Showing papers in "AIAA Journal in 1973"

Free vibrations of multilayered composite plates.

Abstract: Summary of some of the results of a recent study of the reliability and range of validity of two-dimensional plate theories in application to low-frequency free vibration analysis of simply supported, bidirectional, multilayered plates consisting of a large number of layers. These results show that for composite plates the error in the predictions of the classical plate theory is strongly dependent on the number and stacking of the layers, in addition to the degree of orthotropy of the individual layers and the thickness ratio of the plate.

Structure of Shock Waves in Cylindrical Ducts

Abstract: Wall static and in-stream phot pressure distributions are presented for confined, nonreacting, supersonic flows in cylindrical sections wherein a shock structure has been stabilized. Based on an analysis of these measurements, the character of the wave structure is shown to be oblique rather than normal, with the flow remaining primarily supersonic downstream of the shock system. When additional cylindrical sections are either added or deleted the shock structure is, with the exception of slight changes due to the different initial conditions, independent of location in the duct. The parameters which govern the distance st, over which the pressure rise is spread, viz., Mach number, momentum thickness Reynolds number, duct diameter, and the momentum thickness of the upstream boundary layer, were varied as follows: 1.53 ^ Ma ^ 2.72, 5 x 10 ^ Ree ^ 6 x 10, 1.0 D 6.1 in., and 0.007 ^ 6 ^ 0.036 in. In each test the wave structure was generated by either lowering the pressure in the air supply system so that the cylindrical duct was, in effect, overexpanded when discharging to ambient conditions, or by throttling the flow leaving the duct. For a given pressure ratio across the disturbance, Pf/pa, st varies approximately directly with the product 0D and inversely with (Ma — l)Re0. A simple quadratic expression is presented which adequately represents this corespondence for the complete range of conditions tested and for data from the cited reference.

A survey of the mean turbulent field closure models.

Abstract: C solutions to the differential boundary-layer equations have for some years now been applied to turbulent boundary layers where relief from the difficulty of solution permits more concern for the physical elements of models which purport to simulate some statistical features of turbulent flowfields. A first step has been accomplished; that is, accurate, quite versatile, and practically/useful computer programs have been combined with rather simple and successful empirical statements" which allow one to estimate the Reynolds shear stress in the equations for the mean velocity field. We call this Mean Velocity Field (MVF) closure since it predicts only the mean velocity field in addition to the mean shear stress. For boundarylayer flows a set of empirical constants must be selected. However, it is then possible to accurately predict flows with wall transpiration, heat transfer, and a variety of other boundary conditions, and, remarkably, with no adjustment in the constants. However, the constants must be adjusted for, say, pipe or channel flow or free shear flows. By moving on to the more complicated Mean Turbulent Field (MTF) closure there is some hope of discovering increasingly universal models and a greater range of predictability. There are two other incentives: First, it is rather comforting actually to compute the turbulent kinetic energy; it is, after all, the premier property that distinguishes turbulent from laminar flow. Second, it appears possible to include body forcelike effects such as curvature, buoyancy, and Coriolis effects with no further empiricism. The latter is a line of thought that is not new,' and it has occupied the present authors' interest for some time. However, in this paper we avoid these topics in order to simplify discussion of an already complicated field. We also assume that the fluid is incompressible. Extension to high Mach number flows does not, however, seem to be a major problem. A basis for MTF calculations began appropriately enough with the semiheuristic models of Kolmogoroff and Prandtl in the early 1940's; they include the turbulent kinetic energy transport equation, a turbulent-energy-related eddy viscosity, and either a prescribed length scale function or a differential equation for a length scale. We wish to call this Mean Turbulent Energy (MTE) closure which together with Mean Reynolds Stress (MRS) closure forms two subsets of MTF closure.* MRS closure implies a closed set of equations which include equations for all nonzero components of the Reynolds stress tensor. Chou' seems to be the first to initiate a study of the full set of equations with an eye towards closure. However, it was Rotta in 1951 who laid the foundation for almost all of the current models. In the Reynolds stress tensor equation (the tensor equation for the single-point, double-velocity correlations, the trace of which is the kinetic energy equation) there appear pressure-velocity gradient correlations, (pdujdxj), which Rotta called the energy redistribution terms and which he argued should be proportional to the deviation from isotropy — dtj(uky/3. On the whole, the assumption seems physically correct, but of further importance is the fact that it provides a unity that was lacking, say, in the 1940's.f Thus, the Reynolds shear stress is now determined as a part of the whole; MTE closure can be obtained as an analytic simplification of MRS closure, and, furthermore, MVF closure (that is, eddy viscosity or mixing length concepts) can be viewed as a further simplification. We shall follow this process of simplification in this paper. Despite the unity of thought provided by Rotta's basic assumption, it is, of course, an approximation to nature and is subject to modification in the hands of investigators eager to achieve agreement with data. Furthermore, there are other terms in the Reynolds stress equations, such as the dissipation and diffusion terms, which are modeled differently by different investigators and represent some impass to a consensus theory such as is the near state of MVF closure. In the present development we have attempted to present the basic ideas and a core model for MRS and MTE closure and

Analysis of Embedded Shock Waves Calculated by Relaxation Methods

Abstract: The requirements for uniqueness of the calculated jump conditions across embedded shock waves are investigated for type-dependent difference systems used in transonic flow studies. A mathematical analysis shows that sufficient conditions are (1) the equations should be differenced in conservative form and (2) a special difference operator should be used when switching from a hyperbolic to an elliptic operator. The latter results in a consistency condition on the integral equations, rather than the differential, at these points. Calculated jump conditions for several embedded and detached shock waves are analyzed in the physical and hodograph planes. Comparisons are made with previous results, a time-dependent calculation, and data.

Reduction of structural frequency equations.

Abstract: References 1 Goldstein, R. J. and Hagen, W. R, "Turbulent Flow Measurements Utilizing the Doppler Shift of Scattered Laser Radiation," The Physics of Fluids, Vol. 10, 1967, pp. 1349-1351. 2 Pike, E. R., Jackson, D. A., Bourke, P. J., and Page, D. I., "Measurement of Turbulent Velocities from the Doppler Shift in Scattered Laser Light," Journal of Scientific Instruments, Vol. 1, 1968, pp. 727-730. 3 Edwards, R. V., Angus, J. C, French, M. J., and Dunning, J. W., Jr., "Spectral Analysis of the Signal from the Laser Doppler Flowmeter : Time-Independent System," Journal of Applied Physics, Vol. 42, 1971, pp. 837-850. 4 Adrian, R. J. and Goldstein, R. J., "Analysis of a Laser Doppler Anemometer," Journal of Physics, Ser. E, Vol. 4, 1971, pp. 505-511. 5 Lumley, J. L., George, W. K., and Yobashi, Y., "The Influence of Ambiguity and Noise on the Measurement of Turbulent Spectra by Doppler Scattering," Proceedings of the Symposium on Turbulent Measurement in Liquids, Rolla, Mo., 1969. 6 Lennert, A. E., Brayton, E. B., Crosswy, F. L., "Summary Report of the Development of a Laser Velocimeter to be Used in AEDC Wind Tunnels," TR-70-101, 1970, Arnold Engineering Development Center, Arnold Air Force Station, Tullahoma, Tenn. 7 Kognelnik, H., "Imaging of Optical Modes—Resonators with Internal Lenses," Bell System Technical Journal, Vol. 44, 1965, pp. 435-494.

Theories for the Dynamic Response of Laminated Plates

Abstract: The effect of the heterogeneous shear deformation over the thickness of the plate on the dynamical behavior of laminated plates is investigated. Three sets of governing equations are derived according to different assumptions on the local transverse shear deformation and the interface conditions. The equations are evaluated by comparing the solutions with the exact solution for harmonic wave propagations. A special formulation for laminates with midplane symmetry is also presented and discussed. It is found that the effect of the local shear deformation depends highly on the transverse shear rigidities of the constituent layers.

Estimation of possible excitation frequencies for shallow rectangular cavities.

Abstract: The physical processes that sustain discrete-frequency oscillations of cavities adjacent to compressible flow are modeled analytically, yielding a formula which predicts excitation frequencies as a function of Mach number and cavity geometry. These physical processes are similar to those used by Powell in describing the mechanism underlying the production of edge tones. The empirically determined constants appearing in Rossiter's formula for excitation frequencies are computed from the model. It appears that instability of the shear layer as well as interaction between the shear layer and the cavities' trailing edge is required to sustain discrete-frequency oscillation. It is suggested that the simultaneous excitation of two or more discrete frequencies (which are not harmonic), as have been observed in practice, correspond to the simultaneous participation of two or more vortex sheet displacement modes. The model analyzed yields qualitatively correct acoustic mode shapes in the cavity. Theoretical results include the calculation of possible excitation frequencies over the range 0.8 ^ M ^ 3 for rectangular cavities and show their dependence on cavity depth. Analytic results are in general agreement with experimental data.

An Analytical and Experimental Study of Supersonic Combustion of Hydrogen in Vitiated Air Stream

Abstract: Detailed probe measurements of total temperature, pressure, and composition were taken in a two-dimensional test section 35.6 cm downstream of hydrogen injection. A high pressure gas generator supplied Mach 2.44 vitiated air or inert gas at elevated temperatures and at a static pressure equal to that of the hydrogen. Special water-cooled probes and sampling techniques were developed for the short test times required by heat-sink hardware. Independent methods of measuring stream total temperatures are compared. For the pure mixing case, the computed composition profile agreed well with the experimental profile. The analysis takes into account the wall boundary layer and the initial boundary layer in the main stream. Ignition of hydrogen, as determined from photographic exposures of the radiating gases, varied from 30 to 10 cm downstream from injection for a 45 K increase in local free-stream static temperature.

Mathematical modeling of spinning elastic bodies for modal analysis.

Abstract: The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.

Fast triangular formulation of the square root filter.

Abstract: A new, triangular formulation of the square root Kalman filter is presented. An efficient analytic algorithm is derived for maintaining the covariance square root matrix in triangular form during the incorporation of measurements. The triangular form provides significant computational savings in the square root time update calculations. This savings tends to offset the computational disadvantage of square root methods in general, due to the greater complexity of incorporating process noise. The new square root method is shown to be typically 50% faster than the Potter square root method, 100% faster than the Joseph conventional method, and comparable in speed to the standard Kalman method. Numerical precision of the new method is greater, and storage requirements equal to or less than those of other methods.

A Finite Element Method for the Optimal Design of Variable Thickness Sheets

Abstract: References 1 Hsu, C. T., "Swirling Nozzle Flow Equations from Crocco's Relation," AIAA Journal, Vol. 9, No. 9, Sept. 1971, pp. 1866-1868. 2 Hsu, C. T., "Errata: 'Swirling Nozzle Flow Equations from Crocco's Relation,'" AIAA Journal, Vol. 10, No. 3, March 1972, p. 368. 3 Batson, J. L. and Sforzini, R. H., "Swirling Flow through a Nozzle," Journal of Spacecraft and Rockets, Vol. 7, No. 2, Feb. 1970, pp. 159-163. 4 DeJoode, A. D., "Mach Number Distribution and Mass Flow Rate for Swirling Flow in a Choked Nozzle Throat," MS thesis, Feb. 1973, Iowa State Univ., Ames, Iowa. 5 Lewellen, W. S., Burns, W. J., and Strickland, H. J., "Transonic Swirling Flow," AIAA Journal, Vol. 7, No. 7, July 1969, pp. 1290-1297.

Shock Wave/Turbulent Boundary-Layer Interactions in Rectangular Channels

Abstract: Interaction regions created by the impingement of full span, externally generated, shock waves on a nozzle wall boundary layer were investigated. Incident shock strength was varied to produce unseparated, incipient, and fully separated flow fields. Significant departures from two-dimensionality were observed over the entire range of shock strengths tested and were identified with sidewall and corner boundary layer effects. However, comparisons of present centerline results with published two-dimensional data, obtained under similar test conditions and geometrical constraints, showed excellent agreement (e.g., incipient separation pressure levels, wall pressure distributions, free-interaction, and scale of the interaction region). This raises some question concerning the degree of two-dimensionality achieved in these previous investigations.

Buckling and Vibration of Unsymmetrically Laminated Cross-Ply Rectangular Plates

Abstract: An exact solution and numerical results are presented for simply supported plates that are laminated unsymmetrically about their middle surface. The coupling between bending and extension induced by the lamination asymmetry substantially decreases buckling loads and vibration frequencies for common composite materials such as boron/epoxy and graphite/epoxy. For antisymmetric laminates, the effect of the coupling dies out rapidly as the number of layers is increased. For generally unsymmetric laminates, however, the effect of coupling dies out very slowly as the number of layers increases. That is, having a large number of layers is no guarantee that coupling will not seriously degrade buckling resistance and vibration frequencies. Thus, designers must include coupling between bending and extension in all analyses of unsymmetrically laminated plates.

Automated Structural Synthesis Using a Reduced Number of Design Coordinates

Abstract: The automated synthesis of large structural systems using a reduced number of design variables is investigated. The synthesis is accomplished by generating a Fiacco-McCormi ck Penalty function which is minimized with a deflected gradient procedure. The optimization algorithm is modified using a reduced set of design variables which greatly reduces the computer effort usually required for large structural problems and provides an upper bound solution. A rational procedure based on the external loads and constraints on the system is developed for generating the reduced set of coordinates. Examples of truss systems subjected to stress constraints, displacement constraints, and constraints on the design variables are studied in detail. For the examples considered, the results show large reductions in computer effort and demonstrate the effectiveness and efficiency of the method. The method provides a powerful tool for preliminary design studies, and appears to be the most effective method for obtaining near optimal designs of large systems.

Starting Transient of Solid-Propellant ocket Motors with High Internal Gas Velocities

Abstract: A comprehensive analytical model which considers time and space development of the flow field in solid propellant rocket motors with high volumetric loading density is described. The gas dynamics in the motor chamber is governed by a set of hyperbolic partial differential equations, that are coupled with the ignition and flame spreading events, and with the axial variation of mass addition. The flame spreading rate is calculated by successive heating-to-ignition along the propellant surface. Experimental diagnostic studies have been performed with a rectangular window motor (50 cm grain length, 5 cm burning perimeter and 1 cm hydraulic port diameter), using a controllable head-end gaseous igniter. Tests were conducted with AP composite propellant at port-to-throat area ratios of 2.0, 1.5, 1.2, and 1.06, and head-end pressures from 35 to 70 atm. Calculated pressure transients and flame spreading rates are in very good agreement with those measured in the experimental system.

Theoretical and Measured Electron-Density Distributions at High Altitudes

Abstract: A viscous shock-layer analysis has been developed and applied to the calculation of nonequilibrium-flow species distributions in the plasma layer of a blunt-nosed vehicle at high altitudes. The theoretical electron-density results obtained are in good agreement with those measured in flight for a hemisphere-9 cone entry vehicle. The flight measurements were obtained using electrostatic probes that protruded well into the shock layer. In addition, the theoretically obtained heavy-particle translational temperatures appear to agree fairly well with the electron temperatures that were measured in the flight experiments using voltage-swept thin-wire electrostatic probes. The influence of the reaction-rate coefficients on the calculated electron densities has been assessed and shown to be within the uncertainty in the flight data. The theoretical results demonstrate the importance of including in the chemical model the positive ions N2 + , O2 + , N + , and O + , in addition to NO + , for the high altitudes and velocities considered here.

Time-Split Finite-Volume Method for Three-Dimensional Blunt-Body Flow

Abstract: An efficient numerical method for calculating plane, axisymmetric, and fully three-dimensional blunt-body flow is presented. It is a second-order-accurate, time-dependent finite-volume procedure that solves the Euler equations in integral conservation-law form. These equations are written with respect to a Cartesian coordinate system in which an embedded mesh adjusts in time to the motion of the bow shock that is automatically captured as part of the weak solution. With such an adjusting mesh, oscillations in flow properties near the shock are shown to be virtually eliminated. The scheme uses a time-splitting concept that accelerates the convergence appreciably. Comparisons are made between computed and experimental results.

Multishocked, Three-Dimensional Supersonic Flowfields with Real Gas Effects

Abstract: This program determines the supersonic flowfield surrounding three-dimensional wing-body configurations of a delta wing. It was designed to provide the numerical computation of three dimensional inviscid, flowfields of either perfect or real gases about supersonic or hypersonic airplanes. The governing equations in conservation law form are solved by a finite difference method using a second order noncentered algorithm between the body and the outermost shock wave, which is treated as a sharp discontinuity. Secondary shocks which form between these boundaries are captured automatically. The flowfield between the body and outermost shock is treated in a shock capturing fashion and therefore allows for the correct formation of secondary internal shocks . The program operates in batch mode, is in CDC update format, has been implemented on the CDC 7600, and requires more than 140K (octal) word locations.

Study of Vortex Rings Using a Laser Doppler Velocimeter

Abstract: filter resulting when the gyro drifts, accelerometer errors, and DME biases are neglected performs nearly optimally. Hence, alignment can be accomplished by using an eighth-order filter when using one VOR/DME, or a seventh-order filter when using two DME's. The quantitative results presented here are, of course, dependent upon the validity of the error models assumed. In particular, the VOR/DME error model proposed here has not been as thoroughly checked experimentally as the inertial navigation system model.

Finite Element Structural Analysis of Local Instability

Abstract: A finite element analysis is presented for predicting local buckling stresses in plates, stiffened panels, and thin-walled columns for which the cross section is made up of thin flat plates. The analysis leads to the formulation of the elastic and geometrical stiffness matrices appearing in an eigenvalue equation used to determine the buckling stress. The stiffness matrices are derived from the exact sinusoidal lengthwise variation of displacements. The resulting sinusoidal stiffness matrices depend on the wavelength of the buckled pattern, but this dependence is of a very simple form, since all stiffness coefficients contain the buckling wavelength as a common factor. Examples are given to illustrate application of the method to several typical aircraft structural components.

A Simple Correlation for Incipient-Turbulent Boundary-Layer Separation due to a Skewed Shock Wave

Abstract: References 1 Fingerson, L. M., "A Heat Flux Probe for Transient Measurements in High Temperature Gases," Ph.D. thesis, 1961, Univ. of Minnesota, Minneapolis, Minn.; also ARS Journal, Vol. 13, No. 11, Nov. 1962, p. 1709. 2 McCroskey, W. J., "Density and Velocity Measurements in HighSpeed Flows," AIAA Journal, Vol. 6, No. 9, Sept. 1968, pp. 1805-1808. 3 Horstman, C. C. and Kussoy, M. I, "Hypersonic Viscous Interaction on Slender Cones," AIAA Paper 68-2, New York, 1968. 4 Vas, I. E., "An Experimental Investigation of the Flow About a Slender Cone at Hypersonic Speeds," Ph.D. thesis, 1970, New York Univ., New York. 5 Becker, M., Papanikas, D. G., and Schweiger, G., "Experimental Study of the Flow Field in Front of Hemispheres in the Transition and Shock Formation Regime," presented at the 7th RGDS, July 1970, Deutsche Forschungsurid Versuchsanstalt fur Luftund Raumfahrt, (DFVLR) Porz-Wahn, W. Germany. 6 Harbour, P. J. and Lewis, J. H., "Preliminary Measurements of the Hypersonic Rarefield Flow Field on a Sharp Flat Plate Using an Electron Beam Probe," Rarefied Gas Dynamics, Supp. 4, Vol. 1, Academic Press, New York, 1967. 7 Petraites, R. J., "An Experimental Investigation of the Effects of Three-Dimensionality on the Flow Over a Flat Plate at M ~ 25," MSE thesis, Aug. 1972, Dept. of Aerospace and Mechanical Sciences, Princeton Univ., Princeton, N.J. 8 Dewey, C. F., 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, 1965, pp. 245-252. 9 Rubin, S. G., Rudman, S., Lin, T. C, and Pierucci, M., "Hypersonic Viscous-Inviscid Interaction by a New Type of Analysis," AGARD CP 30, Hypersonic Boundary Layers and Flow Fields, May 1968. 10 Mayne, A. W., Jr., Gilley, G. E., and Lewis, C. H., "Binary Boundary Layers on Sharp Cones in Low-Density Supersonic and Hypersonic Flow," AIAA Journal, Vol. 7, No. 4, April 1969, pp. 699-706.

Computation of Space Shuttle Flowfields Using Noncentered Finite-Difference Schemes

Abstract: Second- and third-order, noncentered finite-difference schemes are described for the numerical solution of the hyperbolic equations of fluid dynamics. The advantages of noncentered methods over the more conventional centered schemes are: simpler programming logic, nonhomogeneous terms are easily included, and generalization to multidimensional problems is direct. Second- and third-order methods are compared with regard to dissipative and dispersive errors and shock-capturing ability. These schemes are then used in a shock-capturing technique to determine the inviscid, supersonic flow field surrounding space shuttle vehicles (SSV). Resulting flow fields about typical pointed and blunted, delta-winged SSVs at angle of attack are presented and compared with experiment.

Evaluation of Solution Procedures for Material and/or Geometrically Nonlinear Structural Analysis

Abstract: This paper presents an assessment of the solution procedures available for the analysis of inelastic and/or large deflection structural behavior. A literature survey is given which summarizes the contribution of other researchers in the analysis of structural problems exhibiting material nonlinearities and combined geometric-material nonlinearities. Attention is focused at evaluating the available computational and solution techniques. Each of the solution techniques is developed from a common equation of equilibrium in terms of pseudo forces. The solution procedures are applied to circular plates and shells of revolution in an attempt to compare and evaluate each with respect to computational accuracy, economy, and efficiency. Based on the numerical studies, observations and comments are made with regard to the accuracy and economy of each solution technique.