Scaling analysis of momentum, heat, and mass transfer in binary alloy solidification problems

A systematic approach is developed for scaling analysis of momentum, heat and species conservation equations pertaining to the case of solidification of a binary mixture. The problem formulation and description of boundary conditions are kept fairly general, so that a large class of problems can be addressed. Analysis of the momentum equations coupled with phase change considerations leads to the establishment of an advection velocity scale. Analysis of the energy equation leads to an estimation of the solid layer thickness. Different regimes corresponding to different dominant modes of transport are simultaneously identified. A comparative study involving several cases of possible thermal boundary conditions is also performed. Finally, a scaling analysis of the species conservation equation is carried out, revealing the effect of a non-equilibrium solidification model on solute segregation and species distribution. It is shown that non-equilibrium effects result in an enhanced macrosegregation compared with the case of an equilibrium model. For the sake of assessment of the scaling analysis, the predictions are validated against corresponding computational results.

A scaling analysis of momentum and heat transport in laser surface melting

In this paper, we outline a systematic procedure for scaling analysis of momentum and heat transfer in laser melted pools. With suitable choices of non-dimensionalising parameters, the governing equations coupled with appropriate boundary conditions are first scaled, and the relative significance of various terms appearing in them are accordingly analysed. The analysis is then utilised to predict the orders of magnitude of some important quantities, such as the velocity scale at the top surface, velocity boundary layer thickness, maximum temperature rise in the pool, fully developed pool-depth, and time required for initiation of melting. Using the scaling predictions, the influence of various processing parameters on the system variables can be well recognised, which enables us to develop a deeper insight into the physical problem of interest. Moreover, some of the quantities predicted from the scaling analysis can be utilised for optimised selection of appropriate grid-size and time-steps for full numerical simulation of the process. The scaling predictions are finally assessed by comparison with experimental and numerical results quoted in the literature, and an excellent qualitative agreement is observed.

Three-dimensional computational modeling of momentum, heat, and mass transfer in a laser surface alloying process

A three- dimensional, transient model is developed for studying heat transfer, fluid flow, and mass transfer for the case of a single- pass laser surface alloying process. The coupled momentum, energy, and species conservation equations are solved using a finite volume procedure. Phase change processes are modeled using a fixed-grid enthalpy-porosity technique, which is capable of predicting the continuously evolving solid- liquid interface. The three- dimensional model is able to predict the species concentration distribution inside the molten pool during alloying, as well as in the entire cross section of the solidified alloy. The model is simulated for different values of various significant processing parameters such as laser power, scanning speed, and powder feedrate in order to assess their influences on geometry and dynamics of the pool, cooling rates, as well as species concentration distribution inside the substrate. Effects of incorporating property variations in the numerical model are also discussed.

A nonlinear spectral finite element model for analysis of wave propagation in solid with internal friction and dissipation

A geometrically non-linear Spectral Finite Flement Model (SFEM) including hysteresis, internal friction and viscous dissipation in the material is developed and is used to study non-linear dissipative wave propagation in elementary rod under high amplitude pulse loading. The solution to non-linear dispersive dissipative equation constitutes one of the most difficult problems in contemporary mathematical physics. Although intensive research towards analytical developments are on, a general purpose cumputational discretization technique for complex applications, such as finite element, but with all the features of travelling wave (TW) solutions is not available. The present effort is aimed towards development of such computational framework. Fast Fourier Transform (FFT) is used for transformation between temporal and frequency domain. SFEM for the associated linear system is used as initial state for vector iteration. General purpose procedure involving matrix computation and frequency domain convolution operators are used and implemented in a finite element code. Convergnence of the spectral residual force vector ensures the solution accuracy. Important conclusions are drawn from the numerical simulations. Future course of developments are highlighted.

Zero momentum gluons and the total pp and pbarp cross-sections

We describe a QCD motivated model for total cross-sections which uses the eikonal representation and incorporates QCD mini-jets to drive the rise with energy of the cross-section, while the impact parameter distribution is obtained through the Fourier transform of the transverse momentum distribution of soft gluons emitted in the parton-parton interactions giving rise to mini-jets in the final state. A singular but integral expression for the running coupling constant in the infrared region is part of this model.

Suppressed rf dissipation in 107Ag17+ ion irradiated Bi2Sr2CaCu2O8 single crystals by enhanced flux line tilt modulus

We have studied the isothermal, magnetic field (H‖c) dependent rf power P(H) dissipation (Hrf‖a) in the superconducting state of Bi2Sr2CaCu2O8 single crystals prior to and after irradiation with 250 MeV 107Ag17+ ions. In the pristine state, P(H) shows an initial decrease with increase in field, reaches a minimum at HM(T) and increases monotonically for H>HM(T). This behavior arises when the electromagnetic coupling between the pancake vortices in adjacent CuO layers becomes dominant on increasing the field and minimizes the distortions of the flux lines by confining the 2D vortices. In the post irradiated state, such an initial decrease and the minimum in P(H) is not observed but only a much reduced rf dissipation that monotonically increases with field from H = 0 onwards is seen. We attribute this difference to the strong enhancement of the tilt modulus C44 of the flux lines on irradiation when the pancake vortices in adjacent CuO bilayers are pinned along the track forming a well-stacked flux line in the field direction (‖c). We have also observed that the rf dissipation disappears at a certain temperature Tsf, at which the normal core of the flux line becomes commensurate with the columnar track diameter.

Validation of a Modified Eddy Dissipation Concept Model for Stationary and Nonstationary Turbulent Diffusion Flames

A transient flame simulation tool based on unsteady Reynolds average Navier Stokes (RANS) is characterized for stationary and nonstationary flame applications with a motivation of performing computationally affordable flame stability studies. Specifically, the KIVA-3V code is utilized with incorporation of a recently proposed modified eddy dissipation concept for simulating turbulence-chemistry interaction along with a model for radiation loss. Detailed comparison of velocities, turbulent kinetic energies, temperature, and species are made with the experimental data of the turbulent, non-premixed DLR_A CH4/H-2/N-2 jet flame. The comparison shows that the model is able to predict flame structure very well. The effect of some of the modeling assumptions is assessed, and strategies to model a stationary diffusion flame are recommended. Unsteady flame simulation capabilities of the numerical model are assessed by simulating an acoustically excited, experimental, oscillatory H-2-air diffusion flame. Comparisons are made with oscillatory velocity field and OH plots, and the numerical code is observed to predict transient flame structure well.

2.5PN linear momentum flux from inspiralling compact binaries in quasicircular orbits and associated recoil: Nonspinning case

Anisotropic emission of gravitational waves (GWs) from inspiralling compact binaries leads to the loss of linear momentum and hence gravitational recoil of the system. The loss rate of linear momentum in the far-zone of the source (a nonspinning binary system of black holes in quasicircular orbit) is investigated at the 2.5 post-Newtonian (PN) order and used to provide an analytical expression in harmonic coordinates for the 2.5PN accurate recoil velocity of the binary accumulated in the inspiral phase. The maximum recoil velocity of the binary system at the end of its inspiral phase (i.e at the innermost stable circular orbit (ISCO)) estimated by the 2.5PN formula is of the order of 4 km s(-1) which is smaller than the 2PN estimate of 22 km s(-1). Going beyond inspiral, we also provide an estimate of the more important contribution to the recoil velocity from the plunge phase. The maximum recoil velocity at the end of the plunge, involving contributions both from inspiral and plunge phase, for a binary with symmetric mass ratio nu = 0.2 is of the order of 182 km s(-1).

Excess dissipation in dense emulsions

A new model for the structure, elastic properties and dynamics of foams and concentrated emulsions is presented, based on the idea of local regions lacking shear-rigidity in one or more directions which vary randomly through the medium. It is shown to lead naturally to slow (t(-1/2)) stress-relaxation, implying a piece of the dynamic modulus scaling with frequency omega as omega(1/2). Striking experimental confirmation of this prediction using a novel experimental technique is reported, and challenges for the theoretician are offered. This work was done in collaboration with Andrea Liu, Tom Mason, Hu Gang, and David Weitz [1].

Effect of base dissipation on the granular flow down an inclined plane

The effect of base dissipation on the granular flow down an inclined plane is examined by altering the coefficient of restitution between the moving and base particles in discrete element (DE) simulations. The interaction laws between two moving particles are kept fixed, and the coefficient of restitution (damping constant in the DE simulations) between the base and moving particles are altered to reduce dissipation, and inject energy from the base. The energy injection does result in an increase in the strain rate by up to an order of magnitude, and the temperature by up to two orders of magnitude at the base. However, the volume fraction, strain rate and temperature profiles in the bulk (above about 15 particle diameters from the base) are altered very little by the energy injection at the base. We also examine the variation of h(stop), the minimum height at the cessation of flow, with energy injection from the base. It is found that at a fixed angle of inclination, h(stop) decreases as the energy dissipation at the base decreases.

Radial infall of two compact objects: 2.5-post-Newtonian linear momentum flux and associated recoil

The loss rate of linear momentum from a binary system composed of compact objects (radially falling towards each other under mutual gravitational influence) has been investigated using the multipolar post-Minkowskian approach. The 2.5PN accurate analytical formula for the linear momentum flux is provided, in terms of the separation of the two objects, in harmonic coordinates, both for a finite and an infinite initial separation. The 2.5PN formulas for the linear momentum flux are finally used to estimate the recoil velocity accumulated during a premerger phase of the binary evolution.

Automatic energy-momentum conserving time integrators for hyperelastic waves

An energy-momentum conserving time integrator coupled with an automatic finite element algorithm is developed to study longitudinal wave propagation in hyperelastic layers. The Murnaghan strain energy function is used to model material nonlinearity and full geometric nonlinearity is considered. An automatic assembly algorithm using algorithmic differentiation is developed within a discrete Hamiltonian framework to directly formulate the finite element matrices without recourse to an explicit derivation of their algebraic form or the governing equations. The algorithm is illustrated with applications to longitudinal wave propagation in a thin hyperelastic layer modeled with a two-mode kinematic model. Solution obtained using a standard nonlinear finite element model with Newmark time stepping is provided for comparison. (C) 2012 Elsevier B.V. All rights reserved.