Generalized numerical modelling of unsteady heat transfer during cooling and freezing using an improved enthalpy method and quasi-one-dimensional formulation

A numerical solution of a generalized Stefan problem is presented. It covers a great variety of unsteady heat conduction cases accompanied by phase transformations. A mathematical model is developed for determination of the unsteady-state temperature and enthalpy fields (as well as the space-time evolution of the phase content) and of the cooling and freezing (heating and thawing) times of food materials and other bodies of various configuration (representing multicomponent two-phase systems having one freezable component). An improved enthalpy method is proposed by which all non-linearities, caused by the temperature dependence of the thermophysical coefficients, are introduced in a functional relationship between the volumetric specific enthalpy and the Kirchhoff function. Thus the non-linearities are eliminated as a factor making the solution difficult. The applied approach possesses great adaptivity and flexibility in solving complicated moving boundary problems: it is suitable for both isothermal and non-isothermal phase change, reaches a high degree of correspondence between the real physical phenomenon and its mathematical formalization, uses uniform and easy fixed-grid computational techniques, makes it possible to avoid complications and to eliminate possible errors caused by ‘jumping’ of the equivalent specific heat capacity peak at the maximum of the latent heat effect, etc. Efficient procedures and algorithms for computer simulation of complex refrigerating technological processes are created. Experimental verification demonstrating the applicability and accuracy of the model is carried out.     

Synthesis of shape and topology of multi-material structures with a phase-field method

In this paper, we present a phase-field method to the problem of shape and topology synthesis of structures with three materials. A single phase model is developed based on the classical phase-transition theory in the fields of mechanics and material sciences. The multi-material synthesis is formulated as a continuous optimization problem within a fixed reference domain. As a single parameter, the phase-field model represents regions made of any of the three distinct material phases and the interface between the regions. The Van der Waals–Cahn-Hilliard theory is applied to define a dynamic process of phase transition. The Γ-convergence theory is used for an approximate numerical solution to this free-discontinuity problem without any explicit tracking of the interface. Within this variational framework, we show that the phase-transition theory leads to a well-posed problem formulation with the effects of “domain regularization” and “region segmentation” incorporated naturally. The proposed phase-field method is illustrated with several 2D examples that have been extensively used in the recent literature of topology optimization, especially in the homogenization based methods. It is further suggested that such a phase-field approach may represent a promising alternative to the widely-used homogenization models for the design of heterogeneous materials and solids, with a possible extension to a general model of multiple material phases.     

Analytical solution for the simultaneous heat and mass transfer problem in air washers

An analytical solution approach for the simultaneous heat and mass transfer problem in air washers operating as evaporative coolers is presented. A one-dimensional model using the coupled mass and energy balance equations in the air washer is presented. Then, starting from a linear approach for the experimental curve of the air saturation, an analytical solution for the model was derived. The solution showed an excellent agreement with the available results found in the literature. The influence of several important parameters for the cooling process such as temperature and ambient air humidity, air flow rate and feeding water temperature, in the air cooling rate was investigated. The efficacy of the process can be greatly increased by reducing the cooling water temperature and the applied air flow rate. The analytical solution can be easily included into the models used for simulating desiccant air-conditioning systems operating in conjunction with air washers.     

Equi-axed growth and related segregations in cast metallic alloys

Full-scale trials of DC ingots and laboratory scale directional solidification experiments have been performed to study the effect of grain structure on macro-segregation in industrial cast products. An Al alloy sheet ingot was cast with constant casting conditions (speed, superheat, cooling rate) except for the grain refiner: the first half of the ingot was non-inoculated, while the second half was inoculated. The results indicate that the extent and intensity of the centreline segregation is modified via the grain-refinement treatment: the finer the grains are, the more intense is the macro-segregation.Numerical simulations of directional solidification of binary Al–Cu alloys have been carried out with the help of a 2D finite volume software which takes account of the movement of the liquid with respect to the solid in the mushy zone. It is possible to account for the segregation pattern of the directionally solidified ingots that exhibit columnar or coarse equi-axed grain structures. Contrarily, the intense segregation of the fine-grained ingots is not yet understood.     

Equi-axed growth and related segregations in cast metallic alloys

Full-scale trials of DC ingots and laboratory scale directional solidification experiments have been performed to study the effect of grain structure on macro-segregation in industrial cast products. An Al alloy sheet ingot was cast with constant casting conditions (speed, superheat, cooling rate) except for the grain refiner: the first half of the ingot was non-inoculated, while the second half was inoculated. The results indicate that the extent and intensity of the centreline segregation is modified via the grain-refinement treatment: the finer the grains are, the more intense is the macro-segregation.

Numerical simulations of directional solidification of binary Al-Cu alloys have been carried out with the help of a 2D finite volume software which takes account of the movement of the liquid with respect to the solid in the mushy zone. It is possible to account for the segregation pattern of the directionally solidified ingots that exhibit columnar or coarse equi-axed grain structures. Contrarily, the intense segregation of the fine-grained ingots is not yet understood.     

A Streamline-Upwind-Full-Galerkin method for space–time convection dominated -transport problems

An original space-time finite element approach for the solution of the diffusion-convection equation is proposed in this paper. A slight manipulation of the differential equation suggests that transient transport problems may in fact be seen as ‘steady-state space-time transport problems’, accurately and easily soluble by the standard Galerkin technique. However, concerning convective transport involving sharp fronts or coarse discretization, it is shown that implementation of dissipation along space-time trajectories significantly improves the solutions. Classical comparative test problems are run to establish the performances of this method, and to show the limits of the more sophisticated Petrov and Taylor-Galerkin schemes. Evocation of a possible space-time anisotropy generated by usual finite difference time-stepping procedures, as well as comparative analysis of amplification matrices, help to understand the accuracy and the robustness of the proposed approach.     

利用昼夜温差的太阳能电水联产系统

太阳能作为一种清洁无污染,取之不尽用之不竭的能源越来越受到人们的关注。太阳能光伏发电是现今太阳能利用的主要方式,在光伏发电过程中如果硅板散热不好将使得硅板温度的上升,从而导致发电效率降低。针对此,我们小组提出了基于吸附式制冷的电水联产系统,利用沙漠昼夜的巨大温差,通过水的蒸发解决硅板散热问题,且在夜间进行空气取水。该系统结构简单,稳定可靠,无能耗无水耗,既解决太阳能发电的硅板散热问题,又可制水供缺水地区生活所用。     

Perimeter-based coverage optimization to improve lifetime in wireless sensor networks

The most important problem in a Wireless Sensor Network (WSN) is to optimize the use of its limited energy provision, so that it can fulfil its monitoring task as long as possible. Among known available approaches that can be used to improve power management, lifetime coverage optimization provides activity scheduling which ensures sensing coverage while minimizing the energy cost. In this article an approach called Perimeter-based Coverage Optimization protocol (PeCO) is proposed. It is a hybrid of centralized and distributed methods: the region of interest is first subdivided into subregions and the protocol is then distributed among sensor nodes in each subregion. The novelty of the approach lies essentially in the formulation of a new mathematical optimization model based on the perimeter-coverage level to schedule sensors' activities. Extensive simulation experiments demonstrate that PeCO can offer longer lifetime coverage for WSNs compared to other protocols.     

Modelling the pressure die casting process with the boundary element method: Steady state approximation

This paper describes a model which can predict the temperatures on the cavity surfaces of a die. The time varying boundary conditions are averaged so that the process can be modelled as a steady state problem. Since the model considers only thin components, it is reasonable to assume that the melt has totally solidified before ejection, and therefore the quantity of heat energy entering the die over the casting cycle can be estimated. This and other assumptions relating to the boundary conditions also enable the value of thermal resistance between the melt and the die to be estimated. Under certain conditions, subcooled nucleate boiling takes place in the cooling channels of the die. An iterative procedure is used to take account of this, which involves the repeated calculation of global heat transfer coefficients for the cooling channels, with the criteria that the total energy transferred through the channels is equal to that transferred due to boiling and convection. The boundary element method is used to predict the cavity temperatures. In die casting, only the temperatures on the cavity surfaces are of interest since the surface quality of a component is related significantly to the temperature distribution over the cavity. Since only thin components are considered herein, it is not necessary to model the solidifcation process and discretize the cast. These factors make the BEM ideally suited for the work described in this paper. To verify the model, the predicted temperatures for two components are compared with experimental values measured using thermocouples and a thermal imaging camera. It was found that there is fairly good agreement between the two sets of results.     

Numerical study on cooling characteristics of two-phase closed thermosyphon embankment in permafrost regions

The two-phase closed thermosyphon (TPCT) is an effective heat transfer device decreasing the ground temperature around it in cold season, but not absorbing heat energy in warm season. In this paper, in order to research the efficiency of the TPCT applied to the embankment in permafrost regions, a three-dimension model for the TPCT embankment was presented based on the work characteristics of the TPCT and on the related heat transfer theories. The numerical results showed that 1) the model can reasonably solve the coupled heat transfer problem of air-TPCT-soil for TPCT embankment; 2) the TPCT embankment is effective to protect the underlying permafrost and to ensure the stability of roadway in permafrost regions; furthermore, it could play rapidly a cooling effect and approach a thermal balance state after 5 years of construction; and 3) the TPCT, if combined with other engineering methods such as insulation, crushed rock, etc., can be an more effective engineering measure to ensure the stability of roadway engineering in warm permafrost regions.     

A Fast Charging–Cooling Coupled Scheduling Method for a Liquid Cooling-Based Thermal Management System for Lithium-Ion Batteries

Efficient fast-charging technology is necessary for the extension of the driving range of electric vehicles. However, lithium-ion cells generate immense heat at high-current charging rates. In order to address this problem, an efficient fast charging–cooling scheduling method is urgently needed. In this study, a liquid cooling-based thermal management system equipped with mini-channels was designed for the fast-charging process of a lithium-ion battery module. A neural network-based regression model was proposed based on 81 sets of experimental data, which consisted of three sub-models and considered three outputs: maximum temperature, temperature standard deviation, and energy consumption. Each sub-model had a desirable testing accuracy (99.353%, 97.332%, and 98.381%) after training. The regression model was employed to predict all three outputs among a full dataset, which combined different charging current rates (0.5C, 1C, 1.5C, 2C, and 2.5C (1C = 5 A)) at three different charging stages, and a range of coolant rates (0.0006, 0.0012, and 0.0018 kg·s⁻¹). An optimal charging–cooling schedule was selected from the predicted dataset and was validated by the experiments. The results indicated that the battery module’s state of charge value increased by 0.5 after 15 min, with an energy consumption lower than 0.02 J. The maximum temperature and temperature standard deviation could be controlled within 33.35 and 0.8 °C, respectively. The approach described herein can be used by the electric vehicles industry in real fast-charging conditions. Moreover, optimal fast charging–cooling schedule can be predicted based on the experimental data obtained, that in turn, can significantly improve the efficiency of the charging process design as well as control energy consumption during cooling.     

基于变分渐近法预测饱和多孔介质流固耦合性能的细观力学模型

饱和岩土类多孔材料内固、液相不同属性产生的各向异性和多孔微结构的不均匀性使得材料的细观力学特性计算变得十分复杂。为准确预测岩土类材料的有效弹性性能和细观应力-应变场,基于Biot多孔弹性介质理论,建立可描述岩土类多孔材料固液相运动的能量泛函和相应的多孔弹性本构关系;利用细、宏观尺度比作为小参数将能量变分泛函渐近扩展为系列近似泛函;以场变量波动函数为未知量,通过解决近似泛函的最小化问题(驻值问题)得到波动函数的解析解,从而建立逼近物理和工程真实性的细观力学模型,并通过有限元技术得以数值实现。多孔介质材料细观力学特性算例表明:与经典均匀化理论(将液体类比为具有较高泊松比的固体材料)相比,基于变分渐近均匀化细观模型预测的多孔介质材料细观力学特性更精确,尤其是能准确重构多孔微结构内局部应力-应变场分布,为损伤破坏、局部断裂分析奠定了坚实基础。      

集中空调系统的冷量计量

分析了我国冷量计量的现状,并且对国内目前采用的冷计量方法进行了介绍和比较.认为集中空调系统的冷计量对建筑节能有着重大意义,应引起建筑环境、物业管理和建筑节能研究工作者的关注,并共同促进冷计量在国内的发展.     

A novel cooling scheme for superconducting power cables

Long distance transmission of electrical power with superconducting cables is likely necessary for energy conservation and effective utilization of renewable energy sources. The performance and cost of such superconducting lines is as significantly influenced by cryogenic issues as by superconductor performance. One significant cryogenic issue is that in the usual method of cooling using sub-cooled cryogen flow there is a limited cable length before the cryogen needs to be re-cooled. This adds complexity and cost to the cable system. Here we address this problem by utilizing the latent heat of the cryogen without the complication of multi-phase flow. The cryogen is distributed to the superconducting components by spraying it through small holes in a pressurized line. The pressurized liquid exiting the holes turns into mixed liquid and vapor with a temperature near the boiling point of the cryogen at the pressure of the space surrounding the superconducting components. The pressure in the space surrounding the superconducting components is then kept near atmospheric by maintaining short distances to a vent. The sprayed liquid accumulates but rapidly vaporizes in response to the heat load, providing even cooling power at a fixed temperature for the entire length of the line. Our work indicates that it may be possible to implement a cooling system with much simplified cryogenic stations at the cable ends and allowing cable lengths of up to 100 km with no intermediate cooling stations.     

真空冷却过程中水分蒸发沸腾的数值模拟（Ⅰ）：模型的建立

真空冷却过程是复杂的相变传热传质过程。在真空冷却期间,当真空室内的真空压力低于或者等于熟肉温度对应的饱和压力时,熟肉内部的水分将会沸腾蒸发以产生冷却效应。在能量和质量守恒的基础上,经过适当的简化,建立了真空冷却过程中水分迁移的数学模型。此模型能够预测真空冷却过程中熟肉内部的温度、压力和水分含量分布。     

Variational eigenerosion for rate-dependent plasticity in concrete modeling at small strain

In the context of eigenfracture scheme, the work at hand introduces a variational eigenerosion approach for inelastic materials. The theory seizes situations where the material accumulates large amounts of plastic deformations. For these cases, the surface energy entering the energy balance equation is rescaled to favor fracture, thus energy minimization delivers automatically the crack-tracking solution also for inelastic cases. The minimization approach is sound and preserves the mathematical properties necessary for the Γ-limit proof, thus the existence of (local) minimizers is guaranteed by the Γ-convergence theory. Although it is not possible to demonstrate that the obtained minimizers are global, satisfactory results are obtained with the local minimizers provided by the method. Furthermore, with the goal of addressing the constitutive behavior of concrete, a Drucker-Prager viscoplastic consistency model is introduced in the microplane setting. The model delivers a rate-dependent three-surface smooth yield function that requires hardening and hardening-rate parameters. The independent evolution of viscoplasticity in different microplanes induces anisotropy in the mechanical response. The sound performance of the model is illustrated via numerical examples for both rate-independent and rate-dependent plasticity.     

Solute redistribution and segregation in solidification processes

In this review paper, research on solute redistribution coefficients for equilibrium, near equilibrium and non-equilibrium solidification processes were first analyzed. Then, different models advanced since the 1950s for solute redistribution during the directional solidification process with a planar interface were summarized. The so-called second-order opposite diffusion compensation method (SODCM) presented by the author was described in detail. Thirdly, solute redistribution in the dendritic solidification process and the segregation were discussed. It is concluded that the problem can be described resulting ϕ_S−w_L functions. Among the different models, that obtained by the present author in 1994 was explained. Fourthly, the formation of macro-segregation mainly caused by liquid flow in the mushy zone is analyzed. A parameter about the driving force for the liquid flow is described. The parameter is considered to be the controlling parameter for the formation of macro-segregation. The relationship between the parameter and the compositions in steel is also given in the paper as an example.     

Novel cooling channel shapes in pressure die casting

The pressure die casting involves die designs incorporating cooling channels positioned to facilitate the controlled extraction of energy from a solidifying casting. It is now known that subcooled nucleate boiling can occur in cooling channels and this paper is concerned with novel cooling channel shapes that are optimized to promote and enhance this boiling and thus reduce casting times. Shape sensitivity analysis is applied to a boundary element model using the material derivative adjoint variable technique. Mesh node positions on the cooling channels are used as the design parameters. The sensitivities are used in a conjugate gradient non‐linear optimization routine. It is shown that with this approach cooling channels can be designed to maximize boiling heat transfer whilst at the same time allow some degree of control of spatial temperature variation over the die cavity surface. Simulation and experimental results are presented for a traditional die and an optimized die. A 60 per cent reduction in cycle time is achieved with the optimized die. Copyright © 2001 John Wiley & Sons, Ltd.     

Bayesian ranking of sites for engineering safety improvements: decision parameter, treatability concept, statistical criterion, and spatial dependence

In recent years, there has been a renewed interest in applying statistical ranking criteria to identify sites on a road network, which potentially present high traffic crash risks or are over-represented in certain type of crashes, for further engineering evaluation and safety improvement. This requires that good estimates of ranks of crash risks be obtained at individual intersections or road segments, or some analysis zones. The nature of this site ranking problem in roadway safety is related to two well-established statistical problems known as the small area (or domain) estimation problem and the disease mapping problem. The former arises in the context of providing estimates using sample survey data for a small geographical area or a small socio-demographic group in a large area, while the latter stems from estimating rare disease incidences for typically small geographical areas. The statistical problem is such that direct estimates of certain parameters associated with a site (or a group of sites) with adequate precision cannot be produced, due to a small available sample size, the rareness of the event of interest, and/or a small exposed population or sub-population in question. Model based approaches have offered several advantages to these estimation problems, including increased precision by "borrowing strengths" across the various sites based on available auxiliary variables, including their relative locations in space. Within the model based approach, generalized linear mixed models (GLMM) have played key roles in addressing these problems for many years. The objective of the study, on which this paper is based, was to explore some of the issues raised in recent roadway safety studies regarding ranking methodologies in light of the recent statistical development in space-time GLMM. First, general ranking approaches are reviewed, which include na?ve or raw crash-risk ranking, scan based ranking, and model based ranking. Through simulations, the limitation of using the na?ve approach in ranking is illustrated. Second, following the model based approach, the choice of decision parameters and consideration of treatability are discussed. Third, several statistical ranking criteria that have been used in biomedical, health, and other scientific studies are presented from a Bayesian perspective. Their applications in roadway safety are then demonstrated using two data sets: one for individual urban intersections and one for rural two-lane roads at the county level. As part of the demonstration, it is shown how multivariate spatial GLMM can be used to model traffic crashes of several injury severity types simultaneously and how the model can be used within a Bayesian framework to rank sites by crash cost per vehicle-mile traveled (instead of by crash frequency rate). Finally, the significant impact of spatial effects on the overall model goodness-of-fit and site ranking performances are discussed for the two data sets examined. The paper is concluded with a discussion on possible directions in which the study can be extended.     

Two‐phase thermo‐mechanical and macrosegregation modelling of binary alloys solidification with emphasis on the secondary cooling stage of steel slab continuous casting processes

As an approach towards a better modelling of solidification problems, we introduce a thermo‐mechanical and macrosegregation model that considers a solidifying alloy as a binary mixture made of a liquid and a solid phase. Macroscopic conservation laws for mass, momentum and solute are obtained by spatial averaging of the respective microscopic conservation equations. Assuming local thermal equilibrium, a single equation for the conservation of the mixture energy is then written. A single equation can be obtained for the solute as well by invoking a proper microsegregation rule. The numerical implementation in a two‐dimensional finite element code is then detailed. Lastly, some examples of simulations of academic tests as well as industrial applications for continuous casting of steel slabs are discussed. They particularly enlighten the ability of the formulation to describe the formation of central macrosegregation during the secondary cooling of slab continuous casting processes. Copyright © 2006 John Wiley & Sons, Ltd.