Rheo-PIV analysis of the slip flow of a metallocene linear low-density polyethylene melt

The continuous extrusion of a metallocene linear low-density polyethylene through a transparent capillary die with and without slip was analyzed in this work by rheometrical measurements and particle image velocimetry (PIV). For this reason, a comparison was made between the rheological behaviors of the pure polymer and blended with a small amount of fluoropolymer polymer processing additive. Very good agreement was found between rheometrical and PIV measurements. The pure polymer exhibited stick-slip instabilities with nonhomogeneous slip at the die wall, whereas the blend showed stable flow. The slip velocity was measured directly from the velocity profiles and was negligible for the pure polymer before the stick-slip but increased monotonously as a function of the shear stress for the blend. The flow curves and the slip velocity as a function of the shear stress deviated from a power law and were well fitted by continuous “kink” functions. Comparison of PIV data with rheometrical ones permitted a direct proof of the basic assumption of the Mooney theory. Finally, the analysis of the velocity profiles showed that there is a maximum in the contribution of slip to the average fluid velocity, which is interpreted as the impossibility for the velocity profile to become plug like in the presence of shear thinning.     

Apparent wall slip velocity measurements in free surface flow of concentrated suspensions

In this work we have experimentally measured the apparent wall slip velocity in open channel flow of neutrally buoyant suspension of non-colloidal particles. The free surface velocity profile was measured using the tool of particle imaging velocimetry (PIV) for two different channels made of plane and rough walls. The rough walled channel prevents wall slip, whereas the plane wall showed significant wall slip due to formation of slip layer. By comparing the velocity profiles from these two cases we were able to determine the apparent wall slip velocity. This method allows characterization of wall slip in suspension of large sized particles which cannot be performed in conventional rheometers. Experiments were carried out for concentrated suspensions of various particle volume concentrations and for two different sizes of particles. It was observed that wall slip velocity increases with particle size and concentration but decreases with increase in the viscosity of suspending fluid. The apparent wall slip velocity coefficients are in qualitative agreement with the earlier measurements. The effect of wall slip on free surface corrugation was also studied by analyzing the power spectral density (PSD) of the refracted light from the free surface. Our results indicate that free surface corrugation is a bulk flow response and it does not arise from boundary problem such as development of slip layer.     

Slip of complex fluids in viscometry

Concentrating on viscometry, the concept of (apparent) slip in rotational viscometers requires an angular slip velocity. This, as well as the customary concept of a slip velocity for unidirectional viscometric flow, is estimated by means of dimensional reasoning. It is demonstrated that slip is very well possible, despite the fact that experiments might indicate no slip.     

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.     

Near-wall measurements of turbulence statistics in a fully developed channel flow with a novel laser Doppler velocity profile sensor

This paper reports on the measurements of the near-wall turbulence statistics in a fully developed channel flow. The flow measurements were carried out with a novel laser Doppler velocity profile sensor with a high spatial resolution. The sensor provides both the information of velocity and position of individual tracer particles inside the measurement volume. Hence, it yields the velocity profile inside the measurement volume, in principle, without the sensor being mechanically traversed. Two sensor systems were realized with different techniques. Typically the sensor has a relative accuracy of velocity measurement of 10⁻³ and the spatial resolution of a few micrometers inside the measurement volume of about 500 μm long. The streamwise velocity was measured with two independent sensor systems at three different Reynolds number conditions. The resulting turbulence statistics show a good agreement with available data of direct numerical simulations up to fourth order moment. This demonstrates the velocity profile sensor to be one of the promising techniques for turbulent flow research with the advantage of a spatial resolution more than one magnitude higher than a conventional laser Doppler technique.     

Application of the ultrasonic velocity profile method to the mapping of liquid metal flows under the influence of a non-uniform magnetic field

An ultrasonic velocity profile (UVP) method has been successfully applied to the investigation of a liquid metal channel flow under the influence of an inhomogeneous magnetic field. Using velocity profiles obtained by the ultrasonic velocimeter and their numerical post processing, two-dimensional time-averaged flow maps were efficiently produced. A single transducer immersed directly into the working fluid was used in order to simplify alignment of measurement lines and avoid the undesirable refraction of the acoustic beam on the walls. An M-shaped flow and wake behind a magnetic obstacle were reconstructed as the patterns of shear and large-scale vortical flows.     

Analysis on creeping channel flows of compressible fluids subject to wall slip

Creeping channel flows of compressible fluids subject to wall slip are widely encountered in industries. This paper analyzes such flows driven by pressure in planar as well as circular channels. The analysis elucidates unsteady flows of Newtonian fluids subject to the Navier slip condition, followed by steady flows of viscoplastic fluids, in particular, Herschel–Bulkley fluids and their simplifications including power law and Newtonian fluids, that slip at wall with a constant coefficient or a coefficient inversely proportional to pressure. Under the lubrication assumption, analytical solutions are derived, validated, and discussed over a wide range of parameters. Analysis based on the derived solutions indicates that unsteadiness alters cross-section velocity profiles. It is demonstrated that compressibility of the fluids gives rise to a concave pressure distribution in the longitudinal direction, whereas wall slip with a slip coefficient that is inversely proportional to pressure leads to a convex pressure distribution. Energy dissipation resulting from slippage can be a significant portion in the total dissipation of such a flow. A distinctive feature of the flow is that, in case of the pressure-dependent slip coefficient, the slip velocity increases rapidly in the flow direction and the flow can evolve into a pure plug flow at the exit.     

Rheology of shear thickening suspensions and the effects of wall slip in torsional flow

The rheological characterisation of concentrated shear thickening materials suspensions is challenging, as complicated and occasionally discontinuous rheograms are produced. Wall slip is often apparent and when combined with a shear thickening fluid the usual means of calculating rim shear stress in torsional flow is inaccurate due to a more complex flow field. As the flow is no longer “controlled”, a rheological model must be assumed and the wall boundary conditions are redefined to allow for slip. A technique is described where, by examining the angular velocity response in very low torque experiments, it is possible to indirectly measure the wall slip velocity. The suspension is then tested at higher applied torques and different rheometer gaps. The results are integrated numerically to produce shear stress and shear rate values. This enables the measurement of true suspension bulk flow properties and wall slip velocity, with simple rheological models describing the observed complex rheograms.     

Heat transfer enhancement with deformation of the velocity profile

The problem of enhancing the heat transfer in channels and boundary layers by the appropriate deformation of the fluid velocity profile is considered. The resulting additional hydraulic losses, the price of heat transfer enhancement, are determined. The possibilities of controlling heat transfer by redistributing the fluid velocity in channels are demonstrated with reference to flows at low Prandtl numbers. Laminar and turbulent liquid and gas flows with heat transfer in channels and boundary layers are numerically modeled on the basis of modern models of turbulence (flow development in channels with different initial velocity profiles, flows with wall roughness and boundary layer flows with forces acting on the flow to cause deformation of the velocity profile). In all cases it is found that the heat transfer can be enhanced only at the expense of a considerable increase in the hydaulic losses. A class of self-similar thermal problems for flows in plane diffusers is formulated. The eigenfunctions — temperature modes — for various velocity profiles are determined with allowance for the nonuniqueness of the solution of the classical dynamical problem for a plane diffuser and the corresponding heat transfer coefficients are found.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 94–105, May–June, 1993.The authors are grateful to A. Yu. Klimenko for useful discussions.     

Exact solutions of incompressible Couette flow with porous walls for slightly rarefied gases

In this work, the transient incompressible Couette flow and steady-state temperature profiles between two porous parallel plates for slightly rarefied gases are solved exactly. The first-order approximation of slip velocity at the boundaries is used in the formulation. The solution is also applicable for Couette flow in micro-channels under certain circumstances. The influences of mass transfer and a nondimensional slip parameter on slip velocities are discussed. It is also found that the transient slip velocities at the walls are greatly different from the steady-state velocity slips. The influences of velocity slip and temperature slip parameters on the temperature distribution and heat transfer at the walls are analyzed and discussed. It is shown that the slip parameters can greatly change the temperature profiles and heat transfer characteristics at the walls.     

Experimental study of thermally stratified unsteady flow by NMR-CT

Thermally stratified unsteady flow caused by two-dimensional surface discharge of warm water into a rectangular reservoir is investigated. Experimental study is focused on the rapidly developing thermal diffusion at small Richardson number.The basic objectives are to develop a measurement system for the unsteady flow phenomena and to study the interfacial mixing between a flowing layer of warm water and the underlying body of cold water.Mean velocity field measurement is carried out by using NMR-CT (Nuclear Magnetic Resonance — Computerized Tomography). It detects a quantitative flow image of any desired section in any direction of flow. Transient mean temperature profiles are obtained by fine thermocouple arrays and a microcomputer-based data acquisition system.Results show that the warm layer penetrates more rapidly into the cold layer at smaller Richardson number because of decrease instability. This is clearly verified by flow visualization using thymol blue solution. It is found that the transport of heat across the interface is more vigorous than that of momentum.     

Effect of the measurement volume in turbulent pipe flow measurement by the ultrasonic velocity profile method (mean velocity profile and Reynolds stress measurement)

 The ultrasonic velocity profile measurement method has some favorable advantages over the conventional flow measurement methods, such as measurement of the instantaneous velocity profile over the measuring line and its applicability to opaque liquids. The method has another advantage of being non-intrusive. Hence, it is applicable to various flow conditions, although it requires a relatively large measurement volume. In this paper, the effects of the measurement volume on the mean velocity profile and the Reynolds stress measurement have been investigated for fully developed turbulent flows in a vertical pipe. The results were then compared with data obtained by direct numerical simulation. Received: 9 March 2000 / Accepted: 27 March 2001 Published online: 29 November 2001     

Radial flow velocity profiles of a yield stress fluid between smooth parallel disks

In rock grouting, idealized 2D-radial laminar flow of yield stress fluids (YSF) is a fundamental flow configuration that is used for cement grout spread estimation. A limited amount of works have presented analytical and numerical solutions on the radial velocity profiles between parallel disks. However, to the best of our knowledge, there has been no experimental work that has presented measured velocity profiles for this geometry. In this paper, we present velocity profiles of Carbopol (a simple YSF), measured by pulsed ultrasound velocimetry within a radial flow model. We describe the design of the physical model and then present the measured velocity profiles while highlighting the plug-flow region and slip effects observed for three different apertures and volumetric flow rates. Although the measured velocity profiles exhibited wall slip, there was a reasonably good agreement with the analytical solution. We then discuss the major implications of our work on radial flow.

     

Influence of the inlet velocity profiles on the prediction of velocity distribution inside an electrostatic precipitator

The influence of the velocity profile at the inlet boundary on the simulation of air velocity distribution inside an electrostatic precipitator is presented in this study. Measurements and simulations were performed in a duct and an electrostatic precipitator (ESP). A four-hole cobra probe was used for the measurement of velocity distribution. The flow simulation was performed by using the computational fluid dynamics (CFD) code FLUENT. Numerical calculations for the air flow were carried out by solving the Reynolds-averaged Navier–Stokes equations coupled with the realizable k-ε turbulence model equations. Simulations were performed with two different velocity profiles at the inlet boundary – one with a uniform (ideal) velocity profile and the other with a non-uniform (real) velocity profile to demonstrate the effect of velocity inlet boundary condition on the flow simulation results inside an ESP. The real velocity profile was obtained from the velocity measured at different points of the inlet boundary whereas the ideal velocity profile was obtained by calculating the mean value of the measured data. Simulation with the real velocity profile at the inlet boundary was found to predict better the velocity distribution inside the ESP suggesting that an experimentally measured velocity profile could be used as velocity inlet boundary condition for an accurate numerical simulation of the ESP.     

Slip velocity measurements in an upward bubbly flow by combined LDA and electrodiffusional techniques

 An experimental technique for the measurement of the local slip velocity of spherical bubbles is reported. It is based on the measurement of the local liquid velocity by an electrodiffusional method, and the bubble velocity by a specially adapted LDA (Laser Doppler anemometer) with a short measuring volume. The bubble velocity is measured taking into account the shift between the bubble centre and the centre of the LDA measuring volume. The slip velocity is obtained by subtracting the liquid velocity from the bubble velocity at the point corresponding to the bubble centre. The technique is applicable for flows with high velocity gradients. Results of the slip velocity measurements in an upward bubbly flow at laminar pipe Reynolds numbers are presented. Received: 25 July 1996/Accepted: 13 April 1998     

Calculation by the Krylov-Bogolyubov method of the velocity profile and fluxes in the nonisothermal flow of a rarefied gas in a cylindrical capillary

The Krylov-Bogolyubov numerical method is used to solve integral transfer equations obtained from the kinetic equation with the BHC (Bhatnagar—Cross—Krook) model of the collision operator. The velocity profiles and the thermal-creep flows and Poiseuille flow are calculated in different modes of flow under conditions of incomplete accommodation of the tangential momentum of molecules at the wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 143–150, November–December, 1978.     

Simulations of Spatially Developing Two-Dimensional Shear Layers and Jets

A computational study of spatially evolving two-dimensional free shear flows has been performed using direct numerical simulation of the Navier–Stokes equations in order to investigate the ability of these two-dimensional simulations to predict the overall flow-field quantities of the corresponding three-dimensional “real” turbulent flows. The effects of inflow forcing on these two-dimensional flows has also been studied. Simulations were performed of shear layers, as well as weak (large co-flow and relatively weak shear) and strong (small co-flow and relatively strong shear) jets. Several combinations of discrete forcing with and without a broadband background spectrum were used. Although spatially evolving direct simulations of shear layers have been performed in the past, no such simulations of the plane jet have been performed to the best of our knowledge. It was found that, in the two-dimensional shear layers, external forcing led to a strong increase in the initial growth of the shear-layer thickness, followed by a region of decreased growth as in physical experiments. The final downstream growth rate was essentially unaffected by forcing. The mean velocity profile and the naturally evolving growth rate of the shear layer in the case of broadband forcing compare well with experimental data. However, the total and transverse fluctuation intensities are larger in the two-dimensional simulations with respect to experimental data. In the weak-jet simulations it was found that symmetric forcing completely overwhelms the natural tendency to transition to the asymmetric jet column mode downstream. It was observed that two-dimensional simulations of “strong” jets with a low speed co-flow led to a fundamentally different flow with large differences even in mean velocity profiles with respect to experimental data for planar jets. This was a result of the dominance of the two-dimensional mechanism of vortex dipole ejection in the flow due to the lack of spanwise instabilities. Experimental studies of planar jets do not show vortex dipole formation and ejection. A three-dimensional “strong”-jet simulation showed the rapid evolution of three-dimensionality effectively preventing this two-dimensional mechanism, as expected from experimental results. Received: 25 November 1996 and accepted 17 April 1997     

Interpretation of wake instability at slip line in rotating detonation

ABSTRACT

In studies on instabilities of flowfield in rotating detonation, one of the most common concerns is the instability at the slip line originating from the conjunction of the detonation wave and oblique shock. Using Euler equations associated with the 7-species-and-8-reaction finite-rate chemical reaction model of hydrogen/air mixtures, further studies are performed to simulate the 2-D rotating detonation, and the flow mechanism of instability at the slip line is investigated in depth. The results show that the distinct wake profile exists at the slip line, which is different from the typical mixing layer. Analysis indicates that the generation of wake is caused by the transition shock between the detonation wave and oblique shock. Because of the wake profile, the vorticity distribution therein appears in a double-layer layout, and different evolutions exist in different vorticity layers. Based on the velocity profile across the slip line, the analysis by the linear stability theory is made, and two main unstable modes which have different shape profiles and phase velocities are found. Discrete Fourier transformation is utilised to analyse the numerical results, and similar shape profiles are obtained. A general coincidence in velocity of vortex movement is also attained between the theoretical predictions and simulations. Investigations show that the wake instability is responsible for the unstable mechanism, and corresponding unstable structures differ from the canonical ones in typical mixing layers.     

[100]LiF单晶在60 GPa以内冲击加载下的高压屈服强度特性

获取光学窗口自身的高压强度特性是开展材料高压高应变率冲击响应行为精密测量和数据反演的重要基础。利用平板撞击和双屈服面法,通过冲击-卸载、冲击-再加载原位粒子速度剖面精细测量和数据反演,获得了约60 GPa范围内[100]LiF屈服强度特性随冲击压力的变化规律。结果表明:在实验压力范围内,[100]LiF的屈服强度随加载压力的提高而显著提高,压力硬化效应显著;同时,LiF在冲击加载下的屈服强度高于磁驱准等熵加载结果,应变率硬化效应强于热软化效应。采用Huang-Asay模型确定了可描述冲击加载[100]LiF强度特性的本构模型参数,为LiF在强度、相变、层断裂等加窗测量实验中的深入应用和数据准确解读提供了重要支撑。     

Minimum-drag cascade design for supersonic flow with subsonic normal velocity component

The variational problem of designing the slender profile of a plane cascade in a supersonic ideal (inviscid and nonheat-conducting) gas flow with a subsonic normal velocity component is solved in the linear approximation. The optimum profiles constructed differ fundamentally from the closest analog — the supersonic single profile creating minimum wave drag for given lift. Following [1], it is easy to show that in this case the optimum profile is a plate at an angle of attack determined by the given lift.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 137–146, January–February, 1995.