Showing papers in "AIAA Journal in 1998"

Data-Parallel Line Relaxation Method for the Navier -Stokes Equations

Abstract: The Gauss‐Seidel line relaxation method is modie ed for the simulation of viscous e ows on massively parallel computers. The resulting data-parallel line relaxation method is shown to have good convergence properties for a seriesoftestcases.Thenewmethodrequiressignie cantlymorememorythanthepreviouslydevelopeddata-parallel relaxation methods, but it reaches a steady-state solution in much less time for all cases tested to date. In addition, the data-parallel line relaxation method shows good convergence properties even on the high-cell-aspect-ratio grids required to simulate high-Reynolds-number e ows. The new method is implemented using message passing on the Cray T3E, and the parallel performance of the method on this machine is discussed. The data-parallel line relaxation method combines the fast convergence of the Gauss ‐Seidel line relaxation method with a high parallel efe ciency and thus shows promise for large-scale simulation of viscous e ows.

Verification of Codes and Calculations

Abstract: Background discussion, definitions, and descriptions are given for some terms related to confidence building in computational fluid dynamics. The two principal distinctions made are between verification vs validation and between verification of codes vs verification of individual calculations. Also discussed are numerical errors vs conceptual modeling errors; iterative convergence vs grid convergence (or residual accuracy vs discretization accuracy); confirmation, calibration, tuning, and certification; error taxonomies; and customer illusions vs customer care. Emphasis is given to rigorous code verification via systematic grid convergence using the method of manufactured solutions, and a simple method for uniform reporting of grid convergence studies using the Grid Convergence Index (GCI). Also discussed are surrogate single-grid error indicators.

Turbulence modeling for time-dependent RANS and VLES : a review

Abstract: Reynolds stress models and traditional large-eddy simulations are reexamined with a view toward developing a combined methodology for the computation of complex turbulent flows. More specifically, an entirely new approach to time-dependent Reynolds-averaged Navier-Stokes (RANS) computations and very large-eddy simulations (VLES) is presented in which subgrid scale models are proposed that allow a direct numerical simulation (DNS) to go continuously to a RANS computation in the coarse mesh/infinite Reynolds number limit. In between these two limits, we have a large eddy simulation (LES) or VLES, depending on the level of resolution. The Reynolds stress model that is ultimately recovered in the coarse mesh/infinite Reynolds number limit has built in nonequilibrium features that make it suitable for time-dependent RANS. The fundamental technical issues associated with this new approach, which has the capability of bridging the gap between DNS, LES and RANS, are discussed in detail. Illustrative calculations are presented along with a discussion of the future implications of these results for the simulation of the turbulent flows of technological importance.

Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

Abstract: The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the primary advantage of the Kirchhoff formulation (namely, that nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed to be impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based on the conservation laws of fluid mechanics rather than on the wave equation. Thus, the FW-H equation is valid even if the integration surface is in the nonlinear region. This advantage is demonstrated numerically. With the Kirchhoff approach, substantial errors can result if the integration surface is not positioned in the linear region, and these errors may be hard to identify. Finally, new metrics, based on the Sobolev norm, are introduced that may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Robust and efficient Cartesian mesh generation for component-based geometry

Abstract: This work documents a new method for rapid and robust Cartesian mesh generation for component-based geometry. The new algorithm adopts a novel strategy that first intersects the components to extract the wetted surface before proceeding with volume mesh generation in a second phase. The intersection scheme is based on a robust geometry engine that uses adaptive precision arithmetic and automatically and consistently handles geometric degenerades with an algorithmic tie-breaking routine. The intersection procedure has worst-case computational complexity of O(N log N) and is demonstrated on test cases with up to 121 overlapping and intersecting components, including a variety of geometric degeneracies. The volume mesh generation takes the intersected surface triangulation as input and generates the mesh through cell division of an initially uniform coarse grid. In refining hexagonal cells to resolve the geometry, the new approach preserves the ability to directionally divide cells that are well aligned with local geometry. The mesh generation scheme has linear asymptotic complexity with memory requirements that total approximately 14-17 words/cell. The mesh generation speed is approximately 10 6 cells/minute on a typical engineering workstation

Experimental and Computational Investigation of the Knoller-Betz Effect

Abstract: The ability of a sinusoidally plunging airfoil to produce thrust, known as the Knoller-Betz or Katzmayr effect, is investigated experimentally and numerically. Water-tunnel experiments are performed providing flow visualization and laser Doppler velocimetry data of the unsteady wakes formed by the plunging foils. Vortical structures and time-averaged velocity profiles in the wake are compared with numerical computations from a previously developed inviscid, unsteady panel code that utilizes a nonlinear wake model

Evaluation of Layerwise Mixed Theories for Laminated Plates Analysis

Abstract: The evaluation of mixed layerwise theories to calculate the in-plane and out-of-plane responses of thick plates in two-dimensional modeling of multilayered structures is made. The employed models, which were proposed by the author in earlier works, a priori fulfill the continuity of transverse shear and normal stress components at the interface between two adjacent layers. A Reissner's mixed variational equation is used to derive the governing equations, in terms of introduced stress and displacement variables. The interface continuity conditions are imposed by writing the governing equations at a multilayered level. The related standard displacement formulations are also discussed for comparison purpose. Closed-form solutions are presented for plates made of orthotropic lamina and bent by harmonic distribution of transverse pressure. Symmetrically and unsymmetrically laminated, as well as sandwich, plates have been investigated. A comparison with a three-dimensional-elasticity analysis shows that present mixed layerwise models furnish a better description of the in-plane and out-of-plane response of thick plates with respect to existing layerwise and equivalent single-layer theories. In particular, the proposed models describe, with excellent accuracy, the transverse shear and normal stress fields. Unlike available current models, these fields are herein determined a priori without requiring implementation of any postprocessing procedures. The distribution of the transverse displacement and transverse normal stress in the plate thickness direction are also shown for most of the problems.

Reordering of Hybrid Unstructured Grids for Lower-Upper Symmetric Gauss-Seidel Computations

Abstract: This note is devoted to the three-dimensional hybrid grid implementation of the LU-SGS method The original method was based on sweeps through grid node numbers and was applied to two-dimensional Euler computations Unfortunately, in its original formulation, the method cannot be vectorized; in addition the method is not compatible with commonly used edge-based data structure To fit the method to the three-dimensional computations on a vector supercomputer, grid reordering is necessary It was applied to the cell-centered finite volume method

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

Abstract: A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplyfying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.

Low-Diffusion Flux-Splitting Methods for Flows at All Speeds

Abstract: Methods for extending the advective upwind splitting method (AUSM) family of low-diffusion flux-splitting schemes to operate effectively at all flow speeds are developed. The extensions developed are designed for use with time-derivative preconditioning and are based on the idea that the speed of sound should cease to be an important scaling parameter for the diffusive contributions to the interface flux as the Mach number becomes small. Using this criterion, alternative definitions for the interface Mach numbers are developed, and methods for ensuring pressure-velocity coupling at low speeds are formulated. Results are presented for inviscid flows through a channel at various Mach numbers, developing viscous flow in a two-dimensional duct, driven-cavity flows at various Mach and Reynolds numbers, flow over a backward-facing step, and hydrogen-nitrogen mixing layers

Bi-Level Integrated System Synthesis

Abstract: BLISS is a method for optimization of engineering systems by decomposition. It separates the system level optimization, having a relatively small number of design variables, from the potentially numerous subsystem optimizations that may each have a large number of local design variables. The subsystem optimizations are autonomous and may be conducted concurrently. Subsystem and system optimizations alternate, linked by sensitivity data, producing a design improvement in each iteration. Starting from a best guess initial design, the method improves that design in iterative cycles, each cycle comprised of two steps. In step one, the system level variables are frozen and the improvement is achieved by separate, concurrent, and autonomous optimizations in the local variable subdomains. In step two, further improvement is sought in the space of the system level variables. Optimum sensitivity data link the second step to the first. The method prototype was implemented using MATLAB and iSIGHT programming software and tested on a simplified, conceptural level supersonic business jet design, and a detailed design of an electronic device. Satisfactory convergence and favorable agreement with the benchmark results were observed. Modularity of the method is intended to fit the human organization and map well on the computing technology of concurrent processing.

Turbulent boundary-layer control by means of spanwise-wall oscillation

Abstract: An experimental investigation into the changes in turbulence structure of the boundary layer over a wall oscillating in spanwise direction was carried out in a wind tunnel using hot-wire anemometry and flow visualisation. The main purpose of this investigation is to confirm recent numerical results which seem to indicate that the turbulent skinfriction drag can be reduced by up to 40 percent over the oscillating wall. The results from the present investigation clearly indicate that the logarithmic velocity profiles are shifted upwards and turbulence intensities reduced by the spanwise-wall oscillation, confirming the basic conclusions of recent direct numerical simulation. Also, the skinfriction reductions as much as 45% are observed in the present experiment at an optimum speed of wall oscillation. The flow-visualisation study indicates that the longitudinal vortices in the near-wall region of the boundary layer are twisted towards the direction of spanwise-wall motion with oscillation. As a result, the vortices are realigned into the cross-flow direction, resulting in a reduction of turbulent wall-skin friction by spanwise-wall oscillation. A conceptual model for a turbulent boundary layer over an oscillating wall is proposed to examine the mechanism of turbulent drag reduction by spanwise-wall oscillation.

Efficient Approach for Analysis of Unsteady Viscous Flows in Turbomachines

Abstract: A nonlinear harmonic methodology has been developed to calculate unsteady viscous flows through turbomachinery blades. Flow variables are decomposed into time-averaged variables and unsteady perturbations, resulting in the time-averaged equations with extra nonlinear stress terms depending on the unsteady perturbations. An efficient evaluation of an unsteady flowfield is obtained by solving the first-order harmonic equations. The nonlinear interactions between the time-averaged flowfield and the unsteady perturbations were included by a strong coupling approach. The basic computational methodology was applied to the two-dimensional Navier-Stokes equations, and the method was validated against several test cases. Computational results show that this method is much more efficient than the nonlinear time-marching methods while still modeling dominant nonlinear effects

Use of Piezoelectric Actuators for Airfoil Separation Control

Abstract: Surface-mounted piezoelectric actuators are used to excite the turbulent boundary layer upstream of separation, where the actuators interact directly with the boundary layer. The actuators are rigid and do not attenuate with increased aerodynamic loading up to the maximum tested speed of 30 m/s

Tetrahedral Unstructured Navier-Stokes Method for Turbulent Flows

Abstract: A method is presented for solving the Navier-Stokes equations for turbulent flow problems on three-dimensional unstructured grids. Spatial discretization is accomplished by a cell-centered, finite volume formulation using an accurate linear reconstruction scheme and upwind flux differencing. Time is advanced by an implicit backward Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the sublayer region of the boundary layer. A systematic assessment of the method is presented to devise guidelines for more strategic application of the technology to complex problems. The assessment includes the accuracy in predictions of the skin-friction coefficient, law-of-the-wall behavior, and surface pressure for a flat-plate turbulent boundary layer and for the ONERA M6 wing under a high-Reynolds-number, transonic, separated flow condition

Effects of Periodic Excitation on Turbulent Flow Separation from a Flap

Abstract: The effects of periodic perturbations on delaying separation or promoting reattachment of initially separated flow were experimentally investigated. The leading parameters affecting the flow are the flap deflection, the input momentum, and its reduced frequency. The sensitivity of the flow to the imposed oscillations depends on its initial state, and this leads to hysteresis with respect to changes in any of the aforementioned parameters. For example, the most effective frequency required to attach the flow to the surface is much lower than the one required to prevent its separation. The amplitude needed to force reattachment may be an order of magnitude larger than the amplitude required to prevent separation at a given inclination of the flap. Nevertheless, periodic forcing is much more effective than steady blowing for boundary-layer control

Direct Updating of Damping and Stiffness Matrices

Abstract: This note has outlined an extension to the available direct methods of model updating to estimate both the damping and stiffness matrices of a structure. The method minimizes the change in the damping and stiffness matrices, with the constraint that the measured modal data is reproduced

Vibration Technique for Locating Delamination in a Composite Beam

Abstract: An experimental nondestructive vibration-based technique for locating a delamination in a composite beam is presented. The method operates on the fundamental displacement eigenvector, which is converted to a curvature mode shape. The application of a unique, gapped smoothing damage detection method to the curvature yields a damage index that locates the delamination, irrespective of its position along the beam or depth within the beam. The procedure can operate solely on data obtained from the damaged structure. Models or data from the undamaged structure are specifically not required or used during the analysis. The procedure reported here is highly satisfactory for experimental data, where small variations in the measurement cause false features in other published curvature-based damage detection methods. The damage location method is demonstrated with a finite element model of a composite beam, where a delamination is modeled by relaxing connectivity between elements at the desired location of the delamination. The results of an experimental investigation of a composite beam with a manufactured delamination are also presented. When the gapped smoothing method was used on the experimental modal data, the delamination was successfully located.

Characterization of the Pressure Fluctuations Under a Fully Developed Turbulent Boundary Layer

Abstract: Accurate measurements of the turbulent wall pressure have been difficult to achieve due to signal contamination at low frequencies by background facility noise and/or attenuation at high frequencies due to sensor averaging effects. The current study utilizes a new noise cancellation scheme based on an optimal filtering technique to capture the noise-canceled time series. Furthermore, to address the high-frequency attenuation problem, a number of pinholes are utilized along with high-sensitivity micropbones to obtain measurements of the wall pressure at a resolution down to d + = du τ /v ≅2. The results show that the maximum allowable nondimensional sensing diameter to avoid spectral attenuation for frequencies up to f + = fv/u τ 2 = 1 is in the range of 12.0 ≤d + < 18.0. Additionally, it is shown that the wall-pressure rms level when scaled on the wall-shear stress seems to increase slowly with increasing Reynolds number, apparently due to the influence of large-scale structures in the outer part of the boundary layer. On the other hand, it is demonstrated that, even though √p '2 /q 0 appears to become invariant with increasing Reynolds number, p' is not generated by structures whose velocity scale is U 0 .

Issues in Computational Fluid Dynamics Code Verification and Validation

Abstract: A broad range of mathematical modeling errors of fluid flow physics and numerical approximation errors are addressed in computational fluid dynamics (CFD). It is strongly believed that if CFD is to have a major impact on the design of engineering hardware and flight systems, the level of confidence in complex simulations must substantially improve. To better understand the present limitations of CFD simulations, a wide variety of physical modeling, discretization, and solution errors are identified and discussed. Here, discretization and solution errors refer to all errors caused by conversion of the original partial differential, or integral, conservation equations representing the physical process, to algebraic equations and their solution on a computer. The impact of boundary conditions on the solution of the partial differential equations and their discrete representation will also be discussed. Throughout the article, clear distinctions are made between the analytical mathematical models of fluid dynamics and the numerical models. Lax`s Equivalence Theorem and its frailties in practical CFD solutions are pointed out. Distinctions are also made between the existence and uniqueness of solutions to the partial differential equations as opposed to the discrete equations. Two techniques are briefly discussed for the detection and quantification of certain types ofmore » discretization and grid resolution errors.« less

Frequency-Domain Karhunen -Loeve Method and Its Application to Linear Dynamic Systems

Abstract: Forthee rsttime,theKarhunen ‐Loeve(KL)procedureisderivedinthefrequencydomainasatoolforcalculating eigenmodes of linear systems. The new derivation is based on the discrete Fourier transform representation of a time average of proe le energy including a proper system response and a proe le function. Taking the variational problem posed as such with respect to the proe le function leads to an eigenformulation in the frequency domain. Choice of a system response for efe cient KL mode calculation and construction of reduced-order systems using the KL eigenmodes are also discussed. To demonstrate themethod, both mechanical and e uid dynamic models are considered. The method is equally useful in extracting eigenmodes of an experimentally generated database. Nomenclature c = wing chord length F = snapshot matrix as dee ned in Eq. (13) F = Fourier operator GIk = impulse response for the kth input GSk = step response for the kth input i

Construction of Response Surface Approximations for Design Optimization

Abstract: Using response surface approximations for design constraints in design optimization provides the designer with an overall perspective of the system response within the design space. Response surface approximations also reduce the numerical noise inherent in many numerical models and simplify the process of integrating several design codes, as is typically required in multidisciplinary optimization. Procedures are discussed for constructing accurate response surface approximations to represent design constraints in design optimization. Response surface approximations are constructed for the stresses and buckling loads of an isotropic plate with an abrupt change of thickness. These response surface approximations are constructed from numerical experiments conducted with a finite element analysis procedure and are used for minimum-weight optimum design of the plate. Nondimensional variahles and stepwise regression are used to reduce the complexity and increase the accuracy of the response surface approximations. Additionally, higher-order polynomials (cubic and quartic instead of the more traditional quadratic) are used as response surface approximations, and a detailed error analysis, using an independent data set, is performed. Finally, it is shown that, by making use of response surface approximations, the optimum weight of the plate may be presented in the form of a design chart for a wide range of geometric, loading, and material constants.

Experimental Methodology for Computational Fluid Dynamics Code Validation

Abstract: Validation of Computational Fluid Dynamics (CFD) codes is an essential element of the code development process. Typically, CFD code validation is accomplished through comparison of computed results to previously published experimental data that were obtained for some other purpose, unrelated to code validation. As a result, it is a near certainty that not all of the information required by the code, particularly the boundary conditions, will be available. The common approach is therefore unsatisfactory, and a different method is required. This paper describes a methodology developed specifically for experimental validation of CFD codes. The methodology requires teamwork and cooperation between code developers and experimentalists throughout the validation process, and takes advantage of certain synergisms between CFD and experiment. The methodology employs a novel uncertainty analysis technique which helps to define the experimental plan for code validation wind tunnel experiments, and to distinguish between and quantify various types of experimental error. The methodology is demonstrated with an example of surface pressure measurements over a model of varying geometrical complexity in laminar, hypersonic, near perfect gas, 3-dimensional flow.

Hybrid Prismatic/Tetrahedral Grid Generation for Viscous Flow Applications

Abstract: A method for the automatic generation of unstructured grids composed of tetrahedra and prisms is proposed. The prismatic semistructured grid is generated around viscous boundary surfaces and covers viscous regions, whereas the tetrahedral grid covers the rest of the computational domain. The Delaunay approach for tetrahedral grid generation is used. The proposed prismatic grid is structured in directions normal to the boundary faces, but the number of prisms generated from one boundary face is variable from face to face. Unlike conventional prismatic grid generators, this technique works well even in regions of cavities and gaps. The Delaunay background grid generated for surface nodes serves as an efficient data structure to check possible intersections of prisms. Particular attention is given to the boundary-constraining problem. A robust algorithm for the boundary recovery by edge swapping followed by a direct subdivision of tetrahedra is used. Grid examples for internal and external flow problems of complex shapes demonstrate the efficiency of the method

Sensor placement methodologies for dynamic testing

Abstract: Two methods are presented for structural sensor placement. The first scheme selects the most linearly independent impulse responses at all candidate sensor locations from a Gram-Schmidt orthogonalization procedure. The second scheme is based on a principal component analysis and iteratively removes sensors that do not contribute significant information to the Fisher information matrix. Furthermore, use of a model reduction criterion is proposed to address the optimality issue. Several sensor placement methods were implemented to compare results and were applied to an Euler-Bernoulli beam and a cantilevered frame structure. It is shown that the proposed frequency criterion appears to be a selective criterion for choosing optimum sensor locations. Finally, the optimum measurement locations from several of the methods studied yield acceptable results based on data from an experimental study on the frame structure.

Method for Generating Equilibrium Swirling Inflow Conditions

Abstract: The azimuthal body force technique, described here, represents a means of predicting, rather than prescribing, swirling inflow boundary conditions

Radiated noise from airfoils in realistic mean flows

Abstract: The long-term objective of the research described is to use computational aeroacoustics methodology and parallel computers to increase the understanding of broadband blade noise. In a systematic progression toward simulations of completely realistic configurations and conditions, some simplified problems that address the important features of the flow are investigated. A two dimensional Navier-Stokes code, implemented using the message passing library and Fortran 90 on the IBM SP2, is used to perform the calculations. Results are presented for the interaction of a vortical gust and NACA airfoils, including nonlinear effects. The influence of gust frequency and airfoil thickness is described. A multigrid method is used to obtain converged steady-state solutions before the gust is introduced in a source region inside the domain.

Study of Passive Control in a Transonic Shock Wave/Boundary-Layer Interaction

Abstract: Passive control applied to a turbulent shock wave/boundary-layer interaction has been investigated by considering a two-dimensional channel flow. The field has been probed in great detail by using a two-component laser Doppler velocimetry system to execute mean velocity and turbulence measurements. Four different perforated plates have been considered along with the solid wall reference case. These measurements have shown that passive control deeply modifies the inviscid flowfield structure, the single shock being replaced by a lambda shock system. This modified compression induces a substantial reduction of the wave drag associated with the interaction. On the other hand, the combined injection-suction effect taking place in the control region provokes an increase of the viscous drag, which nearly outbalances the reduction in wave drag. It was found that passive control induced a modest decrease of the total drag compared to the solid wall case. Moreover, the experimental wall transpiration velocity distribution in the control region is well represented by the usual laws

Numerical Simulation of the Generation of Axisymmetric Mode Jet Screech Tones

Abstract: An imperfectly expanded supersonic jet invariably radiates both broadband noise and discrete frequency sound called screech tones. Screech tonesareknown to begenerated by a feedback loop driven by the large-scaleinstabilitywavesofthejete ow. Insidethejet plumeisa quasiperiodicshockcellstructure.Theinteractionoftheinstability waves and the shock cell structure, as the former propagates through the latter, is responsible for the generation of the tones. Currently, there are formulas that can predict the tone frequency fairly accurately. However, there is no known way to predict the screech tone intensity. In this work, the screech phenomenon of an axisymmetric jet at low supersonic Mach number is reproduced by numerical simulation. The computed mean velocity proe les and the shock cell pressure distribution of the jet are found to be in good agreement with experimental measurements. The same is true with the simulated screech frequency. Calculated screech tone intensity and directivity at selected jet Mach number are reported. The present results demonstrate that numerical simulation using computational aeroacoustic methods offers not only a reliable way to determine the screech tone intensity and directivity but also an opportunity to study the physics and detailed mechanisms of the phenomenon by an entirely new approach.