Showing papers in "AIAA Journal in 1999"

High-Order-Accurate Methods for Complex Unsteady Subsonic Flows

Abstract: Several issues related to the application of very high-order schemes for the finite difference simulation of the full Navier-Stokes equations are investigated. The schemes utilize an implicit, approximately factored time-integration method coupled with spatial fourth- and sixth-order compact-difference formulations and a filtering strategy of up to tenth order. For this last aspect a consistent optimization approach is developed to treat points near the boundary resulting in minimal degradation of accuracy. The problems investigated exhibit many of the challenging features of practical flows and include several with complications introduced by curvilinear meshes, viscous effects, unsteadiness, and three-dimensionality. The high-order method is observed to be very robust for every problem considered. The algorithm is demonstrated to be highly accurate compared to both second-order and upwind-biased methods. For several cases, particularly very-low-Mach-number flows, filtering is determined to be a superior alternative to scalar damping

Jet Mixing Noise from Fine-Scale Turbulence

Abstract: It is known that turhulent mixing noise from high-speed jets consists of two components. They are the noise from large turbulent structures in the form of Mach wave radiation and the less directional fine-scale turbulence noise. The Mach wave radiation dominates in the downstream direction. The fine-scale turbulence noise dominates in the sideline and upstream directions. A semiempirical theory is developed for the prediction of the spectrum, intensity, and directivity of the fine-scale turhulence noise. The prediction method is self-contained. The turbulence information is supplied by the k-e turhulence model. The theory contains three empirical constants beyond those of the k-e model. These constants are determined by best fit of the calculated noise spectra to experimental measurements. Extensive comparisons between calculated and measured noise spectra over a wide range of directions of radiation,jet velocities, and temperatures have heen carried out. Excellent agreements are found. It is believed that the present theory offers significant improvements over current empirical or semiempirical jet noise prediction methods in use. There is no first principle jet noise theory at the present time.

Monotonically integrated large eddy simulation of free shear flows

Abstract: With a view to ensure that proper interaction between resolvable or grid scale and subgrid scale (SGS) motions are mimicked, it is vital to determine the necessary physics that must be built into the SGS models. In ordinary large eddy simulation (LES) approaches, models are introduced for closure in the low-pass filtered Navier-Stokes equations (NSEs), which are the ones solved numerically. A promising LES approach is monotonically integrated LES (MILES), which involves solving the unfiltered NSE using high-resolution monotone algorithms; in this approach, implicit SGS models, provided by intrinsic nonlinear high-frequency filters built into the convection discretization, are coupled naturally to the resolvable scales of the flow. Formal properties of the effectual SGS modeling using MILES are documented using databases of simulated homogeneous turbulence and transitional freejets; mathematical and physical aspects of (implicit) SGS modeling through the use of nonlinear flux limiters are addressed in this context

Jet characteristics of a plunging airfoil

Abstract: Water-tunnel tests of a NACA 0012 airfoil that was oscillated sinusoidally in plunge are described. The flowered downstream of the airfoil was explored by dye flow visualization and single-component laser Doppler velocimetry (LDV) measurements for a range of freestream speeds, frequencies, and amplitudes of oscillation. The dye visualizations show that the vortex patterns generated by the plunging airfoil change from drag-producing wake flows to thrust-producing jet flows as soon as the ratio of maximum plunge velocity to freestream speed, i.e., the nondimensional plunge velocity, exceeds approximately 0.4. The LDV measurements show that the nondimensional plunge velocity is the appropriate parameter to collapse the maximum streamwise velocity data covering a nondimensional plunge velocity range from 0.18 to 9.3

Oscillatory Control of Separation at High Reynolds Numbers

Abstract: An experiment conducted in a pressurized, cryogenic wind tunnel demonstrates that unsteady flow control using oscillatory blowing (with essentially zero mass flux) can effectively delay flow separation and reattach separated flow on an airfoil at chord Reynolds numbers as high as 38 × 10 6 . Oscillatory blowing at frequencies that generate one to three vortices over the controlled region at all times are effective over the entire Reynolds number range, in accordance with previous low-Reynolds-number tests. Stall is delayed and poststall characteristics are improved when oscillatory blowing is applied from the leading-edge region of the airfoil, whereas flap effectiveness is increased when control is applied at the flap shoulder. Similar gains in airfoil performance require steady blowing with a momentum coefficient that is two orders of magnitude greater. A detailed experimental and theoretical investigation was undertaken to characterize the oscillatory blowing disturbance, in the absence of external flow, and to estimate the oscillatory blowing momentum coefficient used in the cryogenic wind tunnel experiment. Possible approaches toward closed-loop active separation control are also presented

Numerical investigation of synthetic-jet flowfields

Abstract: The flowflelds surrounding a synthetic-jet actuating device are investigated numerically by direct simulation. Solutions are obtained to the unsteady compressible Navier-Stokes equations for both the interior of the actuator cavity and for the external jet flowfield. The interior results are generated on an overset deforming zonal mesh system, whereas the jet flowfield is obtained by a high-order compact-difference scheme. Newton-like subiterations are employed to achieve second-order temporal accuracy. Details of the computations are summarized, and the quality of the results is assessed via grid resolution and time-step size studies. Several aspects of the actuator configuration are investigated, including cavity geometry and Reynolds number. Differences between two-dimensional and three-dimensional external unsteady flowfields are elucidated, and comparison is made with experimental data in terms of the mean and fluctuating components of the jet velocity

Bidirectional Evolutionary Method for Stiffness Optimization

Abstract: Evolutionary structural optimization (ESO) method was originally developed based on the idea that by systematically removing the inefficient material, the residual shape of the structure evolves toward an optimum. This paper presents an extension of the method called bidirectional ESO (BESO) for topology optimization subject to stiffness and displacement constraints. BESO allows for the material to be added as well as to be removed to modify the structural topology. Basic concepts of BESO including the sensitivity number and displacement extrapolation are proposed and optimization procedures are presented. Integrated with the finite element analysis technique, BESO is applied to several two-dimensional plane stress problems. Its effectiveness and efficiency are examined in comparison with the results obtained by ESO. It is found that BESO is more reliable and computationally more efficient than ESO in most cases. Its capability and limitation are discussed.

Implicit Solution of Preconditioned Navier- Stokes Equations Using Algebraic Multigrid

Abstract: We describe an algorithm for the solution of the Navier-Stokes equations on unstructured meshes that employs a coupled algebraic multigrid method to accelerate a point-implicit symmetric Gauss-Seidel relaxation scheme. The equations are preconditioned to permit solution of both compressible and incompressible flows. A cell-based, finite volume discretization is used in conjunction with flux-difference splitting and a linear reconstruction of variables. We present results for flowfields representing a range of Mach numbers and Reynolds numbers. The scheme remains stable up to infinite Courant number and exhibits CPU usage that scales linearly with cell count

Steady and Unsteady Flow Simulations Using the Hybrid Flow Solver AVBP

Abstract: The unstructured flow solver AVBP of CERFACS is presented. The basic concepts of the program are described, and various computational results are presented for a large spectrum of applications ranging from steady-state external aerodynamics to unsteady turbulent flows with and without combustion. The code solves the compressible Navier-Stokes equations on hybrid grids of arbitrary cell type. The code is built on a modular software library and has been ported to a wide range of parallel computers.

Blunt-Body Wave Drag Reduction Using Focused Energy Deposition

Abstract: A parametric computational study of energy deposition upstream of generic two-dimensional and axisymmetric blunt bodies at Mach numbers of 6.5 and 10 is performed utilizing a full Navier-Stokes computational fluid dynamics code. The energy deposition modifies the upstream shock structure and results in large wave drag reduction and very high power effectiveness. Specifically, drag is reduced to values as low as 30% of baseline drag (no energy deposited into flow) and power effectiveness ratios (ratio of thrust power saved to power deposited into the flow) of up to 33 are obtained. The fluid dynamic and thermodynamic bases of the observed drag reduction are examined

Effect of Isolated Micron-Sized Roughness on Transition in Swept-Wing Flows

Abstract: Boundary-layer transition-to-turbulence studies are conducted in the Arizona State University Unsteady Wind Tunnel on a 45-deg swept airfoil. The pressure gradient is designed so that the initial stability characteristics are purely crossflow dominated. Flow-visualization and hot-wire measurements show that the development of the crossflow vortices is influenced by roughness near the attachment line. Comparisons of transition location are made between a painted surface (distributed 9-μm peaks and valleys on the surface), a machine-polished surface (0.5-μm rms finish), and a hand-polished surface (0.25-μm rms finish). Then isolated 6-μm roughness elements are placed near the attachment line on the airfoil surface under conditions of the final polish (0.25-μm rms). These elements create an enhanced packet of stationary crossflow waves, which results in localized early transition. The diameter, height, and location of these roughness elements are varied in a systematic manner. Spanwise hot-wire measurements are taken behind the roughness element to document the enhanced vortices. These scans are made at several different chord locations to examine vortex growth

Airfoil Design on Unstructured Grids for Turbulent Flows

Abstract: An aerodynamic design algorithm for turbulent e ows using unstructured grids is described. The current approachusesadjoint (costate)variablestoobtainderivativesofthecostfunction.Thesolutionoftheadjointequations is obtained by using an implicit formulation in which the turbulence model is fully coupled with the e ow equations when solving for the costate variables. The accuracy of the derivatives is demonstrated by comparison with e nite difference gradients, and a few sample computations are shown. Recommendations on directions of further research into the Navier ‐Stokes design process are made. Nomenclature A = area of control volume a = speed of sound C ¤ = constant used in Sutherland’ s law for viscosity cb1;cb2;cv1; = constants used in Spalart ‐Allmaras cw1;cw2;cw3 turbulence model cd = drag cl = lift c1

Effects of Dynamic Stall on Propulsive Efficiency and Thrust of Flapping Airfoil

Abstract: Numerical simulations of dynamic stall phenomena around an airfoil oscillating in a coupled mode, in which the pitching and heaving oscillations have some phase difference, have been performed with a Navier ‐Stokes code. The propulsive efe ciency and the thrust have been calculated for various combinations of the phase difference and the reduced frequency for two different amplitude ratios. The effects of the dynamic stall phenomena on the behaviors of the propulsive efe ciency and thrust are discussed in detail by examination of each e ow pattern obtained. Highest efe ciency has been observed for the case in which the pitching oscillation advances 90 deg ahead of the heaving oscillation and the reduced frequency is at some optimum value, for which there appears no appreciable e ow separation in spite of large-amplitude oscillations. For phase angles and reduced frequency other than thisbestcondition, efe ciency israpidly degraded by theoccurrenceof thelarge-scaleleading-edgeseparation.

Penetration and Mixing of Fully Modulated Turbulent Jets in Crossflow

Abstract: Fully-modulated, incompressible, turbulent transverse jets were studied experimentally over a range of pulsing frequencies, duty-cycles, and at two jet-to-crossflow velocity ratios. The jet flow was completely modulated by operating a solenoid valve resulting in the shut off of jet supply during a portion of the cycle. The planar laserinduced fluorescence technique was used to determine the penetration, dilution, and structural features of the pulsed jets. The molecular mixing rate was quantified through a chemical reaction between the jet and crossflow fluids. Short injection times resulted in creation of vortex ring structures whereas long injection times produced axially elongated turbulent puffs, similar to a segment of the steady jet. The latter case resulted in only modest enhancement of the jet penetration depth and dilution. Pulsed jets dominated by vortex ring had penetration depths significantly greater than a steady jet with the same velocity ratio. Penetration of up to about 5 times the steady jet value at 50 jet diameters downstream of the jet exit was observed with 200 ms pulses. Duty-cycle had a significant effect on the performance of pulsed jets with short injection times. Increasing the duty-cycle for a fixed injection time diminished the jet penetration. The dilution and mixing rates of pulsed jets with short injection time were also increased over the steady jet. The greatest reduction in the mixing rate was approximately 50% for well-separated pulses with short injection times.

Multilayered Shell Theories Accounting for Layerwise Mixed Description, Part 1: Governing Equations

Abstract: A Reissner mixed variational equation is employed in this paper to derive the differential governing equations of multilayered, double curved shells made of orthotropic laminae In linear static cases. A layerwise description is referred to by assuming two independent fields in the thickness direction for the transverse stress (both shear and normal components) and displacement variables in each layer. Interlaminar values are used as the unknown variables of the introduced expansions. The continuity conditions of displacements and transverse shear and normals stresses at the interfaces between two consecutive layers, referred to as C 0 z requirements, have been a priori fulfilled. These have been used to drive the governing equations from a layer to a multilayered level. Classical displacement formulations and related equivalent single-layer equations have been derived for comparison purposes. No assumptions have been made concerning the terms of type thickness to radii shell ratio h/R. Donnell's shallow shell-type equations are given as particular cases for all of the considered theories. Indicial notations and arrays have been used extensively to handle the presented developments in a concise manner. Numerical evaluations and comparisons to exact and other available two-dimensional solutions are given in a companion paper (E. Carrera, Multilayered Shell Theories Accounting for Layerwise Mixed Description, Part 2: Numerical Evaluations, AIAA Journal, Vol. 37, No. 9, 1999, pp. 1117-1124).

Computational Aeroacoustic Analysis of Slat Trailing-Edge Flow

Abstract: An acoustic analysis based on the Ffowcs Williams and Hawkings equation was performed for a high-lift system. As input, the acoustic analysis used unsteady flow data obtained from a highly resolved, time-dependent, Reynolds-averaged Navier-Stokes caclulation. The analysis strongly suggests that vortex shedding from the trailing edge of the slat results in a high-amplitude, high-frequency acoustic signal, similar to that which was observed in a corresponding experimental study of the high-lift system.

Robust Design Approach for Achieving Flexibility in Multidisciplinary Design

Abstract: The interdisciplinary nature of complex systems design presents challenges associated with computational burdens and organizational barriers as these issues cannot be resolved with faster computers and more efficient optimization algorithms. There is a need to develop design methods that could model different degrees of collaboration and help to resolve the conflicts between different disciplines. In this paper, an approach to providing flexibility in resolving the conflicts between the interests of multiple disciplines is proposed. We propose to integrate the robust design concept into the existing game protocol, in particular the Stackelberg leader/follower protocol. Specifically, the solution for the design parameters which involve the coupled information between multiple players (disciplines) are developed as a range of solutions rather than a single point solution. This additional flexibility provides more freedom to the discipline that takes the role of follower while the performance of the discipline that takes leader's role is stable within a tolerable range. The method is demonstrated by a passenger aircraft design problem. NOMENCLATURE

Mathematical and Physical Constraints on Large-Eddy Simulation of Turbulence

Abstract: Recent progress in the theoretical foundations of large-eddy simulation is reviewed. Most of the work reported is motivated by conceptual difficulties encountered in applying the large eddy simulation method to inhomogeneous complex geometry flows. Among the topics covered are the problem of the lack of commutation between filtering and derivative operators for inhomogeneous flows, the issues of enforcing symmetry and realizability conditions in subgrid modeling, and the problem of unacceptably high numerical errors in large eddy simulation implementations with finite difference methods

Airfoil and Wing Design Through Hybrid Optimization Strategies

Abstract: Real-world design problems need robust and effective system-level optimization tools inasmuch as they are ruled by several criteria, most often in multidisciplinary environments. In this work a hybrid optimization algorithm has been obtained by adding a gradient-based technique to the set of operators of a multiobjective genetic algorithm. This makes it possible to increase the computational efficiency of the genetic algorithm while preserving its favorable features of robustness, problem independence, and multiobjective optimization capabilities. Aerodynamic shape design problems, including both airfoil and wing designs, are considered

Static Shape Control of Smart Structures Using Compliant Mechanisms

Abstract: A novel approach to static shape control of smart structures is introduced. This approach uses a special class of mechanisms called compliant mechanisms powered by a single input actuator. The key design Issue in this approach is the synthesis of a suitable compliant mechanism for the task. A systematic procedure for synthesis of such compliant mechanisms is presented by combining the first principles of mechanics and kinematics through a structural optimization scheme. The procedure is illustrated by an example wherein a prescribed smooth shape change in the camber of an idealized airfoil structure is accomplished by a specially synthesized compliant mechanism actuated by a single torque input. The scope and benefits of the proposed approach in providing viable simple solutions for real-scale static shape control applications are also discussed.

Multilayered Shell Theories Accounting for Layerwise Mixed Description, Part 2: Numerical Evaluations

Abstract: The mixed layerwise shell theories that are presented in the companion article (E. Carrera, Multilayered Shell Theories Accounting for Layerwise Mixed Description, Part 1: Governing Equations' AIAA Journal, Vol. 37, No. 9, 1999, pp. 1107-1116) are evaluated here by solving several problems related to orthotropic cross-ply laminated, circular, cylindrical, and spherical shells subjected to static loadings for which closed-form solutions are given. Particular cases related to layerwise and equivalent single-layer models, based on classical displacement formulations, are evaluated for comparison purpose. A further comparison with three-dimensional elasticity exact solutions and to other higher-order shear deformations studies have been made. Results are given in the form of tables and diagrams. Approximations introduced by Donnell's shallow shell theories are evaluated for most of the problems. It has been concluded that the proposed mixed layerwise theories leads to a better description than the related analyses, which are based on displacement formulations. An excellent agreement, with respect to the exact solution, has been found for displacement and transverse stress components. These stresses have been herein calculated a priori. The importance of an adequate description of curvature terms related to the shell thickness to radii ratio h/R is also underlined. These effects have been contrasted by extensive use of fictitious interfaces in the conduced layerwise investigations.

New Shear Actuated Smart Structure Beam Finite Element

Abstract: We present the formulation and validation of a new adaptive sandwich-beam finite element, capable of dealing with either extension or shear actuation mechanisms, which is reached by coating an elastic core with piezoelectric sheets or sandwiching a piezoelectric core between two elastic faces. The poling direction is taken parallel to the transversely applied electric field for the first mechanism and in the axial direction for the second one. The sandwich construction is made of asymmetric thin faces (Euler-Bernoulli beams) and a relatively thick core (Timoshenko beam). The obtained two-node finite element has only four mechanical degrees of freedom that are the deflection and its derivative and the mean and relative axial displacements of the faces midplanes. Finite element analysis of segmented and continuous cantilever adaptive sandwich beams with active faces (extension actuated) or core (shear actuated) show good comparisons with results found in the Iiterature, Additional parametric studies (actuator's position and thickness, structure's stiffness) with the present element indicate that the shear actuation mechanism presents several promising features over the conventional extension actuation mechanism. In fact, the shear actuation mechanism is better than the extension one for stiff structures and thick piezoelectric actuators.

Role of anisotropy in turbulent mixing noise

Abstract: The objective is to explore the role of anisotropy on aerodynamic mixing noise because of fine-scale turbulence. The usual assumption of isotropic turbulence is replaced with that of axisymmetric turbulence. The analysis is based on source terms of Lilley's equation. In addition, flowlacoustic interaction is accounted for in terms of a high-frequency solution to the axisymmetric Lilley's equation. In the limiting case of isotropy, various source correlation terms derived here simplify to those obtained with an isotropic turbulence model of Batchelor. A Reynolds-averaged Navier-Stokes solution with a k-∈ turbulence model for a Mach 1.0 jet is used to make flow and acoustic predictions. A parametric study of the turbulence scales indicates that anisotropy increases the peak noise level.

Accuracy of Shock Capturing in Two Spatial Dimensions

Abstract: An assessment of the accuracy of shock capturing schemes is made for two-dimensional steady flow around a cylindrical projectile. Both a linear fourth-order method and a nonlinear third-order method are used in this study. It is shown, contrary to conventional wisdom, that captured two-dimensional shocks are asymptotically first-order, regardless of the design accuracy of the numerical method. The practical implications of this finding are discussed in the context of the efficacy of high-order numerical methods for discontinuous flows.

Rates of Change of Eigenvalues and Eigenvectors in Damped Dynamic System

Abstract: Rates of change of eigenvalues and eigenvectors of a damped linear discrete dynamic system with respect to the system parameters are presented. A non-proportional viscous damping model is assumed. Due to the non-proportional nature of the damping the mode shapes and natural frequencies become complex, and as a consequence the sensitivities of eigenvalues and eigenvectors are also complex. The results are presented in terms of the complex modes and frequencies of the second order system and the use of rather undesirable state-space representation is avoided. The usefulness of the derived expressions is demonstrated by considering an example of a non-proportionally damped two degree-of-freedom system.

Finite Volume Discretization Aspects for Viscous Flows on Mixed Unstructured Grids

Abstract: A solution method for compressible turbulent flows on unstructured grids in two dimensions is described. The method can be used on grids consisting of triangular and/or quadrilateral cells. Control volumes are constructed from dual cells, and the solution variables are stored at the vertices of the grid. Grid-transparent algorithms are developed that do not require knowledge of cell types, leading to simple discretization schemes on mixed grids. The inviscid fluxes are computed from limited high-resolution schemes originally developed for unstructured triangular grids. They are easily applied to quadrilateral or mixed grids and are grid transparent. The discretization of the viscous fluxes is studied in detail. A positive, grid-transparent discretization of Laplace's equation is developed. The existence of tangential derivatives in the viscous terms prevents grid transparency. By neglecting tangential derivatives, an approximate form of the viscous fluxes is developed, which recovers grid transparency. The approximate form is shown to be similar to the thin-shear-layer approximation. Results are obtained for a transonic inviscid flow, a laminar separated flow, and a transonic turbulent flow

Dynamic Response and Wave Propagation in Plane Trusses and Frames

Abstract: The dynamics of planar frames and trusses is analyzed in terms of the propagation of axial (longitudinal) and flexural (transverse) stress waves being structural members. The waves are multiscattered at the joints, and scattering coefficients representing the reflection and transmission of both types of waves at each joint are derived from the dynamics and compatibility conditions of the joint. The complex multireflected waves within the structure are evaluated in the frequency domain by a newly developed reverberation matrix, which is formulated from scattering coefficients and propagating phase factors. Transient waves are then analyzed by Fourier synthesis and evaluated by a fast Fourier transform algorithm. Transient responses for the axial and bending strains in all structural members are calculated over a long duration for a model truss with rigid joints. Comparison to experimental data of the model truss under a step loading shows good agreement for the early as well as considerably long time responses.

Planar Symmetry in the Unsteady Wake of a Sphere

Abstract: III. Conclusion Several conclusions can be drawn from the study. 1) A periodical surface  ow control can produce a three-dimensionalperturbationthat leads to the formationof streamwisevortical  ow structuresin the separatedshear layer.Thoughsuctionwas used in this study, boundary-layercontrols in general should achieve the same effect when applied in a similar fashion. 2) The vortical structures cause a normally separated  ow to reattach. 3) The control is most effective when applied near and upstream of the natural separation. 4) The control device size, as measured in this particular case by the combinationof suction hole diameter, hole number density, and associated porosity, is small. 5) Similar results are obtained over different control patterns, indicating a broadband instability.

Validation of an Impedance Eduction Method in Flow

Abstract: Results are reported for validating a method for educing the normal incidence impedance of a locally reacting liner in a grazing incidence, nonprogressive acoustic wave environment with flow. The results demonstrate the ability of the method to reproduce the normal incidence admittance of a solid steel plate and normal incidence impedance of two soft test liners in a uniform flow. The selected test liners are known to be locally reacting and exhibit no amplitude-dependent impedance nonlinearities and only minimal flow effects. Baseline results for these liners are, therefore, established from measurements in a conventional normal incidence impedance tube. A key feature of the method is the expansion of the unknown impedance function as a piecewise continuous polynomial with undetermined coefficients. Stewart's adaptation (Stewart, G. W., III, A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives, Journal of ACM, Vol. 14, No. 1, 1967, pp. 72-83) of the Davidon-Fletcher-Powell optimization algorithm is used to educe the normal incidence impedance at each Mach number by optimizing an objective function. The method very Marly reproduces the normal incidence impedance spectrum for each of the test liners; thus, its usefulness for determining the normal incidence impedance of test liners for a broad range of source frequencies and flow Mach numbers is demonstrated.

Reynolds-Stress-Transport Modeling for Compressible Aerodynamics Applications

Abstract: Progress is reported in the development of a nonlinear Reynolds-stress-transport model for compressible, turbulent flow. The focus is on a variation of a particular cublc model that does not require the usual topography-related parameters, such as normal-to-wall vectors. However, certain wall-proximity corrections that have been used in the model to replace conventional wall-reflection terms display the wrong response to shocks, which are falsoly interpreted as localized regions of strong inhomogeneity. A modified cubic variant is proposed that allows integration across the semiviscous sublayer and incorporates additional constraints to guard against unphysical response of the pressure-strain model in the vicinity of shock waves. The modified model is applied to both two- and three-dimensional compressible flows, involving shock-wave/boundary-layer interaction, and is shown to yield generally favorable results