Modellierung der Einlaufstrecke und deren Auswirkungen auf die Verweilzeitverteilung in laminar durchströmten Rohren und Kanälen

A one‐range and a two‐range model for the laminar velocity distribution in the entrance region of tubes and ducts are presented. These allow the calculation of the residence time distribution under the impact of the flow development in the hydrodynamic entrance region. For the dispersion‐free case, an analytical solution is given. A cell model with place‐changing probability (ZEMP) is applied for the consideration of dispersion. This approach allows the fast quantification of the influence of different parameters on the residence time distribution for relatively short pipes and ducts. The numerical results are compared with earlier presented results of semi‐empirical models.     

Comparative analysis of residence and diffusion times in rotating bed used for biogas upgrading

Rotating bed can be used in desorption operation of biogas upgrading as a new technology. For enough time to desorb, it is important to study the relationship between the residence time of liquid in rotating bed and the material diffusion time of liquid droplet in desorption process. By theoretical deduction, the exponential relation between residence time and liquid flow rate and rotational speed and kinematic viscosity is obtained. By analyzing the solution of nonlinear partial differential equation, the time law of material diffusion in the droplet is obtained. Moreover, by comparing the residence and diffusion times, the diffusion time can be within or out of residence time range, which has a direct relationship to rotational speed and liquid flow. By experiment, the comparison between residence and diffusion times is more realistic when the rotational speed is higher.     

THE RESIDENCE TIME DISTRIBUTION FOR LAMINAR FLOW OF NON-NEWTONIAN LIQUIDS THROUGH HELICAL TUBES

The residence time distribution in a helically coiled tubular reactor is computed for laminar flow of inelastic non-Newtonian liquid at small Dean number. Effect of pseudoplasticity on the residence time distribution is explored. It was found that pseudoplaslicity of the liquid makes the residence time distribution narrower. The effect of dialalant fluid behavior is opposite but very small in magnitude. The results of numerical integrations are correlated with power law index, allowing predictions over a wide range of the index. The results could be used to predict conversion of reactions in a coiled reactor, such as continuous polymerization or fermentation reactors, where the reaction mixtures are likely to be non-Newtonian in nature. Results will be also useful in characterization of coiled chromatographic columns.     

The residence time distribution for ideal laminar flow in helical tube

A theoretical residence time distribution is derived for ideal laminar flow through a helical tube with no diffusion. It is shown that, when the flow pattern is fully developed, the residence time distribution becomes approximately independent of curvature and Reynolds number and may be closely approximated by the expression E θ(0) = 0 for 0 < θ(0) < 0.613, E θ(0) = 0.7050−3.81 for θ0 > 0.613. The conditions of applicability are considered and it is shown that the theory should be a reasonable approximation for liquid phase systems over a limited range of conditions.     

Casson流体层流反应器中连串反应的产品分布

引　言目前化工流体力学涉及的范围已由传统的牛顿流体发展到非牛顿流体 .常见的非牛顿流体包括幂律流体、Bingham流体和Casson流体 .有许多高聚物反应物系和生化反应物系属于非牛顿流体 .特别是某些生化反应系统 ,所处理的物系常由各种天然物质组成 ,因而表现出典型的非牛顿流     

Influence of Rheological Behavior of Purely Viscous Fluids on Analytical Residence Time Distribution in Straight Tubes

In an effort to better understand the homogeneity of heat treatment of foodstuffs in holding tubes, the cumulative residence time distribution function is derived for a Herschel‐Bulkley fluid from fully developed laminar flow in a straight circular tube under isothermal conditions when diffusional effects are negligible. The proposed analytical solution can be reduced to solutions for Newtonian, shear‐thinning, dilatant, Bingham fluids by setting particular rheological parameters, and consequently, it is possible to successfully explain the dependence of residence time distribution on fluid properties for almost all of the rheological models used for time‐independent purely viscous fluids.     

Diffusion Deposition on a Fiber in Nontransverse Flow

The effect of a nontransverse flow on the diffusional deposition of particles in an aerosol on a cylindrical fiber is investigated. The aerosol is transported by a slow laminar flow whose mean direction is at an arbitrary angle ? to the axis of the cylinder. The particle concentration and the subsequent deposition rate on a cylinder for such a flow are found by using the first two terms of the asymptotic solution in terms of the diffusion boundary layer thickness. This is inversely proportional to the cube root of the Peclet number, a parameter which is large for many problems of practical importance. For a given flow angle ? an expression for the diffusion efficiency η(?) is obtained. Under the assumption that the angular distribution of the fibers is uniform, a relation for the average value (η) for the diffusion efficiency is also derived. These formulas are generalizations of the results of Natanson and Stechkina for the diffusion efficiency in the case of purely transverse flow and with those of Banks and Kurowski for the mean flow at a small angle to the fiber     

Coiled configuration for flow inversion and its effect on residence time distribution

Flatter velocity profiles and more uniform thermal environents are extremely desirous factors for improved performance in flow reactors and heat exchangers. One means of achieving this in laminar flow systems is to use mixers and flow inverters. These improve performance but at higher initial and operating costs. This paper introduces a new and more effective device for flow inversion which is achieved by changing the direction of centrifugal force in helically-coiled tubes. Transient response experiments carried out under the conditions of both negligible and significant molecular diffusion reveal drastic narrowing of the residence time distribution (RTD). The effectiveness of the present device can be assessed by the fact that even at a Dean number of 3 the value of dispersion number as low as 0.0013 is obtained under the condition of significant diffusion, and in the case of negligible diffusion the value of dimensionless time at which the first element of tracer appears at the outlet is as high as 0.85.     

Analyse des interactions fluide-paroi dans un système ouvert a partir de la connaissance de la distribution des temps de sejour. Application aux dépôts d'aérosols par thermophorèse

In an open material system where the residence time distribution of a fluid is known, it is possible, using micromixing Zwietering' model to predict the results of linear interaction between the fluid and the wall of system but also for the aerosol particles transported by the fluid flow. This methodology is applied for aerosol deposition by thermophoresis in cylindrical pipe with constant wall temperature. The interpretation of experimental results in laminar flow shows that, for Knudsen numbers between 0.2 and 1.0, the thermophoresis coefficient must be calculated by Talbot' correlation. Finally, in transition flow, the aerosol mass deposition by thermophoresis and turbulent diffusion becomes probably minimal.     

Characterization of Residence Time Distribution in a Plug Flow Reactor

One of the biggest advantages of plug flow reactors lies in their narrow residence time distribution. The pulse experiment, as a common method on acquiring that distribution, relies on the tracer injection being a perfect pulse. A deviation from a perfect pulse leads to erroneous results if not taken into account. With a numerical analysis of experimental data, this effect is quantified in turbulent and laminar flow regime and the results are compared to an analytical method. Significant deviations occur mostly in the turbulent regime, which has the greatest technical relevance.     

Distribution of striation thickness from impingement mixers in reaction injection molding

The striation thickness distribution developed in an impingment T-mixer is predicted using the statistical theory of turbulent diffusion. The predicted distribution is independent of the mixing nozzle Reynolds number, in agreement with some experiments, and is primarily a function of the mixing head geometry, the ratio of the reagent flow rates and the residence time distribution of the flow in the mixing head. Mixing is described as the result of fluid deformation in the intertial subrange of turbulent flow. The relationship of deformation to time and energy dissipation rate ? is examined. In the impingement T-mixer ? is related to the kinetic energies of the streams entering and leaving the head. (There are no surface tension effects and pressure is relatively uniform in the mixing head, so that the kinetic energy is dissipated by viscous forces.) The distribution of residence times of fluid elements in the T-mixer is responsible for varying degrees of deformation and hence a distribution of striation thickness. This residence time distribution does not seem to have been studied and the flow pattern was thus modeled as perfect macromixing, having an exponential distribution. The procedure developed in this paper to calculate the distribution of striation thickness allows reasonable estimates of its parameters from fluid mechanical information and showed good agreement with experimental values, without having to fit any quantities. This new approach to striation thickness distribution is worth further evaluation.     

Entwurf und Betrieb eines Rohrreaktors mit enger Verweilzeitverteilung

In process engineering the residence time is an important design parameter, and a narrow residence time distribution is advantageous to avoid possible by-products in complex chemical reactions. A good radial mixing with low axial dispersion provides a narrow residence time distribution in a tube reactor. The axial dispersion of laminar flow in a straight tube is very high and generates a wide residence time distribution. However, secondary flows improve the radial mixing, which are investigated in this paper for curved tube reactors. Design notes for good radial mixing and geometric designs of tube reactors with baffles are presented.     

On Relaxation Phenomena in Field-Flow Fractionation

Abstract

The two-dimensional unsteady convective diffusion equation satisfied by the local concentration of the colloid introduced in a field-flow fractionation (FFF) column is solved by the method of finite differences. The alternating direction implicit (ADI) method proposed by Peaceman and Rachford is used. The axial convection term is approximated by a backward difference approximation to obtain a stable and convergent scheme.

Numerical results are obtained for various values of the transverse Peclet number for the case of steady laminar flow and a slug input. The numerical results from the ADI method are validated by comparison with numerical solutions obtained using an explicit scheme as well as by internal consistency checks.

The results of this work show that the transverse concentration profiles depend in a complex fashion on axial position along the cloud during relaxation. In the presence of a field, asymptoticity in the transverse profiles is approached first in the rear of the colloid cloud, and progresses gradually through the axial extent of the cloud. Ultimately, at a sufficiently large value of time, almost all of the colloid relaxes to asymptotic exponential distributions in the transverse coordinate as predicted from theory. The local concentration of colloid in the system is observed to reach a global maximum value at intermediate values of time during relaxation. The area average concentration distribution is observed to exhibit strong asymmetry when plotted against the axial coordinate at intermediate times both in the presence and in the absence of a field. This asymmetry is in accord with pure convection theory. In contrast, truncated two-term dispersion equations only predict symmetric distributions for symmetric initial conditions. Thus there may be a need to retain higher order terms in the application of generalized dispersion theory in order to predict the observed results.     

Residence Time Distribution Models Derived from Non‐Ideal Laminar Velocity Profiles in Tubes

The theoretical E‐curve for the laminar flow of non‐Newtonian fluids in circular tubes may not be accurate for real tubular systems with diffusion, mechanical vibration, wall roughness, pipe fittings, curves, coils, or corrugated walls. Deviations from the idealized laminar flow reactor (LFR) cannot be well represented using the axial dispersion or the tanks‐in‐series models of residence time distribution (RTD). In this work, four RTD models derived from non‐ideal velocity profiles in segregated tube flow are proposed. They were used to represent the RTD of three tubular systems working with Newtonian and pseudoplastic fluids. Other RTD models were considered for comparison. The proposed models provided good adjustments, and it was possible to determine the active volumes. It is expected that these models can be useful for the analysis of LFR or for the evaluation of continuous thermal processing of viscous foods.     

Fluiddynamische Aspekte in Mikrostrukturreaktoren

Fluid Dynamics in Microchannel Reactors . The possible benefits of using microchannel reactors in the chemical process industries have been under discussion for several years. Outstanding heat transfer properties, short residence times and short diffusion lengths are considered key advantages, while the cost of the approach and the pending question of long-term stability are still major sources of skepticism. A good starting point for a feasibility study is to investigate some major fluid dynamic properties. For a unit consisting of hundreds of parallel microchannels, the pressure drop for the laminar flow is just a few millibar. However, at high gas flows the distribution over the numerous channels may become non-uniform. It is shown how the resulting residence time distribution affects both the yield of intermediates in consecutive reactions, and step functions of the concentration during periodic operation, respectively. All in all, the results of the estimations are encouraging.     

Micro-macropore model for sorption of water on silica gel in a dehumidifier

A mathematical model for laminar flow through a duct of an isothermally maintained dehumidifier and for simultaneous diffusion and absorption of water vapor into a desiccant was formulated as an integral equation. The macro-micro pore model for the desiccant was fitted to transient experimental data for isothermal adsorption of water on a silica gel sheet with an average deviation of four percent. The data could not be explained by the conventional Rosen model which considers diffusion in the macropores only.A Graetz type analysis of experimental data showed that the mass transfer in the channel could be approximated by constant mass transfer coefficients which agreed with the asymptotic Nusselt numbers for the laminar Graetz problems. However, the corresponding mass transfer coefficients for the desiccant are highly time dependent. Hence a more complicated model is required.     

Residence time distribution analysis from a continuous couette flow device around critical taylor number

This paper presents an experimental study of residence time distribution (RTD) analysis by pulse response technique in a continuous Couette flow device with rotating inner cylinder and stationary outer cylinder. Two kinds of experimental tests using pulses of tracer dye solution and particles resulting from a fast precipitation were performed in the region near the critical Taylor number characterizing boundary between laminar and laminar vortex flow. For most experiments performed in laminar and laminar vortex flow regime around the critical Taylor number over the ranges 0 < T_a < 120 and 0 < R_e < 5.5 the normalized response can be described by a dispersion model. The results of the critical Taylor number as characterized by the minimum dispersion number appear consistent with both theoretical predictions and other empirical observations.     

On the residence time distribution for systems with open boundaries

Tracer tests cannot in general be used to determine the residence time distribution in systems with open boundaries. However the most commonly employed model for such systems, the diffusion model, turns out to be exceptional in this respect: its residence time distribution is derived and found to resemble closely the impulse response function.The general problem is then viewed with reference to the lifespan and drop-out distributions which, together with the residence time distribution, characterize flow through open boundaries. The familiar result for closed systems that the mean residence time is equal to the ratio of system hold-up to flow rate is shown to apply also for open systems.     

MEASUREMENT OF AEROSOL EFFECTIVE TRANSPORT COEFFICIENTS IN CYLINDRICAL TUBES

Transport of submicrometer aerosols in flows in tubes can be described by an effective one-dimensional axial convection–diffusion equation with apparent aerosol transport properties: mean aerosol velocity, mean aerosol diffusion coefficient (dispersivity) and mean aerosol deposition coefficient. These quantities are investigated experimentally by shape analyses of boluses of submicrometer Latex aerosol particles injected in the clean air flow through long tubes and a diffusion battery of capillary tubes. It is shown that the aerosol effective dispersivity and volumetric deposition coefficient significantly depend on the particle transit (residence) time within the tubes. For sufficiently long residence times these quantities are found to approach their asymptotic limiting values, predicted by the existing theories of the hydrodynamic dispersion. On the other hand, the mean aerosol velocity only weakly differs from the mean air velocity, and is almost independent of the aerosol residence time. The results obtained are important in several applications, including particle sampling using long tubes or lines.     

Direct methanol fuel cell (DMFC): analysis of residence time behaviour of anodic flow bed

This paper studies the residence time behaviour and concentration distribution in a simplified rhomboidal DMFC anode flow bed by 3D numerical flow simulations and by experimental measurements. The rhomboidal DMFC anode flow bed and the applied volume flow are discussed with regard to data given in the literature. Simulations with CFX, based on Finite Volume Method, and MooNMD, based on Finite Element Method, show strongly similar results and the reliability of the computed residence time distributions (RTD) is proved by showing that they depend only slightly on parameters of the numerical schemes applied. The realisation of the RTD and concentration distribution measurements are described. Experimentally obtained RTD results are in good agreement with the numerical simulations. Also, the experimentally obtained concentration distribution inside the anode flow bed is very similar to the computed distribution. By analysing the RTDs and concentration distributions, the obtained results provided evidence of weaknesses of the flow bed design.