变系数各向异性热传导问题边界元解法

提出了一种用边界元法求解一般变系数各向异性热传导问题时建立基本解的方法,并导出了求解一般二维和三维各向异性稳态热传导问题的纯边界积分方程。所建立的基本解考虑了热导率是空间坐标的函数,因此所导出的积分方程可用于求解非均质材料传热问题。由热源项引起的域积分,运用径向积分法将其转换成边界积分,形成不需要内部点的纯边界元算法。给出了二维和三维问题3个分析算例,并通过将边界元法结果与有限元法结果进行对比,证明了方法的正确性和有效性。     

Simple, robust, and fast iterative solution of Underwood's equation for minimum reflux

This work has developed a simple, robust, and fast method for the solution of Underwood's equation f(x) for minimum reflux. The new scheme involves devising an iterative solver g by re-arranging this equation, obtaining a secondary function equal to g − x, and finally applying Ostrowski's fourth-order technique to find the roots of this function. The use of Ostrowski's method in place of Newton's popular second-order formula requires little extra calculation per iteration other than a function value at an auxiliary point. The novel method is successful where the direct applications of Newton's and Ostrowski's solvers to Underwood's equation fail. It keeps iterations within bounds and rapidly converges to the root of interest.     

Computation and measurements of mass transfer and dispersion coefficients in fluidized beds

Conventional design of circulating fluidized beds requires the knowledge of dispersion and mass transfer coefficients, expressed in dimensionless forms as Sherwood numbers. However, these are known to vary by five or more orders of magnitude. Furthermore, the Sherwood numbers for fine particles reported in the literature are several orders of magnitude lower than the Sherwood number of two for diffusion to a single particle. We have shown that by replacing the particle diameter in the conventional Sherwood number with cluster or bubble diameter, the modified Sherwood number is again of the order of two.We have also shown that the kinetic theory based computational fluid dynamics codes correctly compute the dispersion and mass transfer coefficients. Hence, the kinetic theory based computational fluid dynamics codes can be used for fluidized bed reactor design without any such inputs.     

Computation of gas and solid dispersion coefficients in turbulent risers and bubbling beds

A literature review shows that dispersion coefficients in fluidized beds differ by more than five orders of magnitude. To understand the phenomena, two types of hydrodynamics models that compute turbulent and bubbling behavior were used to estimate radial and axial gas and solid dispersion coefficients. The autocorrelation technique was used to compute the dispersion coefficients from the respective computed turbulent gas and particle velocities.The computations show that the gas and the solid dispersion coefficients are close to each other in agreement with measurements. The simulations show that the radial dispersion coefficients in the riser are two to three orders of magnitude lower than the axial dispersion coefficients, but less than an order of magnitude lower for the bubbling bed at atmospheric pressure. The dispersion coefficients for the bubbling bed at 25 atm are much higher than at atmospheric pressure due to the high bed expansion with smaller bubbles.The computed dispersion coefficients are in reasonable agreement with the experimental measurements reported over the last half century.     

基于复变量求导法的共轭梯度法及其在热传导反问题边界条件辨识中的应用

为了利用共轭梯度法的计算精度高和收敛速度快的优点, 避免传统共轭梯度法在求解非线性热传导反问题中的微分处理、复杂的推导过程等问题, 给出一种改进的共轭梯度法, 即将复变量求导法引入传统的共轭梯度法, 准确计算了各灵敏度系数, 进而对瞬态非线性热传导反问题进行求解, 并对边界条件进行辨识。算例验证了本文方法的有效性与精度。与传统共轭梯度法相比, 在处理非线性问题方面, 本文方法具有操作简单和精度高的优点。     

An algorithm for the estimation of parameters in models with stochastic differential equations

An algorithm for the estimation of parameters of stochastic differential equations (SDEs) is presented. It is based on a nonlinear weighted least-squares formulation, in which the objective function is evaluated based on mean values of the measured variables predicted through an Euler discretisation of the SDEs and their integration by Monte-Carlo simulation. The problem is solved using a Levenberg-Marquardt algorithm. The presence of simulation noise is handled by choosing a convergence criterion based on the noise level and by ensuring that the optimality criterion is met for a large simulation size and hence a low noise level. In order to increase the reliability of the algorithm and to decrease its computational cost, stochastic sensitivity equations are derived. Furthermore, the number of trajectories used in the Monte-Carlo simulations is changed adaptively throughout the execution of the algorithm. This leads to a significant decrease in computational requirements. These concepts are illustrated on a simple example and a more complex model of polymer rheology. In all cases, parameter estimates close to the true parameter values are identified.     

Computation of system turbulences and dispersion coefficients in circulating fluidized bed downer using CFD simulation

In this study, the Eulerian computational fluid dynamics model with the kinetic theory of granular flow model was effectively used to compute the system turbulences and dispersion coefficients in a circulating fluidized bed (CFB) downer. In addition, the obtained model was used to simulate all the system velocities.     

Calculation of infinite dilution activity coefficients by the NRTL and UNIQUAC models

Infinite dilution activity coefficients have been calculated for 42 binary systems using the NRTL and UNIQUAC models. Temperature dependent parameters of the models are used in the calculations. These parameters have been estimated by using excess Gibbs free energy and enthalpy of mixing data simultaneously. The calculated values are compared with experimental infinite dilution activity coefficients obtained by extrapolation of vapor-liquid equilibrium (VLE) data published in the literature. The agreement between the calculated and experimental values is poor for highly nonideal system. The selection of the best model is difficult and may be system dependent.     

Trajectory modeling of gas–liquid flow in microchannels with stochastic differential equation and optical measurement

The numbering‐up of microchannel reactors definitely faces great challenge in uniformly distributing fluid flow in every channel, especially for multiphase systems. A model of stochastic differential equations (SDEs) is proposed based on the experimental data recorded by a long‐term optical measurement to well quantify the stochastic trajectories of gas bubbles and liquid slugs in parallel microchannels interconnected with two dichotomic distributors. The expectation and variance of each subflow rate are derived explicitly from the SDEs associated with the Fokker–Planck equation and solved numerically. A bifurcation in the trajectory is found using the original model, then a modification on interactions of feedback and crosstalk is introduced, the evolutions of subflow rates calculated by the modified model match well with experimental results. The established methodology is helpful for characterizing the flow uniformity and numbering‐up the microchannel reactors of multiphase system. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4028–4034, 2015     

油田掺水集输系统掺水、回站双流程仿真的实现

为解决油田掺水集输系统仿真精度不高,掺水、回站双流程不能同时实现的弊端,基于拟牛顿的循环迭代方法,提出了一种在线算法。该方法把系统各节点的流量作为约束条件,以实际生产数据为基础,通过拟牛顿方法求出掺水流程节点和管线参数,根据计算结果及油井采出液参数,应用混合量热原理,构造回站流程仿真的初值及迭代公式,最终使其回站温度与联合站加热炉入口温度达到一致。     

用线性回归方程计算离子选择电极法测定的氟含量

研究一种基于氟离子选择电极的线性范围,提出了用四点校正法和线性回归方法计算测定氟含量的方法,w(F)在0.02%～5.00%,回收率94%～100.2%,相对标准偏差(RSD)0.4%～2.1%。该方法具有准确、简便、快速、灵敏、选择性好的特点,明显优于传统的测定计算方法。     

Optimization of sub-ambient separation systems with embedded cubic equation of state thermodynamic models and complementarity constraints

A previously developed equation-based flowsheet optimization framework is extended and applied to design sub-ambient separation systems for oxy-fired coal power systems with carbon capture. Unlike most commercial flowsheet design and optimization tools, the proposed methods use exact derivatives and large-scale nonlinear programming algorithms to solve large flowsheet design problems with many degrees of freedom, including the simultaneous design of air separation units (ASUs) and their accompanying multistream heat exchangers. Emphasis is placed on additional model improvements regarding thermodynamic calculations. In order to maintain differentiability, complementarity constraints are used to model switches, including vanishing and reappearing phases. Nevertheless, these complementarity constraints may construct trivial phase equilibrium solutions, and a procedure based on embedded bubble and dew points calculations is proposed to avoid them. Furthermore, additional complementarity constraints for the cubic equation of state model are proposed to ensure correct phase identification in the supercritical region. Finally, the efficacy of these new models are demonstrated by optimization of the CO₂ processing unit and compression train for an oxy-fired power plant.     

Time-Dependent Unitary Transformation Method in the Strong-Field-Ionization Regime with the Kramers-Henneberger Picture

Time evolution operators of a strongly ionizing medium are calculated by a time-dependent unitary transformation (TDUT) method. The TDUT method has been employed in a quantum mechanical system composed of discrete states. This method is especially helpful for solving molecular rotational dynamics in quasi-adiabatic regimes because the strict unitary nature of the propagation operator allows us to set the temporal step size to large; a tight limitation on the temporal step size (δt<<1) can be circumvented by the strict unitary nature. On the other hand, in a strongly ionizing system where the Hamiltonian is not Hermitian, the same approach cannot be directly applied because it is demanding to define a set of field-dressed eigenstates. In this study, the TDUT method was applied to the ionizing regime using the Kramers-Henneberger frame, in which the strong-field-dressed discrete eigenstates are given by the field-free discrete eigenstates in a moving frame. Although the present work verifies the method for a one-dimensional atom as a prototype, the method can be applied to three-dimensional atoms, and molecules exposed to strong laser fields.     

Comparison between Cottrell diffusion and moving boundary models for determination of the chemical diffusion coefficients in ion-insertion electrodes

Using PITT technique, the various shapes of the Cottrellian diffusion plots, It^1/2 versus log t, were studied as a function of the electrode potential for the Li ions insertion into graphite electrodes. Single maximum appeared on the It^1/2 versus log t plots for stoichiometries close to pure staged phases, whereas two maxima were always observed in the two-phase coexistence domains. Slow nucleation rate during phase 2/phase 1 transition was revealed by the characteristic shape of the initial time domains of both chronoamperometric and chronovoltammetric curves. Corrected for nucleation, the longer time domain of the response was treated chronocoulometrically in the framework of two alternative approaches using the moving boundary and the classical Cottrellian models. The alternative approaches resulted in virtually the same value of D. The diffusion of Li ions during phase 2/phase 1 transition is largerly affected by slow interfacial charge transfer. In this case, the spinodal domain in the free-energy curve is effectively degenerated even at small overvoltages. This substantiates the formal application of the Cottrellian diffusion approach to determine D during the processes of intercalation and deintercalation, accompanied by first-order transitions; however, involvement of the slow interfacial kinetics in the measured response should be adequatly taken into account.     

Recent advances on the neuroprotective potential of antioxidants in experimental models of Parkinson's disease

Parkinson's disease (PD), a neurodegenerative movement disorder of the central nervous system (CNS) is characterized by a progressive loss of dopaminergic neurons in the substantia nigra pars compacta region of the midbrain. Although the etiology of PD is not completely understood and is believed to be multifactorial, oxidative stress and mitochondrial dysfunction are widely considered major consequences, which provide important clues to the disease mechanisms. Studies have explored the role of free radicals and oxidative stress that contributes to the cascade of events leading to dopamine cell degeneration in PD. In general, in-built protective mechanisms consisting of enzymatic and non-enzymatic antioxidants in the CNS play decisive roles in preventing neuronal cell loss due to free radicals. But the ability to produce these antioxidants decreases with aging. Therefore, antioxidant therapy alone or in combination with current treatment methods may represent an attractive strategy for treating or preventing the neurodegeneration seen in PD. Here we summarize the recent discoveries of potential antioxidant compounds for modulating free radical mediated oxidative stress leading to neurotoxicity in PD.     

Comparing the bias and misspecification in ARFIMA models

We investigate the bias in both the short-term and long-term parameters for a range of autoregressive fractional integrated moving-average (ARFIMA) models using both semi-parametric and maximum likelihood (ML) estimation methods. The results suggest that, provided the correct model is estimated, the ML method outperforms the semi-parametric methods in terms of the bias and smaller mean square errors in both the long-term and short-term parameter estimates. These biases often cause model selection criteria to select an incorrect ARFIMA specification. Taking account of the potential misspecification the biases associated with the ML procedure tend to increase, although it continues to have a smaller worst-case bias than either of the semi-parametric procedures.     

Measurement and thermodynamic modeling of partition coefficients in N,N-dimethylacetamide-water-carbon dioxide system

The partition coefficients of N,N-dimethylacetamide (N,N-DMA) between the water and the supercritical and near-critical carbon dioxide (CO₂) phases were measured in the temperature range of 298.15-328.15 K and the pressure range of 8.3-24.1 MPa. The measurements were carried out in a 56 ml vessel by contacting the carbon dioxide and the aqueous phases. The partition coefficients of N,N-DMA increased from 0.05 to 0.150 with increasing pressure at a constant temperature and increased with temperature at a constant density. The bubble point pressures of N,N-DMA-CO₂ mixtures were measured at 298.15 K, 308.15 K and 318.15 K and were found to increase with increasing mole fraction of CO₂. The partition coefficients were modeled using the Peng-Robinson Equation of State (PREOS) combined with modified van der Waals mixing rule. The binary interaction parameters for the CO₂-H₂O pair were taken from the literature and were regressed for CO₂-N,N-DMA and H₂O-N,N-DMA pairs by fitting partition coefficients data. The binary interaction parameter for CO₂-N,N-DMA pair was found to depend linearly on temperature. The bubble point pressures of N,N-DMA and CO₂ were also measured and could be predicted fairly well using the regressed binary interaction parameters.