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At least 37 records · Page 2

Measurement and analysis of grain boundary grooving by volume diffusion

Experimental measurements of isothermal grain boundary grooving by volume diffusion are carried out for Sn bicrystals in the Sn-Pb system near the eutectic temperature. The dimensions of the groove increase with a temporal exponent of 1/3, and measurement of the associated rate constant allows the determination of the product of the liquid diffusion coefficient D and the capillarity length Gamma associated with the interfacial free energy of the crystal-melt interface. The small-slope theory of Mullins is generalized to the entire range of dihedral angles by using a boundary integral formulation of the associated free boundary problem, and excellent agreement with experimental groove shapes is obtained. By using the diffusivity measured by Jordon and Hunt, the present measured values of Gamma are found to agree to within 5 percent with the values obtained from experiments by Gunduz and Hunt on grain boundary grooving in a temperature gradient.

Hardy, S. C.↗

Boundary-conforming mapping applied to computations of highly deformed solidification interfaces

A new boundary-conforming mapping is developed for the calculation of highly deformed cellular solidification interfaces in a model of directional solidification of a binary alloy. The mapping is derived through a variational formulation that is designed so that the grid penetrates the grooves between cells along the interface without causing a loss of ellipticity of the mapping equations. A finite element/Newton method is presented for simultaneous solution of the free boundary problem described by the solutal model of directional solidification and the mapping equations. Results are compared to previous calculations and demonstrate the importance of accurate representation of the interface shape for understanding the solution structure.

Tsiveriotis, K.↗

Nonlinear development and secondary instability of large-amplitude Goertler vortices in hypersonic boundary layers

The weakly nonlinear development of large-amplitude Goertler vortices in a small neighborhood of the neutral stability position given by the linear theory is considered. It is shown that if the basic state and the wall curvature satisfy a certain condition, the Goertler vortices will grow until they become so large as to drive a mean flow correction as large as the basic state. Attention is then given to the further downstream evolution of these large-amplitude vortices, and it is shown that the vortices have a triple layer structure which consists of a region of vortex activity bounded by two transition layers over which the amplitude of the harmonic part of the vortex decays to zero exponentially. The positions of the two transition layers are found to be governed by a free boundary problem, which is solved for a number of curvature distribution cases. The secondary instability of the two transition layers is investigated with respect to traveling waves which are pi/2 out of phase in the spanwise direction with the steady Goertler vortices.

Fu, Y.↗

Diffuse-Interface Methods in Fluid Mechanics

The authors review the development of diffuse-interface models of hydrodynamics and their application to a wide variety of interfacial phenomena. The authors discuss the issues involved in formulating diffuse-interface models for single-component and binary fluids. Recent applications and computations using these models are discussed in each case. Further, the authors address issues including sharp-interface analyses that relate these models to the classical free-boundary problem, related computational approaches to describe interfacial phenomena, and related approaches describing fully-miscible fluids.

SURFACE DIFFUSION↗

Drop Ejection From an Oscillating Rod

The dynamics of a drop of a Newtonian liquid that is pendant from or sessile on a solid rod that is forced to undergo time-periodic oscillations along its axis is studied theoretically. The free boundary problem governing the time evolution of the shape of the drop and the flow field inside it is solved by a method of lines using a finite element algorithm incorporating an adaptive mesh. When the forcing amplitude is small, the drop approaches a limit cycle at large times and undergoes steady oscillations thereafter. However, drop breakup is the consequence if the forcing amplitude exceeds a critical value. Over a wide range of amplitudes above this critical value, drop ejection from the rod occurs during the second oscillation period from the commencement of rod motion. Remarkably, the shape of the interface at breakup and the volume of the primary drop formed are insensitive to changes in forcing amplitude. The interface shape at times close to and at breakup is a multi-valued function of distance measured along the rod axis and hence cannot be described by recently popularized one-dimensional approximations. The computations show that drop ejection occurs without the formation of a long neck. Therefore, this method of drop formation holds promise of preventing formation of undesirable satellite droplets.

Wilkes, E. D.↗

New Method Developed to Measure Contact Angles of a Sessile Drop

The spreading of an evaporating liquid on a solid surface occurs in many practical processes and is of importance in a number of practical situations such as painting, textile dyeing, coating, gluing, and thermal engineering. Typical processes involving heat transfer where the contact angle plays an important role are film cooling, boiling, and the heat transfer through heat pipes. The biological phenomenon of cell spreading also is analogous to a drop spreading (ref. 1). In the study of spreading, the dynamic contact angle describes the interfacial properties on solid substrates and, therefore, has been studied by physicists and fluid mechanics investigators. The dynamic contact angle of a spreading nonvolatile liquid drop provides a simple tool in the study of the free-boundary problem, but the study of the spreading of a volatile liquid drop is of more practical interest because the evaporation of common liquids is inevitable in practical processes. The most common method to measure the contact angle, the contact radius, and the height of a sessile drop on a solid surface is to view the drop from its edge through an optical microscope. However, this method gives only local information in the view direction. Zhang and Yang (ref. 2) developed a laser shadowgraphy method to investigate the evaporation of sessile drop on a glass plate. As described here, Zhang and Chao (refs. 3 and 4) improved the method and suggested a new optical arrangement to measure the dynamic contact angle and the instant evaporation rate of a sessile drop with much higher accuracy (less than 1 percent). With this method, any fluid motion in the evaporating drop can be visualized through shadowgraphy without using a tracer, which often affects the field under investigation.

Chao, David F.↗

Numerical Studies of Phase Transition Phenomena in Microgravity

This work was aimed at developing and applying a new methodology for the efficient and accurate computation of problems involving several phases of matter. In particular, solidification processes typically involve melt/solid and sometimes melt//gas interfaces, whose location and shape is unknown a priori. This class of problems is called the free or moving boundary problem, and the numerical approaches for its solution to date are inaccurate, inefficient, and can not be readily extended to multi-dimensions or to time dependent phenomenon. Ongoing research on crystal growth at NASA and other institutions falls into the category of free boundary problems. It is exactly the accurate determination of the process dynamics and the shape and location of the interface between the phases which is responsible for the ultimate chemical segregation and the mechanical properties in the solid. This work developed the Triad Field Formalism approach for the computation of general multi-dimensional and time dependent free boundary problems. The particular subject addressed is solidification phenomena. All the relevant boundary conditions on the developing interface were exactly resolved. Several computer programs were developed during the course of this research, enabling us to determine for the first time the interplay among the various fields operating in tandem to produce the phenomena observed during solidification processes in weld pools and during crystal growth.

Source record↗

Boundary-value problem of configurations with compressible free vortex flow

A self-consistent version of the compressible boundary-value problem for configurations with leading-edge vortex separation is formulated, based on the assumption that the compressible flow field is controlled by the linearized potential equation. The stream surface boundary condition and the zero pressure jump condition of the compressible free vortex flows are analyzed; application of the Goethert rule permits the compressible nonlinear boundary-value problem for the subsonic flow domain to be transformed into an equivalent nonlinear incompressible problem. The compressibility corrections developed are used in numerical calculations of subsonic leading-edge vortex flows about planar wing geometries. The sample calculations, employing an inviscid flow model in which the wing and vortex sheets are represented by piecewise continuous quadratic doublet sheet distributions, are applicable to high subsonic Mach numbers.

Brune, G. W.↗

An explicit example of Hopf bifurcation in fluid mechanics

It is observed that a complete and explicit example of Hopf bifurcation appears not to be known in fluid mechanics. Such an example is presented for the rotating Benard problem with free boundary conditions on the upper and lower faces, and horizontally periodic solutions. Normal modes are found for the linearization, and the Veronis computation of the wave numbers is modified to take into account the imposed horizontal periodicity. An invariant subspace of the phase space is found in which the hypotheses of the Joseph-Sattinger theorem are verified, thus demonstrating the Hopf bifurcation. The criticality calculations are carried through to demonstrate rigorously, that the bifurcation is subcritical for certain cases, and to demonstrate numerically that it is subcritical for all the cases in the paper.

Kloeden, P.↗

Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The out-come of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the uid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the uid model realization. Using this approach, structural and uid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary uid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross ow. The hybrid Volterra-POD approach provides a low-order uid model in state-space form. The linear uid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional uid and structural solvers.

Lucia, David J.↗

Vertical slender jets

The shape of a vertical slender jet of fluid falling steadily under the force of gravity is studied. The problem is formulated as a nonlinear free boundary-value problem for the potential. Surface tension effects are neglected. The use of perturbation expansions results in a system of equations that can be solved by an efficient numerical procedure. Computations were made for jets issuing from orifices in various shapes including an ellipse, a rectangle, and an equilateral triangle. Computational results are presented illustrating the propagation of discontinuities and the formation of thin sheets of fluid.

Geer, J. F.↗

Approximate solutions to the Navier-Stokes initial value problem

A Galerkin-Ritz procedure for any arbitrary system of field equations is shown to follow generically from 'two-functional' variational conditions. The initial-value problem for boundary-free incompressible Navier-Stokes flow is solved analytically in the two-parameter-function approximation.

Rosen, G.↗

On the Lagrangian Method for Steady and Unsteady Flow

A new and general Lagrangian formulation of fluid motion is given in which the independent variables are three material functions and a Lagrangian time, which differs for different fluid particles and is distinct from the Eulerian time. For steady flow it requires only three independent variables - the Lagrangian time and two stream functions - in contrast with the conventional Lagrangian formulation which apparently still requires four independent variables for describing a steady flow. This places the Lagrangian formulation for steady flow on the same footing as the Eulerian. For unsteady flow, the new formulation includes the conventional formulation as a special case when the Lagrangian time is identified with the Eulerian time and when the material functions are taken to be the fluid particle's position at some given time. The distinction between the Lagrangian and Eulerian time, however, is found useful in applications, e.g., to problems involving a free boundary.

Hui, W. H.↗

A Chebyshev Collocation Method for Moving Boundaries, Heat Transfer, and Convection During Directional Solidification

Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and name propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectra collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.

Zhang, Yiqiang↗

On some properties of force-free magnetic fields in infinite regions of space

Techniques for solving boundary value problems (BVP) for a force free magnetic field (FFF) in infinite space are presented. A priori inequalities are defined which must be satisfied by the force-free equations. It is shown that upper bounds may be calculated for the magnetic energy of the region provided the value of the magnetic normal component at the boundary of the region can be shown to decay sufficiently fast at infinity. The results are employed to prove a nonexistence theorem for the BVP for the FFF in the spatial region. The implications of the theory for modeling the origins of solar flares are discussed.

Aly, J. J.↗

A study of non-unique solutions of the two-dimensional boundary layer equations at laminar separation and reattachment points

Nonunique laminar boundary layer equation solutions in direct problem calculations are identified for the case of accelerating flow. As a separation or reattachment point is approached, the multiple solutions approach each other and become identical. The computer code used to generate these results was developed for the solution of compressible, laminar or turbulent boundary layer, and free wake problems, in either direct or inverse mode. Similarity solutions in either a primitive variable or a stream function form are possible, and the resulting equations are solved by means of a modified Keller's Box scheme in which the energy equation and turbulence modeling equations are solved simultaneously with the continuity and momentum equations. Examples illustrating the nature of the solutions at the separation and reattachment points are presented.

Drela, M.↗

Motion of Drops on Surfaces with Wettability Gradients

A liquid drop present on a solid surface can move because of a gradient in wettability along the surface, as manifested by a gradient in the contact angle. The contact angle at a given point on the contact line between a solid and a liquid in a gaseous medium is the angle between the tangent planes to the liquid and the solid surfaces at that point and is measured within the liquid side, by convention. The motion of the drop occurs in the direction of increasing wettability. The cause of the motion is the net force exerted on the drop by the solid surface because of the variation of the contact angle around the periphery. This force causes acceleration of an initially stationary drop, and leads to its motion in the direction of decreasing contact angle. The nature of the motion is determined by the balance between the motivating force and the resisting hydrodynamic force from the solid surface and the surrounding gaseous medium. A wettability gradient can be chemically induced as shown by Chaudhury and Whitesides who provided unambiguous experimental evidence that drops can move in such gradients. The phenomenon can be important in heat transfer applications in low gravity, such as when condensation occurs on a surface. Daniel et al have demonstrated that the velocity of a drop on a surface due to a wettability gradient in the presence of condensation can be more than two orders of magnitude larger than that observed in the absence of condensation. In the present research program, we have begun to study the motion of a drop in a wettability gradient systematically using a model system. Our initial efforts will be restricted to a system in which no condensation occurs. The experiments are performed as follows. First, a rectangular strip of approximate dimensions 10 x 20 mm is cut out of a silicon wafer. The strip is cleaned thoroughly and its surface is exposed to the vapor from an alkylchlorosilane for a period lasting between one and two minutes inside a desiccator. This is done using an approximate line source of the vapor in the form of a string soaked in the alkylchlorosilane. Ordinarily, many fluids, including water, wet the surface of silicon quite well. This means that the contact angle is small. But the silanized surface resists wetting, with contact angles that are as large as 100 degs. Therefore, a gradient of wettability is formed on the silicon surface. The region near the string is highly hydrophobic, and the contact angle decreases gradually toward a small value at the hydrophilic end away from this region. The change in wettability occurs over a distance of several mm. The strip is placed on a platform within a Plexiglas cell. Drops of a suitable liquid are introduced on top of the strip near the hydrophobic end. An optical system attached to a video camera is trained on the drop so that images of the moving drop can be captured on videotape for subsequent analysis. We have performed preliminary experiments with water as well as ethylene glycol drops. Results from these experiments will be presented in the poster. Future plans include the refinement of the experimental system so as to permit images to be recorded from the side as well as the top, and the conduct of a systematic study in which the drop size is varied over a good range. Experiments will be conducted with different fluids so as to obtain the largest possible range of suitably defined Reynolds and Capillary numbers. Also, an effort will be initiated on theoretical modeling of this motion. The challenges in the development of the theoretical description lie in the proper analysis of the region in the vicinity of the contact line, as well as in the free boundary nature of the problem. It is known that continuum models assuming the no slip condition all the way to the contact line fail by predicting that the stress on the solid surface becomes singular as the contact line is approached. One approach for dealing with this issue has been to relax the no-slip boundary condition using the Navier model. Molecular dynamics simulations of the contact line region show that for a non-polar liquid on a solid surface, the no-slip boundary condition is in fact incorrect near the contact line. Furthermore, the same simulations also show that the usual relationship between stress and the rate of deformation breaks down in the vicinity of the contact line. In developing continuum theoretical models of the system, we shall accommodate this knowledge to the extent possible.

Subramanian, R. Shankar↗

Traction free finite elements with the assumed stress hybrid model

An effective approach in the finite element analysis of the stress field at the traction free boundary of a solid continuum was studied. Conventional displacement and assumed stress finite elements were used in the determination of stress concentrations around circular and elliptical holes. Specialized hybrid elements were then developed to improve the satisfaction of prescribed traction boundary conditions. Results of the stress analysis indicated that finite elements which exactly satisfy the free stress boundary conditions are the most accurate and efficient in such problems. A general approach for hybrid finite elements which incorporate traction free boundaries of arbitrary geometry was formulated.

Kafie, Kurosh↗