# Showing papers in "AIAA Journal in 1971"

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TL;DR: In this paper, the transonic small disturbance theory is used to solve for the flow past thin airfoils including cases with imbedded shock waves, and a boundary value problem is formulated for the case of a subsonic freestream Mach number.

Abstract: Transonic small disturbance theory is used to solve for the flow past thin airfoils including cases with imbedded shock waves. The small disturbance equations and similarity rules are presented, and a boundary value problem is formulated for the case of a subsonic freestream Mach number. The governing transonic potential equation is a mixed (elliptic-hyperbolic) differential equation which is solved numerically using a newly developed mixed finite difference system. Separate difference formulas are used in the elliptic and hyperbolic regions to account properly for the local domain of dependence of the differential equation. An analytical solution derived for the far field is used as a boundary condition for the numerical solution. The difference equations are solved with a line relaxation algorithm. Shock waves, if any, and supersonic zones appear naturally during the iterative process. Results are presented for nonlifting circular arc airfoils and a shock free Nieuwland airfoil. Agreement with experiment for the circular arc airfoils, and exact theory for the Nieuwland airfoil is excellent.

651 citations

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TL;DR: In this article, a method is presented to determine the vibration modes of a complex structural system by using component vibration modes, which is suitable for structures with a large number of component interface coordinates, such as finite element shell models.

Abstract: A method is presented to determine the vibration modes of a complex structural system by using component vibration modes. The structural system is considered to be an assemblage of subsystems or components. The vibration modes for each component are determined separately and then used to synthesize the system modes. The number of component modes used may be truncated to reduce the number of generalized coordinates required for a vibration analysis. Only component vibration modes are retained as generalized coordinates when the system modes are obtained; hence, the method is particularly suitable for structures with a large number of component interface coordinates, such as finiteelement shell models. The boundary conditions used for determining component vibration modes can be either free-free or constrained. An optional technique to modify the component modes is included in order to obtain more accurate system modes. Numerical results from two examples are included.

346 citations

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TL;DR: In this article, the authors measured the drag on spheres and disks moving rectilinearly through an incompressible fluid and used hydrogen bubble flow visualization to relate these forces to the unsteady wake flows.

Abstract: The drag on spheres and disks moving rectilinearly through an incompressible fluid has been measured for Reynolds numbers (Re) from 5 to 100,000. Test models were mounted on a carriage which rode along a linear air bearing track system. Tests were performed by towing the models through a channel filled with glycerine-water mixtures. Forces and moments on the models were sensed by strain gage transducers; hydrogen bubble flow visualization was utilized in relating these forces to the unsteady wake flows. Steady drag results agreed with existing data except for the disk at 100 < Re < 1000, in which the drag coefficient values were up to 50% below the level of existing data; drag force unsteadiness during steady motion was always <5% for the sphere and <3% for the disk. Sphere drag measurements under constant acceleration from rest showed the apparent mass concept to be valid (at high Re) until the sphere had traveled approximately one diameter, after which the quasi-steady drag (based on instantaneous velocity) showed good agreement with the actual drag. Interference effects of the sting supports used in these tests are discussed.

289 citations

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TL;DR: Turbulent skin friction and heat transfer prediction on flat plates and wind tunnel walls at supersonic and hypersonic Mach numbers, using Van Driest theory, was performed by.

Abstract: Turbulent skin friction and heat transfer prediction on flat plates and wind tunnel walls at supersonic and hypersonic Mach numbers, using Van Driest theory

284 citations

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281 citations

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Kaman Aircraft

^{1}TL;DR: In this article, a method is presented for identifying parameters in a linear, discrete model of a structure by using measured normal modes to modify an analytically derived model, which has a relatively large number of points of interest and a frequency range of interest influenced by a relatively small number of normal modes.

Abstract: A method is presented for identifying parameters in a linear, discrete model of a structure by using measured normal modes to modify an analytically derived model. The structure considered has a relatively large number of points of interest and a frequency range of interest influenced by a relatively small number of normal modes. The analytical model which is introduced has fewer degrees of freedom (normal modes) than coordinates (points of interest). The parameters of this "incomplete model" are obtainable from the limited, but quantitative, test data, and the conceptually valid, but approximate, analytical data. The characteristics of this model and methods of using it are discussed, in particular, means of computing the effects of mass and stiffness changes on natural frequencies and normal modes. Computer experiments illustrate these methods and demonstrate that such a model can be useful and that the procedure is not overly sensitive to measurement errors.

221 citations

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TL;DR: In this article, a linear closed loop guidance law was proposed to compensate for the acceleration and time varying navigation gain in short-range intercept trajectories, which is applicable to short range air-to-ground and airto-air interception.

Abstract: Introduction "IVTISSILE dynamic time lags, guidance command satura1? JL tion, and target acceleration are major factors contributing to excessive terminal miss distances resulting from shortrange intercept trajectories. The objective of this Technical Note is to describe a linear closed loop guidance law which compensates for these factors. Optimal control theory is utilized where the missile dynamics, represented as a single time lag, and target acceleration are defined in the constraint equations. A quadratic performance index is employed which implicitly effects a "soft" limit on the acceleration command. A zero terminal miss distance is the only boundary constraint imposed on the problem. The final form of the guidance law which includes a time varying navigation gain represents an extension of the guidance laws discussed by Bryson, Garber, and Abzug and is applicable to short range air-to-ground and air-to-air interception.

217 citations

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TL;DR: In this paper, a generalized Duhamel-Neumann form of Hooke's law is used to develop laminated plate equations which include the effect of expansional strains, such as temperature, absorption by a polymeric matrix material of a swelling agent such as water vapor, and by sudden expansion of absorbed gases in the matrix.

Abstract: A generalized Duhamel-Neumann form of Hooke's law is used to develop laminated plate equations which include the effect of expansional strains. Such strains are induced in composite materials by temperature, absorption by a polymeric matrix material of a swelling agent such as water vapor, and by sudden expansion of absorbed gases in the matrix. Solutions to specific boundary value problems are presented for both symmetric and nonsymmetric laminates. Numerical results indicate that in addition to inducing residual stresses, expansional strains can substantially affect the gross response characteristics of a composite material.

211 citations

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194 citations

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TL;DR: In this paper, the authors identify some potentially critical areas of viscous interactions associated with high Mach number vehicles and briefly review their state of knowledge in these areas with emphasis on the basic flow phenomena.

Abstract: T most severe problems of atmospheric flight at high Mach numbers are associated with viscous-inviscid interactions. Cruise vehicles for Mach numbers above four and lifting re-entry vehicles have highly complex three-dimensional configurations in which exist many regions of high compression that can cause boundary layers to separate. Although separation can result in loss of control effectiveness or flow degradation in an engine inlet, flow reattachment gives rise to heat rates that can far exceed those for an attached boundary layer. A further, and possibly far more severe viscous interaction problem is the impingement of shock waves generated by the forebody and other external components of a vehicle on aft sections resulting in local heat rates that may be many times larger than stagnation point values. Peak heating conditions may be laminar for lifting re-entry configurations, though our knowledge of boundary layertransition is far from adequate so that transitional and turbulent flows cannot be ruled out. However, Reynolds num, bers of potential high Mach number cruise vehicles are high— 10 to 10—so that viscous interactions will be predominately associated with turbulent boundary layers and their attendant higher heat rates. The high local heat rates resulting from viscous interactions cause "hot spots" that could lead to catastrophic failure. Vivid examples of damage resulting from viscous interactions are given in Figs. 1 and 2. A ventral pylon on the X-15 airplane, shown in Fig. 1, caused high^local heating of the fuselage around its root, and developed large holes near its tip due to the impingement of the shock wave from a dummy ramjet it supported, during a flight at Mach 6.7 in 1967. A study of the flowfield of the pylon-mounted dummy ramjet configuration is reported in Ref. 1. Figure 2 shows considerable damage due to interaction heating to the underside of a sled and its supporting slipper as a result of a run at 7000 fps on the 7-mile test track at Holloman Air Force Base. Unlike stagnation-point heating where the location is obvious, the problem with complex configurations is to determine "where" high heat rates are likely to occur, as well as their magnitude. It is the purpose of this paper to identify some potentially critical areas of viscous interactions associated with high Mach number vehicles and briefly review our state of knowledge in these areas with emphasis on the basic flow phenomena.

189 citations

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TL;DR: In this paper, the authors describe some experiments in swirling flows in a mildly diverging cylindrical tube in which three types of vortex breakdown were observed: double-helix and spiral forms (followed by turbulent mixing), and axisymmetric form (often followed by a spiral breakdown, then by turbulent mixes).

Abstract: This paper describes some experiments in swirling flows in a mildly diverging cylindrical tube in which three types of vortex breakdown were observed: double-helix and spiral forms (followed by turbulent mixing), and axisymmetric form (often followed by a spiral breakdown, then by turbulent mixing). The type and location of the breakdowns were found to be dependent upon the Reynolds and circulation numbers of the flow. The observations reported and the evidence presented herein revealed that the axisymmetric breakdown is basically a finite transition between two sequent states of flow, from a uniform state of swirling flow (supercritical) to one (subcritical) featuring a series of standing waves of finite amplitude. The double-helix and spiral forms, which occur in a region well defined by Reynolds and circulation numbers, appear to be a consequence of the instability of the vortical viscous flow to spiral disturbances.

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TL;DR: In this paper, the authors derived the intermittency factor for arbitrary axisymmetric body with zero angle of attack, which can be reduced to the form of universal intermittency distribution of Dhawan and Narasimha in the case of straight tube or flat plate.

Abstract: The transition region is considered to be characterized by the intermittent appearance of turbulent spots, which grow as they move downstream until they finally merge into one another to form the turbulent boundary layer. The intermittency factor for arbitrary axisymmetric body with zero angle of attack has been derived in an expression which can be reduced to the form of universal intermittency distribution of Dhawan and Narasimha in the case of straight tube or flat plate. A key factor to control flow conditions in the transition zone appears to be the spot formation rate, which has been deduced from the available data of the extent of transition zone. It was found that the spot formation rate depends not only on the transition Reynolds number but also on the Mach number. A comparison of the deduced spot formation rate with the neutral stability curves indicated that the neutral stability curves can be used as a guide to relate the spot formation rate to the transitional Reynolds number. Calculations of the transitional heat-transfer rate on a sphere in supersonic flow agree well with the experimental results.

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Virginia Tech

^{1}TL;DR: In this paper, a finite element analysis technique which includes the effects of transverse shear deformation and is readily adaptable to arbitrary laminated plates is described, where the displacement formulation is based on a refined theory for laminates which allows the deformed normal to rotate to include transverse deformation.

Abstract: A finite-element analysis technique which includes the effects of transverse shear deformation and is readily adaptable to arbitrary laminated plates is described. The discrete element employed is a rectangle with 28 degrees-of-freedom which include extension, bending, and transverse shear deformation states. The displacement formulation is based on a refined theory for laminates which allows the deformed normal to rotate to include transverse shear deformations. Results for plate deformations and internal stress distributions, including transverse shear stresses, are shown to compare quantitatively with the theory of elasticity for selected example problems. Additional results for laminate deformation behavior are in good agreement with the shear deformation theory of Ambartsumyan. The method described can easily be incorporated into existing matrix analysis schemes which can then be used with confidence in analyzing advanced composite structures.

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TL;DR: In this paper, the characteristics of a unique meteorological wind tunnel with a capability for simulating thermally stratified boundary layers are described, and mean wind speed, mean temperature and turbulence statistics measured in this laboratory facility are found to be similar to corresponding data obtained from measurements in the atmosphere.

Abstract: Similarity criteria are given for micro-, small-, and meso-scale motion of the atmospheric boundary layer. Requirements for simulation of dispersion of passive contaminants in the atmosphere are discussed. The characteristic features of a unique meteorological wind tunnel with a capability for simulating thermally stratified boundary layers are described. Mean wind speed, mean temperature and turbulence statistics measured in this laboratory facility are found to be similar to corresponding data obtained from measurements in the atmosphere. Examples of simulated dispersion over a variety of surface features including urban areas and complex topography are described.

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TL;DR: Viscous flow in supersonic de Laval nozzle, measuring gas density and rotational temperatures by electron beam techniques as discussed by the authors, was used to measure gas density in the de Lval nozzle.

Abstract: Viscous flow in supersonic de Laval nozzle, measuring gas density and rotational temperatures by electron beam techniques

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TL;DR: In this paper, a general method for calculating turbulent boundary layers in two-dimensional flows is presented, based on the ideas of eddy transport coefficients and the numerical solution of the governing equations in differential form.

Abstract: In this paper we present a general method for calculating turbulent boundary layers in twodimensional flows and investigate its accuracy for compressible flows with heat and mass transfer The method is based on the ideas of eddy transport coefficients and the numerical solution of the governing equations in differential form The experimental data considered cover a Mach number range of 0 to 67 and include flows with and without pressure gradients The results indicate good agreement at high Reynolds numbers At low Reynolds numbers the agreement is not as good, and further work needs to be done in such cases

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TL;DR: Kaufman, L. and Nesor, H. as discussed by the authors, "Stability Characterization of Refractory Materials Under High Velocity Atmospheric Flight Conditions," AFML-TR-69-84, Pt. IV, Vol. I, No. 3, March 1970, ManLabs Inc., Cambridge, Mass.

Abstract: 1 Kaufman, L. and Nesor, H., "Stability Characterization of Refractory Materials Under High Velocity Atmospheric Flight Conditions," AFML-TR-69-84, Pt. I, Vol. I, March 1970, ManLabs Inc., Cambridge, Mass. 2 Bernstein, H. and Baron, J. R., "Stability Characterization of Refractory Materials Under High Velocity Atmospheric Flight Conditions," AFML-TR-69-84, Pt. IV, Vol. II, Dec. 1969, ManLabs Inc., Cambridge, Mass. 3 Scala, S. M., "The Ablation of Graphite in Dissociated Air," Paper 62-154,1962, IAS. 4 Gilbert, L. M., "The Hypersonic Diffusion Controlled Oxidation of Tungsten," Rept. R67SD38, 1967, General Electric Co., King of Prussia, Pa. 5 Welsh, W. E. and Chung, P. M., "A Modified Theory for the Effect of Surface Temperature on the Combustion Rate of Carbon Surfaces in Air," Proceedings of the Heat Transfer and Fluid Mechanics Institute, Stanford University Press, 1963, pp. 146-159. 6 Nachtsheim, P. R., "Multicomponent Diffusion on Chemically Reacting Laminar Boundary Layers," Proceedings of the Heat Transfer and Fluid Mechanics Institute, Stanford University Press, 1967, pp. 58-87. 7 Bartlett, E. P., Kendall, R. M., and Rindal, R. A., "Unified Approximation for Mixture Transport Properties for Multicomponent Boundary Layer Applications," Rept. 66-7, Pt. IV, March 1967, Aerotherm Corp., Palo Alto, Calif. 8 JANAF Thermochemical Data, Dow Chemical Co., Midland, Mich., 1960. 9 Hirchfelder, J. O., Curtiss, C. F., and Bird, R. B., Molecular Theory of Gases and Liquids, Wiley, New York, 1966. 10 Kendall, R. M. and Bartlett, E. P., "Nonsimilar Solution of the Multicomponent Laminar Boundary Layer by an Integral Matrix Method," Rept. 66-7, Pt. Ill, March 1967, Aerotherm Corp., Palo Alto, Calif. 11 Fay, J. A. and Riddell, F. R., "Theory of Stagnation Point Heat Transfer in Dissociated Air," Journal of the Aeronautical Sciences, Vol. 25, No. 2, Feb. 1958, pp. 73-85. 12 Diaconis, N. S., Gorsuch, P. D., and Sheridan, R. A., "The Ablation of Graphite in Dissociated Air, Part 2, Experiment," Paper 62-155, 1962, IAS. 13 Metzger, J. W., Engel, M. J., and Diaconis, N. S., "Oxidation and Sublimation of Graphite in Simulated Re-Entry Environments," AIAA Journal, Vol. 5, No. 3, March 1967, pp. 451-460.

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TL;DR: In this article, a set of stability criteria involving the system parameters, such as the body moments of inertia, the length and mass distribution of the elastic rods, the lowest natural frequencies of the rods, and the satellite spin velocity, is solved.

Abstract: thin rods, is solved. The analysis yields a set of stability criteria involving the system parameters such as the body moments of inertia, the length and mass distribution of the elastic rods, the lowest natural frequencies of the rods, and the satellite spin velocity. The power of the method is illustrated by the relative ease with which closed-form stability criteria are derived and by the amount of information which can be extracted from their ready physical interpretation. In particular, the analysis shows that, for stability, the spinning motion is to be imparted about the axis of maximum moment of inertia. This is the well-known "greatest moment of inertia" requirement. Moreover, the initial spin velocity flc should not be merely lower than the first natural frequencies Aiu and Air associated with the transverse vibration of the rods (as the frequency of simple harmonic excitation of the rods should be if resonance is to be prevented), but the ratios Os/AiM and fi./Ai,, are dictated by the system parameters. Of course, for very stiff rods the natural frequencies AI« and AIV may be sufficiently high that the satisfaction of criteria (40) is ensured. References

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TL;DR: Aircraft structural parameters optimization satisfying flutter velocity constraint and minimum mass, applying to box beam design, is presented in this paper, where the authors apply this approach to a single-aisle aircraft.

Abstract: Aircraft structural parameters optimization satisfying flutter velocity constraint and minimum mass, applying to box beam design

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TL;DR: In this paper, axial buckling tests on machined integrally stiffened cylindrical shells were carried out and complete mappings of the shell imperfections and the prebuckling growth were obtained.

Abstract: : Axial buckling tests on machined integrally stiffened cylindrical shells were carried out. Complete mappings of the shell imperfections and the prebuckling growth were obtained. The lightly ring-stiffened shells behaved in a manner similar to the isotropic shells that were previously tested. For these shells, the predominant prebuckling deformation consisted of a half-wave in the axial direction with several circumferential waves. The similarity of the lightly ring-stiffened shells and the isotropic ones suggests that the uniqueness of the buckling mode for stiffened shells may not greatly influence the prebuckling behavior. The heavily ring-stiffened shells showed a sizable amount of short wave length axisymmetric growth before buckling. Buckling in all cases resulted in an asymmetric pattern. The stringer-stiffened shells showed a prebuckling behavior also similar to the isotropic results. However, the buckling pattern consisted of longer axial wave lengths. Correlation of the experimentally obtained buckling loads with linear buckling theory showed good agreement in most cases. (Author)

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TL;DR: In this paper, a geometrically nonlinear dynamic analysis of shells of revolution under symmetric and asymmetric loads is presented, and the nonlinear strain energy expression is evaluated using linear functions for all displacements.

Abstract: A formulation and computer program is developed for the geometrically nonlinear dynamic analysis of shells of revolution under symmetric and asymmetric loads. The nonlinear strain energy expression is evaluated using linear functions for all displacements. Five different procedures are examined for solving the equations of equilibrium, with Houbolt's method proving to be the most suitable. Solutions are presented for the symmetrical and asymmetrical buckling of shallow caps under step pressure loadings and a wide variety of other problems including some highly nonlinear ones.

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TL;DR: In this article, large strain elastoplastic analysis by finite element method, using variational principles to derive equilibrium equations is presented. But the analysis is restricted to two dimensional structures.

Abstract: Two dimensional structures large strain elastoplastic analysis by finite element method, using variational principles to derive equilibrium equations

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TL;DR: In this article, an experimental study of the interaction of a high-velocity airstream with jets from single row, multihole wall injectors is presented, and the influence of a disturbed approach flow boundary layer on jet penetration and mixing is determined in tests with blowing upstream of the injector.

Abstract: An experimental study of the interaction of a high-velocity airstream with jets from single row, multihole wall injectors is presented. Results are reported for tests conducted at nominal airstream Mach numbers of 0.6, 2, and 3. Injectant fluids included helium, argon, and Freon-12. One supersonic and twelve sonic wall injectors having various hole spacings, hole diameters, and injection angles were employed in these tests. The influence of a disturbed approach flow boundary layer on jet penetration and mixing was determined in tests with blowing upstream of the injector. Schlieren photographs of the injectant flowfield were taken and Pitot pressure, total temperature, and species concentration profiles were obtained at several tunnel locations. These data were employed to develop correlations for the penetration height, the distance required to achieve two-dimensional flow, and the kinematic eddy viscosity. The latter correlation establishes a connection between downstream mixing and initial jet penetration. It was found that small amounts of blowing upstream of the injectors significantly increases jet penetration and the rate of subsequent jet-airstream mixing.

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TL;DR: In this paper, the effect of swirling inlet flow on diffuser performance was found to be a strong function of flow regime in the same diffuser with axial inlet flows.

Abstract: An experimental investigation was conducted to determine the effect of swirling inlet flow on the performance and outlet flow profile of conical diffusers. Twenty four different diffusers were tested, with total divergence angles ranging from 4.0 to 31.2°, and with area ratios from 1.30 to 8.27. The effect of swirling inlet flow on diffuser performance was found to be a strong function of flow regime in the same diffuser with axial inlet flow. Swirling inlet flow did not affect performance of diffusers which were unseparated or only slightly separated with axial inlet flow. For diffusers which were moderately or badly separated for axial inlet flow, swirling inlet flow caused large performance increases based on total inlet kinetic energy. The results indicate that optimum diffuser performance for swirling inlet flow may be higher than that for axial inlet flow. However, the geometry of the optimum diffuser will differ considerably from that for axial inlet flow. New optimums are presented for the three swirl ratios investigated.