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Three missile body shapes tested at Mach numbers of 1.50, 2.16, and 2.86 with angles of attack up to 30 degrees are described. The flow characteristics for each body shape are examined. The measured aerodynamic forces and moments are presented. The use of flow visualization techniques are described and the results such as vortex effects are discussed.
Stress intensity factor equations are presented for an embedded elliptical crack, a semielliptical surface crack, a quarter elliptical corner crack, a semielliptical surface crack along the bore of a circular hole, and a quarter elliptical corner crack at the edge of a circular hole in finite plates. The plates were subjected to either remote tension or bending loads. The stress intensity factors used to develop these equations were obtained from previous three dimensional finite element analyses of these crack configurations. The equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and, where applicable, hole radius. The ratio of crack depth to plate thickness ranged from 0 to 1, the ratio of crack depth to crack length ranged from 0.2 to 2, and the ratio of hole radius to plate thickness ranged from 0.5 to 2. The effects of plate width on stress intensity variation along the crack front were also included.
Empirical stress intensity factor equations are presented for embedded elliptical cracks, semi-elliptical surface cracks, quarter-elliptical corner cracks, semi-elliptical surface cracks at a hole, and quarter-elliptical corner cracks at a hole in finite plates. The plates were subjected to remote tensile loading. Equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. The stress intensity factors used to develop the equations were obtained from three dimensional finite element analyses of these crack configurations.
Strapped-down inertial reference assembly and digital computer for Saturn booster guidance
Total equilibrium shock layer radiation data for Martian entry body shapes at various angles of attack extrapolated to trajectory condition
Satellite system survival probability expressed as function of launch probability, time and number of satellites available
Measurements of surface pressure and heat flux at Mach 6.8 for a nonaxisymmetric body, typical of the forward fuselage of an entry vehicle, have been obtained in the Langley 8-ft high-temperature tunnel. Comparisons of these data with predictions obtained from two numerical methods, which treat the test medium as an ideal gas with a laminar boundary layer, are presented. In general, the numerical results are consistent with each other and follow the data in regions of laminar flow; however, the data for angle of attack 14.9 deg indicate transitional flow on most of the windward surface. Also, the two numerical methods disagree slightly in regions of zero or nearly zero pressure gradients.
Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.
Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, an extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.
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In this work, we present a new set of basis functions, de ned over a pair of planar triangular patches, for the solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped surfaces using the method of moments solution procedure. The basis functions are constant over the function subdomain and resemble pulse functions for one and two dimensional problems. Further, another set of basis functions, point-wise orthogonal to the first set, is also de ned over the same function space. The primary objective of developing these basis functions is to utilize them for the electromagnetic solution involving conducting, dielectric, and composite bodies. However, in the present work, only the conducting body solution is presented and compared with other data.
In this work, we present a new set of basis functions, defined over a pair of planar triangular patches, for the solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped surfaces using the method of moments solution procedure. The basis functions are constant over the function subdomain and resemble pulse functions for one and two dimensional problems. Further, another set of basis functions, point-wise orthogonal to the first set, is also defined over the same function space. The primary objective of developing these basis functions is to utilize them for the electromagnetic solution involving conducting, dielectric, and composite bodies. However, in the present work, only the conducting body solution is presented and compared with other data.
We are developing computational tools for the simulations of three-dimensional flows past bodies undergoing arbitrary motions. High resolution viscous vortex methods have been developed that allow for extended simulations of two-dimensional configurations such as vortex generators. Our objective is to extend this methodology to three dimensions and develop a robust computational scheme for the simulation of such flows. A fundamental issue in the use of vortex methods is the ability of employing efficiently large numbers of computational elements to resolve the large range of scales that exist in complex flows. The traditional cost of the method scales as Omicron (N(sup 2)) as the N computational elements/particles induce velocities at each other, making the method unacceptable for simulations involving more than a few tens of thousands of particles. In the last decade fast methods have been developed that have operation counts of Omicron (N log N) or Omicron (N) (referred to as BH and GR respectively) depending on the details of the algorithm. These methods are based on the observation that the effect of a cluster of particles at a certain distance may be approximated by a finite series expansion. In order to exploit this observation we need to decompose the element population spatially into clusters of particles and build a hierarchy of clusters (a tree data structure) - smaller neighboring clusters combine to form a cluster of the next size up in the hierarchy and so on. This hierarchy of clusters allows one to determine efficiently when the approximation is valid. This algorithm is an N-body solver that appears in many fields of engineering and science. Some examples of its diverse use are in astrophysics, molecular dynamics, micro-magnetics, boundary element simulations of electromagnetic problems, and computer animation. More recently these N-body solvers have been implemented and applied in simulations involving vortex methods. Koumoutsakos and Leonard (1995) implemented the GR scheme in two dimensions for vector computer architectures allowing for simulations of bluff body flows using millions of particles. Winckelmans presented three-dimensional, viscous simulations of interacting vortex rings, using vortons and an implementation of a BH scheme for parallel computer architectures. Bhatt presented a vortex filament method to perform inviscid vortex ring interactions, with an alternative implementation of a BH scheme for a Connection Machine parallel computer architecture.
This study reports on the short-term in vivo precision and absolute measurements of three combinations of whole-body scan modes and analysis software using a Hologic QDR 2000 dual-energy X-ray densitometer. A group of 21 normal, healthy volunteers (11 male and 10 female) were scanned six times, receiving one pencil-beam and one array whole-body scan on three occasions approximately 1 week apart. The following combinations of scan modes and analysis software were used: pencil-beam scans analyzed with Hologic's standard whole-body software (PB scans); the same pencil-beam analyzed with Hologic's newer "enhanced" software (EPB scans); and array scans analyzed with the enhanced software (EA scans). Precision values (% coefficient of variation, %CV) were calculated for whole-body and regional bone mineral content (BMC), bone mineral density (BMD), fat mass, lean mass, %fat and total mass. In general, there was no significant difference among the three scan types with respect to short-term precision of BMD and only slight differences in the precision of BMC. Precision of BMC and BMD for all three scan types was excellent: < 1% CV for whole-body values, with most regional values in the 1%-2% range. Pencil-beam scans demonstrated significantly better soft tissue precision than did array scans. Precision errors for whole-body lean mass were: 0.9% (PB), 1.1% (EPB) and 1.9% (EA). Precision errors for whole-body fat mass were: 1.7% (PB), 2.4% (EPB) and 5.6% (EA). EPB precision errors were slightly higher than PB precision errors for lean, fat and %fat measurements of all regions except the head, although these differences were significant only for the fat and % fat of the arms and legs. In addition EPB precision values exhibited greater individual variability than PB precision values. Finally, absolute values of bone and soft tissue were compared among the three combinations of scan and analysis modes. BMC, BMD, fat mass, %fat and lean mass were significantly different between PB scans and either of the EPB or EA scans. Differences were as large as 20%-25% for certain regional fat and BMD measurements. Additional work may be needed to examine the relative accuracy of the scan mode/software combinations and to identify reasons for the differences in soft tissue precision with the array whole-body scan mode.
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.
Three-dimensional analyses are presented for the viscous, reactive flow over a complete entry-body configuration with a wide-angle conic surface. The predictive method uses a split approach that solves iteratively the Navier-Stokes and the continuity equations of chemical species. The finite-difference formulation and the computational grid are adapted to the bow shock and the conformally mapped body such that the velocity components are in the computational spherical-polar space. Combinations of several conic forebody and afterbody configurations have been studied using wind-tunnel, Space Shuttle, and aerobraking orbital transfer vehicle (AOTV) entry conditions. The effects of the borebody bluntness and of finite-rate chemical reactions on the shock layer, the wall catalycity on the boundary layer, the shear-layer impingement on the afterbody, and the base-flow environment are discussed.