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Supersonic asymmetric flutter and divergence characteristics of truncated conical shells with ring-supported edges under three types of flow-induced instabilities
A probability model is presented for the distribution of thunderstorms over a small area given that thunderstorm events (1 or more thunderstorms) are occurring over a larger area. The model incorporates the negative binomial and truncated Poisson distributions. Probability tables for Cape Kennedy for spring, summer, and fall months and seasons are presented. The computer program used to compute these probabilities is appended.
A study of the buckling of thin shells was conducted using a digital computer program for the geometrically nonlinear analysis of arbitrarily loaded shells of revolution. The objective was an evaluation of the program's applicability to bifurcation buckling and imperfection sensitivity analysis. Clamped spherical caps under pressure loading and clamped truncated hemispheres under axial tension were investigated. Buckling loads were determined for axisymmetric and nearly axisymmetric loads and are compared with previously published analytical results based on geometric imperfections.
The flowfield and base pressure characteristics of an internal-external expansion, truncated plug nozzle are described over the pressure ratio range from 'open' wake to 'closed' wake conditions. The effect of plug length on these characteristics, including the process of wake 'closure' is also presented. An existing method for calculating the flowfield and base pressure, for 'closed' wake operation, is modified to include the internal shock wave generated near the shroud exit. The supersonic portion of the flow is calculated using rotational axisymmetric method of characteristics. The technique of Hartree is employed so that the downstream characteristic point locations can be chosen to fit the developing flowfield. An overexpansion technique is used to detect the internal shock wave in the vicinity of the shroud exit so that its effect on the plug base pressure could be determined. Good agreement between the analytical results and experimental data is obtained for 'closed' wake operations.
A solution for film condensation on the inside of slender rotating truncated cones is established in the region where the half cone angle phi is close to zero and where the equation of Dhir and Lienhard (1971) is no longer valid. All the familiar assumptions used in Nusselt's theory of laminar film condensation are assumed valid, including negligible sub-cooling and momentum changes in the condensate film, no interfacial shear between the condensate and the vapor, and pure conduction within the condensate film. A Runge-Kutta numerical integration method using a digital computer was used. Results for a specific geometry are given for water condensing at 212 F on a condenser wall maintained at 70 F.
The performance of a medium size, truncated reverberation chamber is evaluated in detail. Chamber performance parameters are predicted, using classical acoustic theory, and are compared to results from actual chamber measurements. Discrepancies are discussed in relation to several available empirical corrections developed by other researchers. Of more practical interest is the confirmation of a recent theory stating that the present guide for the ratio of specimen volume to test chamber volume, approximately 10 percent, is overly conservative, and can be increased by a factor of at least 2 and possibly 3. Results and theoretical justification of these findings are presented.
Reflector-antenna calculations using idealised truncated feed patterns can lead to incorrect values of total secondary radiated power. It is demonstrated that this discrepancy is due to the presence of higher-order spherical modes incident on the reflector. When a proper spherical-wave expansion of the incident field is used, in conjunction with the physical-optics technique, to determine the scattered field, the total power of the scattered field will equal the power radiated by the feed.
Cylindrical diffuser performance for a truncated plug nozzle without external flow was tested in a blowdown wind tunnel. The nozzle was designed for an exit Mach number of 1.9 and the plug was conical in shape from the throat and converged to the axis of symmetry at an angle of 10 degrees. The diffuser section was fashioned into two 13.97 cm lengths to facilitate boring of the duct diameter and to allow for testing of two different duct lengths. A slotted hypotube was installed in the base of the diffuser to measure pressure distribution down the centerline of the diffuser. The data obtained included: the typical centerline and sidewall pressure ratio variation along the diffuser, cell pressure ratio vs overall pressure ratio for long and short diffusers and a comparison of minimum experimental cell pressure ratio vs area ratio.
The 'box-type' finite-difference method includes a weighted average of the pressure gradient with weights proportional to the surface of the grid walls. It is shown that this averaging introduces first-order truncation errors near the poles. An example is shown in which the relative error is of zero order and the scheme produces large distortions in the solution at high latitudes.
The solar concentrating properties of specularly reflecting truncated pyramidal, hexagonal, and circular cones are evaluated. Pyramidal and hexagonal configurations are discussed with reference to the concentration factor as a function of half apex angle and the length of the side over the width, and to the irradiance distribution. Expressions are derived for the concentration factor and the irradiance at the base of a circular cone when the sunlight is incident normal to the aperture and for oblique incidence.
Constant amplitude and transport wing spectrum compressive loading tests were used to explore the fatigue behavior of a notched, graphite/epoxy T300/5208 laminate specimen. Results indicate that (1) the amount of buckling near the notch allowed in the tests significantly affected fatigue life; (2) load spectrum truncation at either high or low ends produced lives greater than those obtained for the baseline complete-spectrum test, but with greater impact at the high-load end; and (3) the predictions of the Palmgren-Miner cumulative damage theory were found to always be far longer than those obtained in the spectrum loading tests.
Multilevel, severely truncated, quasi-geostrophic models with damping that extend from the surface to 100 km, are used to study the stationary-wave response to orography and the concomitant feedbacks on the zonal flow. For a typical winter zonal-wind profile, it is shown that large amplitude or resonant planetary waves of intermediate zonal wavenumbers of about 4 or 5 occur with an equivalent barotropic structure. It is also shown that wave-zonal flow interaction with a mountain torque and temperature transport is stable to small perturbations on the low side of resonance and unstable on the high side of resonance. Resonant zonal wavenumbers of lower wave wavenumber also occur for the same zonal profile and have a node in the vertical with a small amplitude maximum near the surface and a larger amplitude maximum in the stratosphere. Instability depends on the presence of the orography and the basic asymmetric state as Newtonian damping and surface friction are sufficient to damp the baroclinic instability associated with a linear inviscid model.
The effects of truncation error on the numerical solution of transonic flows using the full potential equation are studied. The effects of adapting grid point distributions to various solution aspects including shock waves is also discussed. A conclusion is that a rapid change of grid spacing is damaging to the accuracy of the flow solution. Therefore, in a solution adaptive grid application an optimal grid is obtained as a tradeoff between the amount of grid refinement and the rate of grid stretching.
It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.
A study of electron propagation using the leaky box model is discussed. It is shown that a truncated pathlength distribution due to a lack of nearby sources is responsible for the steepening of the electron spectrum. The electron spectrum is broken into three regions: a low-energy region where electron storage is dominated by escape, a medium energy region in which the electron energy loss lifetime is sufficiently short to dominate propagation, but not so short as to prevent electrons from propagating throughout the storage region, and a third energy region in which the energy loss lifetime is shorter than the time it takes for cosmic rays to diffuse to earth from the nearest source. The asymptotic slope of the electron spectrum is shown to be steeper than that of the injection spectrum by more than one power of energy.
A novel technique is introduced for efficient computations of unsteady transonic aerodynamics. The steady flow corresponding to body shape is maintained by truncation error injection while the perturbed unsteady flows corresponding to unsteady body motions are being computed. This allows the use of different grids comparable to the characteristic length scales of the steady and unsteady flows and, hence, allows efficient computation of the unsteady perturbations. An example of typical unsteady computation of flow over a supercritical airfoil shows that substantial savings in computation time and storage without loss of solution accuracy can easily be achieved. This technique is easy to apply and requires very few changes to existing codes.
The effects on calculated lower-level population densities of the truncation of Na and Sr(+) model atoms are determined in the context of the present spectral diagnostic scheme for solar prominences and spicules. It is shown that neglect of the upper atomic levels in Na, in particular, leads to overestimates in electron density and gas pressure by factors of about 2 and about 4, respectively, and to underestimates in the degree of hydrogen ionization and in the line-of-sight thickness of emitting material again by factors of about 2 and about 4, respectively. The implications of the revised emitting region extents, in particular, on the validity of the diagnostic method for these features are discussed.
An approach to viscous-inviscid interaction which is based on truncation error injection is presented in the context of solving flow over an airfoil. A two-dimensional interpolation scheme is used to restrict the fine grid solutions to the global coarse grid. Details on the current implementation of the approach are given, and the boundary conditions being used are discussed. Inviscid results from a NACA0012 airfoil test case and the viscous results are presented.