Showing papers in "AIAA Journal in 1972"

Experiments on a Turbulent Jet in a Cross Flow

Abstract: Experiments on turbulent circular jets issuing into cross flow from both heated and unheated jets

Elastic Behavior of Multilayered Bidirectional Composites

Abstract: SEVERAL recent papers1–5 have addressed the problem of defining the exact (elastic) response of composite laminates under static bending. However, all of these studies have treated laminates consisting of only a few layers, while in practical applications, composite structures may consist of many layers, in some cases, 100 or more. It is therefore appropriate that we consider the response of multi-ply laminates with a view toward examining the generality of previous conclusions regarding the range of validity of the approximate theory normally used in the analysis of these bodies, namely, classical laminated plate theory (CPT).6 Open image in new window Fig. 1 Normal stress distribution.

Accurate Numerical Methods for Boundary-Layer Flows. II: Two Dimensional Turbulent Flows

Abstract: Description of a very simple and accurate numerical scheme which is applicable to quite general boundary-layer-flow problems. The scheme has been tested extensively on laminar flows, turbulent flows, wake flows etc. It is much faster, easier to program, and more flexible than most other numerical methods employed so far on such problems. It makes it also possible to compute extremely close to the point of separation with no special precautions. The inclusion of chemically reacting species offers no difficulties. The efficiency of the scheme clearly makes it applicable to three-dimensional steady, unsteady two-dimensional, and perhaps even unsteady three-dimensional, boundary-layer flows.

Random Eigenvalue Problems in Structural Analysis

Abstract: A computerized Monte Carlo simulation is presented for calculating the statistical properties of the eigenvalues of a spring supported beam-column. The spring supports and axial force are treated as random variables ; the distributions of material and geometric properties are considered to be correlated homogeneous random functions. Each sample distribution is generated using a new method for simulating multivariate homogeneous random processes having a specified cross-spectral density matrix. This method of solution is used to investigate the accuracy of the perturbation method for calculating the variance of the nth vibration and buckling eigenvalues. Numerical results are presented for the case where the axial load is equal to 27 % of the fundamental buckling load and the distributions of material and geometric properties are uncorrelated. The perturbation method is shown to be acceptable for limited ranges of the statistical variations of properties.

Condition of finite element matrices generated from nonuniform meshes.

Abstract: N a previous Note1 it has been shown (see also Refs. 2 and 3) that the spectral condition number Cn(K) of the global (stiffness) matrix K arising from a uniform mesh of finite elements (or of finite differences) discretization can be expressed by Cn(K) = cNes2m where 2m is the order of the differential equation and c a coefficient independent of Nes, the number of elements per side, but dependent on the order of the interpolation polynomials inside the element. This condition is "natural", since it is inherently associated with the approximation of the continuous problem by the discrete (algebraic) one. Nonuniform meshes of finite elements introduce many additional factors which may adversely affect the condition of the system. It is the purpose of this Note to describe a technique for establishing bounds on the condition number for irregular meshes of finite elements. With these bounds it becomes possible to study the effect of element geometry, the order of interpolation functions and other intrinsic and discretization parameters on Cn(K) and to isolate the factors that may lead to ill-conditioning. The matrix K is termed ill-conditioned when \Q~sCn(K) = 1, where s denotes the number of decimals in the computer. The bounds on Cn(K) are expressed in terms of the extremal eigenvalues of the element matrices. Since the element matrices are of restricted size, derivation of the bounds on Cn(K) as a function of the discretization parameters become straightforward for any problem and any element. Particular attention is focused on the possibility of improving the condition of the matrix by scaling. Bounds on the Extremal Eigenvalues

Dynamics of oil slicks

Abstract: The spread of an oil slick onto calm water is considered from a theoretical viewpoint. The equations of motion are derived for the gravity-inertial and gravity-viscous flow regimes (in which the spreading force of gravity is balanced by, respectively, inertia and viscous drag at the water surface). Approximate formulations for the viscous drag are suggested. The initial growth of the one-dimensional slick is described. For both one-dimensional and radial slicks, similarity solutions are obtained for the flow regimes which give adequate agreement with available experimental data. Approximate solutions are also given for the surface tension-viscous region, in which the slick becomes so thin that surface tension rather than gravity is the primary spreading mechanism. Based on these solutions, a general picture of the slick development is presented.

Convergence Criteria for Iterative Processes

Abstract: Introduction D the last few years, a considerable amount of effort has been put into the development of new methods of analysis for nonlinear structural systems. Taking advantage of the capabilities of modern electronic computers, these methods have been widely applied to problems of large deformations and stability, elasto-plasticity, creep, etc. Often, the numerical solution of these nonlinear problems is based on some iterative process or it involves the combination of an incremental and an iterative procedure. An ever-recurrent problem associated with iterative techniques is the decision as to whether the current iterate is sufficiently close to the root without knowing the true solution itself. In the following, a discussion of the convergence problem will be given and some practical convergence criteria will be presented. For simplicity, a pure displacement formulation of the structural problem will be assumed.

Sphere Drag Coefficients for a Broad Range of Mach and Reynolds Numbers

Abstract: The purpose of the present investigation was to establish accurate values of sphere drag coefficient in the flight regime 0.1 < Mx < 6.0 and 2 x 10 < Re^ < 10 for TJT^ % 1.0. To this end, an extensive series of measurements was made in a ballistic range. These measurements, together with other published data, permit the derivation of sphere drag confidents with an uncertainty of + 2 % in this flight regime. In addition, sifficient information is presented such that reasonable estimates of sphere drag confident can be made for TJT^ ^ 1.0, 0.05 < M^ < 20.0, and 2 x 10~ < Re*, < W\

Calculation of Turbulent Shear Flows for Atmospheric and Vortex Motions

Abstract: Turbulent shear flows transport properties, computing atmospheric and vortex motions by invariant modeling of Reynolds stress term in boundary layer momentum equation

Effect of nozzle boundary layers on rocket exhaust plumes.

Abstract: T expansion of a nozzle boundary layer into a vacuum has been treated numerically by Boynton. Following Weinbaum and Weiss and Weinbaum, Boynton treated the expansion as inviscid with the initial conditions specified by the viscous layer. Boynton demonstrated large differences in the plume properties when the influence of the supersonic portion of the nozzle boundary layer was included. In this Note, an effort is made to generalize Boynton's results and express the plume properties in terms of the boundary-layer thickness and nozzle exit conditions.

Separation Patterns of Boundary Layer over an Inclined Body of Revolution

Abstract: Based on recent symmetry-plane boundary-layer solutions, new separation patterns over an inclined body of revolution are presented. Support by experimental evidence as well as differences from other predictions in the literature are noted. Existing three-dimensional separation criteria are mostly inapplicable, and the resulting patterns found are compatible only with MaskelPs general description of separation—i.e., a combination of the free vortex layer type and a bubble type. For a not too blunt body, a bubble type prevails at low incidence, and a free vortex layer type dominates a high incidence. At extremely high incidence or for a more blunt body, a bubble type prevails again.

Spreading of a turbulent disturbance.

Abstract: The presented paper shows the effect of local Mach number on the turbulent disturbance spreading angle relative to the wall and on lateral disturbance spreading angles. Almost all the disturbances angles relative to the wall were determined from investigations where hot-wire contours or hot-film surveys of a 'laminar' boundary layer were obtained. Lateral disturbance spreading angles were obtained from investigations of various conditions including turbulent bursts, reported observations of transverse contamination, and observed transitional flow. It is noted that the disturbance spreading angle relative to the wall seems to remain essentially invariant with Mach number, while the lateral spreading angle decreases sharply with increasing Mach number up to about 6. The good agreement between lateral disturbance spreading angle data and data for the variation of turbulent jet spreading angle with Mach number implies that in the lateral dimension, turbulence in a boundary layer may develop essentially free of wall constraints (similar to a free shear layer).

Monte Carlo Solution of Nonlinear Vibrations

Abstract: A Monte Carlo technique is presented which can effectively be used for nonlinear response analysis of a structure subjected to a random pressure field undergoing large deflections. The pressure field is idealized as a multidimensional Gaussian process with mean zero and homogeneous both in time and space. The response analysis is performed in the time domain by numerically simulating generalized forces rather than in the frequency domain. The solution satisfies the boundary conditions and the differential equation in a Galerkin sense. Two numerical examples involving large deflections of a string and a plate are worked out. The result indicates that the present method indeed provides a powerful tool in solving nonlinear structural response problems under random excitations.

Film-Cooling Effectiveness and Skin Friction in Hypersonic Turbulent Flow

Abstract: Experimental equilibrium temperatures and skin friction at the surface of a flat plate cooled by two-dimensional, tangential slot injection are presented for a Mach 6 mainstream. Effects of slot height, slot mass-flow rate, injection gas temperature, and heat conduction to the slot are investigated. Experimental skin friction and effectiveness data in general agree well with predictions from a finite-difference method. Film cooling at Mach 6 was found significantly more effective than at lower speeds, with large reductions in friction drag measured downstream of the slot These results indicate the necessity for a new evaluation of film-cooling systems for hypersonic vehicles.

A small, Fast-Response Probe to Measure Composition of a Binary Gas Mixture

Abstract: A probe to measure the concentration of the components in a binary mixture of gases is described. The probe is simple to construct and quite rugged. It samples from a very small volume, has a fast time response and can very easily detect 1% of helium in nitrogen. The explanation of the principle of operation is a good example of the power of dimensional analysis when applied to what may seem to be quite a complicated and unfamiliar problem. The analysis suggest several experiments which in turn lead to a more detailed understanding of the probe and improvements in its design.

Analysis of Flow of Viscous Fluids by the Finite-Element Method

Abstract: General tinite-element models of compre ol>e local approximations of the 'elocit~· field, the density. and the tempemture for compressible fluids and the ,'e1ocity. temperature. and prl'S'i,re ror incompressihlc tluids. Thcuries or local solenoidal approximl.tions and mixed tiniteclement models ror coml,n'ssihle film lIn' lIerh·ed. A numhl'r or cumpulallonal s..ht'mes are lIe"elopt'll ror Ihe uumerical solulion or hoth lransient and stl':IlI~'nOllllniformtlow prohlems illml\'illg illcol1lpressihlelIuids. Numericlll resulls ohtllinro rrom seH~rallest problel1lsllre gh'el1. It is Shllllil Ihat Ihe finile elel1lenl ml,thod ha" grelll llolenlial for U'ie ill tlo" prohll'I1I".and represenls II p,,"erful new 1001 for Ihe llllalysis of I'iwous flows. ..

Incipient Separation of a Supersonic, Turbulent Boundary Layer, Including Effects of Heat Transfer

Abstract: An experimental study of the interaction of a turbulent boundary layer with a compression corner has been conducted at a Mach number of 29, Reynolds number based upon boundary-layer thickness of 22 to 59 x 104, and ratio of wall-temperat ure-to-recovery-temperature of 105 to 047 Adiabatic wall data showed an incipient separation angle of 65°, as determined by the liquid line method The static pressure distribution was found to be insensitive to the presence of small regions of separated flow The present results, combined with other data, shown an increasing trend of incipient separation angle with Reynolds number The effect of wall cooling was to increase the incipient separation angle and reduce the separation distance

Computation of Transonic Flows past Lifting Airfogs and Slender Bodies

Abstract: Solutions of the transonic small disturbance equation are presented for flow past thin lifting airfoils and slender bodies with M^ < 1, including cases with imbedded shock waves. The results are obtained numerically using a mixed finite-difference relaxation method previously reported by the authors. Results are presented for four lifting airfoils at various angles of attack and are compared with shock free theory and experimental data. For the slender body case, comparisons with experiments are given for five geometries both with and without aft stings. The results are also compared with approximate theory. Discussion is given on the treatment of the boundary conditions, computing times and accuracies, and ranges of applicability of the small disturbance theory.

Shock-Tube Study of Nitrogen Dissociation Rates Using Pressure Measurements

Abstract: Thermal dissociation rate of undiluted nitrogen in shock tube over 5700 to 12,000 K range, using pressure measurements

Numerical Solution for Three-Dimensional Inviscid Supersonic Flow

Abstract: An exact finite-difference solution is developed for steady, inviscid, supersonic flow over smooth threedimensional bodies The method is applied to a blunt delta wing having straight leading edges and an elliptical cross section Results are presented for angles of attack up to 30° in both perfect gas and equilibrium air at typical freestream conditions for space shuttle orbiter re-entry The effects of angle of attack on shock layer structure, on surface pressure distributions, and on surface streamline patterns are investigated Marked variations are found in the structure of the entropy layer over different portions of the surface; the implications for boundary-layer heat-transfer analyses are discussed

Minimum Weight Design of Elastic Redundant Trusses under Multiple Static Loading Conditions

Abstract: A method for automated selection of a minimum weight truss, from a subset of configurations obtained by omitting various member combinations from a primary configuration, is presented. A feasible direction algorithm is used to find an upper bound solution for any selected configuration. A dual simplex algorithm is used to rapidly generate lower bound solutions for many subset configurations considering only equilibrium conditions and stress limits. The lower bound solutions guide the selection of subset configurations for which upper bound solutions of reduced weight are sought. Examples of planar and space trusses illustrate the efficacy of the bounding technique presented. I. Mathematical Formulation C ONSIDER an elastic redundant truss with given geometric configuration and support conditions. The truss is to sustain several given alternative systems of static loads applied at the joints. Only q of these load systems which are supposed to govern the design will be considered. For simplicity, the truss is conventionally idealized; that is, the members of the truss are assumed to be joined together by frictionless connections and only axial forces, tension or compression, occur in the members under the loading. The design problem addressed herein is the selection of a minimum weight optimum truss configuration, as well as its member sizing, from a subset of truss configurations obtained by omitting various members from the given primary configuration. The design is subject to the following constraints: the crosssectional area Aj of member j, when it remains in the truss, is restricted to a given continuous range, the upper limit A? of which is finite and the lower limit A! may be, and usually is, greater than zero; the stress ajk, defined as the internal force/^ of the member j under the kih loading condition divided by Aj, has given lower limit — ffjk and upper limit ajk, and these stress limits are assumed independent of the cross-sectional area of the member; and the displacement component uik of a joint under loading condition k also has specified lower — uikl and upper uik" limits (each joint, except for fixed supports, has at least one degree of freedom, the corresponding displacement components are numbered in a fixed order and identified as ut). The problem can thus be formulated as with

Development and Evaluation of Solution Procedures for Geometrically Nonlinear Structural Analysis

Abstract: This paper presents a comparative study of the solution techniques which are applicable to the solution of the nonlinear algebraic or differential equations characterizing geometrically nonlinear structural behavior. After reviewing the currently available solution techniques, attention is focused at developing procedures which are computationally economical. The new solution procedures are compared numerically with some of the more conventional procedures such as the Newton-Raphson method, incremental methods, and iterational procedures. Application is made to highly nonlinear problems including a simple truss-spring problem and symmetrically and asymmetrically loaded shells of revolution. Results indicate that a new self-correcting initial-value formulation has possibilities as a powerful tool for nonlinear analysis.

Subsonic and Transonic Potential Flow over Helicopter Rotor Blades

Abstract: Compressible potential flows over nonlifting, hovering helicopter blades are described by suitable linear and nonlinear equations of motion for subsonic and transonic cases, respectively. Analytical and numerical results are presented for the linearized subsonic three-dimensional flow in the tip region. When the tip Mach number is transonic, the flowfield is calculated using a computational method that is a formal extension to three dimensions of recently developed nonlinear two-dimensional relaxation schemes. Calculations are presented for rectangular blades with 6% thick biconvex sections. Calculations show the relative importance of tip Mach number and aspect ratio on the growth and extent of shock waves in the tip region, and indicate a significant reduction in shock strength with decreasing aspect ratio. ELICOPTER rotor blades that can operate at high tip Mach numbers without the penalties usually associated with super-critical flow would permit high-forward speeds at relatively low-advance ratios. As the advance ratio decreases, the portion of the retreating blade that is stalled would be diminished, the portion of the retreating blade that is unstalled could operate at smaller angles of attack, and the advancing blade could generate lift without also generating an excessive rolling moment. Vibratory loads would be diminished, and severe unsteady pitching moments on the lifting portion of the retreating blade would decrease if that portion could usefully operate at higher tip speeds and smaller angles of attack. The design of rotor blade geometries that can support a transonic flowfield that is nearly shock-free requires a method for computing the detailed pressure distribution on the blade for a specified rotor geometry and advance ratio. However, the unsteady aerodynamic environment of a lifting rotor that is operating at or near the critical Mach number is extremely complicated. It is easy to appreciate the difficulty of describing such flowfields when one recalls that we do not yet have an adequate model for describing the details of the flow about a lifting, hovering rotor operating in an essentially incompressible flow. Our purpose here is therefore to focus on a portion of the high-speed rotor problem that is sufficiently limited to allow for some analytical and numerical treatment, but which retains important linear and nonlinear features of the flow. We consider a two-bladed nonlifting and hovering rotor operating in the range of tip Mach numbers where compressibility effects are important. The pressure distribution near the rotor tip is studied. In this region, the flowfield is fully three-dimensional, and blade element (strip) theory is in no sense a reasonable approximation to the rotor aerodynamics. It is assumed that the flow is inviscid. The flow is steady relative to a coordinate system attached to the blades. Analytical and numerical results presented here are based on suitable approximations to the full three-dimensional potential equation for compressible flow. When the tip Mach number is subcritical, the potential equation is the usual acoustic

Perturbation and harmonic balance methods for nonlinear panel flutter.

Abstract: A systematic way of applying both perturbation methods and harmonic balance methods to nonlinear panel flutter problems is developed here. Results obtained by both these methods for two-dimensional simply supported and three-dimensional clamped-clamped plates with six modes agree well with those obtained by the straightforward direct integration method, yet require less computer time and provide better insight into the solutions. Effects of viscoelastic structural damping on the flutter stability boundary are generally found to be destabilizing and the postflutter behavior becomes more explosive. The methods developed here may be of interest in related vibration problems.

Turbulent properties of a compressible boundary layer.

Abstract: Turbulent shear-stress, eddy-viscosity, mixing-length, heat-flux and Prandtl number distributions across a hypersonic turbulent boundary layer have been determined from the 'time-averaged' conservation equations using experimental mean profile data obtained at several streamwise locations in a fully developed turbulent boundary layer with negligible pressure gradient. The eddy-viscosity, mixing-length and Prandtl number results show general agreement with previous incompressible and adiabatic compressible correlations. However, when the turbulent Prandtl number is defined using total enthalpy as opposed to static enthalpy no clear correlation of the results in the outer portion of the boundary layer could be obtained.

Supersonic Interaction in the Corner of Intersecting Wedges at High Reynolds Numbers

Abstract: As the distance from the orifice in the tip to the wire is small and the gas velocity is of the order of the speed of sound a time response of [isec might be expected, unless the size of the hot wire and the electronics limit it to a longer time. A new probe with a smaller wire diameter (0.0001 in.) and a less rapid area expansion (based on the findings in Sec. 6) was constructed and placed in the end wall of a shock tube. The gas in the tube was nitrogen, initially at atmospheric pressure. A shock wave passing by the probe produced an instantaneous change in the stagnation conditions of the sampled gas and the corresponding change in probe output was photographed (Fig. 6), (time scale =100 jusec/cm, vertical scale = 0.05 v/cm). The response time is evidently about 200 //sec. The experiment was repeated using helium instead of nitrogen and, as expected, the rise time was faster. It is noted that a much longer time response is associated with the warming up of the glass. References 1 Blackshear, Perry L. and Lingerson, Leroy, "Rapid-Response Heat Flux Probe for High Temperature Gases," ARS Journal, Vol 32 No. 1, Nov. 1962, pp. 1709-1715. 2 D'Souza, Gerard J., Montealegre, Anthony, and Weinstein, Herbert, "Measurement of Turbulent Correlations in a Coaxial Flow of Dissimilar Fluids," CR-970, Jan. 1968, NASA. 3 Baldwin, L. V., Sandborn, V. A., and Laurence, J. C, "HeatTransfer from Transverse and Yawed Cylinders in Continuum, Slip and Free Molecule Air Flows," Journal of Heat Transfer, Vol 82 No. 1, May 1960, pp. 77-86. 4 Aihara, Y., Kassoy, D. R., and Libby, Paul A., "Heat Transfer from Circular Cylinders at Low Reynolds Numbers," The Physics of Fluids, Vol. 10, No. 1, May 1967, pp. 947-952. 5 Loeb, Leonard B., "The Laws of Rarefied Gases and Surface Phenomena," The Kinetic Theory of Gases, 3rd ed., Dover, 1961, pp. 278-364. 6 Faust, J. W., "Accommodation Coefficient of Inert Gases on Al and Pt and Their Dependence on Surface Condition," Ph.D. thesis, 1954, Univ. of Missouri, Columbia, Mo. 7 Dewey, C. Forbes, Jr., "A Correlation of Convective Heat Transfer and Recovery Temperature Data for Cylinders in Compressible Flow," International Journal of Heat and Mass Transfer, Vol. 8, No. 1, Feb. 1965, pp. 245-252. 8 Brown, G. L., and Roshko, Anatol, "The Effect of Density Differences on the Turbulent Mixing Layer," AGARD Conference Proceedings Turbulent Shear Flows, Nov. 1971, to be published.