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BUCKO is computer program developed to predict buckling of rectangular compression-loaded orthotropic plate with centrally located cutout. Plate assumed balanced, symmetric laminate of uniform thickness. Cutout shape elliptical, circular, rectangular, or square. Package includes sample data demonstrating essence of program and ease of use. Written in FORTRAN V.
Periodic rib turbulators were used in advanced turbine cooling designs to enhance the internal heat transfer. The objective of the present project was to investigate the combined effects of the rib angle of attack and the channel aspect ratio on the local heat transfer and pressure drop in rectangular channels with two opposite ribbed walls for Reynolds number varied from 10,000 to 60,000. The channel aspect ratio (W/H) was varied from 1 to 2 to 4. The rib angle of attack (alpha) was varied from 90 to 60 to 45 to 30 degree. The highly detailed heat transfer coefficient distribution on both the smooth side and the ribbed side walls from the channel sharp entrance to the downstream region were measured. The results showed that, in the square channel, the heat transfer for the slant ribs (alpha = 30 -45 deg) was about 30% higher that of the transverse ribs (alpha = 90 deg) for a constant pumping power. However, in the rectangular channels (W/H = 2 and 4, ribs on W side), the heat transfer at alpha = 30 -45 deg was only about 5% higher than 90 deg. The average heat transfer and friction correlations were developed to account for rib spacing, rib angle, and channel aspect ratio over the range of roughness Reynolds number.
The minimum weight design of a helicopter rotor blade subject to constraints on coupled flap-lag natural frequencies has been studied. A constraint has also been imposed on the minimum value of the autorotational inertia of the blade in order to ensure that it has sufficient inertia to autorotate in the case of engine failure. The program CAMRAD is used for the blade modal analysis and CONMIN is used for the optimization. In addition, a linear approximation analysis involving Taylor series expansion has been used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function and the autorotational inertia constraint and central finite difference derivatives of the frequency constraints. Optimum designs have been obtained for both rectangular and tapered blades. Design variables include taper ratio, segment weights, and box beam dimensions. It is shown that even when starting with an acceptable baseline design, a significant amount of weight reduction is possible while satisfying all the constraints for both rectangular and tapered blades.
The minimum weight design of a helicopter rotor blade subject to constraints on coupled flap-lag natural frequencies has been studied. A constraint has also been imposed on the minimum value of the autorotational inertia of the blade in order to ensure that it has sufficient inertia to aurorotate in the case of engine failure. The program CAMRAD is used for the blade modal analysis and CONMIN is used for the optimization. In addition, a linear approximation analysis involving Taylor series expansion has been used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function and the autorotational inertia constraint and central finite difference derivatives of the frequency constraints. Optimum designs have been obtained for both rectangular and tapered blades. Design variables include taper ratio, segment weights, and box beam dimensions. It is shown that even when starting with an acceptable baseline design, a significant amount of weight reduction is possible while satisfying all the constraints for both rectangular and tapered blades.
A modeling technique for predicting the axial and transverse velocity characteristics of rectangular nozzle plumes is developed. In this technique, modeling of the plume cross section is initiated at the nozzle exit plane. The technique is demonstrated for the plume issuing from a rectangular nozzle having an aspect ratio of 6.0 and discharging into quiescent air. Application of the present procedures to a nozzle discharging into a moving airstream (flight effect) are then demonstrated. The effects of plume shear layer structure modification on the velocity flowfield are discussed and modeling procedures are illustrated by example.
A flutter test of a low-aspect-ratio rectangular wing was conducted in the Langley Transonic Dynamics Tunnel (TDT). The model used in this flutter test consisted of a rigid wing mounted to the wind-tunnel wall by a flexible, rectangular beam. The flexible support shaft was connected to the wing root and was cantilever mounted to the wind-tunnel wall. The wing had an aspect ratio of 1.5 based on the wing semispan and an NACA 64A010 airfoil shape. The flutter boundary of the model was determined for a Mach number range of 0.5 to 0.97. The shape of the transonic flutter boundary was determined. Actual flutter points were obtained on both the subsonic and supersonic sides of the flutter bucket. The model exhibited a deep transonic flutter bucket over a narrow range of Mach number. At some Mach numbers, the flutter conditions were extrapolated using a subcritical response technique. In addition to the basic configuration, modifications were made to the model structure such that the first bending frequency was changed without significantly affecting the first torsion frequency. The experiment showed that increasing the bending stiffness of the model support shaft through these modifications lowered the flutter dynamic pressure. Flutter analysis was conducted for the basic model as a comparison with the experimental results. This flutter analysis was conducted with subsonic lifting-surface (kernel function) aerodynamics using the k method for the flutter solution.
The radar cross-section (RCS) analysis of open-ended cavities with rectangular and circular cross sections is carried out using the waveguide modal approach and the shooting-and-bouncing ray (SBR) approach. For a cavity opening on the order of ten wavelengths or larger, the comparison between the two approaches is excellent. It is also observed that at lower frequencies the SBR results deviate from the more accurate modal results. On the other hand, the SBR approach allows for greater flexibility in geometrical modeling, and can be applied to problems where waveguide modes cannot be easily found. SBR results for an offset rectangular cavity and a circular cavity with rounded endplate are presented.
The effect of a standing wave field in a rectangular chamber on the shape and location of an acoustically positioned drop or bubble is calculated. The sample deformation and equilibrium position are obtained from an analysis of the spherical harmonic projections of the total surface stress tensor. The method of calculation relies on the assumed condition that the sample is only slightly distorted from a spherical form. The equilibrium location of a levitated drop is combined with a formula introduced by Hasegawa (1979) to calcualte the ka dependence of the radiation force function. The present theory is valid for large as well as small ka values. Calculations in the small ka limit agree with previous theories and experimental results. Examples are presented for nonplane-wave modes as well as plane-wave rectangular modes.
A modeling technique for predicting the axial and transverse velocity characteristics of rectangular nozzle plumes is developed. In this technique, modeling of the plume cross section is initiated at the nozzle exit plane. The technique is demonstrated for the plume issuing from a rectangular nozzle having an aspect ratio of 6.0 and discharging into quiescent air. Application of the present procedures to a nozzle discharging into a moving airstream (flight effect) are then demonstrated. The effects of plume shear layer structure modification on the velocity flowfield are discussed and modeling procedures are illustrated by example.
A new rectangular waveguide to coplanar waveguide (CPW) transition is described. The transition uses a ridge in one of the broad walls of the waveguide and a nonradiating slot in the opposite wall to split and rotate the electromagnetic fields of the rectangular waveguide TE10 mode into the CPW fields.
An incompressible, turbulent, swirl-free flow through a circular-to-rectangular transition duct was studied experimentally. The cross-sectional geometry all along the duct was defined using the equation of a superellipse. The three mean velocity components and the six Reynolds stress components were measured at two axial stations downstream from the transition. It is shown that a secondary flow vortex pair which develops along the duct sidewalls significantly distorts the mean and turbulence fields. At the duct exit, the flow is not in local equilibrium, but recovers to local equilibrium conditions in the rectangular extension duct. Analysis demonstrates that conventional wall functions are not applicable at all streamwise locations in the duct.
Rectangular supersonic free and coaxial jets were used to enhance mixing relative to a circular jet in a convective Mach number range of 0.5 to 2.2. The different convective Mach numbers were obtained by changing the central jet gas composition, the temperatures of the inner and outer flows, and the velocity of the coaxial flow. The experimental techniques used were schlieren photography, total pressure, and gas-sampling measurements. For all test conditions the rectangular jets showed substantial improved mixing relative to a circular jet. The free jets showed high mixing in the circumferential region of the jet while the coaxial jet had a high mixing rate inside the central jet.
Circular-to-rectangular transition duct flows with and without inlet swirl were investigated experimentally in order to determine the effect of inlet swirl on the transition duct flow field and to provide detailed duct flow data for comparison with numerical code predictions. Coefficients based on detailed measurements of velocity, total pressure and static pressure, acquired in four cross stream planes within a circular-to-rectangular transition duct, with and without inlet swirl, are presented, as are surface static pressure and surface oil film visualization results.
A boundary element formulation, along with detailed solution procedure for determining the acoustic field inside a three-dimensional, rectangular duct is presented in this paper. The results of classical and boundary element solutions are compared for a typical rectangular duct by restricting the input frequency in such a way that only plane wave propagation is possible. The effect of changing the type and number of discrete boundary elements on the computed sound pressure levels inside the duct is also presented.
An analysis is carried out to determine the discontinuity susceptance of a circular or rectangular aperture in the transverse plane of a circular waveguide. Closed-form solutions based on the scattered amplitude calculation and aperture coupling theory are derived. Example solutions for a small circular aperture and a resonant rectangular aperture are given. The calculated results agree very well with the experiments. The results have many applications in the design of circular waveguide components and circular waveguide-backed aperture antennas.
A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite rectangular thin plates. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite rectangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, different boundary conditions, aspect ratios, lamination angles and number of plies are presented. The finite element results are compared with available approximate continuum solutions.
This paper presents the results of a Computational Fluid Dynamics (CFD) calibration study of flow through a circular-to-rectangular transition duct. The design of these ducts is critical to the optimum performance of aircraft with rectangular exhaust nozzles, since these ducts transfer the flow from the gas turbine engine to the exhaust nozzle. Two duct inflow conditions are considered, the first with straight inflow and the second with swirling inflow. Both flows contain realistic wall boundary layers. The first case permits examination of the effects of the geometric transition on the flowfield, while the second case adds in the rotational flow effect that can be present from the gas turbine engine. The flowfields associated with the two cases have been shown, both with CFD and experiment, to have significant differences. The Navier-Stokes CFD code PARC with the Baldwin and Lomax turbulence model was used in this study. The turbulence model had to be modified for both cases in order to achieve accurate determination of the edge of the wall bounded vorticity layers and thus turbulent viscosity. The results of this calibration study will be valuable to aircraft designers who rely on CFD to assist in the design and evaluation of propulsion systems.
An experiment was performed in the Langley 0.3 meter Transonic Cryogenic Tunnel to study the internal acoustic field generated by rectangular cavities in transonic and subsonic flows and to determine the effect of Reynolds number and angle of yaw on the field. The cavity was 11.25 in. long and 2.50 in. wide. The cavity depth was varied to obtain length-to-height (l/h) ratios of 4.40, 6.70, 12.67, and 20.00. Data were obtained for a free stream Mach number range from 0.20 to 0.90, a Reynolds number range from 2 x 10(exp 6) to 100 x 10(exp 6) per foot with a nearly constant boundary layer thickness, and for two angles of yaw of 0 and 15 degs. Results show that Reynolds number has little effect on the acoustic field in rectangular cavities at angle of yaw of 0 deg. Cavities with l/h = 4.40 and 6.70 generated tones at transonic speeds, whereas those with l/h = 20.00 did not. This trend agrees with data obtained previously at supersonic speeds. As Mach number decreased, the amplitude, and bandwidth of the tones changed. No tones appeared for Mach number = 0.20. For a cavity with l/h = 12.67, tones appeared at Mach number = 0.60, indicating a possible change in flow field type. Changes in acoustic spectra with angle of yaw varied with Reynolds number, Mach number, l/h ratios, and acoustic mode number.