Contact angle studies of the surface properties of covalently bonded poly-L-lysine to surfaces treated by glow-discharge

Contact angle data, measured by using a sessile drop arrangement in conjunction with Axisymmetric Drop Shape Analysis-contact Diameter (ADSA-CD), were used to quantify the effects of ammonia gas plasma treatment on the surface properties of previously untreated polystyrene surfaces. The surface tension of treated polystyrene samples is considerably higher than that of untreated samples. The increase in surface tension following plasma treatment is attributed to the addition of amine groups to the surface.Next, conformational changes following the attachment of poly-L-lysine to the untreated samples by simple adsorption and plasma treated samples by covalent bonding were investigated. Surface tension values obtained from contact angle data indicate that conformational changes to poly-L-lysine occur in both cases, because these values are lower than the surface tension of poly-L-lysine in solution. However, contact angle data show that covalently bonded poly-L-lysine undergoes less conformational changes than simply adsorbed poly-L-lysine.     

Stress function method in shakedown analysis of axisymmetric shells

A self-equilibrated stress obtained from the stress functions of thin shells is used for the static shakedown theorem as a residual stress. In combination with the finite element method, a linear programming formulation of the shakedown analysis of axisymmetric shells is derived. The physical meaning of the stress function method is clear and its computing amount is small. Some examples of the plates and shells show that the method is reasonable and efficient.The project was supported by the National Natural Science Foundation of China     

Similarity solution of thermal boundary layers for laminar narrow axisymmetric jets

In this work, the similarity equation describing the thermal boundary layers of laminar narrow axisymmetric jets is derived based on boundary layer assumptions. The equation is solved exactly. Some properties of the thermal jet are discussed. By introducing new-defined non-dimensional coordinates, the similarity solution results in a “universal” format. The results can also be applied in the boundary layer problem of species diffusion.     

An algorithm for rotating axisymmetric flows: model,validation and industrial applications

The study of axisymmetric flows is of interest not only from an academic point of view, due to the existence of exact solutions of Navier–Stokes equations, but also from an industrial point of view, since these kind of flows are frequently found in several applications. In the present work the development and implementation of a finite element algorithm to solve Navier–Stokes equations with axisymmetric geometry and boundary conditions is presented. Such algorithm allows the simulation of flows with tangential velocity, including free surface flows, for both laminar and turbulent conditions. Pseudo‐concentration technique is used to model the free surface (or the interface between two fluids) and the k–ε model is employed to take into account turbulent effects. The finite element model is validated by comparisons with analytical solutions of Navier–Stokes equations and experimental measurements. Two different industrial applications are presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical Study of Axisymmetric Richtmyer–Meshkov Instability and Azimuthal Effect on Spherical Mixing

In this paper, we present a numerical study of the axisymmetric Richtmyer–Meshkov instability in converging spherical geometry by the front tracking method for the first time. The front tracking method has been successfully used in solving fluid instability problems in both rectangular and curved geometry.^(1–6) The central issue for axisymmetric flows is the absence of the rotational symmetry in the (r, z) plane, although the perturbed shape of the initial contact interface appears to have it. The cause of the asymmetry is somewhat obvious. The sinusoidal perturbations appear symmetric only in the cross-sectional view; in actuality they are not symmetric because they represent rings around the z-axis and hence the perturbed mass at the equator, for example, is different from the perturbed mass at the pole. The first purpose of this paper is to quantify the effect of this inherited asymmetry on the growth of the spherical mixing. We find this asymmetry drives the original structure to some degree so that the mixing radius at the north pole is noticeably larger than at the equator during the evolution of chaotic mixing. We also study quantitatively the azimuthal dependence of the mixing statistics, such as the mixing edges, the growth rate and volume fraction. Richtmyer–Meshkov (RM) instabilities in spherical geometry have been a challenge due to the inherent difficulty of their accurate simulation. Our second purpose is to demonstrate that our Front Tracking method can describe the Richtmyer–Meshkov instability growth in a complex flow involving multiple reshocks. We have successfully displayed the converging geometry, reshock process, asymmetry phenomenon through the density and pressure color plots. The quantitative growth rate analysis is also presented.     

On regularity criterion to the 3D axisymmetric incompressible MHD equations

This paper is concerned with the regularity criterion for a class of axisymmetric solutions to 3D incompressible magnetohydrodynamic equations. More precisely, for the solutions that have the form of u = u_re_r+u_θe_θ+u_ze_z and b = b_θe_θ, we prove that if |ru(x,t)|≤C holds for ?1≤t < 0, then (u,b) is regular at time zero. This result can be thought as a generalization of recent results in for the 3D incompressible Navier‐Stokes equations. Copyright © 2016 John Wiley & Sons, Ltd.     

Linear stability analysis of supersonic axisymmetric jets

Stabilities of supersonic jets are examined with different velocities, momentum thicknesses, and core temperatures. Amplification rates of instability waves at inlet are evaluated by linear stability theory (LST). It is found that increased velocity and core temperature would increase amplification rates substantially and such influence varies for different azimuthal wavenumbers. The most unstable modes in thin momentum thickness cases usually have higher frequencies and azimuthal wavenumbers. Mode switching is observed for low azimuthal wavenumbers, but it appears merely in high velocity cases. In addition, the results provided by linear parabolized stability equations show that the mean-flow divergence affects the spatial evolution of instability waves greatly. The most amplified instability waves globally are sometimes found to be different from that given by LST.     

矩形非球面圆弧半径误差分离及补偿技术

研究了砂轮圆弧半径误差对大口径矩形轴对称非球面加工的影响。采用直线光栅式平行磨削的加工方式,建立了砂轮圆弧半径的误差分离的数学模型,分析影响面形精度的因素,根据加工及测量方式将砂轮圆弧半径误差分离出来,利用分离的砂轮圆弧半径误差更新砂轮圆弧半径,同时采用分离后的误差数据进行补偿加工。实验结果表明:对比不分离的补偿加工结果,粗磨和精磨条件下的分离误差补偿加工后的面形误差分别减小了14%和35%,该误差模型能够有效地分离出砂轮圆弧半径误差,分离误差效果明显,提高了加工的精度。     

MODIFICATION OF THE κ-ε TURBULENCE MODEL FOR SWIRLING RECIRCULATING FLOW IN A PIPE EXPANSION

SUMMARY

A modified turbulence model, incorporating anisotropic effects into the standard κ-ε model, is proposed for the numerical simulation of swirling recirculating flow in a pipe expansion. The new modification follows the concept that the correction to the standard κ-ε model is made only in the flow regions where the anisotropic effects are appreciable. The performance of the present hybrid κ-ε model for two swirling flows with moderate and high swirl levels is better than that of the standard κ-ε model and the modified κ-ε model proposed by Abujelala and Lilley and is also competitive with our previously developed hybrid κ-ε model. Moreover, the present hybrid modification provides a relatively simpler form compared to our previously developed model; this also helps alleviate the numerical instability in the calculation procedure. Encouraging improvement in the prediction of the size of the central toroidal recirculation zone using the present hybrid modification is also exhibited     

轴对称横观各向同性热弹性圆柱的分解

为了得到精确的应力场、位移场、温度场,将扭转圆轴的精化理论研究方法推广到轴对称横观各向同性热弹性圆柱。利用Bessel函数以及轴对称横观各向同性热弹性圆柱的通解,给出了轴对称横观各向同性热弹性圆柱的分解定理。根据柱面齐次边界条件获得了精确的精化方程,精化方程可以分解为一阶方程、超越方程、温度方程,从而将横观各向同性热弹性圆柱的轴对称问题分解为轴向拉压问题、超越问题、热-应力耦合问题。超越部分对应端部自平衡情况,可以清晰地了解到端部应力分布对内部应力场的影响,热-应力耦合部分对应无外加应力场时圆柱内部因温度变化引起的热应力。