Wavy Boundary Research Articles

The Isothermal Transformation of Low-Alloy Low-C CMnSi Steels below M<sub>S</sub>

An isothermal transformation was observed when a low-alloy, low-carbon steel was quenched and held in the MS–Mf temperature range after austenitized above A3. The precise nature of this isothermal transformation is still unclear. The present contribution is a comprehensive comparison using EBSD, internal friction (IF) and TEM analysis of the isothermal transformation product, the athermal martensite and the lower bainite. The observations revealed that the isothermal transformation product in the MS-Mf temperature range had its own microstructural characteristics with wavy lath boundaries and orientation relationship.

Microstructure of Interfacial Region Between Cold-Sprayed Copper Coating and AlN Substrate Coated with Sputtered Titanium and Copper

Cold spraying has been developed as a high-quality coating technique. In this article, copper is deposited on an AlN substrate coated by the sputtering of titanium and copper at a low pressure of less than 1.0 MPa, making this approach suitable for a wide range of engineering applications. In order to understand the adhesion mechanism at the atomic scale, the interfacial regions are carefully observed in thin foil samples from the cross sections of the specimens with a HREM. We find a unique wavy boundary between the sputtered titanium and the sputtered copper. It is assumed that the shear-instability phenomenon occurs due to the cold-spraying process and influences the adhesive strength. Furthermore, the cold-sprayed copper particles are connected directly without any oxidation layer due to the appearance of new metallic surfaces during the impact process. The TEM data clearly reveal the phenomena and mechanisms related to the impact of powder sprayed on the substrate.

Implicit formulation with the boundary element method for nonlinear radiation of water waves

An accurate and efficient numerical method is presented for the two-dimensional nonlinear radiation problem of water waves. The wave motion that occurs on water due to an oscillating body is described under the assumption of ideal fluid flow. The governing Laplace equation is effectively solved by utilizing the GMRES (Generalized Minimal RESidual) algorithm for the boundary element method (BEM) with quadratic approximation. The intersection or corner singularity in the mixed Dirichlet–Neumann problem is resolved by introducing discontinuous elements. The fully implicit trapezoidal rule is used to update solutions at new time-steps, by considering stability and accuracy. Traveling waves generated by the oscillating body are absorbed downstream by the damping zone technique. To avoid the numerical instability caused by the local gathering of grid points, the re-gridding technique is employed, so that all the grids on the free surface may be re-distributed with an equal distance between them. The nonlinear radiation force is evaluated by means of the acceleration potential. For a mixed Dirichlet–Neumann problem in a computational domain with a wavy top boundary, the present BEM yields numerical solutions for the quadratic rate of convergence with respect to the number of boundary elements. It is also demonstrated that the present time-marching and radiation condition work successfully for nonlinear radiation problems of water waves. The results obtained from this study concur reasonably well with other numerical computations.

The oscillations of layered elastic media with a wavy boundary

Block element methods are used to investigate the oscillations of an elastic layer with a rough surface. For simplification, the investigation is carried out separately for the rotational and potential components of the boundary-value problem, which enables the solution to be obtained by analysing Helmholtz's equations.

The ω-phase formation in titanium upon deformation under pressure

The ω-phase formation in titanium of the VT1-00 grade upon deformation under pressure has been investigated by X-ray diffraction analysis and diffraction electron microscopy. The deformation was effected by two methods: shear under a pressure of 6 GPa in Bridgman anvils and high-strain-rate equal-channel angular pressing at a pressure of about 2 GPa. Upon deformation under a pressure of 6 GPa, the ω phase is formed as grains that are isolated or clustered into groups. Upon deformation at a pressure of 2 GPa, this phase arises in the form of nanosized particles that are orientationally related to the α phase. After deformation by shear under pressure using one revolution of the anvils, new grains of the α phase up to 2–3 μm in size have been detected. The grains are nearly free of dislocations and have wavy boundaries. The origin of these grains is tracealle the reverse ω → α phase transformation that takes place upon pressure release and occurs via the “normal” rather than martensitic mechanism, at the expense of migration of the inter-phase boundaries. Upon heating, the reverse ω → α transformation at 100°C does not yet begin, whereas at 220°C the transformation proceeds almost completely. A temperature distribution in the titanium sample upon shear under pressure at a rate of 0.3 rpm has been calculated; according to this distribution, the maximum temperature rise is 12 K.

J0401-1-3 コールドスプレー粒子/基材界面の微細組織観察([J0401-1]固相粒子成膜技術とその応用(1):粒子付着因子の検討)

Cold spraying has been developed as a high-quality coating process. However, the bonding mechanisms of cold sprayed solid particles have not been clarified yet. In this study, copper particles were deposited on an aluminum nitride substrate coated by the sputtering of copper and titanium at a low pressure of less than 1.0 MPa, making this approach suitable for a wide range of engineering applications. The interfacial boundaries were carefully observed in thin foils from the cross sections of the specimen with a high-resolution transmission electron microscope (TEM). The cold-sprayed copper particles are connected directly without any oxidation film due to the appearance of new metallic surfaces. A wavy boundary was observed between cold-sprayed copper and the substrate, as seen in the joint boundary by explosive welding, which is caused by shear instability. TEM data clearly revealed some phenomena related to the impact of spraying powder toward the substrate.

Lagrangian drift near a wavy boundary in a viscous oscillating flow

The formation of sand ripples in oscillating flows is thought to be due to a steady streaming current which near the bottom is towards the crests. We present quantitative observations of this mean flow over self-formed and artificial ripples, by observing the displacement of a coloured filament after a number of oscillations in the simple situation of viscous Couette flow. Confusingly, the filament moves in the ‘wrong’ direction, because it follows the Lagrangian mean flow. We calculate the Lagrangian mean flow. A complication is that the amplitudes of the oscillations in the experiments are not small. We compare the predictions with the experimental observations of displacements of the filament, showing good agreement.

Observations of Turbulence in the Ocean Surface Boundary Layer: Energetics and Transport

AbstractObservations of turbulent kinetic energy (TKE) dynamics in the ocean surface boundary layer are presented here and compared with results from previous observational, numerical, and analytic studies. As in previous studies, the dissipation rate of TKE is found to be higher in the wavy ocean surface boundary layer than it would be in a flow past a rigid boundary with similar stress and buoyancy forcing. Estimates of the terms in the turbulent kinetic energy equation indicate that, unlike in a flow past a rigid boundary, the dissipation rates cannot be balanced by local production terms, suggesting that the transport of TKE is important in the ocean surface boundary layer. A simple analytic model containing parameterizations of production, dissipation, and transport reproduces key features of the vertical profile of TKE, including enhancement near the surface. The effective turbulent diffusion coefficient for heat is larger than would be expected in a rigid-boundary boundary layer. This diffusion coefficient is predicted reasonably well by a model that contains the effects of shear production, buoyancy forcing, and transport of TKE (thought to be related to wave breaking). Neglect of buoyancy forcing or wave breaking in the parameterization results in poor predictions of turbulent diffusivity. Langmuir turbulence was detected concurrently with a fraction of the turbulence quantities reported here, but these times did not stand out as having significant differences from observations when Langmuir turbulence was not detected.

Effect of Aluminum and Nitrogen on Microstructure of Ultra-Low-Carbon Nb-IF Steels

The effect of aluminum and nitrogen on the microstructure of the ultra-low-carbon Nb-IF (interstitial free) steel was investigated. Steel with higher aluminum and nitrogen contents showed equiaxed ferrite grains in the hot-rolled steel and continuously annealed steel. Decrease in either aluminum or nitrogen content, however, resulted in the mixed microstructure of small and large grains with wavy grain boundaries in the hot-rolled steel and the pancake-shaped ferrite grains in the continuously annealed steel.

The effects of Prandtl number on wavy weld boundary

The effects of Prandtl number on two-dimensional thermocapillary convection and molten pool shape induced by negative surface tension coefficient in welding or melting with a time-dependent and distributed incident flux are numerically predicted in this study. This work is also applicable for predicting the quasi-steady three-dimensional thermocapillary convection. In this model, the time-dependent incident flux is specified as a function of scanning speed and energy distribution parameter. The computed flow patterns and molten pool shapes under the flat free surface are found to have distinct regions for different Marangoni and Prandtl numbers. Prandtl number indicates the thickness ratio between momentum and thermal boundary layers, whereas Marangoni number with negative surface tension coefficient induces an outward surface flow. Rather than the enhanced pool depth resulted from melting from an induced vortex cell near the bottom in the case of Prandtl number much less than unity, the molten pool shape for Prandtl number much greater than unity can produce a thin and narrow edge. The variations of Peclet number and dimensionless beam power with flow and temperature fields and fusion zone shapes are similar. The dimensionless peak surface speed versus product of Marangoni and Prandtl number, which involve predicted peak speed and temperature and molten pool width on the surface, agree with scale analysis and experimental data provided in the literature.

Origin of wavy weld boundary

In conduction mode laser welding, the shape of the fusion boundary affects the solidification process, microstructure, and properties of the weld. Although significant progress has been made in the calculations of the shape and size of the fusion zone in recent decades, the conditions for the formation of the wavy fusion boundary are still not well understood. Here we examine the conditions for its formation in terms of important dimensionless numbers. In particular, the computed flow patterns, temperature fields, and molten pool shapes under the flat free surface are examined for various values of Marangoni, Prandtl, Peclet, and dimensionless heat input values. In the absence of electromagnetic force, it is shown that the wavy fusion boundary forms for specific ranges of Marangoni and Prandtl numbers.

Onset of wavy vortices in Taylor-Couette flow with imperfect reflection symmetry

We reveal experimentally a mechanism that alters the critical behavior of a Hopf bifurcation substantially due to the presence of imperfections of the reflection symmetry in a hydrodynamic system. The onset of rotating waves in Taylor vortex flow, which is widely considered as a "classical" example for a Hopf bifurcation in hydrodynamics, is investigated primarily by transient response experiments. While wavy vortex flow is not influenced by such (unavoidable) experimental imperfections, the critical behavior of the axially subharmonic rotating wave with wavy outflow boundaries, also called the small-jet mode, is qualitatively altered. Experimental evidence is provided that the modified critical behavior at the Hopf bifurcation is associated with imperfections of the reflection symmetry of the Taylor-Couette setup. The experimental results on Hopf bifurcation are discussed in the context of a cusp-Hopf bifurcation model recently proposed by Harlim and Langford [Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, 2547 (2007)] and compared to experimental results on imperfect pitchfork bifurcation in small-aspect ratio Taylor-Couette flow.

Unusual wavy weld pool boundary from dimensional analysis

The geometry of a weld pool affects its solidification behavior. Here we show that the welding parameters and material properties responsible for the formation of unusual, wavy fusion boundaries can be identified from heat and fluid flow calculations and confirmed by independent experiments. These parameters and properties can be expressed by dimensionless numbers using the Buckingham π-theorem. The wavy boundary originates from the interaction of counter-rotating liquid metal loops at high Marangoni numbers. The Prandtl number affects the type of inflection.

Direct Mapping of Magnetoresistance to Magnetic Domain Image in Permalloy Thin Films by Simultaneous Measurement

We report the rst simultaneous measurements of the magnetoresistance (MR) and the magnetic domain images in two-dimensional permalloy thin lms by utilizing a magneto-optic magnetic microscope. In this way, we could directly map the MR to the domain patterns without any ambiguity. For 30-nm-thick permalloy lms with in-plane uniaxial magnetization, negative MR was observed when the domain wall was nucleated. An analysis of the MR change with the anisotropic magnetoresistance resulted in a rather large domain wall thickness of 1.7 m compared to the well-known theoretical value of 0.3 m. We discuss possible origins of this discrepancy in terms of wide domain tails, wavy domain boundaries, and intrinsic properties associated with permalloy. This new method can be utilized to investigate the magnetic properties of newly emergent materials.

A vertical dispersion model for solute exchange induced by underflow and periodic hyporheic flow in a stream gravel bed

Interstitial flows in stream gravel beds are driven by stream slope and controlled by hydraulic conductivity (underflows) or induced by pressure differentials on the streambed surface (hyporheic flows). They enhance solute exchange between surface water and a streambed. To study the solute transport in a stream gravel bed, a 2‐D transient advection–dispersion mass transfer model was formulated. The velocity field includes an underflow and a spatially periodic hyporheic flow, e.g., due to standing surface waves or bed forms. Two dimensionless scaling parameters emerged: R measures the relative strength of hyporheic flow to underflow in the streambed and λ is the ratio of dispersivity of the gravel bed to the pressure wavelength along the streambed. In the analysis of mass transfer of nonconservative substances into a streambed, an explicit 2‐D analysis of interstitial flow is often undesirable. Therefore the numerical solutions for the 2‐D concentration fields under periodic boundary conditions were reduced to 1‐D vertical concentration profiles (by streamwise averaging of the solute concentrations). The profiles were matched to the solution of an unsteady vertical 1‐D dispersion equation that introduces a depth variable “enhanced dispersion coefficient DE(y)” that lumps all forms of interstitial advective and dispersive transport in the streambed. Functions DE(y) were determined for many combinations of independent parameters by inverse modeling, and the dependence of DE(y) on the dimensionless parameters R and λ was determined from these results. Analytical relationships for DE(y, R, λ) have been proposed and validated against available experimental data. Knowledge of DE(y) allows the estimation of solute/mass transfer rates in streambeds under wavy boundary conditions, without explicit analysis of the interstitial flow. This is a distinct advantage for applications in stream water quality and/or pore water quality studies.

Structure of martensite in Ti-rich Ti–Ni–Cu thin films annealed at different temperatures

After annealing at different temperatures, there are different types of precipitates in Ti-rich Ti–Ni–Cu thin films: plate-like Guinier–Preston (GP) zones, Ti 2Cu precipitates and spherical Ti 2Ni precipitates. The (0 1 1) compound twins and (1 1 1) type I twins are dominant in Ti-rich Ti–Ni–Cu thin films annealed at different temperatures, which suggests that the precipitates do not change the twinning modes of the B19 martensite. However, the amount of the (0 1 1) compound twin increases with increasing annealing temperature due to its small twinning shear. In thin films with GP zones or Ti 2Ni precipitates, the amount of martensite with a single-pair morphology is less than that in thin films without precipitates. And in thin film with Ti 2Cu + Ti 2Ni precipitates, hardly any martensite with a single-pair morphology is observed. For the different types of precipitates at the different annealing temperatures, the obstacle of the precipitates to the growth of the B19 martensite plate also varies. The GP zones slightly hinder the growth in the width of martensite, resulting in wavy twin boundaries at the martensite variant tip. The Ti 2Cu precipitates can change both the width and the direction of the martensite plates. Ti 2Ni precipitates also significantly disturb or impede the growth of the martensite variants. These effects lead to a decrease in the maximum shape recoverable strain with increasing annealing temperature.

Semi‐coupled air/water immersed boundary approach for curvilinear dynamic overset grids with application to ship hydrodynamics

AbstractFor many problems in ship hydrodynamics, the effects of air flow on the water flow are negligible (the frequently called free surface conditions), but the air flow around the ship is still of interest. A method is presented where the water flow is decoupled from the air solution, but the air flow uses the unsteady water flow as a boundary condition. The authors call this a semi‐coupled air/water flow approach. The method can be divided into two steps. At each time step the free surface water flow is computed first with a single‐phase method assuming constant pressure and zero stress on the interface. The second step is to compute the air flow assuming the free surface as a moving immersed boundary (IB). The IB method developed for Cartesian grids (Annu. Rev. Fluid Mech. 2005; 37:239–261) is extended to curvilinear grids, where no‐slip and continuity conditions are used to enforce velocity and pressure boundary conditions for the air flow. The forcing points close to the IB can be computed and corrected under a sharp interface condition, which makes the computation very stable. The overset implementation is similar to that of the single‐phase solver (Comput. Fluids 2007; 36:1415–1433), with the difference that points in water are set as IB points even if they are fringe points. Pressure–velocity coupling through pressure implicit with splitting of operators or projection methods is used for water computations, and a projection method is used for the air. The method on each fluid is a single‐phase method, thus avoiding ill‐conditioned numerical systems caused by large differences of fluid properties between air and water. The computation is only slightly slower than the single‐phase version, with complete absence of spurious velocity oscillations near the free surface, frequently present in fully coupled approaches. Validations are performed for laminar Couette flow over a wavy boundary by comparing with the analytical solution, and for the surface combatant model David Taylor Model Basin (DTMB) 5512 by comparing with Experimental Fluid Dynamics (EFD) and the results of two‐phase level set computations. Complex flow computations are demonstrated for the ONR Tumblehome DTMB 5613 with superstructure subject to waves and wind, including 6DOF motions and broaching in SS7 irregular waves and wind. Copyright © 2008 John Wiley & Sons, Ltd.

Ekman layers near wavy boundaries

We investigate the effect of boundary roughness on the dynamical properties of the flow in laminar Ekman boundary layers. The study considers wavy boundaries having both horizontal wavelength and vertical extent comparable in size with the boundary layer width. In the case of flat boundaries, Ekman layers are known to be active, i.e. to affect significantly the dynamics of the mainstream flow. We show how the layer modelling needs to be modified to account for such wavy boundaries. In particular, nonlinear terms enter the laminar description. This model can be linearized in the limit of small Reynolds numbers. The resulting equations are studied using both asymptotic expansions and full numerical simulations. We find that small-scale roughness significantly alters energy dissipation in the boundary layer. This can result in either a reduction or an increase of dissipation, depending on, in particular, the orientation of the mainstream flow with respect to boundary modulation. Agreement is obtained between theoretical and computational results.

Asymptotic homogenization model for generally orthotropic reinforcing networks in smartcomposite plates

A general three-dimensional micromechanical model pertaining to smart composite layerswith wavy boundaries is applied to the case of thin smart plates reinforced with a networkof generally orthotropic bars that may also exhibit piezoelectric behavior. The method usedfor the development of the structural model is that of asymptotic homogenization, whichreduces the original boundary value problem into a set of three decoupled problems, eachproblem being characterized by two differential equations. These three sets of differentialequations, referred to as ‘unit cell problems’, deal, independently, with the elastic,piezoelectric, and thermal expansion behavior of the network-reinforced smart compositeplates. The solution of the unit cell problems yields expressions for effective elastic,piezoelectric and thermal expansion coefficients which, as a consequence of theiruniversal nature, can be used to study a wide variety of boundary value problemsassociated with a smart structure of a given geometry. The model can be used tocustomize the effective properties of a smart structure by changing some materialor geometric parameters such as the size or nature of the reinforcements. Thedeveloped general methodology is applied to smart network-reinforced compositestructures with generally orthotropic reinforcements and actuators. As particularexamples, spatial rectangular, triangular, and rhombic smart network plates areanalyzed. The general orthotropy of materials is very important from the practicalviewpoint and this orthotropy makes micromechanical modeling significantlymore complex. In the limiting case of isotropic reinforcements and absence ofactuators, the above general orthotropic micromechanical model converges to resultsthat are consistent with those of previous models obtained by either asymptotichomogenization, or stress–strain relationships in the isotropic reinforcements.

STABILITY OF QUANTUM FLUIDS: WAVY INTERFACE EFFECT

A numerical investigation for the stability of the incompressible slip flow of normal quantum fluids (above the critical phase transition temperature) inside a microslab where surface acoustic waves propagate along the walls is presented. Governing equations and associated slip velocity and wavy interface boundary conditions for the flow of normal fluids confined between elastic wavy interfaces are obtained. The numerical approach is an extension (with a complex matrix pre-conditioning) of the spectral method. We found that the critical Reynolds number ( Re cr or the critical velocity) decreases significantly once the slip velocity and wavy interface effects are present and the latter is dominated ( Re cr mainly depends on the wavy interfaces).