General Bodies Research Articles

Hydrodynamic characteristics of bodies in channels

The effect of channel walls on the hydrodynamic characteristics of fixed or oscillating bodies is discussed using classical linear water wave theory. Particular attention is paid to the occurrence of trapped modes persisting local to the fixed body and which are manifested in a non-uniqueness of the corresponding forced problem at the trapped mode frequency. The general ideas are illustrated by consideration of two simple geometries for which semi-analytic solutions are available, namely a circular cylinder either partly immersed or extending throughout the water depth, and a thin vertical plate parallel to the channel walls which extends throughout the water depth. Conclusions are drawn concerning the conditions under which trapped modes may exist and their effect on the hydrodynamic characteristics of more general bodies.

テンションレグプラットフォームの非線形周波数和応答 : 理論および実験計測

Model tests have been performed in regular waves to measure second-order sum-frequency wave. excitations, and resultant motions and tether forces of a tension-leg platform (TLP). These test results are used to validate the predictions based on a recently developed second-order diffraction theory for general three-dimensional bodies. It is found that the vertical-plane motions and result- ing tether forces of the TLP include second-order sum-frequency resonant components which are comparable in magnitude with first-order wave-frequency responses. The correlation between predicted and measured results is satisfactory, confirming the validity of the theoretical predictions.

Second-order sum-frequency oscillations of tension-leg platforms: prediction and measurement

A series of model tests has been performed in regular waves to measure secondorder sum-frequency oscillations and tether forces of tension-leg platforms (TLPs). These test results are used to validate the predictions based on a recently developed second-order diffraction theory for general three-dimensional bodies. It is found that the vertical-plane motions and resulting tether forces of the TLPs include second-order sum-frequency resonant components which are comparable in magnitude with first-order wave-frequency responses. The correlation between predicted and measured results is satisfactory, overall confirming the validity of the theoretical predictions.

Entropy-free theories for differential materials

A thermodynamic theory was set up for general bodies of the differential type and complexity one without postulating entropy as a primitive. Indeed, a theory was proposed for such bodies in which the entropy is not postulated to exist from the outset, and in which the Clausius-Duhem inequality is replaced by a dissipative inequality involving stress, internal energy and heat flux. Entropy rate-of-change, v, is denned by means of equilibrium stress and internal energy without having at disposal a response function for the entropy, and shows that a certain condition of integrability regarding the response functions of the stress and internal energy is equivalent to the existence of a response function for the entropy. Hence, by postulating this condition to hold within the theory proposed here, we can prove the Clausius-Duhem inequality to hold, and thus also all the theorems of the corresponding classical theory. Any argument above holds in the particular case of an elastic body.

The initial value problem for a class of general relativistic fluid bodies

A body or collection of bodies made of perfect fluid can be described in general relativity by a solution of the Einstein–Euler system where the mass density has spatially compact support. It is shown that for certain equations of state there exists a wide class of solutions of this type corresponding to appropriate initial data given on a spacelike hypersurface. This class is not constrained by any symmetry requirements. The key element of the proof is to write the equations as a symmetric hyperbolic system which is regular both for nonvanishing density and in vacuum.

Irreducible convex sets

This paper is concerned with convex subsets of finite dimensional vtctor spaces, over the field of real scalars. As in [10, p. 244] and [20] we say that a compact convex set A, symmetric about the origin, is reducible, if there is a nonsymmetric closed convex set B for which A = B - B. The latter term denotes the set of all differences, {x-y: x, y є B}. Equivalently, A is reducible if, and only if, A =1/2 (B - B) for some B which is not a translate of A. If the identity A = B - B is only possible when B is centrally symmetric, then A is irreducible. If A is symmetric about a point other than the origin, we can say that it is (ir)reducible when it is the translate of an (ir)reducible set which is symmetric about the origin. It is well known that a parallelotope of any dimension is irreducible [6, Hilfssatz 3], that any 2-dimensional convex body other than a parallelogram is reducible [9, p. 217], and that euclidean balls of any dimension (other than one) are reducible [4, Ch. 7]. For more general convex bodies, the determination of reducibility is not a simple problem. Shephard [20] showed that a set is reducible if, and only if, it has an asymmetric summand, and he used this to study reducibility of polytopes. The main purpose of this paper is to give a new condition, necessary and sufficient for a symmetric polytope to be reducible. This condition may be expressed in the form: does a certain finite family of linear equations have a nontrivial solution? Thus, to determine the reducibility of a given polytope, it suffices to find the rank of some matrix. Using our criterion, we are able to describe some large families of irreducible polytopes. For example, every n- dimensional symmetric polytope with 4n – 2 or fewer vertices is irreducible (unless n = 2). We also establish the existence of irreducible, smooth, strictly convex bodies.

Uniformly second-order-accurate essentially nonoscillatory schemes for the Euler equations

Two time-level explicit and implicit finite-difference shock-capturin g schemes based on the characteristic flux difference splitting method and the modified flux approach with the essentially nonoscillatory (ENO) property of Harten and Osher have been developed for the two-dimensional Euler equations. The methods are conservative, uniformly second-order accurate in time and space, even at local extrema. General coordinate systems are used to treat complex geometries. Standard alternating direction implicit approximate factorization is used for constructing implicit schemes. Numerical results have been obtained for unsteady shock wave reflection around general two-dimensional blunt bodies and for steady transonic flows over a circular arc bump in a channel. Properties of ENO schemes as applied to two-dimensional flows with multiple embedded discontinuities are discussed. Comparisons of the performance between the present ENO schemes and our previous total variation diminishing schemes is also included.

Modelling Clip: Some More Results

AbstractThe modedling clip of the PHIGS ISO Standard is mathematically analysed. The most important result of this analysis is the fact that the projective image of a modding clip body (that is a not necessarily bounded convex body in space) is simply the union of two convex bodies. Furthermore, it will also be proved that in some cases one of these two bodies is empty. This fact makes the implementation of the modelling clip fairly straightforward and makes it also possible to use all already existing results on clipping against general convex bodies without change.

Residual stress modelling by experimental measurements and finite element analysis

The paper describes an experimental-numerical technique for modelling plane residual stress fields with application to steel slabs containing laser welds of different geometry. This technique is based on the analysis of the strain measured by several small-size strain gauges as a function of the depth of a narrow slot which was cut in the slab itself in small increments. This information was combined with sensitivity coefficients obtained via finite element models in order to derive initial strain distributions for the welded plates. These distributions allowed a prediction to be made of the residual stresses acting in generic bodies extracted from the original plates. The stress fields predicted for square specimens cut from the slabs were then compared with the measured values, showing a fairly good agreement.

On minimization of stress concentration for three-dimensional models

A solution procedure is described for the minimization of stress concentration in general three-dimensional bodies. The formulation is based on tetrahedral finite element analysis and linear programming optimization. Analytical sensitivity analysis, omitting the use of repeated analyses, is presented. Two examples are described in detail. Firstly, a three-dimensional recalculation of the plane stress/plane strain optimal elliptical shape demonstrates the reliability of the procedure, since extremely good agreement is found. Secondly, the three-dimensional cavity problem is treated. The known solution of an ellipsoid is found to an accuracy governed by the finite element mesh. This example demonstrates the need for a better finite element model, and the paper therefore finally focuses on the problem of model-optimization (best finite element model) of a given design. It is shown that the formulation of this optimal remodelling problem is parallel to that of the optimal redesign problem. A remodelling criterion based on combined global/local accuracy is suggested.

COPPER ALLOY No. C93900

Abstract Copper Alloy No. C93900 is a cast bronze of fairly low strength. It has good machinability and good resistance to corrosion. Its commercial names formerly used (not recommended) are: (1) High-Leaded Tin Bronze and (2) 79-6-15. Among its uses are bearings for general service and pump bodies. This datasheet provides information on composition, physical properties, hardness, elasticity, and tensile properties. It also includes information on corrosion resistance as well as casting, heat treating, machining, and joining. Filing Code: Cu-487. Producer or source: Copper alloy foundries. See also Alloy Digest Cu-475, April 1984.

Nonlinear aerodynamic effects on bodies in supersonic flow

The supersonic flow about generic bodies was analyzed to identify the elments of the nonlinear flow and to determine the influence of geometry and flow conditions on the magnitude of these nonlinearities. The nonlinear effects were attributed to separated-flow nonlinearities and attached-flow nonlinearities. The nonlinear attached-flow contribution was further broken down into large-disturbance effects and entropy effects. Conical, attached-flow bundaries were developed to illustrate the flow regimes where the nonlinear effects are significant, and the use of these boundaries for angle of attack and three-dimensional geometries was indicated. Normal-force and pressure comparisons showed that the large-disturbance and separated-flow effects were the dominant nonlinear effects at low supersonic Mach numbers and that the entropy effects were dominant for high supersonic Mach number flow. The magnitude of all the nonlinear effects increased with increasing angle of attack. A full-potential method, NCOREL, which includes an approximate entropy correction, was shown to provide accurate attached-flow pressure estimates from Mach 1.6 through 4.6.

Finite area method for nonlinear supersonic conical flows

A fully conservative numerical method for the computation of steady inviscid supersonic flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell; a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is symmetrized by adding artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point lift off correctly. Results are compared with those of other investigators.

On the Clausius inequality

A condition equivalent to the existence of the absolute temperature scale satisfying the Clausius inequality is exhibited. The condition is close to the classical statements of the second law of thermodynamics due to Clausius and others. It is formulated as an assertion about cyclic processes of bodies whose totality is called a universe of bodies. The universe can contain general (local or not) bodies with memory but the validity of the result (i.e., the mentioned equivalence) requires that it must contain enough elastic bodies. With each universe of bodies one can associate a collection of Borel measures on the real line, and the restrictions imposed on the universe of bodies induce certain properties of this collection. Also the condition equivalent to the existence of the absolute temperature scale as well as the Clausius inequality can be stated completely in terms of the collection of measures. The proof of the main result is given in this more general setting without recourse to bodies.

Implementation implications of Ada generics

Generic program units as defined in Ada pose several important design issues for compilers, both in semantic analysis and in runtime implementation. Chief among these issues are separate compilation of generic bodies and the sharing of code among several instantiations of a generic. An implementation is described that allows separate compilation of generic bodies with full semantic checking and that automatically shares instance bodies based on the characteristics of the actual parameters. A single instance body is generated for each "Instance class". Instance classes are formed by actual parameters with the same representation attributes.

Application of computer technology to the collection, analysis and use of veterinary data.

The value of a common pool of veterinary data, using clinical records from general practices, welfare organisations, research bodies and veterinary schools is described. Developments in computer technology are outlined and the computer's application to integrated data collection, storage, querying and dissemination is indicated. Proposals for a computerised integrated veterinary clinical data base, using a standard coded case record, are presented.

Hypersonic viscous flows past general bodies at angle of attack and yaw

Computational results of hypersonic viscous flows over blunt-nosed complex re-entry bodies are presented. An implicit iterative numerical scheme at each marching step is used to solve the parabolized Navier-Stokes (PNS) equations. An existing PNS code has been extended to treat nonaxisymmetric bodies at angle of attack and yaw, multiconic bodies with spin, surface mass transfer, and adiabatic wall conditions. Boundary conditions take into account the periodic condition around the body due to the yaw or spin, and the mass-transfer and/or spin effects at the body surface. The computational results presented include surface-measurable quantities and aerodynamic force and moment coefficients for complex geometries; available data were used for comparison. Grid-size effects on the accuracy of the Magnus force components due to spin are also discussed.

Implicit Solution for the Shock-Layer Flow around General Bodies

The simplified forms of the Navier-Stokes equations are solved by an iterative implicit scheme along the body axis for angles of incidence up to 30 deg. The method of solution yields both the inviscid and viscous flows simultaneously and predicts bow shock at stations normal to the axis. The technique is developed from a comparatively simple linearization procedure and has an option to iterate between body stations for higher accuracy. Reliable procedures have been introduced to account for the effect of the axial pressure gradient and to adjust the step increment for a given convergence requirement. A blunt cone and a Shuttle Orbiter-like configuration were studied and good agreement is obtained with available laminar boundary-layer solutions and experimental data. ISCOUS flowfield solutions around a re-entry vehicle are needed for the prediction of heating distributions as well as for the interpretation of aerodynamic data to support the design and flight test processes. The traditional boundary- layer (BL) approach that decouples the viscous flow from the outer inviscid flow has been valuable in the past; however, for the problems of current interest, such as the Space Shuttle Orbiter and the maneuverable re-entry vehicle, a more ac- curate solution is being obtained from the coupled fluid dynamics equations. This paper presents a method suitable for complex configurations that may be described by a lofting technique used by the aerospace industry. The method is devised to solve the Euler equations for the inviscid region and the parabolic Navier-Stokes (PNS) equations for the viscous region along an identifiable main-flow direction. The PNS equations are obtained from the full NS equation by omitting the second-order and the mixed derivatives and by approximating the exact pressure gradient in the designated direction. The flowfield of interest is bounded between the shock, the body, an initial-data plane normal to the specified direction, and a downstream station parallel to the initial plane. Although the length scales associated with the flow phenomena differ greatly on that plane, highly nonuniform grid spacings near the wall are not desirable in practice, as the shock must be calculated accurately. Hence, a detailed shock- layer solution requires a large number of grid points and consequently long computation time. In return for its cost, this method does not have any of the known shortcomings associated with the BL analyses and offers new capabilities for predicting leeside flow and crossflow separation. For this reason, there has been an intensive research effort in this decade to solve for the viscous flow as an integral part of the flowfield.

Numerical Procedure for the Computation of Irrotational Conical Flows

A numerical procedure has been developed for the computation of steady inviscid supersonic flow about general conical bodies at incidence. The method is based on solutions of the exact nonlinear potential equation in an orthogonal coordinate system generated through a stereographic projection and standard conformal mapping techniques. Accurate numerical solutions are obtained through the application of mixed-flow relaxation procedures. Results are presented for a wide variety of configurations from slender cones to thin wings with blunt leading edges, and are compared with existing theories and experimental data. Some interesting results have been obtained depicting the lift-off of the vortical singularity on elliptic cones at high angles of attack.

Slowly rotating, relativistic stars

view Abstract Citations (6) References (46) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Slowly rotating, relativistic stars. Abramowicz, M. A. ; Wagoner, R. V. Abstract The paper presents an analytic theory of slowly and uniformly rotating, general relativistic bodies, (neutron stars) which is based on Bardeen's variational principle. Analytic formulas for the total mass, total angular momentum, total baryon number, moment of inertia, and the angular velocity of the dragging of inertial frames are obtained. Analytic formulas are also derived for the rotational corrections to various physical quantities. These results indicate that the maximum mass of a stable neutron star in which the speed of sound is less than c can be increased by at most about 20% due to rotation. Publication: The Astrophysical Journal Pub Date: December 1978 DOI: 10.1086/156683 Bibcode: 1978ApJ...226.1063A Keywords: Dynamic Models; Neutron Stars; Relativity; Stellar Models; Stellar Rotation; Angular Momentum; Density (Mass/Volume); Gravitation Theory; Stellar Mass; Variational Principles; Astrophysics; Masses:Neutron Stars; Relativistic Stars:Rotation full text sources ADS |