Prediction of 10-mm Hydrocyclone Separation Efficiency Using Computational Fluid Dynamics

It has been estimated that particles within the flow field of a 10-mm or mini-hydrocyclone experience local accelerations as high as 10 000 gravitation units. Although their operation is simple, the turbulent, swirling flow field within these devices offers a unique challenge to computational fluid dynamics (CFD). In addition to the computational challenge, very few experimental measurements have been reported in the literature on the flow field of the mini-hydrocyclone to which the CFD results may be compared. This research addresses the issue of predicting the separation efficiency of a volute entry 10-mm hydrocyclone. The feed flow rate is 4.5 litres/m (l/m) yielding a Reynolds number (based on the hydrocyclone diameter) of 9500 and a swirl number of 8.4. Using previously published flow simulation data, a multiphase system (consisting of a discrete oil phase and a continuous water phase) was analyzed for the purpose of obtaining separation information. These separation data were compared with laboratory separation experiments. Results indicate differences less than 20% for each droplet diameter. This information increased the level of confidence in the simulated flow field since there are no published velocity field data for the 10-mm hydrocyclone.     

The confined impeller stirred tank (CIST): A bench scale testing device for specification of local mixing conditions required in large scale vessels

A new stirred tank geometry, the confined impeller stirred tank (CIST), was designed to provide repeatable testing of the effect of mixing on the performance of chemical additives at the bench scale. The CIST (T = 0.076 m, H = 3T) is filled with five or six impellers. Three impeller geometries were tested: A310, Rushton and Intermig. This paper presents the following hydrodynamic characteristics of the CIST: power number, flow number, momentum number, velocity profiles at different locations in the tank and the transition point from fully turbulent to transitional flow. Based on the scaled velocity profiles, the CIST was able to keep the flow turbulent at Re < 2000 for Rushton turbines and 3200 for Intermigs. The ratio ?_max/?_average was lower for the CIST than for a conventional stirred tank, indicating that the energy dissipation is more uniformly distributed in the CIST. The CIST consistently maintains turbulent flow down to a Reynolds number 10× smaller than that needed in a conventional stirred tank.     

Experimental and CFD investigation of convective heat transfer in helically coiled tube heat exchanger

Experimental studies on isothermal steady state and non-isothermal unsteady state conditions were carried out in helical coils for Newtonian as well as for non-Newtonian fluids. Water and glycerol–water mixture (10 and 20% glycerol) were used as Newtonian, and 0.5–1% (w/w) dilute aqueous polymer solutions of Sodium Carboxy Methyl Cellulose (SCMC) and Sodium Alginate (SA) as non-Newtonian fluids are used in this study. These experiments were performed for coil curvature ratios as δ = 0.0757, 0.064 and 0.055 in laminar and turbulent flow regimes (total 258 tests). The CFD analyses for laminar and turbulent flow were carried out using FLUENT 12.0.16 solver of CFD package. The CFD calculation results (Nu_i, U, T₂ and Tw_o) for laminar and turbulent flow are compared with the experimental results and the work of earlier investigators which were found to be in good agreement. For the first time, an innovative approach of correlating Nusselt number to dimensionless number, ‘M’, Prandtl number and coil curvature ratio using least-squares power law fit is presented in this paper which is not available in the literature. Several other correlations for calculation of Nusselt number for Newtonian and non-Newtonian fluids, and two correlations for friction factor in non-Newtonian fluids (based on 78 tests and 138 tests) are proposed. These developed correlations were compared with the work of earlier investigators and are found to be in good agreement.     

A numerical study of particle wall-deposition in a turbulent square duct flow

The deposition of dense solid particles in a downward, fully developed turbulent square duct flow at Re_τ = 360, based on the mean friction velocity and the duct width, is studied using large eddy simulations of the fluid flow. The fluid and the particulate phases are treated using Eulerian and Lagrangian approaches, respectively. A finite-volume based, second-order accurate fractional step scheme is used to integrate the incompressible form of the unsteady, three-dimensional, filtered Navier-Stokes equations on an 80 × 80 × 128 grid. A dynamic subgrid kinetic energy model is used to account for the unresolved scales. The Lagrangian particle equation of motion includes the drag, lift, and gravity forces and is integrated using the fourth-order accurate Runge-Kutta scheme. Two values of particle to fluid density ratio (ρ_p/ρ_f = 1000 and 8900) and five values of dimensionless particle diameter (d_p/δ × 10⁶ = 100, 250, 500, 1000 and 2000, δ is the duct width) are studied. Two particle number densities, consisting of 10⁵ and 1.5 × 10⁶ particles initially in the domain, are examined.Variations in the probability distribution function (PDF) of the particle deposition location with dimensionless particle response time, i.e. Stokes number, are presented. The deposition is seen to occur with greater probability near the center of the duct walls, than at the corners. The average streamwise and wall-normal deposition velocities of the particles increase with Stokes number, with their maxima occurring near the center of the duct wall. The computed deposition rates are compared to previously reported results for a circular pipe flow. It is observed that the deposition rates in a square duct are greater than those in a pipe flow, especially for the low Stokes number particles. Also, wall-deposition of the low Stokes number particles increases significantly by including the subgrid velocity fluctuations in computing the fluid forces on the particles. Two-way coupling and, to a greater extent, four-way coupling are seen to increase the deposition rates.     

Engineering study of continuous supercritical hydrothermal method using a T-shaped mixer: Experimental synthesis of NiO nanoparticles and CFD simulation

In the synthesis of metal oxide fine particles by continuous supercritical hydrothermal method, rapid mixing of starting solution with supercritical water is a key factor for producing nanoparticles that have a narrow size distribution. In this paper, continuous hydrothermal synthesis of NiO nanoparticles from Ni(NO₃)₂ aqueous solution at 400 °C and 30 MPa was carried out with T-shaped mixers and the effect of inner diameter, flow rate, and mixing directions on the particle size was examined. The computational fluid dynamics (CFD) simulation of the mixers was performed to evaluate the heating rate of the starting solution. When the inner diameter of the T-shaped mixer was decreased from 2.3 to 0.3 mm and the flow rate was increased from 30 to 60 g/min, the produced NiO particle size decreased remarkably from 54.3 to 20.1 nm. This trend of the decrease in particle size could be described as a function of the heating rate. The experimental and CFD results showed the detail regions of local heating that correlated with the NiO nanoparticle size.     

Two regime transitions to pseudo-homogeneous and heterogeneous bubble flow for various liquid viscosities

The gas hold-up variation and regime transition were investigated with different liquid viscosities ranging from 1.0 mPa s to 31.5 mPa s using a 0.15-m-in-diameter bubble column. In contrast to common observations, the gas hold-up graph with the superficial gas velocity could be categorized into three flow regimes: homogeneous, pseudo-homogeneous and heterogeneous flow regimes. The formation of large bubbles caused a transition from the homogeneous to the pseudo-homogenous flow regime, in which large bubbles rose vertically without oscillatory turbulence. According to the results from the dynamic gas disengagement (DGD) technique, large bubbles began to form at the transition superficial gas velocity to the pseudo-homogeneous flow regime. The transition to a heterogeneous flow regime was initiated by the turbulent movement of large bubbles. The transition superficial velocities to pseudo-homogeneous and heterogeneous flow regimes, u_t1 and u_t2, decreased with increasing liquid viscosity below a critical viscosity and converged to a certain value above that viscosity. However, the correlations from the literatures could not make a reasonable estimation of the transition superficial velocities because they did not consider the possible transition to a pseudo-homogeneous flow regime. Therefore, the two transition points should be predicted separately.     

Electrospinning and characterization of highly sulfonated polystyrene fibers

Nanofibers of highly sulfonated (IEC ∼4.5 meq/g) polystyrene (SPS) were successfully electrospun. To accomplish this, the process of electrospinning this difficult-to-spin material was studied in detail. Fiber quality was optimized by manipulating the process and solution variables to fabricate continuous bead-free fibers. Bead-free fibers (average diameter 260 nm) were electrospun from 25 wt% SPS (500 kDa) in DMF at an electrode separation of 10 cm, an applied voltage of 16.5 kV and a flow rate of 0.3 mL/h. With increasing solution concentration, and thereby the solution viscosity, the morphology changed from beads to bead-on-string fibers to continuous cylindrical fibers. Beaded fibers and continuous bead-free fibers of SPS (500 kDa) could be spun at ∼2 C_e and 3.5 C_e, respectively, where C_e is the entanglement concentration determined from solution-viscosity measurements. The onset of formation of beaded fibers coincided with a sharp transition in the scaling of the storage modulus-concentration relationship.     

Aggregation in dilute solutions of high molar mass poly(ethylene) oxide and its effect on polymer turbulent drag reduction

We apply methods of dynamic light scattering (DLS) and fluid mechanics to quantitatively establish the role of aggregation in the turbulent drag reduction of high molar mass poly(ethylene oxide) (PEO) solutions. By means of DLS, we show that the dilute aqueous solutions of high molar mass PEO (M_w ∼ 4 × 10⁶ g/mol) are aggregated and that this aggregate structure can be manipulated by addition of the chaotropic salt guanidine sulfate (GuS) or the divalent salt magnesium sulfate (MgSO₄). In aqueous solution, we find Γ ∼ q^2.8±0.1, where Γ is the DLS correlation function relaxation rate and q is the scattering vector. This scaling is consistent with internal motions of a large coil or aggregate. Addition of salt progressively decreases the scaling to Γ ∼ q^2.0±0.1 (at 0.5 M of MgSO₄) consistent with center-of-mass diffusion of isolated coils. We further find that manipulating the aggregation state of PEO with MgSO₄ shifts the critical condition for onset of turbulent drag reduction at dilute concentrations in pipe flow by a factor of 2.5. Because this critical condition is inversely proportional to the viscoelastic relaxation time of the polymer solution, we conclude that the aggregation state and the turbulent drag reduction behavior of PEO are strongly correlated. This correlation definitively confirms prior speculation (Cox et al. Nature 1974;249; Vlachogiannis et al. Physics of Fluids 2003;15(12)) that the high molar mass PEO commonly used in literature studies of turbulent drag reduction is in a state of aggregation. Furthermore, the quantitative differences in quiescent DLS characterization and turbulent flow pressure drop measurements suggest that high molar mass PEO undergoes flow-induced de-aggregation in transport systems with shear stresses as low as 0.5 Pa.     

Liquid backmixing in oscillatory flow through a periodically constricted meso-tube

This paper deals with the measurement and modelling of axial liquid dispersion in a 4.5 mm internal diameter tube provided with smooth-periodic constrictions (meso-tube) in steady and oscillatory flow conditions. The residence time distribution (RTD) in the meso-tube was monitored for a range of fluid oscillation frequency (f) and amplitude (x₀) at laminar flow. The RTD response was modelled with three hydrodynamic models: (i) tanks-in-series, (ii) tanks-in-series with backflow and (iii) plug flow with axial dispersion. The steady flow through the meso-tube at flow rates up to 21.30 ml/min resulted in broad RTDs, mainly due to the parabolic velocity profile. The use of fluid oscillations allowed a fine-control of the axial liquid dispersion in the meso-tube due to generation of secondary flow in the regions between the constrictions. The axial dispersion coefficient D was reduced by up to 13-fold in comparison with the steady flow situation. Values of x₀ ≤ 1 mm and f = 10 Hz generally resulted in a maximum reduction in axial dispersion through, therefore maximum improvements in RTD. The tanks-in-series model was generally not capable of predicting RTDs in the meso-tube. The potential of this platform for the continuous, sustainable production of added-value products is herein demonstrated.     

CFD simulation of Taylor–Couette flow in scraped surface heat exchanger

The flow between two concentric cylinders which is termed as Taylor–Couette flow has been studied in scraped surface heat exchanger with and without blades. Shear rate in annular flow with and without blades was measured by Dumont et al. (2000a) using electrochemical method and determined the onset of Taylor vortices at specific Taylor number in both cases for Newtonian flow. CFD simulations have been carried out to determine the transition zone from laminar Couette flow to Taylor vortex flow using the same geometry for which Dumont et al. (2000a) had carried out the experiments. The Reynolds stress model (RSM) and k–? model are used for Taylor vortex flow (Ta > 300) to characterize the flow pattern in annular flow and SSHE respectively. The aim of the present work is to analyze the effect of rotating scraper on the existing flow patterns in simple annular flow using CFD simulations.     

Nitrogen dilution effect on flame stability in a lifted non-premixed turbulent hydrogen jet with coaxial air

The nitrogen dilution effect on flame stability was experimentally investigated in a lifted non-premixed turbulent hydrogen jet with coaxial air. Hydrogen gas was used as the fuel and coaxial air was injected to initiate flame liftoff. Hydrogen was injected into an axisymmetric inner nozzle (d_F = 3.65 mm) and coaxial air jetted from an axisymmetric outer nozzle (d_A = 14.1 mm). The fuel jet and coaxial air velocities were fixed at u_F = 200 m/s and u_A = 16 m/s, while the mole fraction of the nitrogen diluent gas varied from 0.0 to 0.2 with a 0.1 step. For the analysis of the flame structure and the flame stabilization mechanism, the simultaneous measurement of PIV/OH PLIF was performed. The stabilization point was in the region of the flame base with the most upstream region and was defined as the point where the turbulent flame propagation velocity was found to be balanced with the axial component of the local flow velocity. The turbulent flame propagation velocity increased as the nitrogen mixture fraction decreased. The nitrogen dilution makes the flame structure more premixed. That is, the stabilization mechanism shifts from edge flame propagation based mechanism toward premixed flame propagation based mechanism. We concluded that the turbulent flame propagation velocity was expressed as a function of the turbulent intensity and the axial strain rate, even though the mole fraction of the nitrogen diluent varied.     

CFD studies of solids hold-up distribution and circulation patterns in gas-solid fluidized beds

Numerical results for a gas-fluidized bed using a 2D Eulerian model including the kinetic theory for the particulate phase were provided. The circulation patterns for various operating conditions were discussed. Modeling parameters of drag function, algebraic and transport equations of granular temperature, frictional stress model, turbulent model and discretization scheme were investigated for a bed with different gas distributors and a slotted draft tube. CFD results showed that the drag model is an important hydrodynamics parameter for gas-fluidized beds with various gas distributors. Transport and algebraic equations for granular temperature should be utilized, respectively, for beds including partial and complete sparging at U_g = 2.18 m/s. Frictional stresses play an important role for the beds containing partial sparging with and without draft tube. Discretization schemes should be examined to achieve better results. The Simonin and k-ε turbulent models can improve the CFD results at high gas velocities. Considering perforated plate distributor improves the results.     

Phase transitions in hydrothermal K2HPO4 solutions

A 0.1 M potassium phosphate (K₂HPO₄) solution was reacted in a flow-through cell pressurized to 22 MPa. Reduced light transmission through the cell windows was observed at a setpoint temperature ≥400 °C, along with a decrease in effluent conductivity, but with no effect on flow. These observations suggest solution separation at ∼360 °C, with accumulation of a salt-concentrated liquid in the cell body and transition of a dilute liquid to a supercritical fluid at temperature >374 °C. High-pressure differential scanning calorimetry experiments confirm an onset temperature of 354 °C with an endothermic transition at 377 °C and 22 MPa. For apparent density, ρ = 150-500 kg/m³, the average transition temperature for 0.1 M solutions, 375 ± 5 °C, is slightly elevated relative to that of water at 371 ± 4 °C. Highest deviation for 1.0 M solutions, 365 ± 15 °C, is attributed to increased K₂HPO₄ hydrolysis and polymerization reactions.     

Experimental and CFD studies of fluid dynamic gauging in duct flows

Experimental and computational fluid dynamics (CFD) studies of the technique of fluid dynamic gauging (FDG) in duct flows have been performed. Experiments were performed using a stainless steel gauging nozzle located on the centreline of a Perspex duct of square cross section. The test fluid was water, flowing through the duct at 0.0077-0.74 m/s (Re_duct 116-11 100). The success of the experiments was confirmed by the results of Tuladhar et al. [2003. Dynamic gauging in duct flows. Canadian Journal of Chemical Engineering 81, 279-284].For the first time, CFD has been applied to simulate FDG in an imposed flow for steady, incompressible, laminar flows. Experimental data and simulation results agreed to within 6%, supporting the validity of both the experiments and the assumptions underpinning the simulation. CFD simulations predicted the stresses beneath the lip of the nozzle and confirmed the practical working range of the gauge (0.1<h/d_t<0.25). This is a major achievement, proving that CFD can be used to model this flow-FDG accurately, which is valuable for future work in this area, namely fouling in food, crude oil and cross-flow membrane systems.     

Mass transfer in vertical liquid-solids flow of coarse particles

Wall-to-bed mass transfer in the hydraulic transport of spherical glass particles was studied. The experiments were performed by transporting spherical glass particles 1.20, 1.94 and 2.98 mm in diameter with water in a 25.4 mm I.D. tube. The mass transfer coefficients were determined by following rate of dissolution of a segment of the transport tube prepared from benzoic acid.In the runs in hydraulic transport, the Reynolds number of the tube varied between 1826 and 27597. The loading ratio (G_p/G_f) was between 0.026 and 0.474, and the fluid superficial velocity was between 0.267 · U_t and 4.904 · U_t, where U_t represents the single particle terminal velocity. For these ratios, the voidage ranged from 0.7123 to 0.9228.Also, wall-to-bed mass transfer in the single phase flow regime was studied. In the runs without particles, the Reynolds number of the tube varied between 122 and 39132. The data for the mass transfer factor (j_D) in single phase flow are correlated for turbulent flow regime, using the Chilton-Colburn's type equations, j_D = f(Re). Those investigations were conducted in aim to compare with results for wall-to-bed mass transfer in hydraulic transport.The data for wall-to-bed mass transfer (j_D) in hydraulic transport of spherical particles were correlated by treating the flowing fluid-particle suspension as a pseudofluid, by introducing a modified suspension-wall friction coefficient (f_w) and a modified Reynolds number (Re_m). The data for wall-to-bed mass transfer in the hydraulic transport of particles show that an analogy between mass and momentum transfer exists.     

Experimental and numerical study of gas hold-up in surface aerated stirred tanks

Although the distribution of gas hold-up in stirred tanks is a key factor to their design and operation, systematic experimental data on local gas hold-up of surface-aerated stirred tanks are not available in open literature. In this work, turbulent two-phase flow in a surface aeration stirred tank with a diameter of 0.380 m was investigated experimentally and numerically. The gas hold-up was measured with a conductance probe at various operating conditions. A surface baffle to improve the efficiency of surface aeration of a Rushton disk turbine was designed and tested. The experimental data suggest that the gas hold-up distribution in the surface aeration tank is very non-uniform, and the surface baffle improves the aeration rate particularly at a high agitation speed. A three-dimensional in-house computational fluid dynamic (CFD) two-fluid model with the standard k?A_p turbulence model was used to predict the gas-liquid flow, and the impeller region was handled using the improved inner-outer iterative procedure. Based on Kolmogoroff's theory of isotropic turbulence, a constitutive equation for surface aeration strength was proposed. The numerical prediction, in combination with the measurements, gives insight to the surface aeration performance of stirred tanks. It was found that the simulation reasonably predicted the gas hold-up distribution in the upper tank, but underestimated it in the region below the stirrer.     

Jet mixing in tall tanks: Comparison of methods for predicting blend times

Grenville and Tilton (1996) presented a simple model that correlates blend time data from jet mixed vessels up to 12,000 m³ in volume. The model is based on the idea that the turbulent kinetic energy dissipation rate at the end of the jet's free path determines the mixing rate for the whole vessel. Maruyama et al. (1982) and Revill (1992) had previously proposed that the blend time should be proportional to the circulation time of the fluid entrained by the jet. Grenville and Tilton (1997) compared their proposed Jet Turbulence model with the Circulation Time model and found that, over the range of the data studied, both can be used to accurately predict blend times. Extrapolation of the models showed that their predictions diverge as the ratio of fluid depth to vessel diameter increases. In this paper blend time data taken in vessels with aspect ratios of 2, 3 and 4 are included in the analysis. The results show that the Grenville and Tilton (1996) Jet Turbulence model fits all data for 0.2 < H/T < 3. The ratio of blend time to the circulation time is dependent on the ratio of fluid depth to vessel diameter.     

Drag of non-spherical solid particles of regular and irregular shape

The drag of a non-spherical particle was reviewed and investigated for a variety of shapes (regular and irregular) and particle Reynolds numbers (Re_p). Point-force models for the trajectory-averaged drag were discussed for both the Stokes regime (Re_p ? 1) and Newton regime (Re_p ? 1 and sub-critical with approximately constant drag coefficient) for a particular particle shape. While exact solutions were often available for the Stokes regime, the Newton regime depended on: aspect ratio for spheroidal particles, surface area ratio for other regularly-shaped particles, and min-med-max area for irregularly shaped particles. The combination of the Stokes and Newton regimes were well integrated using a general method by Ganser (developed for isometric shapes and disks). In particular, a modified Clift-Gauvin expression was developed for particles with approximately cylindrical cross-sections relative to the flow, e.g. rods, prolate spheroids, and oblate spheroids with near-unity aspect ratios. However, particles with non-circular cross-sections exhibited a weaker dependence on Reynolds number, which is attributed to the more rapid transition to flow separation and turbulent boundary layer conditions. Their drag coefficient behavior was better represented by a modified Dallavalle drag model, by again integrating the Stokes and Newton regimes. This paper first discusses spherical particle drag and classification of particle shapes, followed by the main body which discusses drag in Stokes and Newton regimes and then combines these results for the intermediate regimes.     

Modeling spatial distribution of floc size in turbulent processes using the quadrature method of moment and computational fluid dynamics

A study was performed that utilizes the quadrature method of moments (QMOM) to model the transient spatial evolution of the floc size in a heterogeneous turbulent stirred reactor. The QMOM approach was combined with a commercial computational fluid dynamics (CFD) code (PHOENICS), which was used to simulate the turbulent flow and transport of these aggregates in the reactor. The CFD/QMOM model was applied to a 28 l square reactor containing an axial flow impeller and 100 mg/l concentration of 1 μm nominal clay particles. Simulations were performed for different average characteristic velocity gradients (40,70,90, and 150 s^-1). The average floc size and growth rate were compared with experimental measurements performed in the bulk region and the impeller discharge region. The CFD/QMOM results confirmed the experimentally measured spatial heterogeneity in the floc size and growth rate. In addition, the model predicts spatial variations in the aggregation and breakup rates. Finally, the model also predicts that the transport of flocs into the high shear impeller discharge zone was responsible for the transient evolution of the average floc size curve displaying a maximum before decreasing to a steady-state floc size.     

Open-Source CFD Simulations of Liquid–Liquid Flow in the Annular Centrifugal Contactor

Simulation of the fluid dynamics of solvent extraction in centrifugal contactors requires advanced models to account for complex physical phenomena including turbulent free-surface flow and liquid-liquid dispersion physics. The use of an open-source computational fluid dynamics (CFD) framework allows for implementation of advanced models not feasible in commercial CFD applications. The open-source CFD package OpenFOAM has been used to simulate turbulent, multiphase flow in the annular centrifugal contactor, including simulations of the mixing zone (annular region), and of the coupled operation of the mixing and separation (rotor interior) zones. These simulations are based on the Volume of Fluid (VOF) methodology along with Large Eddy Simulation (LES) for turbulence. The results from these simulations compare favorably with previous simulations using a commercial CFD tool and with available experimental data. They also give insight into the requirements for more advanced multiphase models needed to accurately capture flows in these devices.