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At least 271 records · Page 15

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NASA NTRS1971

Numerical solution of flowfields behind rectangular wings

The numerical solution of flow fields behind rectangular wings is described. Subjects discussed are: (1) evaluation of various differencing methods applied to the hyperbolic partial differential equations encountered in gas dynamics, (2) application of the numerical differencing techniques to the wedge flow, two dimensional shock reflection for the three dimensional finite thickness wing at zero degrees angle of attack, and (3) calculation of preliminary results for wedge flows using optimum differencing methods.

Anderson, D.↗

NASA NTRS1971

Nonplanar Method for Predicting Incompressible Aerodynamic Coefficients of Rectangular Wings with Circular-Arc Camber

The development of a nonplanar lifting surface method having a continuous distribution of singularities and satisfying the tangent flow boundary condition on the mean camber surface is given. The method predicts some incompressible longitudinal aerodynamic coefficients of rectangular wings which have circular-arc camber. The solution method is of the integral-equation type and the resulting surface integrals are evaluated by either using numerical or analytical techniques, as are appropriate. Applications are made and the results compared with those from an exact two-dimensional circular-arc camber solution, a three-dimensional flat-wing solution which represents the camber by a projected slope onto the flat surface, and a flat-wing experiment. From these comparisons, the present method is found to predict well the flat-wing experiment and limiting values, in addition to the center of pressure variation at an angle of attack of zero for any camber. For wings having camber ratios larger than about 1.25% and moderate to high aspect ratios, the results deterioriate due to the inadequacy of lifting pressure modes employed.

Lamar, J. E.↗

NASA NTRS1972

Wind tunnel investigation of aerodynamic characteristics of scale models of three rectangular shaped cargo containers

Wind tunnel tests were conducted on scale models of three rectangular shaped cargo containers to determine the aerodynamic characteristics of these typical externally-suspended helicopter cargo configurations. Tests were made over a large range of pitch and yaw attitudes at a nominal Reynolds number per unit length of 1.8 x one million. The aerodynamic data obtained from the tests are presented.

Laub, G. H.↗

NASA NTRS1971

Pressure losses for laminar flow in the entrance region of ducts of rectangular and equilateral triangular cross section.

The velocity profiles upon which the pressure-loss calculations are based, are recomputed using the previously described method of reference (1960). The pressure drop is then computed using the energy integral equation; both rectangular and equilateral triangular ducts are considered. It is demonstrated that, using this equation, the pressure-drop parameter can be improved.

Miller, R. W.↗

NASA NTRS1972

Radiation resistance of a rectangular panel.

The radiation resistance corresponding to the natural modes of a finite rectangular panel is theoretically determined from the total energy radiated to the farfield. The panel is assumed to be simply supported in an infinite baffle. Asymptotic solutions for the low-frequency region are derived, and curves covering the entire frequency range for various mode shapes and aspect ratios are obtained through numerical integration. When the ratio of the acoustic wavenumber to the panel wavenumber is a constant much less than unity, the radiation resistance for all modes is a minimum if the intranodal area (the area between adjacent node lines) is square, and increases with the aspect ratio of the intranodal area.

Wallace, C. E.↗

NASA NTRS1972

A non-linear dynamic lumped-parameter model of a rectangular plate.

A lumped-parameter model of a rectangular plate is developed by assuming fundamental mode solutions and using Hamilton's Principle and the Euler equations to set up the differential equation of motion for the system. The plate theory used may be described as the dynamic analogue of the von Karman large-deflection theory. Four sets of symmetrical boundary conditions are considered with the restriction of uniform pressure dynamic loads. The model takes the form of a mass on a cubic-hardening spring with each term defined by algebraic expressions of the plate parameters. The results for some specific problems are compared with two previous solutions. This method is less accurate but simpler to develop and apply.

Bayles, D. J.↗

NASA NTRS1972

Elastostatic stress analysis of orthotropic rectangular center-cracked plates

A mapping-collocation method was developed for the elastostatic stress analysis of finite, anisotropic plates with centrally located traction-free cracks. The method essentially consists of mapping the crack into the unit circle and satisfying the crack boundary conditions exactly with the help of Muskhelishvili's function extension concept. The conditions on the outer boundary are satisfied approximately by applying the method of least-squares boundary collocation. A parametric study of finite-plate stress intensity factors, employing this mapping-collocation method, is presented. It shows the effects of varying material properties, orientation angle, and crack-length-to-plate-width and plate-height-to-plate-width ratios for rectangular orthotropic plates under constant tensile and shear loads.

Gyekenyesi, G. S.↗

NASA NTRS1973

Study of the far wake vortex field generated by a rectangular airfoil in a water tank

Underwater towing experiments were carried out with a rectangular airfoil of aspect ratio 5.3 at 4 and 8 deg angles of attack and at chord-based Reynolds numbers between 2 x 100,000 and 7.5 x 100,000. Quantitative measurements by means of the hydrogen bubble technique indicated lower peak swirl velocities in the range of 100 to 1000 lenghts downstream than have been measured in wind tunnel of flight tests. The maximum circumferential velocity decayed whereas the turbulent eddy viscosity increased. This behavior and other known rates of vortex decay are explained in terms of an analytical solution for the vortex problem with time varying eddy viscosity. It is shown that this case corresponds to nonequilibrium turbulent vortex flow.

Lezius, D. K.↗

NASA NTRS1973

Generalized random forces for rectangular panels.

Generalized random forces for rectangular panels under subsonic and supersonic boundary-layer turbulence are studied in time domain by a Monte Carlo approach. Panels with simple, fixed, elastic-free, and periodic elastic boundary conditions are considered. The nature of probability structure, peak distribution, threshold crossing, and cross spectral density is investigated.

Vaicaitis, R.↗

NASA NTRS1974

Elastic stability of laminated, flat and curved, long rectangular plates subjected to combined inplane loads

A method is presented to predict theoretical buckling loads of long, rectangular flat and curved laminated plates with arbitrary orientation of orthotropic axes each lamina. The plate is subjected to combined inplane normal and shear loads. Arbitrary boundary conditions may be stipulated along the longitudinal sides of the plate. In the absence of inplane shear loads and extensional-shear coupling, the analysis is also applicable to finite length plates. Numerical results are presented for curved laminated composite plates with boundary conditions and subjected to various loadings. These results indicate some of the complexities involved in the numerical solution of the analysis for general laminates. The results also show that the reduced bending stiffness approximation when applied to buckling problems could lead to considerable error in some cases and therefore must be used with caution.

Viswanathan, A. V.↗

NASA NTRS1974

Nonlinear acoustic propagation in rectangular ducts

The method of multiple scales is used to obtain a second-order uniformly valid expansion for nonlinear acoustic wave propagation in a rectangular duct whose walls are treated with a nonlinear acoustic material. The wave propagation in the duct is characterized by the unsteady nonlinear Euler equations. The results show that nonlinear materials attenuate sound more than linear materials except at high acoustic frequencies. The nonlinear materials produce higher and combination tones which have higher attenuation rates than the fundamentals. Moreover, the attenuation rates of the fundamentals increase with increasing amplitude.

Nayfeh, A. H.↗

NASA NTRS1974

Supercirculation effects induced by vectoring a partial-span rectangular jet

Thrust-induced supercirculation effects from thrust vectoring have indicated a potential for not only increasing maneuverability of fighter aircraft but also as a means of improving cruise performance. The current study investigated a partial-span rectangular jet-exhaust nozzle located at the wing trailing edge that acts similar to a jet flap by increasing lift due to supercirculation. This paper summarizes experimental studies including the effects of nozzle deflection angle, wing camber, and nozzle shape and exit location on lift, drag and load distributions. The results indicate that significant increases in thrust-induced lift along with substantial decreases in drag are possible.

Capone, F. J.↗

NASA NTRS1975

Stress analysis and stress intensity factors for finite geometry solids containing rectangular surface cracks

The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement field in a finite geometry bar containing a variable depth rectangular surface crack under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Using the obtained displacement field, normal stresses and the stress intensity factor variation along the crack periphery are calculated for different crack depth to bar thickness ratios. Crack opening displacements and stress intensity factors are also obtained for a through-thickness, center cracked bar with variable thickness. The reported results show a considerable potential for using this method in calculating stress intensity factors for commonly encountered surface crack geometries in finite solids.

Gyekenyesi, J. P.↗

NASA NTRS1974

Mutual coupling between circular waveguide-fed apertures in a rectangular ground plane

A method is presented whereby the infinite ground plane analytical model for the self-admittance and mutual admittance of waveguide-fed apertures can be supplemented (using the geometrical theory of diffraction) to include the edge effects of a rectangular ground plane. The H-plane coupling between two TE-11 mode excited circular apertures is calculated and compared with measurements.

Bailey, M. C.↗

NASA NTRS1975

Radiative equilibrium in a rectangular enclosure bounded by gray walls

Two-dimensional temperature and heat-flux distributions are calculated for an absorbing-emitting gray medium at radiative equilibrium in a rectangular enclosure. The bounding walls are gray and diffuse with arbitrary surface-temperature distributions, and heat generation may take place inside the medium. As a first approximation, the problem is solved for optically thick systems (differential approximation). These results are subsequently improved by the introduction of a number of geometrical parameters to yield good accuracy for all optical thicknesses. As examples, two cases are discussed in detail: (1) uniform heat generation in a black enclosure, and (2) an enclosure with one gray surface at constant temperature. Comparison with some numerical solutions generated by Hottel's /Hottel and Cohen (1958) and Einstein (1963)/ zonal method shows excellent agreement.

Modest, M. F.↗

NASA NTRS1975

Pressure- and buoyancy-driven thermal convection in a rectangular enclosure

Results are presented for unsteady laminar thermal convection in compressible fluids at various reduced levels of gravity in a rectangular enclosure which is heated on one side and cooled on the opposite side. The results were obtained by solving numerically the equations of conservation for a viscous, compressible, heat-conducting, ideal gas in the presence of a gravitational body force. The formulation differs from the Boussinesq simplification in that the effects of variable density are completely retained. A conservative, explicit, time-dependent, finite-difference technique was used and good agreement was found for the limited cases where direct comparison with previous investigations was possible. The solutions show that the thermally induced motion is acoustic in nature at low levels of gravity and that the unsteady-state rate of heat transfer is thereby greatly enhanced relative to pure conduction. The nonlinear variable density profile skews the streamlines towards the cooler walls but is shown to have little effect on the steady-state isotherms.

Spradley, L. W.↗

NASA NTRS1975

Propagation of high amplitude higher order sounds in slightly soft rectangular ducts, carrying mean flow

The resonance expansion method, developed to study the propagation of sound in rigid rectangular ducts is applied to the case of slightly soft ducts. Expressions for the generation and decay of various harmonics are obtained. The effect of wall admittance is seen through a dissipation function in the system of nonlinear differential equations, governing the generation of harmonics. As the wall admittance increases, the resonance is reduced. For a given wall admittance this phenomenon is stronger at higher input intensities. Both the first and second order solutions are obtained and the results are extended to the case of ducts having mean flow.

Wang, K. S.↗

NASA NTRS1976

Pressure distributions for a rectangular supersonic inlet at subsonic speeds

Pressure distribution data are provided for a supersonic rectangular inlet at subsonic speeds. Variations in cowl and ramp geometry as well as sideplate sweep were investigated. Tests were made in the Langley 16-foot transonic tunnel and the Langley high speed 7- by 10-foot tunnel for Mach numbers of 0.6, 0.7, and 0.8. Angles of attack investigated were 0 deg, 4 deg, and 8 deg for a range of mass flow ratios.

Fuller, D. E.↗