Showing papers in "AIAA Journal in 2004"

Separation Control on HIgh Angle of Attack Airfoil Using Plasma Actuators

Abstract: This work involves the documentation and control of leading-edge flow separation that occurs over an airfoil at high angles of attack, well above stall. A generic airfoil shape (NACA 663-018) was used because of its documented leading-edge stall characteristics. It was instrumented for surface-pressure measurements that were used to calculate lift coefficients. Mean-velocity profiles downstream of the airfoil were used to determine the drag coefficient. In addition to these, smoke streakline flow visualization was used to document the state of flow separation. The airfoil was operated over a range of freestream speeds from 10 to 30 m/s, giving chord Reynolds numbers from 77 × 10 3 to 333 × 10 3 .T wo types of plasma actuator designs were investigated. The first produced a spanwise array of streamwise vortices. The second produced a two-dimensional jet in the flow direction along the surface of the airfoil. The plasma actuators were found to lead to reattachment for angles of attack that were 8 deg past the stall angle (the highest investigated). This was accompanied by a full pressure recovery and up to a 400% increase in the lift-to-drag ratio.

Mechanisms and Responses of a Single Dielectric Barrier Plasma Actuator: Plasma Morphology

Abstract: We present simultaneous optical, electrical, and thrust measurements of an aerodynamic plasma actuator. These measurements indicate that the plasma actuator is a form of the dielectric barrier discharge, whose behavior is governed primarily by the buildup of charge on the dielectric-encapsulated electrode. Our measurements reveal the temporal and macroscale spatial structure of the plasma. Correlating the morphology of the plasma and the electrical characteristics of the discharge to the actuator performance as measured by the thrust produced indicates a direct coupling between the interelectrode electric field (strongly modified by the presence of the plasma) and the charges in the plasma. Our measurements discount bulk heating or asymmetries in the structure of the discharge as mechanisms for the production of bulk motion of the surrounding neutral air, although such asymmetries clearly exist and impact the effectiveness of the actuator.

Mechanisms and Responses of a Dielectric Barrier Plasma Actuator: Geometric Effects

Abstract: The single dielectric barrier discharge plasma, a plasma sustainable at atmospheric pressure, has shown considerable promise as a flow control device operating at modest (tens of watts) power levels. Measurements are presented of the development of the plasma during the course of the discharge cycle, and the relevance of these measurements to the modeling of the actuator's electrical properties is discussed. Experimental evidence is presented strongly pointing to the electric field enhancement near the leading edge of the actuator as a dominant factor determining the effectiveness of momentum coupling into the surrounding air

Aerodynamic Data Reconstruction and Inverse Design Using Proper Orthogonal Decomposition

Abstract: The application of proper orthogonal decomposition for incomplete (gappy) data for compressible external aerodynamic problems has been demonstrated successfully in this paper for the first time. Using this approach, it is possible to construct entire aerodynamic flowfields from the knowledge of computed aerodynamic flow data or measured flow data specified on the aerodynamic surface, thereby demonstrating a means to effectively combine experimental and computational data. The sensitivity of flow reconstruction results to available measurements and to experimental error is analyzed. Another new extension of this approach allows one to cast the problem of inverse airfoil design as a gappy data problem. The gappy methodology demonstrates a great simplification for the inverse airfoil design problem and is found to work well on a range of examples, including both subsonic and transonic cases.

Empirical Spectral Model of Surface Pressure Fluctuations

Abstract: An empirical model of the surface pressure spectrum beneath a two-dimensional, zero-pressure-gradient boundary layer is presented that is based on the experimental surface pressure spectra measured by seven research groups. The measurements cover a large range of Reynolds number, 1.4 × 10 3 < Reθ < 2.34 × × 10 4 . The model is a simple function of the ratio of the timescales of the outer to inner boundary layer. It incorporates the effect of Reynolds number through the timescale ratio and compares well to experimental data. It is proposed that the effect of Reynolds number is more aptly described as the effect of the range of relevant scales. Spectral features of the experimental data and the scaling behavior of the surface pressure spectrum are also discussed.

Interfacing Statistical Turbulence Closures with Large-Eddy Simulation

Abstract: Progress toward a general purpose hybrid Reynolds-averaged Navier-Stokes (RANS)/large-eddy simulation (LETS) framework is described, in which large-scale, statistically represented turbulence kinetic energy is converted automatically into resolved-scale velocity fluctuations wherever the local mesh resolution is sufficient to support them. Existing hybrid RANS/LES approaches alter the nature of the local partial differential equations according to the local mesh resolution, but they do not alter the nature of the data on which these equations operate. The implications of this are discussed. Subsequently, a simple mechanism is introduced to transfer statistical kinetic energy into resolved-scale fluctuations in a manner that preserves a given set of space/time correlations and set of second moments. This process, which can appropriately be termed Large-Eddy STimulation (LEST), generates the large-scale eddies needed to form the unsteady boundary conditions at RANS interfaces to LES regions, into which turbulence energy can be deposited either through mean convection or through turbulent transport

Geometrically Exact, Intrinsic Theory for Dynamics of Curved and Twisted Anisotropic Beams

Abstract: A formulation is presented for the nonlinear dynamics of initially curved and twisted anisotropic beams. When the applied loads at the ends of, and distributed along, the beam are independent of the deformation, neither displacement nor rotation variables appear: an intrinsic formulation. Like well-known special cases of these equations governing nonlinear dynamics of rigid bodies and nonlinear statics of beams, the complete set of intrinsic equations has a maximum degree of nonlinearity equal to two. Advantages of such a formulation are demonstrated with a simple example. When the initial curvature and twist are constant along the beam, two space-time conservation laws are shown to exist, one being a work-energy relation and the other a generalized impulse-momentum relation. These laws can be used, for example, as benchmarks to check the accuracy of any proposed solution, including time-marching and finite element schemes. The structure of the intrinsic equations suggests parallel approaches to spatial and temporal discretization. A particularly simple spatial discretization scheme is presented for the special case of the nonlinear static behavior of end-loaded beams that, by virtue of the Kirchhoff analogy, leads to a time-marching scheme for the dynamics of a pivoted rigid body in a gravity field. This time-marching scheme conserves both the angular momentum about a vertical line passing through the pivot and total mechanical energy, whereas the analogous spatial discretization scheme for the nonlinear static behavior of end-loaded beams satisfies analogous integrals of deformation along the beam span. Remarkably, a straightforward generalization of these discretization schemes is shown to satisfy both space-time conservation laws for the nonlinear dynamics of beams when the applied loads are constant within a space-time element.

Low Aspect Ratio Aerodynamics at Low Reynolds Numbers

Abstract: The recent interest in the development of small unmanned aerial vehicles (UAVs) and micro air vehicles has revealed a need for a more thorough understanding of the aerodynamics of small airplanes flying at low speeds. In response to this need, a study of the lift, drag, and pitching moment characteristics of wings of low aspect ratio operating at low Reynolds numbers are presented. Wind-tunnel tests of wings with aspect ratios between 0.5 and 2.0, four distinct planforms, thickness-to-chord ratios of ≈ 2%, and 5-to-1 elliptical leading edges have been conducted as part of this research. The Reynolds numbers considered were in the range of 7 × × 10 4 to 2 × × 10 5 . Analysis of the data includes comparison of lift-curve slope, nonlinear equation approximations, maximum lift coefficient, and center of lift.

Normal Constraint Method with Guarantee of Even Representation of Complete Pareto Frontier

Abstract: Multiobjective optimization is rapidly becoming an invaluable tool in engineering design. A particular class of solutions to the multiobjective optimization problem is said to belong to the Pareto frontier. A Pareto solution, the set of which comprises the Pareto frontier, is optimal in the sense that any improvement in one design objective can only occur with the worsening of at least one other. Accordingly, the Pareto frontier plays an important role in engineering design—it characterizes the tradeoffs between conflicting design objectives. Some optimization methods can be used to automatically generate a set of Pareto solutions from which a final design is subjectively chosen by the designer. For this approach to be successful, the generated Pareto set must be truly representative of the complete optimal design space (Pareto frontier). In other words, the set must not overrepresent one region of the design space, or neglect others. Some commonly used methods comply with this requirement, whereas others do not. This paper offers a new phase in the development of the normal constraint method, which is a simple approach for generating Pareto solutions that are evenly distributed in the design space of an arbitrary number of objectives. The even distribution of the generated Pareto solutions can facilitate the process of developing an analytical expression for the Pareto frontier in n dimension. An even distribution of Pareto solutions also facilitates the task of choosing the most desirable (final) design from among the set of Pareto solutions. The normal constraint method bears some similarities to the normal boundary intersection and � -constraint methods. Importantly, the developments presented in this paper define its critical distinction, namely, the ability to generate a set of evenly distributed Pareto solutions over the complete Pareto frontier. Examples are provided that show the normal constraint method to perform favorably under the new developments when compared with the normal boundary intersection method, as well as with the original normal constraint method.

Oscillation Frequency and Amplitude Effects on the Wake of a Plunging Airfoil

Abstract: The flow over a NACA 0012 airfoil, oscillated sinusoidally in plunge, is simulated numerically using a compressible two-dimensional Navier-Stokes solver at a Reynolds number of 2 ×10 4 . The wake of the airfoil is visualized using a numerical particle tracing method. Close agreement is obtained between numerically simulated wake structures and experimental wake visualizations in the literature, when the flow is assumed to be fully laminar. The wake structures, and the lift and thrust of the airfoil, are shown to be strongly dependent on both the Strouhal number and the reduced frequency k of the plunge oscillation at this Reynolds number. Leading-edge separation appears to dominate the generation of aerodynamic forces for reduced frequencies below approximately k = 4 but becomes secondary for higher frequencies. Wake structures appear to be controlled primarily by trailing-edge effects at all frequencies tested up to k=20. Aerodynamic force results obtained at this Reynolds number show marked differences from those predicted by potential flow analyses at low plunge frequency and high amplitude but are similar at high frequency and low amplitude, consistent with the effect of leading-edge separation.

Breakup of round nonturbulent liquid jets in gaseous crossflow

Abstract: An experimental investigation of the primary breakup of nonturbulent round liquid jets in gas crossflow is described. Pulsed shadowgraph and holograph observations of jet primary breakup regimes, conditions for the onset of breakup, properties of waves observed along the liquid surface, drop sue and velocity properties resulting from breakup and conditions required for the breakup of the liquid column as a whole, were obtained for air crossflows at normal temperature and pressure. When combined with the earlier studies of Mazallon et al. (1999), the test range included crossflow Weber numbers of 02000, liquidgas momentum ratios of 100-8000, liquidgas density ratios of 683-1021, and Ohnesorge numbers of 0.003-0.12. The results suggest qualitative similarities between the primary breakup of nonturbulent round liquid jets in crossflows and the secondary breakup of drops subjected to shock wave disturbances (e.g., bag, multimode and shear breakup regimes are observed in both instances) with relatively little effect of the liquidgas momentum ratio on breakup properties over the present test range. Effects of liquid viscosity were also small for present observations where Ohnesorge numbers were less than 0.4. Phenomenological analyses were successful for helping to interpret and correlate the properties of primary breakup of round liquid jets in gas crossflows that were measured during the present investigation.

Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability

Abstract: A computationally efficient procedure for quantifying uncertainty and finding significant parameters of uncertainty models is presented. To deal with the random nature of input parameters of structural models, several efficient probabilistic methods are investigated. Specifically, the polynomial chaos expansion with Latin hypercube sampling is used to represent the response of an uncertain system. Latin hypercube sampling is employed for evaluating the generalized Fourier coefficients of the polynomial chaos expansion. Because the key challenge in uncertainty analysis is to find the most significant components that drive response variability, analysis of variance is employed to find the significant parameters of the approximation model. Several analytical examples and a large finite element model of a joined-wing are used to verify the effectiveness of this procedure.

Selecting Probabilistic Approaches for Reliability-Based Design Optimization

Abstract: During the past decade, numerous endeavors have been made to develop effective reliability-based design optimization (RBDO) methods. Because the evaluation of probabilistic constraints defined in the RBDO formulation is the most difficult part to deal with, a number of different probabilistic design approaches have been proposed to evaluate probabilistic constraints in RBDO. In the first approach, statistical moments are approximated to evaluate the probabilistic constraint. Thus, this is referred to as the approximate moment approach (AMA). The second approach, called the reliability index approach (RIA), describes the probabilistic constraint as a reliability index. Last, the performance measure approach (PMA) was proposed by converting the probability measure to a performance measure. A guide for selecting an appropriate method in RBDO is provided by comparing probabilistic design approaches for RBDO from the perspective of various numerical considerations. It has been found in the literature that PMA is more efficient and stable than RIA in the RBDO process. It is found that PMA is accurate enough and stable at an allowable efficiency, whereas AMA has some difficulties in RBDO process such as a second-order design sensitivity required for design optimization, an inaccuracy to measure a probability of failure, and numerical instability due to its inaccuracy. Consequently, PMA has several major advantages over AMA, in terms of numerical accuracy, simplicity, and stability. Some numerical examples are shown to demonstrate several numerical observations on the three different RBDO approaches.

Large-Eddy Simulation Inflow Conditions for Coupling with Reynolds-Averaged Flow Solvers

Abstract: Hybrid approaches using a combination of Reynolds-averaged Navier-Stokes (RANS) approaches and large eddy simulations (LES) have become increasingly popular. One way to construct a hybrid approach is to apply separate flow solvers to components of a complex system and to exchange information at the interfaces of the domains. For the LES flow solver, boundary conditions then have to be defined on the basis of the Reynolds-averaged flow statistics delivered by a RANS flow solver. This is a challenge, which also arises, for instance, when defining LES inflow conditions from experimental data. The problem for the coupled RANS-LES computations is further complicated by the fact that the mean flow statistics at the interface may vary in time and are not known a priori but only from the RANS solution. The present study defines a method to provide LES inflow conditions through auxiliary, a priori LES computations, where an LES inflow database is generated. The database is modified to account for the unsteadiness of the interface flow statistics

First-order saddlepoint approximation for reliability analysis

Abstract: In the approximation methods of reliability analysis, nonnormal random variables are transformed into equivalent standard normal random variables. This transformation tends to increase the nonlinearity of a limit-state function and, hence, results in less accurate reliability approximation. The first-order saddlepoint approximation for reliability analysis is proposed to improve the accuracy of reliability analysis. By the approximation of a limit-state function at the most likelihood point in the original random space and employment of the accurate saddlepoint approximation, the proposed method reduces the chance of an increase in the nonlinearity of the limit-state function. This approach generates more accurate reliability approximation than the first-order reliability method without an increase in the computational effort. The effectiveness of the proposed method is demonstrated with two examples and is compared with the first- and second-order reliability methods.

Cavity Resonance Suppression Using Miniature Fluidic Oscillators

Abstract: We present a novel approach to suppressing jetcavity interaction tones using miniature fluidic devices. We first characterize miniature fluidic oscillators and then assess their effectiveness for cavity tone suppression. Further, we evaluate mass flow requirements for effective unsteady fluid mass addition. The fluidic devices used had no moving parts and could provide oscillatory flow of prescribed waveforms (sine, square, and saw-toothed) at frequencies up to 3 KHz. Our testbed for a detailed evaluation of the fluidic excitation (square wave) technique was the flow-induced resonance produced by a jet flowing over a cavity with an (length/depth) ratio of 6. In addition to schlieren photography and acoustic measurements we used photoluminescent Pressure Sensitive Paint (PSP) to map pressures on the cavity’s floor for the unperturbed and fluidically excited cases. When located at the upstream end of the cavity floor, the miniature fluidic device was successful in suppressing cavity tones by as much as ’ Senior Research Engineer, Associate Fellow AIAA ’ Principal Research Scientist, Senior Member AIAA 3 Electronics Engineer Copyright

Role of Transient Growth in Roughness-Induced Transition

Abstract: Surface roughness can have a profound effect on boundary-layer transition. However, the mechanisms responsible for transition with three-dimensional distributed roughness have been elusive. Various Tollmien-Schlichting-based mechanisms have been investigated in the past but have been shown not to be applicable. More recently, the applicability of transient growth theory to roughness-induced transition has been studied. A model for roughness-induced transition is developed that makes use of computational results based on the spatial transient growth theory pioneered by the present authors. For nosetip transition, the resulting transition relations reproduce the trends of the Reda and passive nosetip technology (PANT) data and account for the separate roles of roughness and surface temperature level on the transition behavior

Broadband Self Noise from Loaded Fan Blades

Abstract: An experimental investigation and analytical modeling were conducted of the broadband self-noise radiated by an industrial cambered airfoil embedded in an homogeneous flow at low Mach number. The instrumented airfoil is placed at the exit of an open jet anechoic wind tunnel. Sound is measured in the far field at the same time as the statistical properties of the wall pressure fluctuations close to the trailing edge. Three different flows with different statistical behaviors are investigated by changing the angle of attack, namely, the turbulent boundary layer initiated by a leading-edge separation, the nearly separated boundary layer with vortex shedding at the trailing edge, and the laminar boundary layer with Tollmien‐Schlichting waves. The far-field spectrum is related to the spectrum and spanwise correlation length of the wall pressure fluctuations. Simple statistical models based on Howe’s theory and on an extension of the original Amiet’s theory show a good agreement with the experimental results. They provide helpful tools to predict the self-noise from subsonic fans in an industrial context.

Free Vibration Analysis of Rotating Blades With Uniform Tapers

Abstract: A spectral finite element method (SFEM) is proposed to develop a low-degree-of-freedom model for dynamic analysis of rotating tapered beams. The method exploits semi-analytical progressive wave solutions of the governing partial differential equations. Only one single spectral finite element is needed to obtain any modal frequency or mode shape, which is as accurate or better than other approaches reported in the literature for straight or uniformly tapered beams. The minimum number of such spectral finite elements corresponds to the number of substructures, that is, beam sections with different uniform tapers, in a rotating beam to capture the complete system dynamic characteristics. The element assembly procedure is accomplished in the same fashion as the conventional finite element approach. Results are for a number of examples such as a straight beam and beams with uniform taper or compound tapers. Overall, for a rotating blade system, our SFEM provides highly accurate predictions for any modal frequency using a single element or very few elements corresponding to the number of uniform taper changes in the blade system. Nomenclature EI (x) = beam bending flexural stiffness EI 0 = reference beam bending flexural stiffness L = beam length M(x) = beam bending moment m(x) = beam mass per unit length m0 = reference beam mass per unit length R =o ffset length between beam and rotating hub T (x) = beam axial force due to centrifugal stiffening V (x) = beam shear force W(x) = beam bending mode shape function w(x, t) = beam transverse displacement α = beam mass per unit length constant βi = beam bending flexural stiffness constant, i = 1, 4 η = nondimensional axial force µ = nondimensional natural frequency � = beam rotation speed ω =e xcitation frequency

Actual impedance of nonreflecting Boundary conditions: Implications for computation of resonators

Abstract: Nonreflecting boundary conditions are essential elements in the computation of many compressible flows. Such simulations are very sensitive to the treatment of acoustic waves at boundaries. Nonreflecting conditions allow acoustic waves to propagate through boundaries with zero or small levels of reflection into the domain. However, perfectly nonreflecting conditions must be avoided because they can lead to ill-posed problems for the mean flow. Various methods have been proposed to construct boundary conditions that can be sufficiently nonreflecting for the acoustic field while still making the mean flow problem well-posed. A widely used technique for nonreflecting outlets is analyzed (Poinsot, T., and Lele, S., "Boundary Conditions for Direct Simulations of Compressible Viscous Flows," Journal of Computational Physics, Vol. 101, No.1,1992, pp. 104-129; Rudy, D. H., and Strikwerda, J. C., "A Non-Reflecting Outflow Boundary Condition for Subsonic Navier-Stokes Calculations," Journal of Computational Physics, Vol. 36, 1980, pp. 55-70). It shows that the correction introduced by these authors can lead to large reflection levels and resonant behavior that cannot be observed in the experiment. A simple scaling is proposed to evaluate the relaxation coefficient used in these methods for a nonreflecting outlet. The proposed scaling is tested for simple cases (ducts) both theoretically and numerically.

Magnetohydrodynamic and Electrohydrodynamic Control of Hypersonic Flows of Weakly Ionized Plasmas

Abstract: The focus of this work is on theoretical analysis of fundamental aspects of high-speed flow control using electric and magnetic fields. The principal challenge is that the relatively cold gas is weakly ionized in electric discharges or by electron beams, with ionization fraction ranging from 10 −8 to 10 −5 . The low ionization fraction means that, although electrons and ions can interact with electromagnetic fields, transfer of momentum and energy to or from the bulk neutral gas can be quite inefficient. Analytical estimates show that, even at the highest values of the electric field that can exist in cathode sheaths of electric discharges, electrohydrodynamic, or ion wind, effects in a single discharge can be of significance only in low-speed core flows or in laminar sublayers of high-speed flows. Use of multi-element discharges would amplify the single-sheath effect, so that the cumulative action on the flow can conceivably be made significant. However, Joule heating can overshadow the cathode sheath ion wind effects. Theoretical analysis of magnetohydrodynamic (MHD) flow control with electron beam ionization of hypersonic flow shows that the MHD interaction parameter is a steeply increasing function of magnetic field strength and the flow velocity. However, constraints imposed by arcing between electrode segments can reduce the performance and make the maximum interaction parameter virtually independent of Mach number. Estimates also show that the MHD interaction parameter is much higher near the wall (in the boundary layer) than in the core flow, which may have implications for MHD boundary layer and transition control. The paper also considers “electrodeless” MHD turning and compression of high-speed flows. Computations of a sample case demonstrate that the turning and compression of hypersonic flow ionized by electron beams can be achieved; however, the effect is relatively modest due to low ionization level.

Implementation of k-w Turbulence Models in an Implicit Multigrid Method

Abstract: Three κ-ω turbulence models using linear and nonlinear eddy-viscosity formulations are implemented in an implicit multigrid method. Detailed techniques of implementation are presented and discussed. Freezing and limiting strategies are applied to improve robustness and convergence of the multigrid method. The Wilcox κ-ω, κ-w shear-stress transport, and Wilcox-Durbin+ (WD+) models are first tested for flat-plate flow, and the results are in good agreement with the empirical correlations. Numerical results for unseparated and separated transonic flows show that the WD+ model using weakly nonlinear eddy viscosity is in better overall agreement with the experimental data. Particularly for the separated flows, the present multigrid diagonalized alternating-direction implicit method provides good convergence without any robustness problems

Pressure History at the Thrust Wall of a Simplified Pulse Detonation Engine

Abstract: Gas dynamics in a simplified pulse detonation engine (PDE) was theoretically analyzed. A PDE was simplified as a straight tube with a fixed cross section. One end of the tube was closed, namely, this end was the thrust wall, and the other end was open. A detonation wave was initiated at the closed end and simultaneously started to propagate toward the open end. When the detonation wave broke out from the open end, a rarefaction wave started to propagate from the open end toward the closed end. This rarefaction wave was reflected by the closed end. By considering this rarefaction wave to be self-similar in the analysis of the interference between this rarefaction wave and its reflection from the closed end, we analytically formulated the decay portion of the pressure history at the closed end (thrust wall) without any empirical parameters. By integrating the obtained pressure history at the thrust wall with respect to time, important performance parameters of a PDE were also formulated. The obtained formulas were compared with numerical and experimental results and agreed with them very well.

Turbulent Inflow Conditions for Large-Eddy-Simulation of Compressible Wall-Bounded Flows

Abstract: The issue of turbulent inflow conditions for large-eddy simulation (LES) is addressed through three representative examples recently treated at ONERA. First, the performance of an extension to compressible flows of the rescaling method of Lund et al. is assessed. The second example, the flow above a deep cavity shows that the imposition of turbulent fluctuations has nearly no influence on the accuracy of the simulation on this acoustically driven flow. The third case demonstrates that particular attention must he paid to the response of the inflow condition to acoustic perturbations when local hybrid Reynolds-averaged Navier-Stokes/LES approaches are considered

Calculation of sound propagation in nonuniform flows: Suppression of instability waves

Abstract: Acoustic waves propagating through nonuniform flows are subject to convection and refraction. Most noise prediction schemes use a linear wave operator to capture these effects. However, the wave operator can also support instability waves that, for a jet, are the well-known Kelvin-Helmholtz instabilities. These are convective instabilities that can completely overwhelm the acoustic solution downstream of the source location. A general technique to filter out the instability waves is presented. A mathematical analysis is presented that demonstrates that the instabilities are suppressed if a time-harmonic response is assumed, and the governing equations are solved by a direct solver in the frequency domain. Also, a buffer-zone treatment for a nonreflecting boundary condition implementation in the frequency domain is developed

Truss Optimization on Shape and Sizing with Frequency Constraints

Abstract: An optimality criteria algorithm is presented for three-dimentional truss structure optimization with multiple constraints on its natural frequencies. Both nodal coordinates and element cross-sectional areas, which are quite different in their natures, are treated simultaneously in a unified design space for structural weight minimization. First the optimality criterion is developed for a single constraint based on differentiation of the Lagrangian function. It states that, at the optimum, all of the variables should have equal efficiencies. Then, the global sensitivity numbers are introduced to solve multiple constraints of frequencies, avoiding computation of the Lagrange multipliers. Finally, upon the sensitivity analysis, the most efficient variables are identified and modified in priority. The optimal solution is achieved gradually from the initial design with a minimum weight increment. Four typical trusses are used to demonstrate the feasibility and validity of the proposed method.

Generation of Three-Dimensional Turbulent Inlet Conditions for Large-Eddy Simulation

Abstract: A method for generating realistic (i.e., reproducing in space and time the large-scale coherence of the flows) inflow conditions based on two-point statistics and stochastic estimation is presented. The method is based on proper orthogonal decomposition and linear stochastic estimation. This method allows a realistic representation with a minimum of information to be stored. Most of the illustrations of this method are given for a plane turbulent mixing layer that contains most of the basic features of organized turbulent flows. Examples of the application of the method are given first for the generation of inflow conditions for direct numerical simulation (DNS) and for large-eddy simulation from experimental results. Second, DNS results are used to generate realistic inflow conditions for two- and three-dimensional DNS, retaining only a minimum size of relevant information.

Adjoint-Based, Three-Dimensional Error Prediction and Grid Adaptation

Abstract: Engineering computational fluid dynamics analysis and design applications often focus on output functions, such as lift or drag. Errors in these output functions are generally unknown, and conservatively accurate solutions may be computed. Computable error estimates can offer the possibility to minimize computational work for a prescribed error tolerance. Such an estimate can be computed by solution of the flow equations and the linear adjoint problem for the functional of interest. The computational mesh can be modified to minimize the uncertainty of a computed error estimate. This robust mesh-adaptation procedure automatically terminates when the simulation is within a user-specified error tolerance. This procedure for estimation and adaptation to error in a functional is demonstrated for three-dimensional Euler problems. An adaptive mesh procedure that links to a CAD surface representation is demonstrated for wing, wing-body, and extruded high lift airfoil configurations. The error estimation and adaptation procedure yielded corrected functions that are as accurate as functions calculated on uniformly refined grids with many more grid points

On large eddy simulation of high Reynolds number wall bounded flows

Abstract: Large-eddy simulation (LES) of wall-bounded flows becomes prohibitively expensive at high Reynolds numbers if one attempts to resolve the small but dynamically important vortical structures in the near-wall region. The LES wall-boundary condition problem is thus to account for the effects of the near-wall turbulence between the wall and the first node and its transfer of momentum to the wall. Here we state the problem and give a brief overview of methods currently in use and possible future methods. To illustrate the problem and quantify the accuracy of some of the models, we present a few results from test cases ranging from fully developed turbulent channel flows to three-dimensional problems of practical engineering interest

Model validation via uncertainty propagation and data transformations

Abstract: Model validation has become a primary means to evaluate accuracy and reliability of computational simulations in engineering design. Because of uncertainties involved in modeling, manufacturing processes, and measurement systems, the assessment of the validity of a modeling approach must be conducted based on stochastic measurements to provide designers with confidence in using a model. A generic model validation methodology via uncertainty propagation and data transformations is presented. The approach reduces the number of physical tests at each design setting to one by shifting the evaluation effort to uncertainty propagation of the computational model. Response surface methodology is used to create metamodels as less costly approximations of simulation models for the uncertainty propagation. Methods for validating models with both normal and nonnormal response distributions are proposed. The methodology is illustrated with the examination of the validity of two finite element analysis models for predicting springback angles in a sample flanging process.