Pressure effects on viscosity and flow stability of polyethylene melts during extrusion

In the present work, the effects of pressure on the viscosity and flow stability of four commercial grade polyethylenes (PEs) have been studied: linear-low-density polyethylene copolymer, high-density polyethylene, metallocene polyethylenes with short-chain branches (mPE-SCB), and metallocene polyethylenes with long chain branching (mPE-LCB). The range of shear rates considered covers both stable and unstable flow regimes. “Enhanced exit-pressure” experiments have been performed attaining pressures of the order of 500×10⁵ Pa at the die exit. The necessary experimental conditions have been clearly defined so that dissipative heating can be neglected and pressure effects isolated. The results obtained show an exponential increase in both shear and entrance-flow pressure drop with mean pressure when shear rate is fixed and as long as flow is stable. These pressure effects are described by two pressure coefficients, β_S under shear and, β_E under elongation, that are calculated using time–pressure superposition and that are independent of mean pressure and flow rate. For three out of four PE, pressure coefficient values can be considered equal under shear and under elongation. However, for the mPE-LCB, the pressure coefficient under elongation is found to be about 30% lower than under shear. Flow instabilities in the form of oscillating flows or of upstream instabilities appear at lower shear rates as mean pressure increases. Nevertheless, the critical shear stress at which they are triggered remains independent of mean pressure. Moreover, it is found that the β_S values obtained for stable flows do not differ much from the values obtained during upstream instability regimes, and differ really from pressure effects observed under oscillating flow and slip conditions.     

The transmission of turbulent boundary layer unsteady pressure and shear stress through a viscoelastic layer

The transmission of unsteady pressure and shear stress, generated by a turbulent boundary layer in water, through a viscoelastic layer backed by a rigid plate is investigated. Analytical models are used to estimate the unsteady pressure and shear stress from 10 to 1000 Hz for a flat plate boundary layer with zero pressure gradient. Additionally, models for the transfer of the unsteady pressures and shear stress through the viscoelastic layer are developed. The models are used to predict the unsteady pressure fluctuations, or flow noise, which would be seen by a finite size sensor embedded under the elastomer layer. The unsteady pressure levels are found to be 20 dB greater than the unsteady shear stress levels across all frequency ranges computed, in agreement with recent measurements. The unsteady pressure transfer functions have a peak at the shear wavenumber and are larger than the shear stress transfer magnitudes from 10 to 50 Hz. The unsteady shear stress transfer functions have a peak at the acoustic wavenumber and are larger than the pressure transfer magnitudes from 50 to 1000 Hz. Over the frequency range examined, the unsteady pressures were found to be the dominant contributor to the sensor flow noise due to the considerably larger magnitude of the unsteady pressures on the top of the viscoelastic layer.     

On pressure and thermal flux in gas-mixture flows and in two-phase flows

To begin with, two different definitions of pressure, thermal flux, etc. in the diffusion model and two-fluid model are given. Then the physical interpretations of the pressure and the thermal flux are provided by introducing the momentum and energy fluxes,M and ε, through a surface dS in the flow field. The quantities defined in the diffusion model are suggested when the motion of the mixture is studied as a whole, while the quantities defined in the two-fluid model are suggested when the motion of individual species is studied. The collision pressure and thermal flux in dense gas-mixtures are also discussed in detail, i.e. their origin, their expressions in the momentum and energy equations, and their distinctions from the normal partial pressure and thermal flux. A gas-particle flow can be treated as a flow of dense gas-mixtures. The long-standing controversy whether the “inertial coupling term” should exist in the momentum equation can be clarified by the two different definitions of pressure.     

Pressure and friction dependent mechanical strength – cracks and plastic flow

The mechanical properties of a polymer composite plastic bonded explosive, EDC37, have been investigated as a function of hydrostatic confining pressure between 0.1 and 138 MPa. The results indicate different failure processes in two pressure ranges, a low pressure range between about 0.1 and 7 MPa and a higher pressure range between about 7 and 138 MPa. In the low pressure range slow crack processes are important in failure while in the higher pressure range plastic flow dominates. The pressure dependence of the compressive strength in the low pressure range is attributed to coulomb friction between surfaces of closed shear cracks and from the observed linear increase of the strength with pressure and the angle of the fracture plane a friction coefficient is obtained. Friction coefficients can also be obtained from the ratio of the compressive to tensile strength and directly from the above angle. The friction coefficients obtained from these separate observations are in agreement and this is taken as strong evidence for the importance of this friction in determining strength and mechanical failure. These results clearly establish experimentally the role of friction in determining strength with or without applied pressure. An empirical relationship between strength, pressure and strain rate is also obtained for this pressure range and the failure strength of EDC37 is more sensitive to pressure than strain rate.     

Dynamic responses of a solid wall in contact with a bubbly liquid excited by thermal shock loading

Several MW-class spallation neutron sources are being developed in the world. Specifically, intensive and high energy protons are injected into heavy liquid metals (mercury, lead or lead-bismuth eutectic) to induce the spallation reaction that produces neutrons. At the moment when the proton beams are injected, thermal shock occurs in the liquid metal, causing pressure waves to propagate in the liquid metal, collide against the container and damage it.It is proposed that microbubbles are injected into the liquid metal to mitigate the impulsive pressure waves by means of absorption and attenuation effects. These effects are dependent on the relationship between bubble size and the rate of pressure increase. In the present experiment, a very rapid rise in pressure in the order of MPa/μs, equivalent to the rise in pressure due to proton beam injection, was simulated by the electric discharge method in a water loop test to investigate the impulsive pressure mitigation effect of injected microbubbles. The solid wall response was measured using an accelerometer, and the dynamic responses of microbubbles were observed using an ultra-high-speed camera filming at 5 × 10⁵ frame/s. The sound velocity in bubbly water was estimated using a differential image technique. It was confirmed from the experimental results that microbubbles are effective in reducing impulsive pressure waves and to suppressing the impact vibration of the solid wall in contact with the liquid.     

Comparison of Uniform and Non-uniform Pressure Approaches Used to Analyze an Adsorption Process in a Closed Type Adsorbent Bed

Heat and mass transfer in an annular adsorbent bed filled with silica gel particles is numerically analyzed by uniform and non-uniform pressure approaches. The study is performed for silica gel–water pair, particle radius from 0.025 to 1 mm and two bed radii of 10 and 40 mm. For uniform pressure approach, the energy equation for the bed and the mass transfer equation for the particle are solved. For non-uniform pressure approach, the continuity and Darcy equations due to the motion of water vapor in the bed are added, and four coupled partial differential equations are solved. The changes of the adsorbate concentration, pressure, and temperature in the bed throughout the adsorption process for both approaches are obtained and compared. The obtained results showed that the particle size plays an important role on the validity of uniform pressure approach. Due to the interparticle mass transfer resistance, there is a considerable difference between the results of the uniform pressure and non-uniform pressure approaches for the beds with small size of particles such as $r_\mathrm{{p}} =$ 0.025 mm.     

The Influence of Air Entrainment on the Fluid Pressure Transients in a Pumping Installation

A four-equation, two-fluid model of two-component flow has been developed to study the effects of air entrainment on the pressure transients in a pumping installation. A semi-implicit hydrodynamic numerical scheme is applied. Free and dissolved gases in the fluid and cavitation at the gas saturation pressure are modeled. The mechanism and behaviors of the pressure transients are discussed. Numerical experiments show that the first pressure peak is mainly dominated by two factors: one is the delay in wave reflection from the reservoir; the other is the change of wave speed in the mixture, which directly cause changes in wave speed. The magnitude of the first pressure peak depends on the overlapping of the effects of these two factors. The air volume at the check valve is mainly controlled by the local pressure there and the initial air void fraction. Comparably, the air volume at peak level is dependent on the local pressure and air release with initial air entrainment less than 10^-2, but dependent on the local pressure, air release and initial air void fraction together with initial air entrainment greater than 10^-2.     

Nodal operator splitting adaptive finite element algorithms for the Navier–Stokes equations

Solution algorithms for solving the Navier–Stokes equations without storing equation matrices are developed. The algorithms operate on a nodal basis, where the finite element information is stored as the co-ordinates of the nodes and the nodes in each element. Temporary storage is needed, such as the search vectors, correction vectors and right hand side vectors in the conjugate gradient algorithms which are limited to one-dimensional vectors. The nodal solution algorithms consist of splitting the Navier–Stokes equations into equation systems which are solved sequencially. In the pressure split algorithm, the velocities are found from the diffusion–convection equation and the pressure is computed from these velocities. The computed velocities are then corrected with the pressure gradient. In the velocity–pressure split algorithm, a velocity approximation is first found from the diffusion equation. This velocity is corrected by solving the convection equation. The pressure is then found from these velocities. Finally, the velocities are corrected by the pressure gradient. The nodal algorithms are compared by solving the original Navier–Stokes equations. The pressure split and velocity–pressure split equation systems are solved using ILU preconditioned conjugate gradient methods where the equation matrices are stored, and by using diagonal preconditioned conjugate gradient methods without storing the equation matrices. © 1998 John Wiley & Sons, Ltd.     

A parametric study of adverse pressure gradient turbulent boundary layers

There are many open questions regarding the behaviour of turbulent boundary layers subjected to pressure gradients and this is confounded by the large parameter space that may affect these flows. While there have been many valuable investigations conducted within this parameter space, there are still insufficient data to attempt to reduce this parameter space. Here, we consider a parametric study of adverse pressure gradient turbulent boundary layers where we restrict our attention to the pressure gradient parameter, β, the Reynolds number and the acceleration parameter, K. The statistics analyzed are limited to the streamwise fluctuating velocity. The data show that the mean velocity profile in strong pressure gradient boundary layers does not conform to the classical logarithmic law. Moreover, there appears to be no measurable logarithmic region in these cases. It is also found that the large-scale motions scaling with outer variables are energised by the pressure gradient. These increasingly strong large-scale motions are found to be the dominant contributor to the increase in turbulence intensity (scaled with friction velocity) with increasing pressure gradient across the boundary layer.     

Buckling and postbuckling of concentric cylindrical tubes under external pressure

The problem considered involves a structure composed of two concentric and bonded tubes subjected to external and uniform pressure. Compression tests are conducted using structures formed by a thin-walled internal rubber tube and a thick-walled external foam tube. Experimental results are plotted under the form of a bifurcation diagram representing the inner cross-sectional area of the thin tube as a function of pressure. The buckling pressure P_b and the contact pressure P_co are determined from this non linear diagram. A numerical computation by the Finite Element Method (FEM) is used in order to calculate the Euler buckling pressure P_b and the results are compared with experimental data. It is shown that the buckling pressure and the associated buckling mode n, strongly depend upon the elastic and geometrical parameters of both the tubes. The experimental and numerical investigations are also extended to postbuckling behaviour. The contact between the opposite sides of the inner wall is occured with a buckling mode index n = 2, 3. This contact phenomenon is given rise to the discontinuity of a previous diagram and was characterized by the contact pressure P_co.     

A pressure probe for the detection of the flow direction close to walls. Case study: flow through a bend

We report on the development of a new pressure probe that detects the flow direction in wall-bound flow. Two pressure differences are measured and combined in a pressure coefficient which is proportional to the flow direction in a ±20° range. The probe is applied to the secondary flow vortex pair generated in a 90° pipe bend, with excellent results. The vortex pair, and its downstream decay, are identified. Furthermore, the stability of the vortex pair is found to depend sensitively on the upstream conditions. When these are fixed, the vortices stay put; in other words they are spatially stabilized. The consequences for installation effects on flow metering are discussed.     

Relative Permeability Analysis of Tube Bundle Models,Including Capillary Pressure

The analytical equations for calculating two-phase flow, including local capillary pressures, are developed for the bundle of parallel capillary tubes model. The flow equations that are derived were used to calculate dynamic immiscible displacements of oil by water under the constraint of a constant overall pressure drop across the tube bundle. Expressions for averaged fluid pressure gradients and total flow rates are developed, and relative permeabilities are calculated directly from the two-phase form of Darcy's law. The effects of pressure drop and viscosity ratio on the relative permeabilities are discussed. Capillary pressure as a function of water saturation was delineated for several cases and compared to a steady-state mercury-injection drainage type of capillary pressure profile. The bundle of serial tubes model (a model containing tubes whose diameters change randomly at periodic intervals along the direction of flow), including local Young-Laplace capillary pressures, was analyzed with respect to obtaining relative permeabilities and macroscopic capillary pressures. Relative permeabilities for the bundle of parallel tubes model were seen to be significantly affected by altering the overall pressure drop and the viscosity ratio; relative permeabilities for the bundle of serial tubes were seen to be relatively insensitive to viscosity ratio and pressure, and were consistently X-like in profile. This work also considers the standard Leverett (1941) type of capillary pressure versus saturation profile, where drainage of a wetting phase is completed in a step-wise steady fashion; it was delineated for both tube bundle models. Although the expected increase in capillary pressure at low wetting-phase saturation was produced, comparison of the primary-drainage capillary pressure curves with the pseudo-capillary pressure profiles, that are computed directly using the averaged pressures during the displacements, revealed inconsistencies between the two definitions of capillary pressure.     

Preconditioned finite element algorithms for 3D Stokes flows

Preconditioned conjugate gradient algorithms for solving 3D Stokes problems by stable piecewise discontinuous pressure finite elements are presented. The emphasis is on the preconditioning schemes and their numerical implementation for use with Hermitian based discontinuous pressure elements. For the piecewise constant discontinuous pressure elements, a variant implementation of the preconditioner proposed by Cahouet and Chabard for the continuous pressure elements is employed. For the piecewise linear discontinuous pressure elements, a new preconditioner is presented. Numerical examples are presented for the cubic lid-driven cavity problem with two representative elements, i.e. the Q2-PO and the Q2-P1 brick elements. Numerical results show that the preconditioning schemes are very effective in reducing the number of pressure iterations at very reasonable costs. It is also shown that they are insensitive to the mesh Reynolds number except for nearly steady flows (Re_m → 0) and are almost independent of mesh sizes. It is demonstrated that the schemes perform reasonably well on non-uniform meshes.     

Evaluation and comparison of routes to obtain pressure coefficients from high-pressure capillary rheometry data

A capillary rheometer equipped with a pressure chamber is used to measure the pressure-dependent viscosity of polymethylmethacrylate (PMMA), poly-α-methylstyrene-co-acrylonitrile (PαMSAN), and low-density polyethylene (LDPE). Data analysis schemes are discussed to obtain pressure coefficients at constant shear rate and at constant shear stress. It is shown that the constant shear stress pressure coefficients have the advantage of being shear stress independent for the three polymers. The constant shear rate pressure coefficients, on the other hand, turn out to depend on shear rate, which makes them less suitable for use, e.g., in process simulations. In addition to the commonly used superposition method, a direct calculation method for the pressure coefficients is tested. Values obtained from both methods are equivalent. However, the latter requires less experimental and calculational efforts. From the obtained pressure coefficients, it is clear that PMMA and PαMSAN have a very similar pressure dependence, while LDPE is less sensitive to pressure.     

Combined Forced and Free Convective Flow in a Vertical Porous Channel: The Effects of Viscous Dissipation and Pressure Work

Buoyant flow is analysed for a vertical fluid saturated porous layer bounded by an isothermal plane and an isoflux plane in the case of a fully developed flow with a parallel velocity field. The effects of viscous dissipation and pressure work are taken into account in the framework of the Oberbeck–Boussinesq approximation scheme and of the Darcy flow model. Momentum and energy balances are combined in a dimensionless nonlinear ordinary differential equation solved numerically by a Runge–Kutta method. Both cases of upward pressure force (upward driven flows) and of downward pressure force (downward driven flows) are examined. The thermal behaviour for upward driven flows and downward driven flows is quite different. For upward driven flows, the combined effects of viscous dissipation and pressure work may produce a net cooling of the fluid even in the case of a positive heat input from the isoflux wall. For downward driven flows, viscous dissipation and pressure work yield a net heating of the fluid. A general reflection on the roles played by the effects of viscous dissipation and pressure work with respect to the Oberbeck–Boussinesq approximation is proposed.     

A Parametric Model for Predicting Relative Permeability-Saturation-Capillary Pressure Relationships of Oil–Water Systems in Porous Media with Mixed Wettability

A parametric two-phase, oil–water relative permeability/capillary pressure model for petroleum engineering and environmental applications is developed for porous media in which the smaller pores are strongly water-wet and the larger pores tend to be intermediate- or oil-wet. A saturation index, which can vary from 0 to 1, is used to distinguish those pores that are strongly water-wet from those that have intermediate- or oil-wet characteristics. The capillary pressure submodel is capable of describing main-drainage and hysteretic saturation-path saturations for positive and negative oil–water capillary pressures. At high oil–water capillary pressures, an asymptote is approached as the water saturation approaches the residual water saturation. At low oil–water capillary pressures (i.e. negative), another asymptote is approached as the oil saturation approaches the residual oil saturation. Hysteresis in capillary pressure relations, including water entrapment, is modeled. Relative permeabilities are predicted using parameters that describe main-drainage capillary pressure relations and accounting for how water and oil are distributed throughout the pore spaces of a porous medium with mixed wettability. The capillary pressure submodel is tested against published experimental data, and an example of how to use the relative permeability/capillary pressure model for a hypothetical saturation-path scenario involving several imbibition and drainage paths is given. Features of the model are also explained. Results suggest that the proposed model is capable of predicting relative permeability/capillary pressure characteristics of porous media mixed wettability.     

Investigation of pressure drop in horizontal pipes with different diameters

The pressure drop has a significant importance in multiphase flow systems. In this paper, the effect of the volumetric quality and mixture velocity on pressure drop of gas-liquid flow in horizontal pipes of different diameters are investigated experimentally and numerically. The experimental facility was designed and built to measure the pressure drop in three pipes of 12.70, 19.05 and 25.40 mm. The water and air flow rates can be adjusted to control the mixture velocity and void fraction. The measurements are performed under constant water flow rate (CWF) by adding air to the water and constant total flow rate (CTF) in which the flow rates for both phases are changed to give same CTF. The drift-flux model is also used to predict the pressure drop for same cases. The present data is also compared with a number of empirical models from the literature. The results show that: i) the pressure drop increases with higher volumetric qualities for the cases of constant water flow rate but decreases for higher volumetric qualities of constant total flow rate due to the change in flow pattern. ii) The drift-flux model and homogenous model are the most suitable models for pressure drop prediction.     

Bioluminescence-based imaging technique for pressure measurement in water

The dinoflagellate Pyrocystis lunula emits light in response to water motion. We developed a new imaging technique for measuring pressure using plankton that emits light in response to mechanical stimulation. The bioluminescence emitted by P. lunula was used to measure impact water pressure produced using weight-drop tests. The maximum mean luminescence intensity correlated with the maximum impact pressure that the cells receive when the circadian and diurnal biological rhythms are appropriately controlled. Thus, with appropriate calibration of experimentally determined parameters, the dynamic impact pressure can be estimated by measuring the cell-flash distribution. Statistical features of the evolution of flash intensity and the probability distribution during the impacting event, which are described by both biological and mechanical response parameters, are also discussed in this paper. The practical applicability of this bioluminescence imaging technique is examined through a water drop test. The maximum dynamic pressure, occurring at the impact of a water jet against a wall, was estimated from the flash intensity of the dinoflagellate.     

高压环境条件下注浆模型试验系统设计

注浆工程常常在高地层压力、高水压力的地质环境条件下进行(如煤矿堵水或注浆加固工程)。为了研究高压环境条件下注浆浆液的渗流扩散特征,作者研制了可形成5MPa以上高压环境的注浆试验系统。该试验系统由四个功能模块组成,并可分为四个设备子系统。该试验系统的核心设备高压注浆模型试验装置中应用压力传导管解决了高压罐体内部监测设计所遇到的尺寸效应、传感器防腐、高压密封等难题。     

Polymer melt rheology with a slit die

A piston driven high pressure slit die rheometer with three pressure holes along the die and one in the barrel was used to investigate viscosity, entrance and exit pressure losses, and pressure coefficient of viscosity of a LDPE melt. Hydrostatic calibration of melt pressure transducers can be performed in the rheometer. The slit die results are compared with measurements on circular dies assuming linear and parabolic pressure profiles in both cases. A simplified conversion from apparent to true viscosity, applicable for single point measurements, has been used. In spite of the different symmetries the Bagley correction from the linear pressure profile of circular dies was found to be equal to the sum of exit and entrance pressure losses in the slit. The magnitude and sign of the exit pressure loss depend on the type of pressure profile used. The influence of a pressure dependent viscosity and a temperature gradient along the die on the curvature of the pressure profile is discussed. To directly investigate the effect of pressure the pressure level at constant flow rate was increased stepwise by means of a valve attached to the exit of the slit die.