Fine particle deposition in laminar and turbulent flows

The deposition of fine silica and polystyrene spheres was measured for conditions of laminar and turbulent flow (960 ≤ Re ≤ 16040) in a rectangular channel using image analysis. The plate glass deposition surfaces were rendered positively charged by coating them with a cationic copolymer while, under the water chemistry conditions employed, both types of particles were negatively charged. It was found that, contrary to the results for laminar flow, the initial depositon rates in turbulent flow decreased with increasing Re, indicating that deposition was no longer mass-transfer controlled and that particle attachment played an increasingly important role as Re was raised. Attachment was modelled as a rate process in series with mass transfer in which the attachment rate varies inversely as the square of the friction velocity. Under the conditions of the present experiments, no particle re-entrainment was observed, so that the declining rate of particle accumulation on the wall recorded in each run could only be attributed to a declining deposition rate. Even where asymptotic accumulations were reached, particle coverages never exceeded 3.5%.     

THE LAMINAR FLOW TUBULAR REACTOR WITH HOMOGENEOUS AND HETEROGENEOUS REACTIONS II. Application to Reactor Modeling Involving Free Radical Reactions

The simulation of the complex polychlorination of methane in a non-isothermal photoreactor with laminar flow regime shows the usefulness of the integral equations deduced in Part I of this contribution. Improved iterative schemes for numerical solution have been implemented by using the particular equations proposed for species having slow, very fast and instantaneous reaction regimes.

From such integral equations, in a mathematically consistent form, deviations in the fields of predicted concentrations with and without the application of the local steady-state approximation for homogeneous reactions involving atomic and free radical species have been obtained. Similarly the fields of predicted concentrations applying the usual assumption of negligible wall reactions for the same highly reactive intermediate species has been compared with the reaction mechanisms that includes the wall reactions. A comprehensive analysis of the validity of these simplifying assumptions is presented.     

Mass transfer in horizontal flow channels with thermal gradients

Mass transfer to a wall of a horizontal rectangular channel reactor was investigated by the limiting current technique for Reynolds numbers ranging from 200 to 32000. Overall mass transfer coefficients at various mass transfer surface angles were obtained while the reactor was operated under isothermal and non-isothermal conditions. Dimensionless correlations were developed for isothermal flows from 25 to 55°C and for non-isothermal flows with applied temperature differences up to 30°C. In the laminar flow range natural convection dominated, but under turbulent conditions combined natural and forced convection prevailed. Mass transfer was approximately doubled under optimum selection of channel surface rotation, temperature gradient and flow rate.     

Circulation of Geldart D type particles: Part II—Low solids fluxes: Measurements and computation under dilute conditions

In Part I of this paper, solids slugging phenomena were studied for high solids fluxes. In this study, the solids slugging was eliminated for extremely low solids fluxes. Here, gamma ray densitometry and PIV techniques were used to measure radially averaged solids volume fractions, and solids laminar and turbulent properties near the wall, respectively.The PIV system measured turbulent properties for solids, such as stresses, granular temperatures, and dispersion coefficients, non-invasively near the wall, in the developing region. This study was the first known measurement of solids dispersion coefficients in the axial and radial directions, using the PIV technique. A two-dimensional kinetic theory based IIT CFD code was used to perform simulations. The measured and computed radially averaged total granular temperatures, axial and radial solids and axial gas dispersion coefficients, reasonably agreed with the literature. This study also showed the capabilities of the kinetic theory based CFD codes to reasonably match the solids dispersion coefficients measured using the PIV technique.     

Dispersion of water into oil in a rotor–stator mixer. Part 1: Drop breakup in dilute systems

Most previous studies of liquid–liquid dispersion in complex geometry are limited to turbulent flow at low continuous phase viscosity. In this study, a viscous continuous phase was employed over a range of flow conditions including both the laminar and turbulent regimes. Equilibrium drop size was measured for water dispersed into viscous food grade mineral oils in a batch Silverson L4R rotor–stator mixer. The influence of fluid viscosities and interfacial tension (by adding an oil-soluble surfactant) were examined. In order to isolate the effect of drop breakage from coalescence, Part 1 is limited to dilute conditions (water phase fraction, ? = 0.001). In the laminar regime, drop breakup was more likely due to a simple shear breakage mechanism than one for extension. Following Grace (1982), a semi-empirical drop size correlation was developed. For turbulent flow, the validity of the sub-Kolmogorov inertial stress model for correlating equilibrium mean drop size was verified. Surfactants were found to mostly decrease drop size by lowering interfacial tension. Except for laminar systems near the critical micelle concentration, where Marangoni stresses appear to play some role, the effect of surfactants on the drop size could be correlated using the equilibrium or static interfacial tension. The influence of water phase fraction and coalescence is considered in Part 2 ( Rueger and Calabrese, 2013) of this paper.     

矩形截面高宽比对射流强化螺旋通道传热性能的影响

为了进一步探究具有不同截面高宽比的单一螺旋通道内流体湍流流动与换热特性以及射流对矩形截面螺旋通道的强化传热效果,采用计算流体动力学软件模拟研究了高宽比γ分别为0.625, 1.1, 1.6和2.5时,单一矩形螺旋通道及射流作用下螺旋通道内的湍流流场、二次流场及强化换热特性。结果表明,对于单一矩形螺旋通道,相同横截面积和流量时,仅当γ≥1.6的通道在高雷诺数下二次流会出现四涡结构,其余为两涡结构。对于单一螺旋通道,γ值越大流动阻力越小,同时换热性能越差。加入射流后,矩形截面四个壁面的换热能力均有提高,γ值越大射流的强化传热效果越显著,研究范围内局部壁面换热努塞尔数的平均值(Nulocal)m最高可为单一螺旋通道的2.51倍。考虑流量增加的影响,射流影响下的螺旋通道区域内综合强化传热因子PEC2在1.05~1.21之间。     

Transient regime in a parallelepipedic cell induced by a current or a potential step

On the basis of previous studies dealing with laminar flow in a channel electrode reactor, this work concerns the transient regime in a parallelepipedic cell induced by a current or a potential step for various types of flow. The response was shown theoretically to be governed by the wall velocity gradient. Experiments conducted in a rectangular cell provided with either flat or porous electrodes confirm the results of the model. Assuming a reversible electrochemical process, the transient behavior of a parallelepipedic cell can therefore be predicted through hydrodynamic and mass transfer data.     

A novel device for quenching: The cylindrical annular exchanger in laminar flow

Previous studies have brought evidence for the efficiency of mass transfer at the wall of annular catalytic reactors in laminar flow, a regime where exAnnular exchangers with small intersticial space thus appear as excellent tools for quenching reacting mixtures in laminar flow.     

Experimental Analysis of Hydrodynamics Induced by a Moritz HAS Impeller in Laminar and Turbulent Regimes

The hydrodynamics induced by a Moritz HAS impeller are investigated using the PIV technique. The purpose of this study is to extend the knowledge of this kind of impeller, well known in turbulent flow, to the transition regime and laminar flow. Measurements of instantaneous velocity fields are synchronized with the position of the blade of the impeller. The periodic motion induced by the impeller blade rotation is measured by this conditional averaging. A triple decomposition is used to analyze the levels of turbulent kinetic energy and periodic kinetic energy induced by the impeller. In a turbulent regime, the impeller induces axial flow: the magnitude of periodic fluctuation is low compared to the turbulent one. In a laminar regime, the impeller induces a tangential‐radial discharge flow, and periodic velocity fluctuations are limited to the vicinity of the impeller.     

A macroscopic agglomeration kernel model for gibbsite precipitation in turbulent and laminar flows

A macroscopic agglomeration kernel model has been developed that is capable of describing gibbsite agglomeration over a broad range of process conditions, including both the laminar and turbulent flow regimes. The agglomeration kernel model was derived using chemical reaction engineering principles and data from an extensive experimental program covering a wide range of temperatures, supersaturations, seed sizes, shear rates and mixing regimes. The experimental precipitation data in the laminar flow regime were generated using a novel Taylor-Couette precipitator. Data in the turbulent regime were generated in a stirred reactor. The developed agglomeration kernel model incorporates terms for the collision, capture, rupture and cementation rates affecting the formation of agglomerates. The model is shown to be able to predict the data from independent experiments. The proposed model also captures the complex non-linear shear rate and size-dependency observed experimentally, e.g. (1) for small particles the agglomeration kernel exhibits a maximum with respect to the shear rate, increasing at low shear rates in the laminar flow, but decreasing in the unstable Taylor-Couette flows and turbulent regimes; (2) for large particles the agglomeration kernel decreases monotonically with increasing shear.     

The influence of hydrodynamic and mass transfer entrance effects on the operation of a parallel plate electrolytic cell

Experimental measurements of mass transfer in an electrochemical flow cell of rectangular cross section with different hydrodynamic entrance and electrode lengths have been made. For fully developed flow, average Sherwood numbers under laminar conditions vary with Graetz number to a power 0·30. For turbulent flow, fully developed mass transfer conditions occur about twelve equivalent diameters along the electrode and are best represented by the Chilton-Colburn analogy which predicts Sherwood numbers varying with Reynolds number to a power of 0·8 and Schmidt number to a one-third power. For shorter electrodes Sherwood numbers can be adequately correlated by an expression with Reynolds number to a two-thirds power and dimensionless electrode length to a power of −0·2. For hydrodynamic entrance lengths of not less than eight equivalent diameters, data in the laminar region can be expressed by an emperical boundary layer type of equation which includes terms for the hydrodynamic entrance length and electrode length. In the turbulent regime substantially developed flow occurs after eight entrance lengths and correlations with fully developed flow equations are satisfactory     

Numerical Study of the Effect of Methane Combustion on Heat and Mass Transfer and Friction in the Boundary Layer

Calculation results are presented for laminar and turbulent boundary-layer flows on a porous plate with methane injection and combustion. The mathematical model is based on the boundary-layer approximation. Combustion was simulated by one global finite-rate reaction and the kinetic mechanism of hydrogen and carbon oxide afterburning. It is shown that injection and combustion in laminar and turbulent flows lead to more intense displacement of the flow away from the wall than in the case of injection into an isothermal flow, which decreases the friction drag and heat and diffusion fluxes. Combustion in a turbulent flow leads to flow laminarization and delay of the laminar–turbulent transition.     

Thermophoretic Deposition of Particles in Laminar and Turbulent Tube Flows

Thermophoretic deposition of aerosol particles (particle diameter ranges from 0.038 to 0.498 μm) was measured in a tube (1.18 m long, 0.43 cm inner diameter, stainless steel tube) using monodisperse NaCl test particles under laminar and turbulent flow conditions. In the previous study by Romay et al., theoretical thermophoretic deposition efficiencies in turbulent flow regime do not agree well with the experimental data. In this study, particle deposition efficiencies due to other deposition mechanisms such as electrostatic deposition for particles in Boltzmann charge equilibrium and laminar and turbulent diffusions were carefully assessed so that the deposition due to thermophoresis alone could be measured accurately. As a result, the semiempirical equation developed by Lin and Tsai in laminar flow regime and the theoretical equation of Romay et al. in turbulent flow regime are found to fit the experimental data of thermophoretic deposition efficiency very well with the differences of less than 1.0% in both flow regimes. It is also found that Talbot's formula for the thermophoretic coefficient is accurate while Waldmann's free molecular formula is only applicable when Kn is greater than about 3.0.     

Flow effects on the kinetics of a second-order reaction

Flow effects on the kinetics of an isothermal, equimolar, second-order reaction taking place in a channel were investigated using a Lagrangian numerical method. The reactants were released instantaneously from the two opposite walls of the channel into fully developed turbulent or laminar flow. The overall conversion, the residence time and reactor length required to achieve 80% conversion, and the effective reaction rate coefficient were calculated. A correlation of the efficiency ratio, defined as the effective rate coefficient divided by the reaction rate constant, with the flow parameters was found.     

Untersuchung der Strömung im Taylor‐Couette‐System bei geringen Spaltbreiten

The shaft bushings in many machines form a Taylor‐Couette system with a thin clearance. The flow in such a clearance was studied in this paper by means of CFD simulation. Two different gap width ratios have been chosen to investigate the flow from laminar to turbulent range. Based on the simulation results a critical gap width ratio is determined in the turbulent regime, which is of importance to the transition of a turbulent flow with Taylor vortex in a turbulent flow without Taylor vortex.     

Explicit calculation of the friction factor in pipeline flow of Bingham plastic fluids: a neural network approach

An artificial neural network (ANN) approach was used in this paper to develop an explicit procedure for calculating the friction factor, f, under both laminar and turbulent flow conditions of Bingham plastic fluids in closed conduits and pipe networks. The procedure aims at reducing the computational efforts as well as eliminating the need for conducting complex and time-consuming iterative solutions of the governing implicit equations for calculating the friction factor, f. The ANN approach involved the establishment of an explicit relationship among the Reynolds number, Re, Hedstrom number, He, and the friction factor, f, under both laminar and turbulent flow conditions. Although, an analytical solution of the governing equation under the laminar flow regime was also feasible (such an equation is also provided in this paper), the ANN model is applicable under both laminar and turbulent flow conditions where the analytical approach will have major limitations (especially when considering the implicit equation that govern the turbulent flow regime).     

Electrodiffusion diagnostics of the flow and mass transfer inside a network of crossing minichannels

The global mass transfer and the local flow structure inside a set of crossing minichannels were characterized using the electrodiffusion method. The individual square-cross channel sections (a = 1.5 mm in sides) intersect at right-angles in order to form the flow cell. An array of 39 circular platinum electrodes (0.25 mm in diameter) was flush-mounted into the wall of the flow cell to investigate the wall shear rate at different locations. This array of small sensors allowed characterization of longitudinal and lateral variations in wall shear rate across the flow cell, flow distribution at the inlet and outlet sections, transition between laminar and turbulent flow regimes, and flow behaviour at the channel crossings. The results of global wall mass transfer measurements demonstrated that, from a mass transfer point of view, the flow cell exhibits similar behaviour to a porous medium.     

矩形小通道内气液两相流垂直向上流动特性

以氮气和水为实验介质,利用高速摄像机对水力直径为1.15 mm的矩形小通道内的气液两相垂直向上流动特性进行可视化研究,依次得到泡状流、弹状流、搅拌流和环状流4种典型的流型图像。针对小通道内气泡之间相互无遮掩性的优势,运用图像处理技术对流型图像分形增强,检测气泡边缘并填充后根据提出的气相体积模型,得到两相流动的含气率。结合实验数据,根据分液相Reynolds数把流动分为层流区、过渡区和紊流区,并对Chisholm关系式进行修正,结果表明：修正后的压降模型能较好地预测本文实验结果。     

Non-newtonian flow through open channels

A general method is proposed for prediction of the flow rate and maximum velocity in the isothermal, steady, uniform, laminar flow of any incompressible, time-independent non-Newtonian fluid in straight open channels of arbitrary cross section. The method requires only a knowledge of two geometric coefficients and a function of shear stress, used to characterize the behavior of the fluid model. The slip effect at the solid boundary has been taken into consideration. Numerical values of the geometric parameters have been determined for flow through an inclined plane of infinite width, semi-circular, semi-elliptical, rectangular, and 90° and 60° symmetric triangular open channels. Applications have been made to various non-Newtonian fluid models such as the power-law, Bingham, Ellis, Meter and the Reiner-Rivlin general model. Numerical examples are presented. A generalization of the Fanning friction factor — Reynolds number is also presented. The problem of determining the point of transition from laminar to turbulent flow in the general case is examined, as is the problem of prediction of the friction factor in turbulent flow.