Penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions

The penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation is a variational inequality problem of the second kind. Using the penalty finite element approximation, we obtain optimal error estimates between the exact solution and the finite element approximation solution. Finally, we show the numerical results which are in full agreement with the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Free (open) boundary condition: some experiences with viscous flow simulations

The free (or open) boundary condition (FBC, OBC) was proposed by Papanastasiou et al. (A new outflow boundary condition, International Journal for Numerical Methods in Fluids, 1992; 14:587–608) to handle truncated domains with synthetic boundaries where the outflow conditions are unknown. In the present work, implementation of the FBC has been tested in several benchmark problems of viscous flow in fluid mechanics. The FEM is used to provide numerical results for both cases of planar and axisymmetric domains under laminar, isothermal or non‐isothermal, steady‐state conditions, for Newtonian fluids. The effects of inertia, gravity, compressibility, pressure dependence of the viscosity, slip at the wall, and surface tension are all considered individually in the extrudate‐swell benchmark problem for a wide range of the relevant parameters. The present results extend previous ones regarding the applicability of the FBC and show cases where the FBC is inappropriate, namely in the extrudate‐swell problem with gravity or surface‐tension effects. Particular emphasis has been given to the pressure at the outflow, which is the most sensitive quantity of the computations. In all cases where FBC is appropriate, excellent agreement has been found in comparisons with results from very long domains. The formulation for Picard‐type iterations is given in some detail, and the differences with the Newton–Raphson formulation are highlighted regarding some computational aspects. Copyright © 2011 John Wiley & Sons, Ltd.     

基于代数滑移模型的光催化反应器内催化剂颗粒分布特性研究

针对光催化制氢反应器内液固两相流的特点,运用代数滑移模型,对反应器内的催化剂颗粒-水两相流动进行了数值模拟。采用分块的结构化网格,并运用多重网格方法进行求解。通过与前人实验中压力梯度结果的比较,对模型进行了验证,并最终得到了反应器内催化剂颗粒的典型分布及相应的类型图。     

机械故障模糊诊断中模糊矩阵的可视化处理与分析

通过对机械故障诊断中的模糊矩阵及采用不同数学模型运算后的结果进行可视化处理,得到二维图谱和三维图谱,使故障与征兆之间的关系更加明确     

Mathematical modeling of a steam generator for sensor fault detection

A dynamic model for a nuclear power plant steam generator (vertical, preheated, U-tube recirculation-type) is formulated as a sixth-order nonlinear system. The model integrates nodal mass and energy balances for the primary water, the U-tube metal and the secondary water and steam. The downcomer flow is determined by a static balance of momentum. The mathematical system is solved using transient input data from the Philippsburg 2 (FRG) nuclear power plant. The results of the calculation are compared with actual measured values. The proposed model provides a low-cost tool for the automatic control and simulation of the steam generating process. The “parity-space” algorithm is used to demonstrate the applicability of the mathematical model for sensor fault detection and identification purposes. This technique provides a powerful means of generating temporal analytic redundancy between sensor signals. It demonstrates good detection rates of sensor errors using relatively few steps of scanning time and allows the reconfiguration of faulty signals.     

Calculation of the Slip Velocity of a Rarefied Gas on a Solid Spherical Surface with Allowance for Accommodation Coefficients

The slip velocity of a rarefied gas with inhomogeneous temperature and mass velocity on a solid spherical surface is calculated with the use of a twomoment boundary condition in the linear approximation in terms of the Knudsen number. The dependence of the slip velocity on accommodation coefficients of the two first moments of the distribution function is studied.     

Stick-slip flow of high density polyethylene in a transparent slit die investigated by laser Doppler velocimetry

The oscillating flow instability of a molten linear high-density polyethylene is carefully studied using a single screw extruder equipped with a transparent slit die. Experiments are performed using laser Doppler velocimetry in order to obtain the local velocities field across the entire die width. At low flow rate, the extrusion is stable and steady state velocity profiles are obtained. During the instability, the velocity oscillates between two steady state limits, suggesting a periodic stick-slip transition mechanism. At high flow rate, the flow is mainly characterized by a pronounced wall slip. We show that wall slip occurs all along the die land. An investigation of the slip flow conditions shows that wall slip is not homogeneous in a cross section of the slit die, and that pure plug flow occurs only for very high flow rates. A numerical computation of the profile assuming wall slip boundary conditions is done to obtain the true local wall slip velocity. It confirms that slip velocities are of the same order of magnitude as those measured with a capillary rheometer.     

Growth of Fe on Ge(1 1 1) at room temperature studied by X-ray photoelectron diffraction

The growth of ultrathin Fe films of various coverages on Ge(1 1 1) at room temperature using molecular beam epitaxy (MBE) was studied via X-ray photoelectron diffraction (XPD or XPED) together with low energy electron diffraction (LEED) and X-ray photoelectron spectroscopy (XPS). All experimentally observed XPD patterns suggested local order structures of the Fe layers for all thicknesses studied. The short-range order of the resulting structures was found to be enhanced for thinner layers whereas the long-range order was gradually lost with increasing Fe thicknesses. At a very low coverage of 0.8 Å Fe and Ge tend to react to the partly ordered structure in which Fe atoms were located in local environments similar to those for higher Fe coverages. Comparison of theoretical and experimental XPD patterns, along with XPS results, showed that intermixing between Fe and Ge occurred during the pseudomorphic growth with a stacking fault near the interface for all Fe coverages under study. Nevertheless, small percentage of domains without the stacking fault was also found to coexist with those with the stacking fault by performing a quantitative analysis of a reliability factor R of the Fe2p pattern for 5.4 Å. The orientation changes of the Ge2p and Ge3d XPD patterns with Fe thickness were unambiguously explained in terms of their different dependencies on the overlayer thickness due to the different inelastic mean free path lengths used in the simulations. Also, Fe got increasingly enriched in the grown layers with increased Fe coverage. The resulting structures and intermixing are discussed in detail.     

Misalignment Fault Prediction of Wind Turbines Based on Improved Artificial Fish Swarm Algorithm

A misalignment fault is a kind of potential fault in double-fed wind turbines. The reasonable and effective fault prediction models are used to predict its development trend before serious faults occur, which can take measures to repair in advance and reduce human and material losses. In this paper, the Least Squares Support Vector Machine optimized by the Improved Artificial Fish Swarm Algorithm is used to predict the misalignment index of the experiment platform. The mixed features of time domain, frequency domain, and time-frequency domain indexes of vibration or stator current signals are the inputs of the Least Squares Support Vector Machine. The kurtosis of the same signals is the output of the model, and the 3σ principle of the normal distribution is adopted to set the warning line of misalignment fault. Compared with other optimization algorithms, the experimental results show that the proposed prediction model can predict the development trend of the misalignment index with the least prediction error.     

遥感技术在孝丰-三门湾活动断裂调查中的应用——以杭州地区为例

遥感技术可以在宏观上对活动断裂及其构造特征进行全面的解译和识别．在区域遥感影像图制作和地质解译的基础上，采用增强和融合等图像处理方法，提高了遥感影像清晰度和解译精度，同时结合野外调查、测量以及断裂活动年代样品的采集和测定，对孝丰-三门湾断裂进行了详细的研究，查明了它的空间展布，并鉴定了活动时代和运动性质．研究结果表明，孝丰-三门湾断裂在杭州地区以挤压逆冲运动为主，兼有左旋走滑运动，并在各个地段和各个时期表现形式截然不同，影响了杭州南部地区地层沉积和构造演化．该断裂对杭州地区历史地震和现代地震具备一定的控制作用，可能在晚更新世以来有过活动．