Effects of the curvature radius of a cylindrical shell on the stress intensity factors of surface cracks

The effects of the curvature radius of a cylindrical shell on stress intensity factors are investigated in circumferential (inner and outer) semielliptical surface cracks in a cylindrical shell. What is new in this paper is to have given: (1) The stress intensity factors for surface cracks in a cylindircal shell are determined by photoelastic technique. (2) By a special method photoelastic slices are handled for obtaining a clear caustic curve, and the stress intensity factors for surface cracks in a cylindrical shell are determined by the caustic method. (3) An approximate equation of curvature correction factor F_c is proposed. (4) Effects of the curvature radius R of a cylindrical shell on the stress intensity factors of surface cracks are obtained. The results of this paper are in fair agreement with already existing analytical results. The approximate equation of curvature correction factor F_c can be widely used for engineering purposes.     

Prise en compte des effets non linéaires de surface libre en écoulement instationnaire

This Note describes a computational method for three dimensional unsteady flows around a submerged body with forward speed. The two free-surface boundary conditions are written under their non linear form. The calculations are carried out in the time domain using a mixed Euler–Lagrange scheme based on the knowledge, at each time step, of the potential on the free surface and of the location of this surface. A mixed problem with a Neumann condition on the body and a Dirichlet one on the free surface is then solved. The panel method uses desingularized sources to represent free surface effects. Validations are carried out on steady flows. To cite this article: A. Rebeyrotte et al., C. R. Mecanique 333 (2005).     

A numerical method to solve the m‐terms of a submerged body with forward speed

To model mathematically the problem of a rigid body moving below the free surface, a control surface surrounding the body is introduced. The linear free surface condition of the steady waves created by the moving body is satisfied. To describe the fluid flow outside this surface a potential integral equation is constructed using the Kelvin wave Green function whereas inside the surface, a source integral equation is developed adopting a simple Green function. Source strengths are determined by matching the two integral equations through continuity conditions applied to velocity potential and its normal derivatives along the control surface. After solving for the induced fluid velocity on the body surface and the control surface, an integral equation is derived involving a mixed distribution of sources and dipoles using a simple Green function and one component of the fluid velocity. The normal derivatives of the fluid velocity on the body surface, namely the m‐terms, are then solved by this matching integral equation method (MIEM). Numerical results are presented for two elliptical sections moving at a prescribed Froude number and submerged depth and a sensitivity analysis undertaken to assess the influence of these parameters. Furthermore, comparisons are performed to analyse the impact of different assumptions adopted in the derivation of the m‐terms. It is found that the present method is easy to use in a panel method with satisfactory numerical precision. Copyright © 2002 John Wiley & Sons, Ltd.     

Determination of the deformed position of a thin shell from surface strains and height function

This paper focuses on the following problem: given the strain tensor of a deformed reference surface of a thin shell and the distances of the points on this surface from some arbitrarily fixed reference plane (the so-called height function) find the position of this reference surface. Two alternative procedures supplying the solution are developed. The first one follows from the ideas developed by Darboux (Leçons sur la Théorie Général des Surfaces, Troisiéme Partie, Gauthier-Villars, Paris, 1894), whereas the second one is based on the polar decomposition theorem and techniques developed in continuum mechanics. These procedures are purely kinematic, valid for arbitrary surface geometry and for unrestricted surface strains. Szwabowicz (Deformable surfaces and almost inextensional deflections of thin shells, Habilitation Thesis, 1999) proposed a relatively simple non-linear boundary-value problem (BVP) for thin elastic shells, which was expressed in three surface strains and the height function as basic independent field variables. The results of this paper suggest that this approach to the non-linear problems of thin shells may be an attractive alternative to other BVPs developed in the literature.     

Modified von Kármán equations for elastic nanoplates with surface tension and surface elasticity

In this paper, modified von Kármán equations are derived for Kirchhoff nanoplates with surface tension and surface tension-induced residual stresses. The simplified Gurtin-Murdoch model which does not contain non-strain displacement gradients in surface stress-strain relations is adopted, so that the von Kármán strain-compatibility equation can be expressed in terms of the stress function and deflection. The modified von Kármán equations derived here are different than the existing related models especially for elastic plates with in-plane movable edges. Unlike the existing models which predict a surface tension-induced tensile pre-stress for an elastic plate with in-plane movable edges, the present model predicts that this tensile pre-stress is actually cancelled by the surface tension-induced residual compressive stress. Our this result is consistent with recent clarification on similar issue for cantilever beams with surface tension, which implies that the existing models have incorrectly predicted an invalid tensile pre-stress for an elastic plate with in-plane movable edges which leads to significant overestimation of postbuckling load and free vibration frequencies. In addition, our numerical examples indicated that surface stresses can moderately increase or decrease postbuckling load and free vibration frequency of Kirchhoff nanoplate with all in-plane movable edges, depending on the surface elasticity parameters and the geometrical dimensions of nanoplates.     

Experimental investigation of the failure mechanism of fiber-reinforced composites subjected to uniaxial tension

In this investigation, the components of displacement in the axial direction throughout the surface of a unilayer, fiber-reinforced-composite tension specimen subjected to low-speed loading are established experimentally. The experimental results are used to evaluate the strain distribution throughout the surface of the specimen; to establish the strain concentration at the surface in the neighborhood of broken fibers; and to evaluate other factors.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅳ)——SURFACE COUSERVATION LAWS

The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived. The existing related results are naturally derived as special cases from the results proposed in this paper. The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction. The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization. Contributed by DAI Tian-min, Original Member of Editorial Committee, AMM Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001) Biography: DAI Tian-min (1931 ~)     

On the Two-Phase Navier–Stokes Equations with Boussinesq–Scriven Surface Fluid

Two-phase flows with interface modeled as a Boussinesq–Scriven surface fluid are analysed concerning their fundamental mathematical properties. This extended form of the common sharp-interface model for two-phase flows includes both surface tension and surface viscosity. For this system of partial differential equations with free interface it is shown that the energy serves as a strict Ljapunov functional, where the equilibria of the model without boundary contact consist of zero velocity and spheres for the dispersed phase. The linearizations of the problem are derived formally, showing that equilibria are linearly stable, but nonzero velocities may lead to problems which linearly are not well-posed. This phenomenon does not occur in absence of surface viscosity. The present paper aims at initiating a rigorous mathematical study of two-phase flows with surface viscosity.     

The surface hot wire as a means of measuring mean and fluctuating wall shear stress

 The paper describes some applications of a wall shear stress sensor technique which is based on hot-wire anemometry. The “surface hot wire” is a flush-mounted thermal resistive wire with a tiny slot underneath. The arrangement of this sensor guarantees an improved signal-to-noise ratio compared to a common surface hot film. The setup and the application of single sensors and of surface hot-wire arrays are shown. Some results are presented that were acquired in several experiments in the field of laminar-turbulent transition. Received: 26 May 2000/Accepted: 7 February 2001     

Radar imaging of water surface flow fields

 We describe the capabilities of coherent high resolution radar to observe remotely the effects of an upwelling subsurface flow on the water surface. This observation is possible because the radar radiation backscatters very strongly from surface features with dimensions similar to its wavelength, in this case X-band at 0.03 m. This technique provides imaging capability with relatively high spatial resolution (∼0.3 m) and fast time sampling (∼0.006 s) over a large surface area. The processed data reveal both the line-of-sight velocity spectrum of moving water surface features, and their water surface radar backscatter cross-section. We believe that the surface features are generated by subsurface vortices oriented normal to the surface. The vortices are advected with the bulk flow of the jet. Our radar observations of the down-stream flow from a submerged waterjet that is directed parallel to the surface are consistent with those previously measured by laser velocimetry. Received: 25 February 1994/Accepted: 16 May 1996     

Measurement of the surface concentration (liquid) of an evaporating multicomponent droplet using pendant droplet method

The surface concentration on the liquid side of the interface of an evaporating multicomponent droplet could be different from the bulk concentration. In this work, surface tension is used as a means to measure surface concentration of an evaporating multicomponent droplet. Surface tension is measured using pendant droplet method that relies on the best fit between theoretical and experimental drop profiles. Surface tension is a surface property, and it exhibits a dependence on concentration. Hence, it is an ideal candidate to track the variation of surface concentration during the evaporation of a multicomponent droplet. This method is used to study the evaporation of ethanol–water and methanol–water droplets. The correctness and applicability of this technique are critically assessed, and important observations are made for single droplet evaporation for these binary mixtures.     

Simulation of free surface flows using the flux‐difference splitting scheme on the hybrid Cartesian/immersed boundary method

In this study, a method is developed to simulate the interaction between free surface flows and moving or deforming boundaries using the flux‐difference splitting scheme on the hybrid Cartesian/immersed boundary method. At each physical time step, the boundary is defined by an unstructured triangular surface grid. Immersed boundary (IB) nodes are distributed inside an instantaneous fluid domain based on edges crossing the boundary. At an IB node, dependent variables are reconstructed along the local normal line to the boundary. Inviscid fluxes are computed using Roe's flux‐difference splitting scheme for immiscible and incompressible fluids. The free surface is considered as a contact discontinuity in the density field. The motion of free surface is captured without any additional treatment along the fluid interface. The developed code is validated by comparisons with other experimental and computational results for a piston‐type wave maker, impulsive motion of a submerged circular cylinder, flow around a submerged hydrofoil, and Rayleigh–Taylor instability. The developed code is applied to simulate wave generation due to a continuously deforming bed beneath the free surface. The violent motion of a free surface caused by sloshing in a spherical tank is simulated. In this case, the free surface undergoes breakup and reconnection. Copyright © 2011 John Wiley & Sons, Ltd.     

A semi‐implicit finite volume implementation of the CSF method for treating surface tension in interfacial flows

We present an implementation of Hysing's (Int. J. Numer. Meth. Fluids 2006; 51 :659–672) semi‐implicit method for treating surface tension, for finite volume models of interfacial flows. Using this method, the surface tension timestep restriction, which is often very stringent, can be exceeded by at least a factor of 5 without destabilizing the solution. The surface tension force in this method consists of an explicit part, which is the regular continuum surface force, and an implicit part which represents the diffusion of velocities induced by surface tension on fluids interfaces. The surface tension force is applied to the velocity field by solving a system of equations iteratively. Since the equations are solved only near interfaces, the computational time spent on the iterative procedure is insignificant. Copyright © 2008 John Wiley & Sons, Ltd.     

Problems of heat transfer and thermal protection of entry vehicles for an unmanned mission to mars

The problems of heat transfer and thermal protection for an orbitalMartian lander touching down on the planetary surface are investigated. A broad scenario of the mission is given and several possible aerodynamic shapes are considered. Several versions of the landing on the planetary surface are studied. The version with intermediate orbiting of an artificial Mars satellite using aerodynamic deceleration in the atmosphere is adopted as the main variant. The landing on the planetary surface is realized from satellite orbit. This landing pattern requires reusable thermal protection. The convective and radiative heat fluxes are calculated at characteristic points on the surface of a vehicle of the chosen shape. For this shape the necessary weight of thermal protective coating consisting of indestructible reusable TZMK material, used previously for shielding the Buran orbiter, is determined.     

Numerical methods for conjunctive two‐dimensional surface and three‐dimensional sub‐surface flows

Sophisticated catchment runoff problems necessitate conjunctive modeling of overland flow and sub‐surface flow. In this paper, finite difference numerical methods are studied for simulation of catchment runoff of two‐dimensional surface flow interacting with three‐dimensional unsaturated and saturated sub‐surface flows. The equations representing the flows are mathematically classified as a type of heat diffusion equation. Therefore, two‐ and three‐dimensional numerical methods for heat diffusion equations were investigated for applications to the surface and sub‐surface flow sub‐models in terms of accuracy, stability, and calculation time. The methods are the purely explicit method, Saul'yev's methods, the alternating direction explicit (ADE) methods, and the alternating direction implicit (ADI) methods. The methods are first examined on surface and sub‐surface flows separately; subsequently, 12 selected combinations of methods were investigated for modeling the conjunctive flows. Saul'yev's downstream (S‐d) method was found to be the preferred method for two‐dimensional surface flow modeling, whereas the ADE method of Barakat and Clark is a less accurate, stable alternative. For the three‐dimensional sub‐surface flow model, the ADE method of Larkin (ADE‐L) and Brian's ADI method are unconditionally stable and more accurate than the other methods. The calculations of the conjunctive models utilizing the S‐d surface flow sub‐model give excellent results and confirm the expectation that the errors of the surface and sub‐surface sub‐models interact. The surface sub‐model dominates the accuracy and stability of the conjunctive model, whereas the sub‐surface sub‐model dominates the calculation time, suggesting the desirability of using a smaller time increment for the surface sub‐model. Copyright © 2000 John Wiley & Sons, Ltd.     

Analysis of the heterogeneous recombination of oxygen atoms on aluminum oxide by methods of quantum mechanics and classical dynamics

On the basis of the density-functional theory, cluster models of the adsorption of oxygen atoms on aluminum oxide are constructed and the corresponding potential-energy surface is calculated. Quantum-mechanical calculations showed that it is necessary to take into account the angular dependence of the potential-energy surface and the relaxation of the surface monolayers. Using this surface in molecular dynamics calculations made it possible to obtain the probabilities of the heterogeneous recombination of oxygen atoms on the α-Al₂O₃ surface, which are in good agreement with experimental data. The calculations performed substantially decrease the amount of experimental investigations necessary reliably to describe the heterogeneous catalysis on promising reusable heat shield coatings for analyzing heat transfer during spacecraft entry into the atmosphere.     

Aspects of the transpiration model for aerofoil design

Transpiration is a technique in which extra non-physical normal flows are created on an aerofoil surface in order to form a new streamline pattern such that the surface streamlines no longer follow the aerofoil surface under inviscid flow. The transpiration model is an important technique adopted in aerofoil design either to avoid mesh regeneration when aerofoil profile co-ordinates are adjusted or to find shape corrections in inverse design methods. A first-order approximation (with respect to the normal streamline displacement) to the transpiration model is commonly adopted; it is shown that this can be a poor approximation especially in regions of high curvature. In this paper more accurate approximations are developed to address this problem and improve the accuracy.     

The Effect of Time-Periodic Surface Temperature Oscillations on Free Convection from a Vertical Surface in a Porous Medium

In this paper, we consider the unsteady free convection boundary layer flow which is induced by time-periodic variations in the surface temperature of a vertical surface embedded in a porous medium. The basic steady flow is that of a power-law distribution where the surface temperature varies as the nth power of the distance from the leading edge. Small-amplitude time-periodic disturbances are added to this basic distribution. Both the low- and high-frequency limits are considered separately, and these are compared with a full numerical solution obtained by using the Keller-box method. Attention is restricted to the cases n1; when n=1, the flow is locally self-similar for any prescribed frequency of modulation.     

Ignition of solid propellants

At present, the study of solid-propellant ignition is of particular interest owing to the adoption of hybrid motors [1–3]. The status of experimental and theoretical research in this field can be evaluated on the basis of the rather extensive survey of American papers in [2]. It is noteworthy that a common deficiency in available references is the absence of exact ignition criteria; in most cases the propellant is assumed to have ignited when its surface temperature reaches a prescribed level (gasification temperature), or when the rate at which the temperature increases with time at the propellant surface is sufficiently high. Exact criteria for this rate, however, are not given. In this article, we present ignition criteria for solid propellants and these are based on a diffusion-burning model. It is shown that for a diffusion flame to exist above the propellant surface, two conditions must be satisfied simultaneously: 1) the propellant surface temperature must equal the gasification temperature for that propellant and 2) the temperature gradient at the surface must be smaller than some value which depends on the kinetics of the chemical reaction in the diffusion flame and on the rate of oxidizer input to the propellant surface during burning.Two ignition techniques are examined as examples: ignition by hot gases or radiant heat flow and ignition by means of an active film which reacts with a cold oxidizer; the film is applied to the propellant surface prior to ignition.     

On the theory of loaded inhomogeneous cylinders

This article is concerned with the relaxed Saint-Venant’s problem in the case when the body forces and surface tractions on the lateral surface are polynomials in the axial coordinate. A new method of solving this problem is presented. The method is applied to study the problem of a uniformly loaded cylinder.