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Showing papers in "Journal of Engineering Mathematics in 2008"


Journal ArticleDOI
TL;DR: In this article, a new family of numerical schemes for kinematic flows with a discontinuous flux is presented, which preserve an invariant region of admissible concentration vectors, provided that all velocities have the same sign.
Abstract: Multiphase flows of suspensions and emulsions are frequently approximated by spatially one-dimensional kinematic models, in which the velocity of each species of the disperse phase is an explicitly given function of the vector of concentrations of all species. The continuity equations for all species then form a system of conservation laws which describes spatial segregation and the creation of areas of different composition. This class of models also includes multi-class traffic flow, where vehicles belong to different classes according to their preferential velocities. Recently, these models were extended to fluxes that depend discontinuously on the spatial coordinate, which appear in clarifier–thickener models, in duct flows with abruptly varying cross-sectional area, and in traffic flow with variable road surface conditions. This paper presents a new family of numerical schemes for such kinematic flows with a discontinuous flux. It is shown how a very simple scheme for the scalar case, which is adapted to the “concentration times velocity” structure of the flux, can be extended to kinematic models with phase velocities that change sign, flows with two or more species (the system case), and discontinuous fluxes. In addition, a MUSCL-type upgrade in combination with a Runge–Kutta-type time discretization can be devised to attain second-order accuracy. It is proved that two particular schemes within the family, which apply to systems of conservation laws, preserve an invariant region of admissible concentration vectors, provided that all velocities have the same sign. Moreover, for the relevant case of a multiplicative flux discontinuity and a constant maximum density, it is proved that one scalar version converges to a BV t entropy solution of the model. In the latter case, the compactness proof involves a novel uniform but local estimate of the spatial total variation of the approximate solutions. Numerical examples illustrate the performance of all variants within the new family of schemes, including applications to problems of sedimentation, traffic flow, and the settling of oil-in-water emulsions.

81 citations


Journal ArticleDOI
TL;DR: In this paper, the motion of a spherical particle in infinite linear flow and near a plane wall, subject to the slip boundary condition on both the particle surface and the wall, is studied in the limit of zero Reynolds number.
Abstract: The motion of a spherical particle in infinite linear flow and near a plane wall, subject to the slip boundary condition on both the particle surface and the wall, is studied in the limit of zero Reynolds number. In the case of infinite flow, an exact solution is derived using the singularity representation, and analytical expressions for the force, torque, and stresslet are derived in terms of slip coefficients generalizing the Stokes–Basset–Einstein law. The slip velocity reduces the drag force, torque, and the effective viscosity of a dilute suspension. In the case of wall-bounded flow, advantage is taken of the axial symmetry of the boundaries of the flow with respect to the axis that is normal to the wall and passes through the particle center to formulate the problem in terms of a system of one-dimensional integral equations for the first sine and cosine Fourier coefficients of the unknown traction and velocity along the boundary contour in a meridional plane. Numerical solutions furnish accurate predictions for (a) the force and torque exerted on a particle translating parallel to the wall in a quiescent fluid, (b) the force and torque exerted on a particle rotating about an axis that is parallel to the wall in a quiescent fluid, and (c) the translational and angular velocities of a freely suspended particle in simple shear flow parallel to the wall. For certain combinations of the wall and particle slip coefficients, a particle moving under the influence of a tangential force translates parallel to the wall without rotation, and a particle moving under the influence of a tangential torque rotates about an axis that is parallel to the wall without translation. For a particle convected in simple shear flow, minimum translational velocity is observed for no-slip surfaces. However, allowing for slip may either increase or decrease the particle angular velocity, and the dependence on the wall and particle slip coefficients is not necessarily monotonic.

71 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the flow due to a moving extensible sheet that obeys a more general stretching law, and the features of the flow and heat-transfer characteristics for different values of the governing parameters are analyzed and discussed.
Abstract: The flow due to a moving extensible sheet that obeys a more general stretching law is considered. The sheet occupies the negative x-axis and is moving continually in the positive x-direction, in an incompressible viscous and electrically conducting fluid. The sheet somehow disappears in a sink that is located at (x, y) = (0, 0). The governing system of partial differential equations is first transformed into a system of ordinary differential equations, and the transformed equations are solved numerically using a finite-difference scheme, namely the Keller-box method. The features of the flow and heat-transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that dual solutions exist for the flow near x = 0, where the velocity profiles show a reversed flow.

49 citations


Journal ArticleDOI
TL;DR: In this paper, the authors considered the problem of thermo-elastic stress analysis in multi-layered nonhomogeneous beams and provided closed-form solutions for the normal stresses in the layers and for the interface tangential stresses.
Abstract: The problem of thermo-elastic stress analysis in multi-layered nonhomogeneous beams is considered. The proposed analytical approach based on the multi-layered beam theory permits to take into account an arbitrary distribution of the Young’s modulus, of the thermal-expansion coefficient, and of the temperature variation along the beam depth. The effect of shear deformability of the interfaces is also carefully analyzed. Useful closed-form solutions for the normal stresses in the layers and for the interface tangential stresses are provided in the case of nonhomogeneous bi- and tri-layered beams. The obtained results show the effectiveness of using functionally graded materials to relieve stress-concentrations due to the thermo-elastic mismatch typical of laminated beams with homogeneous layers.

43 citations


Journal ArticleDOI
TL;DR: In this paper, an asymptotic analysis of the thickness of the liquid film that coats a smooth solid substrate when it is withdrawn from a bath of non-Newtonian fluid, and compares the results with experimental measurements is presented.
Abstract: This paper presents an asymptotic analysis of the thickness of the liquid film that coats a smooth solid substrate when it is withdrawn from a bath of non-Newtonian fluid, and compares the results with experimental measurements. The film thickness is, to a good approximation, uniform above the point where the film is withdrawn from the fluid bath, and depends on the rotation rate, the fluid properties and the substrate geometry. Theoretical predictions of the film thickness for a number of different substrate geometries (an inclined plate, roller and fiber) are presented, and are compared with experimental measurements in a single roller geometry. Results are obtained for two different limits of the Criminale–Ericksen–Filbey constitutive equation in which the fluid rheology is either weakly elastic and dominated by shear thinning, or strongly elastic and dominated by elastic stresses. A lubrication analysis yields a thin-film equation which characterizes the film thickness as a function of spatial position. The rheological properties of the test fluids are measured independently using steady and oscillatory shearing deformations. The viscometric parameters are then used, in conjunction with the governing thin-film equation, which is solved using matched asymptotics, to give a quantitative prediction of the thickness of the fluid coating. The onset of an instability which causes the film thickness to vary with axial position along the roller is also observed experimentally.

41 citations


Journal ArticleDOI
TL;DR: In this article, the basic problems arising in the analysis of conservation laws with discontinuous flux are discussed, and the contributions of the Special Issue are presented. And the basic problem considered in the eight contributions of this special issue is discussed.
Abstract: Conservation laws with discontinuous flux have attracted recent attention both due to their numerous applications and the intriguing theoretical challenges raised by their well-posedness and numerical analysis. This introductory note states the basic problem considered in the eight contributions of this Special Issue. Three different types of applications are surveyed where these equations appear, motivated by spatially heterogeneous physical models, adjoint problems for parameter identification, and numerical methods for systems of conservation laws, respectively. Basic problems arising in the analysis of these equations are discussed, and the contributions of the Special Issue are presented.

38 citations


Journal ArticleDOI
TL;DR: In this article, an analytical approach to solve plane static non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders is presented.
Abstract: An analytical approach to solve plane static non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders is presented. This approach is based upon the direct integration method proposed by Vihak (Vigak). The essence of the method mentioned is in the integration of the original differential equilibrium equations, which are independent of the stress–strain relations. This gives the opportunity to deduce the relations, which are invariant with respect to various properties of the material, for the stress-tensor components. From these relations each of the stress-tensor components have been expressed in terms of the governing one. A solution of the equation for the governing stress in the form of Fourier series is presented. To determine the Fourier coefficients, an integral Volterra-type equation is derived and solved by a simple iteration method with rapid convergence. Other stress-tensor components are expressed through the obtained governing stress in the form of an explicit functional dependence on force and thermal loadings.

38 citations


Journal ArticleDOI
TL;DR: An analysis of the mapping properties of three commonly used domain integro-differential operators for electromagnetic scattering by an inhomogeneous dielectric object embedded in a homogeneous background is presented in this paper.
Abstract: An analysis of the mapping properties of three commonly used domain integro-differential operators for electromagnetic scattering by an inhomogeneous dielectric object embedded in a homogeneous background is presented in the Laplace domain. The corresponding three integro-differential equations are shown to be equivalent and well-posed under finite-energy conditions. The analysis allows for non-smooth changes, including edges and corners, in the dielectric properties. The results are obtained via the Riesz-Fredholm theory, in combination with the Helmholtz decomposition and the Sobolev embedding theorem.

36 citations


Journal ArticleDOI
TL;DR: The reservoir pressure concept showed large similarities to the classical 3-element windkessel model, especially in subjects characterized by a high reflection magnitude and high “windkesselness” of their arterial system, when applied to the Asklepios population.
Abstract: Traditionally the arterial system is either modeled as a lumped-parameter windkessel or a wave system. Recently, a hybrid model has been proposed in which the arterial system is considered to be a reservoir allowing for superimposed wave phenomena. This approach was applied to non-invasively obtained carotid pressure waveforms from 2019 subjects from the Asklepios population to investigate the contribution of reservoir pressure (PP res,WS) to carotid pulse pressure (PP car) with age and gender. Additionally, reservoir pressures were compared to the reservoir pressure (PP res,WK) obtained from a 3-element windkessel model. PP res,WK and PP res,WS were determined by applying a 3-element windkessel model and the wave separation model to scaled carotid artery tonometry readings. The evolution of PP car, PP res,WK and PP res,WS was examined for men and women after stratification into age quartiles. PP car increased with age regardless of sex, but was more pronounced in women, with significant (P < 0.001) age–gender interaction. PP res increases with age (P < 0.001), regardless of the model used for its determination, but more significantly for women. In men it only increases markedly in the oldest age group. Overall, the reservoir pressure concept showed large similarities to the classical 3-element windkessel model, especially in subjects characterized by a high reflection magnitude and high “windkesselness” of their arterial system. When applied to the Asklepios population, both models show the increase of pulse pressure with age to be largely due to increasing reservoir pressures.

35 citations


Journal ArticleDOI
TL;DR: In this paper, a multi-component, multi-phase flow model in a fibrous porous medium with phase change is proposed, which is a generalization of a single component model used in a previous study by taking the air resistance to moisture transport into account.
Abstract: In this paper, moisture transport in fibrous clothing assemblies is investigated in a one-dimensional setting A multi-component, multi-phase flow model in a fibrous porous medium with phase change is proposed The model is a generalization of a single-component model used in a previous study by taking the air resistance to moisture transport into account Capillary effect on liquid water motion is also included in the model Using dimensional analysis, it is shown that there exist several different time scales As a result, the fast-scale moisture transport is coupled with the energy equation while accumulation of liquid water in the pore and absorption of water by the fibers occur at slower time scales By exploring scale separation, computations can be greatly simplified by decoupling these physical processes An efficient semi-implicit numerical scheme is proposed for solving the gas (vapor and air) and energy equations, while the water equations are solved separately At the time scale of experimental measurement, a quasi-steady approximate solution is also derived for gas concentration and temperature as a benchmark for numerical computation Qualitative comparison between the numerical solutions and experimental measurements are also given The results show that the new multi-component model proposed in this study gives a better prediction of total water accumulation near the outer boundary of the clothing assemblies

34 citations


Journal ArticleDOI
Stefan Diehl1
TL;DR: In this paper, a nonlinear regulator for the continuous-sedimentation process in a clarifier-thickener unit is presented. But the model is a scalar hyperbolic conservation law with space-discontinuous flux function and point source.
Abstract: The purpose of this paper is to present a regulator for control of the continuous-sedimentation process in a clarifier–thickener unit when this is modelled in one space dimension and when the settling properties of the solids obey Kynch’s assumption. The model is a scalar hyperbolic conservation law with space-discontinuous flux function and point source. The most desired type of solution contains a large discontinuity. A common objective is to control the movement of this discontinuity subject to the requirement that the effluent of the process have zero concentration of particles. In addition, there may be a requirement that the underflow concentration of the thickened suspension lie above a predefined value. Based on previous results on the nonlinear behaviour of the process, a nonlinear regulator is presented. It controls the location of the large discontinuity indirectly by controlling the total mass. The process is stabilized significantly and large input oscillations can be handled.

Journal ArticleDOI
TL;DR: In this paper, the effects of the extension-twist elastic coupling in conjunction with the volume fraction of the two constituent phases and of the thermal degradation of material properties on eigenfrequencies are discussed.
Abstract: Problems involving the modeling and free vibration of pre-twisted rotating blades made of functionally graded materials (FGMs) and operating in a high-temperature field are considered. The blade, mounted on a rigid hub, is modeled as a thin-walled beam that incorporates the warping restraint and the pre-twist effects. As a result of the latter feature, an extension-twist elastic coupling is induced. Consistent with the concept of the FGM structures, the two constituent materials, ceramic and metal, experience a continuous variation across the beam wall thickness, and, as a result, the adverse effects featured by the standard laminated structures, such as delamination/debonding, are precluded to occur. Numerical results highlighting the effects of the extension-twist elastic coupling considered in conjunction with the volume fraction of the two constituent phases and of the thermal degradation of material properties on eigenfrequencies are presented, and pertinent conclusions are outlined. Comparisons of predictions, as well as validations of results against those obtained in some special cases, which are available in the specialized literature, are also supplied. In addition to a better understanding of the implication of incorporation of FGMs, the results of this research can be instrumental toward the reliable design of advanced turbomachinery blades that operate in a high-temperature environment.

Journal ArticleDOI
TL;DR: In this article, the properties of a three-dimensional shear flow overpassing a hemispherical droplet resting on a plane wall are investigated and the exact solution is computed as a function of the viscosity ratio between the droplet and the surrounding fluid.
Abstract: The properties of a three-dimensional shear flow overpassing a hemispherical droplet resting on a plane wall are investigated. The exact solution is computed as a function of the viscosity ratio between the droplet and the surrounding fluid and generalizes the solution for the hemispherical no-slip bump given in an earlier paper by Price (QJMAM (1985) 38: 93–104). Several expressions, including the torque and the force acting on the drop, are considered as well as the importance of the deformations on the surface for small capillary numbers.

Journal ArticleDOI
TL;DR: In this article, the interaction of large-amplitude water waves with a compliant floating raft such as a sea-ice floe or a pontoon-type VLFS is considered.
Abstract: The interaction of large-amplitude water waves with a compliant floating raft such as a sea-ice floe or a pontoon-type VLFS (very large floating structure) is considered. The solution is expressed as a series using a perturbation expansion, the first two components of which are solved inductively using a boundary-integral method. The primary interest of this paper is to the ways in which the second-order potential can be modified in order to apply the boundary-integral method and to the comparison of results with those derived using eigenfunction matching methods.

Journal ArticleDOI
TL;DR: In this paper, the authors derived new fundamental solutions for micropolar fluids in explicit form for two-and three-dimensional steady unbounded Stokes and Oseen flows due to a point force and a point couple.
Abstract: New fundamental solutions for micropolar fluids are derived in explicit form for two- and three-dimensional steady unbounded Stokes and Oseen flows due to a point force and a point couple, including the two-dimensional micropolar Stokeslet, the two- and three-dimensional micropolar Stokes couplet, the three-dimensional micropolar Oseenlet, and the three-dimensional micropolar Oseen couplet. These fundamental solutions do not exist in Newtonian flow due to the absence of microrotation velocity field. The flow due to these singularities is useful for understanding and studying microscale flows. As an application, the drag coefficients for a solid sphere or a circular cylinder that translates in a low-Reynolds-number micropolar flow are determined and compared with those corresponding to Newtonian flow. The drag coefficients in a micropolar fluid are greater than those in a Newtonian fluid.

Journal ArticleDOI
TL;DR: A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux using the Engquist–Osher approximation for the flux and explicit time-stepping is presented.
Abstract: A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the Engquist-Osher approximation for the flux and explicit time-stepping. An adaptive multiresolution scheme with cell averages is then used to speed up CPU time and meet memory requirements. A particular feature of our scheme is the storage of the multiresolution representation of the solution in a dynamic graded tree, for the sake of data compression and to facilitate navigation. Applications to traffic flow with driver reaction and a clarifier-thickener model illustrate the efficiency of this method.

Journal ArticleDOI
TL;DR: In this article, the evolution of a characteristic shock in a relaxing gas is investigated and its interaction with a weak discontinuity is studied, where a particular solution to the governing system, which exhibits space-time dependence, is used to study the evolutionary behaviour of the characteristic shock; the properties of incident, reflected and transmitted waves, influenced by the relaxation mechanism, together with the geometry of the fluid flow and the background state at the rear of the shock, are studied.
Abstract: The evolution of a characteristic shock in a relaxing gas is investigated and its interaction with a weak discontinuity is studied. A particular solution to the governing system, which exhibits space–time dependence, is used to study the evolutionary behaviour of the characteristic shock; the properties of incident, reflected and transmitted waves, influenced by the relaxation mechanism, together with the geometry of the fluid flow and the background state at the rear of the shock, are studied.

Journal ArticleDOI
TL;DR: In this article, the geometry and kinematics of one-parameter dual spherical motions are presented using Study's dual-line coordinates, and the relations between invariants of the axodes are expressed in simple form with geometrical reasoning and explanation.
Abstract: The geometry and kinematics of one-parameter dual spherical motions is presented using Study’s dual-line coordinates. The relations between invariants of the axodes are expressed in simple form with geometrical reasoning and explanation. In terms of this, the dual version of associated space curves is demonstrated for a ruled surface to be associated with the axodes of the motion. The relative motion between the axodes is used for deriving the geometry and kinematics of the paths instantaneously traced in the fixed space by a line associated with the moving axode. Especially, the distribution parameter and the inflection-line congruence are investigated. Furthermore, a new metric is developed and used to investigate the geometrical properties and kinematics of line trajectory as well as Disteli axis. Finally, as an application an example is put forward and explained in detail.

Journal ArticleDOI
TL;DR: In this paper, the boundary conditions in one-dimensional transient inverse heat-conduction problems (IHCP) are represented by linear relations between the temperature and the heat flux, together with an initial condition as a function of space.
Abstract: The restoration of boundary conditions in one-dimensional transient inverse heat-conduction problems (IHCP) is described. In the formulation, the boundary conditions are represented by linear relations between the temperature and the heat flux, together with an initial condition as a function of space. The temperature inside the solution domain, together with the space or time-dependent ambient temperature of the environment surrounding the heat conductor, are found from additional boundary-temperature or average boundary-temperature measurements. Numerical results obtained using the boundary-element method are presented and discussed.

Journal ArticleDOI
TL;DR: In this paper, simple formulae for the components of the added-mass coefficient tensor of a sphere moving near a wall with variable velocity in an ideal fluid bounded by a solid surface are derived.
Abstract: Simple formulae for the components of the added-mass coefficient tensor of a sphere moving near a wall with variable velocity in an ideal fluid bounded by a solid surface are derived. The added mass is calculated numerically as a function of the dimensionless distance between the sphere and the wall for both perpendicular and parallel motions. The calculation is performed by the method of successive images. The velocity field is computed as the sum of the velocity fields of sequences of dipoles located along the axis. The obtained dependences of the added-mass tensor components are fitted by simple continuous functions with high accuracy.

Journal ArticleDOI
TL;DR: In this paper, the authors considered the problem of the motion of an irrotational incompressible fluid driven by an assembly of stirrers, of arbitrary shape, moving at specified velocities in the fluid.
Abstract: The motion of an irrotational incompressible fluid driven by an assembly of stirrers, of arbitrary shape, moving at specified velocities in the fluid is considered. The problem is shown to be equivalent to a standard mathematical problem in potential theory known as the modified Schwarz problem. It turns out that the solution to this problem can be written down, in closed form, as an explicit integral depending on the conformal mapping to the fluid region from a canonical pre-image region and a kernel function expressed in terms of a transcendental function called the Schottky–Klein prime function. In this way, an explicit integral solution, up to conformal mapping, for the complex potential of the flow generated by an arbitrary assembly of stirrers can be written down.

Journal ArticleDOI
TL;DR: In this article, complete dynamical PDE systems of one-dimensional nonlinear elasticity satisfying the principle of material frame indifference are derived in Eulerian and Lagrangian formulations.
Abstract: Complete dynamical PDE systems of one-dimensional nonlinear elasticity satisfying the principle of material frame indifference are derived in Eulerian and Lagrangian formulations. These systems are considered within the framework of equivalent nonlocally related PDE systems. Consequently, a direct relation between the Euler and Lagrange systems is obtained. Moreover, other equivalent PDE systems nonlocally related to both of these familiar systems are obtained. Point symmetries of three of these nonlocally related PDE systems of nonlinear elasticity are classified with respect to constitutive and loading functions. Consequently, new symmetries are computed that are: nonlocal for the Euler system and local for the Lagrange system; local for the Euler system and nonlocal for the Lagrange system; nonlocal for both the Euler and Lagrange systems. For realistic constitutive functions and boundary conditions, new dynamical solutions are constructed for the Euler system that only arise as symmetry reductions from invariance under nonlocal symmetries.

Journal ArticleDOI
Stefan Diehl1
TL;DR: The nonlinear behavior of a one-dimensional idealized model of continuous sedimentation has been investigated in this series of papers as discussed by the authors, where the model is a scalar hyperbolic conservation law with a space-discontinuous flux function and a point source.
Abstract: The nonlinear behaviour of a one-dimensional idealized model of continuous sedimentation has been investigated in this series of papers. The model is a scalar hyperbolic conservation law with a space-discontinuous flux function and a point source. Parameters in the equation are the two input variables (concentration and flux) and the control variable (a volume flow). The most desired type of solution contains a large concentration discontinuity and is referred to as ‘optimal operation’. Operating charts (concentration-flux diagrams) have proved to be a means for classifying the nonlinear behaviour. In this paper, some fundamental results on the dynamic behaviour are presented, which give information on the limitations of the range of the control variable. When this is used together with the previously introduced optimal control strategies for step inputs, the process can be controlled.

Journal ArticleDOI
TL;DR: In this article, a general formulation for the flow of a Newtonian fluid over manifolds with curvature is presented. But it is only applicable to flows that conserve a general volume: Riemannian or otherwise.
Abstract: The main purpose of the present work is the development of a general formulation for the flow of a Newtonian fluid over manifolds with curvature. The novel formulation includes an explicit contribution of the Ricci curvature in the diffusion of momentum and is applicable to flows that conserve a general volume: Riemannian or otherwise. The general solution of the Stokes flow on a sphere and the associated Stokeslet are also computed.

Journal ArticleDOI
TL;DR: In this article, the flow of two superposed viscous fluid layers in a two-dimensional channel confined between a plane and a wavy or indented wall is studied by analytical and numerical methods at arbitrary Reynolds numbers.
Abstract: The flow of two superposed viscous fluid layers in a two-dimensional channel confined between a plane and a wavy or indented wall is studied by analytical and numerical methods at arbitrary Reynolds numbers. The interface between the two fluids may exhibit constant or variable surface tension due to an insoluble surfactant. The flow is computed from a specified initial condition using the immersed-interface method on a curvilinear grid constructed by conformal mapping. The numerical simulations illustrate the effect of geometrical nonlinearity and reveal that inertia may increase or decrease the amplitude of the interface profile at steady state depending on the flow parameters. Increasing either the Reynolds number or the wall amplitude above a certain threshold value provokes flow instability and overturning of the interface. In the Appendix, a linear perturbation analysis is performed for arbitrary Reynolds numbers on the assumption of small-amplitude sinusoidal undulations, and results for the amplitude and phase shift of the interfacial and surfactant concentration wave are documented for a broad range of flow conditions. It is found that inertia may have a mixed effect on the deformation and phase shift, while the surfactant promotes the deformation of the interface under most conditions.

Journal ArticleDOI
TL;DR: In this paper, the transformation of flexural gravity waves due to wave scattering by heterogeneous boundaries is investigated under the assumption of the linearized water-wave theory, and explicit relations for the shoaling and scattering coefficients due to the change in water depth and heterogeneous ice-sheet are derived.
Abstract: The transformation of flexural gravity waves due to wave scattering by heterogeneous boundaries is investigated under the assumption of the linearized water-wave theory. The heterogeneous boundaries include step-type bottom topography as well as heterogeneity in the material property of a floating ice-sheet. By applying the generalized expansion formulae along with the corresponding orthogonal mode-coupling relations, the boundary-value problem (BVP) is reduced to linear system of algebraic equations. The system of equations is solved numerically to determine the full solution of the problem under consideration. Energy relations are derived and used to check the accuracy of the computational results of the scattering problem. Explicit relations for the shoaling and scattering coefficients due to the change in water depth and heterogeneous ice-sheet are derived. These derivations are based on the law of conservation of energy flux under the assumptions of the linearized shallow-water theory. The change in water depth and the structural characteristics of the medium significantly contribute to the change in the scattering and shoaling coefficients and the deflection of the structure. The present results are likely to play a significant role in the analysis of flexural gravity-wave propagation in problems of variable topography for which a direct computational approach is being utilized.

Journal ArticleDOI
TL;DR: In this article, the stability of two-layer eccentric annular Hele-Shaw flows is analyzed using a transient version of the usual HeleShaw approach, in which fluid acceleration terms are retained.
Abstract: Primary-cementing displacement flows occur in long narrow eccentric annuli during the construction of oil and gas wells. A common problem is that the displacing fluid fingers up the upper wide side of the annulus, leaving behind a “mud channel” of displaced fluid on the lower narrow side of the annulus. Tehrani et al. report that the interface between displacing fluid and mud channel can in certain circumstances become unstable, and a similar phenomenon has been observed in our ongoing experiments. Here an explanation for these instabilities is provided via analysis of the stability of two-layer eccentric annular Hele-Shaw flows, using a transient version of the usual Hele-Shaw approach, in which fluid acceleration terms are retained. Two Newtonian fluids are considered, as a simplification of the general case in which the fluids are shear-thinning yield-stress fluids. It is shown that negative azimuthal buoyancy gradients are in general stabilizing in inclined wells, but that buoyancy may also have a destabilizing effect via axial buoyancy forces that influence the base-flow interfacial velocity. In a variety of special cases where buoyancy is not dominant, it is found that instability is suppressed by a positive product of interfacial velocity difference and reduced Reynolds-number difference between fluids. Even a small positive azimuthal buoyancy gradient, (heavy fluid over light fluid), can be stabilized in this way. Eccentricity of the annulus seems to amplify the effect of buoyancy on stability or instability, e.g. stably stratified fluid layers become more stable as the eccentricity is increased.

Journal ArticleDOI
TL;DR: In this article, the authors present the formulation and analysis of composite plates serving as STATs, i.e., spatially tailored advanced thermal structures where the distribution of the constituent phases varies throughout the surface as well as through the thickness.
Abstract: The paper presents the formulation and analysis of composite plates serving as STATs, i.e., spatially tailored advanced thermal structures where the distribution of the constituent phases varies throughout the surface as well as through the thickness. This is an extension of the well-known concept of functionally graded materials (FGM) and structures with the constituent phases varying only in the latter direction. As a result of two- or three-dimensional grading it is possible to optimize the response and properties of the structure providing multitask and multi-scale optimization. The response of plates with two- or three-dimensional grading to an arbitrary thermal loading is elucidated, including the conditions that result in thermal bending versus thermal instability.

Journal ArticleDOI
TL;DR: In this article, the mass burning rate was derived from a recently introduced flamelet model using integral analysis and compared with well-known expressions based on large activation energy asymptotics.
Abstract: New expressions for the mass burning rate are derived from a recently introduced flamelet model using integral analysis The results are compared with well-known expressions, based on large-activation-energy asymptotics There is no restriction on Lewis numbers and the expressions reduce to the same results as found earlier with asymptotic techniques for Lewis numbers close to 1 From our analysis it appears that the burned edge of a stretched flamelet is most appropriate to determine the mass burning rate The consequences for experimental and numerical studies are investigated

Journal ArticleDOI
TL;DR: In this article, an effective method of modeling the presence of thin inclusions of arbitrary physical nature in bodies is discussed, using this method, the plane thermoelastic problem for two bounded dissimilar semi-planes with thin heat-active interface inclusions is reduced to two separate systems of singular integral equations.
Abstract: An effective method of modeling the presence of thin inclusions of arbitrary physical nature in bodies is discussed. Using this method, the plane thermoelastic problem for two bounded dissimilar semi-planes with thin heat-active interface inclusions is reduced to two separate systems of singular integral equations. The concept of generalized stress-intensity factors is introduced and their dependence on the material characteristics and several methods of thermal loading are analyzed.