A spectral/hp least‐squares finite element analysis of the Carreau–Yasuda fluids

A least‐squares finite element model with spectral/hp approximations was developed for steady, two‐dimensional flows of non‐Newtonian fluids obeying the Carreau–Yasuda constitutive model. The finite element model consists of velocity, pressure, and stress fields as independent variables (hence, called a mixed model). Least‐squares models offer an alternative variational setting to the conventional weak‐form Galerkin models for the Navier–Stokes equations, and no compatibility conditions on the approximation spaces used for the velocity, pressure, and stress fields are necessary when the polynomial order (p) used is sufficiently high (say, p > 3, as determined numerically). Also, the use of the spectral/hp elements in conjunction with the least‐squares formulation with high p alleviates various forms of locking, which often appear in low‐order least‐squares finite element models for incompressible viscous fluids, and accurate results can be obtained with exponential convergence. To verify and validate, benchmark problems of Kovasznay flow, backward‐facing step flow, and lid‐driven square cavity flow are used. Then the effect of different parameters of the Carreau–Yasuda constitutive model on the flow characteristics is studied parametrically. Copyright © 2016 John Wiley & Sons, Ltd.     

A fully automatic system for underway N2O measurements based on cavity ring-down spectroscopy

N₂O is one of the most important greenhouse and ozone-depleting gases and has been the source of considerable concern in recent years. The oceans account for ~ 1/4 of the global N₂O emission budget; however, the oceanic N₂O source/sink characteristics are not well understood. To enhance the study of oceanic N₂O source/sink characteristics, our laboratory developed a fully automatic underway system for surface water N₂O concentration and atmospheric N₂O mole fraction measurements consisting of a cavity ring-down spectroscopy (CRDS) instrument and an upstream device. The developed device can be programmed to switch the CRDS measurements from the equilibrator headspace to the atmospheric sample and the reference gas sample. The surface water N₂O concentration is calculated from the equilibrium headspace N₂O mole fraction in the equilibrator. The response time of this equilibrator is ~ 3.4 min, and the estimated precision of this method for surface water N₂O measurements is better than 0.5% (relative standard deviation, RSD), which is one order of magnitude better than that of traditional gas chromatographic methods and can be further optimised. Data are acquired every 20 s, and the calibration frequency requirement of this system is approximately 7–10 days. This labor-saving underway system is a powerful tool for high-precision and high-resolution measurements of atmospheric and oceanic N₂O and can significantly improve the study of the characteristics of oceanic N₂O sources/sinks and their response to climate change.     

Experimental observations of the thermal flow around a square obstruction on a vertical wall in a differentially heated cavity

The transient thermal boundary layer flow around a square obstruction placed at the middle of the hot wall in a differentially heated cavity is visualized using a shadowgraph technique. The results show that the thermal boundary layer flow, which is blocked by the obstruction, firstly forms an intrusion head under the obstruction (the lower intrusion head). Subsequently, the lower intrusion head bypasses the obstruction and reattaches to the down-stream boundary. During the reattachment process, a more complicated flow is induced, and eventually both the lower intrusion head and the thermal boundary layer destabilize. After the lower intrusion head is convected away, the thermal boundary layer flow re-stabilizes. At the quasi-steady state, the thermal boundary layer forms a double-layer structure, which is split into two sections by the obstruction. It is demonstrated that both the transient processes and the quasi-steady state flow structures of the thermal boundary layer are significantly altered by the obstruction in comparison with the case without the obstruction.     

Dynamics of ellipsoidal cavities in fluid

A mathematical model of the hydrodynamics of free closed surfaces in a fluid is expounded. It is used for studying the dynamics of ellipsoidal cavities during their development. The model is based on a system of differential equations that accounts for the influence exerted on the dynamics of cavities by various perturbations such as gravity, surface tension, viscosity, and geometrical features of the cavity. Solving this system makes it possible to determine the hydrodynamic characteristics of the flow around the cavity and to plot cavity shapes depending on time and flow regimes. Characteristic features of the development of such cavities under gravity and surface tension are established __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 24–31, February 2006.     

界面上圆形衬砌结构对平面SH波散射

研究界面上的圆形衬砌结构对平面SH波散射与动应力集中问题.在一个含有半圆形衬砌缺口的弹性半空间水平面上,Green函数是受时间谐和的出平面线源载荷作用的位移基本解.采用沿界面“剖分”圆形衬砌结构的方法,并利用界面连续性条件建立起问题的定解积分方程组,进而得到圆形衬砌上的动应力集中解.最后给出了关于界面圆形衬砌结构上动应力集中系数的数值结果,并对界面圆形衬砌结构的动应力集中系数的影响进行了讨论.     

浅埋圆形孔洞附近的半圆形凸起对SH波的散射

采用"契合"的思想，给出了地下孔洞与地面上的半圆形凸起地形对SH波散射问题的 解答. 将整个求解区域分割成两部分来处理. 其一为包括半圆形凸起地形在内的一个圆形区 域I，其余为区域II. 在区域I和II中分别构造位移解，并在两个区域的"公共边界"上 实施"契合". 在区域I中构造一个上半部边界应力为零，而其余部分位移、应力任意的驻 波解，在区域II中构造出半圆形凹陷和浅埋圆孔的散射波，且要求它满足水平界面上应力 为零的约束条件. 然后再通过移动坐标，满足"公共边界"的"契合"条件和地下孔洞的边 界条件，建立起求解该问题的无穷代数方程组. 最后，给出了分析例题和数值结果，并 对其进行了讨论.     

On the Shape and Dimensions of Three-Dimensional Cavities in Supercavitating Flows

The shape of long, trailing cavities behind three-dimensional headforms is discussed. The case of a flat elliptic wing is specifically treated. Three distinct shape regimes are found: quasi-planar, long-flat, spheroidal. These appear in successively higher speed ranges (lower cavitation numbers, ). It is argued that the cavities may be replaced by surrogates in the form of slender ellipsoids. The pressures on these are almost constant and correspond to a cavitation number equal to twice their longitudinal added mass coefficient, k₁. A heuristic theory based on kinetic energy fields is given, relating k₁ to the product of headform drag and cavity length. This theory correlates with an exact theory in the same form given by Garabedian for axi-symmetric cones and also with its extension to planar flows. Results are given here for the shape of the cavity behind an elliptic wing of any aspect ratio, given drag, and cavitation number. Specific formulae are given in the form, = f (C_D/AR), for the transition between the quasi-planar and long-flat regime, and the long-flat and spheroidal regime.     

液滴撞击结构液靶成坑特点分析

本文介绍了液滴对多层液靶的撞击实验研究,实验中液体从不同高度滴落,同时改变液靶的液层厚度,通过高速摄影机记录撞击成坑的过程,将胶片扫描数据输入计算机,并通过图像软件处理获得最终成坑数据。由实验结果分析了液滴撞击多层液靶成坑的特点,在一定的撞击能量情况下,撞击成坑现象发生于第一层液靶内,界面能在多层液靶不互溶时成为影响成坑状态的一个重要参数。根据能量守恒定律,并通过对撞击能量转化过程的分析,得出了撞击成坑最大坑径公式。     

Elliptic cavity in a three-dimensional anisotropic body with inclined strata deformed by line loads and dislocations

Summary Analytical solutions are proposed for the stress and displacement fields in a quasi three-dimensional elastic anisotropic body containing an elliptic cavity or rigid inclusion. The directions of the principal elastic axes are allowed to be inclined arbitrarily with respect to the axes of the elliptic cavity. As an application, expressions for the stress intensity factors are formulated when the cavity reduces to a colinear crack.