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There are still some challenges, such as grid quality, numerical stability, and boundary schemes, in the practical application of high-order finite difference schemes for complex configurations. This study presents some improved strategies that indicate potential engineering applications of high-order schemes. The formally fifth-order weighted compact nonlinear scheme developed by the authors is implemented on point-matched multiblock structured grids, which are generated over complex configurations to ensure the grid quality of each component block. The information transmission between neighboring blocks is carried out by new characteristic-based interface conditions that directly exchange the spatial derivatives on each side of an interface by means of a characteristic-based projection to keep the high-order accuracy and high resolution of a spatial difference scheme. The high-order scheme combined with the interface conditions is shown to be asymptotically stable. The engineering-oriented applications of the high-order strategy are demonstrated by solving several two- and three-dimensional problems with complex grid systems. DOI: 10.2514/1.J050285

A semi-analytical model for the prediction of the broadband noise due to the interaction between turbulent rotor wakes and a rotor in contra-rotating open rotors is presented. The unsteady loading of the rear rotor is modeled using classical isolated flat-plate theory. Strip theory is used to treat the spanwise variations of aerodynamic quantities and blade geometry. The turbulent wake is assumed to be homogeneous and isotropic turbulence that is modulated by a train of wake profiles. The model is presented in detail and insight into its modal behavior is provided. A parameter study is conducted to investigate the effects of blade number, rotor-rotor gap and rotor speeds on broadband noise emissions due to rotor-wake/rotor interaction in contra-rotating open rotors. Scaling laws for sound power levels have been established analytically and show good agreement with the results of the parameter study. DOI: 10.2514/1.J050566

A hybrid mesh generation method is described to discretize complex geometries. The idea behind this hybrid method is to combine the orthogonality and directionality of a structured grid, the efficiency and simplicity of a Cartesian grid, and the flexibility and ease of an unstructured grid in an attempt to develop an automatic, robust, and fast hybrid mesh generation method for configurations of engineering interest. A semistructured quadrilateral grid is first generated on the wetted surfaces. A background Cartesian grid, covering the domain of interest, is then constructed using a Quadtree-based Cartesian Method. Those Cartesian cells overlapping with the semistructured grids or locating outside of computational domain are then removed using an Alternating Digital Tree method. Finally, an unstructured grid generation method is used to generate unstructured triangular cells to fill all empty regions in the domain as a result of the trimming process. The automatic placement of sources at the geometrical irregularities is developed to render these regions isotropic, thus effectively overcoming the difficulty of generating highly stretched good-quality elements in these regions. The self-dividing of the exposed semistructured elements with high aspect ratio and the adaptation of the background mesh using the cell size information from the exposed semistructured elements for generating Cartesian cells are introduced to improve the quality of unstructured triangular elements and guarantee the success of the unstructured grid generation in the void regions. The developed hybrid grid generation method is used to generate a hybrid grid for a number of test cases, demonstrating its ability and robustness to mesh complex configurations. DOI: 10.2514/1.J050491

There are various condensation methods for substructure techniques in structural dynamics. A generalized condensation method that comprises most of the classical condensation techniques and allows for arbitrary mode shapes within a standardized approach is described here. Within the framework of this method, a flexible boundary method is introduced that allows for elastic and mass-loaded boundaries for eigenmode determination, as well as for mode shapes that reflect the influence of damping. The relationship to other approaches taken from existing literature is examined. For damped structures, the flexible boundary method provides a condensation process that takes into account the influence of the complex eigenmodes of structures with nonproportional and high damping. To couple substructures with different component damping, the equivalent structural damping approach is provided. The problems associated with diagonal system damping of substructures and the full triple matrix product are overcome. DOI: 10.2514/1.J050484

Reliability-based design often uses the Monte--Cario method as a sampling procedure for predicting failure. The combination of designing for very small failure probabilities (~[10.sup.-8] - [10.sup.-6]) and using computationally expensive finite element models, makes Monte--Carlo simulations very expensive. This paper uses an improved sampling procedure for calculating the probability of failure, called separable Monte--Carlo method. The separable Monte--Carlo method can improve the accuracy of the traditional crude Monte--Carlo when response and capacity are independent. In previous research, accuracy of separable Monte--Carlo for a simple limit state was estimated via expectation calculus for a simple form of the limit state. In this paper, error estimates for a general limit state are developed through bootstrapping, and it is demonstrated that the estimates are reasonably accurate. Separable Monte--Carlo allows us to choose different sample sizes of the response and capacity in the limit state, and the paper demonstrates that bootstrapping may be used to estimate the contribution of the response and capacity to the total error. When the accuracy of the probability of failure is not good enough, the paper proposes reformulation of the limit state as another way to reduce uncertainty associated with the expensive random variable (usually the response). The accuracy of the bootstrapping estimates and the effectiveness of regrouping is demonstrated with an example of prediction of failure in a composite laminate with the Tsai--Wu failure criterion. DOI: 10.2514/1.J050439

The present work has the objective of demonstrating the capabilities of a spectral finite volume scheme implemented in a cell-centered finite volume context for unstructured meshes. The two-dimensional Euler equations are considered to represent the flows of interest. The spatial discretization scheme is developed to achieve high resolution for flow problems governed by hyperbolic conservation laws. Roe's flux difference splitting method is used as the numerical approximate Riemann solver. Several applications are performed in order to assess the method capability compared to data available in the literature and also compared to an weighted essentially nonoscillatory scheme. There is good agreement with the comparison data, and efficiency improvements over the weighted essentially nonoscillatory method are observed. The features of the present methodology include an implicit time-marching algorithm; second-, third-, and fourth-order spatial resolution; exact high-order domain boundary representation; and a hierarchical moment limiter to treat flow solution discontinuities. DOI: 10.2514/1.J050395

The use of surrogates (also known as metamodels) for facilitating optimization and statistical analysis of computationally expensive simulations has become commonplace. Surrogate models are usually fit to be unbiased (i.e., the error expectation is zero). However, in certain applications, it might be important to safely estimate the response (e.g., in structural analysis, the maximum stress must not be underestimated in order to avoid failure). In this work we use safety margins to conservatively compensate for fitting errors associated with surrogates. We propose the use of cross validation for estimating the required safety margin for a desired level of conservativeness (percentage of safe predictions). The approach was tested on three algebraic examples for two basic surrogates: namely, kriging and polynomial response surface. For these examples we found that cross validation is effective for selecting the safety margin. We also applied the approach to the probabilistic design optimization of a composite laminate. This design under uncertainty example showed that the approach can be successfully used in engineering applications. DOI: 10.2514/1.J050327

Compressible large-eddy simulations of turbulent flow over a wall-mounted hump with active flow control are performed and compared with previous experiments. The flow is characterized by the unsteady separation before the steep trailing edge, which naturally reattaches downstream of the hump to form an unsteady turbulent separation bubble. The low Mach number large-eddy simulation demonstrated a good prediction of surface pressure coefficient, separation-bubble length, and velocity profiles compared with experiments. The effect of compressibility on the baseline flow is documented and analyzed and is found to increase the separation-bubble size, due to a reduced growth rate. Control is applied just before the natural separation point via steady suction and zero-net-mass-flux oscillatory forcing, and steady suction is shown to be more effective in decreasing the size of the separation bubble and pressure drag for the control parameters investigated. Controlled flow at a compressible subsonic Mach number is applied, and found to be slightly less effective than the same control parameters at low Mach numbers. DOI: 10.2514/1.44756

The replacement of the analysis portion of an optimization problem by its equivalent metamodel usually results in a lower computational cost. In this paper, a conventional nonapproximative approach is compared against three different metamodels: quadratic-interpolation-based response surfaces, Kriging, and artificial neural networks. The results obtained from the solution of four different case studies based on aircraft design problems reinforces the idea that quadratic interpolation is only well-suited to very simple problems. At higher dimensionality, the usage of the more complex Kriging and artificial neural networks models may result in considerable performance benefits. DOI: 10.2514/1.45790

This paper deals with aerodynamic shape optimization using a high-fidelity solver. Because of the computational cost needed to solve the Reynolds-averaged Navier--Stokes equations, the performance of the shape must be improved using very few objective function evaluations, despite the high number of design variables. In our framework, the reference algorithm is a quasi-Newton gradient optimizer. An adjoint method inexpensively computes the sensitivities of the functions, with respect to design variables, to build the gradient of the objective function. As usual, aerodynamic functions show numerous local optima when the shape varies, and a more global optimizer is expected to be beneficial. Consequently, a kriging-based optimizer is set up and described. It uses an original sampling refinement process that adds up to three points per iteration by using a balancing between function minimization and error minimization. To efficiently apply this algorithm to high-dimensional problems, the same sampling process is reused to form a cokriging (gradient-enhanced model) based optimizer. A comparative study is then described on two drag-minimization problems depending on 6 and 45 design variables. This study was conducted using an original set of performance criteria, characterizing the strength and weakness of each optimizer in terms of improvement, cost, exploration, and exploitation. DOI: 10.2514/1.45331

This paper deals with the numerical study of installation effects, a subject which comes under the more general purpose of aircraft noise prediction and reduction. As an example of installation effects, we study here the potential acoustic shield that an empennage airfoil could constitute against the aft fan noise emitted by a coaxial engine. To that end, we make use of a structured computational aeroacoustics solver (sAbrinA code), taking benefits from its coupling functionality in order to handle more easily the solid obstacles that are to be accounted for. Several full-3D simulations are then conducted, which involve an exhaust installed over an empennage airfoil and allotted with two thermodynamics conditions (quiescent medium and takeoff flight). Being validated against boundary element method results, such calculations provide a validation of the numerical strategy adopted here as well as a good illustration of its abilities to solve installed engine noise problems. Coming in addition to such methodological outcomes, these calculations deliver important conceptual insights, demonstrating the potential high efficiency of empennage airfoils in terms of aft fan noise reduction. DOI: 10.2514/1.42153

Formulas for calculating the effect of centerbody scattering on the sound radiated from an advanced open rotor are presented. The effects of blade sweep and distributed blade loading are considered. Mach number effects are also implicitly included in the model. The work extends a previously published method and applies it to a practical situation in which scattering by the centerbody has a significant effect on the radiated sound field. DOI: 10.2514/1.44659

This paper deals with the experimental validation of an analytical trailing-edge noise model dedicated to low-speed fans operating in free field. The model is intrinsically related to the aerodynamics of the blades and should lead to a useful fast-running tool to be included in a blade-design process in an industrial context. The investigations are made on a two-bladed low-speed axial fan without shroud, installed inside an anechoic room. The blades are instrumented with two sets of embedded small-size microphones (2.5 mm diam), and the wall-pressure signals are acquired via a slip ring mounted on the fan axis. The chord-based Reynolds number is about 200,000, and the tip Mach number about 0.07. The data base is completed by far-field measurements made with a single microphone on a moving support. The analytical model is based on a previously published extension of Amiet's trailing-edge noise theory. A blade is split into several strips in the spanwise direction, and the model is applied to each strip. For this the input data are interpolated from the measurements performed with the aforementioned sets of microphones. The trailing-edge noise model is more reliable for observer positions within [+ or -]30[degrees] from the fan-rotation plane. DOI: 10.2514/1.43840

Measurements and predictions are made of a short-cowl coflowing jet with a bypass ratio of 8:1. The Reynolds number is 300,000, and the inlet Mach numbers are representative of aeroengine conditions. The low Reynolds number of the measurements makes the case well suited to the assessment of large-eddy-simulation-related strategies. The nozzle concentricity is carefully controlled to deal with the emerging metastability issues of jets with coflow. Measurements of mean quantities and turbulence statistics are made using both laser Doppler anemometry and particle image velocimetry. The simulations are completed on 6 x [10.sup.6], 12 x [10.sup.6], and 50 x [10.sup.6] cell meshes. To overcome near-wall modeling problems, a hybrid large-eddy-simulation--Reynolds-averaged-Navier--Stokes-related method is used. The near-wall Reynolds-averaged-Navier--Stokes layer is helpful in preventing nonphysical separation from the nozzle wall. DOI: 10.2514/1.44534

When carrying out design searches, traditional variable screening techniques can find it extremely difficult to distinguish between important and unimportant variables. This is particularly true when only a small number of simulations are combined with a parameterization that results in a large number of variables of seemingly equal importance. Here, the authors present a variable reduction technique that employs proper orthogonal decomposition to filter out undesirable or badly performing geometries from an optimization process. Unlike traditional screening techniques, the presented method operates at the geometric level instead of the variable level. The filtering process uses the designs that result from a geometry parameterization instead of the variables that control the parameterization. The method is shown to perform well in the optimization of a two-dimensional airfoil for the minimization of drag-to-lift ratio, producing designs better than those resulting from traditional kriging- based surrogate model optimization and with a significant reduction in surrogate tuning cost. DOI: 10.2514/1.41420

A new approach for the distribution of grid points on the surface and in the volume has been developed. In addition to the point and line sources of previous works, the new approach uses surface and volume sources for automatic curvature-based grid sizing and convenient point distribution in the volume. A new exponential growth function produces smoother and more efficient grids and provides superior control over the distribution of grid points in the field. All types of sources support anisotropic grid stretching, which not only improves the grid economy but also provides more accurate solutions for certain aerodynamic applications. The new approach does not require a threedimensional background grid as in the previous methods. Instead, it makes use of an efficient bounding-box auxiliary medium for storing grid parameters defined by surface sources. The new approach is less memory intensive and more efficient computationally. The grids generated with the new method either eliminate the need for adaptive grid refinement for certain class of problems or provide high-quality initial grids that would enhance the performance of many adaptation methods. DOI: 10.2514/1.41355

In this study, a deterministic compressible solver is coupled to a nonintrusive stochastic spectral projection method to propagate several aerodynamic uncertainties through a transonic steady flow around a NACA0012 airfoil. The stochastic model is solved in a generalized polynomial chaos framework. This approach combines the advantage of not modifying the existing deterministic solver while maintaining accurate representations of the stochastic solution and its statistics. The major difficulty of this work is to deal with deterministic transonic flows for which aerodynamics nonlinearities are reported in the uncertain probabilistic space. The efficiency of the present methodology are evaluated for the propagation of random disturbances associated with the angle of attack and the freestream Math number. An error analysis is carried out in order to determine appropriate physical and stochastic discretization levels. Different stochastic flow regimes are analyzed in details by means of various postprocessing procedures, including error bars, probabilistic density function of the aerodynamic field, and Sobol's coefficients. DOI: 10.2514/1.42637

The basic formulation of the least-squares method, based on the L2 norm of the residuals, is still widely used today for identifying elastic constants of aerospace materials from experimental data. While this method often works well, methods that can benefit from statistical information, such as the Bayesian method, may sometimes be more accurate. We seek situations with significant difference between the material properties identified by the two methods. For a simple three-bar truss example we illustrate three situations in which the Bayesian approach systematically leads to more accurate results: different sensitivity of the measured response to the parameters to be identified, different uncertainty in the measurements, and correlation among response components. When all three effects add up, the Bayesian approach can be much more accurate. Furthermore, the Bayesian approach has the additional advantage of providing the uncertainty in the identified parameters. We also compare the two methods for a more realistic problem of identification of elastic constants from natural frequencies of a composite plate. DOI: 10.2514/1.40922

An investigation of inlet injection in a scram jet having a three-dimensional inlet and an elliptical combustion was undertaken. Experiments were conducted using a test flow simulating a Mach 8.1 flight condition with an altitude of 32 km. The objective was to determine the feasibility of reducing the combustion-chamber length by injection of hydrogen fuel in the inlet. The study involved a self-starting three-dimensional inlet with an overall geometric contraction ratio of 5.80, of which 2.08 was internal. The fuel was injected through multiple portholes in the forward portion of the inlet to allow significant mixing upstream of the combustion chamber. The divergent elliptical combustion chamber had a length sized for fuel ignition and combustion only and used a fluid-dynamic ignition scheme requiring no physical obstructions to the towpath. Results indicated that inlet injection produced robust combustion at good combustion efficiency over a large fueling range up to an equivalence ratio of 0.92. A further key result was that no evidence of combustion was observed in the inlet. These experiments suggest that fuel injection in the inlet is a promising concept for higher-speed scramjet applications. DOI: 10.2514/1.J050052

Two techniques are proposed in a new regularization method for the inverse identification of local damages in a structure. One technique is the introduction of a new side condition, and the other technique restricts the range of variation of the regularization parameter by consistently choosing the optimal point on the L-curve. Both techniques fully make use of the information from results obtained in previous iteration steps. A plane frame structure is studied with two damaged elements and different levels of noise and model errors. Numerical results show that the proposed consistent regularization method is very effective at improving the results of the ill-conditioned inverse-problem phenomenon, compared with the Tikhonov regularization. DOI: 10.2514/1.43322

For many engineering and aerospace applications, detection and quantification of multiscale damage in fiber-reinforced composite structures is increasing in importance. Consequently, the development of an efficient and cost-effective diagnosis scheme that can accurately sense, characterize, and evaluate the existence of any form of damage will offer significant potential for improving the performance, reliability, and extending the operational life of these complex systems. We present an approach to characterize and classify different damage states in composite laminates by measuring the change in the signature of the resultant wave that propagates through the anisotropic media under forced excitation. The wave propagation is measured using surface-mounted piezoelectric transducers. Sensor signals collected from test specimens with various forms of induced damage are analyzed using a pattern-recognition algorithm known as the one-class support vector machines. The one-class support-vector-machine algorithm performs automatic anomaly detection and classification of damage signatures using various features from the sensor readings. The results obtained suggest that the one-class support-vector-machine algorithm, along with appropriate preprocessing techniques, can often achieve better accuracy than the popular k-nearest-neighbor method in detecting and classifying anomalies caused by structural defects, even when the perturbations caused in the sensor signals due to different damage states are minimal. DOI: 10.2514/1.37282

We consider the question of how to reconcile integrated forces and moments from a pressure-sensitive paint measurement with measured forces and moments from a balance. We show that it is possible to compute the smallest change in pressure distribution that would be required to bring the two sets of data into agreement. We refer to this as the gap distribution and show that it can be expressed in terms of a set of basis functions that are determined by the geometry of the test article. The use of these gap basis functions allows discrepancies in forces and moments to be expressed in terms of a common unit of measure, namely the magnitude of the implied gap distribution. We apply this gap analysis to data from a wind-tunnel test of the NASA Orion command module, for which both pressure-sensitive paint data and balance data are available. Results of the analysis confirm earlier suspicions that there was a problem with the normal component of force of the balance. Still, it is shown that application of the gap correction leads to improved pressure-sensitive paint data, as determined by the level of agreement with pressure tap data. The analysis procedure involving a pressure-gap distribution should be applicable to the comparison of balance data to integrated forces and moments from computational fluid dynamics calculations and other techniques. DOI: 10.2514/1.38376

Three-dimensional simulations are employed to examine the effect of inlet distortion and model fidelity with Reynolds averaged Navier--Stokes or large eddy simulation approaches for a generic circular cross-sectional supersonic combustor at a flight condition of Mach 6 and an altitude of about 24.2 km. To examine inlet distortion effects on combustion, frozen and finite rate chemistry simulations are performed on combustors connected to two different types of streamline-traced inlets (denoted 'Scoop' and 'Jaws') with the Wilcox k-[omega] turbulence model. For comparison, uniform inflow boundary condition to the combustor is also simulated. The metrics employed include qualitative assessments related to flow structure as well as quantitative values of fuel combustion efficiency and thrust ratios. The results indicate a complex overall effect of distortion due to inlet design. For Jaws, the increased pressure loss associated with distortion is mitigated slightly by improved combustion efficiency and better thrust performance. The Scoop inlet has lower distortion and better recovery, but the combustion coefficient is lower than Jaws. In the second part of this study, finite rate chemistry results with unsteady Reynolds averaged Navier--Stokes are compared with those from large eddy simulation with an uniform inflow profile. Differences in transient processes include the manner in which large-and small-scale structures originate and evolve in the cavity recirculation and downstream regions. The finer details observed with the large eddy simulation model have significant consequences on the overall field, including the unsteady position of the shock structure arising from the interaction of the incoming flow with the cavity shear layer, combustion processes, and injection jet interactions. DOI: 10.2514/1.43646

Reynolds-averaged and hybrid Reynolds-averaged/large-eddy simulations have been applied to a supersonic coaxial jet flow experiment. The experiment was designed to study compressible mixing flow phenomenon under conditions that are representative of those encountered in scram jet combustors. The experiment used either helium or argon as the inner jet nozzle fluid, and the outer jet nozzle fluid consisted of laboratory air. The inner and outer nozzles were designed and operated to produce nearly pressure-matched Math 1.8 flow conditions at the jet exit. The purpose of the computational effort was to assess the state of the art for each modeling approach and to use the hybrid Reynolds-averaged/large-eddy simulations to gather insight into the deficiencies of the Reynolds-averaged closure models. The Reynolds-averaged simulations displayed a strong sensitivity to choice of turbulent Schmidt number. The initial value chosen for this parameter resulted in an overpredictiou of the mixing layer spreading rate for the helium case, but the opposite trend was observed when argon was used as the injectant. A larger turbulent Schmidt number greatly improved the comparison of the results with measurements for the helium simulations, but variations in the Schmidt number did not improve the argon comparisons. The hybrid Reynolds-averaged/large-eddy simulations also overpredicted the mixing layer spreading rate for the helium ease, while underpredicting the rate of mixing when argon was used as the injectant. The primary reason conjectured for the discrepancy between the hybrid simulation results and the measurements centered around issues related to the transition from a Reynolds- averaged state to one with resolved turbulent content. Improvements to the inflow conditions were suggested as a remedy to this dilemma. Second-order turbulence statistics were also compared with their modeled Reynolds-averaged counterparts to evaluate the effectiveness of common turbulence closure assumptions. DOI: 10.2514/1.43771

Understanding the physics of supersonic combustion is the key to design a performing engine for scramjet-powered vehicles. Despite studies on supersonic combustion dating back to the 1950s, there are still numerous uncertainties and misunderstandings on this topic. The following questions need to be answered: How does compressibility affect mixing, flame anchoring, and combustion efficiency? How long must a combustor be to ensure complete mixing and combustion while avoiding prohibitive performance losses? How can reacting turbulent and compressible flows be modeled? Experimental results in the past have shown that supersonic combustion of hydrogen and air is feasible and takes place in a reasonable distance, which is a necessary requirement in actual hypersonic vehicles powered by supersonic combustion ramjets. These results are explained based on a theoretical analysis of the physical mechanisms driving mixing and combustion in supersonic airstreams, where they are found to be different from those in the incompressible regime. In particular, the classic Kolmogorov scaling is shown to be no longer strictly valid, and the flame regime is predicted to be significantly affected by compressibility and different from that of subsonic flames. This analysis is also supported by the results of the numerical simulations presented, showing that by generating sufficiently intense turbulence, a supersonic combustion flame is short and can indeed anchor within a small distance from fuel injectors, with the flame typically burning in the so-called flamelets-in- eddies regime. DOI: 10.2514/1.43652

The flowfield downstream of a strut-based injection system in a supersonic combustion ramjet is investigated using large-eddy simulation with a new localized dynamic subgrid closure for compressible turbulent mixing. Recirculations are formed at the base of the strut in the nonreacting flow and trap some of the injected fluid. The high levels of turbulence along the underexpanded hydrogen jets and in the shear layer lead to a high level of mixing of fuel and freestream fluids. Furthermore, the shear layer unsteadiness permits efficient large-scale mixing of freestream and injected fluids. In the reacting flowfield, the flame anchoring mechanism is, however, found to depend more on a recirculation region located downstream of the injectors than on their sides. A region of reverse flow is formed that traps hot products and radicals. Intermittent convection of hot fluid toward the injector occurs and preheats the reactants. DOI: 10.2514/1 .43647

A theoretical and experimental aeroelastic study of a typical airfoil section with control surface free play for nonzero angle of attack in low subsonic flow is presented. The study includes the flutter and limit cycle oscillation behavior and also the linear and nonlinear aeroelastic responses excited by periodic gust loads. The theoretical approach uses Peters's finite state airloads model. The experimental investigation has been carried out in the Duke University wind tunnel using a rotating slotted cylinder gust generator. The theoretical and experimental results show that the serf-excited aeroelastic limit cycle oscillation is sensitive to the effect of initial pitch angle. For the gust response, the effect of initial pitch angle is smaller for the plunge and pitch responses and is larger for the flap response. The fair to good quantitative agreement between theory and experiment verifies that the present analytical approach has reasonable accuracy and good computational efficiency for nonlinear aeroelastic response analysis of such systems. DOI: 10.2514/1.44538

We present and discuss results on the development and application of extremizing feedback control to high-speed and high Reynolds number axisymmetric jets. In particular, we demonstrate control authority on the near-field pressure of a Mach 0.9 jet with a Reynolds number based on jet diameter of 6.4 c [10.sup.5]. Open-loop forcing experimental results are presented, wherein localized are filament plasma actuators are shown to have two distinct effects on the irrotational near-field pressure, similar to their effects on the far-field acoustics reported earlier. At low forcing Stroubal numbers near the jet preferred mode, a large amplification in the pressure fluctuations is observed. At much higher forcing Strouhal numbers, an attenuation is observed in the pressure fluctuations over a broad range of excitation frequencies, especially in the axisymmetric mode of the pressure fluctuations. Previous experiments have shown that forcing the jet with these low and high Strouhal numbers results in jet mixing enhancement and farfield noise reduction, respectively. Two different gradient-free extremizing feedback control algorithms have been developed and implemented, each of which can perform online minimum seeking, as well as maximum seeking. Both methods demonstrate fast convergence to the optimum followed by steady operation. We also show that the far-field acoustic spectrum in steady-state operation of the closed-loop control is quite similar to that observed with optimal open-loop forcing. DOI: 10.2514/1.44012

A turbulence model that calculates the turbulent Prandtl and Schmidt numbers as part of the solution is presented. This model also accounts for compressibility effects, and addresses turbulence/chemistry interaction. Its predictions are compared with two experiments: an axisymmetric case involving mixing, hydrogen combustion, and ethylene combustion; and a three-dimensional ethylene mixing experiment. Fair to good agreement is indicated in the cases where data is available. Chemical mechanisms are found to have an influence on autoignition for hydrogen combustion cases, and on ignition location and flame size for hydrogen/ethylene combustion cases using reduced mechanisms. DOI: 10.2514/1.43213

This paper presents a reduced-order-modeling approach for nonlinear, multi-degree-of-freedom aerodynamic systems using multi-input Volterra theory. The method is applied to a two-dimensional, 2 degree-of-freedom transonic airfoil undergoing simultaneous forced pitch and heave harmonic oscillations. The so-called Volterra cross kernels are identified and shown to successfully model the aerodynamic nonlinearities associated with the simultaneous pitch and heave motions. The improvements in accuracy over previous approaches that effectively ignored the cross kernels by using superposition are demonstrated. DOI: 10.2514/1.38964

The method of analysis is a combination of Sander's thin shell theory and the classic finite element method, m which the nodal displacements are found from the exact solution of shell governing equations rather than approximated by polynomial functions. Piston theory with and without a correction factor for curvature is applied to derive aerodynamic damping and stiffness matrices. The influence of stress stiffness due to internal pressure and axial loading is also taken into account. Aeroelastic equations in hybrid finite element formulation are derived and solved numerically. Different boundary conditions of the shell, geometries, and flow parameters are investigated. In all study cases, the shell loses its stability due to coupled-mode flutter and a traveling wave is observed during this dynamic instability. The results are compared with existing experimental data and other analytical and finite element solutions. The present study shows efficient and reliable results that can be applied to the aeroelastic design and analysis of shells of revolution in aerospace vehicles. DOI: 10.2514/1.39580

Tremendous efforts have been devoted to developing efficient approaches to reliability analysis for multidisciplinary systems. Most of the approaches are only capable of dealing with random variables modeled by probability distributions. Both random and interval variables, however, may exist in multidisciplinary systems. Their propagation through coupled subsystems make s reliability analysis computationally expensive. In this work, a unified reliability analysis framework is proposed to deal with both random and interval variables in multidisciplinary systems. The framework is an extension of an existing unified uncertainty analysis framework for single-disciplinary problems. The new framework involves probabilistic analysis and interval analysis. Both probabilistic analysis and interval analysis are decoupled from each other and are performed sequentially. The first order reliability method is used for probabilistic analysis. Three supporting algorithms are developed. The effectiveness of the algorithms is demonstrated with a mathematical example and an engineering application. DOI: 10.2514/1.39696

We study the correspondence between analytical and empirical slow-flow analyses. Given a sufficiently dense set of sensors, measured time series recorded throughout a mechanical or structural system contains all information regarding the dynamics of that system. Empirical mode decomposition is a useful tool for decomposing the measured time series in terms of intrinsic mode functions, which are oscillatory modes embedded in the data that fully reproduce the time series. The equivalence of responses of the analytical slow-flow models and the dominant intrinsic mode functions derived from empirical mode decomposition provides a physics-based theoretical foundation for empirical mode decomposition, which currently is performed formally in an ad hoc fashion. To demonstrate correspondence between analytical and empirical slow flows, we derive appropriate mathematical expressions governing the empirical slow flows and based on analyticity conditions. Several nonlinear dynamical systems are considered to demonstrate this correspondence, and the agreement between the analytical and empirical slow dynamics proves the assertion. DOI: 10.2514/1.43207

The results obtained on two closed structural boxes composed by four graphite-epoxy curved stringer-stiffened panels, and manufactured by Agusta/Westland, are presented. The closed-box configuration allowed easily applying shear on each panel by subjecting the box to a torsion moment. The boxes were tested under combined axial compression and torque loading, both statically and cyclically. The tests allowed, on one hand, evaluating the effect of different procedures of loading application and, on the other hand, to investigate the influence of cyclic post-buckling combined loads in terms of global and local behaviors, as well as in terms of collapse modalities. The results show the reliability of these structures to safely operate in the postbuckling field, even when the buckling load is reached thousands of times during the operative life. DOI: 10.2514/1.42309

A new correlation-based transition model has been developed, which is built strictly on local variables. As a result, the transition model is compatible with modern computational fluid dynamics techniques such as unstructured grids and massively parallel execution. The model is based on two transport equations, one for intermittency and one for a transition onset criterion in terms of momentum-thickness Reynolds number. A number of validation papers have been published on the basic formulation of the model. However, until now the full model correlations have not been published. The main goal of the present paper is to publish the full model and release it to the research community so that it can continue to be further validated and possibly extended or improved. Included in this paper are a number of test cases that can be used to validate the implementation of the model in a given computational fluid dynamics code. The authors believe that the current formulation is a significant step forward in engineering transition modeling, as it allows the combination of transition correlations with general-purpose computational fluid dynamics codes. There is a strong potential that the model will allow the first-order effects of transition to be included in everyday industrial computational fluid dynamics simulations. DOI: 10.2514/1.42362

This paper focuses on the analysis of limit-cycle oscillations of aeroelastic systems with multiple lumped nonlinearities. It aims at a comprehensive investigation capable of identifying limit cycles and their stability. The goal is achieved by using an incremental complexity approach. At the beginning, a solution based on dual-input describing functions is sought, to find both symmetric and asymmetric cycles approximated to their first harmonic. The related stability is investigated afterward by extending the single-input describing function 'quasi-static' method. Such an approach is simple and quite similar to well-established existing methods used to evaluate linear flutter conditions directly. If higher harmonics are required, an extended harmonic balance based on a numerical minimization in the frequency domain is adopted and the stability of the computed solutions is then determined by using Floquet theory. The presented approach is applied to several nonlinear aeroelastic examples and validated by comparing stable limit cycles with solutions obtained through direct time marching integrations.

Sound pressure level contours and spectral sound distributions around the Vega launch system are computed by means of a standard empirical model developed by NASA and a novel hybrid empirical/computational aeroacoustics approach. The empirical prediction is validated against available noise spectra measured on a scaled mock-up, showing a fairly good agreement when standard values for the model constants are used. The jet sources employed in the empirical prediction are then used to convolute a database of tailored Green's functions computed by means of a frequency-domain computational aeroacoustics code. This second approach allows the consideration of the real launch pad geometry and, in the limit of the grid resolution drawn by the acoustic wavelength, the mean flow refraction effects in the jet stream. The mean flow is supplied by a FLUENT simulation and projected onto the computational aeroacoustics grid. This is a Cartesian grid generated automatically and used in connection with an immersed-boundary approach. It is shown that the hybrid empirical/computational aeroacoustics prediction is able to explain some discrepancies observed between the experimental data and the empirical predictions. In addition, it generates a basis of elementary fields to be used in a source localization method under development in the framework of the Innovative Aerothermodynamic Configurations for Space Transport Systems research project, funded by the Italian Space Agency. DOI: 10.2514/1.38634

Experiments to stabilize an unsteady Mach 3 shock wave on a truncated body fitted with a central spike have been conducted in the ONERA R1Ch blowdown wind tunnel. Stabilization was achieved by means of a negative corona discharge created at the tip of the spike. Several runs have been performed, with a freestream unit Reynolds number varying in the range of [0.9[10.sup.7]-3.5[10.sup.7] [m.sup.-1]]. Onboard discharges can be generated using an ac or dc potential between the tip of the spike and the truncated face, similar to the setup of Kuo (Kuo, S., Kalkhoran, I., Bivolaru, D., and Orlick, L., 'Observation of Shock Wave Elimination by a Plasma in a Mach = 2.5 Flow,' Physics of Plasmas, Vol. 7, No. 5, 2000, pp. 1345-1348.). Without discharge, for a certain spike length we observe that, depending on the Reynolds number or the surface state of the spike, the shock front is unsteady or not. In the case of a naturally unsteady shock front, we observe a complete stabilization of the shock when a negative discharge is generated at the spike tip. With positive discharges, the effect is weaker. Both discharges are pulsed, and their input power is less than 1 W. Discharge imaging and current measurements indicate that the negative discharge is a Trichel-pulsed corona discharge, whereas the positive discharge is a streamer discharge. An order-of-magnitude analysis and infrared imaging indicate that continuous volume and surface heating are negligible. To explain the stabilization mechanism, we argue that the pulsed discharge acts as an acoustic source tripping the boundary layer, thus leading to a bypass transition to turbulence.

A new method to create a jet of a virtually monodisperse microbubble suspension of prescribed bubble size into a quiescent cavity is proposed. The method is insensitive to gravity and is based on the creation of a slug flow at a T junction in a capillary tube before injection. We develop a theoretical analysis that establishes the validity and efficiency of the method, as controlled by the crossflow Weber number, and yields a simple explicit prediction for the bubble size in terms of the injection parameters. The method operates efficiently for small Weber numbers, yet it generates small bubbles of very uniform size. The reduced size dispersion is also explained within the theoretical model. The method of bubble formation, injection, and spreading by the resulting turbulent jet is validated experimentally in 4.7 s of free fall in the drop tower at the University of Bremen. Experiments demonstrate the physical principle behind the method of bubble formation and allow us to explore the dynamics of the resulting bubble jet after injection of the slug flow into a quiescent cavity in microgravity conditions as an efficient method of bubble spreading and transport. Detailed measurements of average local velocities show that bubbles are essentially passive with respect to the carrier mean flow, and the inherent turbulence of the flow is crucial for optimal spreading of the bubble distribution and reduction of bubble coalescence. The shape of the bubble jet is studied as a function of the Reynolds number. Finally, the degree of coalescence is also characterized and found to be remarkably small.

Exact solutions for the steady-state response of a viscously damped linear system to excitations of sinusoidally varying frequency are presented. Solutions for the response to forces and base motions are derived, along with an expression for the root-mean-square response that does not require integration of the equation of motion. The solutions are used to calculate the response of a flexibly supported component to base motions and applied forces. It is shown that resonant response can occur even if the instantaneous excitation frequency never approaches the natural frequency. The dynamic attenuation for various rates of passage through resonance is calculated. Dependence of the response on system parameters is investigated. Finally, the response to a rotating unbalance with sinusoidally varying speed, such as may occur in turbomachinery under closed-loop speed control, is investigated. An exact but cumbersome solution valid for all speeds may be obtained. As a practicable alternative, it is shown that a force input may be constructed such that the exact solution to that simpler problem closely approximates the response to the unbalance. The approximation is valid when the rotational speed changes slowly compared with the period of the underlying oscillation.

Sonic transverse gaseous injection into a Mach 5.0 freestream flow was numerically simulated using two-equation and detached-eddy turbulence models. Circular- and diamond-shaped injectors were investigated in this study. The numerical simulations were compared with available experimental results and it was determined that both the Reynolds-averaged Navier-Stokes and detached-eddy simulation models captured the secondary flow structure. A detailed comparison of the secondary structures was performed for both injectors. Two new vortex structures of practical importance were observed in the diamond-injector flowfield. First, a leading-edge mixing mechanism was identified. Second, a trapped lateral counter-rotating vortex pair was produced. These new structures were observed in both Reynolds-averaged Navier-Stokes and detached-eddy simulation simulations. The detached-eddy simulations indicated that the large-scale structures observed in the plume/wake region of the flowfield were more organized in the diamond-injector test case. To better understand the secondary flow advection mechanism, the magnitudes of the terms in the compressible vorticity transport equation were compared. The diamond-injector structured-grid Reynolds-averaged Navier-Stokes solution was used as a baseline for this study. The inviscid compressibility, vortex-stretching, and baroclinic-torque terms were dominant. Downstream of the barrel-shock region, the baroclinic term was found to diminish when compared with the other inviscid terms. Planar-averaged results for the transport quantities confirmed this behavior. Vortex stretching was found to persist the longest.

We find closed-form solutions for axisymmetric plane strain radial deformations of a functionally graded circular hollow cylinder and radial expansion/contraction of a hollow sphere loaded on inner and outer surfaces by uniform hydrostatic pressures. The cylinder and the sphere are presumed to be made of isotropic and incompressible linear elastic materials with the shear modulus a general function of the radius. It is found that the optimal value of the hoop or the circumferential stress in a cylinder and a sphere is a constant and occurs for the linear variation in the radial direction of the shear modulus. The analytical results presented here should serve as benchmarks for verifying numerical solutions of problems.

The precise nature of the origin of jet noise remains in question to this day. Apart from the scientific importance of gaining a better understanding of the noise sources, there is the practical consideration of our ability to alter/manipulate the sources so as to achieve noise reduction. In this study, the sources of jet noise have been investigated with 1) the analyses of far-field spectra, and 2) the measurements of the far-field correlations, both in the polar and azimuthal directions. Two geometries were used: a round nozzle and a beveled nozzle. The acoustic characteristics of these nozzles exhibit interesting trends at different jet velocities ([V.sub.j]/a), thereby permitting a better understanding of the nature of the noise sources. The far-field spectra from unheated round jets at extremely low Mach numbers conform to the large-scale similarity shape at angles close to the jet axis; there is a gradual progression from the finescale similarity shape to the large-scale similarity shape for all jet velocities. This seems to be a fundamental characteristic of jet noise and is a new finding. The far-field correlations indicate that there is very little correlation at the lower polar angles; in the peak aft radiation sector, high correlations prevail. It is established with both the round and beveled nozzles that low correlations are associated with fine-scale-similarity-shaped spectra and high correlations with large-scale-similarity-shaped spectra. Experimental evidence for the importance of the noise from large coherent structures even at low velocities is offered. The data indicate the existence of two independent sources in both high-speed and low-speed jets, with the coherent large structures radiating to the aft angles and the random turbulence radiating to the lower angles. It is shown that the noise reduction of the beveled nozzle is due to the alteration of the noise from the coherent structures. The beveled nozzle thus provides indirect evidence for the importance of large coherent structures.

The far field of an incompressible swirling jet has been studied using two-component laser Doppler anemometry. Three pairs of symmetric injectors were used to produce weak-to-moderate swirling jets. Velocity profiles of the mean and fluctuating streamwise and azimuthal velocity components were measured in jets with two swirl numbers (S = 0.15 and 0.25) at axial locations up to 50 jet exit diameters. The velocity and turbulence intensity profiles, centerline decay, and growth rates for the various swirling jets have been compared with those obtained in the same facility without swirl (S = 0). Like the previous observations for the near jet, there was no observable effect on the properly scaled far jet for the S = 0.15 case. The results were virtually identical to the nonswirling jet. For the S = 0.25 case, the only statistically significant effect was a shift in the virtual origin (from x/D, = 0.75 to -2.9). The recent predictions of equilibrium similarity theory were found to be in excellent agreement with the experimental results. In particular, the mean azimuthal component of velocity fails off as the inverse square of the downstream distance. By contrast, the mean streamwise velocity and turbulence intensifies fall off with the inverse of the downstream distance. As a consequence, the mean azimuthal equation uncouples from the rest, and so the asymptotic swirling jet behaves like the nonswirling jet.

A hybrid multicode computational method is developed that allows combining compressible and low Mach number codes into a single computational solver. The proposed methodology can be used for integrated simulations of multicomponent engineering problems. The unsteady coupling between the two codes is performed via exchanging time-dependent state information through the interfaces using overlapping meshes. The proposed coupling procedure is validated on laminar steady and unsteady test problems. Both constant-density and variable-density regimes of the low Mach number code are investigated. Results of the test cases performed in frameworks of one-way coupling and two-way coupling are documented. Several methods of implementation of interface conditions for the compressible code are compared by looking at the levels of dilatation, as well as numerical errors. The injection method (when all the variables are simply transformed from one code to another through an interpolation procedure) is chosen for its superior stability, accuracy, and simplicity of implementation. Numerical results for the coupled calculations obtained with the injection method show good agreement with both standalone calculations and analytical solutions.

This paper deals with thermally induced deformation buckling and postbuckling of a unidirectional sandwich panel with a soft core. The mathematical formulation is based on the high-order sandwich-panel approach and it incorporates the effects of the flexibility of the core in the vertical direction, along with its expansion or contraction in the vertical direction as a result of the imposed thermal field. The nonlinear governing equations are derived using a variational approach following the principles of the high-order sandwich-panel theory. The governing equations of the prebuckling and buckling states are determined through linearization following a perturbation approach. The effects of the vertical thermal core normal strains of the core, which are usually ignored by various computational models, are studied at the buckling and the postbuckling stages, with emphasis on the differences in the mechanical behavior. A comparison with results obtained using a classical elastic foundation approach is conducted, and the differences are presented and discussed. The postbuckling behavior of thermally loaded sandwich panels in the vicinity of the temperatures that cause buckling, based on a simplified model, is presented through numerical examples involving a uniform temperature field, along with finite element results using ANSYS that compare very well. In addition, the results for a gradient thermal field are described. The results are presented through various structural quantities along the panel and through equilibrium path curves of temperature vs extreme values of these structural quantities. An important conclusion of the study is that the postbuckling behavior of a heated sandwich panel with a soft core is of a stable type for the cases investigated (i.e., that of a plate rather than of a column or a shell).

We examined the coefficient of lift for rotating and nonrotating spheres of varying surface texture under a variety of flight conditions. At Reynolds number less than 500,000 the direction of lift on a nonrotating polished sphere in a uniform flowfield is nonzero and in a direction that varies randomly with Reynolds number. However, once established, the direction and magnitude of lift appears to be stable over time at a particular Reynolds number. This phenomenon has not been reported previously. Additionally, the texture of a rotating sphere in a uniform flow can modulate direction and magnitude of lift generated by the spin. Although the expected direction of the net force on a spinning sphere is in a direction from the advancing to retreating surface ('Magnus effect'), in certain flight regimes the net force is in the opposite direction ('negative Magnus effect'). In this paper we present the first systematic windtunnel characterization of the flow parameters generating a negative Magnus effect on a sphere.

A truss-lattice panel is modeled under shear loading, up to and beyond the critical buckling load. Nondimensional buckling loads and corresponding buckling mode shapes are obtained for such panels with increasing numbers of diagonally placed internal struts. A method for minimum-mass optimization of the truss lattice is given, based upon simultaneous in-plane and out-of-plane buckling. The finite element method is applied to examine the buckling performance and postbuckling stability. The postbuckling response of the optimized truss lattice is shown to be stable in all cases. The advantages of using the truss-lattice structure are demonstrated by comparing the volume requirements with those of a conventional continuous shear panel, based on the load carried and the buckling capabilities. It is shown that although the continuous shear panel is more efficient for heavy load applications, the truss lattice offers potential weight savings when fighter loads are applied.

A new multimodel computational framework for optimal control of aeroacoustic noise is presented using a nearfield compressible Navier-Stokes solver coupled with a far-field linearized Euler solver, both based on a discontinuous Galerkin formulation. In this approach, the coupling of near- and far-field domains is achieved by weakly enforcing continuity of normal fluxes across a coupling surface that encloses all nonlinearities and noise sources. For optimal control, gradient information is obtained by the solution of an appropriate adjoint problem that involves the propagation of adjoint information from the far field to the near field. This computational framework is applied to study optimal boundary control of blade-vortex interaction, which is a significant noise source for helicopters on approach to landing. In the prototype problem presented here, the noise propagated toward the ground is reduced by 12 dB, demonstrating the potential of an optimization-based approach to blade-vortexinteraction noise control.