Thermoelastic solutions for thermal distributions moving over thin slim rod under memory-dependent three-phase lag magneto-thermoelasticity

Abstract

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of three-phase lag (TPL) theory of thermoelasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress, and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. For the better understanding of the effect of moving heat source on all the distributions, three animations are added.     

Structured water chains in external electric fields

ABSTRACT

We study the structural, energetic and electronic properties of the structured water chain clusters within the density functional theory. We refer the structured water chains to those water clusters that have specific geometric patterns stretched along one direction. External electric field required to keep the structures open chain, thereby preventing them to form closed structures, is applied along the length of the chain. The structures are essentially periodic with basic repeating unit consisting of the corner- or edge-sharing 4-, 5- or 6-membered ring water clusters. Our calculations underscore the possible existence of such structured water clusters in the electrostatic environments, which we simulate in its simplicity employing a dipolar, uniform and static electric field. Analysis reveals that the 5-membered ring water chain clusters, i.e. the pentamer chain clusters have the lowest average dipole moment per water molecule while the threshold field, that marks the onset of the field-induced closure of the HOMO (highest occupied molecular orbital)-LUMO (lowest unoccupied molecular orbital) energy gap, is highest, followed by that for the tetramer and hexamer chains. The results suggest that the pentamer chains are the most stable clusters over a wide range of electric fields.     

An analysis of overlapping Schwarz method for a weakly coupled system of singularly perturbed convection-diffusion equations

In this article, we have developed an overlapping Schwarz method for a weakly coupled system of convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region, we use the central finite difference scheme on a uniform mesh, whereas on the nonlayer region, we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations converge in the maximum norm to the exact solution. We have proved that, when appropriate subdomains are used, the method produces almost second-order convergence. Furthermore, it is shown that two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantage of this method used with the proposed scheme is that it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.     

A compressible two-phase flow framework for Large Eddy Simulations of liquid-propellant rocket engines

Atomization of liquid jets is a key feature of many propulsion systems, such as jet engines, internal combustion engines or liquid-propellant rocket engines (LRE). As it controls the characteristics of the spray, atomization has a great influence on the complex interaction between phenomena such as evaporation, turbulence, acoustics and combustion. In this context, Computational Fluid Dynamics is a promising way to bring better understanding of dynamic phenomena involving atomization, such as e.g. high-frequency combustion instabilities in LRE. However the unsteady simulation of primary atomization in reactive compressible two-phase flows is very challenging, due to the variety of the spatial and temporal scales, as well as to the high density, velocity and temperature gradients which require robust and efficient numerical methods. To address this issue, a numerical strategy is proposed in this paper, which is able to describe the dynamics of the whole chain of mechanisms from the liquid injection to its atomization and combustion. Primary atomization is modeled by a coupling between a homogeneous diffuse interface model and a kinetic-based Eulerian model for the spray. This strategy is successfully applied to the unsteady simulation of an operating point of the Onera’s Mascotte test bench, representative of one coaxial injector of LRE operating under subcritical conditions. The dynamics of the liquid core is retrieved and the flame shape as well as Sauter mean diameters are in good agreement with experimental results. These results demonstrate the ability of the strategy to deal with the harsh conditions of cryogenic combustion, and provide a promising framework for future studies of combustion instabilities in LRE.     

Nonnegative solutions to reaction–diffusion system with cross-diffusion and nonstandard growth conditions

We establish the existence of nonnegative weak solutions to nonlinear reaction–diffusion system with cross-diffusion and nonstandard growth conditions subject to the homogeneous Neumann boundary conditions. We assume that the diffusion operators satisfy certain monotonicity condition and nonstandard growth conditions and prove that the existence of weak solutions using Galerkin's approximation technique.     

Finite element computations of viscoelastic two-phase flows using local projection stabilization

A three-field local projection stabilized (LPS) finite element method is developed for computations of a three-dimensional axisymmetric buoyancy driven liquid drop rising in a liquid column where one of the liquid is viscoelastic. The two-phase flow is described by the time-dependent incompressible Navier-Stokes equations, whereas the viscoelasticity is modeled by the Giesekus constitutive equation in a time-dependent domain. The arbitrary Lagrangian-Eulerian (ALE) formulation with finite elements is used to solve the governing equations in the time-dependent domain. Interface-resolved moving meshes in ALE allows to incorporate the interfacial tension force and jumps in the material parameters accurately. A one-level LPS based on an enriched approximation space and a discontinuous projection space is used to stabilize the numerical scheme. A comprehensive numerical investigation is performed for a Newtonian drop rising in a viscoelastic fluid column and a viscoelastic drop rising in a Newtonian fluid column. The influence of the viscosity ratio, Newtonian solvent ratio, Giesekus mobility factor, and the Eötvös number on the drop dynamics are analyzed. The numerical study shows that beyond a critical Capillary number, a Newtonian drop rising in a viscoelastic fluid column experiences an extended trailing edge with a cusp-like shape and also exhibits a negative wake phenomena. However, a viscoelastic drop rising in a Newtonian fluid column develops an indentation around the rear stagnation point with a dimpled shape.     

HILITE—A tool to investigate interactions of matter and light

Detailed investigations of laser–ion interactions require well-defined ion targets and detection techniques for high-sensitivity measurements of reaction educts and products. To this end, we have designed and built the High-Intensity Laser-Ion Trap Experiment Penning trap setup, which features various ion-target preparation techniques including selection, cooling, compression, and positioning as well as destructive and non-destructive measurement techniques to determine the number of stored ions for all charge states individually and simultaneously. We have recently performed first commissioning experiments of ion deceleration and dynamic ion capture with highly charged ion bunches from an electron beam ion source. We have characterized our single-pass non-destructive ion counter in detail and were able to determine the ion velocity as well as the number of ions from the signals acquired.