Initial Temperature Gradient Research Articles

Investigations into Improvement in Formability of AA5754 and AA6082 Sheets at Elevated Temperatures

Warm forming is an attractive formability improvement technique which can be utilized to intensify the usage of aluminum alloy sheets in autobody constructions. In the present work, laboratory-scale stretch forming and deep drawing experiments were performed to demonstrate the comparative formability improvement in AA6082-O and AA5754-H22 aluminum alloy sheets at elevated temperatures. Significant enhancement of limiting dome height and forming limit diagram (FLD) was observed when stretch forming was performed at 200 °C. Warm deep drawing under both isothermal and nonisothermal conditions was carried out, and drastic improvement in drawability was found only under nonisothermal condition with an initial temperature gradient of 93 °C across the blank. Thermomechanical finite element (FE) models of the warm forming processes were developed using temperature-dependent Barlat-89 yield model coupled with Cowper–Symonds strain rate sensitivity model. The limiting dome heights, failure locations and strain distributions were well predicted by implementing experimental FLD as the failure criterion. Further, the effect of evolution of nonisothermal temperature gradient on the improvement in drawability of both the materials was analyzed in terms of cup height, earing profile, thickness distribution and surface strain evolution.

Temperature development of cardboard in contact with high-frequency vibrating metal surfaces

The heating of cardboard was studied when it is in contact with ultrasonic sonotrodes, whose vibrations were orientated parallel and perpendicular to the material surface. The parameters that were varied included the contact pressure on the sonotrode, vibration amplitude, and moisture content of the material. It was shown that there was a major decrease in the contact pressure shortly after the beginning of the experiment when the gap between the sonotrode and anvil was kept constant and thus a decrease in the temperature gradient of the material occurred. With parallel vibration, the material heated up from the sonotrode side, whereas heating started from the center of the material in the case of vertical vibration. This suggested that in cases of vertical vibration, heat is mostly generated by internal dissipation, and in cases of parallel vibration, heat is generated by friction losses on the surface. Furthermore, the results revealed the influence of the parameters on the initial temperature gradient, the maximum temperature, and the moisture content of the material.

Cellular automaton simulation of molten pool migration due to temperature gradient zone melting

Directional solidification is a common and important process in both scientific research and industrial practice. Owing to the presence of temperature gradients during directional solidification, local remelting and solidification in the mushy zone occurs, resulting in some typical phenomena such as temperature gradient zone melting (TGZM). The TGZM influences the solidifying microstructure and microsegregation significantly. In the present work, a two-dimensional (2D) cellular automaton (CA) model involving the mechanism of both solidification and melting is adopted to investigate the migration phenomena of molten liquid pools in the mushy zone due to the TGZM. The effect of pulling velocity, initial liquid pool position, temperature gradient, and alloy composition on the TGZM kinetics are studied. The simulation results are compared with the analytical predictions, and good agreement between two models is obtained. It is found that under a temperature gradient, the liquid pool always migrates towards the high temperature direction. When the pulling velocity is lower than the critical velocity, the liquid pool migrates through the liquidus into the bulk liquid and the time required for a liquid pool to reach the liquidus increases with pulling velocity increasing. On the other hand, when a pulling velocity higher than the critical value is adopted, the liquid pool moves towards the solidus and the time required for migrating liquid pool to reach the solidus decreases with pulling velocity increasing. For a given pulling velocity, the liquid pools located above the critical position move towards the liquidus, while the others gradually approach to the solidus. When a molten liquid pool migrates towards the liquidus, the migration velocity and liquid pool thickness are found to gradually increase, while the liquid pool composition decreases with time. Inversely, for the molten liquid pool that moves towards the solidus, the migration velocity and liquid pool thickness gradually decrease, while the liquid pool composition increases with time going by. The average migration velocity of liquid pool caused by the TGZM effect increases with temperature gradient increasing and alloy composition decreasing. The CA simulations provide an insight into the complicated interactions among the local temperature, solute distribution and diffusion, and the kinetics of local remelting and solidification in the TGZM process.

Influence of chemical kinetics on detonation initiating by temperature gradients in methane/air

Different simplified and detailed chemical models and their impact on simulations of combustion regimes initiating by the initial temperature gradient in methane/air mixtures are studied. The limits of the regimes of reaction wave propagation depend upon the spontaneous wave speed and the characteristic velocities of the problem. The present study mainly focus to identify conditions required for the development a detonation and to compare the difference between simplified chemical models and detailed chemistry. It is shown that a widely used simplified chemical schemes, such as one-step, two-step and other simplified models, do not reproduce correctly the ignition process in methane/air mixtures. The ignition delay times calculated using simplified models are in orders of magnitude shorter than the ignition delay times calculated using detailed chemical models and measured experimentally. This results in considerably different times when the exothermic reaction affects significantly the ignition, evolution, and coupling of the spontaneous reaction wave and pressure waves. We show that the temperature gradient capable to trigger detonation calculated using detailed chemical models is much shallower (the size of the hot spot is much larger) than that, predicted by simulations with simplified chemical models. These findings suggest that the scenario leading to the deflagration to detonation transition (DDT) may depend greatly on the chemical model used in simulations and that the Zel'dovich gradient mechanism is not necessary a universal mechanism triggering DDT. The obtained results indicate that the conclusions derived from the simulations of DDT with simplified chemical models should be viewed with great caution.

Dynamic analysis and wave propagation in rotating heterogeneous cylinders under moving load and thermal conditions; implementing an efficient mesh free method

In this paper, dynamic analysis of thick hollow rotating cylinder with finite length made of two-dimensional functionally graded material subjected to a moving mechanical load is investigated. Before applying of any mechanical load, the cylinder is under initial stresses due to initial steady state temperature gradient and rotational velocity. Then a moving mechanical distributed load excites the inner boundary surface of the cylinder. Meshless local Petrov–Galerkin (MLPG) method has been rearranged and implemented in order to discretize the governing equations in the spatial domain. The resulting sets of differential equations are then solved by Newmark time integration scheme in the temporal domain. The time histories of displacements and stresses components as well as 2D stress wave propagation are obtained for various scheme of volume fraction distribution. By implementing the presented meshless technique, the effects of material distribution, moving load, rotational body forces and thermal loading on the dynamic behavior of the FG cylinder have been investigated. The achieved results show that the effects of temperature on the stresses are greater and more important than the internal moving pressure or body force due to rotational speed. The MLPG method introduces itself as a very effective method with high accuracy for stress wave propagation and dynamic analysis of 2D-FGMs.

Influence of Vertical Vibrations on the Stability of a Binary Mixture in a Horizontal Porous Layer Subjected to a Vertical Heat Flux

We present an analytical and numerical stability analysis of Soret-driven convection in a porous cavity saturated by a binary fluid mixture and subjected to vertical high-frequency and small-amplitude vibrations. Two configurations have been considered and compared: an infinite horizontal layer and a bounded domain with a large aspect ratio. In both cases, the initial temperature gradient is produced by a constant uniform heat flux applied on the horizontal boundaries. A formulation using time-averaged equations is used. The linear stability of the equilibrium solution is carried out for various Soret separation ratios $$\varphi $$ , vibrational Rayleigh numbers Rv, Lewis numbers Le and normalized porosity. For an infinite horizontal layer, the critical Rayleigh number $$\mathrm{Ra}_c$$ is determined analytically. For a steady bifurcation to a one-cell solution (the critical wavenumber is zero), we obtain $$\mathrm{Ra}_{c}={12}/{({\varphi }(\mathrm{Le}+1)+1)}$$ for all Rv. When the bifurcation is a Hopf bifurcation or when the critical wavenumber is not zero, we use a Galerkin method to compute the critical values. Our study is completed by a nonlinear analysis of the bifurcation to one-cell solutions in an infinite horizontal layer that is compared to numerical simulations in bounded horizontal domains with large aspect ratio.

Effect of boundary heat flux on columnar formation in binary alloys: A phase-field study

A non-isothermal phase-field model was employed to simulate the columnar formation during rapid solidification in binary Ni–Cu alloy. Heat flux at different boundaries was applied to investigate the temperature gradient effect on the morphology, concentration and temperature distributions during directional solidifications. With the heat flux input/extraction from boundaries, coupling with latent heat release and initial temperature gradient, temperature distributions are significantly changed, leading to solute diffusion changes during the phase-transition. Thus, irregular columnar structures are formed during the directional solidification, and the concentration distribution in solid columnar arms could also be changed due to the different growing speeds and temperature distributions at the solid–liquid interfaces. Therefore, applying specific heat conditions at the solidifying boundaries could be an efficient way to control the microstructure during solidifications.

LISCIC/PETROFER PROBE TO INVESTIGATE REAL INDUSTRIAL HARDENING PROCESSES AND SOME FUNDAMENTALS DURING QUENCHING OF STEEL PARTS IN LIQUID MEDIA

In the paper some unusual processes are considered during quenching such as self-regulated thermal process when metallic probe is covered by insulating polymeric layer, oscillation of temperature in surface layers of probe, creation a “shoulder” when quenching in polymer solution, possibility to perform austempering process just in cold liquids. Above mentioned processes build a basis for the new intensive quenching technologies and can bring a great benefit for heat treating industry when further carefully investigated. It is shown that initial temperature gradients, which cannot be governed by classical law of Fourier, can be tested by Liscic/Petrofer probe, etc. The paper discusses how organize such international investigation to satisfy contemporary practical needs and solve unsolved problems of science in the field of quenching. Also, the results of investigations can be used for software designing and cooling recipes development during quenching steel parts in liquid media. It makes a great progress because at preset time only cooling curves and cooling rates are available that are used for comparable purpose and cannot be used for recipes development.

Bidispersive vertical convection

A bidispersive porous material is one which has usual pores but additionally contains a system of micro pores. We consider a fluid-saturated bidispersive porous medium in the vertical layer x ∈(−1/2,1/2) with gravity in the − z (downward) direction. The walls of the layer are maintained at different constant temperatures. A suitable Rayleigh number is defined and we derive a global stability threshold below which no instability may arise. We additionally show that the porous layer is stable for all Rayleigh numbers provided the initial temperature gradient is bounded in a precise sense.

Vaporization and condensation in the Al4C3-SiC system

Al4SiC4 is a refractory ceramic with a reported band gap of about 2.5eV, making it an interesting semiconductor material for various applications in the field of energy. However, the synthesis of Al4SiC4 single crystals has so far not been investigated. In this study, the sublimation growth method is explored as a potential route for getting high quality single crystals. Combining a thermodynamic analysis with an extensive experimental approach, the vaporization and condensation phenomena in the Al4C3 – SiC system are described. Experimental conditions, such as initial composition, baking temperature and temperature gradient, are investigated and demonstrated regarding the crystallization of Al4SiC4. From the results obtained, a condensed phase diagram at equilibrium is established for the molar fraction XAl4C3/(Al4C3+SiC)<0.5, which corresponds to the suitable condition for the Al4SiC4 condensation. Indeed, Al4SiC4 single phase could be experimentally condensed either by self-nucleation or as oriented film on SiC substrates.

Stability of exact solutions describing two-layer flows with evaporation at the interface

A new exact solution of the equations of free convection has been constructed in the framework of the Oberbeck–Boussinesq approximation of the Navier–Stokes equations. The solution describes the joint flow of an evaporating viscous heat-conducting liquid and gas-vapor mixture in a horizontal channel. In the gas phase the Dufour and Soret effects are taken into account. The consideration of the exact solution allows one to describe different classes of flows depending on the values of the problem parameters and boundary conditions for the vapor concentration. A classification of solutions and results of the solution analysis are presented. The effects of the external disturbing influences (of the liquid flow rates and longitudinal gradients of temperature on the channel walls) on the stability characteristics have been numerically studied for the system HFE7100-nitrogen in the common case, when the longitudinal temperature gradients on the boundaries of the channel are not equal. In the system both monotonic and oscillatory modes can be formed, which damp or grow depending on the values of the initial perturbations, flow rates and temperature gradients. Hydrodynamic perturbations are most dangerous under large gas flow rates. The increasing oscillatory perturbations are developed due to the thermocapillary effect under large longitudinal gradients of temperature. The typical forms of the disturbances are shown.

Determination of the combined heat transfer coefficient to simulate the fire-induced damage of a concrete tunnel lining under a severe fire condition

To avoid underestimating the severity of damage to tunnel concrete lining under the high-temperature conditions of a fire using thermal analysis, it is important to consider the cross-sectional loss of a concrete lining during heating. This study simulates the structural loss by numerical analysis using an element elimination model and a combined heat transfer coefficient. A series of fire tests was performed with fire curves that differed in the initial temperature gradient and maximum temperature. Values of the optimized combined heat transfer coefficient were obtained from the coincidence of the results of the numerical analysis with experimental data. The results reveal that an increase in both the initial temperature gradient and maximum temperature causes greater damage to the concrete structures and also gives rise to an increase in the combined heat transfer coefficient. Values of the combined heat transfer coefficient can be inferred from values of initial temperature gradient and maximum temperature in the case of structural concrete loss. Two sets of regression equations were derived from the results depending on whether or not a structural loss occurs. The proposed method of thermal analysis outperforms the conventional method in terms of accurately simulating observed results.

Numerical investigation of spontaneous flame propagation under RCCI conditions

This paper presents results from one and two-dimensional direct numerical simulations under Reactivity Controlled Compression Ignition (RCCI) conditions of a primary reference fuel (PRF) mixture consisting of n-heptane and iso-octane. RCCI uses in-cylinder blending of two fuels with different autoignition characteristics to control combustion phasing and the rate of heat release. These simulations employ an improved model of compression heating through mass source/sink terms developed in a previous work by Bhagatwala et al. (2014), which incorporates feedback from the flow to follow a predetermined experimental pressure trace. Two-dimensional simulations explored parametric variations with respect to temperature stratification, pressure profiles and n-heptane concentration. Statistics derived from analysis of diffusion/reaction balances locally normal to the flame surface were used to elucidate combustion characteristics for the different cases. Both deflagration and spontaneous ignition fronts were observed to co-exist, however it was found that higher n-heptane concentration provided a greater degree of flame propagation, whereas lower n-heptane concentration (higher fraction of iso-octane) resulted in more spontaneous ignition fronts. A significant finding was that simulations initialized with a uniform initial temperature and a stratified n-heptane concentration field, resulted in a large fraction of combustion occurring through flame propagation. It was also found that the proportion of spontaneous ignition fronts increased at higher pressures due to shorter ignition delay when other factors were held constant. For the same pressure and fuel concentration, the contribution of flame propagation to the overall combustion was found to depend on the level of thermal stratification, with higher initial temperature gradients resulting in more deflagration and lower gradients generating more ignition fronts. Statistics of ignition delay are computed to assess the Zel’dovich (1980) theory for the mode of combustion propagation based on ignition delay gradients.

CO2 injection simulation into the South Georgia Rift Basin for geologic storage: A preliminary assessment

This study simulated the injection of supercritical phase into the South Georgia Rift (SGR) basin to evaluate the feasibility of long-term storage. Because of the lack of basin data, an equilibrium model was used to estimate the initial hydrostatic pressure, temperature, and salinity gradients that represent our study area. For the equilibrium model, the USGS SEAWAT program was used and for the injection simulation, TOUGH2-ECO2N was used. A stochastic approach was used to populate the permeability in the injection layer within the model domain. The statistical method to address permeability uncertainty and heterogeneity was sequential Gaussian simulation. The target injection depths are well below the 1 km (∼0.62 mi) depth required to maintain as a supercritical fluid. There were very little data pertaining to the properties in the deep Jurassic/Triassic SGR basin formations. So, conservative porosity and permeability starting points were postulated using data from analogous basins. This study simulated 30 million tons of injected at a rate of 1 million tons per year for 30 yr, which is the minimum capacity requirement by the U.S. Department of Energy (DOE) for a viable storage reservoir. In addition to this requirement, a 970-yr shut-in time (no injection) was also simulated to better determine the long-term fate and migration of the injected and to ensure that the SGR basin could effectively contain 30 million tons of . The preliminary modeling of injection indicated that the SGR basin is suitable for geologic storage of this U.S. DOE stated minimum capacity.

Transport Simulation of ECRH H-Mode Experiments on HL-2A Tokamak

Transport simulation of ECRH H-mode experiments on HL-2A tokamak is carried out using ONETWO code, the GLF23 and PEDESTAL models, along with TORAY code for ECRH. It is found that the initial electron and ion temperature profiles affect L-H transition significantly, and larger initial temperature gradient at the edge plasma benefits the transition. The simulation results show that it is possible to achieve ECRH H-mode with appropriate initial electron and ion temperature profiles under present discharge conditions on HL-2A tokamak. In addition, the pedestal density, electron temperature and pedestal width are predicted, and the evolutions of electron and ion temperature profile are calculated.

Numerical experiments on reaction front propagation in n-heptane/air mixture with temperature gradient

Usually different autoignition modes can be generated by a hot spot in which ignition occurs earlier than that in the surrounding mixture. However, for large hydrocarbon fuels with negative temperature coefficient (NTC) behavior, ignition happens earlier at lower temperature than that at higher temperature when the temperature is within the NTC regime. Consequently, a cool spot may also result in different autoignition modes. In this study, the modes of reaction front propagation caused by temperature gradient in a one dimensional planar configuration are investigated numerically for n-heptane/air mixture at initial temperature within and below the NTC regime. For the first time, different supersonic autoignition modes caused by a cool spot with positive temperature gradient are identified. It is found that the initial temperature gradient has strong impact on autoignition modes. With the increase of the positive temperature gradient of the cool spot, supersonic autoignitive deflagration, detonation, shock-detonation, and shock-deflagration are sequentially observed. It is found that shock compression of the mixture between the deflagration wave and leading shock wave produces an additional ignition kernel, which determines the autoignition modes. Furthermore, the cool spot is compared with the hot spot with temperature below the NTC regime. Similar autoignition modes are observed for the hot and cool spots. Different autoignition modes in the considered simplified configuration are summarized in terms of the normalized temperature gradient and acoustic-to-excitation time scale ratio. It is shown that the transition between different autoignition modes is not greatly affected by the NTC behavior. Therefore, our 1-D simulation indicates that like hot spot, the cool spot may also generate knock in engines when fuels with NTC behavior is used and the temperature is within the NTC regime.

Nonequilibrium thermal transport and its relation to linear response

We study the real-time dynamics of spin chains driven out of thermal equilibrium by an initial temperature gradient T_L \neq T_R using density matrix renormalization group methods. We demonstrate that the nonequilibrium energy current saturates fast to a finite value if the linear-response thermal conductivity is infinite, i.e. if the Drude weight D is nonzero. Our data suggests that a nonintegrable dimerized chain might support such dissipationless transport (D>0). We show that the steady-state value J_E of the current for arbitrary T_L \neq T_R is of the functional form J_E=f(T_L)-f(T_R), i.e. it is completely determined by the linear conductance. We argue for this functional form, which is essentially a Stefan-Boltzmann law in this integrable model; for the XXX ferromagnet, f can be computed via thermodynamic Bethe ansatz in good agreement with the numerics. Inhomogeneous systems exhibiting different bulk parameters as well as Luttinger liquid boundary physics induced by single impurities are discussed briefly.

Influence of natural convection in a porous medium when producing from borehole heat exchangers

Convection currents in a porous medium form when the medium is subject to sufficient heating from below (or equivalently, cooling from above) or when cooled or heated from the side. In the context of geothermal energy extraction, we are interested in how the convection currents transport heat when a sealed borehole containing cold fluid extracts heat from the porous medium; also known as a borehole heat exchanger. Using pseudospectral methods together with domain decomposition, we consider two scenarios for heat extraction from a borehole; one system where the porous medium is initialized with constant temperature in the vertical direction and one system initialized with a vertical temperature gradient. We find the convection currents to have a positive effect on the heat extraction for the case with a constant initial temperature in the porous medium, and a negative effect for some of the systems with an initial temperature gradient in the porous medium: Convection gives a negative effect when the borehole temperature is close the initial temperature in the porous medium, but gradually provides a positive effect if the borehole temperature is decreased and the Rayleigh number is larger.

Pore-scale modeling of multiphase reactive transport with phase transitions and dissolution-precipitation processes in closed systems

A pore-scale model based on the lattice Boltzmann (LB) method is developed for multiphase reactive transport with phase transitions and dissolution-precipitation processes. The model combines the single-component multiphase Shan-Chen LB model [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)], the mass transport LB model [S. P. Sullivan et al., Chem. Eng. Sci. 60, 3405 (2005)], and the dissolution-precipitation model [Q. Kang et al., J. Geophys. Res. 111, B05203 (2006)]. Care is taken to handle information on computational nodes undergoing solid-liquid or liquid-vapor phase changes to guarantee mass and momentum conservation. A general LB concentration boundary condition is proposed that can handle various concentration boundaries including reactive and moving boundaries with complex geometries. The pore-scale model can capture coupled nonlinear multiple physicochemical processes including multiphase flow with phase separations, mass transport, chemical reactions, dissolution-precipitation processes, and dynamic evolution of the pore geometries. The model is validated using several multiphase flow and reactive transport problems and then used to study the thermal migration of a brine inclusion in a salt crystal. Multiphase reactive transport phenomena with phase transitions between liquid-vapor phases and dissolution-precipitation processes of the salt in the closed inclusion are simulated and the effects of the initial inclusion size and temperature gradient on the thermal migration are investigated.

Numerical evaluation of inhomogeneity forces in a coating layer due to thermal loading

In order to clarify the mechanical state at the interface between substrate and coating material, numerical analyses are implemented on model materials under thermal loads, and the possibilities of debonding are discussed from the configurational mechanics concept. The intensity of the interfacial singularity can be discussed in relation to the inhomogeneity force which is numerically evaluated in the course of thermal loading via finite element analysis. It is shown that interfacial roughness, a small perturbation at the interface, may have a dominant role in the evolution of inhomogeneity. Effects of initial defects, temperature gradient and additional external load are also evaluated. It is confirmed that the inhomogeneity force is a generalisation of the J-integral, i.e. the energy release rate in fracture mechanics, and this is also applicable to interfacial problems. A possible scenario of layer debonding is discussed in terms of the material inhomogeneity and the deformation characteristics of the thin coating layer under thermal loading.