study the affect of mass coupling on limit cycle oscillation amplitude. Examining the force, power, and energy of the system, the reasons for amplitude growth with wind speed can be determined. The results demonstrate that the influence of mass coupling on the pitch–heave difference is the driving factor in amplitude variation. The pitch–heave phase difference not only controls how much aerodynamic energy is transferred into the system but also how the aerodynamic energy is distributed between the degrees of freedom.}, journal={JOURNAL OF FLUIDS AND STRUCTURES}, author={Kirschmeier, Benjamin and Pash, Graham and Gianikos, Zachary and Medina, Albert and Gopalarathnam, Ashok and Bryant, Matthew}, year={2020}, month={Oct} }
 @article{kirschmeier_gianikos_gopalarathnam_bryant_2020, title={Amplitude Annihilation in Wake-Influenced Aeroelastic Limit-Cycle Oscillations}, volume={58}, ISSN={["1533-385X"]}, DOI={10.2514/1.J058942}, abstractNote={This paper investigates the dynamics of a pitching and heaving aeroelastic wing undergoing large-amplitude limit-cycle oscillations influenced by a vortical wake from an upstream rectangular cylind...}, number={9}, journal={AIAA JOURNAL}, author={Kirschmeier, Benjamin A. and Gianikos, Zachary and Gopalarathnam, Ashok and Bryant, Matthew}, year={2020}, month={Sep}, pages={4117–4127} }
 @article{powers_silverberg_gopalarathnam_2020, title={Artificial Lumbered Flight for Autonomous Soaring}, volume={43}, ISSN={["1533-3884"]}, DOI={10.2514/1.G004397}, abstractNote={Soaring strategies are redefining the flight capabilities of small-class fixed-wing unmanned aerial vehicles. This paper presents an autonomous soaring strategy that exploits updraft energy indepen...}, number={3}, journal={JOURNAL OF GUIDANCE CONTROL AND DYNAMICS}, author={Powers, Thomas C. and Silverberg, Larry M. and Gopalarathnam, Ashok}, year={2020}, month={Mar}, pages={553–566} }
 @article{gianikos_kirschmeier_gopalarathnam_bryant_2020, title={Limit cycle characterization of an aeroelastic wing in a bluff body wake}, volume={95}, ISSN={["1095-8622"]}, DOI={10.1016/j.jfluidstructs.2020.102986}, abstractNote={This paper presents an experimental investigation aimed at characterizing the kinematics of a pitching-heaving aeroelastic wing placed downstream of a rectangular bluff body. The influence of the bluff body wake on the wing is twofold: a viscous wake which produces a velocity deficit downstream and an oscillating induced velocity field due to periodic vortex shedding. The latter effect is the focus of this paper, specifically, the interaction between the wake frequency and the wing limit cycle oscillation (LCO) frequency. Wind tunnel experiments showed that the presence of the upstream bluff body causes modulation of the LCO amplitude. The modulation resembles a beat phenomenon, however the modulation frequency is related to the third harmonic of fLCO rather than the fundamental frequency. The modulation behavior also differs from that of a beat in that the spectral content contains sideband frequencies, characteristic of a multiplication between a carrier wave and a modulation wave rather than a simple sinusoidal superposition. Additionally, the streamwise spacing between the bluff body and the wing significantly influences the wing kinematics, with a closer spacing between the two bodies increasing the intensity of the amplitude modulation. For shedding frequencies sufficiently close to the LCO third harmonic, reducing this streamwise distance was shown to induce an alternation between two distinct modes of amplitude modulation, each with its own intensity and frequency.}, number={0}, journal={JOURNAL OF FLUIDS AND STRUCTURES}, author={Gianikos, Zachary N. and Kirschmeier, Benjamin A. and Gopalarathnam, Ashok and Bryant, Matthew}, year={2020}, month={May} }
 @article{hosangadi_gopalarathnam_2021, title={Low-Order Method for Prediction of Separation and Stall on Unswept Wings}, volume={58}, ISSN={["1533-3868"]}, DOI={10.2514/1.C036027}, abstractNote={A low-order method is presented for aerodynamic prediction of wings operating at near-stall and post-stall flight conditions. The method is intended for use in design, modeling, and simulation. In this method, the flow separation due to stall is modeled in a vortex-lattice framework as an effective reduction in the camber, or "decambering." For each section of the wing, a parabolic decambering flap, hinged at the separation location of the section, is calculated through iteration to ensure that the lift and moment coefficients of the section match with the values from the two-dimensional viscous input curves for the effective angle of attack of the section. As an improvement from earlier low-order methods, this method also predicts the separation pattern on the wing. Results from the method, presented for unswept wings having various airfoils, aspect ratios, taper ratios, and small, quasi-steady roll rates, are shown to agree well with experimental results in the literature, and computational solutions obtained as part of the current work.}, number={3}, journal={JOURNAL OF AIRCRAFT}, author={Hosangadi, Pranav and Gopalarathnam, Ashok}, year={2021}, month={May}, pages={420–435} }
 @article{narsipur_hosangadi_gopalarathnam_edwards_2020, title={Variation of leading-edge suction during stall for unsteady aerofoil motions}, volume={900}, ISSN={["1469-7645"]}, DOI={10.1017/jfm.2020.467}, abstractNote={Abstract}, journal={JOURNAL OF FLUID MECHANICS}, author={Narsipur, Shreyas and Hosangadi, Pranav and Gopalarathnam, Ashok and Edwards, Jack R.}, year={2020}, month={Oct} }
 @article{waghela_yoder_gopalarathnam_mazzoleni_2019, title={Aerodynamic Sails for Passive Guidance of High-Altitude Balloons: Static-Stability and Equilibrium Performance}, volume={56}, ISSN={["1533-3868"]}, DOI={10.2514/1.C035353}, abstractNote={Balloon trajectory control remains a sought-after goal for the current scientific ballooning community. In this work, a trajectory control system capable of passively guiding a high-altitude balloo...}, number={5}, journal={JOURNAL OF AIRCRAFT}, author={Waghela, R. and Yoder, C. D. and Gopalarathnam, A. and Mazzoleni, A. P.}, year={2019}, pages={1849–1857} }
 @article{sureshbabu_ramesh_gopalarathnam_2019, title={Model Reduction in Discrete-Vortex Methods for Unsteady Airfoil Flows}, volume={57}, ISSN={["1533-385X"]}, DOI={10.2514/1.J057458}, abstractNote={Discrete-vortex methods are a class of low-order methods widely used to study unsteady aerodynamic phenomena. However, these methods demand high computational costs when subject to large number of ...}, number={4}, journal={AIAA JOURNAL}, author={SureshBabu, ArunVishnu and Ramesh, Kiran and Gopalarathnam, Ashok}, year={2019}, month={Apr}, pages={1409–1422} }
 @article{hirato_shen_gopalarathnam_edwards_2019, title={Vortex-Sheet Representation of Leading-Edge Vortex Shedding from Finite Wings}, volume={56}, ISSN={["1533-3868"]}, DOI={10.2514/1.C035124}, abstractNote={A characteristic feature of flows past many oscillating airfoils and wings is the leading-edge vortex (LEV). Although considerable progress has been made in the low-order modeling of LEV formation ...}, number={4}, journal={JOURNAL OF AIRCRAFT}, author={Hirato, Yoshikazu and Shen, Minao and Gopalarathnam, Ashok and Edwards, Jack R.}, year={2019}, pages={1626–1640} }
 @article{saini_gopalarathnam_2018, title={Leading-Edge Flow Sensing for Aerodynamic Parameter Estimation}, volume={56}, ISSN={["1533-385X"]}, DOI={10.2514/1.J057327}, abstractNote={The identification of inflow air-data quantities such as the airspeed, angle of attack, and local lift coefficient on various sections of a wing or rotor blade is beneficial for load monitoring, ae...}, number={12}, journal={AIAA JOURNAL}, author={Saini, Aditya and Gopalarathnam, Ashok}, year={2018}, month={Dec}, pages={4706–4718} }
 @article{narsipur_gopalarathnam_edwards_2019, title={Low-Order Model for Prediction of Trailing-Edge Separation in Unsteady Flow}, volume={57}, ISSN={["1533-385X"]}, DOI={10.2514/1.J057132}, abstractNote={Computational and experimental results for pitching and plunging airfoils were used to study the time lag associated with boundary-layer convection and to develop a model that can be used to augmen...}, number={1}, journal={AIAA JOURNAL}, author={Narsipur, Shreyas and Gopalarathnam, Ashok and Edwards, Jack R.}, year={2019}, month={Jan}, pages={191–207} }
 @article{ramesh_granlund_ol_gopalarathnam_edwards_2018, title={Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows}, volume={32}, ISSN={["1432-2250"]}, DOI={10.1007/s00162-017-0442-0}, abstractNote={A leading-edge suction parameter (LESP) that is derived from potential flow theory as a measure of suction at the airfoil leading edge is used to study initiation of leading-edge vortex (LEV) formation in this article. The LESP hypothesis is presented, which states that LEV formation in unsteady flows for specified airfoil shape and Reynolds number occurs at a critical constant value of LESP, regardless of motion kinematics. This hypothesis is tested and validated against a large set of data from CFD and experimental studies of flows with LEV formation. The hypothesis is seen to hold except in cases with slow-rate kinematics which evince significant trailing-edge separation (which refers here to separation leading to reversed flow on the aft portion of the upper surface), thereby establishing the envelope of validity. The implication is that the critical LESP value for an airfoil–Reynolds number combination may be calibrated using CFD or experiment for just one motion and then employed to predict LEV initiation for any other (fast-rate) motion. It is also shown that the LESP concept may be used in an inverse mode to generate motion kinematics that would either prevent LEV formation or trigger the same as per aerodynamic requirements.}, number={2}, journal={THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS}, author={Ramesh, Kiran and Granlund, Kenneth and Ol, Michael V. and Gopalarathnam, Ashok and Edwards, Jack R.}, year={2018}, month={Apr}, pages={109–136} }
 @article{kim_saini_kim_gopalarathnam_zhu_palmieri_wohl_jiang_2016, title={A piezoelectric shear stress sensor}, volume={9803}, ISSN={["1996-756X"]}, DOI={10.1117/12.2219185}, abstractNote={In this paper, a piezoelectric sensor with a floating element was developed for shear stress measurement. The piezoelectric sensor was designed to detect the pure shear stress, suppressing effects of normal stress components, by applying opposite poling vectors to the piezoelectric elements. The sensor was first calibrated in the lab by applying shear forces where it demonstrated high sensitivity to shear stress (91.3 ± 2.1 pC/Pa) due to the high piezoelectric coefficients of 0.67Pb(Mg1∕3Nb2∕3)O3-0.33PbTiO3 (PMN-33%PT, d31=-1330 pC/N). The sensor also exhibited negligible sensitivity to normal stress (less than 1.2 pC/Pa) because of the electromechanical symmetry of the device. The usable frequency range of the sensor is up to 800 Hz.}, journal={SENSORS AND SMART STRUCTURES TECHNOLOGIES FOR CIVIL, MECHANICAL, AND AEROSPACE SYSTEMS 2016}, author={Kim, Taeyang and Saini, Aditya and Kim, Jinwook and Gopalarathnam, Ashok and Zhu, Yong and Palmieri, Frank L. and Wohl, Christopher J. and Jiang, Xiaoning}, year={2016} }
 @article{frink_murthy_atkins_viken_petrilli_gopalarathnam_paul_2017, title={Computational Aerodynamic Modeling Tools for Aircraft Loss of Control}, volume={40}, ISSN={["1533-3884"]}, DOI={10.2514/1.g001736}, abstractNote={This paper summarizes the status of ongoing NASA research supported over the past eight years to advance computational capabilities for modeling civil aircraft loss of control due to airframe damage or wing stall. The research is motivated by a desire to exploit the capabilities of computational methods to create augmented flight simulation models that improve pilot training for such loss-of-control scenarios. Flight of aircraft with either airframe damage or operating near and beyond the stall boundary encounters additional nonlinear aerodynamic influences on stability and control from dynamic motions that, if not included in flight simulation models, may lead to incorrect pilot responses. In the present work, both low- and high-fidelity computational methods are explored for analyzing such nonlinearities. The challenge of creating nonlinear reduced-order models from high-fidelity computational data is also addressed. At the beginning, few guidelines were available for computing or modeling the dynamic s...}, number={4}, journal={JOURNAL OF GUIDANCE CONTROL AND DYNAMICS}, author={Frink, Neal T. and Murthy, Patrick C. and Atkins, Harold L. and Viken, Sally A. and Petrilli, Justin L. and Gopalarathnam, Ashok and Paul, Ryan C.}, year={2017}, month={Apr}, pages={789–803} }
 @article{kim_saini_kim_gopalarathnam_zhu_palmieri_wohl_jiang_2017, title={Piezoelectric Floating Element Shear Stress Sensor for the Wind Tunnel Flow Measurement}, volume={64}, ISSN={["1557-9948"]}, DOI={10.1109/tie.2016.2630670}, abstractNote={A piezoelectric (PE) sensor with a floating element was developed for direct measurement of flow induced shear stress. The PE sensor was designed to detect the pure shear stress while suppressing the effect of normal stress generated from the vortex lift up by applying opposite poling vectors to the PE elements. During the calibration stage, the prototyped sensor showed a high sensitivity to shear stress (91.3 ± 2.1 pC/Pa) due to the high PE coefficients (<inline-formula><tex-math notation="LaTeX">$d_{{31}}=- $</tex-math></inline-formula>1330 pC/N) of the constituent 0.67Pb(Mg<inline-formula><tex-math notation="LaTeX">$_{1/3} $</tex-math></inline-formula>Nb<inline-formula> <tex-math notation="LaTeX">$_{2/3} $</tex-math></inline-formula>)O<sub>3</sub>–0.33PbTiO<sub>3</sub> (PMN–33%PT) single crystal. By contrast, the sensor showed almost no sensitivity to normal stress (less than 1.2 pC/Pa) because of the electromechanical symmetry of the sensing structure. The usable frequency range of the sensor is up to 800 Hz. In subsonic wind tunnel tests, an analytical model was proposed based on cantilever beam theory with an end-tip-mass for verifying the resonance frequency shift in static stress measurements. For dynamic stress measurements, the signal-to-noise ratio (SNR) and ambient vibration-filtered pure shear stress sensitivity were obtained through signal processing. The developed PE shear stress sensor was found to have an SNR of 15.8 ± 2.2 dB and a sensitivity of 56.5 ± 4.6 pC/Pa in the turbulent flow.}, number={9}, journal={IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS}, author={Kim, Taeyang and Saini, Aditya and Kim, Jinwook and Gopalarathnam, Ashok and Zhu, Yong and Palmieri, Frank L. and Wohl, Christopher J. and Jiang, Xiaoning}, year={2017}, month={Sep}, pages={7304–7312} }
 @article{heinzen_hall_gopalarathnam_2015, title={Development and Testing of a Passive Variable-Pitch Propeller}, volume={52}, ISSN={0021-8669 1533-3868}, url={http://dx.doi.org/10.2514/1.C032595}, DOI={10.2514/1.c032595}, abstractNote={A novel approach to passive propeller blade pitch variation is investigated. To effect passive pitch changes, the propeller blades are allowed to pivot freely about a radial axis, and aerodynamic pitching moments are tailored to give favorable blade pitch angles over a wide range of advance ratios. Computational modeling of the system indicated that a large expansion of the efficient operating envelope is possible, compared to a fixed-pitch propeller. Wind-tunnel experiments corroborated the computational results and demonstrated that the propeller maintained near-peak efficiency by passively adjusting blade pitch angles by over 15 deg to the match changing advance ratio. The passive variable-pitch propeller was then successfully demonstrated in flight on an unmanned aerial vehicle. Using tailored aerodynamics in place of active control allows this performance improvement to be realized at a fraction of the weight and complexity of a traditionally actuated variable-pitch propeller. The concept enables the...}, number={3}, journal={Journal of Aircraft}, publisher={American Institute of Aeronautics and Astronautics (AIAA)}, author={Heinzen, Stearns B. and Hall, Charles E., Jr. and Gopalarathnam, Ashok}, year={2015}, month={May}, pages={748–763} }
 @article{ramesh_murua_gopalarathnam_2015, title={Limit-cycle oscillations in unsteady flows dominated by intermittent leading-edge vortex shedding}, volume={55}, ISSN={0889-9746}, url={http://dx.doi.org/10.1016/j.jfluidstructs.2015.02.005}, DOI={10.1016/j.jfluidstructs.2015.02.005}, abstractNote={High-frequency limit-cycle oscillations of an airfoil at low Reynolds number are studied numerically. This regime is characterized by large apparent-mass effects and intermittent shedding of leading-edge vortices. Under these conditions, leading-edge vortex shedding has been shown to result in favorable consequences such as high lift and efficiencies in propulsion/power extraction, thus motivating this study. The aerodynamic model used in the aeroelastic framework is a potential-flow-based discrete-vortex method, augmented with intermittent leading-edge vortex shedding based on a leading-edge suction parameter reaching a critical value. This model has been validated extensively in the regime under consideration and is computationally cheap in comparison with Navier–Stokes solvers. The structural model used has degrees of freedom in pitch and plunge, and allows for large amplitudes and cubic stiffening. The aeroelastic framework developed in this paper is employed to undertake parametric studies which evaluate the impact of different types of nonlinearity. Structural configurations with pitch-to-plunge frequency ratios close to unity are considered, where the flutter speeds are lowest (ideal for power generation) and reduced frequencies are highest. The range of reduced frequencies studied is two to three times higher than most airfoil studies, a virtually unexplored regime. Aerodynamic nonlinearity resulting from intermittent leading-edge vortex shedding always causes a supercritical Hopf bifurcation, where limit-cycle oscillations occur at freestream velocities greater than the linear flutter speed. The variations in amplitude and frequency of limit-cycle oscillations as functions of aerodynamic and structural parameters are presented through the parametric studies. The excellent accuracy/cost balance offered by the methodology presented in this paper suggests that it could be successfully employed to investigate optimum setups for power harvesting in the low-Reynolds-number regime.}, journal={Journal of Fluids and Structures}, publisher={Elsevier BV}, author={Ramesh, Kiran and Murua, Joseba and Gopalarathnam, Ashok}, year={2015}, month={May}, pages={84–105} }
 @article{ramesh_gopalarathnam_granlund_ol_edwards_2014, title={Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding}, volume={751}, ISSN={0022-1120 1469-7645}, url={http://dx.doi.org/10.1017/jfm.2014.297}, DOI={10.1017/jfm.2014.297}, abstractNote={AbstractUnsteady aerofoil flows are often characterized by leading-edge vortex (LEV) shedding. While experiments and high-order computations have contributed to our understanding of these flows, fast low-order methods are needed for engineering tasks. Classical unsteady aerofoil theories are limited to small amplitudes and attached leading-edge flows. Discrete-vortex methods that model vortex shedding from leading edges assume continuous shedding, valid only for sharp leading edges, or shedding governed by ad-hoc criteria such as a critical angle of attack, valid only for a restricted set of kinematics. We present a criterion for intermittent vortex shedding from rounded leading edges that is governed by a maximum allowable leading-edge suction. We show that, when using unsteady thin aerofoil theory, this leading-edge suction parameter (LESP) is related to the $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}A_0$ term in the Fourier series representing the chordwise variation of bound vorticity. Furthermore, for any aerofoil and Reynolds number, there is a critical value of the LESP, which is independent of the motion kinematics. When the instantaneous LESP value exceeds the critical value, vortex shedding occurs at the leading edge. We have augmented a discrete-time, arbitrary-motion, unsteady thin aerofoil theory with discrete-vortex shedding from the leading edge governed by the instantaneous LESP. Thus, the use of a single empirical parameter, the critical-LESP value, allows us to determine the onset, growth, and termination of LEVs. We show, by comparison with experimental and computational results for several aerofoils, motions and Reynolds numbers, that this computationally inexpensive method is successful in predicting the complex flows and forces resulting from intermittent LEV shedding, thus validating the LESP concept.}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Ramesh, Kiran and Gopalarathnam, Ashok and Granlund, Kenneth and Ol, Michael V. and Edwards, Jack R.}, year={2014}, month={Jun}, pages={500–538} }
 @article{cusher_gopalarathnam_2014, title={Drag reduction on aircraft configurations with adaptive lifting surfaces}, volume={34}, ISSN={1270-9638}, url={http://dx.doi.org/10.1016/j.ast.2014.01.012}, DOI={10.1016/j.ast.2014.01.012}, abstractNote={An approach, applicable to multiple-lifting-surface fixed-wing aircraft operating at subcritical Mach numbers, is presented for minimizing induced and profile drag with a constraint on the pitching moment. The approach allows the designer to select surface incidence, twist, and flap angles as variables for the optimization. The numerical formulation uses superposition to construct the spanwise lift distribution from basic and additional loadings, and decomposes the flap-angle distributions for each surface into mean and variation distributions. Together, these elements enable the solution of the problem using semi-analytical methods that also provide insight. Results are presented for a three surface aircraft which highlights low drag possibilities with positive static margins, presents the trade-offs between induced and profile drag, and provides insight into the aerodynamics of multiple lifting surface configurations.}, journal={Aerospace Science and Technology}, publisher={Elsevier BV}, author={Cusher, Aaron A. and Gopalarathnam, Ashok}, year={2014}, month={Apr}, pages={35–44} }
 @article{paul_gopalarathnam_2014, title={Iteration schemes for rapid post-stall aerodynamic prediction of wings using a decambering approach}, volume={76}, ISSN={0271-2091}, url={http://dx.doi.org/10.1002/fld.3931}, DOI={10.1002/fld.3931}, abstractNote={SUMMARYNonlinear aerodynamics of wings may be evaluated using an iterative decambering approach. In this approach, the effect of flow separation due to stall at any wing section is modeled as an effective reduction in section camber. The approach uses a wing analysis method for potential‐flow calculations and viscous airfoil lift curves for the sections as input. The calculation procedure is implemented using a Newton–Raphson iteration to simultaneously satisfy the boundary condition, which comes from potential‐flow wing theory, and drive the sectional operating points toward their respective viscous lift curves, as required for convergence. Of particular interest in this research is the calculation of the residuals during the Newton iteration. Unlike a typical implementation of the Newton iteration, the residual calculation is not performed via a straightforward function evaluation, but rather by estimating the target operating points on the input viscous lift curves. Estimation of these target operating points depends on the assumptions made in the cross‐coupling of the decambering at the different sections. This paper presents four residual calculation schemes for the decambering approach. The residual calculation schemes are compared against each other to assess computational speed and robustness. Decambering results are also compared with higher‐order computational fluid dynamics (CFD) solutions for rectangular and swept wings. Results from the best scheme compare well with the CFD solutions for the rectangular wing, motivating further development of the method. Poor predictions for the swept wings are traced to spanwise propagation of separated flow at stall, highlighting the limitations of the current approach. Copyright © 2014 John Wiley & Sons, Ltd.}, number={4}, journal={International Journal for Numerical Methods in Fluids}, publisher={Wiley}, author={Paul, R. C. and Gopalarathnam, A.}, year={2014}, month={Jul}, pages={199–222} }
 @article{ramesh_gopalarathnam_edwards_ol_granlund_2013, title={An unsteady airfoil theory applied to pitching motions validated against experiment and computation}, volume={27}, ISSN={0935-4964 1432-2250}, url={http://dx.doi.org/10.1007/s00162-012-0292-8}, DOI={10.1007/s00162-012-0292-8}, number={6}, journal={Theoretical and Computational Fluid Dynamics}, publisher={Springer Science and Business Media LLC}, author={Ramesh, Kiran and Gopalarathnam, Ashok and Edwards, Jack R. and Ol, Michael V. and Granlund, Kenneth}, year={2013}, month={Jan}, pages={843–864} }
 @article{cusher_gopalarathnam_2012, title={Drag Reduction Methodology for Adaptive Tailless Aircraft}, volume={49}, ISSN={0021-8669 1533-3868}, url={http://dx.doi.org/10.2514/1.C031454}, DOI={10.2514/1.c031454}, abstractNote={An approach is presented for determining optimum lift distributions for adaptive tailless aircraft. In this study, wing adaptation is achieved using multiple trailing-edge flaps that are used to optimally distribute the lift of the wing such that drag is minimized. For tailless aircraft that are stable in pitch, the lack of a secondary lifting surface makes it necessary that the lift distribution on the wing also satisfies a pitching-moment constraint to ensure trim. The current work implements a numerical approach that solves for the optimal scheduling of multiple trailing-edge flaps on the wing of a tailless aircraft for various flight conditions with a pitching-moment constraint to reduce both induced and profile drag. The approach uses superposition to construct the spanwise lift distribution from basic and additional loadings, and decomposes the flap-angle distribution into mean and variation distributions. Together, these elements enable the solution of the problem using semi-analytical methods that also provide insight. The results are presented for a planar, swept, tapered wing with two airfoil-section choices to verify the theory and provide insight for trade studies.}, number={1}, journal={Journal of Aircraft}, publisher={American Institute of Aeronautics and Astronautics (AIAA)}, author={Cusher, Aaron A. and Gopalarathnam, Ashok}, year={2012}, month={Jan}, pages={161–172} }
 @article{sriram_gopalarathnam_misenheimer_2012, title={High-Downforce Airfoil Design for Motorsports}, volume={5}, ISSN={1946-3987}, url={http://dx.doi.org/10.4271/2012-01-1168}, DOI={10.4271/2012-01-1168}, number={2}, journal={SAE International Journal of Materials and Manufacturing}, publisher={SAE International}, author={Sriram, P.S. and Gopalarathnam, Ashok and Misenheimer, Andrew}, year={2012}, month={Apr}, pages={478–489} }
 @article{johnston_gopalarathnam_2012, title={Investigation of a bio-inspired lift-enhancing effector on a 2D airfoil}, volume={7}, ISSN={1748-3182 1748-3190}, url={http://dx.doi.org/10.1088/1748-3182/7/3/036003}, DOI={10.1088/1748-3182/7/3/036003}, abstractNote={A flap mounted on the upper surface of an airfoil, called a ‘lift-enhancing effector’, has been shown in wind tunnel tests to have a similar function to a bird's covert feathers, which rise off the wing's surface in response to separated flows. The effector, fabricated from a thin Mylar sheet, is allowed to rotate freely about its leading edge. The tests were performed in the NCSU subsonic wind tunnel at a chord Reynolds number of 4 × 105. The maximum lift coefficient with the effector was the same as that for the clean airfoil, but was maintained over an angle-of-attack range from 12° to almost 20°, resulting in a very gentle stall behavior. To better understand the aerodynamics and to estimate the deployment angle of the free-moving effector, fixed-angle effectors fabricated out of stiff wood were also tested. A progressive increase in the stall angle of attack with increasing effector angle was observed, with diminishing returns beyond the effector angle of 60°. Drag tests on both the free-moving and fixed effectors showed a marked improvement in drag at high angles of attack. Oil flow visualization on the airfoil with and without the fixed-angle effectors proved that the effector causes the separation point to move aft on the airfoil, as compared to the clean airfoil. This is thought to be the main mechanism by which an effector improves both lift and drag. A comparison of the fixed-effector results with those from the free-effector tests shows that the free effector's deployment angle is between 30° and 45°. When operating at and beyond the clean airfoil's stall angle, the free effector automatically deploys to progressively higher angles with increasing angles of attack. This slows down the rapid upstream movement of the separation point and avoids the severe reduction in the lift coefficient and an increase in the drag coefficient that are seen on the clean airfoil at the onset of stall. Thus, the effector postpones the stall by 4–8° and makes the stall behavior more gentle. The benefits of using the effector could include care-free operations at high angles of attack during perching and maneuvering flight, especially in gusty conditions.}, number={3}, journal={Bioinspiration & Biomimetics}, publisher={IOP Publishing}, author={Johnston, Joe and Gopalarathnam, Ashok}, year={2012}, month={Apr}, pages={036003} }
 @article{mcgowan_granlund_ol_gopalarathnam_edwards_2011, title={Investigations of Lift-Based Pitch-Plunge Equivalence for Airfoils at Low Reynolds Numbers}, volume={49}, ISSN={["0001-1452"]}, DOI={10.2514/1.j050924}, abstractNote={The limits of linear superposition in two-dimensional high-rate low-Reynolds-number aerodynamics are examined by comparing the lift-coefficient history and flowfield evolution for airfoils undergoing harmonic motions in pure pitch, pure plunge, and pitch―plunge combinations. Using quasi-steady airfoil theory and Theodorsen's formula as predictive tools, pitching motions are sought that produce lift histories identical to those of prescribed plunging motions. It follows that a suitable phasing of pitch and plunge in a combined motion should identically produce zero lift, canceling either the circulatory contribution (with quasi-steady theory) or the combination of circulatory and noncirculatory contributions (with Theodorsen's formula). Lift history is measured experimentally in a water tunnel using a force balance and is compared with two-dimensional Reynolds-averaged Navier―Stokes computations and Theodorsen's theory; computed vorticity contours are compared with dye injection in the water tunnel. Theodorsen's method evinces considerable, and perhaps surprising, resilience in finding pitch-to-plunge equivalence of lift-coefficient―time history, despite its present application to cases in which its mathematical assumptions are demonstrably violated. A combination of pitch and plunge motions can be found such that net lift coefficient is nearly identically zero for arbitrarily high reduced frequency, provided that amplitude is small. Conversely, cancellation is possible at large motion amplitude, provided that reduced frequency is moderate. The product of Strouhal number and nondimensional amplitude is therefore suggested as the upper bound for when superposition and linear predictions remain valid in massively unsteady two-dimensional problems.}, number={7}, journal={AIAA JOURNAL}, author={McGowan, Gregory Z. and Granlund, Kenneth and Ol, Michael V. and Gopalarathnam, Ashok and Edwards, Jack R.}, year={2011}, month={Jul}, pages={1511–1524} }
 @article{cox_gopalarathnam_hall_2010, title={Flight Test of Stable Automated Cruise Flap for an Adaptive Wing Aircraft}, volume={47}, ISSN={0021-8669 1533-3868}, url={http://dx.doi.org/10.2514/1.46789}, DOI={10.2514/1.46789}, abstractNote={0p-optimization function was effective in producing pressure differentials that would have reduced drag. The effectivenessoftheC 0 p-maintenancefunctioncouldnotbedeterminedbecauseoflargesample-to-samplevariations in measured C 0 p values. It remains unknown whether this high-frequency content actually represented rapidly varying pressures on the airfoil surface or if it was the result of noise in the measurement system.}, number={4}, journal={Journal of Aircraft}, publisher={American Institute of Aeronautics and Astronautics (AIAA)}, author={Cox, Craig and Gopalarathnam, Ashok and Hall, Charles E., Jr.}, year={2010}, month={Jul}, pages={1178–1188} }
 @article{ol_reeder_fredberg_mcgowan_gopalarathnam_edwards_2009, title={Computation vs. Experiment for High-Frequency Low-Reynolds Number Airfoil Plunge}, volume={1}, ISSN={1756-8293 1756-8307}, url={http://dx.doi.org/10.1260/175682909789498279}, DOI={10.1260/175682909789498279}, abstractNote={ We seek to extend the literature on sinusoidal pure-plunge of 2D airfoils at high reduced frequency and low Reynolds number, by including effects of camber and nonzero mean incidence angle. We compare experimental results in a water tunnel using dye injection and 2D particle image velocimetry, with a set of computations in 2D – Immersed Boundary Method and unsteady Reynolds-Averaged Navier Stokes. The Re range is from 10,000 to 60,000, based on free stream velocity and airfoil chord, chosen to cover cases where transition in attached boundary layers would be of some importance, and where transition would only occur in the wake. Generally at high reduced frequency there is no Reynolds number effect. Mean angle of attack has significance, notionally, depending on whether it is below or above static stall. Computations were found to agree well with experimentally-derived velocity contours, vorticity contours and momentum in the wake. As found previously for the NACA0012, varying Strouhal number is found to control the topology of the wake, while varying reduced amplitude and reduced frequency together, but keeping Strouhal number constant, causes wake vortical structures to scale with the reduced amplitude of plunge. Flowfield periodicity – as evinced from comparison of instantaneous and time-averaged particle image velocimetry – is generally attained after two periods of oscillation from motion onset. }, number={2}, journal={International Journal of Micro Air Vehicles}, publisher={SAGE Publications}, author={Ol, Michael V. and Reeder, Mark and Fredberg, Daniel and McGowan, Gregory Z. and Gopalarathnam, Ashok and Edwards, Jack R.}, year={2009}, month={Jun}, pages={99–119} }
 @article{cox_gopalarathnam_hall_2009, title={Development of Stable Automated Cruise Flap for an Aircraft with Adaptive Wing}, volume={46}, ISSN={0021-8669 1533-3868}, url={http://dx.doi.org/10.2514/1.38684}, DOI={10.2514/1.38684}, abstractNote={Cruise flaps are devices designed to minimize drag, and previous research has explored using a wing-based pressure differential to automate them. Different presentations of the pressure-differential data tend to lead to the development of different types of controllers for automated cruise flaps. A presentation used by previous researchers led to an unstable drag-minimizing controller, whereas a presentation used in this research leads to a stable controller that implements multiple functions. Techniques previously used for high Reynolds number natural-laminar-flow airfoils are modified for use with the low Reynolds number SD7037 planned for future flight testing. The results of rigid-aircraft simulations are presented, showing the effectiveness of the multifunction controller, which is able to simultaneously reduce drag and alleviate the effects of vertical gusts.}, number={1}, journal={Journal of Aircraft}, publisher={American Institute of Aeronautics and Astronautics (AIAA)}, author={Cox, Craig and Gopalarathnam, Ashok and Hall, Charles E., Jr.}, year={2009}, month={Jan}, pages={301–311} }
 @article{gopalarathnam_norris_2009, title={Ideal Lift Distributions and Flap Angles for Adaptive Wings}, volume={46}, ISSN={0021-8669 1533-3868}, url={http://dx.doi.org/10.2514/1.38713}, DOI={10.2514/1.38713}, abstractNote={An approach is presented for determining the optimum flap angles and spanwise loading to suit a given flight condition. Multiple trailing-edge flaps along the span of an adaptive wing are set to either reduce drag in rectilinear flight conditions or to limit the wing bending moment at maneuvering conditions. For reducing drag, the flaps are adjusted to minimize induced drag, while simultaneously enabling the wing sections to operate within their respective low-drag ranges. For limiting wing bending moment, the flaps are used to relieve the loading near the wing tips. An important element of the approach is the decomposition of the flap angles into a distribution that can be used to control the spanwise loading for induced-drag control and a constant flap that can used for profile-drag control. The problem is linearized using the concept of basic and additional lift distributions, which enables the use of standard constrained-minimization formulations. The results for flap-angle distributions for different flight conditions are presented for a planar and a nonplanar wing. Postdesign analysis and aircraft-performance simulations are used to validate the optimum flap-angle distributions determined using the current approach.}, number={2}, journal={Journal of Aircraft}, publisher={American Institute of Aeronautics and Astronautics (AIAA)}, author={Gopalarathnam, Ashok and Norris, Rachel King}, year={2009}, month={Mar}, pages={562–571} }
 @article{mukherjee_gopalarathnam_2006, title={Poststall Prediction of Multiple-Lifting-Surface Configurations Using a Decambering Approach}, volume={43}, ISSN={0021-8669 1533-3868}, url={http://dx.doi.org/10.2514/1.15149}, DOI={10.2514/1.15149}, abstractNote={A novel scheme is presented for an iterative decambering approach to predict the post-stall characteristics of wings using known section data as inputs. The new scheme differs from earlier ones in the details of how the residual is computed. With this scheme, multiple solutions at high angles of attack are brought to light right during the computation of the residual for the Newton iteration. As with earlier schemes, multiple solutions are obtained for wings at high angles of attack and the resulting converged solution depends on the initial conditions used for the iteration. In general, the new scheme is found to be more robust at achieving convergence. Results are presented for a rectangular wing with two different airfoil lift curves and for a wing-tail configuration.}, number={3}, journal={Journal of Aircraft}, publisher={American Institute of Aeronautics and Astronautics (AIAA)}, author={Mukherjee, Rinku and Gopalarathnam, Ashok}, year={2006}, month={May}, pages={660–668} }
 @article{king_gopalarathnam_2005, title={Ideal aerodynamics of ground effect and formation flight}, volume={42}, ISSN={["1533-3868"]}, DOI={10.2514/1.10942}, abstractNote={The theoretical induced-drag benefits are presented for ideally loaded wings flying in formation and ground effect. An optimum-downwash approach using a vortex-lattice implementation was used to study formations of wings loaded optimally for minimum induced drag with roll trim. An exact approach was also developed to examine the drag of elliptically loaded wings in formation. The exact approach allows for decomposition of the benefits by considering the mutual-interference contributions from different pairs of wings in a formation}, number={5}, journal={JOURNAL OF AIRCRAFT}, author={King, RM and Gopalarathnam, A}, year={2005}, pages={1188–1199} }
 @article{jepson_gopalarathnam_2005, title={Incorporation of aircraft performance considerations in inverse airfoil design}, volume={42}, ISSN={["1533-3868"]}, DOI={10.2514/1.5373}, abstractNote={Although significant advances have been made in inverse airfoil design methodology, the tailoring of an airfoil to maximize one or more aircraft performance parameters still involves cycling between airfoil design and aircraft performance computations. A design formulation is presented that incorporates aircraft performance considerations in the inverse design of low-speed laminar-flow airfoils for piston engine driven propeller-powered airplanes. Two aircraft performance parameters are considered: level-flight maximum speed and maximum range. It is shown that the lift coefficient for the lower and upper corners of the airfoil low-drag range can be appropriately adjusted to tailor the airfoil for these two aircraft performance parameters. The design problem is posed as a part of a multidimensional Newton iteration in an existing conformal-mapping based inverse design code, PROFOIL. This formulation automatically adjusts the lift coefficients for the corners of the low-drag range as required for the airfoil‐aircraft matching. The design formulation also has the capability to handle a constraint on the stall speed by automatically adjusting the wing area to account for changes to the airfoil maximum lift coefficient. Two examples are presented to illustrate the process for a general aviation aircraft, and the results are validated by comparison with results from postdesign aircraft performance computations. Nomenclature A R= wing aspect ratio b = wing span C D = aircraft or wing drag coefficient based on Sw Cd = airfoil drag coefficient based on chord CL = aircraft or wing lift coefficient based on Sw Cl = airfoil lift coefficient based on chord}, number={1}, journal={JOURNAL OF AIRCRAFT}, author={Jepson, JK and Gopalarathnam, A}, year={2005}, pages={199–207} }
 @article{jepson_gopalarathnam_2005, title={Inverse design of adaptive airfoils with aircraft performance considerations}, volume={42}, number={6}, journal={Journal of Aircraft}, author={Jepson, J. K. and Gopalarathnam, A.}, year={2005}, pages={1622–1630} }
 @article{gopalarathnam_broughton_mcgranahan_selig_2003, title={Design of low Reynolds number airfoils with trips}, volume={40}, ISSN={["1533-3868"]}, DOI={10.2514/2.3157}, abstractNote={A design philosophy for low Reynolds number airfoils that judiciously combines the tailoring of the airfoil pressure distribution using a transition ramp with the use of boundary-layer trips is presented. Three airfoils with systematic changes to the shape of the transition ramp have been designed to study the effect of trips on the airfoil performance. The airfoils were wind-tunnel tested with various trip locations and at Reynolds numbers of 100,000 and 300,000 to assess the effectiveness of the design philosophy. The results show that the design philosophy was successfullyusedin integratinga boundary-layertrip from theoutsetin theairfoildesignprocess.FortheReynolds numbers and the range of airfoil shapes considered, however, airfoils designed with trips do not hold any clear advantage over airfoils designed for good performance in the clean condition.}, number={4}, journal={JOURNAL OF AIRCRAFT}, author={Gopalarathnam, A and Broughton, BA and McGranahan, BD and Selig, MS}, year={2003}, pages={768–775} }
 @article{frazier_gopalarathnam_2003, title={Optimum downwash behind wings in formation flight}, volume={40}, ISSN={["0021-8669"]}, DOI={10.2514/2.3162}, abstractNote={other hand, the scaling parameter M1® is more suitable (Fig. 2b). The upstream in uence appears to be a quadratic function of M1®, and the correlation of the downstream in uence and M1® is also reasonablygood.The extentof the interactionregionshowsa similar trend as the upstream and downstream in uences. A good collapse of the data with M1® can be seen. The peakpressuredownstreamof thecornercanbeused to characterize the strength of the upstreamcompressionprocesses. In Fig. 3 it can be seen that the peak pressure downstream of the concave corner can also be scaled with M1®. Stronger compression is associatedwith increasingfreestreamMach number and concave-corner angle. Note that the peak pressure at M1®D 12:30 increases up to 42% of dynamic pressure.}, number={4}, journal={JOURNAL OF AIRCRAFT}, author={Frazier, JW and Gopalarathnam, A}, year={2003}, pages={799–803} }
 @article{mcavoy_gopalarathnam_2002, title={Automated cruise flap for airfoil drag reduction over a large lift range}, volume={39}, ISSN={["0021-8669"]}, DOI={10.2514/2.3051}, abstractNote={A small trailing-edge e ap, often referred to as a cruise e ap or camber-changing e ap, can be used to extend the low-drag range of a natural-laminar-e ow airfoil. Automation of such a cruise e ap is likely to result in improved aircraft performance over a large speed range without an increase in the pilot work load. An important step in achieving the automation is to arrive at a simple approach for determination of the optimum e ap angle for a given airfoil lift coefe cient. This optimum e ap angle can then be used in a closed-loop control system to set the e ap automatically. Two pressure-based schemes are presented for determining the optimum e ap angle for any given airfoil lift coefe cient. The schemes use the pressure difference between two pressure sensors on the airfoil surface close to the leading edge. In each of the schemes, for a given lift coefe cient, this nondimensionalized pressure difference is brought to a predetermined target value by dee ecting the e ap. It is shown that the drag bucket is then shifted to bracket the given lift coefe cient. This nondimensional pressure difference, therefore, can be used to determine and set the optimum e ap angle for a specie ed lift coefe cient. The two schemes differ in the method used for the nondimensionalization. The effectiveness of the two schemesisverie ed using computational and windtunnel results for two NASA laminar e ow airfoils. Finally, an aircraft performance simulation approach is used to analyze the potential aircraft performance benee ts while addressing trim drag considerations.}, number={6}, journal={JOURNAL OF AIRCRAFT}, author={McAvoy, CW and Gopalarathnam, A}, year={2002}, pages={981–988} }
 @article{gopalarathnam_mcavoy_2002, title={Effect of airfoil characteristics on aircraft performance}, volume={39}, ISSN={["1533-3868"]}, DOI={10.2514/2.2968}, abstractNote={Even with all of the advances in airfoil and aircraft design, there remains little guidance on how to tailor an airfoil to suit a particular aircraft. A two-pronged approach is presented to tailor an airfoil for an aircraft: 1) an approach in which aircraft performance simulations are used to study the effects of airfoil changes and to guide the airfoil design and 2) an analytical approach to determine expressions that provide guidance in sizing and locating the airfoil low-drag range. The analytical study shows that there is an ideal value for the lift coefficient for the lower corner of the airfoil low-drag range when the airfoil is tailored for aircraft level-flight maximum speed. Likewise, there is an ideal value for the lift coefficient for the upper corner of the low-drag range when the airfoil is tailored for maximizing the aircraft range. These ideal locations are functions of the amount of laminar flow on the upper and lower surfaces of the airfoil and also depend on the geometry, drag, and power characteristics of the aircraft. Comparison of the results from the two approaches for a hypothetical general aviation aircraft are presented to validate the expressions derived in the analytical approach}, number={3}, journal={JOURNAL OF AIRCRAFT}, author={Gopalarathnam, A and McAvoy, CW}, year={2002}, pages={427–433} }
 @article{gopalarathnam_selig_2002, title={Hybrid inverse airfoil design method for complex three-dimensional lifting surfaces}, volume={39}, ISSN={["0021-8669"]}, DOI={10.2514/2.2966}, abstractNote={A method is presented for inverse design of airfoils for complex three-dimensional wings in incompressible flow. The method allows for prescription of inviscid velocity distributions over different cross sections of the wing in a multipoint fashion. A hybrid approach is used to determine the shapes of the wing cross sections that satisfy the design specifications. The airfoils forming the cross sections of the wing are generated using an inverse code for isolated airfoil design. A three-dimensional panel method is then used to obtain the velocity distributions over the resulting wing. The isolated airfoil velocity distributions are then used as design variables in a multidimensional Newton iteration method to achieve the design specifications on the wing. The method is particularly useful for complex geometries such as junctures, where three-dimensional and interference effects have to be accounted for in the design process. A key feature of the design method is a scheme to avoid using the panel method for sensitivity computations for the Newton iterations. This scheme not only results in significant reductions in computation time but also enables the integration of any readily available three-dimensional analysis code in executable form}, number={3}, journal={JOURNAL OF AIRCRAFT}, author={Gopalarathnam, A and Selig, MS}, year={2002}, pages={409–417} }
 @inproceedings{mckay_gopalarathnam†_2002, title={The Effects of Wing Aerodynamics on Race Vehicle Performance}, url={http://dx.doi.org/10.4271/2002-01-3294}, DOI={10.4271/2002-01-3294}, booktitle={SAE Technical Paper Series}, publisher={SAE International}, author={Mckay, Noah J. and Gopalarathnam†, Ashok}, year={2002}, month={Dec} }
 @article{gopalarathnam_selig_2001, title={Low-speed natural-laminar-flow airfoils: Case study in inverse airfoil design}, volume={38}, ISSN={["0021-8669"]}, DOI={10.2514/2.2734}, abstractNote={A systematic study of the trends in low-speed natural-laminar-eow airfoils for general aviation applications is presented. The airfoils have been designed using a multipoint inverse airfoil design method, which allows for specie cation of velocity and boundary-layer properties over different portions of the airfoil. A panel method with a coupled boundary-layer scheme is used to analyze the characteristics of the resulting airfoils. By systematically adjusting the speciecations, families of airfoils have been designed with different lift, drag, and pitching-moment characteristics. Parametric studies are presented to study the tradeoffs involved in designing laminar-e ow airfoils for general aviation. Although the results of the study are speciec to the class of airplanes considered, the design philosophies and the design approach used inthestudy areapplicable toa widerangeof airplanes. In addition, the examples presented in the paper form an excellent case study to demonstrate the power of modern inverse design techniques in controlling the performance of an airfoil to a ene degree and in generating a custom database of airfoils suitable for airplane multidisciplinary optimization and trade studies.}, number={1}, journal={JOURNAL OF AIRCRAFT}, author={Gopalarathnam, A and Selig, MS}, year={2001}, pages={57–63} }
 @article{gopalarathnam_selig_1998, title={Multipoint Inverse Method for Multielement Airfoil Design}, volume={35}, ISSN={0021-8669 1533-3868}, url={http://dx.doi.org/10.2514/2.2337}, DOI={10.2514/2.2337}, abstractNote={A multipoint inverse method has been developed for the design of multielement airfoils with desired velocity distributions in incompressible potential flow. The method uses an isolated-airfoil, multipoint, inverse code to generate each element of the multielement airfoil and a two-dimensional panel method to analyze the multielement airfoil. Through Newton iteration, the variables associated with the design of the elements in isolation are adjusted to achieve desired multielement velocity distributions. As the paper demonstrates, changes in the velocity distributions over the elements in isolation result in remarkably similar changes in the velocity distributions over the corresponding elements of the multielement airfoil. This similarity results in two key features of the design method: 1) the use of the isolated airfoil velocity distributions as design variables to achieve desired distributions over the multielement airfoil, and 2) the calculation of the gradient information for the Newton iteration during the design of the isolated airfoils rather than by several panel-method analyses, resulting in substantial savings in computation time}, number={3}, journal={Journal of Aircraft}, publisher={American Institute of Aeronautics and Astronautics (AIAA)}, author={Gopalarathnam, Ashok and Selig, Michael S.}, year={1998}, month={May}, pages={398–404} }