Showing papers in "AIAA Journal in 1983"

Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation

Abstract: Presentation d'une methode numerique par volume fini pour la resolution des equations de Navier-Stokes bidimensionnelles, incompressibles, et stationnaires, en coordonnees generales curvilignes Application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur Comparaison des calculs avec des donnees experimentales

Fractional calculus - A different approach to the analysis of viscoelastically damped structures

Abstract: Fractional calculus is used to construct stress-strain relationships for viscoelastic materials. These relationships are used in the finite element analysis of viscoelastically damped structures and closed-form solutions to the equations of motion are found. The attractive feature of this approach is that very few empirical parameters are required to model the viscoelastic material and calculate the response of the structure for general loading conditions.

Improvement of a Large Analytical Model Using Test Data

Abstract: A method has been developed which uses measured normal modes and natural frequencies to improve an analytical mass and stiffness matrix model of a structure. The method directly identifies, without iteration, a set of minimum changes in the analytical matrices which force the eigensolutions to agree with the test measurements. An application is presented in which the analytical model had 508 degrees of freedom and 19 modes were measured at 101 locations on the structure. The resulting changes in the model are judged to be small compared to expectations of error in the analysis. Thus, the improved model is accepted as a reasonable model of the structure with improved dynamic response characteristics. In addition, it is shown that the procedure may be a useful tool in identifying apparent measured modes which are not true normal modes of the structure. Nomenclature - analytical matrix = matrix of changes = identity matrix = full improved stiffness and mass matrices (n x n) = full analytical K, M matrices (n x n) = partitions of KA,MA corresponding to test coordinates = partitions of KA,MA corresponding to coupling elements = partitions of KA,MA corresponding to unmea- sured coordinates = number of measured modes = number of degrees of freedom in the model = measures of changes, Eqs. (15-17) = matrix norm, sum of the squares of all the elements = rectangular modal matrix, normalized (n x m) = /th mode, /th column of $ = measured and unmeasured partitions of ,- = diagonal matrix of measured natural frequencies (m xm) = natural frequency of /th mode = 12 17 = sum of the squares of all elements of matrix ( )

Riblets as a Viscous Drag Reduction Technique

Abstract: T viscous drag of turbulent boundary layers is a significant factor contributing to the fuel costs of the airlines. Several studies have indicated that microsurface geometry variations which change the near-wall structure of the flow have been effective in reducing drag. Summarized here is an investigation into the verification and extension of the most promising of these riblet variations.

Liftoff characteristics of turbulent jet diffusion flames

Abstract: A theoretical analysis of turbulent jet diffusion flames is developed in which the flame is regarded as an ensemble of laminar diffusion flamelets that are highly distorted. The flow inhomogeneities are considered to be sufficiently strong to produce local quenching events for flamelets as a consequence of excessive flame stretch. The condition for flamelet extinction is derived in terms of the instantaneous scalar dissipation rate, which is ascribed a log-normal distribution. Percolation theory for a random network of stoichiometri c sheets is used to predict quenching thresholds that define liftoff heights. Predictions are shown to be in reasonably satisfactory agreement with experimentally measured liftoff heights of methane jet diffusion flames, within experimental uncertainties. UEL issuing from a tube or duct into an oxidizing atmosphere forms a jet in which combustion may occur. The associated combustion process is the most classical example of a diffusion flame. At sufficiently high velocities of fuel flow (fundamentally, at sufficiently large Reynolds numbers) the entire diffusion flame is turbulent. The turbulent jet diffusion flame begins at the mouth of the duct for a range of values of the exit velocity. When a critical exit velocity is exceeded, the flame abruptly is detached from the duct and acquires a new configuration of stabilization in which combustion begins a number of duct diameters downstream. Flames in this state, stabilized in the mixing region, are termed lifted diffusion flames, and the critical exit velocity at which they appear is called the liftoff velocity. The liftoff height is the centerline distance from the duct exit to the plane of flame stabilization. A further increase in the exit velocity increases the liftoff height without significantly modifying the turbulent flame height (the centerline distance from the duct exit to the plane at which, on the average, combustion ceases). There is a second critical value of the exit velocity, called the blowoff velocity, beyond which the flame cannot be stabilized in the mixing region. The present study addresses questions of the structure of lifted turbulent diffusion flames at exit velocities between liftoff and blowoff values. Attention is focused especially on the calculation of liftoff heights. Liftoff characteristics for turbulent jet diffusion flames are of practical importance in connection with flame stabilization. Conditions for liftoff and blowoff must be known in developing rational designs of burners, e.g., in diffusion-flame combustors for power production or in flaring applications for the petroleum industry. They are also of interest in connection with extinguishment of certain fires that may occur in oil or gas rigs. The present work is directed toward developing an improved fundamental understanding of liftoff phenomena that may later prove useful for these applications.

Unsteadiness of the Separation Shock Wave Structure in a Supersonic Compression Ramp Flowfield

Abstract: Wall pressure fluctuations have been measured in a two-dimensional separated compression ramp-induced shock wave turbulent boundary-layer interaction The tests were made at a nominal freestream Mach number of 3 and at Reynolds numbers based on boundary-layer thickness of 78 X 10 and 14x 10 The wall temperature condition was approximately adiabatic Large-amplitude pressure fluctuations exist throughout the interaction, particularly near separation and reattachment In the upstream region of the flowfield, the unsteadiness of the separation shock wave structure generates an intermittent wall pressure signal Mean wall pressures in this region result from the superposition of the relatively low-frequency, large-amplitude, shock wave-induced fluctuations on the pressure signal of the undisturbed boundary layer This behavior is qualitatively similar to that observed in three-dimensional blunt fin-induced flows In these two flowfields, the length scale of the shock motion is a significant fraction of the distance from the interaction start to separation

One-dimensional micromechanical analysis of woven fabric composites

Abstract: The upper and lower bounds of elastic stiffness and compliance constants of woven fabric composites are derived, based upon a mosaic-like model as well as the assumptions of constant stress and constant strain. An approximate analysis taking into account fiber undulation and continuity also is conducted. Fiber undulation leads to a slight softening of the in-plane stiffness and does not affect the stretching/bending coupling constants. A transverse shear deformation is adopted and modified to examine the one-dimensional bending response of fabric composites. The results of a two-dimensional finite element analysis are in good agreement with the predictions of the in-plane, coupling, and bending constants based upon the fiber undulation, mosaic, and transverse shear deformation theory, respectively. The effect of fiber undulation shape on the in-plane compliance also is investigated.

Combustion in a turbulent mixing layer formed at a rearward-facing step

Abstract: A premixed propane/air flame was stabilized in a turbulent mixing layer formed at a rearward-facing step. The mean and rms averages of the turbulent velocity flowfield were determined by laser velocimetry for both reacting (phi = 0.57) and nonreacting flows (Re = 15,000-37,000 based on step height). The reacting-flow was visualized by high-speed schlieren photography. Large-scale structures dominate the reacting mixing layer. The growth of the large-scale structures was tied to the propagation of the flame. The linear growth rate of the reacting mixing layer defined by the mean velocity profiles was unchanged by combustion but the virtual origin moves downstream. The reacting mixing layer boundaries based on the mean velocity profiles were shifted toward the recirculation zone and reattachment lengths were shortened by 30 percent. The edge of the flame controlled by the large-scale structure development propagated faster into the incoming reactants than the boundary of the mixing layer given by the mean velocity flowfield. Thus, the region of high velocity gradient did not coincide with the region of high reaction and heat transfer.

Geometrically nonlinear transient analysis of laminated composite plates

Abstract: Forced motions of laminated composite plates are investigated using a finite element that accounts for the transverse shear strains, rotary inertia, and large rotations (in the von Karman sense). The present results when specialized for isotropic plates are found to be in good agreement with those available in the literature. Numerical results of the nonlinear analysis of composite plates are presented showing the effects of plate thickness, lamination scheme, boundary conditions, and loading on the deflections and stresses. The new results for composite plates should serve as bench marks for future investigations. mation are assumed to remain straight and normal to the midsurface after deformation (i.e., transverse shear strains are zero), has been used to calculate frequencies, static response, and dynamic response under applied loads. Recent studies in the analysis of plates have shown that the effect of the transverse shear strains on the static and dynamic response of plates is significant. For example, the natural frequencies of vibration predicted by the classical plate theory are 25% higher, for plate side-to-thickness ratio of 10, than those predicted by a shear deformation theory (SDT). In transient analysis of plates the classical plate theory predicts unrealistically large phase velocities in the plate for shorter wavelengths. The Timoshenko beam theory,3 which includes transverse shear and rotary inertia effects, has been extended to isotropic plates by Reissner 4'5 and Mindlin,6 and to laminated anisotropic plates by Yang et al.7 A generalization of the von Karman nonlinear plate theory for isotropic plates to include the effects of transverse shear and rotary inertia in the theory of orthotropic plates is due to Medwadawski,8 and that for anisotropic plates is due to Ebcioglu.9 With the increased application of advanced fiber composite material to jet engine fan or compressor blades, and in high performance aircraft, studies involving transient response of plates made of such materials are needed to assess the capability of these materials to withstand the forces of impact due to foreign objects (e.g., the ingestion of stones, nuts and bolts, hailstones, or birds in jet engines). Previous in- vestigations into the linear transient analysis of composite plates include Moon's10'11 investigation of the response of infinite laminated plates subjected to transverse impact loads at the center of the plate; Chow's12 study of laminated plates (with transverse shear and rotary inertia) using the Laplace transform technique; the Wang et al. 13 investigation, by the method of characteristi cs, of unsymmetrical orthotropic laminated plates; and Sun and Whitney's14'15 study of plates under cylindrical bending. More recently, the present author16'17 investigated the linear transient response of layered anisotropic composite rectangular plates and presented extensive numerical results for center deflection and stresses.

Experimental investigation of turbulence properties in transonic shock/boundary-layer interactions

Abstract: Three flows resulting from shock wave/turbulent boundary-layer interactions occurring in a two-dimensional transonic channel have been investigated. The first flow corresponds to incipient shock induced separation, the second to a well separated case, the third to a situation where a large separated bubble forms. The flows were characterized by using two-color laser velocimetry. The results include, for the three flows, mean velocity and Reynolds stress distributions across the viscous layer. The turbulence measurements reveal that the first part of the interaction process entails a very large turbulence production with the development of a very strong anisotropy. In this zone, the neglect of normal stresses in the momentum and turbulence energy equation is not justified. The downstream relaxation toward a new equilibrium state is a very gradual process due to the long lifetime of the large structures which formed in the region of intense turbulence production.

Numerical experiments with the Osher upwind scheme for the Euler equations

Abstract: The Osher algorithm for solving the Euler equations is an upwind finite difference procedure that is derived by combining the salient features of the theory of conservation laws and the mathematical theory of characteristi cs for hyperbolic systems of equations. A first-order accurate version of the numerical method was derived by Osher circa 1980 for the one-dimensional non-isentropic Euler equations in Cartesian coordinates. In this paper, the extension of the scheme to arbitrary two-dimensional geometries is explained. Results are then presented for several example problems in one and two dimensions. Future work will include extension of the method to second-order accuracy and the development of implicit time differencing for the Osher algorithm.

Characteristic frequencies of transonic diffuser flow oscillations

Abstract: Etude en fonction du nombre de Mach du choc et de la longueur du diffuseur des caracteristiques de l'ecoulement moyen et instationnaire d'un diffuseur transsonique supercritique. Les distributions de densite spectrale de puissance du mouvement de choc instationnaire presente trois pics distincts, suivant les conditions d'ecoulement

A stochastic theory of fatigue crack propagation

Abstract: A new mathematical theory is proposed to analyze the propagation of fatigue crack based on the concepts of fracture mechanics and random processes. The time-dependent crack size is approximated by a Markov process. Analytical expressions are obtained for the probability distribution of crack size at any given time and the probability distribution of the random time at which a given crack size is reached, conditional on the knowledge of the initial crack size. Examples are given to illustrate the application of the theory, and the results are compared with available experimental data.

Using a global hydrogen-air combustion model in turbulent reacting flow calculations

Abstract: A two-step global model describing the combustion of hydrogen in air at 1 atm pressure is developed by comparing the temperature histories obtained from a 28 reaction H-O mechanism. Using criteria discussed herein, good agreement is obtained in the range of initial mixture temperatures of 1000-2000 K and in the range of equivalence ratios of 0.2-2.0. The two-step global model is compared with the results obtained using an eightstep, H-O reaction mechanism in a computer program describing the turbulent diffusion of hydrogen in supersonic axisymmetric and two-dimensional reacting flows. Comparisons of profiles of temperature and pitot pressure are presented. The global model is judged to be adequate in flows which are not dominated by long ignition delay times.

A pocket model for aluminum agglomeration in composite propellants

Abstract: This paper presents a model for the purpose of estimating the fraction of aluminum powder that will form agglomerates at the surface of deflagrating composite propellants. The basic idea is that the fraction agglomerated depends upon the amount of aluminum that melts within effective binder pocket volumes framed by oxidizer particles. The effective pocket depends upon the ability of ammonium perchlorate modals to encapsulate the aluminum and provide a local temperature sufficient to ignite the aluminum. Model results are discussed in the light of data showing effects of propellant formulation variables and pressure.

The response of normal shocks in diffusers

Abstract: The frequency response of a normal shock in a diverging channel is calculated for application to problems of pressure oscillations in ramjet engines. Two limits of a linearized analysis arc discussed: one represents isentropic flow on both sides of a shock wave; the other may be a crude appr'l'I;imation to the influence of flow separation induced hy the wave. Numerical results arc given, and the influences of the shock wave on oscillations in the engine are discus,ed.

Compressible Helicoidal Surface Theory for Propeller Aerodynamics and Noise

Abstract: Acceleration potential techniques from three-dimensional thin wing theory have been generalized for propeller and prop-fan analysis. Helicoidal reference surfaces take the place of the planar surface in wing theories; otherwise the theories are equivalent. The acoustic branch of the theory, including nonlinear source terms, extends and unifies frequency domain noise theories dating back to Gutin. For aerodynamic applications, it is shown that prop-fans satisfy well-known criteria for use of linearized theory at transonic speeds by virtue of small aspect ratio and small thickness ratio. The results are in the form of integral equations for downwash as functions of thickness and steady or unsteady loading distributions. For the case of no rotation, the kernel functions reduce to well-known kernels of wing theory. The analysis, within the restrictions of linearization , treats rigorously any planform and any flight condition including the combination of subsonic roots and supersonic tips typical of prop-fans. The effects of thickness, camber, angle of attack, sweep, offset, blade interference, and tip relief are all treated without approximation.

Optimum sensitivity derivatives of objective functions in nonlinear programming

Abstract: The feasibility of eliminating second derivatives from the input of optimum sensitivity analyses of optimization problems is demonstrated. This elimination restricts the sensitivity analysis to the first-order sensitivity derivatives of the objective function. It is also shown that when a complete first-order sensitivity analysis is performed, second-order sensitivity derivatives of the objective function are available at little additional cost. An expression is derived whose application to linear programming is presented.

Rayleigh scattering measurements of the gas concentration field in turbulent jets

Abstract: A technique based on Rayleigh scattering has been developed to measure the concentration field in a cross section of a turbulent gas jet. Such measurements enable one to quantitativel y study turbulent mixing mechanisms and structures. A similar experiment was previously performed using Lorenz/Mie scattered light from aerosol particles introduced into the nozzle gas. The Rayleigh technique provides better spatial resolution, avoiding the limitations due to aerosol seeding, and in particular is capable of monitoring molecular diffusion, a fact which should be of importance in studying reactive turbulence.

Euler equations - Implicit schemes and boundary conditions

Abstract: Implicit boundary condition procedures are presented for use with implicit finite difference schemes for the unsteady Euler equations. This new boundary point treatment is based on the mathematical theory of characteristics for hyperbolic systems of equations. Along with the theoretical background, the practical application of the method to several types of boundaries is also explained using several examples. The specific boundary conditions covered include subsonic inflow and outflow, surface tangency, and shock waves. The example problems include one-dimensional Laval nozzle flow, dual-throat rocket engine nozzle flow, and supersonic flow past a sphere. The implicit boundary treatment permits the use of large time steps allowing the finite difference algorithm to converge to the asymptotic steady state much faster than schemes that use explicitly applied boundary conditions. At least an order of magnitude increase in computational speed is demonstrated in the examples shown.' Background T HE growing popularity of solutions to the Euler equations in transonics and their continued application in supersonics have increased the need for quicker solutions. The potential of implicit schemes in this direction has not been fully exploited for want of correct, implicit application of boundary conditions. The predominant use of implicit algorithms for the Navier-Stokes equations has partly been responsible for the neglect of implicit boundary point treatment for the Euler equations. Thus, there is a need for correct and stable procedures for the easy implicit application of boundary conditions. Such methods will serve the two purposes of 1) reaching time-asymptotic steady state faster and 2) permitting a time step for truly unsteady flow that is not necessarily restricted by the CFL stability criterion but is based upon the magnitude of the transients. For clues and information on how to construct such boundary condition procedures, one must turn to the mathematical theory of characteristi cs for hyperbolic systems of equations. The unsteady Euler equations belong to this category. The theory for hyperbolic systems is rich with information on signal propagation directions. The characteristics theory clearly points to the number of boundary conditions that may and need be prescribed without overdetermining the solution. Boundary condition procedures based on this theory have been known and applied for several years by Kentzer, 1 Porter and Coakley,2 de Neef, 3 and others. In earlier work by this author,4'5 easily understood and implementable methods for boundary point treatment were presented. However, all of the above techniques were developed for explicit finite difference schemes. It seems that it must be easy to extend such methodologies based on mathematical theory for hyperbolic systems to implicit finite difference schemes, and indeed, it is simple enough. The rest of this paper describes such implicit boundary condition procedures. The given examples illustrate in detail the application of the proposed methodology to specific types of boundaries and demonstrate the merits of the new scheme.

A Review of Roughness-Induced Nosetip Transition

Abstract: HE re-entry physics community has for many years recognized the crucial role that nosetip transition plays in re-entry vehicle performance. The onset and progression of the transition front are governed by complex fluid mechanical processes that depend critically on surface roughness, wall temperature, nose-tip geometry, angle of attack, and freestream conditions. The flight analyst must make preflight predktioil~ and postflight data comparisons incorporating a suitable transition model in shape-change code computations. Such calculations of vehicle drag and surface recession contours are sensitive to both the transition correlation and the surface roughness. This sensitivity of nosetip shape change is dramatic, as witnessed by calculated that show that moderate changes in either the surface roughness height (keeping the correlation fixed) or the transition correlation slcne (keeping the roughness fixed) lead to markedly different transition-onset altitudes and nosetip shapes. These vehicle shape-change effects, which are in direct response to the transition process, are further compounded by the inherent stochastic behavior of boundary-layer transition and the .random nature of nosetip-surface roughness. Resulting transition front asymmetries can promote asymmetric nosetip shapes that cause substantial vehicle trim dispersions. The importance of the two key aspects of nose:ip transition, i.e., the transition correlation model and the roughness character, has, of course, been pointed out by previous investigators. Although individual experiments or analyses have been self-contained and have adequately described most of the observed behavior, there still exists in the literature a lack of consistency among the various studies with regard to 1) roughness height definition, 2) transition point identification, and 3) validity and/or interpretation of specific experimental transition data. These deficiencies have limited the extent to which previo:~~ studies can be applied and have provided the primary motivation for the present investigation. The current paper, which essentially summarizes results obtained from the detailed study rer~orted in Ref. 2, reviews previous research on nosetip transition, re-examines surface roughness characterization, and describes a nosetip correlation model bascd in part on thc critical Reynolds number approach as well as on a re.cvaluation of experimental data. In the sections that follow, the emphasis will be upon the consistent evaluation and detailed review of the ground-test data on nosetip transition. A common roughness height definition is developed and subsequently used to reanalyze the data base for wind tunnel, ballistic range, and free-flight experiments.

Generic buckling curves for specially orthotropic rectangular plates

Abstract: Using a double affine transformation, the classical buckling equation for specially orthotropic plates and the corresponding virtual work theorem are presented in a particularly simple fashion. These dual representations are characterized by a single material constant, called the generalized rigidity ratio, whose range is predicted to be the closed interval from 0 to 1 (if this prediction is correct then the numerical results using a ratio greater than 1 in the specially orthotropic plate literature are incorrect); when natural boundary conditions are considered a generalized Poisson's ratio is introduced. Thus the buckling results are valid for any specially orthotropic material; hence the curves presented in the text are generic rather than specific. The solution trends are twofold; the buckling coefficients decrease with decreasing generalized rigidity ratio and, when applicable, they decrease with increasing generalized Poisson's ratio. Since the isotropic plate is one limiting case of the above analysis, it is also true that isotropic buckling coefficients decrease with increasing Poission's ratio.

Wall pressure fluctuations in attached boundary-layer flow

Abstract: An examination has been made to derive a correlation for an aeroacoustic environment associated with attached compressible flow conditions. It was determined that fluctuating pressure characteristics described by incompressible theory as well as empirical correlations could be modified to a compressible state through a transformation function. In this manner, compressible data were transformed to the incompressible plane where direct use of more tractable prediction techniques are available for engineering design analyses. The investigation centered on algorithms associated with pressure magnitude and power spectral density. The method and subsequent prediction techniques are shown to be in excellent agreement with both incompressible and compressible flow data.

Minimum weight design of truss structures with geometric nonlinear behavior

Abstract: The paper presents an optimization method based on optimality criterion for minimum weight design of structures with geometric nonlinear behavior. The nonlinear critical load is determined by finding the load level at which the Hessian of the potential energy ceases to be positive definite. A recurrence relation based on the criterion that at optimum the nonlinear strain energy density be equal in all the members is used to develop an algorithm. Sample problems are given to illustrate the application of the method to truss type structures with a large number of design variables. NUMBER of algorithms based on the optimality criterion approach have been developed to design a minimum weight structure with specified constraints on nodal displacements, element stresses, system stability, etc.1'2 The optimization algorithm consisted of analyzing the structure by the finite element method and using a recurrence relation derived from the appropriate optimality criterion to modify the design variables. The optimality criterion was derived by, differentiating the Lagrangian with respect to the design variables. The displacements were assumed to be small and, in the finite element analysis, linear equilibrium equations were solved to determine the response of the structure to the ap- plied loads. In the case of system stability the constraints were defined (see Refs. 3-6) by the associated linear eigenvalue problem. This definition of system stability for some structures may not be valid because of the nonlinear behavior of the structure which may be due to the geometry of the structure or the presence of geometric imperfections. The correct procedure for these structures would be to analyze the structure* by using nonlinear equilibrium equations. This will be particularly true for large space structures (LSS). In this paper an optimization method based on the optimality criterion approach is presented for structures with geometric nonlinear behavior. In the case of a structure optimized with constraints on linear stability the optimum structure can have more than one critical buckling mode. This design tends to become im- perfection sensitive and a small deviation in the geometry of the structure can reduce its load carrying capacity sub- stantially. The imperfection sensitivity of the optimized structure can be reduced by designing the structure so that buckling loads associated with the critical buckling modes are not equal (see Ref. 7). A real structure has geometric im- perfections and these structures tend to have nonlinear

Some analysis methods for rotating systems with periodic coefficients

Abstract: Two of the more common procedures for analyzing the stability and forced response of equations with periodic coefficients are reviewed: the use of Floquet methods, and the use of multiblade coordinate and harmonic balance methods. The analysis procedures of these periodic coefficient systems are compared with those of the more familiar constant coefficient systems. Previously announced in STAR as N82-23702

Mechanism of impact pressure generation from spark-generated bubble collapse near a wall

Abstract: This paper deals with a detailed experimental investigation on the collapse of a single spark-generated bubble near a solid wall and the mechanism of its induced impact pressure generation. By changing L//?max from 0.14 to 17.1, where L is the distance between the electrodes and the solid wall and /?max a maximum bubble radius, the collapse of the bubble was observed with an Ima-Con high speed camera and, simultaneously, the induced impact wall pressure was measured. Consequently, the induced impact wall pressure history revealed that three types of the bubble collapse modes exist depending on L//?max; i.e., the region where a shock wave is dominant to the impact wall pressure at L//?max 1.5, a liquid jet at 0.6