Funnel Flow Research Articles

Radiation hydrodynamical self-similar funnel jets

ABSTRACT Two-dimensional funnel flows driven by radiation pressure in the conical funnel formed by the critical accretion disc are examined using the self-similar treatment. The flow is assumed to be steady and axisymmetric, and other forces such as viscosity and magnetic fields are ignored. For various boundary conditions on the funnel wall at the disc surface, the self-similar solutions are found to be classified into three types: funnel-filled solutions, where the flow gas fills the whole region of the funnel; polar-hollow ones, where there appears a cavity around the polar axis, and unphysical ones in a sense that, e.g. the radiation energy density becomes negative. For the physically reasonable solutions, the flow gas generally concentrates to the funnel wall, and the flow density and the radiation energy density monotonically decrease from the funnel wall towards the polar axis, while the radial flux becomes negative near the polar axis. The vertical velocity increases towards the polar axis, while the vertical flux has often the maximum between the polar axis and the funnel wall. As a result, the present self-similar funnel jets are such a flow with a slow dense outer part and a fast rarefied inner part.

Analytical approach of funnel flow discharge

Design engineers often encounter problems because of the special mechanical behavior of granular materials. Such a typical problem is predicting discharge rate of silos and hoppers. This important design parameter must be known during the development of material transport devices attached to the container, but the calculation of this parameter may be challenging because well-known theories of hydrodynamics are not applicable. Several models are formed to evaluate discharge rate of silos, although most of them based on experimental observations are unable to explain physics of particle outflow. Oldal’s theory accounts for granular discharge of funnel flow, cylindrical silos with formation, and collapse of unstable arches above the orifice. It is applied to rectangular hoppers in this paper to generalize and prove this theory. An extended equation is derived by applying the original hypothesis that is validated using laboratory experiments and numerical simulations.

Rotating orifice feeding system for continuous and uniform discharge of makhana seeds (Euryale ferox)

Abstract Consistent and slow mass flow rates of granular materials through a small diameter orifice (D) at the center of the bottom of a hopper is difficult to obtain when D is less than 5 times of the characteristic seed size. Rotation of the bottom in the horizontal plane with the orifice placed at an off-center distance (R) from the center of the hopper can sustain controlled flow rates even at small D. A simple feeding system was developed in this study for discharging roasted makhana seeds of different sizes (7.48–12.40 mm diameter) at 10–30 kg h−1 consistent mass flow rates. The feeding system consists of a rotating orifice plate at an off-center distance, which is placed inside a pipe connected with the bottom of a trapezoidal hopper. The effects of rotational rate (ω), D, and R on the mass flow rates of makhana seeds and plastic beads of different sizes have been investigated. The materials did not discharge when the orifice was stationary. The mass flow rate increased with the increase in ω, D and R. Finite mass flow rates in the range of 2.25–29.81 kg h−1 were obtained for different seed sizes of roasted makhana seeds with varying D (15–20 mm), R (20–30 mm), and ω (0.52–7.86 rad s−1). The mass flow rates >30 kg h−1 were obtained at D ≥ 25 mm, however, finite mass flow rate ranges were not be obtained for all seed sizes at R ≥ 20 mm. The seed discharge was in the funnel flow regime for all D, R, ω, and seed sizes because of the geometry of the hopper and feeding system. The existing Beverloo equation did not describe the mass flow rate adequately for the developed system. Therefore, Beverloo equation was modified using a function similar to the Froude number to describe the mass flow rate. The developed feeding system performed well in feeding makhana seeds and plastic beads of different sizes and maintained finite mass flow rates.

Investigation into the Mechanism of the Steel Particle Feeding Process: A Numerical and Experimental Study

The particle feeding system is a prerequisite for the realization of particle impact drilling technology. Because of the high density, the storage and flow of the steel particle are different from those of the other nonviscous particles. The differential equation of the particle movement was built with the liquid bridge force model and the discrete element method. The dynamic movement process and the distribution state of particles in the high-pressure tank were analyzed. For 1 mm steel particles, the mass flow rate decreased with the increase in water content. For 2 mm and 3 mm steel particles, the water content of 15% and 20% was the dividing point of the mass flow rate from increasing to decreasing. When the water content was 10% and 20%, the mass flow rate increased with the steel particle size. But when the water content was 30% and 40%, the mass flow rate decreased with the steel particle size. The study of the control mechanism of the uniformity and stability of particles showed that the funnel flow was the major reason causing the instability and blocking of the feeding process. This research results can provide a basis for the further improvement of the differential pressure feeding system.

Investigation of wet coal flow characteristics in silos by experiments and simulations

AbstractThe investigation of the wet coal flow characteristics is carried out in a three‐dimensional silo system by experiments and simulations. The effect of the moisture content on the flow characteristics is firstly investigated by experiments, which is in terms of bulk density, angle of repose, and flow rate at outlet. When moisture content is below 9%, the coal particles act as the easy flow mode. When moisture content exceeds 9.8%, the flow pattern turns to be cohesive. For the further understanding of the influence of the moisture content, we develop the continuum method with the effect of moisture content being considered in the mathematic model. The simulation results of the discharge rate and the ash content at outlet have good agreements with a maximum deviation of 7.3%. It is found that the Mixing Index decreases with the moisture content increasing because the moisture strengthens mixing among particles. And the velocity difference between particles in the central axis and ones near the wall grows accordingly. Particles with higher moisture content are easier to get the funnel flow mode. For particles with good flowability, the mass flow mode appears in the silo.

Flow Characteristics of Grains in a Conical Silo with a Central Decompression Tube Based on Experiments and DEM Simulations

Grains are widely present in industrial productions and processing, and are stored in silos. In the silo, auxiliary structures are added to achieve efficient production. However, little effort has been devoted to the influence of the internal structure of the silo on the granular flow. In this work, a silo with a central decompression tube is studied through experimental measurements and discrete element methods. Then, the influences of the central decompression tube on the flow behavior of grains and wall pressure are analyzed. Results show that the grains are in mass flow in the silo without a central decompression tube, while the grains are in funnel flow in the silo with a central decompression tube. Moreover, regardless of whether there is a central decompression tube in the silo, the maximum pressure appears at the top of the conical silo. In the lower part of the silo, the wall pressure of the silo with a central decompression tube is lower than that of the silo without a central decompression tube. Therefore, a silo with a central decompression tube is more conducive to grain storage and discharge than a silo without a central decompression tube.

Silo discharge: influence of the particle shape on the velocity profiles

Experiments on the discharge of a silo with an inclined outlet are performed using flattened seeds in order to evaluate the validity of a previous theoretical formulation developed in our work group [1]. In that description, funnel flow regime is assumed to be based on a free fall parabolic arc. The shape of this arc is described with a parameter which is the only one involved in the flow rate formulation. An experimental analysis of the behavior of this parameter is carried out based on the geometry and shape of the grains within the silo. Also, video analysis of the silo discharge is performed in order to investigate the velocity profiles at the outlet of the hopper for these non-spherical particles. Experiments are contrasted with analytical predictions derived from the proposed formulation in order to assess and discuss its validity for the case of flattened particles.

Effect of nonionic side chain length of polycarboxylate-ether-based high-range water-reducing admixture on properties of cementitious systems

Despite the large variations in the behaviors of water-reducing admixtures upon changes in their structures, most previous reports on the cement-admixture compatibility did not provide sufficient information on the structure of the admixture. Hence, the evaluation and generalization of the reports on the cement-admixture compatibility are challenging. In this study, three different polycarboxylate-ether-based water-reducing admixtures with the same free nonionic content, anionic/nonionic molar ratio, and main chain length and different side chain lengths were produced. The compatibility of these admixtures with a CEM I 42.5 R-type cement was investigated. In addition, an analysis of variance was performed on the experiment results to evaluate the contributions of the admixture type, admixture/cement ratio, and elapsing time to the Marsh funnel flow time, mini-slump, slump flow, and compressive strength. The water-reducing admixtures having long or short side chains reduced the initial flow characteristics of the cementitious systems. However, the admixture having the shortest side chain was better with regard to flow retention. The side chain length of the admixture did not have significant effects on the compressive strength and water absorption capacity of the mortar mixtures and mini-slump performances of the cement paste mixtures. Regarding the behaviors of the admixtures in the cementitious systems, an optimal admixture side chain molecular weight is proposed.

Investigating the magnetospheric accretion process in the young pre-transitional disk system DoAr 44 (V2062 Oph)

Context. Young stars interact with their accretion disk through their strong magnetosphere. Aims. We aim to investigate the magnetospheric accretion/ejection process in the young stellar system DoAr 44 (V2062 Oph). Methods. We monitored the system over several rotational cycles, combining high-resolution spectropolarimetry at both optical and near-IR wavelengths with long-baseline near-IR inteferometry and multicolor photometry. Results. We derive a rotational period of 2.96 d from the system’s light curve, which is dominated by stellar spots. We fully characterize the central star’s properties from the high signal-to-noise, high-resolution optical spectra we obtained during the campaign. DoAr 44 is a young 1.2 M⊙ star, moderately accreting from its disk (Ṁacc = 6.5 10−9 M⊙ yr−1), and seen at a low inclination (i ≃ 30°). Several optical and near-IR line profiles probing the accretion funnel flows (Hα, Hβ, HeI 1083 nm, Paβ) and the accretion shock (HeI 587.6 nm) are modulated at the stellar rotation period. The most variable line profile is HeI 1083 nm, which exhibits modulated redshifted wings that are a signature of accretion funnel flows, as well as deep blueshifted absorptions indicative of transient outflows. The Zeeman-Doppler analysis suggests the star hosts a mainly dipolar magnetic field, inclined by about 20° onto the spin axis, with an intensity reaching about 800 G at the photosphere, and up to 2 ± 0.8 kG close to the accretion shock. The magnetic field appears strong enough to disrupt the inner disk close to the corotation radius, at a distance of about 4.6 R⋆ (0.043 au), which is consistent with the 5 R⋆ (0.047 au) upper limit we derived for the size of the magnetosphere in our Paper I from long baseline interferometry. Conclusions. DoAr 44 is a pre-transitional disk system, exhibiting a 25–30 au gap in its circumstellar disk, with the inner and outer disks being misaligned. On a scale of 0.1 au or less, our results indicate that the system is steadily accreting from its inner disk through its tilted dipolar magnetosphere. We conclude that in spite of a highly structured disk on the large scale, perhaps the signature of ongoing planetary formation, the magnetospheric accretion process proceeds unimpeded at the star-disk interaction level.

Particle flow rate in silos under rotational shear.

Very recently, To etal. have experimentally explored granular flow in a cylindrical silo, with a bottom wall that rotates horizontally with respect to the lateral wall [Phys. Rev. E 100, 012906 (2019)10.1103/PhysRevE.100.012906]. Here we numerically reproduce their experimental findings, in particular, the peculiar behavior of the mass flow rate Q as a function of the frequency of rotation f. Namely, we find that for small outlet diameters D the flow rate increased with f, while for larger D a nonmonotonic behavior is confirmed. Furthermore, using a coarse-graining technique, we compute the macroscopic density, momentum, and the stress tensor fields. These results show conclusively that changes in the discharge process are directly related to changes in the flow pattern from funnel flow to mass flow. Moreover, by decomposing the mass flux (linear momentum field) at the orifice into two main factors, macroscopic velocity and density fields, we obtain that the nonmonotonic behavior of the linear momentum is caused by density changes rather than by changes in the macroscopic velocity. In addition, by analyzing the spatial distribution of the kinetic stress, we find that for small orifices increasing rotational shear enhances the mean kinetic pressure 〈p^{k}〉 and the system dilatancy. This reduces the stability of the arches, and, consequently, the volumetric flow rate increases monotonically. For large orifices, however, we detected that 〈p^{k}〉 changes nonmonotonically, which might explain the nonmonotonic behavior of Q when varying the rotational shear.

Theoretical and Experimental Evaluation of Flow Pattern of Pharmaceutical Powder Blends Discharged From Intermediate Bulk Containers (IBCs).

The purpose of this study is to assess the prevalence of funnel flow pattern for common pharmaceutical powder blends, upon discharging from modern intermediate bulk containers (IBCs) in drug product manufacturing. The estimation was built upon Jenike's original radial stress field theory. It was modified to account for the stress-dependence of wall friction angle commonly observed in pharmaceutical powders. A total of 260 flow pattern estimations, based on 20 real-life IBCs and 13 investigational powder blends, were made. The estimated results showed that the mass flow pattern is present in less than 5% of all cases. Funnel flow pattern is clearly prevalent among pharmaceutical powder blends. The prevalence of funnel flow stems from several factors: 1) relatively shallow hopper section shared by all IBCs, 2) the common transition-type geometry, leading to even shallower hopper inclination at the edge of the hopper section, and 3) relatively high wall friction angles resulting from low wall normal stresses. This conclusion was verified through at-scale experiments, by discharging multiple pharmaceutical powder blends from a representative IBC. In general, our study suggests that, unless the powder wall friction can be substantially reduced, pharmaceutical powders are likely to discharge under funnel flow from modern IBCs.

Magnetospheric accretion in the intermediate-mass T Tauri star HQ Tauri

Context. Classical T Tauri stars are pre-main sequence stars surrounded by an accretion disk. They host a strong magnetic field, and both magnetospheric accretion and ejection processes develop as the young magnetic star interacts with its disk. Studying this interaction is a major goal toward understanding the properties of young stars and their evolution. Aims. The goal of this study is to investigate the accretion process in the young stellar system HQ Tau, an intermediate-mass T Tauri star (1.9 M⊙). Methods. The time variability of the system is investigated both photometrically, using Kepler-K2 and complementary light curves, and from a high-resolution spectropolarimetric time series obtained with ESPaDOnS at CFHT. Results. The quasi-sinusoidal Kepler-K2 light curve exhibits a period of 2.424 d, which we ascribe to the rotational period of the star. The radial velocity of the system shows the same periodicity, as expected from the modulation of the photospheric line profiles by surface spots. A similar period is found in the red wing of several emission lines (e.g., HI, CaII, NaI), due to the appearance of inverse P Cygni components, indicative of accretion funnel flows. Signatures of outflows are also seen in the line profiles, some being periodic, others transient. The polarimetric analysis indicates a complex, moderately strong magnetic field which is possibly sufficient to truncate the inner disk close to the corotation radius, rcor ∼ 3.5 R⋆. Additionally, we report HQ Tau to be a spectroscopic binary candidate whose orbit remains to be determined. Conclusions. The results of this study expand upon those previously reported for low-mass T Tauri stars, as they indicate that the magnetospheric accretion process may still operate in intermediate-mass pre-main sequence stars, such as HQ Tauri.

Granular material flow regime map for planar silos and hoppers

This study presents a new theoretical model for granular materials flow regimes during discharge from wedge-shape (planar) silos. The new model takes into account the influence of granular material properties, material height, bin and hopper geometrical dimensions and consider the possible difference between the bin and the hopper wall friction coefficients. In addition, the model allows to found an appropriate transition between mass flow and two kinds of funnel flow regimes. By comparing the new model assessments to experimental results, which were found in the literature, good agreement was achieved. Based on the new model equations a generalized flow regime map was presented. The proposed generalized flow regime map should help designers to increase accuracy and flexibility in the granules flow regime assessment and therefore might improve significantly the process efficiency.

Shear Cell Test and Hopper Design

Relevance of the work. The Hopper and Bin design is the most commonly used technique of storing materials as it is a gravity fed system and is generally used for storing materials such as agricultural grains as well as mined minerals such as sand and coal. Mass flow, which is ideally the most desired flow type sees the bulk material travel uniformly with all particles in motion until all the material leaves the bin. The other types of flow generally occur with flat-bottomed bins with shallow hoppers are not seen as ideal as with this design problems such as arching and rat holing occur. The issue with the current design is that some of the material becomes stagnant in the bin, this can be costly as if the bulk material becomes stuck, degradation can occur over time. It can be observed for the Funnel and Expanded flow, the rat holing and arching occurring due to the stagnant material. Research Objective is to design a novel mass flow acrylic bin and hopper to store bulk quantities of sand without stagnation or degradation Methodology. Two separate experimental procedures were carried out including the measurement of the specific gravity of the sand, shear test and final hopper design. The data was then manipulated and plotted stress transformations and identified multiple key flow property constituents. Using values such as the yield loci and associative yield stresses the hopper half angle α and opening diameter B were tabulated. Results and Conclusions. The optimum opening diameter B for an uncompacted system is 2 mm and the hopper half angle α adjusted to 34.58o , this was tested and provided a successful mass flow hopper system. Overall, the techniques used with specific gravity and shear cell testing gave a sufficient insight into the appropriate procedure for designing efficient and accurate bin and hoppers. Then substituting the values gathered into the appropriate formulae provided a successful mass flow system for the intended bulk material which is sand.

Wall normal stress characteristics in an experimental coal silo

This paper describes experimental research on the wall normal stress in a laboratory-scale coal silo. The stresses were measured during discharge by pressure sensors arranged in the wall of the silo. The results show that the wall normal stresses at the upper part of hopper remain fairly constant for about three-fourths of the discharge, and then oscillate violently. The dead zone and the saturation effect of pressure in silo contribute to the smoothness and steadiness of those stresses in the stable stage of discharge. A tentative procedure is proposed to predict the funnel flow pattern of which the lower merge point has some distance from the edge of the outlet. Furthermore, a large fluctuation traveling upward from the outlet was detected during the initial discharge period. The movement of the lower merge point, which changes the flow pattern and stress state zone, is reasonably responsible for the large fluctuation.

Transition of granular flow patterns in a conical hopper based on superquadric DEM simulations

Granular flow exists widely in nature or industrial production, and particle shape is a crucial factor affecting the flow characteristics of granular materials. In this study, spherical and cylindrical particles are constructed by superquadric equations, and the discharging processes of granular materials in the conical silo are simulated by the discrete element method. Subsequently, the effects of blockiness, aspect ratio and hopper angle on the flow characteristics are investigated. The results show that the discharge rates of cylindrical particles increase and flow fluctuation decreases as the blockiness parameters and aspect ratios decrease or the hopper angles increase. Compared with spherical particles, cylindrical particles are more likely to cause interlocking and hinder sliding or rotation between particles, which results in intermittent granular flow. Furthermore, the flow pattern transition is dominated by the particle shape and hopper angle. The critical height between the mass and funnel flows decreases as the blockiness parameter decreases or the aspect ratio and hopper angle increase and reaches a steady state. However, the effect of particle shape on the flow pattern transition becomes negligible for a larger hopper angle. When the hopper angle is larger than 60°, the granular system basically has a uniform vertical velocity and all particles are in the mass flow. On the microscopic scale, cylindrical particles have a larger average coordination number and greater possibility of strong contact force than spherical particles, which may further cause the flow pattern transition of granular materials on the macroscopic scale.

Discharge and mixing of moisture coal particles in silos

ABSTRACT Due to the limit of traditional models, a revised mathematical model was adopted to describe the movement of packing powder in silos. The model could be used in the area of coal particles with moisture content concerned based on continuum method. The accuracy of the model was validated by comparing with experimental results from the aspects of discharge rate, the flow pattern and the ash content at outlet. With the model, it was also found that the flow pattern was converted from mass flow (θ= 15°) to funnel flow (θ= 45°, 60°) with the half opening angle increasing. Furthermore, the increase of the moisture content led to the transition from mass flow (x=6.91%) to funnel flow (x=14.68%). And the reduction of discharge rate had the same effect when G was converted from 11.46kg/s to 2.86kg/s. Besides, the transformation of flow pattern brought differences of the granular mixing process in silos, which was indicated by the ash content at outlet and Mixing Index. Compared with the mass flow, the mixing degree got more intensive for the funnel flow.

The effect of Isoprenyl Ether polymer molecular structure on cementitious composites

In order to minimize the rapid flow loss issue from the hot weather or during lengthy periods and long-distance transport, the synthesis of the isoprenyl oxy polyethylene ether (T-PEG) was introduced. However, there were scarce amount of reported literature on the influence of main and side chain densities on the fresh and hardened properties of concrete containing T-PEG polymers. This study was conducted to investigate fresh and mechanical properties of cementitious composites containing T-PEG polymers with different main and side chain densities. These T-PEG polymers were comprised of the density ratio of side chain to main chain of 1:1, 1:1.5, 1:2, 1:2.5 and 1:3.5, respectively. The laboratory tests conducted were marsh cone funnel test, standard consistency, flow retention, flexural strength and compressive strength test. The results obtained showed that the increased density ratio of side chain to main chain of T-PEG improves the fluidity of the cement paste and the flow retention ability of the cement mortar. Consequently, the mortar with T2 polymer proved a better performance on mechanical strength tests. In conclusion, the increasing main to side chain densities ratio of T-PEG polymer imposes a significant influence on the fresh and hardened properties of the concrete material produced.

Concrete Silos: Failures, Design Issues and Repair/Strengthening Methods

The review article investigated failure, design issues, repair and strengthening of reinforced concrete (RC) silos, primarily in agricultural set-ups. The durability of RC structures was influenced by the nature of the bulk solids, materials used in the reinforcement of the structures. Traditionally, high-grade steel has been used in silo wall reinforcement because it is affordable and readily available. However, it is susceptible to corrosion. In contrast, fiber-reinforced polymers (FRP) have better mechanical properties (tensile strength, elastic modulus, and Poisson’s ratio) and are not corroded. Additionally, there are limited scalable and facile methods for commercial production. The low ductility elevates the risk of brittle fracture in external pre-stressing concrete repair/strengthening. Beyond the material factors, the existing silo design codes such as BS EN 1991-4:2006, Australian Standard AS 3774-1996, and American Society of Agricultural Engineers ANSI/ASAE EP433 DEC1988 (R2011), and American Concrete Institute ACI 313-97 are limited by simplified characterization of loading/unloading scenarios and exclusion of specific hopper geometries and configurations. The funnel and mass flow scenarios and accumulation of bulk materials contribute to silo failure. In brief, the present repair/strengthening strategies (external pre-stressing, insertion/removal of inserts, shear columns, and FRPs alternatives to steel) do not adequately address the diverse variables that elevate the risk of material failure.

Effect of the polycarboxylate based water reducing admixture structure on self-compacting concrete properties: Main chain length

In this study, the effect of polycarboxylate ether-based water reducing admixture (WRA) main chain length on fresh state properties, compressive strength, ultrasonic pulse velocity (UPV) and water absorption capacity of self-compacting concrete (SCC) mixtures were investigated. Within this aim, three polycarboxylate ether-based high range WRAs with stabilized polyethylene oxide side chain molecular weight, free non-ionic content and constant anionic/non-ionic ratios, but different main chain length were synthesized. FTIR (Fourier transform infrared) and GPC (Gel Permeation Chromatography) analyzes were carried out to characterize admixtures. According to test results, the admixture requirement for reaching targeted main chain length in SCC increased and adsorption of admixture decreased in case the admixture main chain length is higher and lower than a certain value. However, time-dependent flow performance of the mixtures improved with the increase of admixture main chain length and a reverse situation was observed when the length was decreased. Similar behaviors were also observed in V funnel flow, L box and U box passing tests. While the admixture main chain length change affected early age strength, it showed no effect on the strengths of later ages. No considerable differences were observed in the 28-day water absorption, UPV and dynamic modulus of elasticity values of the mixtures with the change of admixture main chain length.