Showing papers on "Supersonic speed published in 2003"

Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions

Abstract: This paper is the first part of a two-part study on the mechanisms of the receptivity to disturbances of a Mach 4.5 flow over a flat plate by using both direct numerical simulations (DNS) and linear stability theory (LST). The main objective of the current paper is to study the linear stability characteristics of the boundary-layer wave modes and their mutual resonant interactions. The numerical solutions of both steady base flow and unsteady flow induced by forcing disturbances are obtained by using a fifth-order shock-fitting method. Meanwhile, the LST results are used to study the supersonic boundary-layer stability characteristics relevant to the receptivity study. It is found that, in addition to the conventional first and second modes, there exist a family of stable wave modes in the supersonic boundary layer. These modes play a very important role in the receptivity process of excitation of the unstable Mack modes, especially the second mode. These stable modes are termed mode I, mode II, etc., in this paper. Though mode I and mode II waves are linearly stable, they can have resonant (synchronization) interactions with both acoustic waves and the Mack-mode waves. Therefore, the stable wave modes such as mode I and mode II are critical in transferring wave energy between the acoustic waves and the unstable second mode. The effects of frequencies and wall boundary conditions for the temperature perturbations on the boundary-layer stability and receptivity are also studied.

Large-Eddy Simulation of Supersonic Cavity Flowfields Including Flow Control

Abstract: Large-eddy simulations of supersonic cavity flowfields are performed using a high-order numerical method. Spatial derivatives are represented by a fourth-order compact approximation that is used in conjunction with a sixth-order nondispersive filter. The scheme employs a time-implicit approximately factored finite difference algorithm, and applies Newton-like subiterations to achieve second-order temporal and fourth-order spatial accuracy. The Smagorinsky dynamic subgrid-scale model is incorporated in the simulations to account for the spatially underresolved stresses. Computations at a freestream Mach number of 1.19 are carried out for a rectangular cavity having a length-to-depth ratio of 5:1. The computational domain is described by 2.06×10 7 grid points and has been partitioned into 254 zones, which were distributed on individual processors of a massively parallel computing platform. Active flow control is applied through pulsed mass injection at a very high frequency, thereby suppressing resonant acoustic oscillatory modes

Aeroelastic Dynamic Analysis of a Full F-16 Configuration for Various Flight Conditions

Abstract: An overview is given of recent advances in a three-field methodology for modeling and solving nonlinear fluid-structure interaction problems, and its application to the prediction of the aeroelastic frequencies and damping coefficients of a full F-16 configuration in various subsonic, transonic, and supersonic airstreams is reported. In this three-field methodology the flow is described by the arbitrary Lagrangian-Eulerian form of the Euler equations, the structure is represented by a detailed finite element model, and the fluid mesh is unstructured, dynamic, and updated by a robust torsional spring analogy method. Simulation results are presented for stabilized, accelerated, low-g, and high-g flight conditions, and correlated with flight-test data. Consequently, the practical feasibility and potential of the described computational-fluid-dynamics-based computational method for the flutter analysis of high-performance aircraft, particularly in the transonic regime, are discussed.

Ion acceleration in plasmas emerging from a helicon-heated magnetic-mirror device

Abstract: Using laser-induced fluorescence, measurements have been made of metastable argon-ion, Ar+*(3d4F7/2), velocity distributions on the major axis of an axisymmetric magnetic-mirror device whose plasma is sustained by helicon wave absorption. Within the mirror, these ions have sub-eV temperature and, at most, a subthermal axial drift. In the region outside the mirror coils, conditions are found where these ions have a field-parallel velocity above the acoustic speed, to an axial energy of ∼30 eV, while the field-parallel ion temperature remains low. The supersonic Ar+*(3d4F7/2) are accelerated to one-third of their final energy within a short region in the plasma column, ⩽1 cm, and continue to accelerate over the next 5 cm. Neutral-gas density strongly affects the supersonic Ar+*(3d4F7/2) density.

Hypersonic Flight Transition Data Analysis Using Parabolized Stability Equations with Chemistry Effects

Abstract: Analysis of boundary-layer transition data from supersonic quiet tunnels, as well as flight experiments has indicated that, in the absence of surface roughness and high levels of freestream disturbances, linear stability theory can be used as a guide for estimation of the onset of transition. Transition data from two different hypersonic flight experiments are analyzed using parabolized stability equations, including chemistry effects associated with high-temperature boundary layers. The results suggest that transition in both of these cases is caused by the amplification of second mode disturbances. The analysis shows that, consistent with previous findings for supersonic flows where first mode disturbances induce laminar-turbulent transition, N factors of about 9.5 and 11.2 correlate the transition onset locations from these two high-Mach-number experiments. Therefore, the e N method can be used for smooth body transition prediction in hypersonic vehicle design. The effect of chemistry on boundary-layer stability is also studied and is shown to be destabilizing.

On some aspects of gas dynamics of the cold spray process

Abstract: This paper presents an overview of results of recent studies conducted at the Institute of Theoretical and Applied Mechanics of the Siberian Division of the Russian Academy of Science in the field of gas dynamics and heat transfer of the supersonic air jet under conditions typically used in the cold spray process. These studies are related to various aspects of the problem including a flow in the nozzle and the outflow of the jet, as well as effects of the interaction of the jet with a flat obstacle. They are conducted with a supersonic nozzle with a rectangular section at the exit with a Mach number M 0 between 2 and 3.5. The gas flow in the nozzle is theoretically and experimentally studied. It is shown that the boundary layer on the walls of the nozzle affects significantly the flow parameters (for example, Mach number M, pressure p, temperature T, and density ρ of the gas). A method of calculation of the gas parameters in the flow core of the nozzle is suggested, and it is shown that they depend mainly on the ratio of the nozzle width to its length. The results of the investigation of the supersonic air jets with stagnation temperature ranging from 300–600 K flowing in the atmosphere are presented. The corresponding dimensions of the jets, profiles, and axial distributions of the gas parameters are obtained. The interactions of the supersonic jet with the flat obstacle are studied. Self-similarity of the distribution of the pressure and of the Mach number on the obstacle surface is shown for the jets with various values of the Mach number and the angle of impingement. The oscillation regimen of the jet impingement, as well as a compressed layer structure is observed with the aid of a Schliren visualization technique. Some problems of heat exchange of the jets with the obstacle are considered. Distributions of stagnation temperature and heat exchange coefficient in the near-wall jet are obtained. The temperature of the obstacle for the stationary case is calculated, and it is shown that for heat conductive materials the surface temperature is lower than the stagnation temperature due to the redistribution of heat inside of the substrate.

Control of supersonic impinging jet flows using supersonic microjets

Abstract: Supersonic impinging jets, such as those occurring in the next generation of short takeoff and vertical landing aircraft, generate a highly oscillatory e ow with very high unsteady loads on the nearby aircraft structures and the landing surfaces. These high-pressure and acoustic loads are also accompanied by a dramatic loss in lift during hover.Previousstudies of supersonic impinging jets suggestthatthehighly unsteady behavioroftheimpinging jets is due to a feedback loop between the e uid and acoustic e elds, which leads to these adverse effects. A unique active control technique was attempted with the aim of disrupting the feedback loop, diminishing the e ow unsteadiness, and ultimatelyreducing theadverseeffectsofthise ow.Flowcontrolwasimplementedbyplacingacirculararray of 400-πm-diamsupersonicmicrojetsaroundtheperipheryofthemainjet.Thiscontrolapproachwasverysuccessful in disrupting the feedback loop in that the activation of the microjets led to dramatic reductions in the lift loss (40%), unsteady pressure loads (11 dB), and near-e eld noise (8 dB). This relatively simple and highly effective control technique makes it a suitable candidate for implementation in practical aircraft systems. NUNDERSTANDINGoftheimpingingjete owe eld isnecessary for the design of efe cient short takeoff and vertical landing (STOVL) aircraft. When such STOVL aircraft are operating in hovermode,thatis,in closeproximityto theground,thedownwardpointing lift jets produce high-speed, hot e ow that impinges on the landing surface and generates the direct lift force. It is well known that in this cone guration several e ow-induced effects can emerge, which substantially diminish the performance of the aircraft. In particular, a signie cant lift loss can be induced due to e ow entrainment bytheliftingjetsfromtheambientenvironmentinthe vicinityofthe airframe. Other adverse phenomena include severe ground erosion on the landing surface and hot gas ingestion into the engine inlets. In addition, the impinging e owe eld usually generates signie cantly highernoiselevelsrelativetothatofafreejetoperatingundersimilar conditions. Increased overall sound pressure levels (OASPL) associated with the high-speed impinging jets can pose an environment pollution problem and adversely affect the integrity of structural elements in the vicinity of the nozzle exhaust due to acoustic loading. Moreover, the noise and the highly unsteady pressure e eld are frequently dominated by high-amplitude discrete tones, which may match the resonant frequencies of the aircraft panels, thus further exacerbating the sonic fatigue problem. These problems become more pronounced when the impinging jets are supersonic, the operating regime of the STOVL version of the future joint strike e ghter. In addition, the presence of multiple impinging jets can potentially further aggravate these effects due to the strong coupling between the jets and the emergence of an upward-moving fountain e ow e owing opposite to the lift jets. 1 A

Turbulence and noise suppression of a high-speed jet by water injection

Abstract: An experimental investigation has been carried out on a supersonic jet of air issuing from an M =1.44 convergingx2013;diverging rectangular nozzle of aspect ratio 4. Particle13; image velocimetry measurements of the flow field along with near-field acoustic measurements were made. The effect of injection of a small amount of water (x223C;5% of the mass flow rate of the jet) into the shear layer of the jet, on the unsteady flow structure and sound generation were examined. The presence of water droplets in the jet modified the turbulence structure significantly, resulting in axial and normal r.m.s.velocity reductions of about 10% and 30%, respectively, as compared to that of a13; normal jet. An even larger effect is found on the peak values of the turbulent shear stress with a reduction of up to 40%. The near-field noise levels (OASPL) were found13; to reduce by about 2x2013;6 dB depending on the location of the injection and the water mass flow rate. Far-field acoustic measurements carried out on a heated M =0.9 (jet13; exit velocity=525msx2212;1) jet show significant (6 dB) reductions in the OASPL with moderate amounts of water injection (17% of the mass flow rate of the jet) suggesting13; that the technique is viable at realistic engine operating conditions.

Condensation limited cooling in supersonic expansions

Abstract: Supersonic expansions of pure and seeded rare gases have been investigated experimentally, measuring the translational and rotational temperatures. The lowest achievable translational temperature in the jet depends on both gas properties as well as on experimental boundary conditions like nozzle shape and nozzle–skimmer distance. We show that there is a limit to the lowest temperature achieved, under practical conditions, set by condensation in the jet. A large cluster binding energy enhances the formation of clusters and they release their condensation energy into the beam. The spatial confinement of the jet extends to long distances, and is sensitive to the shape of the nozzle. The confined jet forms a narrow cone of high intensity, and results in increased collision probability and cluster formation.

Shock leakage through an unsteady vortex-laden mixing layer: application to jet screech

Abstract: In an under-expanded supersonic jet, the interaction between shock-cell structure and vortices in a mixing layer generates intense tonal noise, called jet screech. This noise generation can be explained as a shock-leakage process through an unsteady vortex-laden mixing layer. This paper studies the shock-leakage mechanism based on a geometrical theory and direct numerical simulation (DNS) in two dimensions. In the limit of weak shocks, the analysis becomes analogous to geometrical acoustics: the eikonal equation demonstrates that shock waves tend to leak near the saddle points between vortices. Analysing the wavenumber vector, it is shown that the local vorticity behaves as a barrier against shocks. Using the unsteady DNS data, trajectories of the shock fronts are computed with the time dependent eikonal equation. Furthermore, the interaction between unsteady vortices and a compression wave is solved using DNS. The geometrical theory shows good agreement with DNS for shock-front evolution, but the amplitude of the leaked waves agrees only qualitatively. This study also investigates the effects of a temperature difference across the mixing layer. The analysis based on total internal reflection and the numerical results of both geometrical acoustics and DNS indicate that the direction of the radiated shock noise tends to rotate downstream as the jet temperature increases.

Coherent Anti-Stokes Raman Spectroscopic Thermometry in a Supersonic Combustor

Abstract: An experiment has been conducted to acquire data for the validation of computational fluid dynamics codes used in the design of supersonic combustors. The flow in a supersonic combustor, consisting of a diverging duct with a single downstream-angled wail injector, is studied. Combustor entrance Mach number is 2 and enthalpy nominally corresponds to Mach 7 flight. The primary measurement technique is coherent anti-Stokes Raman spectroscopy, but surface pressures and temperatures have also been acquired. Modern design of experiment techniques have been used to maximize the quality of the data set (for the given level of effort) and to minimize systematic errors. Temperature maps are obtained at several planes in the flow for a case in which the combustor is piloted by injecting fuel upstream of the main injector and one case in which it is not piloted. Boundary conditions and uncertainties are characterized.

The HyShot Scramjet Flight Experiment - Flight Data and CFD Calculations Compared

Abstract: An analysis has been made using CFD of selected points on the HyShot scramjet flight experiment trajectory. Two-dimensional intake calculations have been done to assess the influence of angle of attack on the performance of the intake and cowl shock/boundary layer bleed duct, and have shown that at low angles of attack the configuration is well behaved, but at high angles of attack the cowl shock separates the boundary layer on the main intake ramp. This sends a separation shock into the combustion chamber. For selected altitudes during the flight for which the maximum angle of attack is a local minimum and for which there is zero yaw, intake and combustor calculations have been made. The calculations consistently predict that supersonic combustion has been obtained. At higher altituudes, reasonable agreement between the measured and predicted pressures is found, although the fuel-off pressures are underpredicted by approximately 15%. At lower altitude, further into the experiment, the flight data is well underpredicted. Further investigations of the flight data are required to assess this, including the possibility of leading edge ablation and/or intake distortion due to the high flight heat loads.

Comparison of molecular tagging velocimetry data and direct simulation Monte Carlo simulations in supersonic micro jet flows

Abstract: We present results of a combined experimental computational study of free jet flow produced by a 1 mm (height)×5 mm (span) nominally Mach 2 supersonic jet. Two-dimensional maps of ux, the component of velocity parallel to the principal flow axis, are obtained experimentally, by acetone molecular tagging velocimetry (MTV), and computationally, by the direct simulation Monte Carlo (DSMC) method, at a stagnation pressure and temperature of 10 torr and 300 K, respectively. In all cases, direct comparison of the experimental data and the predictions from DSMC showed excellent agreement, with only minor deviations which, in most cases, can be ascribed to either the inherent uncertainty in the MTV or small uncertainties in the measured wall pressures.

A comparison of modelling methods for polydispersed wet‐steam flow

Abstract: Spontaneous nucleation of water droplets in moist air or steam may result in droplet spectra which are complex in shape and which span a broad range of sizes. This is particularly true if the flow is transonic or supersonic with shock waves present, or if an already droplet-laden flow re-expands to give secondary or tertiary nucleations. Computation of such flows requires careful modelling of the size distributions if two-phase behaviour is to be accurately predicted. In this paper, three methods are presented for treating size distributions and growth of the liquid phase in condensing steam: a mixed Eulerian–Lagrangian method, a fully Eulerian method, and a method based on moments of the droplet spectra. These are compared by computing condensing flow within a one-dimensional supersonic nozzle under conditions that yield very different types of size spectra. Copyright © 2003 John Wiley & Sons, Ltd.

Flowfield Around Spike-Tipped Bodies for High Attack Angles at Mach 4.5

Abstract: The requirements for the design of a new short-range high-velocity missile are both the drag reduction and the correct information acquisition for the optoelectronic sensors embedded in the hemispherical nose. High anglesof attack must be studied to fulfill the maneuverability requirements of present and future missiles. A supersonic missile generates a bow shock around its blunt nose, which causes rather high surface pressure and temperature and, as a result, the development of high drag and damage of embedded sensors. The pressure and the temperature on the hemispherical nose surface can be substantially reduced if an oblique shock is generated by a forward-facing spike. Both the experiments and the computations are carried out to study the flowfield around three-dimensional blunt bodies equipped with forward-facing spikes for a large range of attack angles at a Mach number of 4.5. A blunt body, a classical disk-tip spike, a sphere-tip spike, and a biconical-tip spike are studied. The experiments involve high-pressure shock tunnel investigations using a shock tube facility. The differential interferometry technique is applied to visualize the flowfield around the different missile spike geometries. The differential interferogram pictures as well as surface pressure measurements are compared with numerical results. Numerical simulations based on steady-state three-dimensional Navier-Stokes computations are performed to predict the drag, the lift, and the pitching moment for the blunt body and for each spike-tipped missile. The computations allow one to bring out the advantages of each spike geometry in comparison to the blunt body.

Detached eddy simulations of supersonic flow over cavity

Abstract: Detached Eddy Simulations are performed for unsteady three-dimensional supersonic turbulent flow over an open L/D = 5 cavity at free-stream Mach number of 1.19. Numerical results are obtained from the explicit solution and Shear-Stress-Transport based simulations using the 3 rd order Roe scheme. Computational results are presented for the unsteady vortex and shock structures. The acoustic response of the cavity is presented in the form of pressure fluctuations and sound pressure level spectra. The computational results are compared to existing experimental data and to results obtained from twodimensional Reynolds Averaged Navier Stokes with algebraic turbulence model.

An aerodynamic design method for supersonic natural laminar flow aircraft

Abstract: The computation of boundary-layer properties and laminar-to-turbulent transition location is a complex problem generally not undertaken in the context of aircraft design. Yet this is just what must be done if an aircraft designer is to exploit the advantages of laminar flow while making the proper trade-offs between inviscid drag, structural weight and skin friction. To facilitate this process, a new tool is developed. This thesis presents a designoriented method for the aerodynamic analysis of supersonic wings including approximate means for estimating transition and total drag. The method consists of a boundary-layer solver combined with a fast and robust transition scheme based on the well-known en criterion. The boundary-layer analyses employed are computationally inexpensive but sufficiently accurate to provide guidance for advanced design studies and to be incorporated in multidisciplinary design optimization. The boundary-layer solver is based on an enhanced quasi-3D sweep/taper theory which is shown to agree well with three-dimensional Navier-Stokes results. The transition calculation scheme is implemented within the boundary-layer solver and automatically triggers a turbulence model at the predicted transition front. The laminar instability amplification values used in the en criterion are based on algebraic fits to linear stability results for streamwise and crossflow modes. This parametric transition prediction method compares favorably with exact linear theory on relevant geometries and successfully computes transition for a supersonic flight test. Integration of the present design method with numerical optimization is discussed, and airfoil section and wing/body shape optimizations are performed. Wing/body drag minimization studies suggest that low-sweep supersonic aircraft with extensive laminar flow may have a significant drag advantage over conventional designs.

Diffusion in supersonic turbulent compressible flows.

Abstract: We investigate diffusion in supersonic turbulent compressible flows. Supersonic turbulence can be characterized as network of interacting shocks. We consider flows with different rms Mach numbers and where energy necessary to maintain dynamical equilibrium is inserted at different spatial scales. We find that turbulent transport exhibits superdiffusive behavior due to induced bulk motions. In a comoving reference frame, however, diffusion behaves normal and can be described by mixing-length theory extended into the supersonic regime.

Control of the flow past bodies using localized energy addition to the supersonic oncoming flow

Abstract: A possibility of controlling the supersonic flow past bodies of different shape by adding a small amount of energy to the freestream is studied experimentally. In the numerical calculations the model of a spatially distributed energy source based on the Euler equations for a perfect gas is used. The gasdynamic features of the flow around energy sources are studied, some new effects are revealed, and analytical models for their description are developed. It is shown that by optimizing the energy source parameters it is possible to initiate irregular regimes of flow past bodies characterized by radical changes in the bow shock structure with the formation of return flow zones. In this case an appreciable drag reduction can be achieved with high efficiency of energy expenditure.

Experimental and Numerical Study of Stall Flutter in a Transonic Low-Aspect Ratio Fan Blisk

Abstract: Experiments are performed on a modern design transonic shroudless low-aspect ratio fan blisk that experienced both subsonic/transonic and supersonic stall-side flutter. High-response flush mounted miniature pressure transducers are utilized to measure the unsteady aerodynamic loading distribution in the tip region of the fan for both flutter regimes, with strain gages utilized to measure the vibratory response at incipient and deep flutter operating conditions. Numerical simulations are performed and compared with the benchmark data using an unsteady three-dimensional nonlinear viscous computational fluid dynamic (CFD) analysis, with the effects of tip clearance, vibration amplitude, and the number of time steps-per-cycle investigated. The benchmark data are used to guide the validation of the code and establish best practices that ensure accurate flutter predictions.Copyright © 2003 by ASME

Aeroacoustic Properties of Supersonic Cavity Flows and Their Control

Abstract: A detailed experimental study of supersonic, Mach 2, flow over a 3D cavity was conducted using shadowgraph, particle image velocimetry (PIV), and unsteady surface pressure measurements. Large-scale structures in the cavity shear layer and visible disturbances inside the cavity were observed. The PIV data reveals the highly unsteady nature of the entire flowfield and the presence of a large recirculation zone with reverse velocities as high as 40 % of the freestream velocity. Supersonic microjets at the leading edge are used to control the cavity flow and suppress resonance in the cavity. Using minimal mass flux through the microjets, overall sound pressure level (OASPL) was reduced by greater than 9 dB with tonal reductions greater than 20 dB. The PIV data reveals that microjet injection modifies the cavity shear layer and results in a significant reduction in the unsteadiness of the cavity velocity-field.

Kinetic simulations of the solar wind from the subsonic to the supersonic regime

Abstract: We present and discuss a completely self-consistent kinetic simulation of a steady state transonic solar type wind. The equations of motion of an equal number of protons and electrons plunged in a central gravitational field and a self-consistent electric field are integrated numerically. Particles are allowed to make binary collisions with a Coulombian scattering cross-section. The velocity distributions of the particles injected at the boundaries of the simulation domain are taken to be Maxwellian. As anticipated by previous authors we find that the transonic solution implies the existence of a peak in the proton equivalent potential at some distance above the sonic critical point. Collisions appear to be the fundamental ingredient in the process of accelerating the wind to supersonic velocities. For a given temperature at the base of the simulation domain the acceleration efficiency decreases with decreasing density. The reason is that the plasma has to be sufficiently collisional for the heat flux to be converted efficiently into plasma bulk velocity. Concerning the heat flux we find that even when in the vicinity of the sonic point the collisional mean free path of a thermal particle is is significantly smaller than the typical scales of variation of the density or the temperature, the electron heat flux cannot be described conveniently by the classical Spitzer-Harm conduction law; not even in most of the subsonic region. Indeed, in the simulations where a transonic wind forms the heat flux has been found to strongly exceed the Spitzer-Harm flux, in opposition to recently published results from multi-moment models. We emphasize that given the high coronal temperatures we use in our simulations (3 times the typical solar values) we do not expect the results presented in this report to be uncritically transposable to the case of the "real" solar wind. In particular, the quantitative aspects of our results must be handled with some care.

Nonequilibrium Radio Frequency Discharge Plasma Effect on Conical Shock Wave: M = 2.5 Flow

Abstract: An experimental study of shock modie cation in an M =2:5 supersonic e ow of nonequilibrium plasma over a cone is discussed. The experiments are conducted in a nonequilibrium plasma supersonic wind tunnel. Recent experiments at the Ohio State University using a supersonic plasma e ow over a quasi-two-dimensional wedge showed that an oblique shock can be considerably weakened by a transverse rf discharge plasma. The previously observed shock weakening, however, has been found consistent with a temperature rise in the boundary layers heated by the discharge. In thepresent study, theboundary-layereffects on theshock waveare reduced by placing an entire cone model into a supersonic inviscid core e ow. The electron density in the supersonic plasma e ow in the test section is measured using microwave attenuation. The ionization fraction in the discharge is in the same range as in the previous plasma shock experiments, up to ne/N =(1.2‐3.0)£10 i7 . The results do not show any detectable shock weakening by the plasma. This strongly suggests that the previously observed shock weakening and dispersion in nonequilibrium plasmas are entirely due to thermal effects.

Using Aeroelastic Modes for Nonlinear Panel Flutter at Arbitrary Supersonic Yawed Angle

Abstract: It is commonly accepted that six in vacuo natural modes are needed for converged, limit-cycle oscillations of isotropic rectangular plates exposed to supersonic flow at zero yaw angle to the principle panel length. For isotropic or orthotropic rectangular plates under an arbitrary nonzero yawed supersonic flow, then 36 or 6 x 6 natural modes are needed; for laminated anisotropic rectangular plates even at zero yaw angle, 36 or fewer natural modes are needed. To deal with such a large number of modes is computationally costly for flutter analysis, causing complexity and difficulty in designing controllers for flutter suppression. A thorough examination and understanding of the panel limit-cycle behavior leads to the use of aeroelastic modes for supersonic nonlinear panel flutter analysis. The system equations of motion are formulated first in structural node degrees of freedom. Aeroelastic modes are selected and determined, and the system equations is expressed in the aeroelastic modal coordinates. Limit-cycle amplitudes are then determined using numerical integration. Examples show that the number of modes could be greatly reduced by using aeroelastic modes. For determining limit-cycle oscillations of isotropic or anisotropic composite rectangular plates at zero or an arbitrary yawed flow angle, only two aeroelastic modes are needed; but six to seven aeroelastic modes are needed for designing controllers for flutter suppression.