Constant Void Research Articles

Design and simulation of a multienergy gamma ray absorptiometry system for multiphase flow metering with accurate void fraction and water-liquid ratio approximation

Abstract Multiphase flow meters are used to measure the water-liquid ratio (WLR) and void fraction in a multiphase fluid stream pipeline. In the present study, a system of multiphase flow measurement has been designed by application of three thallium-doped sodium iodide scintillators and a radioactive source of 133Ba simulated by Monte Carlo N-particle (MCNP) transport code. In order to capture radiations passing across the pipe, two direct detectors have been installed on opposite sides of the radioactive source. Another detector has been placed perpendicular to the transmission beam emitted from the 133Ba source to receive radiations scattered from the fluid flow. Simulation was done by the MCNP code for different volumetric fractions of water, oil, and gas phases for two types of flow regimes, namely, homogeneous and annular; training and validation data have been provided for the artificial neural network (ANN) to develop a computation model for pattern recognition. Depending on applications of the neural system, several structures of ANNs are used in the current paper to model the flow measurement relations, while the detector outputs are considered as the input parameters of the neural networks. The first, second, and third structures benefit from two, three, and five multilayer perceptron neural networks, respectively. Increasing the number of ANNs makes the system more complicated and decreases the available data; however, it increases the accuracy of estimation of WLR and gas void fraction. According to the results, the maximum relative difference was observed in the scattering detector. It was clear that transmission detectors would demonstrate the difference between the flow regimes as well. It is necessary to note that the error calculated by the MCNP simulator is <0.5% for the direct detectors (TR1 and TR2). Due to the difference between the data of the two flow regimes and the errors of data in the simulation codes of the MCNP, it was possible to separate these flow regimes. The effect of changing WLR on the efficiency for a constant void fraction confirms a considerable variance in the results of annular and homogeneous flows occurring in the scattering detector. There is a similar trend for the void fraction; hence, one can easily distinguish changes in efficiency due to the WLR. Analysis of the simulation results revealed that in the proposed structure of the multiphase flow meter and the computation model used for simulation, the two flow regimes are simply distinguishable.

Numerical estimation of air core length in two-phase free surface vortex

ABSTRACTThe free-surface vortex is simulated with the homogeneous mixture approach. In order to define suitable boundary conditions in the two-phase flow field, a numerical strategy is proposed on the air mass conservation in a recirculating flow system. The numerical approach is verified from an experiment. Numerical results agreed well with the experiment not only in the vortex circulation but also in the axial velocity gradient. On the homogeneous mixture assumption, the compressibility corrections for the turbulence modelling had almost no effect on the result in this case study. In order to estimate the continuous air–core length, the visible air–core interface was assumed to be characterized by the constant void fraction. With validated numerical results, vortex air core was visualized by the air volume fraction, based on the air–core length in not only the experiment but also the analytical model in the applicable range.

An atomistic modelling and statistical analysis study of crack–void interaction in Aluminum

The interaction between a brittle crack and pre-existing void in front of the crack tip was studied in the realm of molecular dynamics simulations at the nanoscale in face centred cubic Al within the framework of embedded-atom method. The results provide corroborative evidence of the fact that presence of a void in front of a running crack deters further crack growth. By performing an extensive series of simulations with different void sizes and crack-void distances coupled with statistical analysis, it has been found that (1) major role of voids is to decrease the fracture stress with increasing void size, in addition to slight increase in strain at which the crack growth occurs and the consequent strain to fracture, (2) fracture stress for a constant void size follows a sinusoidal distribution by varying the crack-void distance and (3) it is the void size that is most crucial in dictating the fracture properties of the material, rather than the void placement.

Effect of nonplastic silt content on undrained shear strength of sand\u2013silt mixtures

To assess the behavior of sand–silt mixtures, strain-controlled monotonic triaxial tests were conducted on sand–silt mixtures of specimen size 71 mm in diameter and 142 mm in height at various relative densities but same isotropic effective confining pressure of 100 kPa. Concept of limiting fines content (LFC) was verified by these undrained monotonic triaxial tests. LFC was found to be the very important parameter to understand the behavior of sand–silt mixtures. The behavior of sand–silt mixture changes approximately at LFC. At constant relative density, increase in silt content decreases the undrained peak shear strength till LFC. After LFC the strength becomes near about same till pure silt sample. The reason of behavior could not be explained. At constant global void ratio, the peak shear strength decreases with increase in silt content till LFC and for further increment of silt content the peak shear strength increases. Sand–silt mixtures containing certain amount of silt which is near to the LFC showed flow type as well as brittle behavior. Failure of structure on this type of soil will be catastrophic during earthquake. In the case of permeability decreased with increasing silt content up to LFC. After the LFC, dry density is decreasing with increasing silt content but permeability remains constant till pure silt.

Influence of pipeline modeling in stability analysis for severe slugging

In this paper a numerical linear stability analysis is performed to a mathematical model for the two-phase flow in a pipeline-riser system. Most of dynamic models and stability criteria are based on a simplified lumped parameter pipeline, where it is assumed that the void fraction variations can be neglected. As a pipeline with a constant void fraction is not able to describe the flow pattern transition or void fraction propagation waves, the choice of pipeline model influences the stability map. Three different models for the pipeline are considered: (a) A lumped parameter model with constant void fraction; (b) A lumped parameter model with time dependent void fraction; (c) A distributed parameter model, with void fraction dependent on time and position.The results show that the constant void fraction model overestimates the unstable region, pushing the near horizontal branch of the stability boundary beyond the stratified-intermittent transition boundary for high buffer lengths and invalidating the model assumptions. The distributed parameter model is capable of describing void fraction waves along the pipeline under the restriction of a stratified flow pattern, with an additional stabilizing effect, being less sensitive to high buffer lengths and not crossing the stratified-intermittent transition in the nearly horizontal branch. The lumped parameter model with variable void fraction behaves close to the distributed model, but predicting bigger unstable regions.The behavior of the different pipeline models is explained based on the basic assumptions that led to many semi-empirical stability criteria. It is concluded that a distributed parameter model is recommended, with a void fraction correlation that includes the transition from stratified to intermittent flow pattern taken into account in the problem statement.

Macro deformation and micro structure of 3D granular assemblies subjected to rotation of principal stress axes

This paper presents a numerical investigation on the behavior of three dimensional granular materials during continuous rotation of principal stress axes using the discrete element method. A dense specimen has been prepared as a representative element using the deposition method and subjected to stress rotation at different deviatoric stress levels. Significant plastic deformation has been observed despite that the principal stresses are kept constant. This contradicts the classical plasticity theory, but is in agreement with previous laboratory observations on sand and glass beads. Typical deformation characteristics, including volume contraction, deformation non-coaxiality, have been successfully reproduced. After a larger number of rotational cycles, the sample approaches the ultimate state with constant void ratio and follows a periodic strain path. The internal structure anisotropy has been quantified in terms of the contact-based fabric tensor. Rotation of principal stress axes densifies the packing, and leads to the increase in coordination numbers. A cyclic rotation in material anisotropy has been observed. The larger the stress ratio, the structure becomes more anisotropic. A larger fabric trajectory suggests more significant structure re-organization when rotating and explains the occurrence of more significant strain rate. The trajectory of the contact-normal based fabric is not centered in the origin, due to the anisotropy in particle orientation generated during sample generation which is persistent throughout the shearing process. The sample sheared at a lower intermediate principal stress ratio $$(b=0.0)$$ has been observed to approach a smaller strain trajectory as compared to the case $$b=0.5$$ , consistent with a smaller fabric trajectory and less significant structural re-organisation. It also experiences less volume contraction with the out-of plane strain component being dilative.

Shear wave velocity and stiffness of sand: the role of non-plastic fines

Current knowledge on the shear wave velocity (Vs) and associated stiffness (G0) of sand is built mainly on the results of extensive laboratory studies on clean quartz sands. Often natural sands are not clean, but contain a certain amount of fines. The role of fines in altering the stiffness of sands is a matter of great concern, yet remains poorly understood. This paper presents an investigation into the problem through well-controlled laboratory experiments in conjunction with analysis and interpretation at the macro and micro scale. The laboratory experiments were conducted for a sequence of mixtures of clean quartz sand and crushed silica fines under saturated conditions, by the simultaneous use of the resonant column (RC) and bender element (BE) techniques. A broad range of states in terms of void ratio, confining stress and fines content was covered so as to obtain a comprehensive view on the effect of fines and the possible interplay with other factors. Both the RC and BE tests showed that G0tends to decrease continuously as the quantity of fines is increased and the reduction rates are similar; a similar stress dependence is also obtained for G0from both types of testing. Nevertheless, G0values obtained from BE tests are notably greater than those obtained from RC tests, and this effect of testing method is shown to be coupled with the sample reconstitution method. A new approach that allows unified characterisation of G0values for both clean sand and sand–fines mixtures is developed in a sound theoretical framework, thereby providing important insights into the various empirical correlations that involve G0(or Vs) in geotechnical engineering practice. A new micro-scale mechanism is also suggested for the observed effect of fines, which attributes the reduction of G0caused by fines to the decrease in the coordination number at an approximately constant void ratio.

Evaluation of static and dynamic properties of sand–fines mixtures through the state and equivalent state parameters

The results of an experimental investigation on sands with low plastic fines content are presented. Specimens with a low plastic fines content of 0%, 15%, 30%, 40%, 50% and 60% by weight were tested in drained and undrained triaxial compression tests. The soil specimens were tested under three different categories: (1) at a constant void ratio index; (2) at the same peak deviator stress in a triaxial test; and (3) at a constant relative density. By a combination with our published experimental data in recent years, the critical state line and various state parameters have been proposed and discussed for a further understanding the behavior of sand–fines mixtures. Results indicated that a unique critical line was obtained from drained and undrained triaxial compression tests for each fines content. The effects of fines content on critical state line (CSL) were recognized and discussed. In addition, the results revealed that normalized peak undrained shear stress, cyclic resistance ratio, and compression index were found to be a good correlation with state parameter Ψ as well as equivalent state parameter Ψ*. An increasing state parameter decreased the normalized peak undrained shear stress, and cyclic resistance ratio; however, the compression index increased with an increase in state parameter. Finally, there were no correlations such as the coefficient of consolidation–state parameter and maximum shear modulus–state parameter due to the different testing condition.

Effects of Fines Contents on Engineering Properties of Sand-Fines Mixtures

This paper presents a detailed study focused on investigating the effects of fines content on the engineering properties of sand-fines mixtures. Specimens with a low-plastic fines content of 0, 15, 30 and 50% by weight were tested in static triaxial and consolidation tests to determine such parameters as compression index, internal friction angle and cohesion. The test procedures were performed on specimens of three cases: constant void ratio index, e = 0.582; same peak deviator stress of 290kPa; and constant relative density, Dr = 30%. The test results obtained for both the constant-void-ratio-index and constant-relative-density specimens showed that as fines content increased, the internal friction angle decreased, but cohesion increased. In testing of the same deviator stress specimens, both cohesion and internal friction angle were insignificantly altered with the increase in fines content. Furthermore, undrained behavior of sand-fines mixtures were recognized and discussed in three types of specimens.

Engineering behavior and correlated parameters from obtained results of sand–silt mixtures

The results of an experimental study on sands with low-plastic silt content are presented. Flexible wall permeameter tests, drained and undrained triaxial compression tests, one-dimensional consolidation tests, and undrained cyclic triaxial tests were performed on specimens with a low plastic silt content of 0%, 15%, 30%, 40%, 50% and 60% by weight. The soil specimens were tested under three different categories: (1) at a constant void ratio index; (2) at the same peak deviator stress in a triaxial test; and (3) at a constant relative density. The results were observed to be somewhat different from previous studies with non-plastic silt content and plastic fine content. Cyclic triaxial tests showed that an increase in silt content causes a decrease in the cyclic resistance ratio with a silt content up to 40–50% and thereafter causes an increase in the cyclic resistance ratio with further increases in silt content. The results of triaxial tests indicated that the value of the peak deviator stress changed with different types of specimens, and the greater internal friction an angle has, the stronger is the liquefaction resistance. Flexible wall permeameter tests concluded that the saturated hydraulic conductivity slowly decreases with an increase in silt content in the range from 0% to 30% and considerably decreases with a silt content greater than 30%. A one-dimensional consolidation test postulated that increasing silt content decreases the coefficient of consolidation. In addition, the global void ratio did not appear to be a pertinent parameter in explaining the behavior of sand–silt mixtures, while fine content and intergranular void ratio were suitable parameters for explaining the behavior of sand–silt mixtures. Finally, correlated parameters from obtained results were also presented in this study.

State variables for silty sands: Global void ratio or skeleton void ratio?

While the global void ratio has long been used as a density index to characterize sand behavior, concern has been increasing about its applicability to silty sands (sand–fines mixtures), based on the proposition that the fines may fill in the void spaces formed by sand grains and make no contribution to the force transfer. The skeleton void ratio was proposed in the literature as an alternative index for mixed soils, based on the assumption that all fines act as voids. It was further modified into an equivalent skeleton void ratio by taking into consideration the fraction of fines that participates in the force transfer. This paper presents a study aimed at evaluating the three state variables as applied to sand–fines mixtures and especially to explore the rationale behind the concept of the skeleton void ratio. Based on a specifically designed experimental program, it is shown that contrasting conclusions can be drawn as to the role of fines in altering the shear behavior of clean sand when different density indices are used as the comparison basis. When comparisons are made at a constant (global) void ratio, the fines increase the degree of contractiveness, but when comparisons are made at a constant skeleton void ratio, an increase in dilativeness is seen. The equivalent skeleton void ratio does not fulfill the intent of providing a universal means for characterizing the stress–strain behavior of silty sands. This is due to the lack of mechanisms to account for the inter-granular contacts which are highly complex. The study suggests that compared with the skeleton void ratio and its modified form, the usual (global) void ratio remains a simple and useful state variable suitable for the framework of critical state soil mechanics and for geotechnical applications.

Effects of silt contents on the static and dynamic properties of sand-silt mixtures

This paper presents a detailed study focused on investigating the effects of silt content on the static and dynamic properties of sand-silt mixtures. Specimens with a low-plastic silt content of 0, 15, 30 and 50% by weight were tested in static triaxial, cyclic triaxial, and resonant columns in addition to consolidation tests to determine such parameters as compression index, internal friction angle, cohesion, cyclic stress ratio, maximum shear modulus, normalized shear modulus and damping ratio. The test procedures were performed on specimens of three cases: constant void ratio index, e = 0.582; same peak deviator stress of 290 kPa; and constant relative density, <TEX>$D_r$</TEX> = 30%. The test results obtained for both the constant-void-ratio-index and constant-relative-density specimens showed that as silt content increased, the internal friction angle, cyclic stress ratio and maximum shear modulus decreased, but cohesion increased. In testing of the same deviator stress specimens, both cohesion and internal friction angle were insignificantly altered with the increase in silt content. In addition, as silt content increased, the maximum shear modulus increased. The cyclic stress ratio first decreased as silt content increased to reach the threshold silt content and increased thereafter with further increases in silt content. Furthermore, the damping ratio was investigated based on different silt contents in three types of specimens.

Bioinjection treatment: Effects of post-injection residual stress on left ventricular wall stress

Injection of biomaterials into diseased myocardium has been associated with decreased myofiber stress, restored left ventricular (LV) geometry and improved LV function. However, its exact mechanism(s) of action remained unclear. In this work, we present the first patient-specific computational model of biomaterial injection that accounts for the possibility of residual strain and stress introduced by this treatment. We show that the presence of residual stress can create more heterogeneous regional myofiber stress and strain fields. Our simulation results show that the treatment generates low stress and stretch areas between injection sites, and high stress and stretch areas between the injections and both the endocardium and epicardium. Globally, these local changes are translated into an increase in average myofiber stress and its standard deviation (from 6.9±4.6 to 11.2±48.8kPa and 30±15 to 35.1±50.9kPa at end-diastole and end-systole, respectively). We also show that the myofiber stress field is sensitive to the void-to-size ratio. For a constant void size, the myofiber stress field became less heterogeneous with decreasing injection volume. These results suggest that the residual stress and strain possibly generated by biomaterial injection treatment can have large effects on the regional myocardial stress and strain fields, which may be important in the remodeling process.

Modified Analytical Solution to Radial Consolidation with Soil Characteristics in a Disturbed Zone

An analytical solution modified from Hansbo's equation is suggested to evaluate the degree of radial consolidation, considering the consolidation characteristics of remolded clay and variation of soil properties within the disturbed zone. With increasing k h /k s , the time factor T h for a certain degree of radial consolidation continuously increases, while the time factor T hs slightly decreases and finally converges to the almost identical relation. Under the assumption that the settlement occurred between the prefabricated vertical drain (PVD) installation and the surcharge load application is resulted from the reduction of void ratio within the disturbed zone, the radius of the disturbed zone is estimated to be 2.675 r m for a disturbed zone of constant permeability or void ratio, while radii of the transition zone and fully disturbed zone are found to be 4.1 r m and 1.0 r m , respectively, for a disturbed zone with linear variation in the void ratio. The settlement vs. time relation predicted by the suggested solution is in good agreement with the settlement measured at Busan Newport site when k h /k f values of 2.5 and 5.0 are used for clay layers located above and below EL - 30 m, respectively, and linear variation of the void ratio within the disturbed zone is assumed.

Soil-water characteristics of Gaomiaozi bentonite by vapour equilibrium technique

Soil-water characteristics of Gaomiaozi (GMZ) Ca-bentonite at high suctions (3–287MPa) are measured by vapour equilibrium technique. The soil-water retention curve (SWRC) of samples with the same initial compaction states is obtained in drying and wetting process. At high suctions, the hysteresis behaviour is not obvious in relationship between water content and suction, while the opposite holds between degree of saturation and suction. The suction variation can change its water retention behaviour and void ratio. Moreover, changes of void ratio can bring about changes in degree of saturation. Therefore, the total change in degree of saturation includes changes caused by suction and that by void ratio. In the space of degree of saturation and suction, the SWRC at constant void ratio shifts to the direction of higher suctions with decreasing void ratio. However, the relationship between water content and suction is less affected by changes of void ratio. The degree of saturation decreases approximately linearly with increasing void ratio at a constant suction. Moreover, the slope of the line decreases with increasing suction and they show an approximately linear relationship in semi-logarithmical scale. From this linear relationship, the variation of degree of saturation caused by the change in void ratio can be obtained. Correspondingly, SWRC at a constant void ratio can be determined from SWRC at different void ratios.

Postliquefaction Undrained Shear Behavior of Sand-Silt Mixtures at Constant Void Ratio

A detailed study on the postliquefaction undrained shear behavior of sand-silt mixtures at constant void ratios is presented in this article. The influence of different parameters such as density, amplitude of cyclic shear stress, and drainage conditions on the postliquefaction undrained response of sand-silt mixtures has been investigated, in addition to the effect of fines content. The results showed that the limiting silt content plays a vital role in the strength of the soil under both cyclic and monotonic shear loading. Both the liquefaction resistance and postliquefaction shear strength of the soils are found to decrease with an increase in the fines content until the limiting silt content is reached. However, further increase in the silt content beyond the limiting silt content increases the liquefaction resistance as well as the postliquefaction shear strength of the soils. It is also observed that these variations on the liquefaction and postliquefaction resistance of soils are closely related to the variations in relative density.

Bubble effect on pressure drop reduction in upward pipe flow

In this paper, the bubble effect on the pressure drop caused by frictional losses in upward pipe flow was investigated. Pressure drop reduction in variable Reynolds numbers between 15,000 and 30,000 and void fraction values between 0 and 9% was investigated. The diameter of bubbles injected into the flow was 300μm. Increasing Reynolds number in constant void fraction makes the bubbles move away from the wall and decreases the pressure drop reduction level. Increasing void fraction increases the bubbles effect on the frictional stress and decreases the pressure drop in the pipe. Furthermore, in lower Reynolds numbers, the void fraction effect on drag reduction is greater than its effect in higher Reynolds numbers. In the present study, the maximum pressure drop reduction (35%) was obtained in the maximum void fraction value (9%) and minimum studied Reynolds number (15,000). Even in very low void fraction of 0.6%, drag reduction of 13% was observed in Reynolds number of 15,000. The obtained values of pressure drop reduction indicate that the bubble injection into pipe flow can be used to decrease the flow transfer costs.

A hysteretic soil-water retention model accounting for cyclic variations of suction and void ratio

The paper presents a water retention model capable of predicting the hysteretic response of soils during both wetting–drying cycles at constant void ratio and compression–swelling cycles at constant suction. In the proposed model two main surfaces – the main wetting and main drying surfaces – enclose the domain of attainable soil states in the degree of saturation–suction–void ratio space. Inside this domain, the variation of degree of saturation is governed by a reversible scanning law, which describes the transition from one main surface to the other. A simplified calibration procedure is presented to select the values of the four parameters defining the two main surfaces by using a minimum of two compression tests at constant suction and one drying test at constant mean net stress. Model computations are validated against results from an experimental campaign on a compacted mixture of bentonite and kaolin. The proposed formulation is capable of capturing important soil features, such as the influence of hydraulic hysteresis and deformation on the variation of degree of saturation, and the dependence of water retention behaviour during compression on previous wetting–drying history. Moreover, during main wetting or main drying at high suction (i.e. at low saturation), the model correctly predicts a ‘virgin' retention line that uniquely relates water ratio and suction regardless of the current value of void ratio.

Flow of wet powder in a conical centrifugal filter—an analytical model

A one-dimensional analytical model is developed for the steady state, axisymmetric, slender flow of saturated powder in a rotating perforated cone. Both the powder and the fluid spin with the cone with negligible slip in the hoop direction. They migrate up the wall of the cone along a generator under centrifugal force, which also forces the fluid out of the cone through the powder layer and the porous wall. The flow thus evolves from an over-saturated paste at inlet into a nearly dry powder at outlet. The powder is treated as a Mohr–Coulomb granular solid of constant void fraction and permeability. The shear traction at the wall is assumed to be velocity and pressure dependent. The fluid is treated as Newtonian viscous. The model provides the position of the colour line (the transition from over- to under-saturation) and the flow velocity and thickness profiles over the cone. Surface tension effects are assumed negligible compared to the centrifugal acceleration. Two alternative conditions are considered for the flow structure at inlet: fully settled powder at inlet, and progressive settling of an initially homogeneous slurry. The position of the colour line is found to be similar for these two cases over a wide range of operating conditions. Dominant dimensionless groups are identified which control the position of the colour line in a continuous conical centrifuge. Experimental observations of centrifuges used in the sugar industry provide preliminary validation of the model.

Undrained Cyclic and Monotonic Strength of Sand-Silt Mixtures

In an attempt to correlate the monotonic peak strength and the cyclic strength of sand-silt mixtures over a wide range of parameters and to clarify some of the existing confusing conclusions in the literature regarding the undrained strength response of sand-silt mixtures, a series of stress controlled cyclic and strain controlled monotonic triaxial tests was carried out on sand-silt mixture specimens of 50 mm diameter and 100 mm height with varying silt content. In these experiments, various measures of sample density was adopted through different approaches such as constant gross void ratio approach, constant relative density approach, constant sand skeleton void ratio approach, and constant interfine void ratio approach. Also the effect of relative density and confining pressure on these strengths was studied. It is observed that the limiting fines content and the relative density of a specimen play the key role in deciding the cyclic and monotonic resistance of sand-silt mixtures when studied through any approach. For any silt content with relative density more than 70%, cyclic and monotonic resistances are observed to be independent of silt content. When the undrained cyclic strengths of these specimens are plotted against their respective undrained monotonic peak strengths, it is observed that there exists a definite exponential relationship between the two with an excellent correlation coefficient. An expression is proposed in this regard to help engineers assess the cyclic strength of sand-silt mixtures from monotonic test results.