Numerical study on characteristics of turbulent two-phase gas-particle flow using multi-fluid model

The purpose of this research is to study numerically the turbulent gas-particle two-phase flow characteristics using the Eulerian-Eulerian method. A computer code is developed for the numerical study by using the k-ɛ-k _p two-phase turbulent model. The developed code is applied for particle-laden flows in which the particle volume fraction is between 10⁻⁵ and 10⁻² for the Stokes numbers smaller than unity. The gas and particle velocities and the particle volume fraction obtained by using this code are in good agreement with those obtained by a commercial code for the gas-particle jet flows within a rectangular enclosure. The gas-particle jet injected into a vertical rectangular 3D enclosure is numerically modeled to study the effect of the Stokes number, the particle volume fraction and the particle Reynolds numbers. The numerical results show that the Stokes number and the particle volume fraction are important parameters in turbulent gas-particle flows. A small Stokes number (St ≤ 0.07) implies that the particles are nearly at the velocity equilibrium with the gas phase, while a large Stokes number (St ≥ 0.07) implies that the slip velocity between the gas and particle phase increases and the particle velocity is less affected by the gas phase. A large particle volume fraction (α _p ≥ 0.0001) implies that the effect of the particles on the gas phase momentum increases, while a small particle volume fraction (α _p ≤ 0.0001) implies that the particles would have no or small effect on the gas flow field. For fixed Stokes number and particle volume fraction, an increase of the particle Reynolds number results in a decrease of the slip velocity between the gas and particle velocities.     

含气率对往复式油气混输泵排出性能影响

为了研究含气率对往复式油气混输泵排出性能的影响及转速、含气率、流量的相互关系,基于标准k-ε湍流模型和混合多相流模型,采用计算流体力学软件中的动网格技术和用户自定义函数,在介质含气率不同时对混输泵的排出过程进行三维动态仿真模拟。结果表明:介质增压速度、最大流量、平均流量与含气率成反比。根据转速、含气率、流量关系曲线调节转速,使泵的流量与抽油机流量相匹配,为往复式油气混输泵性能参数的选择及现场应用提供数据参考。     

Research on signal amplitude of the Kármán vortex street in gas–liquid two-phase flow with high void fraction

Based on Biot–Savart law and single-phase flow Kármán vortex characteristics, flow field has been analyzed when gas–liquid flow past a fixed bluff body with high void fraction. Vortex signal characteristics have been studied for stratified two-phase flow on atmospheric conditions in a horizontal pipe. To discuss the relation between void fraction and vortex signal amplitude spectrum, this paper sets up the vortex-induced pressure field model for gas–liquid two-phase flow and gives the relationship between void fraction and relative amplitude spectrum of two-phase flow to single-phase flow. An algorithm is proposed for predicting the two-phase flow parameters. Experiments were performed using air–water as working fluid along with a test tube diameter of 50 mm, at gas volume flow rate of 20–68 m³/h, and void fraction of 0.9–1. The results indicate that calculations by the vortex-induced pressure field model on the amplitude spectrum of vortex signal are in good agreement with the experimental data, and relative errors of the algorithm predictions on gas volume flow rate and liquid volume flow rate are 0.08 and 0.56, respectively.     

Rotordynamic analysis for stepped-labyrinth gas seals using Moody’s friction-factor model

The governing equations are derived for the analysis of a stepped labyrinth gas seal generally used in high performance compressors, gas turbines, and steam turbines. The bulk-flow is assumed for a single cavity control volume set up in a stepped labyrinth cavity and the flow is assumed to be completely turbulent in the circumferential direction. The Moody’s wall-friction-factor model is used for the calculation of wall shear stresses in the single cavity control volume. For the reaction force developed by the stepped labyrinth gas seal, linearized zeroth-order and first-order perturbation equations are developed for small motion about a centered position. Integration of the resultant first-order pressure distribution along and around the seal defines the rotordynamic coefficients of the stepped labyrinth gas seal. The resulting leakage and rotordynamic characteristics of the stepped labyrinth gas seal are presented and compared with Scharrer’s theoretical analysis using Blasius’ wall-friction-factor model. The present analysis shows a good qualitative agreement of leakage characteristics with Scharrer’s analysis, but underpredicts by about 20 %. For the rotordynamic coefficients, the present analysis generally yields smaller predictied values compared with Scharrer’s analysis.     

Study of the factors influencing the over-reading characteristics of the precession Venturi

In the energy industry, such as the gas field, precise measurement of wet gas is becoming increasingly crucial. Many studies have focused on the over-reading (OR) of throttle flowmeter in wet gas measurement. By using the dimensional analysis method, we proposed a precession Venturi and established a new OR correlation based on the gas Froude number, liquid-gas density ratio, and the Lockhart–Martinelli parameter. Experimental tests of air-water flow were conducted, and the relationships between differential pressure and OR with liquid volume fraction were investigated at various pressures and superficial gas velocities. The experimental results show that the uncertainty of gas flow rate measurement is in the range of 0.35%–0.56%, and 90.8% of the points are in the range of 0.35%–0.45%, with a relative error band of ±2.94% calculated by the OR correlation at a confidence probability of 95.5%.     

Impeller inlet geometry effect on performance improvement for centrifugal pumps

This research treats the effect of impeller inlet geometry on performance improvement for a boiler feed pump, who is a centrifugal pump having specific speed of 183 m·m³min⁻¹·min⁻¹ and close type impeller with exit diameter of 450 mm. The hydraulic performance and cavitation performance of the pump have been tested experimentally. In order to improve the pump, five impellers have been considered by extending the blade leading edge or applying much larger blade angle at impeller inlet compared with the original impeller. The 3-D turbulent flow inside those pumps has been analyzed basing on RNG k-ɛ turbulence model and VOF cavitation model. It is noted that the numerical results are fairly good compared with the experiments. Based on the experimental test and numerical simulation, the following conclusions can be drawn: (1) Impeller inlet geometry has important influence on performance improvement in the case of centrifugal pump. Favorite effects on performance improvement have been achieved by both extending the blade leading edge and applying much larger blade angle at impeller inlet; (2) It is suspected that the extended leading edge have favorite effect for improving hydraulic performance, and the much larger blade angle at impeller inlet have favorite effect for improving cavitation performance for the test pump; (3) Uniform flow upstream of impeller inlet is helpful for improving cavitation performance of the pump. This paper was presented at the 9^th Asian International Conference on Fluid Machinery (AICFM9), Jeju, Korea, October 16–19, 2007.     

Experimental study of bubbly swirling flow in a vertical tube using ultrasonic velocity profiler (UVP) and wire mesh sensor (WMS)

Two-phase air-water bubbly swirling flow through a pipe is a complex turbulent flow and its prediction is still challenging. The present paper describes the experimental investigation of the air-water bubbly swirling flow in vertical co-current flow. Swirling flow is induced by a twisted tape in a 20 mm inner diameter pipe. The flow is investigated using Ultrasonic velocity profiler (UVP), which allows the measurement of liquid and gas velocities simultaneously. Furthermore, simultaneous measurement of void fraction is performed using Wire mesh sensor (WMS). The experimental results reveal that swirling flow has significant impact on bubbles’ distribution. In low liquid flow rate, the average bubble velocity is fairly uniform along the radial position and void fraction increases in the near wall region. However, increasing liquid flow rate at constant gas flow rate leads to increase in void fraction in the core region, this is mainly due to drift velocity which is affected by centrifugal force. Experimental findings and parametric trends based on the effects of swirling flow are summarized and discussed.     

Effects of the number of inducer blades on the anti-cavitation characteristics and external performance of a centrifugal pump

Installing an inducer upstream of the main impeller is an effective approach for improving the anti-cavitation performance of a highspeed centrifugal pump. For a high-speed centrifugal pump with an inducer, the number of inducer blades can affect its internal flow and external performance. We studied the manner in which the number of inducer blades can affect the anti-cavitation characteristics and external performance of a centrifugal pump. We first use the Rayleigh-Plesset equation and the mixture model to simulate the vaporliquid flow in a centrifugal pump with an inducer, and then predict its external performance. Finally, we tested the external performance of a centrifugal pump with 2-, 3-and 4-bladed inducers, respectively. The results show that the simulations of external performance in a centrifugal pump are in accordance with our experiments. Based on this, we obtained vapor volume fraction distributions for the inducer, the impeller, and in the corresponding whole flow parts. We discovered that the vapor volume fraction of a centrifugal pump with a 3-bladed inducer is less than that of a centrifugal pump with 2-or 4-bladed inducers, which means that a centrifugal pump with a 3-bladed inducer has a better external and anti-cavitation performance.

     

An experimental study on characteristics of two-phase flows in vertical pipe

The characteristics of two-phase flow in a vertical pipe are investigated to provide information for understanding the excitation mechanisms of flow-induced vibration. An analytical model for two-phase flow in a pipe was developed by Sim et al. (2005), based on a power law for the distributions of flow parameters across the pipe diameter, such as gas velocity, liquid velocity and void fraction. An experimental study was undertaken to verify the model. The unsteady momentum flux impinging on a ‘turning tee’ (or a ‘circular plate’) has been measured at the exit of the pipe, using a force sensor. From the measured data, especially for slug flow, the predominant frequency and the RMS value of the unsteady momentum flux have been evaluated. It is found that the analytical method, given by Sim et al. for slug flow, can be used to predict the momentum flux.     

Test investigation on hydraulic losses in the discharge passage of an axial-flow pump

In a discharge passage with a guide blade discharge circulation and secondary flow because of bend pipe, the flow in a 1-channel discharge passage of an axial flow pump is a complicated spiral flow. For a 2-channel passage, the discharge in the left channel is bigger than that in the right, and the passage hydraulic losses are abnormal. In this study, the section current energy of the passage is accurately measured and determined with a 5-hole probe. The hydraulic loss characteristics are determined and analyzed. The methods deducing the hydraulic losses are investigated. The results indicate that the passage hydraulic losses are not proportional to the flow discharge. Compared with a circular pipe, the hydraulic losses of a divergent discharge passage are smaller and the pump assembly efficiency is 10%–30% higher. As for the 1-channel passage, the axial-flow pump outlet circulation is usually too big; the passage hydraulic losses are also big, but a small circulation can slightly reduce hydraulic losses. As for the 2-channel passage, discharges in the two channels are not equal and the hydraulic losses increase. The outlet guide blade with a small discharge circulation or without circulation could reduce discharge passage hydraulic losses and increase pump assembly efficiency by 6%–11%. __________ Translated from Chinese Journal of Mechanical Engineering, 2006, 42(5): 39–44 [译自: 机械工程学报]     

Comparative study of tip leakage vortex trajectory and cavitation in an axial flow pump with various tip clearances

In order to analyze the effect of blade tip-gap size on the tip leakage vortex (TLV) dynamics and TLV-induced cavitation, a scaled axial flow pump model was created and numerically studied by the combination of an improved SST k-w turbulence model and a homogeneous cavitation model. The trajectories of TLV core was obtained by using the swirling strength method at different tip-gap sizes vary significantly. The scale of TLV increases as the tip-gap size increases, and the starting point of TLV is sliding further downstream along the blade chord. The angle between the blade suction surface and the TLV also presented an increasing trend with the tip-gap size. The statistics of the velocity normal to the tip chord, as well as the turbulent kinetic energy (KTE) distributions were employed to illustrate a more disordered flow field, which was generated in the tip clearance in a larger amount of leaking flow due to the increased tip-gap size. The in-plain static pressure and vapor volume fraction distributions at different blade chord sections, coupled with three-dimensional cavitation patterns among three tip gaps, are further analyzed to verify the wandering motion of TLV, which shows good agreement with the visualization experiment. Considering the adverse effect of the TLV cavitation, a small tip gap is recommended for improving the axial flow pump performance.

     

Approximate coordinate transformations for simulation of turbulent flows with wall deformation

In the present paper, approximate coordinate transformations for simulation of turbulent flows with wall deformation, significantly reducing computational cost with little degradation in numerical accuracy, are presented. The Navier-Stokes equations are coordinate-transformed with an approximation of Taylor-series truncation. The performance is evaluated by performing numerical simulations of a channel flow atRe _τ =140 with active wall motions of |η _m ⁺|≤5. The approximate transformations provide flow structures as well as turbulence statistics in good agreement with those from a complete transformation [Phys. Fluids 12, 3301 (2000)] and allow 25–30% savings in the CPU time as compared to the complete one.     

Influence of nozzle exit tip thickness on the performance and flow field of jet pump

The influence of exit tip thickness of nozzle δ _e on the flow field and performance of a jet pump was studied numerically in this paper. It is found that δ _e has influence on the distribution of turbulence kinetic energy k. If δ _e is ignored, k takes the highest value but dissipates rapidly than that of nozzle with a certain tip thickness. δ _e also affect apparently the development of tip vortex, which will occur near the exit tip of nozzle. The bigger the δ _e is, the larger the vortex is. The tip vortex develops with the increase of flow rate ratio q. When q=1 and δ _e =0.6∼0.8mm, a small vortex will be found downstream the tip vortex. And a concomitant vortex happens down the tip vortex in the case of q=1 and δ _e =0.8mm. As q increases to 2, the downstream small vortex disappears and the concomitant vortex becomes bigger. It is also found that the tip vortex might interact with the possible backflow that formed in the throat tube and parts of suction chamber. The center of backflow was affect evidently by δ _e . With the increase of δ _e , the center of backflow under the same q will go downstream. When δ _e =0.4mm, the center of backflow goes farthest. Then, as the further increase of δ _e , the center of backflow will go back some distance. Although, δ _e has relatively great influence on the flow field within the jet pump, it exerts only a little impact on the performance of jet pump. When δ _e =0.2∼0.6mm, the jet pump possess better performance. In most case, it is reasonable to ignore the nozzle exit tip thickness in performance prediction for the purpose of simplicity. This paper was presented at the 9^th Asian International Conference on Fluid Machinery (AICFM9), Jeju, Korea, October 16–19, 2007.     

Calculating frictional force with considering material microstructure and potential on contact surfaces

A method based on the energy dissipation mechanism of an Independent Oscillator model is used to calculate the frictional force and the friction coefficient of interfacial friction. The friction work is calculated with considering the potential change of contact surfaces during sliding. The potential change can be gained by a universal adhesive energy function. The relationships between frictional force and parameters of a tribo-system, such as surface energy and microstructure of interfacial material, are set up. The calculation results of the known experimental data denote that the frictional force is nearly proportional to the surface energy of the material, nearly inversely proportional to the scaling length, and independent of the lattice constant. The results agree with that of adhesion friction equations. They also agree with the experimental results performed with an atomic-force microscope under the ultra high vacuum condition. __________ Translated from Tribology, 2006, 26(2): 159–162 [译自: 摩擦学学报]     

Combined convection and radiation in a tube with circumferential fins and circular disks

Combined convection and radiation heat transfer in a circular tube with circumferential fins and circular disks is investigated for various operating conditions. Using a finite volume technique for steady laminar flow, the governing equations are solved in order to study the flow and temperature fields. TheP- 1 approximation and the weighted sum of gray gases model (WSGGM) are used for solving the radiation transport equation. The results show that the total Nusselt number of combined convection and radiation is higher than that of pure convection. If the temperatures of the combustion gas and the wall in a tube are high, radiation becomes dominant. Therefore, it is necessary to evaluate the effect of radiation on the total heat transfer. Key Words: Convection, Radiation, Nongray Radiation,P- 1 Approximation, Weighted Sum of Gray Gases Model     

Numerical analysis on nanoparticles-laden gas film thrust bearing

Nanoparticles can be taken as additives and added into various fluids to improve their lubricating performances. At present, researches in this area are mainly concentrated on the improvement effects of nanoparticles on the lubricating performances of liquid such as oil and water. Nanoparticles will also affect gas lubrication, but few related studies have been reported. Nanoparticles-laden gas film (NLGF) is formed when adding nanoparticles into gas bearing. Then, the lubricating performances of gas bearing including pressure distribution and load-carrying capacity will change. The variations of pressure distribution and load-carrying capacity in nanoparticles-laden gas film thrust bearing are investigated by numerical method. Taking account of the compressibility of gas and the interactions between gas and nanoparticles, a computational fluid dynamics model based on Navier-Stokes equations is applied to simulate the NLGF flow. The effects of inlet nanoparticles volume fraction and orifice radius on film pressure distribution and load-carrying capacity of the NLGF are calculated. The numerical calculation results show that both of the film land pressure and the maximum film pressure both increase when the nanoparticles are added into gas bearing, and the film pressures increase with the rising of the inlet nanoparticles volume fraction. The nanoparticles have an enhancement effect on load-carrying capacity of the studied bearing, and the enhancement effect becomes greater as the film thickness decrease. Therefore, nanoparticles can effectively improve the lubricating performance of gas bearing. The proposed research provides a theoretical basis for the design of new-type nanoparticles-laden gas film bearings.     

Novel drive mechanism for in-tube micro robots

The volume of an in-tube micro robot is small and its interior space is very limited. However, conventional transmission methods are unfit to drive in-tube micro robots. A novel micro drive mechanism called the micro-elastic-meshing-wheel is presented in this paper. It can be used for transmitting power and locomotion between two shafts, which are upright and cross in a micro space. The mechanical model of the novel drive mechanism is built, and the maximal transmission force is deduced. Then, sufficient experiments are carried out to test maximal transmission force produced by the novel drive mechanism. The calculation and experiment results show that the novel drive mechanism can transmit sufficient power to in-tube micro robots. __________ Translated from Journal of South China University of Technology (Natural Science Edition), 2006, 34(7): 45–49 [译自: 华南理工大学学报 (自然科学版)]     

变转速工况对直线共轭内啮合齿轮泵容积效率的影响

随着液压技术向高压化、轻量化、节能化发展,直线共轭内啮合齿轮泵因具有结构紧凑、流量脉动小、使用寿命长、噪声小等优点,其应用领域逐步扩大。随着内啮合齿轮泵使用转速的变化,其容积效率也出现变化,为了获得内啮合齿轮泵转速对其容积效率的影响规律,采用液压油、纯水两种介质,通过数值计算的方法,研究内啮合齿轮泵转子域空化特性、对比分析出口体积流率。结果表明：随着转速上升,内外齿啮合最小容积腔及吸油口处气相体积分数增加明显,易引起空化、气蚀,从而产生噪声、振动等问题;当转速过高时,介质中的气体析出明显,易出现吸空现象,导致齿轮泵容积效率降低,纯水介质比46#液压油介质下的齿轮泵容积效率更低。因此,要改善高转速工况下的齿轮泵容积效率,需优化内啮合齿轮泵进油口流道,增加入口压力,提升内啮合齿轮泵高转速工况下的综合性能。     

Fuzzy force control of constrained robot manipulators based on impedance model in an unknown environment

To precisely implement the force control of robot manipulators in an unknown environment, a control strategy based on fuzzy prediction of the reference trajectory in the impedance model is developed. The force tracking experiments are executed in an open-architecture control system with different tracking velocities, different desired forces, different contact stiffnesses and different surface figurations. The corresponding force control results are compared and analyzed. The influences of unknown parameters of the environment on the contact force are analyzed based on experimental data, and the tunings of predictive scale factors are illustrated. The experimental results show that the desired trajectory in the impedance model is predicted exactly and rapidly in the cases that the contact surface is unknown, the contact stiffness changes, and the fuzzy force control algorithm has high adaptability to the unknown environment. Translated from Journal of Northeastern University (Natural Science), 2005, 26(8): 766–769 [译自: 东北大学学报 (自然科学版)]     

A CFD study of low pressure wet gas metering using slotted orifice meters

Wet gas metering is becoming an increasingly important problem to many industries, in particular the oil and gas industry. Extensive studies have been done in the past on Venturi and standard orifice differential pressure (DP) flow meters to tackle wet gas flow problems. However in recent years, the slotted orifice flow meter has been developed in the attempt to improve the performance of the standard orifice meter. The novel flow meter is shown to be insensitive to the upstream flow profile with lower head loss and faster pressure recovery. This paper describes the numerical studies to establish the effect of different geometrical perforations on the performance of the slotted orifice. Three sets of slotted orifices with varying aspect ratios (1.5≤l/w≤3.0), of rectangular perforations and one slotted orifice with a circular perforation and a β ratio of 0.40 are simulated in a 1.6 m horizontal pipe using the k-ε turbulence model over a range of parameters, i.e. gas volume fraction (GVF) and gas mass flow rate. The commercial CFD code, FLUENT 6.3 was used to model the wet gas flow. Simulation results revealed that the shape of the perforation has no effect on the differential pressure, However, a marginally better pressure recovery was observed with rectangular perforations of l/w=3.0. The relatively higher over-reading values obtained in this work are consistent with the results of Geng et al. (2006) [1] that for a slotted orifice, a low β ratio is more sensitive to the liquid presence in the stream and hence is preferable for wet gas metering. Mass flow prediction by wet gas correlations showed that the homogeneous model, Steven’s and De Leeuw’s correlations had the best performance, with a calculated mean error of 4%-5%.