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Showing papers in "Journal of Aircraft in 1997"


Journal ArticleDOI
TL;DR: In this paper, a new high-lift airfoil design philosophy has been developed and experimentally validated through wind-tunnel tests, which makes use of a concave pressure recovery with aft loading.
Abstract: A new high-lift airfoil design philosophy has been developed and experimentally validated through wind-tunnel tests A key element of the high-lift design philosophy was to make use of a concave pressure recovery with aft loading Three codes for airfoil design and analysis (PROFOIL, the Eppler code, and ISES) were used to design the example S1223 high-lift airfoil for a Reynolds number of 2 3 10 5 In windtunnel tests, the new airfoil yielded a maximum lift coefe cient of 22 With vortex generators and a 1% chord Gurney eap (used separately), the Cl,max increased to 23 The airfoil demonstrates the rather dramatic gains in Cl,max over those airfoils previously used for high-lift low Reynolds number applications

190 citations


Journal ArticleDOI
TL;DR: This paper presents the development of a tuning paradigm and the capturing of such within an expert system using the University of Toronto classical algorithm, and results are relevant to alternative classical and similarly structured adaptive algorithms.
Abstract: Current motion-drive algorithms have a number of coefficients that are selected to tune the motion of the simulator. Little attention has been given to the process of selecting the most appropriate coefficient values. Final tuning is best accomplished using experienced evaluation pilots to provide feedback to a washout filter expert who adjusts the coefficients in an attempt to satisfy the pilot. This paper presents the development of a tuning paradigm and the capturing of such within an expert system. The focus of this development is the University of Toronto classical algorithm, but the results are relevant to alternative classical and similarly structured adaptive algorithms. This paper provides the groundwork required to develop the tuning paradigm. The necessity of this subjective tuning process is defended. Motion cueing error sources within the classical algorithm are revealed, and coefficient adjustments that reduce the errors are presented.

171 citations



Journal ArticleDOI
TL;DR: In this paper, an unsteady Euler solver is modie ed to calculate the indicial response of a rectangular wing to a step change in the angle of attack, but the mesh is not moved accordingly.
Abstract: An unsteady Euler solver is modie ed to calculate the indicial response of a rectangular wing to a step change in the angle of attack. In this new approach the grid time metrics include the velocity caused by the impulsive change in angle of attack, but the mesh is not moved accordingly. This approach avoids numerical instabilities and decouples the step change in the angle of attack from a pitch rate. Numerical results are validated by comparison with analytical results for two-dimensional indicial responses. The application of the same method to rectangular wings reveals important characteristics of the three-dimensional indicial response. It is found that the direct calculation of the indicial response using computational e uid dynamics gives quite accurate results and provides a rich database, in the absence of experimental data, to validate the approximations to indicial response.

92 citations



Journal ArticleDOI
TL;DR: A unified hypersonic - supersonic lifting surface method has been developed, where the concept of piston theory is generalized and suitably integrated with the aerodynamic influence coefficient (AIC) matrix due to linear theory as mentioned in this paper.
Abstract: A unified hypersonic - supersonic lifting surface method has been developed, where the concept of piston theory is generalized and suitably integrated with the aerodynamic influence coefficient (AIC) matrix due to linear theory. Thus, this unified method can account for the effects of wing thickness and/or flow incidence, upstream influence, and three dimensionality for an arbitrary lifting surface system in an unsteady flow, whereas piston theory fails to account for the latter effects. In particular, the present composite series renders the AIC matrix uniformly valid for all supersonic-hypersonic Mach numbers, thus extending the method applicability to cover both the Ackeret limit at the low supersonic end and the Newtonian limit at the hypersonic end. From various cases studied it is concluded that the present method makes a substantial improvement over the linear lifting surface theory and piston theory in terms of unsteady pressures, stability derivatives, and flutter speeds. Among other theories it also predicts the most conservative flutter boundary and it confirms that the supersonic thickness effect is to reduce the flutter speed.

82 citations


Journal ArticleDOI
TL;DR: Using recursive neural networks, time-dependent models that predict unsteady boundary-layer development, separation, dynamic stall, and dynamic reattachment have been developed in this article, which can be used as the foundation upon which to develop adaptive control systems.
Abstract: The capability to harness or alleviate unsteady aerodynamic forces and moments could dramatically enhance aircraft control during severe maneuvers as well as signie cantly extend the life span of both helicopter and wind turbine blade/rotor assemblies. Using recursive neural networks, time-dependent models that predict unsteady boundary-layer development, separation, dynamic stall, and dynamic reattachment have been developed. Further, these models of the e ow› wing interactions can be used as the foundation upon which to develop adaptive control systems. The present work describes these capabilities for three-dimensional unsteady surface pressures and two-dimensional unsteady shear-stress measurements obtained for harmonic and constant-rate pitch motions. In the near future, it is predicted that such techniques will provide a viable approach for the development of six degree-of-freedom motion simulators for severe vehicle maneuvers as well as a foundation for the active control of unsteady e uid mechanics in a variety of systems.

70 citations


Journal ArticleDOI
TL;DR: In this article, a small jet placed within the cavity just below the front lip was used to force the shear layer with different amplitudes and frequencies, which was successful in reducing the amplitude of the oscillations.
Abstract: A computational investigation of a compressible cavity e ow was conducted. Blowing was implemented to suppress the large pressure oscillations characteristic of cavity e ows. The cavity length-to-depth ratio was 4.33, and the freestream Mach number was 1.75. A two-dimensional, time-accurate Navier› Stokes scheme was used to simulate the e ow. A small jet placed within the cavity just below the front lip was used to force the shear layer with different amplitudes and frequencies. This control technique was successful in reducing the amplitude of the oscillations. Furthermore, the effectiveness of the control was found to depend upon the jet frequency, amplitude, phase angle, and duty cycle. Autocorrelation analysis showed that the jet decreased the size of the structures in the shear layer. Cross-correlation analysis showed that the timing of events within the cavity were unaffected by the jet blowing.

61 citations


Journal ArticleDOI
TL;DR: The NASA Advanced Composites Technology (ACT) program was started in 1989 to develop composite primary structures for commercial transport airplanes with costs that are competitive with metal structures as discussed by the authors, and several contractors investigated the cost, weight, and performance attributes of textile reinforced composites.
Abstract: During the past 15 years NASA has taken the lead role in exploiting the benefits of textile reinforced composite materials for application to aircraft structures. The NASA Advanced Composites Technology (ACT) program was started in 1989 to develop composite primary structures for commercial transport airplanes with costs that are competitive with metal structures. As part of this program, several contractors investigated the cost, weight, and performance attributes of textile reinforced composites. Textile composites made using resin transfer molding type processes were evaluated for numerous applications. Methods were also developed to predict resin infiltration and flow in textile preforms and to predict and measure mechanical properties of the textile composites. This paper describes the salient results of that program.

58 citations


Journal ArticleDOI
TL;DR: In this article, the results of wind-tunnel tests of a Mach 14 Waverider were analyzed to assess its overall performance, and the performance losses associated with spillage were found to be relatively small.
Abstract: The results of wind-tunnel tests of a Mach 14 waverider were analyzed to assess its overall performance. The waverider was optimized using a e gure of merit that included viscosity, volume, and lift-to-drag considerations. The e nal design included a 0.25-in. leading-edge radius. The general performance of the tested waverider was analyzed and compared to the theoretical design from which it was derived. The theoretical design was generated from a conical e owe eld, where the vehicle’ s ine nitely sharp leading edges were everywhere-attached to the conical shock. Since the tested waverider featured blunt leading edges, it was important to assess the performance losses associated with e ow spillage; these losses were found to be relatively small. However, the increased drag due to the blunt leading edges contributed greatly to reducing the aerodynamic performance of the tested waverider. Also, it was found that the aerodynamic coefe cient data were insensitive to changes in Mach number and Reynolds number, indicating excellent off-design performance for the ranges of values tested.

58 citations


Journal ArticleDOI
TL;DR: In this paper, the basic photophysics, calibration, accuracy and time response of a luminescent paints is described followed by applications in low speed, transonic, supersonic and cryogenic wind tunnels and in rotating machinery.
Abstract: Luminescent molecular probes imbedded in a polymer binder form a temperature or pressure paint. On excitation by light of the proper wavelength, the luminescence, which is quenched either thermally or by oxygen, is detected by a camera or photodetector. From the detected luminescent intensity, temperature and pressure can be determined. The basic photophysics, calibration, accuracy and time response of a luminescent paints is described followed by applications in low speed, transonic, supersonic and cryogenic wind tunnels and in rotating machinery.

Journal ArticleDOI
TL;DR: The experiments demonstrate that distributed strain actuation can be effectively employed for aeroelastic control, with gust alleviation of 8-dB broadband and an increase in flutter speed of 11 %.
Abstract: This paper describes an analytical and experimental investigation into the use of active lifting surfaces with distributed strain actuators for dynamic aeroelastic control A detailed analytical aeroelastic model is developed for analysis and control law design using the Rayleigh-Ritz assumed mode method, kernel function unsteady aerodynamics, and modern state-space techniques The models are used to design multivariable dynamic compensators for applications such as gust alleviation, command following, and flutter suppression The effectiveness of the control laws is assessed analytically and verified experimentally through closed-loop wind-tunnel testing The experiments demonstrate that distributed strain actuation can be effectively employed for aeroelastic control, with gust alleviation of 8-dB broadband and an increase in flutter speed of 11 %

Journal ArticleDOI
TL;DR: In this article, the use of multiple control surfaces to effect roll trim of aircraft is investigated, and the results of utilizing multiple control surface on e exible wings are examined to determine if weight savings can be achieved while maintaining a desired level of roll performance.
Abstract: This study investigates the use of multiple control surfaces to effect roll trim of aircraft. Analytic models of a rectangular wing and a e ghter aircraft are used as examples for steady aeroelastic and antisymmetric trim analyses. The e nite element method is used to calculate structural deformations caused by steady aerodynamic input forces, which are generated by a linear panel method. Values of control surface effectiveness, calculated from the e exible rolling moment stability derivatives, are used to determine which control surfaces are most effective in achieving a desired roll maneuver. The roll trim equation of motion is solved for multiple control surface dee ections using an iterative technique that minimizes the control effort to achieve a specie ed roll rate. Roll trim utilizing multiple control surfaces, including leading-edge surfaces, is examined over a range of dynamic pressures. Aircraft models with reduced wing stiffness are investigated to determine if roll performance requirements can be achieved through the use of multiple control surfaces. The results of utilizing multiple control surfaces on e exible wings are examined to determine if weight savings can be achieved while maintaining a desired level of roll performance.

Journal ArticleDOI
TL;DR: In this article, a two-dimensional, three-element, advanced high-lift research airfoil has been tested in the NASA Langley Research Center s Low-Turbulence Pressure Tunnel at a chord Reynolds number up to 1.6 x 107.
Abstract: A new two-dimensional, three-element, advanced high-lift research airfoil has been tested in the NASA Langley Research Center s Low-Turbulence Pressure Tunnel at a chord Reynolds number up to 1.6 x 107. The components of this high-lift airfoil have been designed using a incompressible computational code (INS2D). The design was to provide high maximum-lift values while maintaining attached flow on the single-segment flap at landing conditions. The performance of the new NASA research airfoil is compared to a similar reference high-lift airfoil. On the new high-lift airfoil the effects of Reynolds number on slat and flap rigging have been studied experimentally, as well as the Mach number effects. The performance trend of the high-lift design is comparable to that predicted by INS2D over much of the angle-of-attack range. However, the code did not accurately predict the airfoil performance or the configuration-based trends near maximum lift where the compressibility effect could play a major role.

Journal ArticleDOI
TL;DR: A multilevel design strategy for supersonic missile inlet design is developed that combines an efe cient simple physical model analysis tool and a sophisticated computational computational dynamics (CFD) Navier ‐ Stokes analysis tool.
Abstract: A multilevel design strategy for supersonic missile inlet design is developed. The multilevel design strategy combines an efe cient simple physical model analysis tool and a sophisticated computational e uid dynamics (CFD) Navier ‐ Stokes analysis tool. The efe cient simple analysis tool is incorporated into the optimization loop, and the sophisticated CFD analysis tool is used to verify, select, and e lter the e nal design. The genetic algorithms and multistart gradient line search optimizers are used to search the nonsmooth design space. A geometry model for the supersonic missile inlet is developed. A supersonic missile inlet that starts at Mach 2.6 and cruises at Mach 4 was designed. Signie cant improvement of the inlet total pressure recovery has been obtained. Detailed e owe eld analysis is also presented.

Journal ArticleDOI
TL;DR: In this article, the modal-based aeroelastic optimization approach is reformulated and extended such that it can deal with more structural analysis and optimization features, such as stress constraints under e xed and varied external loads, and the effects of inertial changes on aero-elastic trim.
Abstract: The modal-based aeroelastic optimization approach is reformulated and extended such that it can deal with more structural analysis and optimization features. The disciplines treated in this paper are statics under e xed loads and static aeroelasticity of free ‐ free aircraft. The new formulation includes the application of stress constraints under e xed and varied external loads, and the effects of inertial changes on aeroelastic trim. It also facilitates the integration of the modal-based option in common e nite element structural optimization schemes. The new scheme is applied to realistic design cases using the multidisciplinary automated structural optimization system ASTROS code. Application cases of 3761 and 26,259 degrees of freedom exhibit CPU time reduction factors of 4 ‐ 122 in comparison with the conventional discrete approach.

Journal ArticleDOI
TL;DR: In this paper, the authors evaluated aircraft performance response to various environmental conditions encountered during flight and found a strong relationship between aircraft response and an environmental parameter utilizing a weighted volume diameter and liquid water content.
Abstract: This study evaluated aircraft performance response to various environmental conditions encountered during flight. These conditions included clear air, ice only, mixed phase, and supercooled drops. Supercooled drops consisting of cloud, drizzle and rain sizes were the main focus of this study. Aircraft response was quantified by rates of change in aircraft climb capability, drag coefficient, and lift over drag ratio. The aircraft performance parameters were compared to an environmental hydrometeor parameter quantifying the environmental conditions. Results show that encounters with supercooled drizzle drops, or SCDD, resulted in maximum rates of performance degradation. Encounters with supercooled cloud and rain sized drops resulted in minor to low rates of performance degradation while encounters with supercooled drops in low ice particle concentrations resulted in only minor rates of degradation. In addition, aircraft response to high ice particle concentrations, in low liquid water, following a SCDD encounter resulted in rapid performance recovery. The results presented herein show a strong relationship between aircraft response and an environmental parameter utilizing a weighted volume diameter and liquid water content. The results suggest that the most severe icing is actually caused by SCDD as opposed to freezing rain. (Author)

Journal ArticleDOI
TL;DR: Stereo photogrammetry measurements of the deformation of simple flat-plate, clipped delta wings that were undergoing aeroelastic oscillations in transonic flow are described in this article.
Abstract: Stereo photogrammetry measurements of the deformation of simple, flat-plate, clipped delta wings that were undergoing aeroelastic oscillations in transonic flow are described. The measurements were made in High Reynolds number Channel 2 at NASA Ames Research Center. Two types of aeroelastic responses were measured: 1) highly damped responses in which the tip of the model was deflected and then released at subcritical dynamic pressures; and 2) responses excited by perturbations in the flow as the dynamic pressure was slowly increased until the model became unstable. The model was imaged by three synchronized black-and-white video cameras, and the data were recorded on videotape. Correlated images from two of these cameras were used to estimate the space coordinates of reference marks on the model at each instant, and the motion of each mark was estimated by fitting the deflection data with a damped sinusoid. The resulting estimates of the frequency and damping of the first-bending-mode oscillations compared favorably with strain-gauge measurements. A large increase in the phase difference between motions of the leading and the trailing edges was observed just before the models became unstable.

Journal ArticleDOI
TL;DR: Inverse simulation is used to calculate the control displacements required for a modeled vehicle to perform a particular maneuver as mentioned in this paper, however, the usefulness of the technique depends on the validation of the mathematical model used.
Abstract: Inverse simulation is used to calculate the control displacements required for a modeled vehicle to perform a particular maneuver. As with all simulations, the usefulness of the technique depends on the validity of the mathematical model used. To incorporate the latest forms of helicopter model (individual blade models) in an inverse framework, it has been necessary to modify existing inverse techniques. Such a model is described in this paper along with an inverse algorithm capable of accommodating it, The resulting simulation is validated against flight data and comparisons are made with a more basic model. It is shown that the basic disk model compares well with the more comprehensive individual blade model until the severity of the maneuver is increased to encompass flight states where nonlinear aerodynamics effects are prevalent.

Journal ArticleDOI
TL;DR: In this paper, a series of wind-tunnel tests on a NACA 0012 airfoil was conducted to simulate the aerodynamic effects of runback ice, and the results showed a great degree of sensitivity of the air flow characteristics to the shape and the chordal position of the ice accretion.
Abstract: A series of wind-tunnel tests on a NACA 0012 airfoil was conducted to simulate the aerodynamic effects of runback ice. The drag and lift effects on the airfoil were assessed using wind-tunnel balance for three geometries of triangular section ice shapes at three different chordal positions. The results show a great degree of sensitivity of the aerodynamic flow characteristics to the shape and the chordal position of the ice accretion, and thereby highlight the need for realistic prediction models for runback ice.

Journal ArticleDOI
TL;DR: In this paper, the effect of longitudinal atmospheric turbulence on the dynamics of an airfoil with a hardening cubic structural nonlinearity in pitch is investigated, where the aerodynamics are taken as linear.
Abstract: The effect of longitudinal atmospheric turbulence on the dynamics of an airfoil with a hardening cubic structural nonlinearity in pitch is investigated. The aerodynamics is taken as linear. For the so-called nonexcited case, corresponding to zero turbulence, two distinct regions of dynamic response are obtained. For velocities below the e utter speed, the airfoil response is characterized as a stable equilibrium position; whereas after the onset of e utter, limit cycle oscillations occur. However, three different regions of dynamic behavior are observed when the airfoil is excited by longitudinal turbulence. For the lowest and highest ranges of velocity, the dynamic response is the same as that obtained for the nonexcited case. However, in the middle range of velocities, a new form of dynamic behavior is obtained, where the airfoil response is concentrated about the equilibrium position. The existence of this new region of dynamic behavior is attributed to the parametric nature of the excitation. In addition, for the excited case, e utter occurs at a lower velocity than for the nonexcited case; whereas the onset of limit cycle oscillations occurs at a higher velocity.

Journal ArticleDOI
TL;DR: In this paper, a technique for modeling unsteady three-dimensional compressible viscous flow over lifting rotors in hover and forward e ight is described, which has three modules: 1) a compressible Navier-Stokes solver for modeling the viscous e flow over the rotor and the rotor near wake; 2) an inviscid, isentropic potential e ow regions far away from the rotor, and 3) a Lagrangian model for capturing and convecting the rotor wake once it leaves the Navier Stokes domain.
Abstract: A technique for modeling unsteady three-dimensional compressible viscous e ow over lifting rotors in hover and forward e ight is described. The e ow solver has three modules: 1 ) a compressible Navier› Stokes solver for modeling the viscous e ow over the rotor and the rotor near wake; 2 ) a compressible potential e ow solver for modeling the inviscid, isentropic potential e ow regions far away from the rotor, and 3) a Lagrangian model for capturing and convecting the rotor wake once it leaves the Navier› Stokes domain. Results are presented for viscous e ow over a two-bladed untwisted rotor and a UH-60A rotor in hover. Good agreement is found with measurements.

Journal ArticleDOI
TL;DR: In this paper, an analysis has been performed to define the physical flow processes that could have generated the highly unusual rolling-moment characteristics measured on a 76-deg/40-deg double-delta wing, descrihing high-amplitude pitch oscillations at high angles of attack and nonzero angle of sideslip.
Abstract: The increasing performance demands on advanced aircraft, including maneuvers at high angles of attack, has led to a need for the prediction of vehicle aerodynamics that are dominated by separated flow effects. For aircraft with highly swept wing leading edges, the challenge is to fully understand the flow physics behind the observed dramatic effects of vortex breakdown. An analysis has been performed to define the physical flow processes that could have generated the highly unusual rolling-moment characteristics measured on a 76-deg/40-deg double-delta wing, descrihing high-amplitude pitch oscillations at high angles of attack and nonzero angle of sideslip

Journal ArticleDOI
TL;DR: In this article, a semi-empirical approach is used to predict the location of vortex breakdown and its variation with incidence, coupled to vortex lift expressions based on the leading-edge suction analogy.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this article, a nonstationary random response (NRC) based method for utter boundary prediction of a wing based on a simple bending-torsion wing model is proposed.
Abstract: A time-domain method for the e utter boundary prediction of a wing based on the nonstationary random response is proposed. The feature of this method is that a stability parameter is used as the measure of the aeroelastic stability margin instead of a conventional modal damping. The effectiveness of a stability parameter for the e utter boundary prediction is shown using a simple bending ‐ torsion wing model. Numerical studies are conducted to examine the performance of the method under the nonstationary condition. An application to supersonic wind-tunnel e utter testing data shows that the proposed method is effective to the prediction of the e utter boundary in the actual e utter testing.

Journal ArticleDOI
TL;DR: In this paper, an analytical queueing model that captures key variables in the aircraft de-parture process and offers an approach toward airport capacity estimation and departure delay prediction is presented.
Abstract: This paper develops and implements an analytical queueing model for an aircraft departure process. The model is formulated using data collected at LaGuardia Airport in June 1994. Departure demand is represented by a nonhomogeneous Poisson process, and service times are modeled as appropriate mixtures of exponential stages. Transient analysis of the resulting Markovian system is performed to produce a time-dependent plot of anticipated departure delay. The model and analytical results yield useful insights for airport capacity estimation and departure delay prediction. ROWING congestion at major U.S. airports has created a need for better understanding of factors that can lead to aircraft departure delays. This article presents an analytical queueing model that captures key variables in the aircraft de- parture process and offers an approach toward airport capacity estimation and departure delay prediction. The model is de- veloped and demonstrated using data collected from New York City' s LaGuardia Airport (LGA) during a single week in June 1994. LGA was selected because the airport has characteristics common to many U.S. facilities, including the frequent occur- rence of signie cant departure delays. Like many airports, LGA is cone gured with two intersecting runways. Normal operating procedures assign a primary de- parture runway, which can be viewed as the single server in a queueing system. Several dee nitions are useful in formulating an appropriate queueing model. Departure is synonymous with service completion, which occurs when an aircraft completes takeoff and clears the runway environment sufe ciently for an- other aircraft to be granted takeoff clearance. Service demand occurs when an aircraft enters the departure queue after leav- ing a passenger gate (pushback) and taxiing to the runway. Departure delay is the difference between service demand time and the initiation of service (clearance for takeoff ). Roll-out time is the total time between pushback and takeoff clearance (sum of taxi time and departure delay ). Initial analysis of the LGA activity data reveals that roll-out time varies greatly with time of day, primarily because of time- dependent variation in the frequency of scheduled pushbacks. The queueing model is consequently designed to capture var- iability in pushback rates and runway service time to produce a time-dependent plot of expected roll-out time. While this type of transient analysis has been explored for some aspects of airport operation, the departure process has received rela- tively little attention. There are various published investiga- tions of airport arrival (landing) processes. 1 › 6


Journal ArticleDOI
TL;DR: In this article, two methods for predicting transonic rotor noise for helicopters in hover and forward flight were compared with one another and with experimental data for both hover and advancing rotor cases.
Abstract: This paper compares two methods for predicting transonic rotor noise for helicopters in hover and forward flight. Both methods rely on a computational fluid dynamics (CFD) solution as input to predict the acoustic near and far fields. For this work, the same full-potential rotor code has been used to compute the CFD solution for both acoustic methods. The first method employs the acoustic analogy as embodied in the Ffowcs Williams-Hawkings equation, including the quadrupole term. The second method uses a rotating Kirchhoff formulation. Computed results from both methods are compared with one another and with experimental data for both hover and advancing rotor cases. The results are quite good for all cases tested. The Kirchhoff method was somewhat sensitive to the location of Kirchhoff surface, if the surface was positioned too close to the rotor blade. The acoustic analogy method was not as sensitive to the extent of volume included in the quadrupole calculation. The computational requirements of both methods are comparable; in both cases these requirements are much less than the requirements for the CFD solution.

Journal ArticleDOI
TL;DR: In this article, the results for the unsteady lift and pitching moment on two-dimensional airfoils penetrating sharp-edged traveling gusts are obtained for the incompressible case, exact results are given and are generalized numerically for any gust e eld by means of Duhamel superposition.
Abstract: By means of the reverse e ow theorems, results are obtained for the unsteady lift and pitching moment on two-dimensional airfoils penetrating sharp-edged traveling gusts. Both downstream and upstream traveling gusts are considered. For the incompressible case, exact results are given and are generalized numerically for any gust e eld by means of Duhamel superposition. Results are then given for the airloads and acoustics generated by a two-dimensional airfoil encountering a vortex convecting at different gust speed ratios. Numerical results for the traveling sharp-edged gust problem are also derived for subsonic e ows by means of exact linear theory. Further results for the subsonic case are computed by means of an Euler e nite difference method. It is found that the gust speed ratio has substantial effects on the unsteady airloads and will be an important parameter to represent in helicopter rotor aeroacoustic problems.