SHAPE OF TURBULENT LUMP IN A CIRCULAR PIPE FLOW DETERMINED BY SPATIAL-DEPENDENCE MATRIX

Contour line maps of velocity fluctuation of turbulent flow in a circular pipe are drawn based on the results of simultaneous measurements of axial velocity at sixteen radial positions. The regions where fluid elements are estimated to have the same behavior, i.e. turbulent lump, can be found out by using spatial-dependence matrices which are used in pattern analysis, and the shape of the eddy is made clear by drawing a contour line map of the index which shows the degree of mutual dependence of velocity fluctuations of the two points. The shape of the core part of the turbulent lump is different from that of outer part of the turbulent lump, and the scale of it and so on depend on the Reynolds number and the radial position. These tendencies predicted to have some effects on the diffusion of fluid elements.     

STOCHASTIC MODELING AND ANALYSIS OF A TURBULENT FLOW SYSTEM

A stochastic model is developed to describe the axial movement of an element or particle in a turbulent flow system, where diffusion or local transition is not the major mechanism dictating particle motion. The model is a generalization of the diffusion equation for particle movement and includes both diffusion and random displacements. From this model, one can determine the residence time distribution and estimate the parameters characterizing the flow system.     

DETERMINATION OF THE MIXING RATE OF A HIGH VELOCITY FEED STREAM IN AGITATED VESSELS

In semi-batch or continuously stirred reactors, often a feed containing one or more reactants has to be mixed with the contents of the vessel. For fast competitive or consecutive reactions the mixing rate of the feed stream with the vessel contents has a large influence on the product quality. The mixing rate is often controlled by the turbulent dispersion process. Therefore, it has been suggested in the literature to keep the turbulent dispersion time constant upon scale-up to obtain a constant product quality. In this study, based on a combination of a theoretical model, Planar Laser Induced Fluorescence experiments and Laser Doppler Velocimetry experiments, the turbulent dispersion coefficient is determined. This has been done for the case that a feed stream is mixed in a stirred vessel by a combination of feed stream and stirrer generated turbulence. The turbulent dispersion coefficient is used to derive an equation for the turbulent dispersion time as function of several design and process variables.     

DETERMINATION OF THE MIXING RATE OF A HIGH VELOCITY FEED STREAM IN AGITATED VESSELS

In semi-batch or continuously stirred reactors, often a feed containing one or more reactants has to be mixed with the contents of the vessel. For fast competitive or consecutive reactions the mixing rate of the feed stream with the vessel contents has a large influence on the product quality. The mixing rate is often controlled by the turbulent dispersion process. Therefore, it has been suggested in the literature to keep the turbulent dispersion time constant upon scale-up to obtain a constant product quality. In this study, based on a combination of a theoretical model, Planar Laser Induced Fluorescence experiments and Laser Doppler Velocimetry experiments, the turbulent dispersion coefficient is determined. This has been done for the case that a feed stream is mixed in a stirred vessel by a combination of feed stream and stirrer generated turbulence. The turbulent dispersion coefficient is used to derive an equation for the turbulent dispersion time as function of several design and process variables.     

A PROPOSAL FOR TREATMENT OF TURBULENT MIXING IN A TWO-PHASE SUBCHANNEL FLOW

We propose a practical method for the treatment of turbulent mixing rate in a two-phase subchannel flow in a hydrodynamic non-equilibrium state. Based on the assumption that the fundamental modes of the inter-subchannel fluid transfer in such a state are turbulent mixing, void drift, and diversion cross flow, the turbulent mixing rate is considered to be equal to that in the hydrodynamic equilibrium state that the flow will attain. The applicability of the method is examined by experiments concerning the axial variation in tracer concentration in a non-equilibrium flow without diversion cross flow. A good agreement is seen between the calculations and the measurements.     

A mechanistic model of turbulent drag reduction by additives

The phenomenon of drag reduction in walled turbulent flows of polymer solutions is theoretically modeled. A new mechanistic model of a polymer molecule in a turbulent flow field is suggested. It is argued that the dominant forces on a polymer fiber in the turbulent flow field are elastic and centrifugal. According to this model, an additional route of dissipation exists, in which eddy kinetic energy is converted to polymer elastic energy by the centrifugal elongation of the rotated polymer, which in turn is viscously damped by the surroundings, when the polymer relaxes. A novel approach is then illustrated, where it is shown that this mechanistic model can be accounted for as a turbulent scale alteration, instead of addition, which enables the classical dimensional analysis of a turbulent boundary layer to apply. Using this dimensional analysis with the equivalent altered scale yields remarkable results. Correct-form velocity profiles are obtained, and Virk's asymptote and slope are predicted with no empirical constants. Drag-flow rate curves are also calculated, and compared favorably with Virk's experiments. The onset of drag reduction phenomenon is also explained by this model, and calculations of it are also compared with Virk's data. The parametric dependencies of the onset point agree well with Virk's conclusions.     

A MODEL FOR PREDICTING HEAT TRANSFER TO A TURBULENT FALLING FILM

A modified form of Carey'ls method for predicting the heat transfer to a turbulent falling film is presented. The new model is successfully tested against experimental data as well as other models. This method utilizes an optimization technique along with the Rombcrg integration to determine two universal constants for the modified turbulent diffusivisity model. The results show that in spite of its relative simplicity, the new model is a fairly accurate one, having an overall average error of less than 9%.     

THE CONVECTIVE VELOCITY OF HEAVY PARTICLES IN TURBULENT AIR FLOWS

This paper examines the influence of the “crossing trajectories” effect on the convective velocity for heavy particles suspended in a turbulent air flow. The fluid energy spectrum “experienced” by a falling particle is deduced from experimental data and is used to evaluate the turbulent component of the convective velocity. The results indicate a significant increase in the rms value of the turbulent component due to the “crossing trajectories” effect.     

A Comparison of the Mixing Characteristics in Single‐ and Two‐Phase Grid‐Generated Turbulent Flow Systems

The mixing process is studied in grid‐generated turbulent flow for single‐ and bubbly two‐phase flow systems. Concentration and mixing characteristics in the liquid phase are measured with the aid of a PLIF/PLIF arrangement. A nearly isotropic turbulent flow field is generated at the center of the vertical pipe by using a honeycomb, three grids and a contraction. In two‐phase flow experiments, air bubbles were injected into the flow from a rectangular grid, with mesh size M = 6 mm, which is placed midway between two circular grids each with a mesh size of M = 2 mm. For single‐phase flow, the normalized mean concentration cross‐stream profiles have rather similar Gaussian shapes, and the cross‐stream profiles of the normalized root‐mean‐square (RMS) values of concentration were found to be quite similar. Cross‐stream profiles of the mean concentration, for bubbly two‐phase flow, were also found to be quite similar, but they did not have the Gaussian shape of the profiles for single‐phase flow. Almost self‐similar behavior was also found for the RMS values of the concentration in two‐phase systems. The turbulent diffusion coefficient in the liquid phase was also calculated. At the center of the plume, the flow was found to have a periodic coherent structure, probably of vortex shedding character. Observations showed that the period of oscillation is higher in the case of two‐phase flow than in single‐phase flow.     

FCC细颗粒湍流流化床流体力学性能研究

ＦＣＣ细颗粒湍流流化床流体力学性能研究李俊，张蕴璧，闫遂宁（西安石油学院，西安７１００６１）（西北大学）（洛阳石化公司）关键词：流化床，湍流，气泡，空隙率１前言湍流流化床有着广泛的工业背景。湍流流化床反应器存在着物质空间分布的不均匀现象，这种分布对湍...     

流态化结晶过程中晶体生长的湍流传质模型

根据流态化结晶过程的流体处于湍流运动的事实,将多相湍流理论应用于晶体的生长过程,建立该过程的湍流传质动力学模型.模型计算与实验数据比较表明,湍流传质模型对扩散传质控制的晶体生长过程是可靠的.     

PREDICTION OF A GAS-PARTICLE TURBULENT JET WITH THE FLUCTUATION-SPECTRUM-RANDOM-TRAJECTORY MODEL

A numerical treatment for determining the particle velocity and the trajectories in a two-phase flow is described herein and this new fluctuation-spectrum-random-trajectory (FSRT) model is proposed to account for the turbulent diffusion of particles. It is predicted for the flow of a turbulent axisymmetric gaseous jet laden with spherical solid particles of nonuniform size. The particle velocity and the concentration field are obtained by the revised volume average method. The predictions are compared with experiment.     

MASS TRANSFER IN AC ELECTROLYSIS: EXTENSION OF A FILM MODEL TO TURBULENT FLOW ON A ROTATING HEMISPHERE

Turbulent mass transfer to a rotating hemisphere during AC electrolysis was examined with a film model. The analytical results for the limiting AC current density were compared to the experimental data obtained with sinusoidal, square and triangular wave AC. The limiting AC current density in turbulent flow was found to depend on both the Reynolds number as a dimensionless AC frequency K = (ω/Ω)Sc^1/3. The prediction by the film model agreed with the experimental data to within ±15%. For a given root-mean-square of applied AC, the periodic concentration overpotential decreased in the order of quare, sinusoidal, and triangular AC. The phase shift between the applied AC and the concentration overpotential wave decreased with increasing Reynolds number in turbulent flow.     

MASS TRANSFER IN AC ELECTROLYSIS: EXTENSION OF A FILM MODEL TO TURBULENT FLOW ON A ROTATING HEMISPHERE

Turbulent mass transfer to a rotating hemisphere during AC electrolysis was examined with a film model. The analytical results for the limiting AC current density were compared to the experimental data obtained with sinusoidal, square and triangular wave AC. The limiting AC current density in turbulent flow was found to depend on both the Reynolds number as a dimensionless AC frequency K = (ω/Ω)Sc^1/3. The prediction by the film model agreed with the experimental data to within ±15%. For a given root-mean-square of applied AC, the periodic concentration overpotential decreased in the order of quare, sinusoidal, and triangular AC. The phase shift between the applied AC and the concentration overpotential wave decreased with increasing Reynolds number in turbulent flow.     

MASS TRANSFER IN AC ELECTROLYSIS: EXTENSION OF A FILM MODEL TO TURBULENT FLOW ON A ROTATING HEMISPHERE

Turbulent mass transfer to a rotating hemisphere during AC electrolysis was examined with a film model. The analytical results for the limiting AC current density were compared to the experimental data obtained with sinusoidal, square and triangular wave AC. The limiting AC current density in turbulent flow was found to depend on both the Reynolds number as a dimensionless AC frequency K = (ω/Ω)Sc^1/3 The prediction by the film model agreed with the experimental data to within ±15%. For a given root-mean-square of applied AC, the periodic concentration overpotential decreased in the order of quare, sinusoidal, and triangular AC. The phase shift between the applied AC and the concentration overpotential wave decreased with increasing Reynolds number in turbulent flow.     

MASS TRANSFER IN AC ELECTROLYSIS: EXTENSION OF A FILM MODEL TO TURBULENT FLOW ON A ROTATING HEMISPHERE

Turbulent mass transfer to a rotating hemisphere during AC electrolysis was examined with a film model. The analytical results for the limiting AC current density were compared to the experimental data obtained with sinusoidal, square and triangular wave AC. The limiting AC current density in turbulent flow was found to depend on both the Reynolds number as a dimensionless AC frequency K = (ω/Ω)Sc^1/3 The prediction by the film model agreed with the experimental data to within ±15%. For a given root-mean-square of applied AC, the periodic concentration overpotential decreased in the order of quare, sinusoidal, and triangular AC. The phase shift between the applied AC and the concentration overpotential wave decreased with increasing Reynolds number in turbulent flow.     

PDF method for population balance in turbulent reactive flow

Turbulent reactive flows with particle formation, such as soot formation and precipitation, are characterized by complex interactions between turbulence, scalar transport, particle formation and particle transport and inter-particle events such as coagulation. The effect of formation, growth and coagulation on the particle size distribution (PSD) must be modelled by the population balance equation (PBE). While the PBE has been studied extensively in homogeneous systems and, recently, in simple flows, its coupling with turbulent reactive flows poses a wealth of new questions. Processes such as nucleation, growth and coagulation are described by kinetic laws that link them to the local concentrations of the reactive scalars, which are random in a turbulent flow. This accounts for additional mechanisms that induce randomness and fluctuations to the particle concentration and PSD. Furthermore, conventional RANS closure of the coagulation term PDE (which describes the evolution of the PSD) leads to unknown correlations. In this work a new pdf approach is developed, based on the transport of the joint pdf of reactive scalars and particle number densities at different sizes, which overcomes the additional closure problems. It is also shown how the pdf method can be solved numerically via Monte-Carlo methods, and this is demonstrated via two applications in a partially stirred reactor: precipitation via nucleation-growth and coagulation. In each case the pdf method is compared with models that neglect correlations at various levels, and it is demonstrated that the interaction of turbulence with particle formation mechanisms accounts for significant deviations in the PSD.     

GAS MIXING IN SLUGGING AND TURBULENT FLUIDIZED BEDS

The gas phase mixing in a fluidized bed of glass beads (d_p = 0.362 mm) in the slugging and turbulent flow regimes has been studied in a 0.1 m-ID × 3.0 m high Plexiglas column.

The gas dispersion in the downstream of the bed has been described by a diffusion process with the axial and radial dispersion coefficients. The radial dispersion coefficient of the gas phase is nearly constant with the variation of gas velocity in the slugging flow regime, but it increases with an increase in gas velocity in the turbulent flow regime.

Appreciable backmixing of the gas phase is pronounced in the slugging flow regime whereas the lower gas backmixing is produced in the turbulent flow regime. The gas backmixing coefficient increases with an increase in gas velocity in the slugging flow regime, but it decreases slightly with an increase in gas velocity in the turbulent flow regime.

The radial mixing and backmixing coefficients of the gas in terms of Peclet numbers have been correlated with the relevant dimensionless parameters (U_g/U_mf, p_s/p_g, d_p/D_t).

The gas flow pattern in the bed has been well represented by a simplified model based on the two gas phases in the dilute and dense phases which are percolating through the bed in plug flow. The present model can predict the gas exchange coefficient between the phases, the fractions of the dilute phase, the interstitial gas in the dense phase, and the interstitial gas velocity in the bed.     

A stochastic model for turbulent diffusion

An improved stochastic model for turbulent diffusion is developed. The model is free of arbitrary adjustable constants. The central objective, as in Taylor's approach, is to predict the turbulent diffusion (mean square displacement and/or concentration distribution) given certain statistical information about the turbulent velocity field.The applicability of the model to problems of turbulent diffusion in shear flows is explored. When the cross correlation between the fluctuating velocity and the stochastic forcing function is zero and the forcing function is white noise in character, the conditions necessary to describe Brownian motion are satisfied. However, when the cross correlation is other than zero and when, at the same time, the energy of the velocity fluctuation is concentrated at the lower frequencies, the equation can be used to describe turbulent diffusion. The deterministic coefficient β in the model and the nature of the stochastic forcing function can be calculated from known Eulerian statistics of the flow field.The method is applicable to non-homogeneous flows in three dimensions where correlation exists between fluctuating velocity components. Implementation of the model is most readily accomplished on a modern hybrid computer. Good agreement is obtained in comparisons of predicted results from the model with (a) theoretical solutions for homogeneous turbulent diffusion (b) experimental measurements of diffusion in a turbulent boundary layer and (c) measurements of diffusion in the atmospheric boundary layer.     

方型多火嘴石油化工管式炉中辐射室三维流动及传热的数学模拟

提出方型石油化工管式炉中辐射室的三维流动和传热的数学模型.对某焦化炉计算的结果与实测数据进行了初步比较并作出讨论.