Larry W. Byrd

Modeling and Analysis of Functionally Graded Materials and Structures

This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164

Micrometer-Sized Water Droplet Impingement Dynamics and Evaporation on a Flat Dry Surface

A comprehensive numerical and experimental investigation on micrometer-sized water droplet impact dynamics and evaporation on an unheated, flat, dry surface is conducted from the standpoint of spray-cooling technology. The axisymmetric time-dependent governing equations of continuity, momentum, energy, and species are solved. Surface tension, wall adhesion effect, gravitational body force, contact line dynamics, and evaporation are accounted for in the governing equations. The explicit volume of fluid (VOF) model with dynamic meshing and variable-time stepping in serial and parallel processors is used to capture the time-dependent liquid-gas interface motion throughout the computational domain. The numerical model includes temperature- and species-dependent thermodynamic and transport properties. The contact line dynamics and the evaporation rate are predicted using Blakes and Schrages molecular kinetic models, respectively. An extensive grid independence study was conducted. Droplet impingement and evaporation data are acquired with a standard dispensing/imaging system and high-speed photography. The numerical results are compared with measurements reported in the literature for millimeter-size droplets and with current microdroplet experiments in terms of instantaneous droplet shape and temporal spread (R/D(0) or R/R(E)), flatness ratio (H/D(0)), and height (H/H(E)) profiles, as well as temporal volume (inverted A) profile. The Weber numbers (We) for impinging droplets vary from 1.4 to 35.2 at nearly constant Ohnesorge number (Oh) of approximately 0.025-0.029. Both numerical and experimental results show that there is air bubble entrapment due to impingement. Numerical results indicate that Blakes formulation provides better results than the static (SCA) and dynamic contact angle (DCA) approach in terms of temporal evolution of R/D(0) and H/D(0) (especially at the initial stages of spreading) and equilibrium flatness ratio (H(E)/D(0)). Blakes contact line dynamics is dependent on the wetting parameter (K(W)). Both numerical and experimental results suggest that at 4.5 < We < 11.0 the short-time dynamics of microdroplet impingement corresponds to a transition regime between two different spreading regimes (i.e., for We < or = 4.5, impingement is followed by spreading, then contact line pinning and then inertial oscillations, and for We > or = 11.0, impingement is followed by spreading, then recoiling, then contact line pinning and then inertial oscillations). Droplet evaporation can be satisfactorily modeled using the Schrage model, since it predicts both well-defined transient and quasi-steady evaporation stages. The model compares well with measurements in terms of flatness ratio (H/H(E)) before depinning occurs. Toroidal vortices are formed on the droplet surface in the gaseous phase due to buoyancy-induced Rayleigh-Taylor instability that enhances convection.

Matrix cracking in transverse layers of cross-ply beams subjected to bending and its effect on vibration frequencies

Abstract The solution for the matrix crack distribution in transverse layers of a cross-ply beam subjected to bending is developed based on the model of Han and Hahn (Compos Sci Technol 35 (1989) 377). This solution accounts for a bimodulus-type of the material response. As a result, it is possible to predict the extent and distribution of matrix cracks as well as the stiffness distribution in the beam subjected to bending, accounting for residual thermal stresses. The results of the solution of the bending problem are employed in the analysis of free and forced vibrations of a cross-ply beam with matrix cracks in transverse layers. The solution differs from the case of vibrations of an intact beam due to a difference in response of damaged layers under tension and compression. The results are shown for the natural frequency of a representative ceramic matrix composite (CMC) beam.

Effects of thermal dispersion and stratification on combined convection on a vertical surface embedded in a porous medium

The effects of thermal dispersion and thermal stratification on mixed convection about a vertical surface in a porous medium are studied. The conservation equations that govern the problem are reduced to a system of nonlinear ordinary differential equations. The resulting equations are solved on the basis of the local similarity approximation. The results indicate that both dispersion and stratification effects have considerable influence on the heat transfer rate.

Vibrations of Damaged Cantilever Beams Manufactured from Functionally Graded Materials

This paper is concerned with the effect of damage on free and forced vibrations of a functionally graded cantilever beam. The modes of damage considered in the paper include a region with degraded stiffness adjacent to the root of the beam, a single delamination crack, and a single crack at the root cross section of the beam propagating in the thickness direction. Closed-form solutions are suggested for all cases considered, including both forced and free vibrations; in the case of free vibrations, these solutions are exact. The peculiarities of the frequency analysis of nonprismatic and/or axially graded beams with the root crack in the presence of static thermal loads are also discussed and it is shown that neglecting axial inertia may lead to a qualitative error (this conclusion remains valid in prismatic functionally graded material beams). Numerical examples concentrate on the effect of a single root crack on the fundamental frequency, because such damage was observed in numerous loading scenarios. It is shown that the presence of a crack that has propagated through about one-third of the thickness of the beam significantly affects the fundamental frequency.

Evaporative heat transfer from thin liquid film on a heated cylinder

Simulating a porous surface that is partially saturated with a liquid, a two-dimensional meniscus attaching two adjacent cylinders with the same diameter is studied under heating and convective conditions. A thin liquid film model is presented to predict thin film thickness and evaporative heat transfer coefficient. Experiments are carried out to characterize the temperature and geometry of a liquid meniscus. The evaporating thin film length is determined from measured surface temperature and meniscus shape. The surface temperature data is correlated and used to derive the evaporative heat transfer coefficient with the aid of conjugate heat transfer using a finite element code. The results are compared reasonably with the thin film model. The effects of Bond number, spacing between cylinders and heating power on thin film geometry and heat transfer characteristics are discussed. Correlations to predict the evaporative heat transfer coefficient and ratio of evaporative heat transfer rate to total heat rate are presented.

Mixed Convection in Non-Newtonian Fluids Along a Horizontal Plate in a Porous Medium

The problem of mixed convection from horizontal surfaces in a porous medium saturated with a power-law-type non-Newtonian fluid is investigated. The transformed conservation laws are solved numerically for the case of variable wall heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The viscosity index ranged from 0.5-1.5.

Profile measurements of thin liquid films using reflectometry

Microscope-based reflectometry was used to measure the thickness profile of thin films of n-octane on silicon wafer substrates. Coupled with micro-positioning motorized stages and custom software, two-dimensional profiles of the film thickness from the adsorbed film (∼10 nm) to the intrinsic meniscus (∼1000 nm) were automatically and repeatedly measured. The reflectometer aperture was modified to provide better spatial resolution in areas of high curvature, the transition region, where evaporative flux is at a maximum. This technique will provide data for the validation of both existing and future models of thin film evaporation.

Evaporation Characteristics of Pinned Water Microdroplets

Alejandro M. Briones∗ and Jamie S. Ervin University of Dayton Research Institute, Dayton, Ohio 45469 Larry W. Byrd U.S. Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433 Shawn A. Putnam Universal Technology Corporation, Dayton, Ohio 45434 Ashley White University of Dayton, Dayton, Ohio 45469 and John G. Jones∗∗ U.S. Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433

Damping in Ceramic Matrix Composites with Matrix Cracks

Abstract The paper presents an analytical solution capable of predicting the effect of matrix cracking in ceramic matrix composites (CMC) on damping. The cracking scenarios considered in the paper include through-the-thickness cracks and cracks terminating at the layer interfaces. The increase in damping associated with matrix cracking is mostly due to the frictional energy dissipation along the damaged fiber–matrix interfaces adjacent to the bridging cracks whose plane of propagation intersects the fiber axis. Damping increases with a higher density of matrix cracks. The loss factor is affected by the angle of the lamina relative to the direction of the applied load. The loss factor is also influenced by the frequency and magnitude of local dynamic stresses. Examples of distributions of the local loss factor along the axis of a CMC beam subject to pulsating loads of various frequencies are shown in the paper.