On Maxwell fluids with relaxation time and viscosity depending on the pressure

We study a variant of the well-known Maxwell model for viscoelastic fluids, namely we consider a Maxwell fluid with viscosity and relaxation time depending on the pressure. Such a model is relevant for example in modelling the behaviour of some polymers and geomaterials. Although it is experimentally known that the material moduli of some viscoelastic fluids can depend on the pressure, most of the studies concerning the motion of viscoelastic fluids do not take such effects into account despite their possible practical significance in technological applications. Using a generalized Maxwell model with pressure dependent material moduli we solve a simple boundary value problem and we demonstrate interesting non-classical features exhibited by the model.     

Consideration of viscosity during subsonic penetration of a solid body into isotropic barriers

In solving the problem of the reaction of solids with isotropic barriers during their impact, one of the main questions is determination of the penetration resistance of the solid into the barrier. Currently in calculating this resistance as a basic phenomenological approach use is made of the hydrodynamic anomaly in accordance with which the penetration resistance in the plastic region is assumed to be equivalent to the resistance of an ideal liquid.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 120–125, May–June, 1986.     

The influence of paper compressibility on ink penetration

Summary An analysis on the compressible nature of paper shows that under high pressures the pore size is linearly related to the square root of pressure. An expression for the penetration of ink into paper as a function of pressure is derived and agrees satisfactorily with experimental results. It is also shown that the mean hydraulic radius of the pores of a paper can be calculated directly from the fall in the diffuse reflectance of paper caused by the penetration of black ink under pressure.     

动能弹侵彻机场跑道的参数敏感性分析

为研究倾角、着速、攻角、靶体材料等因素对动能弹侵彻响应的影响,采用正交试验方法设计了数值试验和4参数3水平的正交表,进行了侵彻过程中的参数敏感性分析。经过对参数的研究,得到了影响动能弹侵彻动力学响应的主要因素。研究表明：着速和倾角对弹体减速度影响较大;影响剩余速度的主要因素是着速、倾角、基层强度;倾角和攻角对弹体的偏转影响较大。     

Research on viscosity of metal at high pressure

A new experimental technique, the flyer-impact method, is proposed in this article to investigate the viscosity coefficient of shocked metals. In this technique, a shock wave with a sinusoidal perturbation on the front is induced by the sinusoidal profile of the impact surface of the sample by use of a two-stage light-gas gun, and the oscillatory damping process of the perturbation amplitude is monitored by electric pins. The damping processes of aluminum at 78 and 101 GPa and iron at 159 and 103 GPa are obtained by this technique, which supplement the existing data by measuring the viscosity coefficient via a dynamic high-pressure method. Applying the formula of Miller and Ahrens to fit the experimental data, the shear viscosity coefficients of aluminum at 78 and 101 GPa are \(1350\,\pm \,500\) and \(1200\,\pm \,500~\hbox {Pa}\,\hbox {s}\), respectively, and those of iron at 159 and 103 GPa are \(1150\,\pm \,1000\) and \(4800\,\pm \,1000~\hbox {Pa}\,\hbox {s}\), respectively. The values measured by the flyer-impact method, approximately \(10^{3}~\hbox {Pa}\, \hbox {s}\), are consistent with those measured by Sakharov’s method, while still greatly differing from those measured by static high-pressure methods. In dynamic high-pressure experiments, the shear viscosity is related to dislocation motion in the solid material, while that in static high-pressure experiments is related to the diffusion motion of atoms or molecules in liquids. Therefore, there are different physical meanings of shear viscosity in dynamic and static high-pressure experiments, and there is no comparability among these results.     

Effect of the size and pressure on the modified viscosity of water in microchannels

The phenomenon that flow resistances are higher in micro scale flow than in normal flow is clarified through the liquid viscosity. Based on the experimental results of deionized water flow in fused silica microtubes with the inner radii of 2.5 μm, 5 μm, 7.5 μm, and 10 μm, respectively,the relationship between water flow velocity and pressure gradient along the axis of tube is analyzed, which gradually becomes nonlinear as the radius of the microtube decreases.From the correlation, a viscosity model of water flow derived from the radius of microtube and the pressure gradient is proposed. The flow results modified by the viscosity model are in accordance with those of experiments, which are verified by numerical simulation software and the Hagen–Poiseuille equation. The experimental water flow velocity in a fused silica microtube with diameter of 5.03 μm, which has not been used in the fitting and derivation of the viscosity model,is proved to be comsistent with the viscosity model, showing a rather good match with a relative difference of 5.56%.     

On the anomalous pressure dependence of the viscosity of helium

Summary In contradiction to the general behaviour of gases, the viscosity of helium has been found experimentally to show an initial decrease with increase of pressure. In this paper it has been suggested that association may account for this anomalous behaviour of helium.     

Effect of the turbulent viscosity relaxation time on the modeling of nozzle and jet flows

Certain modifications of three-equation turbulence models are proposed. They are intended for increasing the accuracy of the calculations of turbulent flows in nozzles with boundary layer separation and in supersonic jets with complicated shock wave structures. Basing on the idea of the inclusion of flow prehistory in terms of an additional relaxation equation for nonequilibrium turbulent viscosity we propose three modifications of the k-ω-µ _t model based on the k-ω model and a version of the k- ?-µ _t turbulence model. In these modifications we introduce an additional dependence of the nonequilibrium turbulent viscosity relaxation time on different physical parameters which can be important near the point of boundary layer separation from the nozzle wall, such as viscous effects and effects of large gradients of the mean velocity and the kinetic energy of turbulence (turbulent pressure). The comparison of the results of the calculations with the experimental data shows that all the proposed versions of the three-equation models make it possible to improve the accuracy of the calculations of turbulent flows in nozzles and jets.     

Effect of ambient pressure on penetration of a diesel spray

In the present experimental and theoretical work the propagation of a high-speed fuel spray at distances much longer than the breakup length is studied. The motion of the spray is modeled in two regions: the main region of the steady flow and the front region of the spray. The analysis yields the equation of propagation of the tip of the spray. These theoretical results have been validated against experimental data obtained from a common-rail diesel injection nozzle and from other data available in the literature. The importance of the shock wave propagation at the initial stage of the spray injection is demonstrated.     

Effects of variable viscosity on slider bearing

By considering the now in a slider bearing to be a nearly viscometric flow we have examined the effects of variation in viscosity, and normal stress differences on the total resistance and total normal force. We have found that under certain conditions the normal stress differences may be neglected compared with the variation in viscosity. We have found that the effects of variation in viscosity are to reduce the total resistance, and to increase or decrease the total normal force depending on the ratio of the thickness of the liquid at the entry and exit.     

Effects of bubble deformation on the viscosity of dilute suspensions

The relative viscosity (μ_rel=suspension viscosity/suspending fluid viscosity) of low Reynolds number, dilute and surfactant-free bubble suspensions in simple shear is studied with a rotating cylinder, Couette rheometer. The conditions of the experiments correspond to capillary numbers (Ca) of order 1 and bridge previous experimental, theoretical and numerical results that focused on either Ca⪡1 or Ca⪢1. The suspensions are shear thinning with μ_rel>1 for small Ca. At large Ca, μ_rel approaches a constant that is less than 1. These results are explained by a scaling analysis that considers how regions of viscous dissipation in and around bubbles change as bubbles are deformed by the flow.     

On the pressure dependence of the viscosity of aqueous sugar solutions

New experimental data for the pressure dependence of the viscosity of aqueous solutions of different sugars are presented. Measurements were carried out with a gravity driven high pressure viscometer with a maximum pressure of 700 MPa. The influence of both concentration and temperature on the pressure dependence of the viscosity is considered. Next to the data, a viscosity model based on a suspension model is introduced and it is shown that it is able to predict the viscosity for sugar solutions in a broad parameter range, including pressure. It is demonstrated that the relative viscosity for varying sugar mass fraction at constant pressure coincides with the pressure-dependent relative viscosity for a fixed sugar mass fraction, suggesting that there are no structural changes occurring under pressure. A brief interpretation of the viscosity model is given.     

The time,temperature and shear dependence of the viscosity of polypropylene and its influence upon the extrusion process

The polypropylene melt viscosity dependence upon temperature, shear and molecular weight, and the molecular weight dependence upon temperature and time were measured and mathematically described. For the dependence of the melt viscosity upon temperature, shear and molecular weight (melt index), a master curve has been found. The influence of the progressive degradation of polypropylene during the extrusion upon the temperature, pressure and dissipated energy down-channel profiles is given.     

An experiment to measure the pressure dependence of the zero-shear-rate viscosity

A simple experimental method, based on Stokes' law for falling spheres, has been devised and used to measure the pressure-dependence of the zero-shear-rate viscosity of a polypropylene melt. The experiment was performed by maintaining three thick-walled test cylinders containing the polymer melt and the falling sphere at the same elevated temperature but different pressures for periods of time ranging from 20 to 48 hours.When compared with experiments using high-pressure capillary or rotational viscometers, this experimental method has the advantages that viscous heating is non-existent and the apparatus and data analysis are relatively simple. The principal disadvantage encountered here, thermal degradation at high temperatures, could probably be reduced by molding specimens under vacuum and by shortening the exposure time. Since the falling-sphere experiment provides data at very low shear rates and the capillary and rotational viscometers generate data at high shear rates, the two experimental methods are complementary.The pressure coefficient b [=d(In η₀/dp] was determined for Hercules Pro-fax 6523 polypropylene in two series of experiments at different temperatures. For seven experiments at 218.3°C and pressures up to 97.9 $\text{MN}\text{m}{}^2$ (14,200 psi), the average value of b ± 95% confidence limits was found to be 14.8 ($\text{GN}\text{m}{}^2$)^?1 ± 2.9.The average b was 12.6 ($\text{GN}\text{m}{}^2$)^?1 ± 1.4 in a series of eight experiments at 232.2°C and pressures up to 123 $\text{MN}\text{m}{}^2$ (17,800 psi).     

岩石类介质侵彻效应的理论研究进展

近年来,随着超高速武器的发展,侵彻效应的研究重点逐渐由高速向超高速发展。随着弹体打击速度提高,侵彻机制发生变化,并触发强烈的成坑和地冲击效应。本文综述了大速度范围内岩石类介质侵彻效应的理论研究进展,讨论了长杆弹侵彻速度的分区,介绍了岩石类介质的侵彻、成坑、地冲击效应的理论模型,并对目前研究中尚有待解决的问题和下一步的研究方向进行了展望。     

高速旋转弹头侵彻运动金属薄板的数值模拟

提出了一种利用LS-DYNA程序计算弹头翻转角度曲线的方法。在侵彻过程中,弹头的速度为300 m/s,转速分别为0、3 600和6 370 r/s;金属薄板的速度分别为0、40和80 m/s。其中,弹头直径为7.62 mm,圆形金属薄板的直径为80 mm,厚度为2 mm。材料模型选择了考虑应变、应变率效应和温度效应的Johnson-Cook材料模型。通过数值模拟结果的比较来研究不同弹头转速和金属薄板速度对侵彻过程中弹头最终速度、翻转角度和弹道偏移的影响。     

卵形杆弹对铝靶的斜侵彻

在Lagrange有限元基础上,扼要介绍了一种适用于三维斜侵彻数值模拟计算的滑移面处理技术。该方法放弃了传统滑移计算中从单元的设置,而代之以预设从节点,从而避免三维斜侵彻数值计算中主从单元的相交、滑移面的识别、修正与再定义的困难。在确保计算精度的同时,有效地提高了计算效率。卵形杆弹对铝靶侵彻的系列数值模拟计算表明,无论对于正撞击或斜撞击,本文中所获结果与实验结果都有良好的一致性,这说明本文中所述方法和所建程序的合理性和有效性,为侵彻贯穿过程的数值分析提供了一种实用和有效的手段。