Wake shedding and circulatory flow in bubble and droplet-type contactors

A review of published work on continuous phase circulation in spray columns, and on attached wake volumes for single droplets, revealed an apparent paradox in that reported values of the former were an order of magnitude greater than the latter when expressed as a ratio of the dispersed phase flow. These results were confirmed in experiments using a photochromic tracer to reveal the entrainment and circulatory flow.Theoretical considerations show that droplets translate an amount of continuous phase relative to their own volume of 1.5C_D/d per unit distance traversed. Droplets carry with them an attached wake (“cap”) which for Re_d< about 200 is effectively permanent, the translated continuous phase passing around droplet and “cap” leaving a wake trail. At Re_d > 200 a fraction j of the translated continuous phase accumulates in the “cap”, which becomes unstable and sheds a fraction s_av as toroids at regular intervals of height z_s. Estimated values are given for j, s_av, and z_s.This result is extended to the case of a continuous droplet flow, leading to an expression for the rate of increase in circulatory flow of continuous phase in the central core with height above the droplet distributor. This flow is balanced by an increasing momentum loss to the wall until a steady state is reached. The implications of this result on the performance of spray columns is discussed.     

Effect of surface properties on the flow characteristics and mass transfer performance in microchannels

In this work, the influence of surface properties on the flow characteristics and mass transfer performance of two immiscible liquids are investigated in the opposed and cross-flow configuration microchannels, as the volumetric flux ratio is far <1. For visually identifying flow patterns in transparent PMMA microchannels, dyed de-ionized water and kerosene are selected as test fluids. To investigate the mass transfer characteristics in stainless steel microchannels, water–succinic acid–n-butanol is chosen as a typical system. Reynolds number varied between 11 and 275. Only at low Re_M numbers, the dispersed phase flow pattern can occur in the opposed T-shaped PMMA microchannel before surface modification. At higher Re_M numbers, only the continuous phase flow pattern (parallel flow) is observed before and after surface modification. Moreover, the fluctuation amplitude after surface modification is larger than before surface modification at the opposed T-junction. To eliminate the effects of the sampling intervals and separation process of oil–water two phases on mass transfer performance, one new testing method is established by manufacturing the novel oil–water separator based on the principle of siphon. For the conditions applied during the study, the overall volumetric mean mass transfer coefficients range from 0.19 to 11.96 s^?1, which are one or three orders of magnitude higher than those in typical conventional large scaled contactors.     

Predicting turbulence modulations at different Reynolds numbers in dilute-phase turbulent liquid–particle flow simulations

The present work examines the predictive capability of two-fluid CFD model based on the kinetic theory of granular flow in capturing the Reynolds number (Re) dependence of fluid-phase turbulence modulations in dilute-phase turbulent liquid–particle flows. The model predictions are examined using turbulent liquid–particle flow data in a vertical pipe at Re=17,000, 48,000, 65,000, and 76,000 in the particle concentration range of between 0.5% and 4.0% (v/v). The experimental data indicate that the fluid-phase turbulence intensities are enhanced with respect to the single-phase flow at Re≤48,000 but are attenuated at Re≥65,000. The simulation results indicate that the CFD model can successfully predict the turbulence modulations at Re=17,000, 65,000, and 76,000 both qualitatively and quantitatively, but not at the intermediate Re of 48,000. In this regard, (1) different drag correlations to describe the fluctuating drag force are needed to accurately predict the trends in the turbulence modulations as a function of Re, and (2) appropriate combinations of the drag correlations and turbulence closure models to describe the long-range fluid–particle interactions must be identified in each phase at different Re in order to accurately predict the turbulence modulation, granular temperature, and particle radial concentration profile.     

Investigation of laminar flow in a stirred vessel at low Reynolds numbers

Many mixing applications involve viscous fluids and laminar flows where the detailed as well as overall flow structures are important. In order to understand the fluid dynamic characteristics of low Re laminar flows in mixing vessels, the flow induced by a Rushton impeller for three Re namely, 1, 10 and 28, was studied both experimentally and computationally. It was found that for the highest Re, the flow exhibited the familiar outward pumping action associated with radial impellers under turbulent flow conditions. However, as the Re decreases, the net radial flow during one impeller revolution was reduced and for the lowest Re a reciprocating motion with negligible net pumping was observed. This behaviour has not been reported in the literature in the past and represents a highly undesirable flow pattern from the standpoint of effective mixing. The CFD results successfully reproduced this behaviour. In order to elucidate the physical mechanism responsible for the observed flow pattern, the forces acting on a fluid element in the radial direction were analysed. The analysis indicated that for the lowest Re, the material derivative of radial velocity near the blade tip is small thus a balance exists between pressure and viscous forces; the defining characteristic of creeping flow. The velocity and pressure forces are in phase because the velocity is driven by the pressure field generated by the rotation of the impeller. Based on these findings, a simplified analytic model of the flow was developed that gives a good qualitative as well as quantitative representation of the flow.     

Drag on a single fluid sphere translating in power-law liquids at moderate Reynolds numbers

A numerical investigation has been carried out to obtain the steady state drag coefficients and flow patterns of a single Newtonian fluid sphere sedimenting in power-law liquids. A finite difference method based simplified marker and cell (SMAC) algorithm has been implemented on a staggered grid arrangement to solve the continuity and momentum equations. For both phases, the convective terms have been discretized using the quadratic upstream interpolation for convective kinematics (QUICK) scheme, and diffusive and non-Newtonian terms with central differencing scheme. An exponential transformation has been applied in the radial direction for the continuous phase computational domain. In order to ensure the accuracy of the solver, extensive validation has been carried out by comparing the present results with the existing literature values for a few limiting cases. Further, in this study the effects of the Reynolds number (Re_o), internal to external fluid characteristic viscosity ratio (k) and power-law index (n_o) on the continuous phase flow field, pressure drag (C_dp), friction drag (C_df) and total drag (C_D) coefficients have been analyzed over the range of parameters: 5?Re_o?500, 0.1?k?50 and 0.6?n_o?1.6. Based on numerical results obtained in this work, a simple correlation has been proposed for the total drag coefficient, which can be used to predict the rate of sedimentation of a fluid sphere in power-law liquids.     

Analysis and interpretation of residence time distribution experimental curves in FM01-LC reactor using axial dispersion and plug dispersion exchange models with closed-closed boundary conditions

The liquid phase mixing flow pattern at low (20 < Re < 120) and intermediate liquid flow rate (120 < Re < 400) was studied by means of residence time distribution (RTD) experimental curve in an up-flow Filter Press electrochemical reactor (FM01-LC) bench scale. For this purpose, a plastic turbulence promoter was used with stainless-steel and platinised titanium structural meshes as electrodes in channel configuration. To visualize and determine the mixing flow pattern in the liquid phase, the stimulus-response technique was employed using dextran blue (D_M = 1.058 × 10⁻¹¹ m² s⁻¹, 25 °C, in water) as model tracer. A theoretical analysis and approximation RTD experimental curves with axial dispersion model (ADM) and plug dispersion exchange model (PDE), with “closed-closed vessel” boundary conditions were used in order to establish a better approximation of the axial dispersion, stagnant zones, channelling and by-pass (preference flow) effects present at low and intermediate Re. RTD curves show that the liquid flow pattern in the FM01-LC deviates considerably from axial dispersion model at low Re, where the FM01-LC exhibits large channelling, stagnant zones, and dead zone. The PDE model represents fairly this deviation from ideal flow (less dead zone).     

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.     

Two-dimensional unsteady flow of power-law fluids over a cylinder

The unsteady flow of incompressible power-law fluids over an unconfined circular cylinder in cross-flow arrangement has been studied numerically. The two-dimensional (2-D) field equations have been solved using a finite volume method based solver (FLUENT 6.3). In particular, the effects of the power-law index (0.4?n?1.8) and Reynolds number (40?Re?140) on the detailed kinematics of the flow (streamline, surface pressure and vorticity patterns) and on the macroscopic parameters (drag and lift coefficients, Strouhal number) are presented in detail. The periodic vortex shedding and the evolution of detailed kinematics with time are also presented to provide insights into the nature of flow. The two-dimensional flow transits from steady to unsteady behaviour at a critical value of the Reynolds number Re∼(40-50) and the von-Karman vortex street is observed beyond the critical Reynolds number (Re). Obviously, both the lift coefficient and Strouhal number values are zero for the steady flow, but their values increase with the increasing Reynolds number (Re) in the unsteady flow regime. For highly shear-thickening fluids (n=1.8), the flow becomes unsteady at Re=40 and unsteadiness in the flow appears at Re=50 for all values of power-law index (n). As expected, the evolution of the kinematics and vortex shedding show a complex dependence on the flow parameters near the transition in the flow. For a fixed value of the Reynolds number (Re), the drag coefficient increases and lift coefficient decreases with increasing value of the power-law index (n). For a fixed value of the power-law index (n), the drag coefficient gradually increases with the Reynolds number (Re). Similar to the drag coefficient, lift coefficient also shows a complex dependence on the power-law index (n) near the transition zone. The value of the Strouhal number (St) decreases with the increasing value of the power-law index (n) at a fixed value of the Reynolds number (Re).     

CFD evaluation of internal manifold effects on mass transport distribution in a laboratory filter-press flow cell

The internal manifold geometry strongly influences the flow distribution inside an electrochemical reactor. The mass transport coefficient is a function of the flow pattern and is a key parameter in successful electrochemical reactor design and scale-up. In this work, a commercial computational flow dynamics (CFD) package was used to describe the flow pattern in the FM01-LC reactor at controlled volumetric flow rates (corresponding to mean linear flow velocities past the electrode surface between 0.024 and 0.11 m s^?1). Numerical Re numbers were obtained for each local flow velocity at different positions in the reactor channel. From a known mass transport correlation (based on dimensionless groups, i.e. Sh, Re, Sc), numerical k _m values were obtained (in the range 200 < Re < 1,000) at different positions in the reactor channel. Computed k _m numbers are compared against experimental values. This computational approach could be useful in reactor design or selection since it facilitates a fast, preliminary reactor flow and mass transport characterisation without experimental electrochemical measurements.     

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.     

Mass transfer from ensembles of fluid spheres to a power-law liquid at moderate Reynolds and Peclet numbers

The steady convective mass transfer from ensembles of mono-size Newtonian fluid spheres to power-law liquids has been studied at moderate Reynolds and Peclet numbers. The species continuity equation segregated from momentum equations has been solved numerically using a finite difference method. A simple cell model has been used to account for the modification of the flow field due to the neighbouring droplets. Extensive numerical results have been obtained which elucidate effects of the Reynolds number (Re_o), Schmidt number (Sc), power-law index (n_o), internal to external fluid characteristic viscosity ratio (k) and the volume fraction of the dispersed phase (Φ) on the rate of mass transfer. The ranges of parameters considered herein are: 1?Re_o?200, 1?Sc?10000, 0.6?n_o?1.6, 0.1?k?50 and 0.2?Φ?0.6. For shear-thinning fluids (n_o<1), the rate of mass transfer is somewhat enhanced whereas for shear-thickening fluids (n_o>1), it decreased as compared to that in Newtonian fluids (n_o=1). A simple predictive correlation has been proposed which can be used to estimate the rate of mass transfer in liquid-liquid systems in a new application involving power-law continuous phase.     

Reynolds number effects in a simple planetary mixer

Planetary mixers are widely used in a diverse range of industrial applications. This paper presents an experimental investigation of mixing in a planetary mixer, and a comparison with numerical simulations based on a simple mathematical model of the flow. The model allows an exact expression for the velocity field in the Stokes flow regime, apparently the first for a mixer with genuinely moving parts, which permits accurate numerical tracking of material interfaces. Experiments performed at low Reynolds number (Re?1) show good agreement with corresponding numerical simulations, but as the Reynolds number is increased, the agreement between experiments and Stokes-flow numerics worsens, in a manner that reflects improving experimental mixing quality. Specifically, we find that islands of poor mixing shrink as Re increases. Our results suggest that, while numerical simulations in the Stokes flow regime may be used as a ‘sieve’ to select good mixing protocols at small Re, experiments or computational fluid dynamics simulations are required properly to evaluate mixing protocols operated at finite Reynolds numbers.     

Wall effects on terminal velocity of small drops in newtonian and non-newtonian fluids

This work investigated the extent of the wall effects on the free falling velocity of fluid spheres in quiescent Newtonian and pseudoplastic non-Newtonian media. The terminal velocity has been measured as a function of the physical properties of the both dispersed and continuous phases, and of falling tube diameter. It is shown that inthecreeDing flow region (Re « 1) and for the conditions when the viscosity of the dispersed phase is much smaller khan khat of khe continuous phase, the extent of wall effect is determined only by the ratio of the sizes of the settling fluid sphere and of the vessel. The same analytical relation correlates well the data for both Newtonian and non Newtonian continuous media in the range d/D < 0.45.     

Calcium deficient hydroxyapatite by precipitation: Continuous process by vortex reactor and semi-batch synthesis

Precipitation of calcium deficient hydroxyapatite nanoparticles in an environmentally benign manner by using only dilute solutions of calcium hydroxide and phosphoric acid without pH adjustment and addition of other chemicals, and water, being the only by-product was investigated by using continuous flow Vortex Reactor (VR) and Semi-Batch Reactor (SBR). The effect of hydrodynamics by changing the Reynolds number of the jets providing residence times of 8.4 ms to 4.37 s for VR, and by changing the stirrer speed between 100 rpm (Re = 2656) and 1000 rpm (Re = 26560) for SBR, on the particle size, particle size distribution, and morphology of the particles was investigated for both systems. It has been shown that it is possible to produce pure phase hydroxyapatite nanoparticles in the desired morphology by changing production system, without resorting to additives. While VR produced rod-like particles with the crystallite size around 4 nm, SBR produced spherical particles with the crystallite size of around 5 nm.     

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.     

Effect of the Re number on heat and mass transport in a catalytic monolith

The numerical investigation of inter-phase heat transfer in a catalytic combustor, under laminar flow regime at different values of the Re number, is performed by means of a 2D axi-symmetric model of a single monolith channel. Numerical results highlight that axial diffusion comes to play an important role in the ignition region also at high convective fluxes (high Re) due to the strong flow perturbation accompanying light-off, with the consequences that: (a) the ignition position is not a linear function of contact time, as it would be expected at high Re; (b) the heat and mass transfer between surface and bulk gas phase are non-linearly affected by Re, especially in the entrance and in the ignition regions.A previously developed correlation for Nu and Sh is, hence, extended to include the effect of the Re number on heat and mass fluxes, enabling the prediction of the local value of Nu and Sh in the main features, and in particular the enhancement in the ignition region and the dependence on Re.     

Mass transfer from a single fluid sphere to power-law liquids at moderate Reynolds numbers

The steady-state convective inter-phase mass transfer from a single Newtonian fluid sphere (free from surfactants) to a continuous phase with power-law viscosity has been studied at moderate Reynolds and Schmidt numbers under the conditions when the resistance to mass transfer in the dispersed phase is negligible. The species continuity equation, segregated from the momentum equations of both phases, has been numerically solved using a finite difference method. The effects of the Reynolds number (Re_o), power-law index (n_o), internal to external fluid characteristic viscosity ratio (k) and Schmidt number (Sc) on the local and average Sherwood number (Sh) have been analysed over the following ranges of conditions: 5?Re_o?200, 0.6?n_o?1.6, 0.1?k?50 and 1?Sc?1000. It has been observed that irrespective of the values of the Reynolds number and of the power-law index, as the value of k increases the average Sherwood number decreases for intermediate to large values of the Peclet number. As the value of the power-law index increases, the rate of mass transfer decreases for all values of the Reynolds number and the characteristic viscosity ratio thereby suggesting that shear-thinning behaviour facilitates mass transfer, whereas shear-thickening behaviour impedes it. Based on the present numerical results, a simple predictive correlation is proposed which can be used to estimate the rate of inter-phase mass transfer of a fluid sphere sedimenting in power-law liquids.     

Resistance properties of coal-water paste flowing in pipes

On the basis of analyzing the mechanism of coal-water paste (CWP) slip flow, the similitude criterion, known as general Reynolds number Re_g which can characterize the state of non-Newtonian fluid flow in pipes, was put forward. The energy loss coefficient of CWP laminar flow has the same form as Newtonian fluid, i.e. λ=64/Re_g. Re_g holds good not only for the slip flow of non-Newtonian fluid, but also for slip-free flow as a steady-state laminar flow in pipes. The results obtained from experiments show that the energy loss coefficient of CWP laminar flow in pipes has the same form as Newtonian fluid.     

Effect of the rotor shape on the mixing characteristics of a continuous flow Taylor-vortex reactor

Macro- and micromixing in a continuous flow Taylor-vortex reactor with novel ribbed rotors were investigated and compared to the features of a classical cylindrical rotor. The characterisation was performed in a wide hydrodynamic range (40<Ta<2500 and 0.03<Re<0.51) through tracer experiments and the analysis of the rotor power consumption. Additionally, the flow patterns were visualised by using a rheoscopic fluid. The results show that the novel rotors equipped with ribs immobilise and stabilise the vortices. As compared to cylindrical rotors, micromixing is clearly enhanced while axial dispersion can be simultaneously reduced. Through the use of ribbed rotors, the operational window can be broadened considerably, in which the reactor runs at very low or moderate extent of macromixing.