Search results for: Bubble matrix analysis

Authors: Seong-Su Jeon, Seong-Jin Kim, Goon-Cherl Park

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In this study, direct numerical simulation for the bubble condensation in the subcooled boiling flow was performed. The main goal was to develop the CFD modeling for the bubble condensation and to evaluate the accuracy of the VOF model with the developed CFD modeling. CFD modeling for the bubble condensation was developed by modeling the source terms in the governing equations of VOF model using UDF. In the modeling, the amount of condensation was determined using the interfacial heat transfer coefficient obtained from the bubble velocity, liquid temperature and bubble diameter every time step. To evaluate the VOF model using the CFD modeling for the bubble condensation, CFD simulation results were compared with SNU experimental results such as bubble volume and shape, interfacial area, bubble diameter and bubble velocity. Simulation results predicted well the behavior of the actual condensing bubble. Therefore, it can be concluded that the VOF model using the CFD modeling for the bubble condensation will be a useful computational fluid dynamics tool for analyzing the behavior of the condensing bubble in a wide range of the subcooled boiling flow.

Keywords: Bubble condensation, CFD modeling, Subcooled boiling flow, VOF model.

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Authors: S. Mehran, S. Rouhi, F.Rouzbahani, E. Haghgoo

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In this paper dynamics of a vapour bubble generated due to a local energy input inside a vertical rigid cylinder and in the absence of buoyancy forces is investigated. Different ratios of the diameter of the rigid cylinder to the maximum radius of the bubble are considered. The Boundary Integral Equation Method is employed for numerical simulation of the problem. Results show that during the collapse phase of the bubble inside a vertical rigid cylinder, two liquid micro jets are developed on the top and bottom sides of the vapour bubble and are directed inward. Results also show that existence of a deposit rib inside the vertical rigid cylinder slightly increases the life time of the bubble. It is found that by increasing the ratio of the cylinder diameter to the maximum radius of the bubble, the rate of the growth and collapse phases of the bubble increases and the life time of the bubble decreases.

Keywords: Vapour bubble, Vertical rigid cylinder, Boundaryelement method.

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Authors: Weiling Li, Wenqi Zhong, Baosheng Jin, Rui Xiao, Yong Lu, Tingting He

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Experiments were performed in a three-phase bubble column to study variations of bubble rise velocities. The dynamic gas disengagement (DGD) technique and the fast response pressure transducers were utilized to investigate the bubble rise in the column. The superficial gas velocity of large bubbles and small bubbles, the rise velocities of larger and small bubble fractions were studied considering the effect of particle sizes. The results show that the superficial gas velocity associated with large bubbles linearly increase as superficial gas velocity increasing. Particle size has little effect on the both large and small bubble superficial gas velocities. The rise velocities of larger bubble fractions are larger than that of small bubble fractions, and it had different tendency at low and high superficial gas velocities when changing the particle sizes. The rise velocities of small bubble fractions increased and then had a decrease tendency when the particle size became greater.

Keywords: Bubble rise velocity, gas–liquid–solid, particle size effect, three–phase bubble column.

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Authors: R. S. Hassani, S. Chikh, L. Tadrist, S. Radev

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A bubbly flow in a vertical miniature tube is analyzed theoretically. The liquid and gas phase are co-current flowing upward. The gas phase is injected via a nozzle whose inner diameter is 0.11mm and it is placed on the axis of the tube. A force balance is applied on the bubble at its detachment. The set of governing equations are solved by use of Mathematica software. The bubble diameter and the bubble generation frequency are determined for various inlet phase velocities represented by the inlet mass quality. The results show different behavior of bubble growth and detachment depending on the tube size.

Keywords: Two phase flow, bubble growth, minichannel, generation frequency.

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Authors: M.T. Shervani-Tabar, M. Rezaee, E. Madadi Kandjani

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Dynamics of a vapour bubble generated due to a high local energy input near a circular thin bronze plate in the absence of the buoyancy forces is numerically investigated in this paper. The bubble is generated near a thin bronze plate and during the growth and collapse of the bubble, it deforms the nearby plate. The Boundary Integral Equation Method is employed for numerical simulation of the problem. The fluid is assumed to be incompressible, irrotational and inviscid and the surface tension on the bubble boundary is neglected. Therefore the fluid flow around the vapour bubble can be assumed as a potential flow. Furthermore, the thin bronze plate is assumed to have perfectly plastic behaviour. Results show that the displacement of the circular thin bronze plate has considerable effect on the dynamics of its nearby vapour bubble. It is found that by decreasing the thickness of the thin bronze plate, the growth and collapse rate of the bubble becomes higher and consequently the lifetime of the bubble becomes shorter.

Keywords: Vapour Bubble, Thin Bronze Plate, Boundary Integral Equation Method.

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Authors: Zeinab Galavani, Reza Rezaei-Nasirabad, Rasoul Sadighi-Bonabi

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Using a force balanced translational-radial dynamics, phase space of the moving single bubble sonoluminescence (m- SBSL) in 85% wt sulfuric acid has been numerically calculated. This phase space is compared with that of single bubble sonoluminescence (SBSL) in pure water which has been calculated by using the mere radial dynamics. It is shown that in 85% wt sulfuric acid, in a general agreement with experiment, the bubble-s positional instability threshold lays under the shape instability threshold. At the onset of spatial instability of moving sonoluminescing (SL) bubble in 85% wt sulfuric acid, temporal effects of the hydrodynamic force on the bubble translational-radial dynamics have been investigated. The appearance of non-zero history force on the moving SL bubble is because of proper condition which was produced by high viscosity of acid. Around the moving bubble collapse due to the rapid contraction of the bubble wall, the inertial based added mass force overcomes the viscous based history force and induces acceleration on the bubble translational motion.

Keywords: Bjerknes force, History force, Reynolds number, Sonoluminescence.

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Authors: Reza Rezaei-Nasirabad, Zeinab Galavani, Rasoul Sadighi-Bonabi, Mohammad Asgarian

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Role of acoustic driving pressure on the translational-radial dynamics of a moving single bubble sonoluminescence (m-SBSL) has been numerically investigated. The results indicate that increase in the amplitude of the driving pressure leads to increase in the bubble peak temperature. The length and the shape of the trajectory of the bubble depends on the acoustic pressure and because of the spatially dependence of the radial dynamics of the moving bubble, its peak temperature varies during the acoustical pulses. The results are in good agreement with the experimental reports on m-SBSL.

Keywords: Bubble dynamics, Equation of the gas state, Hydrodynamic force, Moving sonoluminescence.

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Authors: S. Mehran, S. Rouhi, F.Rouzbahani, E. Haghgoo

Abstract:

In this paper, growth and collapse of a vapour bubble generated due to a local energy input inside a rigid cylinder and in the absence of buoyancy forces is investigated using Boundary Integral Equation Method and Finite Difference Method .The fluid is treated as potential flow and Boundary Integral Equation Method is used to solve Laplace-s equation for velocity potential. Different ratios of the diameter of the rigid cylinder to the maximum radius of the bubble are considered. Results show that during the collapse phase of the bubble inside a vertical rigid cylinder, two liquid micro jets are developed on the top and bottom sides of the vapour bubble and are directed inward. It is found that by increasing the ratio of the cylinder diameter to the maximum radius of the bubble, the rate of the growth and collapse phases of the bubble increases and the life time of the bubble decreases.

Keywords: Vapour bubble, Vertical rigid cylinder, Boundaryelement method, Finite difference method, Buoyancy forces.

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Authors: K. Jagannath, Akhilesh Kotian, S. S. Sharma, Achutha Kini U., P. R. Prabhu

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Boiling process is characterized by the rapid formation of vapour bubbles at the solid–liquid interface (nucleate boiling) with pre-existing vapour or gas pockets. Computational fluid dynamics (CFD) is an important tool to study bubble dynamics. In the present study, CFD simulation has been carried out to determine the bubble detachment diameter and its terminal velocity. Volume of fluid method is used to model the bubble and the surrounding by solving single set of momentum equations and tracking the volume fraction of each of the fluids throughout the domain. In the simulation, bubble is generated by allowing water-vapour to enter a cylinder filled with liquid water through an inlet at the bottom. After the bubble is fully formed, the bubble detaches from the surface and rises up during which the bubble accelerates due to the net balance between buoyancy force and viscous drag. Finally when these forces exactly balance each other, it attains a constant terminal velocity. The bubble detachment diameter and the terminal velocity of the bubble are captured by the monitor function provided in FLUENT. The detachment diameter and the terminal velocity obtained are compared with the established results based on the shape of the bubble. A good agreement is obtained between the results obtained from simulation and the equations in comparison with the established results.

Keywords: Bubble growth, computational fluid dynamics, detachment diameter, terminal velocity.

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Authors: Rouhollah Ahmadi, Tatsuya Ueno, Tomio Okawa

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Bubble generation was observed using a high-speed camera in subcooled flow boiling at low void fraction. Constant heat flux was applied on one side of an upward rectangular channel to make heated test channel. Water as a working fluid from high subcooling to near saturation temperature was injected step by step to investigate bubble behavior during void development. Experiments were performed in two different pressures condition close to 2bar and 4bar. It was observed that in high subcooling when boiling was commenced, bubble after nucleation departed its origin and slid beside heated surface. In an observation window mean release frequency of bubble fb,mean, nucleation site Ns and mean bubble volume Vb,mean in each step of experiments were measured to investigate wall vaporization rate. It was found that in proximity of PNVG vaporization rate was increased significantly in compare with condensation rate which remained in low value.

Keywords: Subcooled flow boiling, Bubble dynamics, Void fraction, Sliding bubble.

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Authors: Stoyan Nedeltchev, Markus Schubert

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By means of the ultrafast X-ray tomography facility, data were obtained at different superficial gas velocities U_G in a bubble column (0.1 m in ID) operated with an air-deionized water system at ambient conditions. Raw reconstructed images were treated by both the information entropy (IE) and the reconstruction entropy (RE) algorithms in order to identify the main transition velocities in a bubble column. The IE values exhibited two well-pronounced minima at U_G=0.025 m/s and U_G=0.085 m/s identifying the boundaries of the homogeneous, transition and heterogeneous regimes. The RE extracted from the central region of the column’s cross-section exhibited only one characteristic peak at U_G=0.03 m/s, which was attributed to the transition from the homogeneous to the heterogeneous flow regime. This result implies that the transition regime is non-existent in the core of the column.

Keywords: Bubble column, ultrafast X-ray tomography, information entropy, reconstruction entropy.

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Authors: A. Alhelfi, B. Sunden

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Cavitation in cryogenic liquids is widely present in contemporary science. In the current study, we re-examine a previously validated acoustic cavitation model which was developed for a gas bubble in liquid water. Furthermore, simulations of cryogenic fluids including the thermal effect, the effect of acoustic pressure amplitude and the frequency of sound field on the bubble dynamics are presented. A gas bubble (Helium) in liquids Nitrogen, Oxygen and Hydrogen in an acoustic field at ambient pressure and low temperature is investigated numerically. The results reveal that the oscillation of the bubble in liquid Hydrogen fluctuates more than in liquids Oxygen and Nitrogen. The oscillation of the bubble in liquids Oxygen and Nitrogen is approximately similar.

Keywords: Cryogenic liquids, cavitation, rocket engineering, ultrasound.

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Authors: Chiang-Ho Cheng, An-Shik Yang, Hong-Yih Cheng

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This paper applies the MEMS technology to design and fabricate a micro-bubble generator by a piezoelectric actuator. Coupled with a nickel nozzle plate, an annular piezoelectric ceramic was utilized as the primary structure of the generator. In operations, the piezoelectric element deforms transversely under an electric field applied across the thickness of the generator. The surface of the nozzle plate can expand or contract because of the induction of radial strain, resulting in the whole structure to bend, and successively transport oxygen micro-bubbles into the blood flow for enhancing the oxygen content in blood. In the tests, a high magnification microscope and a high speed CCD camera were employed to photograph the time evolution of meniscus shape of gaseous bubbles dispensed from the micro-bubble generator for flow visualization. This investigation thus explored the bubble formation process including the influences of inlet gas pressure along with driving voltage and resonance frequency on the formed bubble extent.

Keywords: Micro-bubble, nozzle, oxygenator, piezoelectric.

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Authors: Mário A. R. Talaia

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As it is known, buoyancy and drag forces rule bubble's rise velocity in a liquid column. These forces are strongly dependent on fluid properties, gravity as well as equivalent's diameter. This study reports a set of bubble rising velocity experiments in a liquid column using water or glycerol. Several records of terminal velocity were obtained. The results show that bubble's rise terminal velocity is strongly dependent on dynamic viscosity effect. The data set allowed to have some terminal velocities data interval of 8.0 ? 32.9 cm/s with Reynolds number interval 1.3 -7490. The bubble's movement was recorded with a video camera. The main goal is to present an original set data and results that will be discussed based on two-phase flow's theory. It will also discussed, the prediction of terminal velocity of a single bubble in liquid, as well as the range of its applicability. In conclusion, this study presents general expressions for the determination of the terminal velocity of isolated gas bubbles of a Reynolds number range, when the fluid proprieties are known.

Keywords: Bubbles, terminal velocity, two phase-flow, vertical column.

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Authors: Rahim Jafari, Tuba Okutucu-Özyurt

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The hydrodynamics and heat transfer characteristics of a vaporized elongated bubble in a rectangular microchannel have been simulated based on Cahn-Hilliard phase-field method. In the simulations, the initially nucleated bubble starts growing as it comes in contact with superheated water. The growing shape of the bubble compared well with the available experimental data in the literature.

Keywords: Microchannel, boiling, Cahn-Hilliard method, Two-phase flow, Simulation.

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Authors: Stoyan Nedeltchev, Markus Schubert

Abstract:

The gas holdup fluctuations in a bubble column (0.15 m in ID) have been recorded by means of a conductivity wire-mesh sensor in order to extract information about the main transition velocities. These parameters are very important for bubble column design, operation and scale-up. For this purpose, the classical definition of the Shannon entropy was modified and used to identify both the onset (at U_G=0.034 m/s) of the transition flow regime and the beginning (at U_G=0.089 m/s) of the churn-turbulent flow regime. The results were compared with the Kolmogorov entropy (KE) results. A slight discrepancy was found, namely the transition velocities identified by means of the KE were shifted to somewhat higher (0.045 and 0.101 m/s) superficial gas velocities U_G.

Keywords: Bubble column, gas holdup fluctuations, Modified Shannon entropy, Kolmogorov entropy.

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Authors: Sadegh Papari, Mohammad Kazemeini, Moslem Fattahi

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In the present study, a heterogeneous and homogeneous gas flow dispersion model for simulation and optimisation of a large-scale catalytic slurry reactor for the direct synthesis of dimethyl ether (DME) from syngas and CO2, using a churn-turbulent regime was developed. In the heterogeneous gas flow model the gas phase was distributed into two bubble phases: small and large, however in the homogeneous one, the gas phase was distributed into only one large bubble phase. The results indicated that the heterogeneous gas flow model was in more agreement with experimental pilot plant data than the homogeneous one.

Keywords: Modelling, Slurry bubble column, Dimethyl ether synthesis, Homogeneous gas flow, Heterogeneous gas flow

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Authors: Jin Sun Oh, Kyung Ho Lee, S ang Gug Chung, Kyehan Rhee

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Microbubbbles incorporating ultrasound have been used to increase the efficacy of targeted drug delivery, because microstreaming induced by cavitating bubbles affects the drug perfusion into the target cells and tissues. In order to clarify the physical effects of microstreaming on drug perfusion into tissues, a preliminary experimental study of perfusion enhancement by a stably oscillating microbubble was performed. Microstreaming was induced by an oscillating bubble at 15 kHz, and perfusion of dye into an agar phantom was optically measured by histology on agar phantom. Surface color intensity and the penetration length of dye in the agar phantom were increased more than 70% and 30%, respectively, due to the microstreaming induced by an oscillating bubble. The mass of dye perfused into a tissue phantom for 30 s was increased about 80% in the phantom with an oscillating bubble. This preliminary experiment shows the physical effects of steady streaming by an oscillating bubble can enhance the drug perfusion into the tissues while minimizing the biological effects.

Keywords: Bubble, Mass Transfer, Microstreaming, Drug Delivery, Acoustic Wave.

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Authors: Ghazi S. Kahmmash

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New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.

Keywords: Generating functions, Recurrences relation and Generalization of the new class matrix polynomial set.

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Authors: N. Masoudnia, M. Fatahi

Abstract:

An experimental study of saturated pool boiling on a single artificial nucleation site without and with the application of an electric field on the boiling surface has been conducted. N-pentane is boiling on a copper surface and is recorded with a high speed camera providing high quality pictures and movies. The accuracy of the visualization allowed establishing an experimental bubble growth law from a large number of experiments. This law shows that the evaporation rate is decreasing during the bubble growth, and underlines the importance of liquid motion induced by the preceding bubble. Bubble rise is therefore studied: once detached, bubbles accelerate vertically until reaching a maximum velocity in good agreement with a correlation from literature. The bubbles then turn to another direction. The effect of applying an electric field on the boiling surface in finally studied. In addition to changes of the bubble shape, changes are also shown in the liquid plume and the convective structures above the surface. Lower maximum rising velocities were measured in the presence of electric fields, especially with a negative polarity.

Keywords: Single bubbles, electric field, boiling, effect.

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Authors: Yongseok Kwon, Woowon Jeong, Eunjin Cho, Sangkug Chung, Kyehan Rhee

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Steady streaming flow fields induced by a 500 mm bubble oscillating at 12 kHz were measured using microscopic particle image velocimetry (PIV). The accuracy of velocity measurement using a micro PIV system was checked by comparing the measured velocity fields with the theoretical velocity profiles in fully developed laminar flow. The steady streaming flow velocities were measured in the sagittal plane of the bubble attached on the wall. Measured velocity fields showed upward jet flow with two symmetric counter-rotating vortices, and the maximum streaming velocity was about 12 mm/s, which was within the velocity ranges measured by other researchers. The measured streamlines were compared with the analytical solution, and they also showed a reasonable agreement.

Keywords: Oscillating bubble, Particle-Image-Velocimetry microstreaming.

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Authors: N. K. Singh, S. Sarkar

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Direct numerical simulation (DNS) is used to study the evolution of a boundary layer that was laminar initially followed by separation and then reattachment owing to generation of turbulence. This creates a closed region of recirculation, known as the laminar-separation bubble. The present simulation emulates the flow environment encountered in a modern LP turbine blade, where a laminar separation bubble may occur on the suction surface. The unsteady, incompressible three-dimensional (3-D) Navier-Stokes (NS) equations have been solved over a flat plate in the Cartesian coordinates. The adverse pressure gradient, which causes the flow to separate, is created by a boundary condition. The separated shear layer undergoes transition through appearance of ╬ø vortices, stretching of these create longitudinal streaks. Breakdown of the streaks into small and irregular structures makes the flow turbulent downstream.

Keywords: Adverse pressure gradient, direct numerical simulation, laminar separation bubble.

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Authors: Sidharth Talan, Devendra Kumar Yadav, Yuvraj Singh Rajput, Subhajit Bhattacharjee

Abstract:

Mining industry is known for its appetite to spend sizeable capital on mine equipment. However, in the current scenario, the mining industry is challenged by daunting factors of non-uniform geological conditions, uneven ore grade, uncontrollable and volatile mineral commodity prices and the ever increasing quest to optimize the capital and operational costs. Thus, the role of equipment reliability and maintenance planning inherits a significant role in augmenting the equipment availability for the operation and in turn boosting the mine productivity. This paper presents the Risk Based Maintenance (RBM) planning conducted on mine loading equipment namely Load Haul Dumpers (LHDs) at Vedanta Resources Ltd subsidiary Hindustan Zinc Limited operated Sindesar Khurd Mines, an underground zinc and lead mine situated in Dariba, Rajasthan, India. The mining equipment at the location is maintained by the Original Equipment Manufacturers (OEMs) namely Sandvik and Atlas Copco, who carry out the maintenance and inspection operations for the equipment. Based on the downtime data extracted for the equipment fleet over the period of 6 months spanning from 1^st January 2017 until 30^th June 2017, it was revealed that significant contribution of three downtime issues related to namely Engine, Hydraulics, and Transmission to be common among all the loading equipment fleet and substantiated by Pareto Analysis. Further scrutiny through Bubble Matrix Analysis of the given factors revealed the major influence of selective factors namely Overheating, No Load Taken (NTL) issues, Gear Changing issues and Hose Puncture and leakage issues. Utilizing the equipment wise analysis of all the downtime factors obtained, spares consumed, and the alarm logs extracted from the machines, technical design changes in the equipment and pre shift critical alarms checklist were proposed for the equipment maintenance. The given analysis is beneficial to allow OEMs or mine management to focus on the critical issues hampering the reliability of mine equipment and design necessary maintenance strategies to mitigate them.

Keywords: Bubble matrix analysis, LHDs, OEMs, pareto chart analysis, spares consumption matrix, critical alarms checklist.

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Authors: M. R. Nematollahi

Abstract:

Vibration characteristics of subcooled flow boiling on thin and long structures such as a heating rod were recently investigated by the author. The results show that the intensity of the subcooled boiling-induced vibration (SBIV) was influenced strongly by the conditions of the subcooling temperature, linear power density and flow velocity. Implosive bubble formation and collapse are the main nature of subcooled boiling, and their behaviors are the only sources to originate from SBIV. Therefore, in order to explain the phenomenon of SBIV, it is essential to obtain reliable information about bubble behavior in subcooled boiling conditions. This was investigated at different conditions of coolant subcooling temperatures of 25 to 75°C, coolant flow velocities of 0.16 to 0.53m/s, and linear power densities of 100 to 600 W/cm. High speed photography at 13,500 frames per second was performed at these conditions. The results show that even at the highest subcooling condition, the absolute majority of bubbles collapse very close to the surface after detaching from the heating surface. Based on these observations, a simple model of surface tension and momentum change is introduced to offer a rough quantitative estimate of the force exerted on the heating surface during the bubble ebullition. The formation of a typical bubble in subcooled boiling is predicted to exert an excitation force in the order of 10-4 N.

Keywords: Subcooled boiling, vibration mechanism, bubble behavior.

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Authors: S. Levitsky

Abstract:

Acoustic properties of polymeric liquids are high sensitive to free gas traces in the form of fine bubbles. Their presence is typical for such liquids because of chemical reactions, small wettability of solid boundaries, trapping of air in technological operations, etc. Liquid temperature influences essentially its rheological properties, which may have an impact on the bubble pulsations and sound propagation in the system. The target of the paper is modeling of the liquid temperature effect on single bubble dynamics and sound dispersion and attenuation in polymeric solution with spherical gas bubbles. The basic sources of attenuation (heat exchange between gas in microbubbles and surrounding liquid, rheological and acoustic losses) are taken into account. It is supposed that in the studied temperature range the interface mass transfer has a minor effect on bubble dynamics. The results of the study indicate that temperature raise yields enhancement of bubble pulsations and increase in sound attenuation in the near-resonance range and may have a strong impact on sound dispersion in the liquid-bubble mixture at frequencies close to the resonance frequency of bubbles.

Keywords: Sound propagation, gas bubbles, temperature effect, polymeric liquid.

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Authors: Jemai Rabeb, Benhmidene Ali, Hidouri Khaoula, Chaouachi Bechir

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The diffusion-absorption refrigeration cycle consists of a generator bubble pump, an absorber, an evaporator and a condenser, and usually operates with ammonia/water/ hydrogen or helium as the working fluid. The aim of this paper is to study the stability problem a bubble pump. In fact instability can caused a reduction of bubble pump efficiency. To achieve this goal, we have simulated the behaviour of two-phase flow in a bubble pump by using a drift flow model. Equations of a drift flow model are formulated in the transitional regime, non-adiabatic condition and thermodynamic equilibrium between the liquid and vapour phases. Equations resolution allowed to define void fraction, and liquid and vapour velocities, as well as pressure and mixing enthalpy. Ammonia-water mixing is used as working fluid, where ammonia mass fraction in the inlet is 0.6. Present simulation is conducted out for a heating flux of 2 kW/m² to 5 kW/m² and bubble pump tube length of 1 m and 2.5 mm of inner diameter. Simulation results reveal oscillations of vapour and liquid velocities along time. Oscillations decrease with time and with heat flux. For sufficient time the steady state is established, it is characterised by constant liquid velocity and void fraction values. However, vapour velocity does not have the same behaviour, it increases for steady state too. On the other hand, pressure drop oscillations are studied.

Keywords: Bubble pump, drift flow model, instability, simulation.

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Authors: Gu-Fang Mou, Ting-Zhu Huang

Abstract:

An n×n matrix is called an N1 0 -matrix if all principal minors are non-positive and each entry is non-positive. In this paper, we study the partial non-combinatorially symmetric N1 0 -matrix completion problems if the graph of its specified entries is a transitive tournament or a double cycle. In general, these digraphs do not have N1 0 -completion. Therefore, we have given sufficient conditions that guarantee the existence of the N1 0 -completion for these digraphs.

Keywords: Matrix completion, matrix completion, N10 -matrix, non-combinatorially symmetric, cycle, digraph.

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Authors: Mahdi Taheri, Mehrana Niroumand

Abstract:

In this paper a new definition of adjacency matrix in the simple graphs is presented that is called fuzzy adjacency matrix, so that elements of it are in the form of 0 and n N n 1 , ∈ that are in the interval [0, 1], and then some charactristics of this matrix are presented with the related examples . This form matrix has complete of information of a graph.

Keywords: Graph, adjacency matrix, fuzzy numbers

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Authors: Shyam Kumar, Nannuri Srinivasulu, Ashok Khanna

Abstract:

Bubble columns have a variety of applications in absorption, bio-reactions, catalytic slurry reactions, and coal liquefaction; because they are simple to operate, provide good heat and mass transfer, having less operational cost. The use of Computational Fluid Dynamics (CFD) for bubble column becomes important, since it can describe the fluid hydrodynamics on both local and global scale. Euler- Euler two-phase fluid model has been used to simulate two-phase (air and water) transient up-flow in bubble column (15cm diameter) using FLUENT6.3. These simulations and experiments were operated over a range of superficial gas velocities in the bubbly flow and churn turbulent regime (1 to16 cm/s) at ambient conditions. Liquid velocity was varied from 0 to 16cm/s. The turbulence in the liquid phase is described using the standard k-ε model. The interactions between the two phases are described through drag coefficient formulations (Schiller Neumann). The objectives are to validate CFD simulations with experimental data, and to obtain grid-independent numerical solutions. Quantitatively good agreements are obtained between experimental data for hold-up and simulation values. Axial liquid velocity profiles and gas holdup profiles were also obtained for the simulation.

Keywords: Bubble column, Computational fluid dynamics, Gas holdup profile, k-ε model.

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Authors: Zhen Chen, Haitao Zhang, Weiyong Ying, Dingye Fang

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Based on a global kinetics of direct dimethyl ether (DME) synthesis process from syngas, a steady-state one-dimensional mathematical model for the bubble column slurry reactor (BCSR) has been established. It was built on the assumption of plug flow of gas phase, sedimentation-dispersion model of catalyst grains and isothermal chamber regardless of reaction heats and rates for the design of an industrial scale bubble column slurry reactor. The simulation results indicate that higher pressure and lower temperature were favorable to the increase of CO conversion, DME selectivity, products yield and the height of slurry bed, which has a coincidence with the characteristic of DME synthesis reaction system, and that the height of slurry bed is lessen with the increasing of operation temperature in the range of 220-260℃. CO conversion, the optimal operation conditions in BCSR were proposed. 

Keywords: Alcohol/ether fuel, bubble column slurry reactor, global kinetics, mathematical model.

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