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Showing papers in "AIAA Journal in 2002"


Journal ArticleDOI
TL;DR: A new method for performing a balanced reduction of a high-order linear system is presented, which combines the proper orthogonal decomposition and concepts from balanced realization theory and extends to nonlinear systems.
Abstract: A new method for performing a balanced reduction of a high-order linear system is presented. The technique combines the proper orthogonal decomposition and concepts from balanced realization theory. The method of snapshotsisused to obtainlow-rank,reduced-rangeapproximationsto thesystemcontrollability and observability grammiansineitherthetimeorfrequencydomain.Theapproximationsarethenusedtoobtainabalancedreducedorder model. The method is particularly effective when a small number of outputs is of interest. It is demonstrated for a linearized high-order system that models unsteady motion of a two-dimensional airfoil. Computation of the exact grammians would be impractical for such a large system. For this problem, very accurate reducedorder models are obtained that capture the required dynamics with just three states. The new models exhibit far superiorperformancethanthosederived using a conventionalproperorthogonal decomposition. Although further development is necessary, the concept also extends to nonlinear systems.

1,021 citations



Journal ArticleDOI
TL;DR: In this paper, a harmonic balance technique for modeling unsteady nonlinear e ows in turbomachinery is presented, which exploits the fact that many unstaidy e ow variables are periodic in time.
Abstract: A harmonic balance technique for modeling unsteady nonlinear e ows in turbomachinery is presented. The analysis exploits the fact that many unsteady e ows of interest in turbomachinery are periodic in time. Thus, the unsteady e ow conservation variables may be represented by a Fourier series in time with spatially varying coefe cients. This assumption leads to a harmonic balance form of the Euler or Navier ‐Stokes equations, which, in turn, can be solved efe ciently as a steady problem using conventional computational e uid dynamic (CFD) methods, including pseudotime time marching with local time stepping and multigrid acceleration. Thus, the method is computationally efe cient, at least one to two orders of magnitude faster than conventional nonlinear time-domain CFD simulations. Computational results for unsteady, transonic, viscous e ow in the front stage rotor of a high-pressure compressor demonstrate that even strongly nonlinear e ows can be modeled to engineering accuracy with a small number of terms retained in the Fourier series representation of the e ow. Furthermore, in some cases, e uid nonlinearities are found to be important for surprisingly small blade vibrations.

673 citations


Journal ArticleDOI
TL;DR: In this paper, an exact solution is obtained for three-dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and/or bottom surfaces.
Abstract: An exact solution is obtained for three-dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and/or bottom surfaces. Suitable temperature and displacement functions that identically satisfy boundary conditions at the edges are used to reduce the partial differential equations governing the thermomechanical deformations to a set of coupled ordinary differential equations in the thickness coordinate, which are then solved by employing the power series method. The exact solution is applicable to both thick and thin plates. Results are presented for two-constituent metal‐ceramic functionally graded rectangular plates that have a power law through-the-thickness variation of the volume fractions of the constituents. The effective material properties at a point are estimated by either the Mori‐Tanaka or the self-consistentschemes. Exact displacementsand stressesatseveral locations for mechanical and thermal loads are used toassess theaccuracyof the classical plate theory, thee rst-ordershear deformation theory, and athird-order shear deformation theory for functionally graded plates. Results are alsocomputed for a functionally graded plate with material properties derived by the Mori‐Tanaka method, the self-consistent scheme, and a combination of these two methods.

466 citations


Journal ArticleDOI
TL;DR: In this article, the equilibrium and stability equations of a rectangular plate made of functionally graded material under thermal loads are derived, based on the classical plate theory, when it is assumed that the material properties vary as a power form of thicknesscoordinate variable z and when the variational method is used, the system of fundamental differential equations is established.
Abstract: Equilibrium and stability equations of a rectangular plate made of functionally graded material under thermal loads are derived, based on the classical plate theory. When it is assumed that the material properties vary as a power form of thicknesscoordinate variable z and when the variational method is used, the system of fundamental differential equations isestablished. Thederived equilibrium and stability equationsforfunctionally graded plates areidenticalwith theequationsforhomogeneousplates. Bucklinganalysisoffunctionally graded platesunderfour typesofthermalloadsiscarriedoutresultinginclosed-formsolutions.Thebucklingloadsarereducedtothecritical buckling temperature relationsfor functionally graded plates with linearcomposition of constituent materials and homogeneous plates. The results are validated with the reduction of the buckling relations for functionally graded plates to those of isotropic homogeneous plates given in the literature.

381 citations


Journal ArticleDOI
TL;DR: In this paper, a large eddy simulation (LES) of a turbulent flow past an airfoil near stall at a chord Reynolds number of 2.1 x 10 6 is performed and compared with wind-tunnel experiments.
Abstract: A large eddy simulation (LES) of a turbulent flow past an airfoil near stall at a chord Reynolds number of 2.1 x 10 6 is performed and compared with wind-tunnel experiments. This configuration still constitutes a challenging test case for Reynolds-averaged Navier-Stokes (RANS) simulation and LES as a result of the complexity of the suction side boundary layer: an adverse pressure gradient creates successively a laminar separation bubble, a turbulent reattachment, and a turbulent separation near the trailing edge. To handle this high-Reynolds-number flow with LES on available supercomputers, a local mesh-refinement technique and a discretization of the convective fluxes are developed in a block-structured finite volume code to reduce the total number of grid points and the numerical dissipation acting on the small scales, respectively. Influence of subgrid scale modeling (SGS) is assessed through the comparisons of explicit selective mixed scale model (SMSM) and implicit monotone-integrated LES model results. Moreover, the solution sensitiveness to grid refinement and spanwise extent is investigated

334 citations


Journal ArticleDOI
TL;DR: This work investigates computationally inexpensive assessment methods for meetamodel validation based on leave-k-out cross validation and develops guidelines for selecting k for different types of metamodels.
Abstract: In many scientific and engineering domains, it is common to analyze and simulate complex physical systems using mathematical models. Although computing resources continue to increase in power and speed, computer simulation and analysis codes continue to grow in complexity and remain computationally expensive, limiting their use in design and optimization. Consequently, many researchers have developed different metamodeling strategies to create inexpensive approximations of computationally expensive computer simulations. These approximations introduce a new element of uncertainty during design optimization, and there is a need to develop efficient methods to assess metamodel validity. We investigate computationally inexpensive assessment methods for metamodel validation based on leave-k-out cross validation and develop guidelines for selecting k for different types of metamodels. Based on the results from two sets of test problems, k = 1 is recommended for leave-k-out cross validation of low-order polynomial and radial basis function metamodels, whereas k=0.1N or N is recommended for kriging metamodels, where N is the number of sample points used to construct the metamodel.

325 citations


Journal ArticleDOI
TL;DR: In this article, the development of a new plate theory and its two simple variants is given, the theory and one of its variants are variationally consistent, whereasthesecond variant isvariationally inconsistent and usesthe relationships between moments, shear forces, and loading.
Abstract: Thedevelopmentofa newree ned platetheoryand its two simplevariantsisgiven. Thetheorieshavestrongcommonality withtheequationsofclassicalplatetheory (CPT).However,unlikeCPT,thesetheoriesassumethatlateral and axial displacements have bending and shear components such that bending components do not contribute toward shearforces and, likewise, shearing components do not contribute toward bending moments. The theory and one of its variants are variationally consistent, whereasthesecond variant isvariationally inconsistent and usesthe relationships between moments, shear forces, and loading. It should be noted that, unlike any other ree ned plate theory, thegoverning equation as well as the expressions for moments and shear forces associated with thisvariant areidentical tothoseassociated withtheCPT,savefortheappearanceofasubscript. Theeffectivenessofthetheory and itsvariantsisdemonstratedthroughanexample. Surprisingly,theanswersobtained by boththevariantsofthe theory, one of which is variationally consistent and the other one is inconsistent, are same. The numerical example studied, therefore, not only brings out the effectiveness of the theories presented, but also, albeit unintentionally, supports the doubts, e rst raised by Levinson, about the so called superiority of variationally consistent methods.

311 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the effect of nonlinear aerodynamic effects on the divergence, utter, and limit-cycle oscillation (LCO) characteristics of a transonic airfoil cone guration.
Abstract: By the use of a state-of-the-art computational e uid dynamic (CFD) method to model nonlinear steady and unsteady transonice owsin conjunction with a linearstructural model,an investigationismadeinto how nonlinear aerodynamics can effect the divergence, e utter, and limit-cycle oscillation (LCO) characteristics of a transonic airfoil cone guration. A single-degree-of-freedom (DOF) model is studied for divergence, and one- and two-DOF models are studied for e utter and LCO. A harmonicbalancemethod in conjunction with the CFD solver is used to determine the aerodynamics for e nite amplitude unsteady excitations of a prescribed frequency. A procedure for determining the LCO solution is also presented. For the cone guration investigated, nonlinear aerodynamic effects are found to produce a favorable transonic divergence trend and unstable and stable LCO solutions, respectively, for the one- and two-DOF e utter models. Nomenclature a = nondimensional location of airfoil elastic axis, e=b b, c = semichord and chord, respectively cl, cm = coefe cients of lift and moment about elastic axis, respectively e = location of airfoil elastic axis, measured positive aft of airfoil midchord h, ® = airfoil plunge and pitch degrees of freedom I® = second moment of inertia of airfoil about elastic axis

282 citations


Journal ArticleDOI
TL;DR: In this article, it is proved that under convexity assumptions, the analytical target cascading (ATC) process converges to the optimal solution of the original design target problem.
Abstract: Analytical target cascading (ATC) is a relatively new methodology for the design of engineering systems. ATC deals with the issue of propagating desirable top level product design specifications (or targets) to appropriate targets at lower levels in a consistent and ecient manner. Most existing problem formulations for multilevel design often exhibit convergence diculties. In this article, it is proved that under convexity assumptions the ATC process converges to the optimal solution of the original design target problem.

280 citations


Journal ArticleDOI
TL;DR: The VABS (Variational Asymptotic Beam Section Analysis) algorithm as mentioned in this paper uses the variational asymptotics to split a three-dimensional nonlinear elasticity problem into a two-dimensional linear cross-sectional analysis and a one-dimensional, nonlinear beam problem.
Abstract: The computer program VABS (Variational Asymptotic Beam Section Analysis) uses the variational asymptotic method to split a three-dimensional nonlinear elasticity problem into a twodimensional linear cross-sectional analysis and a one-dimensional, nonlinear beam problem. This is accomplished by taking advantage of certain small parameters inherent to beam-like structures. VABS is able to calculate the one-dimensional cross-sectional stiffness constants, with transverse shear and Vlasov refinements, for initially twisted and curved beams with arbitrary geometry and material properties. Several validation cases are presented. First, an elliptic bar is modeled with transverse shear refinement using the variational asymptotic method, and the solution is shown to be identical to that obtained from the theory of elasticity. The shear center locations calculated by VABS for various cross sections agree well with those obtained from common engineering analyses. Comparisons with other composite beam theories prove that it is unnecessary to introduce ad hoc kinematic assumptions to build an accurate beam model. For numerical validation, values of the one-dimensional variables are extracted from an ABAQUS model and compared with results from a one-dimensional beam analysis using cross-sectional constants from VABS. Furthermore, point-wise three-dimensional stress and strain fields are recovered using VABS, and the correlation with the three-dimensional results from ABAQUS is excellent. Finally, classical theory is shown to be insufficient for general-purpose beam modeling. Appropriate refined theories are recommended for some classes of problems.

Journal ArticleDOI
TL;DR: In this paper, the effect of the actuation frequency on the manipulation of the global aerodynamic forces on lifting surfaces using surface-mounted fluidic actuators based on synthetic (zero mass flux) jet technology is demonstrated in wind-tunnel experiments.
Abstract: The effect of the actuation frequency on the manipulation of the global aerodynamic forces on lifting surfaces using surface-mounted fluidic actuators based on synthetic (zero mass flux) jet technology is demonstrated in wind-tunnel experiments. The effect of the actuation is investigated at two ranges of (dimensionless) jet formation frequencies of the order of, or well above, the natural shedding frequency. The vortical structures within the separated flow region vary substantially when the dimensionless actuation frequency F + is varied between O(1) and O(10). When F + is O(1), the reattachment is characterized by the formation of large vortical structures at the driving frequency that persist well beyond the trailing edge of the airfoil. The formation and shedding of these vortices leads to unsteady attachment and, consequently, to a time-periodic variation in vorticity flux and in circulation. Actuation at F + of O(10) leads to a complete flow reattachment that is marked by the absence of organized vortical structures along the flow surface

Journal ArticleDOI
TL;DR: A Newton‐Krylov algorithm is presented for the aerodynamic optimization of single and multi-element airfoil configurations and is used to compute a Pareto front for a multi-objective problem, and the results are validated using a genetic algorithm.
Abstract: A Newton‐Krylov algorithm is presented for the aerodynamic optimization of singleand multi-element airfoil configurations. The flow is governed by the compressible Navier‐Stokes equations in conjunction with a one-equation turbulence model. The preconditioned generalized minimum residual method is applied to solve the discreteadjoint equation, leading to a fast computation of accurate objective function gradients. Optimization constraints are enforced through a penalty formulation, and the resulting unconstrained problem is solved via a quasi-Newton method. Design examples include lift-enhancement and multi-point lift-constrained drag minimization problems. Furthermore, the new algorithm is used to compute a Pareto front for a multi-objective problem, and the results are validated using a genetic algorithm. Overall, the new algorithm provides an ecient and robust approach for addressing the issues of complex aerodynamic

Journal ArticleDOI
TL;DR: In this article, an acoustic analogy using linearized Euler's equations (LEE) forced with aerodynamic source terms is investigated to computetheacousticfare eld. And the results obtained by solving LEE are in good agreement with the reference solution.
Abstract: An acoustic analogy using linearized Euler’ s equations (LEE) forced with aerodynamic source terms is investigated to computetheacousticfare eld. Thishybridmethod isappliedto threemodelproblemssimulatedby solving Navier‐Stokes equations. In this way, its validity is estimated by comparing the predicted acoustic e eld with the reference solution given directly by the Navier ‐Stokes equations. The noise radiated by two corotating vortices is studied: e rst, in a medium at rest and, second, in a mean sheared e ow with no convection velocity. Then the sound e eld generated by vortex pairings in a subsonic mixing layer is investigated. In this case, a simplie ed formulation of LEE is proposed to prevent the exponential growth of instability waves. The acoustic e elds obtained by solving LEE are in good agreement with the reference solution. This study shows that the source terms introduced into the LEE are appropriate for free sheared e ows and that acoustic ‐mean e ow interactions are properly taken into account in the wave operator. Nomenclature b = half-width of the monopolar source c = sound velocity E;F;H = vectors in linearized Euler’ s equations (LEE) f = frequency f0 = fundamental frequency of the mixing layer k = complex wave number, kr Ciki M = Mach number p = pressure Re = Reynolds number rc = vortex core radius r0 = initial half distance between the two vortices S = sound source vector in LEE Si = source terms in the momentum equations T = period Tij = Lighthill’ s tensor t = time U = unknown vector in LEE U1 = slow stream velocity of the mixing layer U2 = rapid stream velocity of the mixing layer u = velocity vector, .u1;u2/ Vµ = initial tangential velocity of vortices

Journal ArticleDOI
TL;DR: In this paper, a multiwavelength flame emission technique was developed for high spatial resolution determination of soot temperature and soot volume fraction in axisymmetric laminar diffusion flames.
Abstract: A multiwavelength flame emission technique is developed for high spatial resolution determination of soot temperature and soot volume fraction in axisymmetric laminar diffusion flames. Horizontal scans of line-integrated spectra are collected over a spectral range of 500-945 nm. Inversion of these data through one-dimensional tomography using a three-point Abel inversion yields radial distributions of the soot radiation from which temperature profiles are extracted. From an absolute calibration of the flame emission and by use of these temperature data, absorption coefficients are calculated, which are directly proportional to the soot volume fractions. The important optical parameters are discussed. It is shown that a uniform sampling cross section through the flame must be maintained and that variations in sampling area produce inconsistencies between measurements and theory, which cannot be interpreted as spatial averaging of the property field. The variations in cross-sectional sampling area have the largest influence on the measurements at the edges of the flame, where the highest resolution is required. Emission attenuation by soot has been shown to have minor influence on the soot temperature and soot volume fraction for the soot loading of the axisymmetric flame tested. An emission correction scheme is outlined, which could be used for more heavily sooting flames. For a refractive index absorption function E(m) = Im[(m 2 - 1)/(m 2 + 2)] that is independent of wavelength, the soot temperatures and soot volume fractions measured with this technique are in excellent agreement with data obtained by coherent anti-Stokes Raman scattering nitrogen thermometry and two-dimensional soot extinction in the same ethylene coflow diffusion flame. The agreement of the results suggests a limit of the slope of the spectral response of E(m) to be between 0 and 20% over the spectral range examined.

Journal ArticleDOI
TL;DR: In this paper, a set of design codes based on a discrete adjoint method is extended to a multiprocessor environment using a shared memory approach, and a nearly linear speedup is demonstrated, and the consistency of the linearizations is shown to remain valid.
Abstract: Recent improvements in an unstructured-grid method for large-scale aerodynamic design are presented. Previous work had shown such computations to be prohibitively long in a sequential processing environment. Also, robust adjoint solutions and mesh movement procedures were difficult to realize, particularly for viscous flows. To overcome these limiting factors, a set of design codes based on a discrete adjoint method is extended to a multiprocessor environment using a shared memory approach. A nearly linear speedup is demonstrated, and the consistency of the linearizations is shown to remain valid. The full linearization of the residual is used to precondition the adjoint system, and a significantly improved convergence rate is obtained. A new mesh movement algorithm is implemented, and several advantages over an existing technique are presented

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the relationship between upstream turbulent boundary-layer properties and the unsteady separation shock behavior in a Mach 5 unswept compression ramp interaction and found that a fuller velocity is associated with increased resistance to separation to the boundary layer and, hence, causes downstream shock motion.
Abstract: Particle image velocimetry and high-frequency response wall pressure measurements have been used to investigate the relationship between upstream turbulent boundary-layer properties and the unsteady separation shock behavior in a Mach 5 unswept compression ramp interaction No correlation is found between variations in the incoming boundary-layer thickness and the separation shock foot position, as has been suggested in earlier work However, themean velocity proe le, conditioned on theseparation shock foot position, exhibits a subtly fullershape when the shock is downstream than when it is upstream More signie cantly, a clear correlation is observed between positivestreamwisevelocity e uctuations in thelowerthird of the upstream boundary layer and downstream shock motions, and vice versa The strongest correlations are found for velocity e uctuations with frequencies of about4‐10 kHz, which is signie cantly lowerthan the frequencies that characterize the large-scale structures in the boundary layer (40 kHz), although spatial limitations in the transducer array may limit the instrument sensitivity to this lower range These results are qualitatively consistent with the simple physical principle that a fuller velocity proe le imparts increased resistance to separation to the boundary layer and, hence, causes downstream shock motion, whereas a less-full velocity proe le is associated with lower resistance to separation and, hence, upstream shock motion

Journal ArticleDOI
TL;DR: In this article, a multidisciplinary robust design procedure that utilizes efficient methods for uncertainty analysis is developed, and the proposed techniques bring the features of a multi-disciplinary design optimization framework into consideration.
Abstract: Robust design has been gaining wide attention, and its applications have been extended to making reliable decisions when designing complex engineering systems in a multidisciplinary design environment. Though the usefulness of robust design is widely acknowledged for multidisciplinary design systems, its implementation is rare. One of the reasons is the complexity and computational burden associated with the evaluation of performance variations caused by the randomness (uncertainty) of a system. A multidisciplinary robust design procedure that utilizes efficient methods for uncertainty analysis is developed here. Different from the existing uncertainty analysis techniques, our proposed techniques bring the features of a multidisciplinary design optimization I MDO) framework into consideration. The system uncertainty analysis method and the concurrent subsystem uncertainty analysis method are developed to estimate the mean and variance of system performance subject to uncertainties associated with both design parameters and design models. As shown both analytically and empirically, compared to the conventional Monte Carlo simulation approach, the proposed techniques used for uncertainty analysis will significantly reduce the number of design evaluations at the system level and, therefore, improve the efficiency of robust design in the domain of MDO. A mathematical example and an electronic packaging problem are used as examples to verify the effectiveness of these approaches.

Journal ArticleDOI
TL;DR: An efe cient and user-friendly approach is presented for constructing unstructured surface grids directly on three-dimensional CAD surface data for surface meshing, and a notable reduction in turnaround time has been achieved.
Abstract: An efe cient and user-friendly approach is presented for constructing unstructured surface grids directly on three-dimensional CAD surface data. This system has the following features: 1 ) use of stereolithography data as surface dee nitions, that is, background grids for surface meshing; 2 ) automatic reconstruction of geometric features for initial front setup; 3 ) graphical user interface for easily controlling surface mesh density by inserting line sources and point sources on the surface; 4 ) adoption of an advancing-front surface triangulation method, which minimizes the necessity to divide the surface into a number of patches; and 5 ) outer boundary generation from templates in the system. The resulting system has been applied to several airplane cone gurations, and a notable reduction in turnaround time has been achieved. OMPUTATIONAL e uid dynamics (CFD) has become an indispensable design and analysis tool for many different types of geometric cone gurations and e eld regimes. The effectiveness of CFD usage in an actual design environment, however, is often limited. Most of these limitations are due to dife culties in generating the computational grid in a reasonable amount of time. The grid generation method should be automated as much aspossible. This is true for volume grid generation; it is now possible to create volume grids automatically. For the surface grid generation, however, user interventions are often required because the surface meshdirectlyaffectsthesolutionaccuraciesinCFDproblems,especiallyfortheaerodynamicevaluationofairplanes.Theaerodynamic performance is usually evaluated by surface values, such as pressure,skin friction,and so on.Thesevalues arehighlyaffected by the dee nition of sound geometric features, as well as the surface grid density. This suggests that surface grid generation methods must easily facilitate changes in grid density to obtain the best result with limited computational resources. Although controllability is often incompatible with the automation of grid generation, it is essential for surface meshing.

Journal ArticleDOI
TL;DR: This work examines a representative class of MDO problem formulations known as collaborative optimization, and discusses an alternative problem formulation, distributed analysis optimization, that yields a more tractable computational optimization problem.
Abstract: Analytical features of multidisciplinary optimization (MDO) problem formulations have significant practical consequences for the ability of nonlinear programming algorithms to solve the resulting computational optimization problems reliably and efficiently. We explore this important but frequently overlooked fact using the notion of disciplinary autonomy. Disciplinary autonomy is a desirable goal in formulating and solving MDO problems; however, the resulting system optimization problems are frequently difficult to solve. We illustrate the implications of MDO problem formulation for the tractability of the resulting design optimization problem by examining a representative class of MDO problem formulations known as collaborative optimization. We also discuss an alternative problem formulation, distributed analysis optimization, that yields a more tractable computational optimization problem.

Journal ArticleDOI
TL;DR: In this paper, several methods for the prediction of jet noise are described, including Lighthill's or Lilley's acoustic analogy, whereas the other is the jet noise generation model recently proposed by Tam and Auriault.
Abstract: Several methods for the prediction of jet noise are described. All but one of the noise prediction schemes are based on Lighthill's or Lilley's acoustic analogy, whereas the other is the jet noise generation model recently proposed by Tam and Auriault. In all of the approaches, some assumptions must be made concerning the statistical properties of the turbulent sources. In each case the characteristic scales of the turbulence are obtained from a solution of the Reynolds-averaged Navier-Stokes equation using a kappa-sigma turbulence model. It is shown that, for the same level of empiricism, Tam and Auriault's model yields better agreement with experimental noise measurements than the acoustic analogy. It is then shown that this result is not because of some fundamental flaw in the acoustic analogy approach, but instead is associated with the assumptions made in the approximation of the turbulent source statistics. If consistent assumptions are made, both the acoustic analogy and Tam and Auriault's model yield identical noise predictions. In conclusion, a proposal is presented for an acoustic analogy that provides a clearer identification of the equivalent source mechanisms, as is a discussion of noise prediction issues that remain to be resolved.

Journal ArticleDOI
TL;DR: In this paper, the axial axial stress distribution of a functionally graded beam is derived for the case of nearly uniform temperature along the length of the beam and a simple Euler-Bernoulli-type beam theory is developed based on the assumption that plane sections remain plane and normal to the beam axis.
Abstract: Thermoelastic equilibrium equations for a functionally graded beam are solved in closed-form to obtain the axial stress distribution. The thermoelastic constants of the beam and the temperature were assumed to vary exponentially through the thickness. The Poisson ratio was held constant. The exponential variation of the elastic constants and the temperature allow exact solution for the plane thermoelasticity equations. A simple Euler ‐ Bernoulli-type beam theory is also developed based on the assumption that plane sections remain plane and normal to the beam axis. The stresses were calculated for cases for which the elastic constants vary in the same manner as the temperature and vice versa. The residual thermal stresses are greatly reduced, when the variation of thermoelastic constants are opposite to that of the temperature distribution. When both elastic constants and temperature increasethrough the thickness in the samedirection, they causea signie cant raise in thermal stresses. For the case of nearly uniform temperature along the length of the beam, beam theory is adequate in predicting thermal residual stresses.

Journal ArticleDOI
TL;DR: In this paper, the second-moment closure and two eddy-viscosity models were evaluated with three versions of thesecondmoments closure and showed that the secondmoment models are superior, especially when the equations are integrated up to the wall.
Abstract: Severaltypesofrotatingandswirlinge owsfora rangeofReynoldsnumbersandrotationratesorswirlintensities have been studied computationally, aimed at identifying specie c features that require special consideration in turbulence modeling. The e ows considered include turbulent channel e ows subjected to streamwise and spanwise rotation,withstationaryandmovingboundaries;developingandfullydevelopede owsinaxiallyrotatingpipes;and swirling e owsin combustorgeometriesand long pipes.Computationsperformed with threeversionsof thesecondmoment closure and two eddy-viscosity models show that the second-moment models are superior, especially when the equations are integrated up to the wall. Such models reproduced the main e ow parameters for all e ows considered in acceptable agreement with the available experimental data and direct numerical simulations. However,challengesstillremaininpredictingaccuratelysomespecie ce owfeatures,suchascapturingthetransition from a freevortex to solid-body rotation in a long straight pipewith a weak swirl, or reproducing the normal stress components in the core region. Also, the so-called uw anomaly in fully developed e ows with streamwise rotation remains questionable. For rotating e ows, the low-Reynolds-number models yield a somewhat premature e ow relaminarization at high rotation speeds.

Journal ArticleDOI
TL;DR: In this paper, an active separation control experiment was conducted in a cryogenic pressurized wind tunnel on a wall-mounted bump at chord Reynolds numbers from 2.4 x 10 6 to 26 x 106 and a Mach number of 0.25.
Abstract: An active separation control experiment was conducted in a cryogenic pressurized wind tunnel on a wall-mounted bump at chord Reynolds numbers from 2.4 x 10 6 to 26 x 106 and a Mach number of 0.25. The model simulates the upper surface of a 20% thick Glauert-Goldschmied-type airfoil at zero incidence. The turbulent boundary layer of the tunnel sidewall flows over the model and eliminates laminar-turbulent transition from the problem. Indeed, the Reynolds number either based on the chord or boundary-layer thickness had a negligible effect on the flow and its control. Without control, a large turbulent separation bubble is formed at the lee side of the model. Periodic excitation and steady suction or blowing were applied to eliminate gradually the separation bubble. Detailed effects due to variations in the excitation frequency, amplitude, and the steady mass flux are described and compared to those of steady suction or blowing

Journal ArticleDOI
TL;DR: A new version is introduced of the bilevel integrated system synthesis method intended for optimization of engineering systems conducted by distributed specialty groups working concurrently in a multiprocessor computing environment that shows that, if the problem is convex, the solution of the decomposed problem is the same as that obtained without decomposition.
Abstract: The paper introduces a new version of the Bi-Level Integrated System Synthesis (BLISS) methods intended for optimization of engineering systems conducted by distributed specialty groups working concurrently and using a multiprocessor computing environment. The method decomposes the overall optimization task into subtasks associated with disciplines or subsystems where the local design variables are numerous and a single, system-level optimization whose design variables are relatively few. The subtasks are fully autonomous as to their inner operations and decision making. Their purpose is to eliminate the local design variables and generate a wide spectrum of feasible designs whose behavior is represented by Response Surfaces to be accessed by a system-level optimization. It is shown that, if the problem is convex, the solution of the decomposed problem is the same as that obtained without decomposition. A simplified example of an aircraft design shows the method working as intended. The paper includes a discussion of the method merits and demerits and recommendations for further research.

Journal ArticleDOI
TL;DR: The von Karman lecture as mentioned in this paper discusses the state of the art in nonlinear aeroelasticity and unsteady aerodynamics and identifies several of the most significant nonlinearities arising in a structure or in an aerodynamic flow field.
Abstract: In this von Karman lecture, a subject is addressed whose foundations were significantly influenced by the work of Theodore von Karman. A classic paper by von Karman and Sears first considered the determination of aerodynamic forces on an airfoil undergoing general time-dependent motion. Also, early in his career, von Karman investigated fundamental issues in structural mechanics and derived the celebrated von Karman plate equations for determining the large (nonlinear) deflections of an elastic plate under a distributed force. Finally, he authored a widely cited paper on the importance of nonlinearities for engineers and engineering. In this lecture, these themes are recalled and the current state of the art in nonlinear aeroelasticity and unsteady aerodynamics is discussed. Several of the most significant nonlinearities arising in a structure or in an aerodynamic flow field are identified. Recent and relevant theoretical and experimental studies are reviewed and future developments are projected that are expected to have a significant impact on our ability to understand and beneficially use nonlinear dynamic aeroelastic behavior

Journal ArticleDOI
TL;DR: In this article, a three-dimensional mixed variational principle is used to derive a Kth-order two-dimensional line-artheory for an anisotropichomogeneous piezoelectric (PZT) plate.
Abstract: A three-dimensional mixed variational principle is used toderive a Kth-order two-dimensional lineartheory for an anisotropichomogeneouspiezoelectric(PZT)plate.Themechanicaldisplacements, theelectricpotential,theinplane components of the stress tensor, and the in-plane components of the electric displacement are expressed as a e niteseries of orderK inthethickness coordinate bytakingLegendrepolynomialsas thebasisfunctions. However, the transverse shear stress, the transverse normal stress, and the transverse electric displacement are expressed as a e nite series of order (K +2) in the thickness coordinate. The formulation accounts for the double forces without moments that may change the thickness of the plate. Results obtained by using the plate theory are given for the bending of a cantilever thick plate loaded on the top and the bottom surfaces by uniformly distributed 1) normal tractions and 2) tangential tractions. Results are also computed for the bending of a cantilever thick PZT beam loaded by 1) a uniformly distributed charge density on the top and the bottom surfaces and 2) equal and opposite normal tractions distributed uniformly only on a part of the beam. The seventh-order plate theory captures well the boundary-layer effects near the clamped and the free edges and adjacent to the top and the bottom surfaces of a thick orthotropic cantilever beam with the span to the thickness ratio of two. Also, through-the-thickness variation of the transverse shear and the transverse normal stresses agree well with those computed from the analytical solution of the three-dimensional elasticity equations. The governing partial differential equations are second order, so that Lagrange basis functions can be used to solve the problem by the e nite element method.

Journal ArticleDOI
TL;DR: In this paper, a variational formulation of Lighthill's acoustic analogy to trailing edge noise is considered, and the effect of e niteness of the chord and the variation of far-e eld pressure directivity with frequency is investigated.
Abstract: Application of the variational formulation of Lighthill’ s acoustic analogy to trailing-edge noise is considered. Use is made of this formulation to study the effect of e niteness of the chord and the variation of far-e eld pressure directivity with frequency. Numerical analytical solution results are validated for certain limiting cases. Use is also made of this methodology to calculate the far-e eld acoustic pressure for a low-Mach-number turbulent e ow. To determine the acoustic sources for this problem, we employ an unstructured mesh, large eddy simulation of the incompressible Navier ‐Stokes equations.

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TL;DR: In this article, a simple equation is derived for expressing the drag reduction rate by spanwise wall oscillations and the relation between near-wall streamwise vortices and low and high-speed flow is scrutinized to extract the key parameters.
Abstract: Drag reduction in turbulent channel and pipe e ows by spanwise (circumferential) wall oscillations is studied numerically. The ine uence of the wall oscillation on near-wall streamwise vortices is examined. By the use of the Stokes second problem, a wall-normal distanceparameter and an acceleration parameterare obtained toestimate the drag reduction rate. A simple equation is derived for expressing the drag reduction rate by spanwise wall oscillations. The relation between near-wall streamwise vortices and low- and high-speed e uids is scrutinized to extract the key parameters. The drag reduction mechanism is analyzed in terms of the attenuation of Reynolds shear stress.

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TL;DR: In this paper, boundary-layer transition experiments were performed on a sharp 5.06-deg half-angle round cone at zero angle of attack in the T5 Hypervelocity Shock Tunnel to test the effects of the porous surface.
Abstract: Recently performed linear stability analyses suggested that transition could be delayed in hypersonic boundary layers by using an ultrasonically absorptive surface to damp the second mode (Mack mode). Boundary-layer transition experiments were performed on a sharp 5.06-deg half-angle round cone at zero angle of attack in the T5 Hypervelocity Shock Tunnel to test this concept. The cone was constructed with a smooth surface around half the cone circumference (to serve as a control) and an acoustically absorptive porous surface on the other half. Test gases investigated included nitrogen and carbon dioxide at M∞ ≃ 5 with specific reservoir enthalpy ranging from 1.3 to 13.0 MJ/kg and reservoir pressure ranging from 9.0 to 50.0 MPa. Comparisons were performed to ensure that previous results obtained in similar experiments (on a regular smooth surface) were reproduced, and the results were extended to examine the effects of the porous surface. These experiments indicated that the porous surface was highly effective in delaying transition provided that the pore size was significantly smaller than the viscous length scale.