Pressure drop for single and two‐phase flow of non‐newtonian liquids in helical coils

New experimental results on pressure loss for the single and two‐phase gas‐liquid flow with non‐Newtonian liquids in helical coils are reported. For a constant value of the curvature ratio, the value of the helix angle of the coils is varied from 2.56° to 9.37°. For single phase flow, the effect of helix angle on pressure loss is found to be negligible in laminar flow regime but pressure loss increases with the increasing value of helix angle in turbulent flow conditions. On the other hand, for the two‐phase flow, the well‐known Lockhart‐Martinelli method correlates the present results for all values of helix angle (2.56‐9.37°) satisfactorily under turbulent/laminar and turbulent/turbulent conditions over the following ranges of variables as: 0.57 ≤ n′ ≤ 1; Re′ < 4000; Re_l < 4000; Re_g < 8000; 8 ≤ x ≤ 1000 and 0.2 ≤ De′ ≤ 1000.     

Liquid‐Solid Mass Transfer Behavior of a Vertical Array of Closely Spaced Horizontal Tubes in Relation to Catalytic and Electrochemical Reactor Design

The rates of mass transfer at a vertical array of closely spaced horizontal tubes were measured by the limiting‐current technique under single‐phase flow, gas sparging and two‐phase flow. The single‐phase flow data were correlated by the equation: Sh = 0.75 Sc^0.33 Re^0.59. The gas sparging data with no net solution flow were correlated by the equation: J = 0.31(Re_g.Fr)^–0.22. For two‐phase flow, the gas flow was found to enhance the rate of array mass transfer by a factor ranging from 1.25 to 5.25, depending on Re_g and Re. The enhancement ratio increases with decreasing Re and increasing Re_g. For Re ≥ 2500, the rate of mass transfer approaches the value of single‐phase flow, regardless of the value of Re_g, which ranged from 7 to 41. The importance of the present geometry in building electrochemical and catalytic reactors, where exothermic liquid‐solid diffusion‐controlled reactions take place, is highlighted. The present geometry offers the advantage that the outer surface acts as a turbulence promoter while the inner surface acts as a heat exchanger.     

Hindered settling in non-newtonian power law liquids

New experimental results on the hindered settling of model glass bead suspensions in non-Newtonian suspending media are reported. The data presented encompass the following ranges of variables: 7.38 × 10^?4 ≤ Re_1∞ ≤ 2; 0.0083 ≤ d/D ≤ 0.0703; 0.13 ≤ C ≤ 0.43 and 1 ≥ n ≥ 0.8. In these ranges of conditions, the dependence of the hindered settling velocity on concentration is adequately represented by the corresponding Newtonian expressions available in the literature. The influence of the power law flow behaviour index is completely embodied in the modified definition of the Reynolds number used for power law liquids.     

Mass transfer behaviour of a flow-by fixed bed electrochemical reactor composed of a vertical stack of screens under single and upward two phase flow

Rates of mass transfer were studied at a vertical array of closely packed screens under single and two phase (gas–liquid) flow by measuring the limiting current for the cathodic reduction of ferricyanide ions. Variables studied were screen characteristics (mesh number and wire diameter), physical properties of the solution, solution flow rate, gas flow rate and the effect of surface active agents. The single phase data were correlated by the equation:J = 0.52 Re _L ^-0.55 while the two phase data were correlated by the equations:Sh=0.87 Sc^0.33 Re _L ^0.35 Re_g ^0.12for the conditions 10 < Re < 125 and 1.4 < Re _g < 77; andSh=0.62 Sc^0.33Re _L ^0.11 Re_g ^0.25for the conditions 1.1 < Re _L < 22 and 1.4 < Re _g < 77. The presence of surfactant was found to reduce the rate of mass transfer in both single phase and two phase flow, the percentage reduction being higher in the case of single phase flow.     

A numerical study of the accelerating motion of a dense rigid sphere in non-newtonian power law fluids

The equations of motion of an accelerating sphere falling through non-Newtonian fluids with power law index n in the range 0.2 ≤ n ≤ 1.8 were integrated numerically using the assumption that the drag on the sphere was a function of both power law index and terminal Reynolds number, Re_t For 10^?2 ≤ Re_t ≤ 10³ both dimensionless time and distance travelled by the sphere under transient conditions showed a much stronger dependence on the flow behaviour index, n, for shear-thinning than for shear-thickening fluids. The form of this dependence is investigated here. Furthermore, results in four typical shear-thinning fluids suggested a strong correlation between the distance and time travelled by the sphere under transient conditions and the value of the fluid consistency index. The analysis reported herein is, however, restricted to dense spheres falling in less dense fluids, when additional effects arising from the Basset forces can be neelected.     

Effects of gas concentration on hydrodynamics of gas absorption in a microchannel

In this article, the effects of gas concentration on hydrodynamics of gas–liquid two-phase flow with mass transfer during gas absorption in a microchannel are investigated, by using 2-amino-2-methyl-1-propanol (AMP) solution to absorb mixtures of CO₂ and N₂ with various volume fractions. The concentration of CO₂ not only affects the driving force of gas–liquid mass transfer, but also affects the pressure drop of gas–liquid two-phase flow. The average linear velocity of the liquid phase is estimated by introducing the void fraction, which accurately characterizes the difference in the bubble velocity versus the liquid velocity. On this basis, the pressure drop model of gas–liquid two-phase flow with mass transfer in a microchannel is established. Through the pressure drop model, the influence mechanism of CO₂ concentration on the pressure drop during gas absorption in a microchannel is revealed.     

RTD studies in trickle bed reactors packed with porous particles

The residence time distribution (RTD) for liquid phase in a trickle bed reactor (TBR) has been experimentally studied for air-water system. Experiments were performed in a 15.2 cm diameter column using commerical alumina extrudates with D/d_p ratio equal to 75 to eliminate the radial flow differences. The range of liquid and gas flow rates covered was 3.76 < Re_L < 9.3 and 0 < Re_G < 2.92. The axial dispersion model was used to compute axial dispersion coefficient. The effect of liquid and gas flow rates on total liquid holdup and axial dispersion was investigated. The total liquid holdup has been correlated to liquid and gas flow rates.     

Prediction of The Kolmogorov Entropy Derived from CT Data in a Bubble Column Operated under The Transition Regime and Ambient Pressure

The Kolmogorov entropy (KE) algorithm was successfully applied to single source γ‐ray Computed Tomography (CT) data measured by three scintillation detectors in a 0.162 m‐ID bubble column equipped with a perforated plate distributor (163 holes × ?? 1.32 · 10^–3 m). The aerated liquid height was set at 1.8 m. Dried air was used as a gas phase, while Therminol LT (ρ_L = 886 kg m^–3, μ_L = 0.88 · 10^–3 Pa s, σ = 17 · 10^–3 N m^–1) was used as a liquid phase. At ambient pressure, the superficial gas velocity, u_G, was increased stepwise with an increment of 0.01 m s^–1 up to 0.2 m s^–1. Based on the sudden changes in the KE values, the boundaries of the following five regimes were successfully identified: dispersed bubble regime (u_G < 0.02 m s^–1), first transition regime (0.02 ≤ u_G < 0.08 m s^–1), second transition regime (0.08 ≤ u_G < 0.1 m s^–1), coalesced bubble regime consisting of four regions (called 4‐region flow; 0.1 ≤ u_G < 0.12 m s^–1), and coalesced bubble regime consisting of three regions (called 3‐region flow; u_G > 0.12 m s^–1). The KE values derived from three scintillation detectors in the first transition regime were successfully correlated to both bubble frequency and bubble impact. The latter was found to be inversely proportional to the bubble Froude number. The KE model implies that the bubble size in this particular flow regime is a weak function of the orifice Reynolds number (d_b = 7.1 · 10^–3Re₀^–0.05).     

An experimental study of non-newtonian fluid flow through fixed and fluidized beds of non-spherical particles

Extensive measurements of pressure drop in fixed beds, minimum fluidization velocity and expansion characteristics for beds of non-spherical particles are reported in the following ranges of conditions: 10^-3 ≤ Re ≤ 20; 0.66 ≤ n ≤ 1 and 0.41 ≤ ? ≤ 0.75. Based on an analysis of these results, it is illustrated that the existing frameworks originally developed for Newtonian fluid flow through beds of spherical particles are also satisfactory for power law fluid flow through beds of non-spherical particles, provided a volume equivalent diameter modified by a sphericity factor and a modified Reynolds number are used instead of their usual definitions.     

Improving the prediction of irrigated pressure drop in packed absorption towers

Various tools estimating irrigated pressure drop in gas–liquid counter‐current randomly dumped packed beds are carefully examined through the perception of a comprehensive database. The reported measurements consisting of Cs. 5000 experiments represent an important portion of the non‐proprietary information released in the literature. Artificial neural network (ANN) modeling is proposed to refine the accuracy and broadness in predicting the irrigated pressure drop across the bed. The ANN correlation [f_LCC = f(Re_G, Ga_G, Re_L, Ga_L, St_L, S_B, χ)] yields an average absolute relative error (AARE) of 20.0% and a standard deviation on the AARE of 19.8% for the whole database and remains in accordance with the physical evidence reported in the literature.     

Packing with Stamped Horizontal Lamellae Operating at Extremely Low Liquid Loads – III. Packing Pressure Drop

It has been discussed in previous papers [1–7] that the design of packings capable of operating at extremely low liquid superficial velocity allows the development of effective countercurrent flow packed bed columns even if the concentration of the absorbed component is very low, the absorption is an equilibrium process, and the gas is well soluble in the liquid phase. The construction of the new packing is described in [7]. The present paper reports the results of an investigation of the pressure drop for dry and irrigated packings up to a gas velocity equal to 3 m/s (F_G factor equal to 3.3 kg^1/2 m^–1/2 s^–1) as well as the equations for its calculation.     

Velocity profiles and frictional pressure drop for shear thinning materials in lid-driven cavities with fully developed axial flow

A finite element numerical study has been carried out on the isothermal flow of power law fluids in lid-driven cavities with axial throughflow. The effects of the tangential flow Reynolds number (Re_U), axial flow Reynolds number (Re_W), cavity aspect ratio and shear thinning property of the fluids on tangential and axial velocity distributions and the frictional pressure drop are studied. Where comparison is possible, very good agreement is found between current numerical results and published asymptotic and numerical results. For shear thinning materials in long thin cavities in the tangential flow dominated flow regime, the numerical results show that the frictional pressure drop lies between two extreme conditions, namely the results for duct flow and analytical results from lubrication theory. For shear thinning materials in a lid-driven cavity, the interaction between the tangential flow and axial flow is very complex because the flow is dependent on the flow Reynolds numbers and the ratio of the average axial velocity and the lid velocity. For both Newtonian and shear thinning fluids, the axial velocity peak is shifted and the frictional pressure drop is increased with increasing tangential flow Reynolds number. The results are highly relevant to industrial devices such as screw extruders and scraped surface heat exchangers.     

Design methodology for barrier‐based two phase flow distributor

The barrier‐based distributor is a multiphase flow distributor for a multichannel microreactor which assures flow uniformity and prevents channeling between the two phases. For N number of reaction channels, the barrier‐based distributor consists of a gas manifold, a liquid manifold, N barrier channels for the gas, N barrier channels for the liquid, and N mixers for mixing the phases before the reaction channels. The flow distribution is studied numerically using a method based on the hydraulic resistive networks (RN). The single phase hydraulic RN model (Commenge et al., 2002;48:345–358) is extended for two phases gas‐liquid Taylor flow. For Re_GL <30, the accuracy for the model was above 90%. The developed‐model was used to study the effects of fabrication tolerance and barrier channel dimensions. A design methodology has been proposed as an algorithm to determine the required hydraulic resistance in the barrier channels and their dimensions. This methodology is demonstrated using a numerical example. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Experimental and analytical study of countercurrent flow limitation in vertical gas/liquid flows

An experimental and analytical study of adiabatic countercurrent flow limitation (flooding) in single vertical ducts is reported. The experiments were carried out in a rectangular channel using saturated liquid and vapour of Refrigerant 12 (CCl₂F₂). The steady-state liquid delivery (flooding) curves as well as local pressure drop and void fraction distributions in the countercurrent flow were measured in a range of system pressures from p/p_crit = 0.16 to p/p_crit = 0.31, and for various total liquid injection rates and locations. The measured flooding curves j₁ = f(j_g) as well as pressure drop and void fraction during partial liquid delivery (j₁ < j₁ⁱⁿ) were not affected either by the axial liquid feed location or by the excess liquid rate carried upwards by the vapour. Moreover, for given flow conditions during flooding pressure drop and void fraction were essentially the same at different axial positions. Radial void fraction distributions evaluated from optical fibre probe data indicate an annular-type flow pattern. Based on this experimental evidence, a mechanistic core/film flow model was developed for the calculation of flooding. The analytical results are compared with the present high pressure and with comparable atmospheric pressure experimental data, showing reasonable overall predictions not only of the flooding curves, but also of the pressure drop in countercurrent flow.     

Gas dispersion in air‐lift reactors: Contribution of the turbulent part of the added mass force

Gas dispersion in an airlift reactor focusing on the closure law on turbulent contribution of added mass is presented. A data bank for bubbly flow in an airlift reactor is presented. The liquid velocity is measured by hot film anemometry and gas fraction and velocity are measured with an optical probe. The sensitivity of numerical simulations of gas dispersion to the modeling of turbulent contribution of added mass is shown. Without the turbulent contribution, the bubbles move toward the region where the turbulence is high and the pressure is low. When the turbulent contribution is introduced, the bubble migration towards the low pressure region is counter‐balanced and the void fraction profile is significantly modified. The modeling of the turbulent contribution of added mass is expressed in terms of the turbulent correlations in the gas phase, u_Gi^′u_Gj^′ , that can be related to the Reynolds stress in the liquid phase, u_i^′u_j^′ . © 2011 American Institute of Chemical Engineers AIChE J, 2011     

The effect of gas injection on the flow of immiscible liquids in horizontal pipes

The flow of two immiscible liquids and the influence of an additional inserted gas phase in horizontal pipes is investigated. The experiments are carried out in a transparent horizontal pipe with an inner diameter of 59 mm and a total length of 48 m. Experimental results are presented for the flow regimes of the two phase and three phase flow of oil, water and gas mixtures. The effect of phase inversion on the pressure drop is measured. The experimental results obtained for the three phase flow of oil, water and air indicate that drag reduction is possible by injecting gas in laminar flowing mixtures of oil and water. In the aerated slug flow regime of oil, water and air a water dominated and an oil dominated flow system can be distinguished. The pressure drop of the three phase flow system is of the magnitude as the pressure drop of the two phase flow of gas and the dominating liquid phase.     

Pressure Drop and Mass Transfer Study in Static Mixers with Gas Continuous Phase

The aim of this work was to characterize both the influence of the gas and the liquid flow rates on the pressure drop generated by static mixers type Sülzer, and on the mass transfer performances of these gas‐liquid contactors. The originality of this work rests on the use of the static mixers with a gas continuous phase. Several configurations were studied: vertical upward flow, vertical downward flow, and horizontal positions, with one to five mixing elements. It was concluded that the pressure drop is mainly generated by the gas phase, whatever the configuration chosen. Moreover, the volumetric mass transfer coefficients k_La found were lower than those obtained with the same static mixers used in classic conditions (that is with a liquid continuous phase), but greater than values obtained with classic reactors like bubble columns or packed columns. The efficiency of these gas‐liquid reactors was found high, as well as the energy dissipated, unfortunately.     

Regime transition in viscous and pseudo viscous systems: A comparative study

A comprehensive quantitative study on the effect of liquid viscosity (1 ≤ µ_L ≤ 1149 mPa‐s) on the local flow phenomena of the gas phase in a small diameter bubble column is performed using ultrafast electron beam X‐ray tomography. The internal dynamic flow structure and the bubble size distribution shows a dual role of the liquid viscosity on the hydrodynamics. Further, the effect of solid concentration (C_s = 0.05, 0.20) on the local flow behavior of the gas phase is studied for the pseudo slurry viscosities similar to the liquid viscosities of the gas–liquid systems. The effects of liquid and pseudo slurry viscosities on flow structure, bubble size distribution, and gas phase distribution are compared. The bubble coalescence is significantly enhanced with the addition of particles as compared to the system without particles for apparently same viscosity. The superficial gas velocity at which transition from homogeneous bubbly to slug flow regime occurs is initiated by the addition of particles as compared to the particle free system for apparently same viscosity. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3079–3090, 2014     

Correlating gas–liquid co‐current flow hydrodynamics in packed beds using the F‐function concept

A phenomenological model based on the generalization of the single‐phase Forchheimer equation was recently proposed for predicting pressure drop and phase saturations in gas–liquid co‐current horizontal and downward high‐pressure packed beds. Here, we extend the model to packed‐bubble (co‐current upflow) and trickle‐bed operation using phase saturation power laws similar to Corey relative permeabilities. The power‐law exponents were fitted using a wide pressure gradient and liquid saturation databank in co‐current up/downward packed‐bed flows. It was found that this approach, as well as other in the literature developed for down‐flow reactors apply also to upward flows; the prediction accuracy was comparable for both flow directions to existing literature approaches. Copyright © 2004 Society of Chemical Industry     

Laminar dispersion of polymer solutions in helical coils

In the present study the step response experiments were carried out with power law fluids in two helical coils to examine the suitability of axial dispersed plug flow model in describing the laminar dispersion of non-Newtonian fluids in helical coils. The ranges of variables covered are 10 ≤ λ ≤ 100,0.01 ≤ N_Regen ≤ 2.5,0.001 ≤ N_De ≤ 0.77 and 0.035 ≤ τ ≤ 1.33. It is found that coiling results in reduced dispersion to that in a straight tube.