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The Spectral Volume (SV) method is extended to the 2D Euler equations. The focus of this paper is to study the performance of the SV method on multidimensional non-linear systems. Implementation details including total variation diminishing (TVD) and total variation bounded (TVB) limiters are presented. Solutions with both smooth features and discontinuities are utilized to demonstrate the overall capability of the SV method.
C-mode scanning acoustic microscopy (C-SAM) is a nondestructive inspection technique that uses ultrasound to show the internal feature of a specimen. A very high or ultra-high-frequency ultrasound passes through a specimen to produce a visible acoustic microimage (AMI) of its inner features. As ultrasound travels into a specimen, the wave is absorbed, scattered or reflected. The response is highly sensitive to the elastic properties of the materials and is especially sensitive to air gaps. This specific characteristic makes AMI the preferred method for finding "air gaps" such as delamination, cracks, voids, and porosity. C-SAM analysis, which is a type of AMI, was widely used in the past for evaluation of plastic microelectronic circuits, especially for detecting delamination of direct die bonding. With the introduction of the flip-chip die attachment in a package; its use has been expanded to nondestructive characterization of the flip-chip solder bumps and underfill. Figure 1.1 compares visual and C-SAM inspection approaches for defect detection, especially for solder joint interconnections and hidden defects. C-SAM is specifically useful for package features like internal cracks and delamination. C-SAM not only allows for the visualization of the interior features, it has the ability to produce images on layer-by-layer basis. Visual inspection; however, is only superior to C-SAM for the exposed features including solder dewetting, microcracks, and contamination. Ideally, a combination of various inspection techniques - visual, optical and SEM microscopy, C-SAM, and X-ray - need to be performed in order to assure quality at part, package, and system levels. This reports presents evaluations performed on various advanced packages/assemblies, especially the flip-chip die version of ball grid array/column grid array (BGA/CGA) using C-SAM equipment. Both external and internal equipment was used for evaluation. The outside facility provided images of the key features that could be detected using the most advanced C-SAM equipment with a skilled operator. Investigation continued using in-house equipment with its limitations. For comparison, representative X-rays of the assemblies were also gathered to show key defect detection features of these non-destructive techniques. Key images gathered and compared are: Compared the images of 2D X-ray and C-SAM for a plastic LGA assembly showing features that could be detected by either NDE technique. For this specific case, X-ray was a clear winner. Evaluated flip-chip CGA and FCBGA assemblies with and without heat sink by C-SAM. Only the FCCGA package that had no heat sink could be fully analyzed for underfill and bump quality. Cross-sectional microscopy did not revealed peripheral delamination features detected by C-SAM. Analyzed a number of fine pitch PBGA assemblies by C-SAM. Even though the internal features of the package assemblies could be detected, C-SAM was unable to detect solder joint failure at either the package or board level. Twenty times touch ups by solder iron with 700degF tip temperature, each with about 5 second duration, did not induce defects to be detected by C-SAM images. Other techniques need to be considered to induce known defects for characterization. Given NASA's emphasis on the use of microelectronic packages and assemblies and quality assurance on workmanship defect detection, understanding key features of various inspection systems that detect defects in the early stages of package and assembly is critical to developing approaches that will minimize future failures. Additional specific, tailored non-destructive inspection approaches could enable low-risk insertion of these advanced electronic packages having hidden and fine features.
The Iowa Flood Studies (IFloodS) is a NASA Global Precipitation Measurement (GPM) ground measurement campaign, which took place in eastern Iowa from May 1 to June 15, 2013. The goals of the field campaign were to collect detailed measurements of surface precipitation using ground instruments and advanced weather radars while simultaneously collecting data from satellites passing overhead. Data collected by the radars and other ground instruments, such as disdrometers and rain gauges, will be used to characterize precipitation properties throughout the vertical column, including the precipitation type (e.g., rain, graupel, hail, aggregates, ice crystals), precipitation amounts (e.g., rain rate), and the size and shape of raindrops. The impact of physical processes, such as aggregation, melting, breakup and coalescence on the measured liquid and ice precipitation properties will be investigated. These ground observations will ultimately be used to improve rainfall estimates from satellites and in particular the algorithms that interpret raw data for the upcoming GPM mission's Core Observatory satellite, which launches in 2014. The various precipitation data collected will eventually be used as input to flood forecasting models in an effort to improve capabilities and test the utility and limitations of satellite precipitation data for flood forecasting. In this preliminary study, the focus will be on analysis of NASA NPOL (S‐band, polarimetric) radar (e.g., radar reflectivity, differential reflectivity, differential phase, correlation coefficient) and NASA 2D Video Disdrometers (2DVDs) measurements. Quality control and processing of the radar and disdrometer data sets will be outlined. In analyzing preliminary cases, particular emphasis will be placed on 1) documenting the evolution of the rain drop size distribution (DSD) as a function of column melting processes and 2) assessing the impact of range on ground‐based polarimetric radar estimates of DSD properties.
Line Integral Convolution (LIC), introduced by Cabral and Leedom in 1993, is an elegant and versatile technique for representing directional information via patterns of correlation in a texture. Although most commonly used to depict 2D flow, or flow over a surface in 3D, LIC methods can equivalently be used to portray 3D flow through a volume. However, the popularity of LIC as a device for illustrating 3D flow has historically been limited both by the computational expense of generating and rendering such a 3D texture and by the difficulties inherent in clearly and effectively conveying the directional information embodied in the volumetric output textures that are produced. In an earlier paper, we briefly discussed some of the factors that may underlie the perceptual difficulties that we can encounter with dense 3D displays and outlined several strategies for more effectively visualizing 3D flow with volume LIC. In this article, we review in more detail techniques for selectively emphasizing critical regions of interest in a flow and for facilitating the accurate perception of the 3D depth and orientation of overlapping streamlines, and we demonstrate new methods for efficiently incorporating an indication of orientation into a flow representation and for conveying additional information about related scalar quantities such as temperature or vorticity over a flow via subtle, continuous line width and color variations.
BACKGROUND Astronauts returning from long-duration exposure to microgravity frequently exhibit alterations in sensorimotor function leading to postural imbalance, impaired locomotion, and operational challenges to manual control. Mission duration and individual responses often influence both the severity of performance decrements and the variability in adaptation timelines. Postflight disruptions during functional tasks are often detected through body-worn inertial measurement unit (IMU) devices. While IMU sensors are relatively compact, the long-term wear may lead to discomfort, displacement of the sensors on the body, and restrictions in movement or crew behavior. Although IMU data offers valuable insights from a research standpoint, interpreting changes in pre- and post-flight measures can be difficult for crew support personnel beyond the research domain, which can hinder the application for medical assessments and rehabilitation. Finally, the availability of inertial sensors in-flight is limited. There is a need for unobtrusive monitoring tools to improve our ability to monitor adaptation following gravitational transitions in various postflight evaluations and rehabilitation settings. Markerless motion capture (MMC) is an evolving unobtrusive technology that builds upon decades of research with marker-based motion capture systems to provide 3D human pose estimation from multiple synchronized 2D camera views using deep learning algorithms. Markerless technology can revolutionize how data is captured pre- and post-flight and potentially in-flight during intravehicular activity by enabling pose estimation of multiple crew members from onboard camera hardware. METHODS The following presents the initial evaluation of a state-of-the-art commercial-off-the-shelf MMC system, Theia Markerless, compared to IMU devices during various ground-based functional tasks and environmental conditions. The featured functional tasks include assessments from Human Research Program (HRP) funded studies such as Sensorimotor Standard Measures and Sensorimotor Assessments. Synchronous data collected using both motion capture and IMUs are analyzed for six male and female subjects of varying anthropometry. The analysis includes limited assessments of clothing, capture volume configurations, and the tool's sensitivity to detecting performance changes after a spaceflight analog centrifuge exposure. The development of visualization tools to enhance the application of the pose estimation output is also presented. RESULTS Initial results demonstrate comparable root mean square error (RMSE) to existing literature evaluating markerless and marker-based motion capture systems. Considering the relative functional range of motion of the cervical spine, normalized error values for the markerless system’s accuracy of the head was 0.032 in pitch, 0.025 in roll, and 0.018 in yaw plane of motion across a subset of functional tasks. The raw RMSE values were 3.49, 2.25, and 2.81 degrees respectively. For the torso, results suggest normalized errors of 0.469 in pitch, 0.191 in roll, and 0.307 in yaw planes of motion and raw RMSE values of 3.52, 1.53, and 3.07 degrees respectively. The data suggests the functional demands of a particular task influences the estimation accuracy of the MMC system where more dynamic motion and cases where subjects are not upright may introduce diminished tracking accuracy. DISCUSSION The following work lays the foundation for future implementations leveraging markerless motion capture to assess the time course of recovery and provide insight for rehabilitation protocols to enhance crew readiness for the resumption of daily activities. These tools offer effective methods for anonymizing sensitive crew data, facilitating numerous applications across research, medical, and rehabilitation groups. Collaborations with the Anthropometry and Biomechanics Facility will provide further comparisons of the Markerless system to a marker-based system. ACKNOWLEDGEMENT</ This work is supported by NASA’s Exploration Systems Development Mission Directorate Mars Campaign Office Crew Health Countermeasures.
An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.
Thrust vector control (TVC) systems for rocket engine propulsion traditionally use a simple linear relationship to convert between actuator forces and torques about the engine gimbal’s center-of-rotation (COR). As shown in Equation (1), the torque about the gimbal COR is proportional to the applied actuator force and the TVC moment arm (MA)—the perpendicular distance between the TVC actuator’s line-of-action (LOA) and the engine gimbal’s COR. While this fundamental relationship remains valid and accurate in a two-dimensional (2D), one-degree-of-freedom (1-DOF) context—particularly in its non-linear formulation as described in the ER63 Technical Bulletin TB-02 (Derivation of Thrust Vector Control (TVC) Engine-Gimbal / Actuator Moment-Arm Geometry)—it becomes limited when extended to three-dimensional (3D), two-degree-of-freedom (2-DOF) analyses. In 3D, out-of-plane angular displacements can arise, causing the gimbaled engine plane-of-motion to become non-coplanar with the respective actuator plane-of-motion. Such misalignments occur due to the rod-end (RE) and/or tail-stock (TE) mounting geometry of individual TVC actuators. These geometric complexities lead to inaccuracies in calculating engine torques and corresponding actuator forces if only the traditional TVC MA relationship is employed. For higher gimbal angular displacements (e.g., greater than 5 degrees), these inaccuracies become more pronounced, necessitating a more robust mathematical framework. This document presents a comprehensive 3D (2-DOF) derivation of a transformation matrix that accurately converts between gimbaled engine torques and TVC actuator forces. By incorporating the necessary geometric and rotational considerations, this new approach corrects the limitations of the traditional TVC MA method. Subsequent sections compare the newly formulated approach to the traditional method, demonstrating its enhanced accuracy and reliability for a broad range of gimbaled engine conditions.
Statistical analysis of test data is currently the preferred method of creating models for uncharacterized side loading in rocket nozzles. However, statistical analysis requires multiple data sets to be reliable; getting these sets requires building and testing multiple rocket motors, which is not feasible given the incredible time and cost required to do so. By using a combination of geometry, simplified finite element analysis (FEA) analogs, and algebra we can create a limited predictive model from only one test data set. Once created, the model requires only the input from one strain gauge located at each yaw and pitch attachment bracket for the actuation system. This process is not computationally intensive, therefore saving an abundance of time and budget over using full 3D FEA models to develop a similar predictive model. To develop the model, conversion factors between the strain at the gauge locations and corresponding actuator load is derived from the data. These conversion factors are used to create a “conversion ellipse” that bounds the constitutive properties of the nozzle as one lumped factor. Using a 2D cross-sectional analog of the nozzle exit plane, we create a function that allows us to determine the azimuthal location of the unexpected load based on the ratio between yaw and pitch strain readings. Combining this with the “conversion ellipse” yields a function that given the strain reading outputs an induced actuator load, regardless of the azimuthal location of the unexpected load. As previously mentioned, this predictive model is limited in its application as there is inaccuracy introduced by the use of data by only one test as well as simplifying assumptions. This approach makes a useful tool to quickly determine whether uncharacterized actuator loading events can damage actuation systems or induce loading that exceeds design limits.
The flow through a 2D experimental diffuser with channel width 2.60 cm and divergence angle (2 theta) 9 or 20 deg is investigated experimentally for inlet Reynolds number 78,300 and velocity 43.9 m/s, with and without vertical rods to generate inlet turbulence in excess of the limits defined by Hoffmann (1981) and Hoffmann and Gonzales (1983). Measurements are obtained using a thermal wall-flow-direction probe and a single hot-wire velocity probe, and the results are presented graphically. Significant increases in the pressure-recovery coefficient of the diffuser (10 percent at 9 deg and 22 percent at 20 deg) are attributed to the action of turbulence to reduce distortion and delay separation, thus creating an altered flow condition with symmetrical velocity profiles.
With an increased emphasis on greener air transports and sustainable aviation, the modeling of laminar-to-turbulent boundary layer transition is anticipated to have an added significance, particularly in the applications related to laminar flow technology. However, unmanned aerial vehicles, crewed reentry vehicles, and ground-to-flight extrapolation all benefit from transition models. Because no single transition model is ideal for the complete spectrum of applications, it is useful to incorporate a variety of models in general-purpose CFD solvers, such as the NASA OVERFLOW Overset CFD code. While the Langtry-Menter 𝛄 − 𝑹𝒆 𝛉𝒕 model, currently available in OVERFLOW, has been widely used for CFD predictions of flows with laminar, transitional, and turbulent boundary layers, it does not possess the Galilean invariance property, a desirable attribute for rotorcraft applications. To help overcome that limitation, we have recently implemented Menter's baseline version of the SST-based γ transition model, along with a Galilean invariant stationary crossflow extension within OVERFLOW (version 2.3e). An initial assessment of the newly implemented model has been carried out using 2D benchmark cases including flat plates and the NLF-0416 airfoil, addressing several transition scenarios ranging from bypass transition due to freestream turbulence, natural transition via Tollmien-Schlichting instabilities, and transition due to a laminar separation bubble. The crossflow extension has been applied to the infinite swept NLF(2)-0415 wing and the 6:1 prolate spheroid. Wherever possible, the results were obtained on a sequence of meshes to ascertain the grid convergence behavior, which has been evaluated through global metrics such as force coefficients as well as local values of the skin-friction coefficient at selected points near and within the transition region. Overall, the model appears to be correctly implemented and the results show promise for further development using the framework of the γ transition model.
The estimation of rain drop size distribution (DSD) parameters from polarimetric radar observations is accomplished by first establishing a relationship between differential reflectivity (Z(sub dr)) and the central tendency of the rain DSD such as the median volume diameter (D0). Since Z(sub dr) does not provide a direct measurement of DSD central tendency, the relationship is typically derived empirically from rain drop and radar scattering models (e.g., D0 = F[Z (sub dr)] ). Past studies have explored the general sensitivity of these models to temperature, radar wavelength, the drop shape vs. size relation, and DSD variability. Much progress has been made in recent years in measuring the drop shape and DSD variability using surface-based disdrometers, such as the 2D Video disdrometer (2DVD), and documenting their impact on polarimetric radar techniques. In addition to measuring drop shape, another advantage of the 2DVD over earlier impact type disdrometers is its ability to resolve drop diameters in excess of 5 mm. Despite this improvement, the sampling limitations of a disdrometer, including the 2DVD, make it very difficult to adequately measure the maximum drop diameter (D(sub max)) present in a typical radar resolution volume. As a result, D(sub max) must still be assumed in the drop and radar models from which D0 = F[Z(sub dr)] is derived. Since scattering resonance at C-band wavelengths begins to occur in drop diameters larger than about 5 mm, modeled C-band radar parameters, particularly Z(sub dr), can be sensitive to D(sub max) assumptions. In past C-band radar studies, a variety of D(sub max) assumptions have been made, including the actual disdrometer estimate of D(sub max) during a typical sampling period (e.g., 1-3 minutes), D(sub max) = C (where C is constant at values from 5 to 8 mm), and D(sub max) = M*D0 (where the constant multiple, M, is fixed at values ranging from 2.5 to 3.5). The overall objective of this NASA Global Precipitation Measurement Mission (GPM/PMM Science Team)-funded study is to document the sensitivity of DSD measurements, including estimates of D0, from C-band Z(sub dr) and reflectivity to this range of D(sub max) assumptions. For this study, GPM Ground Validation 2DVD's were operated under the scanning domain of the UAHuntsville ARMOR C-band dual-polarimetric radar. Approximately 7500 minutes of DSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSD's were then used as input to a T-matrix model for computation of polarimetric radar moments at C-band. All necessary model parameterizations, such as temperature, drop shape, and drop fall mode, were fixed at typically accepted values while the D(sub max) assumption was allowed to vary in sensitivity tests. By hypothesizing a DSD model with D(sub max) (fit) from which the empirical fit to D0 = F[Z(sub dr)] was derived via non-linear least squares regression and a separate reference DSD model with D(sub max) (truth), bias and standard error in D0 retrievals were estimated in the presence of Z(sub dr) measurement error and hypothesized mismatch in D(sub max) assumptions. Although the normalized standard error for D0 = F[Z(sub dr)r] can increase slightly (as much as from 11% to 16% for all 7500 DSDs) when the D(sub max) (fit) does not match D(sub max) (truth), the primary impact of uncertainty in D(sub max) is a potential increase in normalized bias error in D0 (from 0% to as much as 10% over all 7500 DSDs, depending on the extent of the mismatch between D(sub max) (fit) and D(sub max) (truth)). For DSDs characterized by large Z(sub dr) (Z(sub dr) > 1.5 to 2.0 dB), the normalized bias error for D0 estimation at C-band is sometimes unacceptably large (> 10%), again depending on the extent of the hypothesized D(sub max) mismatch. Modeled errors in D0 retrievals from Z(sub dr) at C-band are demonstrated in detail and comparedo similar modeled retrieval errors at S-band and X-band where the sensitivity to D(sub max) is expected to be less. The impact of D(sub max) assumptions to the retrieval of other DSD parameters such as Nw, the liquid water content normalized intercept parameter, are also explored. Likely implications for DSD retrievals using C-band polarimetric radar for GPM are assessed by considering current community knowledge regarding D(sub max) and quantifying the statistical distribution of Z(sub dr) from ARMOR over a large variety of meteorological conditions. Based on these results and the prevalence of C-band polarimetric radars worldwide, a call for more emphasis on constraining our observational estimate of D(sub max) within a typical radar resolution volume is made
The Mars Science Laboratory Curiosity landed in Gale crater in August 2012 with the goal to identify and characterize habitable environments on Mars. Curiosity has been studying a series of sedimentary rocks primarily deposited in fluviolacustrine environments approximately 3.5 Ga. Minerals in the rocks and soils on Mars can help place further constraints on these ancient aqueous environments, including pH, salinity, and relative duration of liquid water. The Chemistry and Mineralogy (CheMin) X-ray diffraction and X-ray fluorescence instrument on Curiosity uses a Co X-ray source and charge-coupled device detector in transmission geometry to collect 2D Debye-Scherrer ring patterns of the less than 150 micron size fraction of drilled rock powders or scooped sediments. With an angular range of approximately 2.52deg 20 and a 20 resolution of approximately 0.3deg, mineral abundances can be quantified with a detection limit of approximately 1-2 wt. %. CheMin has returned quantitative mineral abundances from 16 mudstone, sandstone, and aeolian sand samples so far. The mineralogy of these samples is incredibly diverse, suggesting a variety of depositional and diagenetic environments and different source regions for the sediments. Results from CheMin have been essential for reconstructing the geologic history of Gale crater and addressing the question of habitability on ancient Mars.
Detailed, time-dependent, 2D numerical simulations with full hydrogen-oxygen chemistry are used to investigate the effects of gravity on the stability and structure of laminar flames in lean, premixed hydrogen-air mixtures. The calculations show that the effects of gravity becomes more important as the lean flammability limit is approached. In a 12 percent hydrogen-air mixture, gravity plays only a secondary role in determining the multidimensional structure of the flame with the stability and structure of the flame controlled primarily by the thermo-diffusive instability mechanism. However, in leaner hydrogen-air mixtures gravity becomes more important. Upward-propagating flames are highly curved and evolve into a bubble rising upwards in the tube. Downward-propagating flames are flat or even oscillate between structures with concave and convex curvatures. The zero-gravity flame shows only cellular structures. Cellular structures which are present in zero gravity can be suppressed by the effect of buoyancy for mixtures leaner than 11 percent hydrogen. These observations are explained on the basis of an interaction between the processes leading to buoyancy-induced Rayleigh-Taylor instability and the thermo-diffusive instability.
The main problems with understanding and predicting solar activity are tightly linked to limitations in describing the global evolution of the Sun from the deep interior to the corona. Because of the complexity of interactions in a wide range of dynamical, turbulent, and spatial scales and dramatic changes in thermodynamic and magnetic field conditions, only physics-based models can provide essential background to generate reliable solar activity forecasts. However, performing accurate model calibration and estimating uncertainties is often challenging due to the unavailability of a long time series of observations. To mitigate these limitations, we have developed the Global Solar Activity (GSA) Data Portal, which enables convenient access to a variety of modern and historical data. The portal supports a dynamic visualization for 1D time series (such as the sunspot number and solar irradiance) and quick-look visualization for 2D datasets (e.g., synoptic magnetograms, the solar internal rotation, and flows). The GSA portal includes a search engine that enables data retrieval from user-specified data sources and time intervals. In this presentation, we will discuss the current and upcoming capabilities of the data portal and its potential applications for space weather studies.
The effects of the inertia of a particle on its flow-tracking accuracy and particle dispersion are studied using direct numerical simulations of 2D compressible free shear layers in convective Mach number (Mc) range of 0.2 to 0.6. The results show that particle response is well characterized by tau, the ratio of particle response time to the flow time scales (Stokes' number). The slip between particle and fluid imposes a fundamental limit on the accuracy of optical measurements such as LDV and PIV. The error is found to grow like tau up to tau = 1 and taper off at higher tau. For tau = 0.2 the error is about 2 percent. In the flow visualizations based on Mie scattering, particles with tau more than 0.05 are found to grossly misrepresent the flow features. These errors are quantified by calculating the dispersion of particles relative to the fluid. Overall, the effect of compressibility does not seem to be significant on the motion of particles in the range of Mc considered here.
High-lift system aerodynamics has been gaining attention in recent years. In an effort to improve aircraft performance, comprehensive studies of multi-element airfoil systems are being undertaken in wind-tunnel and flight experiments. Recent developments in Computational Fluid Dynamics (CFD) offer a relatively inexpensive alternative for studying complex viscous flows by numerically solving the Navier-Stokes (N-S) equations. Current limitations in computer resources restrict practical high-lift N-S computations to two dimensions, but CFD predictions can yield tremendous insight into flow structure, interactions between airfoil elements, and effects of changes in airfoil geometry or free-stream conditions. These codes are very accurate when compared to strictly 2D data provided by wind-tunnel testing, as will be shown here. Yet, additional challenges must be faced in the analysis of a production aircraft wing section, such as that of the NASA Langley Transport Systems Research Vehicle (TSRV). A primary issue is the sweep theory used to correlate 2D predictions with 3D flight results, accounting for sweep, taper, and finite wing effects. Other computational issues addressed here include the effects of surface roughness of the geometry, cove shape modeling, grid topology, and transition specification. The sensitivity of the flow to changing free-stream conditions is investigated. In addition, the effects of Gurney flaps on the aerodynamic characteristics of the airfoil system are predicted.
In this paper, a gas-kinetic BGK model is constructed for the Rayleigh-Benard thermal convection in the incompressible flow limit, where the flow field and temperature field are described by two coupled BGK models. Since the collision times and pseudo-temperature in the corresponding BGK models can be different, the Prandtl number can be changed to any value instead of a fixed Pr=1 in the original BGK model. The 2D Rayleigh-Benard thermal convection is studied and numerical results are compared with theoretical ones as well as other simulation results.
FEM is here used to ascertain the stability and aeroelastic response of thin, 2D panels subjected to Mach 0.8-2.5 flows. In the absence of shocks, it is found that the Euler equations used to represent the unsteady flowfield dynamics predict response behaviors resembling those obtained via potential flow methods. Where shocks do play a significant role in the overall motion of the panel, divergence and limit cycle flutter are observed. In the Mach 1.4-1.5 range, flutter involved the higher modes of the panel, tending toward possible chaotic motion.