Numerical simulation of solidification of liquid aluminum alloy flowing on cooling slope

Preparation of semisolid slurry using a cooling slope is increasingly becoming popular, primarily because of the simplicity in design and ease control of the process. In this process, liquid alloy is poured down an inclined surface which is cooled from underneath. The cooling enables partial solidification and the incline provides the necessary shear for producing semisolid slurry. However, the final microstructure of the ingot depends on several process parameters such as cooling rate, incline angle of the cooling slope, length of the slope and initial melt superheat. In this work, a CFD model using volume of fluid (VOF) method for simulating flow along the cooling slope was presented. Equations for conservation of mass, momentum, energy and species were solved to predict hydrodynamic and thermal behavior, in addition to predicting solid fraction distribution and macrosegregation. Solidification was modeled using an enthalpy approach and a volume averaged technique for the different phases. The mushy region was modeled as a multi-layered porous medium consisting of fixed columnar dendrites and mobile equiaxed/fragmented grains. The alloy chosen for the study was aluminum alloy A356, for which adequate experimental data were available in the literature. The effects of two key process parameters, namely the slope angle and the pouring temperature, on temperature distribution, velocity distribution and macrosegregation were also studied.

An accurate numerical integration scheme for finite rotations using rotation vector parametrization

A numerical integration procedure for rotational motion using a rotation vector parametrization is explored from an engineering perspective by using rudimentary vector analysis. The incremental rotation vector, angular velocity and acceleration correspond to different tangent spaces of the rotation manifold at different times and have a non-vectorial character. We rewrite the equation of motion in terms of vectors lying in the same tangent space, facilitating vector space operations consistent with the underlying geometric structure. While any integration algorithm (that works within a vector space setting) may be used, we presently employ a family of explicit Runge-Kutta algorithms to solve this equation. While this work is primarily motivated out of a need for highly accurate numerical solutions of dissipative rotational systems of engineering interest, we also compare the numerical performance of the present scheme with some of the invariant preserving schemes, namely ALGO-C1, STW, LIEMIDEA] and SUBCYC-M. Numerical results show better local accuracy via the present approach vis-a-vis the preserving algorithms. It is also noted that the preserving algorithms do not simultaneously preserve all constants of motion. We incorporate adaptive time-stepping within the present scheme and this in turn enables still higher accuracy and a `near preservation' of constants of motion over significantly longer intervals. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

An Experimental and Numerical Study of Calliphora Wing Structure

Experiments are performed to determine the mass and stiffness variations along the wing of the blowfly Calliphora. The results are obtained for a pairs of wings of 10 male flies and fresh wings are used. The wing is divided into nine locations along the span and seven locations along the chord based on venation patterns. The length and mass of the sections is measured and the mass per unit length is calculated. The bending stiffness measurements are taken at three locations, basal (near root), medial and distal (near tip) of the fly wing. Torsional stiffness measurements are also made and the elastic axis of the wing is approximately located. The experimental data is then used for structural modeling of the wing as a stepped cantilever beam with nine spanwise sections of varying mass per unit lengths, flexural rigidity (EI) and torsional rigidity (GJ) values. Inertial values of nine sections are found to approximately vary according to an exponentially decreasing law over the nine sections from root to tip and it is used to calculate an approximate value of Young's modulus of the wing biomaterial. Shear modulus is obtained assuming the wing biomaterial to be isotropic. Natural frequencies, both in bending and torsion, are obtained by solving the homogeneous part of the respective governing differential equations using the finite element method. The results provide a complete analysis of Calliphora wing structure and also provide guidelines for the biomimetic structural design of insect-scale flapping wings.

Antarctic ice shelf melting and its impact on the global sea ice-ocean system

Earth s ice shelves are mainly located in Antarctica. They cover about 44% of the Antarctic coastline and are a salient feature of the continent. Antarctic ice shelf melting (AISM) removes heat from and inputs freshwater into the adjacent Southern Ocean. Although playing an important role in the global climate, AISM is one of the most important components currently absent in the IPCC climate model. In this study, AISM is introduced into a global sea ice-ocean climate model ORCA2-LIM, following the approach of Beckmann and Goosse (2003; BG03) for the thermodynamic interaction between the ice shelf and ocean. This forms the model ORCA2-LIM-ISP (ISP: ice shelf parameterization), in which not only all the major Antarctic ice shelves but also a number of minor ice shelves are included. Using these two models, ORCA2-LIM and ORCA2-LIM-ISP, the impact of addition of AISM and increasing AISM have been investigated. Using the ORCA2-LIM model, numerical experiments are performed to investigate the sensitivity of the polar sea ice cover and the Antarctic Circumpolar Current (ACC) transport through Drake Passage (DP) to the variations of three sea ice parameters, namely the thickness of newly formed ice in leads (h0), the compressive strength of ice (P*), and the turning angle in the oceanic boundary layer beneath sea ice (θ). It is found that the magnitudes of h0 and P* have little impact on the seasonal sea ice extent, but lead to large changes in the seasonal sea ice volume. The variation in turning angle has little impact on the sea ice extent and volume in the Arctic but tends to reduce them in the Antarctica when ignored. The magnitude of P* has the least impact on the DP transport, while the other two parameters have much larger influences. Numerical results from ORCA2-LIM and ORCA2-LIM-ISP are analyzed to investigate how the inclusion of AISM affects the representation of the Southern Ocean hydrography. Comparisons with data from the World Ocean Circulation Experiment (WOCE) show that the addition of AISM significantly improves the simulated hydrography. It not only warms and freshens the originally too cold and too saline bottom water (AABW), but also warms and enriches the salinity of the originally too cold and too fresh warm deep water (WDW). Addition of AISM also improves the simulated stratification. The close agreement between the simulation with AISM and the observations suggests that the applied parameterization is an adequate way to include the effect of AISM in a global sea ice-ocean climate model. We also investigate the models capability to represent the sea ice-ocean system in the North Atlantic Ocean and the Arctic regions. Our study shows both models (with and without AISM) can successfully reproduce the main features of the sea ice-ocean system. However, both tend to overestimate the ice flux through the Nares Strait, produce a lower temperature and salinity in the Hudson Bay, Baffin Bay and Davis Strait, and miss the deep convection in the Labrador Sea. These deficiencies are mainly attributed to the artificial enlargement of the Nares Strait in the model. In this study, the impact of increasing AISM on the global sea ice-ocean system is thoroughly investigated. This provides a first idea regarding changes induced by increasing AISM. It is shown that the impact of increasing AISM is global and most significant in the Southern Ocean. There, increasing AISM tends to freshen the surface water, to warm the intermediate and deep waters, and to freshen and warm the bottom water. In addition, increasing AISM also leads to changes in the mixed layer depths (MLD) in the deep convection sites in the Southern Ocean, deepening in the Antarctic continental shelf while shoaling in the ACC region. Furthermore, increasing AISM influences the current system in the Southern Ocean. It tends to weaken the ACC, and strengthen the Antarctic coastal current (ACoC) as well as the Weddell Gyre and the Ross Gyre. In addition to the ocean system, increasing AISM also has a notable impact on the Antarctic sea ice cover. Due to the cooling of seawater, sea ice concentration and thickness generally become higher. In austral winter, noticeable increases in sea ice concentration mainly take place near the ice edge. In regards with sea ice thickness, large increases are mainly found along the coast of the Weddell Sea, the Bellingshausen and Amundsen Seas, and the Ross Sea. The overall thickening of sea ice leads to a larger volume of sea ice in Antarctica. In the North Atlantic, increasing AISM leads to remarkable changes in temperature, salinity and density. The water generally becomes warmer, more saline and denser. The most significant warming occurs in the subsurface layer. In contrast, the maximum salinity increase is found at the surface. In addition, the MLD becomes larger along the Greenland-Scotland-Iceland ridge. Global teleconnections due to AISM are studied. The AISM signal is transported with the surface current: the additional freshwater from AISM tends to enhance the northward spreading of the surface water. As a result, more warm and saline water is transported from the tropical region to the North Atlantic Ocean, resulting in warming and salt enrichment there. It would take about 30 40 years to establish a systematic noticeable change in temperature, salinity and MLD in the North Atlantic Ocean according to this study. The changes in hydrography due to increasing AISM are compared with observations. Consistency suggests that increasing AISM is highly likely a major contributor to the recent observed changes in the Southern Ocean. In addition, the AISM might contribute to the salinity contrast between the North Atlantic and North Pacific, which is important for the global thermohaline circulation.

Performance study of high operating temperature HgCdTe mid wave infrared detector through numerical modeling

The design of present generation uncooled Hg1-xCdxTe infrared photon detectors relies on complex heterostructures with a basic unit cell of type (n) under bar (+)/pi/(p) under bar (+). We present an analysis of double barrier (n) under bar (+)/pi/(p) under bar (+) mid wave infrared (x = 0.3) HgCdTe detector for near room temperature operation using numerical computations. The present work proposes an accurate and generalized methodology in terms of the device design, material properties, and operation temperature to study the effects of position dependence of carrier concentration, electrostatic potential, and generation-recombination (g-r) rates on detector performance. Position dependent profiles of electrostatic potential, carrier concentration, and g-r rates were simulated numerically. Performance of detector was studied as function of doping concentration of absorber and contact layers, width of both layers and minority carrier lifetime. Responsivity similar to 0.38 A W-1, noise current similar to 6 x 10(-14) A/Hz(1/2) and D* similar to 3.1 x 10(10)cm Hz(1/2) W-1 at 0.1 V reverse bias have been calculated using optimized values of doping concentration, absorber width and carrier lifetime. The suitability of the method has been illustrated by demonstrating the feasibility of achieving the optimum device performance by carefully selecting the device design and other parameters. (C) 2010 American Institute of Physics. doi:10.1063/1.3463379]

Free vibration of a stochastic beam-column using stochastic fem

The free vibrational characteristics of a beam-column, which is having randomly varying Young's modulus and mass density and subjected to randomly distributed axial loading is analysed. The material property fluctuations and axial loadings are considered to constitute independent one-dimensional, uni-variate, homogeneous real, spatially distributed stochastic fields. Hamilton's principle is used to formulate the problem using stochastic FEM. Vibration frequencies and mode shapes are analysed for their statistical descriptions. A numerical example is shown.

Structure and representation of correlation functions and the density matrix for a statistical wave field in optics

A systematic structure analysis of the correlation functions of statistical quantum optics is carried out. From a suitably defined auxiliary two‐point function we are able to identify the excited modes in the wave field. The relative simplicity of the higher order correlation functions emerge as a byproduct and the conditions under which these are made pure are derived. These results depend in a crucial manner on the notion of coherence indices and of unimodular coherence indices. A new class of approximate expressions for the density operator of a statistical wave field is worked out based on discrete characteristic sets. These are even more economical than the diagonal coherent state representations. An appreciation of the subtleties of quantum theory obtains. Certain implications for the physics of light beams are cited.

Micromechanics Of Fatigue Crack-Growth At Low Stress Intensities In A High-Strength Steel

An attempt to systematically investigate the effects of microstructural parameters in influencing the resistance to fatigue crack growth (FCG) in the near-threshold region under three different temper levels has been made for a high strength low alloy steel to observe in general, widely different trends in the dependence of both the total threshold stress intensity range, DELTA-K(th) and the intrinsic or effective threshold stress intensity range, DELTA-K(eff-th) on the prior austenitic grain size (PAGS). While a low strain hardening microstructure obtained by tempering at high temperatures exhibited strong dependence of DELTA-K(th) on the PAGS by virtue of strong interactions of crack tip slip with the grain boundary, a high strength, high strain hardening microstructure as a result of tempering at low temperature exhibited a weak dependence. The lack of a systematic variation of the near-threshold parameters with respect to grain size in temper embrittled structures appears to be related to the wide variations in the amount of intergranular fracture near threshold. Crack closure, to some extent provides a basis on which the increases in DELTA-K(th) at larger grain sizes can be rationalised. This study, in addition, provides a wide perspective on the relative roles of slip behaviour embrittlement and environment that result in the different trends observed in the grain size dependence of near-threshold fatigue parameters, based on which the inconsistency in the results reported in the literature can be clearly understood. Assessment of fracture modes through extensive fractography revealed that prior austenitic grain boundaries are effective barriers to cyclic crack growth compared to martensitic packet boundaries, especially at low stress intensities. Fracture morphologies comprising of low energy flat transgranular fracture can occur close to threshold depending on the combinations of strain hardening behaviour, yield strength and embrittlement effects. A detailed consideration is given to the discussion of cyclic stress strain behaviour, embrittlement and environmental effects and the implications of these phenomena on the crack growth behaviour near threshold.

MPD arcjet cathode surface current density

The radial current density distribution on the cathode longitudinal surface of magnetoplasmadynamic arcjets for axisymmetric geometries has been obtained by simultaneous solution of the electromagnetic equations for a given uniform gas dynamic field. The problem formulation permits a parametric study of the effects of the Hall parameter and the magnetic Reynolds number. The solution for the current density distribution displays current concentrations at two locations, that is, at the upstream and downstream ends of the cathode. This result is in conformity with known experimental data. The parameters responsible for these current concentrations are identified. It is shown that the effect of the magnetic Reynolds number on the current density distribution is different depending on whether or not the Hall effect is included. This result is also found to be consistent with experimental data.

Numerical estimation of hotspot temperatures in electrodes subjected to pulsed electron beam heating in vacuum

A numerical solution for the transient temperature distribution in a cylindrical disc heated on its top surface by a circular source is presented. A finite difference form of the governing equations is solved by the Alternating Direction Implicit (ADI) time marching scheme. This solution has direct applications in analyzing transient electron beam heating of target materials as encountered in the prebreakdown current enhancement and consequent breakdown in high voltage vacuum gaps stressed by alternating and pulsed voltages. The solution provides an estimate of the temperature for pulsed electron beam heating and the size of thermally activated microparticles originating from anode hot spots. The calculated results for a typical 45kV (a.c.) electron beam of radius 2.5 micron indicate that the temperature of such spots can reach melting point and could give rise to microparticles which could initiate breakdown.

The Single Langmuir Probe under Orbital-Limited Conditions in a Low-Density Collisional Plasma

The cylindrical Langmuir probe under orbital-limited conditions was used to determine the charge density in a low-density collisional plasma. The Langmuir's theory was applied to both electron and ion saturation currents in their respective accelerating regions. Present study indicates that the length of the probe significantly affects the probe characteristics. A probe of suitable length under orbital-limited conditions may be useful under the experimental conditions where the radius of the probe is much smaller than the Debye lengt.

Rocking response of rectangular rigid blocks under random noise base excitations

The response of a rigid rectangular block resting on a rigid foundation and acted upon simultaneously by a horizontal and a vertical random white-noise excitation is considered. In the equation of motion, the energy dissipation is modeled through a viscous damping term. Under the assumption that the body does not topple, the steady-state joint probability density function of the rotation and the rotational velocity is obtained using the Fokker-Planck equation approach. Closed form solution is obtained for a specific combination of system parameters. A more general but approximate solution to the joint probability density function based on the method of equivalent non-linearization is also presented. Further, the problem of overturning of the block is approached in the framework of the diffusion methods for first passage failure studies. The overturning of the block is deemed incipient when the response trajectories in the phase plane cross the separatrix of the conservative unforced system. Expressions for the moments of first passage time are obtained via a series solution to the governing generalized Pontriagin-Vitt equations. Numerical results illustra- tive of the theoretical solutions are presented and their validity is examined through limited amount of digital simulations.

Position and Feed-Rate Control for Contouring Numerical-Control Systems

Numerical control (NC) for contouring operations requires precise control of position and feed rate for approximating the contour by linear moves of the cutter. A control scheme, for generating linear moves with desired slopes for the cutter, is described. This scheme provides for nine successive linear moves, and may be either expanded or implemented in succession, for approximating a contour.