Showing papers in "AIAA Journal in 1985"

Comparison of Finite Volume Flux Vector Splittings for the Euler Equations

Abstract: A flux-splitting method in generalized coordinates has been developed and applied to quasi-one-dim ensional transonic flow in a nozzle and two-dimensional subsonic, transonic, and supersonic flow over airfoils. Computational results using the Steger-Warming and Van Leer flux splittings are compared. Discussed are several advantages of a MUSCL-type approach (differencing followed by flux splitting) over a standard flux differencing approach (flux splitting followed by differencing) . With an approximately factored implicit scheme, spectral radii of 0.978-0.930 for a series of airfoil computations are obtained, generally decreasing as a larger portion of the flow becomes supersonic. The Van Leer splitting leads to higher convergence rates and a sharper representation of shocks, with at most two (but more often, one) zones in the shock transition. The second-order accurate one-sided-difference model is extended to a third-order upwind-biased model with a small additional computational effort. The results for both the second- and third-order schemes agree closely in overall features to a widely used central difference scheme, although the shocks are resolved more accurately with the flux splitting approach.

Features of a reattaching turbulent shear layer in divergent channel flow

Abstract: Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step in a diverging channel flow. Mean velocities, Reynolds stresses, and triple products that were measured by a laser Doppler velocimeter are presented for two cases of tunnel wall divergence. Eddy viscosities, production, convection, turbulent diffusion, and dissipation (balance of kinetic energy equation) terms are extracted from the data. These data are compared with various eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model; however, like the others, it dramatically overpredicts the experimentally determined dissipation rate.

Fractional calculus in the transient analysis of viscoelastically damped structures

Abstract: Fractional calculus is used to model the viscoelastic behavior of a damping layer in a simply supported beam. The beam is analyzed by using both a continuum formulation and a finite element formulation to predict the transient response to a step loading. The construction of the finite element equations of motion and the resulting nontraditional orthogonality conditions for the damped mode shapes are presented. Also presented are the modified forms of matrix iteration required to calculate eigenvalues and mode shapes for the damped structure. The continuum formulation, also incorporating the fractional calculus model, is used to verify the finite element approach. The location of the poles (damping and frequency) are found to be in satisfactory agreement, as are the modal amplitudes for the first several modes.

Artificial Dissipation Models for the Euler Equations

Abstract: Various artificial dissipation models that are used with central difference algorithms for the Euler equations are analyzed for their effect on accuracy, stability, and convergence rates. In particular, linear and nonlinear models are investigated using an implicit approximate factorization code (ARC2D) for transonic airfoils. Fully implicit application of the dissipation models is shown to improve robustness and convergence rates. The treatment of dissipation models at boundaries will be examined. It will be shown that accurate, error free solutions with sharp shocks can be obtained using a central difference algorithm coupled with an appropriate nonlinear artificial dissipation model. I. Introduction T HE solution of the Euler equations using numerical techniques requires the use of either a differencing method with inherent dissipation or the addition of dissipation terms to a nondissipative scheme. This is because the Euler equations do not provide any natural dissipation mechanism (such as viscosity in the Navier-Stokes equations) that would eliminate high frequencies which are caused by nonlinearitie s and especially shocks. A variety of numerical algorithms and computer codes for the Euler equations have been developed. Methods such as MacCormack's1 explicit

A mathematically simple turbulence closure model for attached and separated turbulent boundary layers

Abstract: A new turbulence closure model designed specifically to treat two-dimensional, turbulent boundary layers with strong adverse pressure gradients and attendant separation is presented The influence of history effects are modelled by using an ordinary differential equation derived from the turbulent kinetic energy equation to describe the stream wise development of the maximum Reynolds shear stress in conjunction with an assumed eddy viscosity distribution that has as its velocity scale the maximum Reynolds shear stress In the outer part of the boundary layer, the eddy viscosity is treated as a free parameter which is adjusted in order to satisfy the ODE for the maximum shear stress Because of this, the model is not simply an eddy viscosity model, but contains features of a Reynolds stress model Comparisons with experiment are presented that clearly show the proposed model to be superior to the Cebeci-Smith one in treating strongly retarded and separated flows In contrast to two-equation, eddy viscosity models, it requires only slightly more computational effort than simple models such as the Cebeci-Smith

Stiffness matrix adjustment using mode data

Abstract: A procedure is introduced that uses, in addition to mode data, structural connectivity information to optimally adjust deficient stiffness matrices The adjustments performed are such that the percentage change to each stiffness coefficient is minimized The physical configuration of the analytical model is preserved and the adjusted model will exactly reproduce the modes used in the identification The theoretical development is presented and the procedure is demonstrated by numerical simulation of a test problem

Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates

Abstract: The Harten (1983, 1984) total variation-diminishing (TVD) schemes, constituting a one-parameter explicit and implicit, second-order-accurate family, have the property of not generating spurious oscillations when applied to one-dimensional, nonlinear scalar hyperbolic conservation laws and constant coefficient hyperbolic systems. These methods are presently extended to the multidimensional hyperbolic conservation laws in curvilinear coordinates. Means by which to linearize the implicit operator and solution strategies, in order to improve the computation efficiency of the implicit algorithm, are discussed. Numerical experiments with steady state airfoil calculations indicate that the proposed linearized implicit TVD schemes are accurate and robust.

Measurements of entrainment and mixing in turbulent jets

Abstract: An experimental investigation of entrainment and mixing in the self-similar far field of an axisymmetric free turbulent jet in water is presented. Length and time scales for the flame length fluctuations of reacting jets are shown to be approximately equal to the local characteristic large scale length and time of the flow. It is also shown that instantaneous radial profiles of concentration across the jet do not resemble the mean concentration profile, indicating that the mean profile is a poor representation of the mixed fluid states within the jet. These instantaneous profiles also show that unmixed ambient fluid is transported throughout the entire extent of the jet, and that the mixed fluid composition within the jet can be fairly uniform in regions extending across a large part of the local jet diameter. Lastly, the amount of unmixed ambient fluid on the jet centerline is found to vary roughly periodically with a period approximately equal to the local characteristic large scale time of the flow. These results suggest that large scale transport mechanisms, displaying a characteristic organization, play an important role in entrainment and mixing in the far filed of turbulent jets.

Effect of delamination of axially loaded homogeneous laminated plates

Abstract: A simple one-dimensional model has been developed and analyzed for predicting delamination buckling loads. The model is employed to predict critical loads for delaminated homogeneous plates with both simply supported and clamped ends. The effects of delamination position, size, and thickness on the critical loads are studied in detail for both sets of boundary conditions. The results reveal that for certain geometries the buckling load can serve as a measure of the load carrying capacity of the delaminated configuration. In other cases, the buckling load is very small and delamination growth is a strong possibility, depending on the toughness of the material.

Structural optimization by multilevel decomposition

Abstract: A method for decomposing an optimization problem into a set of subproblems and a coordination problem that preserves coupling between the subproblems is described The decomposition is achieved by separating the structural element optimization subproblems from the assembled structural optimization problem Each element optimization and optimum sensitivity analysis yields the cross-sectional dimensions that minimize a cumulative measure of the element constraint violation as a function of the elemental forces and stiffness The assembled structural optimization produces the overall mass and stiffness distributions optimized for minimum total mass subject to constraints that include the cumulative measures of the element constraint violations extrapolated linearly with respect to the element forces and stiffnesses The method is introduced as a special case of a multilevel, multidisciplinary system optimization and its algorithm is fully described for two-level optimization for structures assembled of finite elements of arbitrary type Numerical results are given as an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition It is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers using different computers to work concurrently on the same large problem

Structural shape optimization with geometric description and adaptive mesh refinement

Abstract: Earlier work on shape optimization indicated that a simple problem description format was crucial to effective use of the program. As a result, a geometric problem description format which uses only boundary information was developed. A finite element mesh generation capability which requires only boundary information is used to generate the mesh, and a solution-based adaptive mesh refinement scheme is used to provide a more accurate estimate of the true solution. During the optimization process, periodic refinements are performed to generate estimates of the refined stresses based on unrefined solutions. Nonlinearities in the constraints led to some convergence difficulties; however, minimum mass designs typically were obtained in 30-40 finite element solutions.

Recirculation in swirling flow - A manifestation of vortex breakdown

Abstract: The addition of a sufficiently high degree of swirl to flow going into a circular pipe produces a limited region of reversed flow. Such a vortex breakdown, as it is termed, represents a zone of transition from a supercritical to a subcritical flow state. If the flow remains subcritical, an unavoidable consequence is that the geometry and conditions downstream directly affect the upstream flow up to, and including, the breakdown region. Laser Dopper anemometer measurements of the swirl and axial velocity components, as well as the corresponding streamline patterns, are presented for water flow in a model based upon the geometry of a swirl combustor. It is shown that a strong exit contraction (55 percent of the diameter) has practically no influence on a flow which reverts to supercritical, whereas even a weak contraction (15 percent of the diameter) has a significant influence on a flow which remains subcritical. It is argued that a cold flow is likely to be totally unrepresentative of a reacting flow through the same geometry, and, also, that great care has to be taken over the boundary conditions to be imposed for the numerical computation of subcritical flows. 20 references.

Simultaneous analysis and design

Abstract: Optimization techniques are increasingly being used for performing nonlinear structural analysis. The development of element by element (EBE) preconditioned conjugate gradient (CG) techniques is expected to extend this trend to linear analysis. Under these circumstances the structural design problem can be viewed as a nested optimization problem. There are computational benefits to treating this nested problem as a large single optimization problem. The response variables (such as displacements) and the structural parameters are all treated as design variables in a unified formulation which performs simultaneously the design and analysis. Two examples are used for demonstration. A seventy-two bar truss is optimized subject to linear stress constraints and a wing box structure is optimized subject to nonlinear collapse constraints. Both examples show substantial computational savings with the unified approach as compared to the traditional nested approach.

Multigrid solution of the Euler equations using implicit schemes

Abstract: On utilise une methode multigrille du type factorisation approchee couplee a un schema de direction alternee implicite pour resoudre les equations d'Euler pour l'ecoulement transsonique sur un profil aerodynamique. On obtient une convergence tres rapide

Upwind relaxation algorithms for the Navier-Stokes equations

Abstract: The development of upwind relaxation algorithms for obtaining efficient steady-state solutions to the compressible Navier-Stokes equations is described. The method is second-order accurate spatially and naturally disipative, using third-order flux splitting of the pressure and convective terms and second-order central differencing for shear and heat flux terms. A line Gauss-Seidel relaxation approach, shown to be unconditionally stable for model convection and diffusion equations, is used. The algorithm is demonstrated for several flows using the thin-layer form of the equations, including the problem of shock-induced separation over a flat plate.

Automatic adaptive grid refinement for the Euler equations

Abstract: A method of adaptive grid refinement for the solution of the steady Euler equations for transonic flow is presented. Algorithm automatically decides where the coarse grid accuracy is insufficient, and creates locally uniform refined grids in these regions. This typically occurs at the leading and trailing edges. The solution is then integrated to steady state using the same integrator (FLO52) in the interior of each grid. The boundary conditions needed on the fine grids are examined and the importance of treating the fine/coarse grid inerface conservatively is discussed. Numerical results are presented.

Application of time-iterative schemes to incompressible flow

Abstract: The computation of steady incompressible flows by an Euler implicit algorithm is studied using both the incompressible equations and the low Mach number compressible equations. The incompressible equations are handled by adding an artificial time derivative to the continuity equation. This allows both the pressure and velocity to be obtained implicitly. In one-dimensional problems, both systems converge rapidly, even at low Mach numbers where the eigenvalues are very stiff. In two dimensions where approximate factorization is required, the presence of stiff eigenvalues is highly detrimental. Stiffness can be avoided in the incompressible equations by selecting an appropriate "pseudo"-Mach number. This insures reliable convergence and results in an efficient incompressible flow algorithm. In the case of compressible equations, the Mach number cannot be chosen arbitrarily and the contamination introduced by approximate factorization must be removed. A matrix preconditioning factor that accomplishes this is developed and demonstrated. With this modification, the convergence rate is the same as in the incompressible case and is independent of Mach number. Rapid convergence is observed at Mach numbers as low as 6.05.

Turbulence modeling for complex shear flows

Abstract: The turbulence models available for the prediction of complex turbulent shear layers are reviewed in this paper, concentrating mainly on three-dimensional flows, flows subjected to curvature and body rotation, separated flows, and vortex flows. A critical review of zero-equation, one-equation, two-equation, algebraic Reynolds stress, and full Reynolds stress models are carried out, with a specific emphasis on their applicability to complex flows. It is concluded that algebraic eddy viscosity models and kappa-epsilon/kappa-omega models, with a constant value of coefficients, are not adequate for complex flows. The models which include a description of stresses, either through an algebraic Reynolds stress model or a full Reynolds stress model, are essential for adequate prediction of these flows. It is recommended that systematic experimental investigations be carried out to isolate various complex interactions in order to understand and model the various effects and to carry out an extension of the present models to include complex flows.

Control of coherent structures in reattaching laminar and turbulent shear layers

Abstract: Etude experimentale du developpement de structures tourbillonnaires a grande echelle dans les couches cisaillees recollees d'un ecoulement sur une marche tournee vers l'aval. Les visualisations de l'ecoulement montrent la formation et l'emergence de structures tourbillonnaires, l'accroissement de l'irregularite de ces structures lorsque la turbulence augmente et la persistence des structures loin en aval du recollement

The discrete vortices from a delta wing

Abstract: Introduction: The Classical View T HE flow over delta wings at an angle of attack is dominated by two large bound vortices that result from the flow separation at the leading edge. The classical view of these vortices is sketched in Fig. la and has been discussed by Hoerner and Borst among others. With a sharp leading edge at an angle of attack a, the flow is separated along the entire leading edge forming a strong shear layer. The shear layer is wrapped up in a spiral fashion, resulting in the large bound vortex as sketched. These vortices appear on the suction surface and increase in intensity downstream. The low pressure associated with the vortices produces an additional lift on the wing, often called nonlinear or vortex lift, which is particularly important at large angles of attack. As sketched in Fig. la, small secondary vortices also appear on the wing near the points of reattachment as a result of the strong lateral flow toward the leading edge.

An analytical investigation of shape control of large space structures by applied temperatures

Abstract: An analytical procedure for the static shape control of flexible space structures subjected to thermal distortions is developed which is based on prescribing temperatures in control elements having much higher coefficients of thermal expansion than the main structure. The temperatures at the control elements are defined so as to minimize the overall thermal distortion of the structure from its ideal shape, and a matrix equation is obtained which can be solved for the set of optimum control temperatures. A formulation of the procedure for continuous structures governed by differential equations and a formulation for discrete (finite element modeled) structures governed by matrix equations are presented. The equations from the continuous formulation are employed for the shape control of a simple beam distorted by nonuniform heating, and the discrete formulation is applied in a general purpose finite-element structural analysis computer program for the shape control of a 750 m radiometer antenna reflector dish subjected to orbital heating. A reduction in thermal distortion by a factor of nearly 50 was obtained with the use of only seven control elements. Results for four different sets of control locations for the antenna are presented in which reductions in distortion of up to a factor of four were obtained.

Aero-optical foundations and applications

Abstract: Nomenclature A = coefficient defined in Eq. (A40) A Q = area B = magnetic field c = speed of light C = correlation function Cn = index of refraction structure function constant Cp = specific heat D = diameter of aperture D = electric displacement E = spectrum E = electric field H = magnetic induction / = intensity // = Bessel function of order / k = wave number / = turbulence scale size L = path length

Injection-induced flows in porous-walled ducts

Abstract: Analyse theorique de l'ecoulement dans des tubes et canaux a paroi poreuse. On tient compte des effets de compressibilite, de conditions aux limites non ideales et de transition turbulente sur le developpement de l'ecoulement. On utilise un modele de turbulence a contrainte de Reynolds et un schema de differences finies implicite pour resoudre le systeme d'equations paraboliques resultant

Stability experiments in the flow over a rotating disk

Abstract: An experimental study of the transitional flow over a flat disk rotating in quiescent ambient air has been conducted. Using digitized hot-wire data, the axes of the stationary spiral vortices, which are the primary instability mechanisms for the disk flow, have been mapped out in terms of both spatial coordinates and velocity fluctuations. Data are presented for a clean disk and a disk with a single, isolated roughness element. The data show that the spiral vortices are generated at discrete roughness disturbance sites on the disk and that they propagate and grow as wave packets. The familiar vortex pattern of 30 or so vortices results only when these wave packets have merged and filled the entire circumference. The appearance of stationary, secondary instabilities prior to turbulent breakdown has also been observed.

Effect of initial condition on subsonic jet noise

Abstract: The initial boundary-layer state can significantly affect the radiated noise from an axisymmetric jet. Jets with initially laminar boundary layers are found to emit more noise. Thus, 'cleaner' far-field noise characteristics are achieved in tripped jets. Data suggest that the additional noise in the initially laminar case partly originates from the first stage of pairing of the coherent shear-layer vortices.

Prediction of low-velocity impact damage in thin circular laminates

Abstract: Clamped circular composite plates were analyzed for static equivalent impact loads. Three plate sizes—25.4, 38.1, and 50.8 mm radii—made of quasi-isotropic graphite/epoxy laminate were analyzed. The analysis was based on the minimum total potential energy method and used the von Karman strain-displacement equations. A step-by-step incremental transverse displacement procedure was used to calculate plate load and ply stresses. The ply failure region and modes (splitting and fiber break) were calculated using the Tsai-Wu and the maximum stress criteria, respectively. Reduced moduli were then used in the failed region in subsequent increments of analyses. The analysis predicted that the failure would initiate as splitting in the bottom-most ply and then progress to other plies. Larger radii plates had a lower splitting threshold (load or energy) and a higher first-fiber failure threshold. The size and shape of the ply damage regions were different for different plies. The bottom ply damage was the largest and elongated in its ply-fiber direction. Calculated splitting damage for a 25.4 mm radius plate agreed with reported test data.

Postbuckling behavior of selected flat stiffened graphite-epoxy panels loaded in compression

Abstract: Results of an experimental study of the postbuckling behavior of selected flat stiffened graphite-epoxy panels loaded in compression are presented. The postbuckling response and failure characteristics of undamaged panels and panels damaged by low-speed impact are described. Each panel had four equally-spaced I-spaced stiffeners and 16- or 24-ply quasi-isotropic skins. Panels with three different stiffener spacings were tested. Some undamaged specimens supported as much as three times their initial buckling load before failing. Failure of all panels initiated in a skin-stiffener interface region. Analytical results obtained from a nonlinear general shell finite element analysis computer code correlate well with typical postbuckling test results up to failure. The analytical modeling detail necessary to predict accurately the response of a panel is described. Test results show that low-speed impact damage can reduce the postbuckling strength of a stiffened panel and that the skin-stiffener interface region is more sensitive to impact damage than the skin midway between stiffeners.

Technology of closed-drift thrusters

Abstract: Introduction A CLOSED-drift thruster is defined herein as a thruster in which ions are electrostatically accelerated in essentially the thrust direction, with the accelerating electric field established by an electron current interacting with a transverse magnetic field. One component of the electron motion is counter to the ion flow. Another component is normal to that direction. The current associated with this normal component is called the Hall current. In a closed-drift accelerator there is a complete, or closed, path for the Hall current. In addition, for the ions to be accelerated in essentially a single thrust direction, the ion cyclotron radius must be much larger than the total acceleration length. Closed-drift thrusters usually employ axially symmetric electrodes and pole pieces, with the magnetic field in the radial direction and the electric field in the axial direction. The Hall current flows in a circular closed path in such a configuration. A few closed-drift thrusters without axial symmetry have also been investigated. The closed-drift thruster is particularly well suited for operation in the 1000-2000 s range of specific impulse (approximately 10,000-20,000 m/s exhaust velocity). It is difficult to operate above about 1000 s with an electrothermal thruster due to excessive excitation and ionization losses. On the other hand, the space-charge-flow limitations of gridded electrostatic thrusters will not permit practical ion current densities below about 2000 s. Within the 1000-2000 s range, the electron backflow required to establish ion acceleration can, for the most part, be used to generate ions. The generation of ions constitutes the major closed-drift thruster loss in this range of specific impulse, and this loss can be under 100 eV per beam ion. The power processing requirements are also moderate. In a properly designed closed-drift thruster only one power circuit is required for steady-state operation, with the voltage of this circuit typically in the 50-500 V range.

Self-adaptive-grid method with application to airfoil flow

Abstract: A self-adaptive-grid method is described that is suitable for multidimensional steady and unsteady computations. Based on variational principles, a spring analogy is used to redistribute grid points in an optimal sense to reduce the overall solution error. User-specified parameters, denoting both maximum and minimum permissible grid spacings, are used to define the all-important constants, thereby minimizing the empiricism and making the method self-adaptive. Operator splitting and one-sided controls for orthogonality and smoothness are used to make the method practical, robust, and efficient. Examples are included for both steady and unsteady viscous flow computations about airfoils in two dimensions, as well as for a steady inviscid flow computation and a one-dimensional case. These examples illustrate the precise control the user has with the self-adaptive method and demonstrate a significant improvement in accuracy and quality of the solutions.