Analysis of choked two-phase flows of gas and particle in a C-D nozzle

Particle–gas two-phase flows show significantly different behaviors compared to single gas flow through a convergent–divergent nozzle. Non-equilibrium effects, thermal and velocity lag results to the inefficiency of nozzle performance. In the present studies, theoretical analysis and numerical simulations were carried out to investigate particle–gas flows in a C-D nozzle. Homogeneous equilibrium model that no lag in velocity and temperature occurs between particles and gas phase was used to derive mass flow rate and sound speed of multiphase flows. Two-phase flows are regarded as isentropic flows that isentropic relations can be used for homogeneous equilibrium model. Discrete phase model(DPM) where interaction with continuous phase and discrete random walk model were considered was used to calculate particle–gas flows. Particle mass loadings were varied to investigate their effects on choking phenomena of particle–gas flows. Mass flow rate and sound speed of mixture flows were theoretically calculated by homogeneous equilibrium model and compared with numerical results. Shock wave structure and particle number density were also obtained to be different at different particle mass loading and operating pressure conditions.     

Characterization of the gas pulse frequency,amplitude and velocity in non-steady dense phase pneumatic conveying of powders

Current modelling techniques for the prediction of conveying line pressure drop in low velocity dense phase pneumatic conveying are largely based on steady state analyses. Work in this area has been on-going for many years with only marginal improvements in the accuracy of prediction being achieved. Experimental and theoretical investigations undertaken by the authors suggest that the flow mechanisms involved in dense phase conveying are dominated by transient effects rather than those of steady state and are possibly the principal reasons for the limited improvement in accuracy. This paper reports on investigations on the pressure fluctuation behaviour in dense phase pneumatic conveying of powders. The pressure behaviour of the gas flow in the top section of the pipeline was found to exhibit pulsatile oscillations. In particular, the pulse velocity showed variation in magnitude while the frequency of the oscillations rarely exceeded 5 Hz. A wavelet analysis using the Daubechie 4 wavelet found that the amplitude of the oscillations increased along the pipeline. Furthermore, there was significant variation in gas pulse amplitude for different types of particulate material.     

Experimental study of the blockage boundary for dense-phase pneumatic conveying of powders through a horizontal slit

The estimation of the blockage boundary for pneumatic conveying through a slit is of significant importance.In this paper,we investigate the characteristics for blockage of powder(48 μm average diameter)through a horizontal slit(1.6 m × 0.05 m × 0.002 m).The results show that the required critical solid mass flow rate increases as the superficial air velocity increases superficial air velocity.The solid loading ratio and superficial air velocity displayed a decreasing power law relationship.This finding agrees with existing theory and experimental results.However,a minimum inlet solid loading ratio exists.When the air velocity is greater than the corresponding air velocity of the minimum solid loading ratio,the solid loading ratio exhibits an increasing trend in power law.We also found that when the inlet conveying pressure increased,the critical solid mass flow rate required for blockage,the inlet solid loading ratio,and the minimum inlet solid loading ratio increased.     

Determination of slug permeability factor for pressure drop prediction of slug flow pneumatic conveying

Current models for pressure drop prediction of slug flow pneumatic conveying in a horizontal pipeline system assume some type of steady state conditions for prediction, which limits their capability for increased predictive accuracy relative to experimental data. This is partly because of the nature of slug flow pneumatic conveying system, which, as a dynamic system, never becomes stable. By utilising conservation of mass （airflow）, a dynamic pressure analysis model is proposed on the basis of the derivative of the upstream pressure behaviour. The rate of air permeation through slug, one of the important factors in the conservation model, is expressed as a function of a slug permeability factor. Other factors such as slug velocity, slug length and the fraction of stationary layer were also considered. Several test materials were conveyed in single-slug tests to verify the proposed pressure drop model, showing good agreement between the model and experimental results.     

Energy loss at bends in the pneumatic conveying of fly ash

An accurate estimation of the total pressure drop of a pipeline is important to the reliable design of a pneumatic conveying system.The present paper presents results from an investigation into the modelling of the pressure drop at a bend in the pneumatic conveying of fly ash.Seven existing bend models were used(in conjunction with solids friction models for horizontal and vertical straight pipes,and initial acceleration losses) to predict the total pipeline pressure drop in conveying fly ash(median particle diameter:30 μm;particle density:2300 kg/m~3;loose-poured bulk density:700 kg/m~3) in three test rigs(pipelines with dimensions of 69 mm inner diameter(I.D.) × 168 m length:105 mm I.D.× 168 m length;69 mm I.D.× 554 m length).A comparison of the pneumatic conveying characteristics(PCC) predicted using the seven bend models and experimental results shows that the predicted total pipeline PCC and trends depend on the choice of bend model.While some models predict trends that agree with the experimental results,other models predicted greater bend pressure drops for the dense phase of fly ash than for the dilute phase.Models of Pan,R.(1992).Improving scale-up procedures for the design of pneumatic conveying systems.Doctoral dissertation,University of Wollongong,Australia.Pan,R., Wypych,P.W.(1998).Dilute and dense phase pneumatic conveying of fly ash.In Proceedings of the sixth International Conference on Bulk Materials Storage and Transportation(pp.183-189),Wollongong,NSW,Australia and Chambers,A.J., Marcus,R.D.(1986).Pneumatic conveying calculations.In Proceedings of the second International Conference on Bulk Materials Storage and Transportation(pp.49-52).Wollongong,Australia reliably predicted the bend losses for systems conveying fly ash over a large range of air flows.     

Predicting the mode of flow in pneumatic conveying systems-- A review

An initial prediction of the particulate mode of flow in pneumatic conveying systems is beneficial as this knowledge can provide clearer direction to the pneumatic conveying design process. There are three general categories of modes of flow, two dense flows： fluidised dense phase and plug flow, and dilute phase oniy. Detailed in this paper is a review of the commonly used and available techniques for predicting mode of flow. Two types of predictive charts were defined： basic particle parameter based （e.g. particle size and density） and air-particle parameter based （e.g. permeability and de-aeration）. The basic particle techniques were found to have strong and weak areas of predictive ability, on the basis of a comparison with data from materials with known mode of flow capability. It was found that there was only slight improvement in predictive ability when the particle density was replaced by loose-poured bulk density in the basic parameter techniques. The air-particle-parameter-based techniques also showed well-defined regions for mode of flow prediction though the data set used was smaller than that for the basic techniques. Also, it was found to be difficult to utilise de-aeration values from different researchers and subsequently, an air-particle-based technique was developed which does not require any de-aeration parameter in its assessment.     

An investigation into flow mode transition and pressure fluctuations for fluidized dense-phase pneumatic conveying of fine powders

This paper presents the results of an ongoing investigation into the fluctuations of pressure signals due to solids-gas flows for dense-phase pneumatic conveying of fine powders.Pressure signals were obtained from pressure transducers installed along different locations of a pipeline for the fluidized dense-phase pneumatic conveying of fly ash(median particle diameter 30μm;particle density 2300kg/m~3;loosepoured bulk density 700kg/m~3) and white powder(median particle diameter 55 u.m;particle density1600kg/m~3;loose-poured bulk density 620kg/m~3) from dilute to fluidized dense-phase.Standard deviation and Shannon entropy were employed to investigate the pressure signal fluctuations.It was found that there is an increase in the values of Shannon entropy and standard deviation for both of the products along the flow direction through the straight pipe sections.However,both the Shannon entropy and standard deviation values tend to decrease after the flow through bend(s).This result could be attributed to the deceleration of particles while flowing through the bends,resulting in dampened particle fluctuation and turbulence.Lower values of Shannon entropy in the early parts of the pipeline could be due to the non-suspension nature of flow(dense-phase),i.e.,there is a higher probability that the particles are concentrated toward the bottom of pipe,compared with dilute-phase or suspension flow(high velocity),where the particles could be expected to be distributed homogenously throughout the pipe bore(as the flow is in suspension).Changes in straight-pipe pneumatic conveying characteristics along the flow direction also indicate a change in the flow regime along the flow.     

SOOT PARTICLES ANALYSIS IN LAMINAR PREMIXED PROPANE／OXYGEN （C3H8／O2） FLAMES USING PUBLISHED MEASUREMENT DATA

A laminar premixed Propane/Air flame with a fuel equivalence ratio of 2.1 was employed for analysis of soot particles. Zeroth-order Iognormal distributions (ZOLD) were used in the analysis of experimental distribution phenomena at different residence times during soot formation in the flame. Rayleigh‘s theory and Mie‘s scattering theory were combined with agglomerate analysis using scattering and extinction data to determine the following soot characteristics: agglomerate parameters, volumetric fractions, mass flow rates and surface growth rate. Soot density measurements were carried out to determine density variations at different stages of growth. The measured results show that for long residence times the soot clearly crystallizes with higher density (up to 1.8 g.cm3). The increases of soot volumetric fraction and mass flow rate indicate that the surface growth rate of soot particles exceeds the oxidation rates in the flame studied. The data obtained in this work would be used to study soot oxidation rate under flaming condition.     

Transient simulation of a pump-turbine with misaligned guide vanes during turbine model start-up

Experimental studies of a model pump-turbine S-curve characteristics and its improvement by misaligned guide vanes （MGV） were extended to prototype pump turbine through 3-D transient flow simulations. The unsteady Reynolds-averaged Navier-Stokes equations with the SST turbulence model were used to model the transient flow within the entire flow passage of a reversible pump-turbine with and without misaligned guide vanes during turbine model start-up. The unstable S-curve and its improvement by using misaligned guide vane were verified by model test and simulation. The transient flow calculations were used to clarify the variations of pressure pulse and internal flow behavior in the entire flow passage. The use of misaligned guide vanes can eliminate the S-curve characteristics of a pump-turbine, and can significantly increase the pressure pulse amplitude in the entire flow passage and the runner radial forces during start-up. The MGV only decreased the pulse amplitude on the guide vane suction side when the rotating speed was less than 50% rated speed. The hydraulic reason is that the MGV dramatically changed the flow patterns inside the entire flow passage, and destroyed the symmetry of the flow distribution inside the guide vane and runner.     

Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field

This paper presents a study of hydromagnetic Couette flow of an incompress- ible and electrically conducting fluid between two parallel rotating plates, one of which is oscillating in its own plane. A uniform transverse magnetic field is used, and the induced magnetic field is taken into account. The exact solution to the governing equations is obtained in a closed form. The solution to the problem in the case of vanishing and small finite magnetic Prandtl numbers is also derived from the general solution. The asymp- totic behavior of the solution for large values of the frequency parameter is analyzed to gain some physical insights into the flow pattern. Expressions for the shear stress at both the oscillatory and stationary plates due to primary and secondary flows and mass flow rate in the primary and secondary flow directions are also obtained. The results of the fluid velocity and the induced magnetic field are presented. The shear stresses on the plates due to the primary and secondary flows and the corresponding mass flow rates are presented in a tabular form.     

Transportation characteristics of gas–solid two-phase flow in a long-distance pipeline

In this study, experiments on fly ash conveying were carried out with a home-made long-distance positive-pressure pneumatic conveying system equipped with a high performance electrical capacitance tomography system to observe the transient characteristics of gas–solid two-phase flow. The experimental results indicated that solids throughput increased with increasing solids–gas ratio when the conveying pipeline was not plugged. Moreover, the optimum operating state was determined for the 1000 m long conveying pipeline with a throttle plate of 26 orifices. At this state the solids throughput was about 12.97 t/h. Additionally, the transportation pattern of fly ash gradually changed from sparse–dense flow to partial and plug flows with increasing conveying distance because of the conveying pressure loss. These experimental results provide important reference data for the development of pneumatic conveying technology.     

Characterization of the gas pulse frequency, amplitude and velocity in non-steady dense phase pneumatic conveying of powders

Current modelling techniques for the prediction of conveying line pressure drop in low velocity dense phase pneumatic conveying are largely based on steady state analyses.Work in this area has been on-going for many years with only marginal improvements in the accuracy of prediction being achieved.Experimental and theoretical investigations undertaken by the authors suggest that the flow mechanisms involved in dense phase conveying are dominated by transient effects rather than those of steady state and are possibly the principal reasons for the limited improvement in accuracy.This paper reports on investigations on the pressure fluctuation behaviour in dense phase pneumatic conveying of powders.The pressure behaviour of the gas flow in the top section of the pipeline was found to exhibit pulsatile oscillations.In particular,the pulse velocity showed variation in magnitude while the frequency of the oscillations rarely exceeded 5 Hz.A wavelet analysis using the Daubechie 4 wavelet found that the amplitude of the oscillations increased along the pipeline.Furthermore,there was significant variation in gas pulse amplitude for different types of particulate material.     

Transportation characteristics of gas-solid two-phase flow in a long-distance pipeline

In this study,experiments on fly ash conveying were carried out with a home-made long-distance positive-pressure pneumatic conveying system equipped with a high performance electrical capacitance tomography system to observe the transient characteristics of gas-solid two-phase flow.The experimental results indicated that sol ids throughput increased with increasing solids-gas ratio when the conveying pipeline was not plugged.Moreover,the optimum operating state was determined for the 1000 m long conveying pipeline with a throttle plate of 26 orifices.At this state the solids throughput was about 12.97 t/h.Additionally,the transportation pattern of fly ash gradually changed from sparse-dense flow to partial and plug flows with increasing conveying distance because of the conveying pressure loss.These experimental results provide important reference data for the development of pneumatic conveying technology.     

Online monitoring of gas–solid two-phase flow using projected CG method in ECT image reconstruction

Electrical capacitance tomography (ECT) is a promising technique for multi-phase flow measurement due to its high speed, low cost and non-intrusive sensing. Image reconstruction for ECT is an inverse problem of finding the permittivity distribution of an object by measuring the electrical capacitances between sets of electrodes placed around its periphery. The conjugate gradient (CG) method is a popular image reconstruction method for ECT, in spite of its low convergence rate. In this paper, an advanced version of the CG method, the projected CG method, is used for image reconstruction of an ECT system. The solution space is projected into the Krylov subspace and the inverse problem is solved by the CG method in a low-dimensional specific subspace. Both static and dynamic experiments were carried out for gas–solid two-phase flows. The flow regimes are identified using the reconstructed images obtained with the projected CG method. The results obtained indicate that the projected CG method improves the quality of reconstructed images and dramatically reduces computation time, as compared to the traditional sensitivity, Landweber, and CG methods. Furthermore, the projected CG method was also used to estimate the important parameters of the pneumatic conveying process, such as the volume concentration, flow velocity and mass flow rate of the solid phase. Therefore, the projected CG method is considered suitable for online gas–solid two-phase flow measurement.     

An experimental investigation of pneumatic swirl flow induced by a three lobed helical pipe

This paper presents a discussion of the results and conclusions drawn from a series of experiments conducted to investigate the swirl flow that are generated by a three lobed helical pipe mounted within a laboratory scale pneumatic conveying rig. The experiments employed Laser Doppler Anemometry (LDA) to quantify the strength of the induced vortex formations and the decay rates of the observed downstream swirl flows over a range of Reynolds number in the turbulent regime. Instantaneous point velocity measurements were resolved in three directions across regular measurement grids transcribed across parallel planes located at four distances downstream of the swirl inducing pipe section. The equivalent axial, radial and tangential velocities were subsequently computed at these grids points. The degree of swirl measured across each measurement plane was expressed in terms of a defined swirl number.It was concluded that the three lobed helical pipe gave rise to a wall jet type of swirl whose rate of observed downstream decay is related to the Reynolds number of the upstream flow and the distance downstream of the swirl pipe. The decay rates for the swirl flows were found to be inversely proportional to the Reynolds number of the upstream flow. The swirl pipe was observed to create a redistribution of the downstream velocity field from axial to tangential, accompanied by a transfer of axial to angular momentum. The findings of this paper are believed to improve understanding to assist the selective use of swirl flow within lean phase particles pneumatic transport systems.     

Numerical solutions of pulsating flow and heat transfer characteristics in a channel with a backward-facing step

The incompressible laminar flow of air and heat transfer in a channel with a backward-facing step is studied for steady cases and for pulsatile inlet conditions. For steady flows the influence of the inlet velocity profile, the height of the step and the Reynolds number on the reattachment length is investigated. A parabolic entrance profile was used for pulsatile flow. It was found with amplitude of oscillation of one by Re=100 that the primary vortex breakdown through one pulsatile cycle. The wall shear rate in the separation zone varied markedly with pulsatile flows and the wall heat transfer remained relatively constant. The time-average pulsatile heat transfer at the walls was greater as with steady flow with the same mean Reynolds number.     

Transient growth and bypass transition in stenotic flow with a physiological waveform

A direct analysis method is applied to compute optimal transient growth initial conditions for physiologically relevant pulsatile flows in a smooth axisymmetric stenosis with 75% occlusion. The flow waveform employed represents phase-average measurements obtained in the human common carotid artery. Floquet analysis shows that the periodic flow is stable to infinitesimal eigenmodal-type perturbations that would grow from one cycle to the next at the Reynolds numbers considered. However, the same flows display explosive transient growth of optimal disturbances, with our analysis predicting disturbance energy growths of order 10²⁵ within half a pulse period at a mean bulk flow Reynolds number Re = 300, which is significantly lower than the physiological value of Re = 450 at this location. Direct numerical simulation at Re = 300 shows that when the base flow is perturbed a small amount with the optimal growth initial condition, the disturbance grows rapidly in time in agreement with the linear analysis, and saturates to provide a locally turbulent state within half a pulse period. This transition resulting from non-normal growth mechanisms shows the flow exhibits bypass transition to turbulence. Our analysis suggests that this route to localized turbulent states could be relatively common in human arterial flows.     

Pressure drop prediction with a modified frictional-kinetic model for alumina in bypass pneumatic conveying system

A new frictional-kinetic model is proposed and modified for pressure drop prediction of alumina in a bypass pneumatic conveying system. This new model is based on the conventional Johnson–Jackson frictional-kinetic model. The critical value of solids volume fraction and maximum packing limit are modified based on the fluidized bulk density and tapped bulk density, respectively. In addition, an offset solid volume fraction is introduced into the frictional pressure model as well as into the radial distribution functions which represents the correction factors to modify the probability of collisions between particles when solid phase becomes excessively dense. For the application of the model, computational fluid dynamics (CFD) simulations were conducted by using kinetic theory, conventional frictional-kinetic model and modified frictional-kinetic model. The simulation results were then compared with the experimental results. It was found that the modified frictional-kinetic model showed the largest improvement on pressure drop prediction results compared with results obtained from applying the kinetic theory and the conventional frictional-kinetic model, especially for denser flows with low air mass flow rates and high solid loading ratios (SLR). In addition, the solids volume investigation of CFD simulations shows a strong comparison to the actual flow conditions in the pipe, as transient slug type flow of alumina is observed.     

水平管道气固两相分层流动过程的研究

以空气作为输送动力、粉煤灰及玻璃微珠作为输送物料,对气力输送管道中气固两相流的流动特性进行了系统的试验研究.对管路系统的特性、操作条件、物料和气体的性质等影响气固两相流压力损失的主要因素进行了探讨.并在实验的基础上对两相流动的沉积速度、经济速度进行了确定.同时在对粉体受力分析的基础上建立了分层流动的物理及数学模型,通过对比数学模型计算值与试验值得出该数学模型具有一定的计算精度,能够用于指导分层流动的研究及应用.