Bodies Of Different Shapes Research Articles

The applicability of continuum models in the transitional regime of hypersonic flow over blunt bodies

Hypersonic rarefied gas flow over blunt bodies in the transitional flow regime (from continuum to free-molecule) is investigated. Asymptotically correct boundary conditions on the body surface are derived for the full and thin viscous shock layer models. The effect of taking into account the slip velocity and the temperature jump in the boundary condition along the surface on the extension of the limits of applicability of continuum models to high free-stream Knudsen numbers is investigated. Analytic relations are obtained, by an asymptotic method, for the heat transfer coefficient, the skin friction coefficient and the pressure as functions of the free-stream parameters and the geometry of the body in the flow field at low Reynolds number; the values of these coefficients approach their values in free-molecule flow (for unit accommodation coefficient) as the Reynolds number approaches zero. Numerical solutions of the thin viscous shock layer and full viscous shock layer equations, both with the no-slip boundary conditions and with boundary conditions taking into account the effects slip on the surface are obtained by the implicit finite-difference marching method of high accuracy of approximation. The asymptotic and numerical solutions are compared with the results of calculations by the Direct Simulation Monte Carlo method for flow over bodies of different shape and for the free-stream conditions corresponding to altitudes of 75–150 km of the trajectory of the Space Shuttle, and also with the known solutions for the free-molecule flow regine. The areas of applicability of the thin and full viscous shock layer models for calculating the pressure, skin friction and heat transfer on blunt bodies, in the hypersonic gas flow are estimated for various free-stream Knudsen numbers.

A Fourier–Karhunen–Loève discretization scheme for stationary random material properties in SFEM

AbstractIn order to overcome the computational difficulties in Karhunen–Loève (K–L) expansions of stationary random material properties in stochastic finite element method (SFEM) analysis, a Fourier–Karhunen–Loève (F–K–L) discretization scheme is developed in this paper, by following the harmonic essence of stationary random material properties and solving a series of specific technical challenges encountered in its development. Three numerical examples are employed to investigate the overall performance of the new discretization scheme and to demonstrate its use in practical SFEM simulations. The proposed F–K–L discretization scheme exhibits a number of advantages over the widely used K–L expansion scheme based on FE meshes, including better computational efficiency in terms of memory and CPU time, convenient a priori error‐control mechanism, better approximation accuracy of random material properties, explicit methods for predicting the associated eigenvalue decay speed and geometrical compatibility for random medium bodies of different shapes. Copyright © 2007 John Wiley & Sons, Ltd.

Wind tunnel investigation on the retention of air pollutants in three-dimensional recirculation zones in urban areas

The article discusses an experimental investigation of turbulent dispersion processes in a typical three-dimensional urban geometry, in reduced scale, in neutrally stable conditions. Wind tunnel experiments were carried out for characterizing the flow and the dispersion of a pollutant around a scaled model (1:400) of a group of eight 10-floor buildings surrounding a square. The situation corresponded to the dispersion of fine inertialess particles released from a line source positioned upstream of the urban geometry. After the sudden interruption of the source generation, the particles persisted in the recirculation cavity between the buildings, with the concentration decaying exponentially with time. This is in accordance with previous works on the dispersion process around bluff bodies of different shapes [e.g., Humphries and Vincent, 1976. An experimental investigation of the detention of airborne smoke in the wake bubble behind a disk. Journal of Fluid Mechanics 73, 453–464; Vincent, 1977. Model experiments on the nature of air pollution transport near buildings. Atmospheric Environment 11, 765–774; Fackrell, 1984. Parameters characterizing dispersion in the near wake of buildings. Journal of Wind Engineering and Industrial Aerodynamics 16, 97–118]. The main parameter in the investigation was the characteristic time constant for the concentration decay. The measurements of the variation in the concentration of the fine particles were performed by means of a photo-detection technique based on the attenuation of light. The velocity fields were evaluated with the particle image velocimetry (PIV) technique. The dimensionless residence time H for the particles ( H= τU/ L, where τ is the time constant for the concentration decay, U the free-stream velocity, and L is a characteristic dimension for the urban geometry, as defined by Humphries and Vincent [1976. An experimental investigation of the detention of airborne smoke in the wake bubble behind a disk. Journal of Fluid Mechanics 73, 453–464] was determined for various locations in the scaled model, in the range of Reynolds numbers ( Re) between 8000 and 64,000. H was found to be 6.5±1.0.

Finite-difference Euler Deconvolution Algorithm Applied to the Interpretation of Magnetic Data from Northern Bulgaria

Here, we propose a new, finite-difference algorithm for Euler deconvolution, based on the Euler’s homogeneity equation accounting for a constant background field which allows simultaneous depth and shape estimation. The algorithm uses as input data the measured anomalous field and its first-order derivatives, in contrast to methods based on the input of higher order field derivatives. The test of the algorithm on a model of interfering fields of elementary sources with different field fall-off rates, resulting in background close to a linear one, shows that it can give a good estimation of both the depth to the sources singular points and their respective structural indices. A set of tests was carried out on column-like models with shapes ranging from the elementary model of a dipole to that of a point pole, and of models of arbitrary shape with two singular points in between. It showed that when the ratio of the distance between the observation plane and the source’s top and the length of the body allows classification of it as a dipole or a point pole, the value of the estimated structural index is close to the integer value, typical for the respective elementary source. In such cases the estimated depth value refers to that of the special internal point of the respective type of source. This can facilitate in certain situations the interpretation of non-integer structural indices and their associated depth estimates obtained with the new Euler deconvolution algorithm. Inversion of a set of magnetic data from northern Bulgaria, caused by basaltic bodies of different shape, with the proposed method confirmed that the most intense anomalies are caused by column-like bodies outcropping on the surface and with considerable depth extent.

Pattern equation method for solving problems of diffraction of electromagnetic waves by axially symmetric dielectric scatterers

A new efficient method is proposed for solving 3D problems of diffraction of electromagnetic waves by a single dielectric body of arbitrary shape. The method offers a high rate of convergence. The method is applied to the problem of scattering by axially symmetrical bodies, and the data are presented that illustrate the convergence rate of the computation algorithm for bodies of different shapes. A possibility is studied to model the scattering characteristics for perfectly absorbing (black) bodies. The Ufimtsev theorem on the ratio of the cross-sections of perfectly reflecting and black bodies is numerically tested.

Control of the Flow Past Bodies Using Localized Energy Addition to the Supersonic Oncoming Flow

A possibility of controlling the supersonic flow past bodies of different shape by adding a small amount of energy to the freestream is studied experimentally. In the numerical calculations the model of a spatially distributed energy source based on the Euler equations for a perfect gas is used. The gasdynamic features of the flow around energy sources are studied, some new effects are revealed, and analytical models for their description are developed. It is shown that by optimizing the energy source parameters it is possible to initiate irregular regimes of flow past bodies characterized by radical changes in the bow shock structure with the formation of return flow zones. In this case an appreciable drag reduction can be achieved with high efficiency of energy expenditure.

Effectiveness of hydraulic tomography: Sandbox experiments

Two sandbox experiments were conducted to evaluate the performance of a sequential geostatistical inverse approach for hydraulic tomography in characterizing aquifer heterogeneity. One sandbox was packed with layered sands to represent a stratified aquifer, while the other was packed with discontinuous sand bodies of different shapes and sizes to represent a more complex and realistic heterogeneous aquifer. Parallel to the sandbox experiments, numerical experiments were conducted to assess the effects of measurement errors and uncertainties associated with laboratory data, and to diagnose the hydraulic conductivity estimates obtained from sandbox experiments. Results of this study show that our sequential inverse approach works well under realistic conditions, in spite of measurement errors and uncertainties associated with pumping rates, boundary conditions, pressure head measurements, and other parameters required by our model. The tomography was found to be ineffective if abundant head measurements were collected at closely spaced intervals in a highly stratified aquifer. On the other hand, it was found to be beneficial when pressure head measurements were limited and the geological structure was discontinuous.

Numerical Solution of a Three-Dimensional Multicomponent Viscous Shock Layer by the Method of Global Iterations

The model of viscous shock layer is used to solve the three-dimensional problem on supersonic flow of nonequilibrium-dissociating air past smooth bodies of different shapes at different angles of attack and slip.

Electrostatic discharges from charged cylindrical bodies to grounded or floating surfaces

Most of the studies carried out on the hazards related to electrostatic discharges (ESD) assume that the breakdown strength of air, at atmospheric pressure, is 30 kV/cm. The authors have developed numerical techniques for a more accurate estimation of the conditions in which a self-sustaining discharge can occur between conductive bodies of different shapes and sizes. An analysis is presented of three ESD events involving charged cylindrical bodies in the proximity of grounded or floating surfaces. The voltage at breakdown, the critical charge that triggers the discharge, the charge exchanged between the two bodies, and the energy transferred in the discharge are evaluated as functions of various geometric parameters. The interpretation of the results provide a better understanding of the multitude of factors which determine the probability of a discharge and the relative severity of such an event in various technical systems.

An analysis of second-order wave forces on floating bodies by using a higher-order boundary element method

The wave diffraction and radiation problem is studied numerically by using a higher-order boundary element method. The convergence of the higher-order boundary element method is tested systematically for bodies of different shapes. For the second-order force, particular attention is paid to the contribution of the second-order potential, following the line of Molin's approach. For numerical evaluation, the free surface is divided into three subregions; inner, intermediate and outer ones. In the inner region, the integral is evaluated numerically by using higher-order boundary elements. In the intermediate region, semi-analytic form is constructed with the help of eigen functions. In the outer domain, the analytic solution is available. This subdivision scheme reduces the numerical burden remarkably.

Local wave theory of elastic-body collision: Plane problem in the ideal-liquid approximation

1. There are several well-known classical approaches to the investigation of elastic-body collision. In elementa~ impact theory, beginning with Newton's work, the basic parameter is the velocity recovery coefficient at impact, which is 1 for absolutely elastic bodies and 0 for absolutely plastic bodies. This approach cannot fully describe the internal state of the bodies. St Venant wave theory considers the longitudinal collision of elastic rods, i.e., one-dimensional objects; an advantage of the theory is the determination of the duration of collision, equal to twice the time for the compression wave to traverse the complete length of the rod. However, the one-dimensional stress----strain state determined in this way cannot be used for adc~iuatr description of the state of bodies of different shape. In addition, attempts to consider oblique or noneentral impact onthe basis of St Venant theory are evidently difficult. Classical local Hertz theory is based on the solution of a static contact problem regarding the action of a point force on the plane boundary of a halfspace, which is extended to the problem of the dynamic contact interaction of elastic bodies in direct central impact. Hertz theory, wifich is essentially quasi-static, is applicable when the contact time of the bodies in collision is considerably greater than the period of the lowest intrinsic oscillations of the bodies. Modification of the local theory by synthesis with St Venant theory has been proposed by Sears, Kil'chevskii, and others. Timoshenko has developed a theory of transverse impact at an elastic beam. Note that the assumption of elastic deformation of the colliding bodies limits the range of relative impact velocities that may be considered. At high velocities, the elastic limit of the material may be exceeded, and the behavior of the body must be described on the basis of more complex theological models, taking account of inelastic deformation. M. A. Lavrent'ev has proposed a hydrodynamic model of collision (interpenetration) of bodies at high velocity. It may be successfully used because the stress ellipsoid resembles a sphere in high-speed collision, i.e., the stress ellipsoid of a low-viscosity liquid. As a rule, numerical methods must be used to consider the collision of bodies with theologically complex behavior. In addition to these and several other approaches in modern continuum mechanics, for three-dimensional bounded by smooth surfaces, we may note an approach associated with the investigation of the collision (interpenetration) of bodies or the impact of a body on a medium in which the behavior of the body or medium is described by the equations of elasticity theory (or an ideal liquid in the case of collision at a liquid surface) and the collision problem is formulated, in the general case, as a nonsteady, often mixed, twoor three-dimensional problem, ff the motion of the bodies is specified only in the initial moment of collision, and their subsequent motion is determined in solving the problem, the boundary of the bodies' contact region is generally mobile and unknown in advance. This relatively complex formulation of the impact problem, which is free from the assumptions of classical appmacbes, has yielded a series of analytical (numerical--analytical) solutions by, among others, Grigolyuk and Gorshkov, Sagomonyan, Pomchikov, Galanov, Borodich, V. N. and V. V. Gavrilenko, Popov, and Tarlakovskii [ 1-3, 81. As a rule, the impact of a solid body or elastic shell on the surface of an infinite elastic or liquid medium is considered in this approach. Inthe present work, an approach to the collision of two elastic bodies such that at least their frontal surface is relatively smooth in the geometric sense (blunt bodies) is developed. The approach is based on research on the impact interaction of bodies of finite size with an infinite acoustic or elastic medium [3-8]. Its development takes into account that the depth of interpenetration of blunt bodies on impact is small in comparison with the clmracteristic dimension of the contact region and, consequently, the corresponding boundary conditions may be formulated at the unperturbed surface of the bodies. In addition, since the surface of a blunt body is only slightly distorted within the contact region, it may be regarded as plane. Finally, the

Third virial coefficient and the hard convex body equation of state

A modified equation of state of hard convex body fluids is proposed in which the ratio of the third virial coefficients is employed as the second parameter (in addition to the parameter of non-sphericity α); the resulting equation of state yields the dependence of the compressibility factor on density for hard convex body fluids with a considerable variety of shapes within the error estimates of the simulation data. The third virial coefficients of hard convex bodies of one type are expressed in terms of parameters α and τ; the proposed expressions discern between convex bodies of different shapes with the same values of α (e.g. prolate and oblate ellipsoids of revolution) and enable accurate determination of the third virial coefficients in a broad range of non-sphericities.

Laminar free convection flow over a cone embedded in a stratified medium

Free convection flows which arise in a thermally stratified medium are of practical importance. Interest lies in the effect of stratification on temperature and velocity fields that arise in the flow and the consequent heat transfer from a heated body. In many engineering applications coneshaped bodies are often used. Free convection flow over a vertical cone has been studied by Hering and Crosh [I], Hering [2], Lin and Chao [3], Lin [4,] Alamgir [5] and recently by Watanabe [6]. A literature review reveals that the free convection flow over a vertical cone immersed in a stratified medium has not been studied so far. This has motivated us to carry out the present analysis. Laminar free convection flows over bodies of different shapes like vertical plate, sphere and cylinder in a stratified medium have been studied by various investigators; see, for example, Chen and Eichhorn [7-8].

Numerical modeling of supersonic flow over wings with varying aspect ratio on a broad range of angles of attack using the law of plane sections

A method and a program based on it for solving the problem of flow in the neighborhood of bodies of different shapes introduced into a high-supersonic stream at arbitrary angles of attack are proposed. The equations of the law of plane sections are integrated by Godunov's method. It is shown that the region of applicability of Sychev's theory is much broader than indicated in [1].

Some observations of the effect of aspect ratio on the influence of turbulence on the drag of rectangular cylinders

1This paper presents the results of an experiment in which the effects of different incident turbulence flow fields acting on bluff bodies of different shapes and sizes are studied. It is concluded that the classical variation of drag with plan shape may be modified by increasing turbulence level in a consistent manner, but that such trends may be disturbed by end effects for short aspects ratio bodies.

Similarity of three-dimensional and axisymmetric chemically-nonequilibrium flows in the neighborhood of a plane of symmetry

Three-dimensional chemically-nonequilibrium flow past blunt bodies in the neighborhood of the plane of symmetry is investigated within the framework of viscous shock layer theory. The similarity of three-dimensional and axisymmetric flows, previously established in [1] for a uniform gas, is extended to chemically-nonequilibrium gas flows. It is shown that the problem of determining the heat fluxes and friction stress in the neighborhood of the line of flow divergence can be reduced to the problem of determining these quantities for the axisymmetric body. The validity of the axisymmetric analogy is verified by carrying out numerical calculations for bodies of different shapes re-entering the earth's atmosphere along a gliding trajectory. Various models of surface catalytic activity are considered. The use of similarity relations makes it possible to apply existing programs for calculating axisymmetric flows to the solution of three-dimensional problems.

Study of the characteristics of coupled heat transfer near symmetry surfaces of bodies with different shape

The results of a study of the characteristics of heat transfer accompanying flow around bodies of different shape at the angles of attack are presented.

Influence of body shape on the spatial boundary layer characteristics on a permeable surface

Results are presented of computations of the flow of a homogeneous gas in the spatial laminar boundary layer on blunt bodies of different shape with a permeable surface around which are flows at angles of attack and slip.

Study of heat- and mass-transfer characteristics in the symmetry planes of bodies of different shapes

Results are presented from comparative studies of heat- and mass-transfer characteristics in flows about bodies of different shapes at angles of attack.

Solution of coupled heat-transfer problems in flow about bodies of different shapes

Solution of coupled heat-transfer problems in flow about bodies of different shapes