Drag Correction Research Articles

Numerical simulation of particulate flows in CFB riser with drag corrections based on particle distribution characterization

A heterogeneous drag force model was developed using a Eulerian-Lagrangian scheme for multiphase flow modeling. The model is based on an idea called particle distribution characterization (PDC), in which transient distribution of particle position is analyzed with an intuitive method to quantify the local heterogeneity of gas-solid flow for drag force correction. The model was implemented into the multiphase particle-in-cell (MP-PIC) method and applied to particulate flow simulation in circulating fluidized bed (CFB) risers. Whereas traditional homogeneous drag models tend to over-estimate gas-particle interactions and present homogeneous flow fields, the developed PDC model successfully predicts the heterogeneous gas-solid flow structures. The PDC predictions on time-averaged distributions and solid fluxes also correspond better with experimental measurements. Effects of the statistical parcel weight, an important parameter in computational parcel assumption in MP-PIC method (wherein parcels are employed to represent real particles), were investigated with both traditional and the PDC drag models. Results show defects of the assumption that agree with literature. It is proved that the PDC drag model is applicable to particulate flow modeling in CFB riser, and considerable for simulation of other industrial processes.

Particle settling in micellar solutions of varying concentration and salt content

The effect of concentration and molar ratio of cetyltrimethylammonium bromide with sodium salicylate (CTAB/NaSal) micellar aqueous solutions on the settling of non-Brownian spheres is determined. The micelles cause shear thinning, which may result in a shear-stress plateau. The measurements were performed in the wide range of Weissenberg numbers showing drag reduction and enhancement. Maximum drag coincides with the minimum relaxation time. For equimolar solutions, a correlation between Weissenberg number and normalized drag correction factor is proposed. The average settling velocity decreases proportionally to the inverse CTAB/NaSal concentration squared and is closely related to the micellar network size. Salt excess in 10 mM CTAB solutions results in an exponential increase in the average velocity. We find steady and unsteady regimes for the particle motion. In equimolar solutions, the frequency decreases with the concentration, whereas the dominant frequency does not change with salt excess, but is associated with the shear-stress oscillations. We show that the unsteady particle motion is related to the rheological time-dependent properties of the micellar solutions.

Numerical simulation of loop seal for a circulating fluidized bed based on an improved EMMS bubbling model

A typical loop seal consists of a supply chamber and a recycle chamber as well as a bottom connection slit in between. The supply chamber is generally operated in the minimum fluidization state, while the recycle chamber in the bubbling fluidization regime. The energy-minimization multi-scale (EMMS) model, as generally used to calculate interphase drag coefficient in previous simulations of the loop seal, is still open to discussion since it is based on the concept of particle clusters. So an EMMS bubbling model was developed to model dense gas–solid flow by taking into account the interphase interaction between the emulsion and bubble phases. In this article, a heterogeneity index is calculated from an improved EMMS bubbling model to measure the interphase drag coefficient and further integrated into the two-fluid-model (TFM) approach to simulate the loop seal for a circulating fluidized bed (CFB) system. This index is dependent on superficial gas velocity in bubbling fluidization, so a region-specific drag correction scheme is proposed to allow the application of various heterogeneity index correlations to different zones of the loop seal, since superficial gas velocity may differ much from the recycle to supply chamber. Several typical cases of drag correction are comparatively investigated by applying various gas velocities and/or drag models in the recycle and supply chambers, and the optimal one is proven to be able to reasonably simulate the parametric effects on gas inverse flow in the loop seal.

A CFD study of a bi-disperse gas–solid fluidized bed: Effect of the EMMS sub grid drag correction

For the first time the bubble-based EMMS drag model developed for a mono-disperse system has been extended to simulate a bi-disperse fluidized bed in conjunction with the multi-fluid model. Simulations with the EMMS drag model reveal that the system attains a fluidized state earlier. Furthermore the model predicts bed height and voidage in better agreement with data from the literature. Inclusion of the sub-grid drag correction is found to have a significant effect on the predicted axial pressure drop profile, mixing and segregation behavior, granular temperatures and turbulent kinetic energy. The effect of the specularity coefficient on the mixing index is also investigated.

Analysis of the time-averaged gas–solid drag force based on data from transient 3D CFD simulations of fluidized beds

In the present work, a qualitative analysis of the time-averaged gas–solid drag force in gas–solid fluidized beds is carried out. The analysis is based on a large number of transient Eulerian–Eulerian 3D CFD simulations of small bubbling, turbulent and circulating fluidized beds. The obtained results significantly differ from corresponding data previously obtained from 2D simulations, especially at high solid concentrations. This confirms that to accurately model the gas–solid drag force in a steady state 3D simulation, the drag model should not be based on data from transient 2D simulations. In the present work, the average drag force is expressed as the product of the drag force calculated from time-averaged velocities and volume fractions and a correction coefficient. The study shows that even when the third dimension is described in the mesh with only three nodes, the 3D character of the flow is captured in the drag correction coefficient. Thus, a large number of parametric studies could be carried out in a reasonable time frame. In the paper, the parameters affecting the time-averaged drag force are identified and the nature of the effects are analyzed. The analysis shows that solid volume fraction, particle size, solid density, gas viscosity, the slip velocity between gas and solids and the lateral distance to a wall have significant effects on the drag correction coefficient. At high gas densities typical e.g. of pressurized fluidization even the gas density has significant effects. A closure relation for the time-averaged drag force for a wide range of fluidization conditions should include these seven variables as inputs.

CFD modeling of gas–solids flow in a large scale circulating fluidized bed furnace

A Eulerian multiphase model was used to study the hydrodynamics of the gas–solids flow in a circulating fluidized bed (CFB) furnace. Alternative modeling approaches were tried to evaluate their effects on the predicted solids distribution in the furnace. Due to high computational costs, large scale calculations are commonly performed by using a coarse mesh, which leads to too uniform solids flow field and an overestimated gas–solid drag force. Thus, a suitable form of correction of the gas–solid drag is needed for coarse mesh simulations. This study presents fluid dynamics simulations of a 235MWe CFB furnace by two sets of interphase momentum exchange coefficients: the model based on the homogeneous flow condition and the model based on the energy-minimization multi-scale (EMMS) approach. The calculations with one solid phase included studies with two mesh resolutions and different particle sizes. Additional simulations were performed using two solid phases and four solid phases to analyze the effect of polydispersity of particles. The model results were compared with the measured vertical pressure profile of the furnace and the locally measured solid concentration and velocity profiles. The results show that with a homogeneous model, the model matches better with measurements if the mesh resolution is finer. The EMMS approach can be used to improve the calculations in a coarse mesh if the average particle size can be determined correctly for the model. With multiple solid phases, the vertical and horizontal segregation could be simulated. However, increasing the number of solid phases did not change the total solid concentration and pressure profiles if the Sauter mean diameter of the total system was constant. The results indicate that with a coarse mesh, similar drag corrections would be necessary between the solid phases that have been developed for gas–solid drag.

Numerical Study of a Bi-disperse Gas-solid Fluidized Bed Using an Eulerian and Lagrangian Hybrid Model

In this paper, we present a hybrid model for the numerical assessment of poly-disperse gas-solid fluidized beds. The main idea of such a modeling strategy is to use a combination of a Lagrangian discrete phase model (DPM) and a kinetic theory based TFM to take advantage of the benefits of those two different formulations. On the one hand, the local distribution of the different particle diameters, which is required for the gas-solid drag force, can be obtained by tracking statistically representative particle trajectories for each particle diameter class. On the other hand, the contribution from the inter-particle stresses, i.e. inter-particle collisions, can be deduced from the TFM solution. These then appear as additional body force in the force balance of the DPM. Note that in a first step we solely consider diameter averaged solids stresses since the drag force is at least on order of magnitude higher than the solids stresses in fluidized beds. Finally, the numerical model is applied to a fluidized bed of a bi-disperse mixture of glass particles (0.5mm and 2.5mm particles) and with a cross-section of 0.15 m x 0.02 m. The results are then analyzed with respect to experimental data of Puttinger et al [1]. This comparison demonstrates that the computed bed hydrodynamics is in fairly good agreement with the experiment. However, the results also suggest that sub-grid drag corrections [2–4] for poly-disperse fluidized beds are required to make the numerical investigation of industrial scale fluidized bed units accessible.

Probabilistic Assessment of Lifetime of Low-Earth-Orbit Spacecraft: Uncertainty Propagation and Sensitivity Analysis

This paper is devoted to the probabilistic uncertainty quantification of orbital lifetime estimation of low-altitude satellites. Specifically, given a detailed characterization of the dominant sources of uncertainty, we map this input into a probabilistic characterization of the orbital lifetime through orbital propagation. Standard Monte Carlo propagation is first considered. The concept of drag correction is then introduced to facilitate the use of polynomial chaos expansions and to make uncertainty propagation computationally effective. Finally, the obtained probabilistic model is exploited to carry out stochastic sensitivity analyses, which in turn allow gaining insight into the impact uncertainties have on orbital lifetime. The proposed developments are illustrated using one CubeSat of the QB50 constellation.

Airfoil wind tunnel correction for angles of attack from −180° to 180°

AbstractWind tunnel corrections are investigated for two‐dimensional low‐speed wind tunnel tests that are performed for three similar airfoils for angles of attack ranging from −180° to 180° at Re = 0.75 × 106. Aided by the Blasius theorem, wind tunnel corrections are deduced for the lift, drag and pitching moment of the airfoil at high angles of attack. The wall pressure signature method is applied to determine the strengths of the equivalent singularities. The tunnel wall‐induced force and pitching moment are obtained by calculating the force and moment exerted on the equivalent singularities. The maximum correction for drag is determined to be about 50%. The corrected forces and pitching moments for three similar airfoils are coincident with one another. A method to determine an optimum singularities distribution range is presented. The results indicate that the correction method in the paper is effective for airfoil testing at high angles of attack. Copyright © 2014 John Wiley & Sons, Ltd.

CFD Prediction of Gas-Liquid Flow in an Aerated Stirred Vessel Using the Population Balance Model

Abstract The main topic of this study is the experimental measurement and mathematical modelling of global gas hold-up and bubble size distribution in an aerated stirred vessel using the population balance method. The air-water system consisted of a mixing tank of diameter T = 0.29 m, which was equipped with a six-bladed Rushton turbine. Calculations were performed with CFD software CFX 14.5. Turbulent quantities were predicted using the standard k-ε turbulence model. Coalescence and breakup of bubbles were modelled using the homogeneous MUSIG method with 24 bubble size groups. To achieve a better prediction of the turbulent quantities, simulations were performed with much finer meshes than those that have been adopted so far for bubble size distribution modelling. Several different drag coefficient correlations were implemented in the solver, and their influence on the results was studied. Turbulent drag correction to reduce the bubble slip velocity proved to be essential to achieve agreement of the simulated gas distribution with experiments. To model the disintegration of bubbles, the widely adopted breakup model by Luo & Svendsen was used. However, its applicability was questioned.

Parametric study of the time-averaged gas–solid drag force in circulating fluidized bed conditions

Steady state modeling based on time-averaged transport equations is a computationally efficient method for CFD simulation of large industrial-scale circulating fluidized beds. The feasible alternative for steady state modeling is to carry out transient simulations in a coarse mesh, which would require mesh resolution dependent closure laws and lead to long simulations in order to characterize the average process behavior. These closures could be avoided by simulations with adequate spatial and temporal resolutions, but the required computational effort renders such simulations unfeasible in industrial scale applications in near future. Equation closures for steady state modeling can be developed by time-averaging results from transient simulations. One of the largest terms to be modeled is the time-averaged drag force. In the present work, parameters that need to be accounted for in a model for the time-averaged drag force were studied by analyzing time-averaged results from a number of transient 2D simulations carried out with fairly fine spatial resolution. The analysis was limited to Geldart B particles. In the literature, the solid volume fraction, distance to the wall and the gas–solid slip velocity have been included as parameters in drag correction functions developed for transient coarse-mesh simulations. In the present work, the same parameters are found to have significant effects on the time-averaged gas–solid drag force. Additionally, solid density, particle size and gas phase laminar viscosity are shown to have significant effects on the average drag force. Thus process conditions, which significantly vary inside a CFB, need to be accounted for in the model.

Development of a CFD Model of Bubble Column Bioreactors: Part Two – Comparison of Experimental Data and CFD Predictions

AbstractThe application of computational fluid dynamics (CFD) as a tool to simulate bubble column bioreactors is investigated. A three‐dimensional model utilizing the Euler‐Euler approach is evaluated. The role of various terms, i.e., lift, drag, bubble‐induced turbulence, and volume fraction correction terms for drag, is determined. Good agreement between experimental data and simulation results was obtained by means of a single‐bubble size model provided that bubble‐induced turbulence and the reduction in drag due to the presence of other bubbles were taken into account.

Influence of magnetic and hydrodynamic forces on chain-aggregation and motion of magnetisable particles and composites

The motion of ferromagnetic single particles and linear aggregates of spheres subjected to a gradient magnetic field in the presence of a non-magnetic fluid was investigated through the experimental validation of a new theoretical model. The theoretical model combines the correction of the mutual magnetisation between particles as well as the interaction with the external magnetic gradient and the hydrodynamic drag corrections for linear aggregates for the first time. The drag for linear aggregates of spheres was corrected using a semiempirical equation which was developed from published work on the drag correction for linear clusters of particles.The experimental results show that the ratio of the velocity of aggregates to the velocity of a single particle with the same diameter can be described by the aspect ratio of the aggregate. The solution for the motion equation obtained by numerical analysis showed an excellent agreement with the experimental data for linear aggregates of spheres, while very similar results were obtained for non-spherical particles.This study also examined the influence of the thickness of a non-magnetic coating around the ferromagnetic particles. Core–shell composites were created by dip-coating ferromagnetic particles in a non-magnetic material. When a pair of the core–shell composite particles (doublet) was formed, the velocity of the doublet was found to be lower than for the aggregates of the non-coated particles. This effect was examined as a function of the film thickness. When the thickness of the shell was approximately 50% of the particle radius, the velocity of the doublet was similar to that of a single uncoated particle.This work establishes an understanding of the fundamental effects of thin coatings on magnetic aggregation. Particle coatings provide a novel and simple means for controlling the separation between the magnetic cores and in turn the kinetics of the aggregation and subsequent magnetisation of the final aggregates.

Aerodynamic Modeling of Swept-Bladed Vertical Axis Wind Turbines

A computationally light time- and space-accurate two-dimensional free vortex model capable of simulating straight- and swept-bladed vertical axis wind turbines operating in a fluctuating wind has been developed. Fast solution times are achieved via vortex merging, limiting the number of calculations necessary at each time step, while solution integrity is maintained through the use of second-order time stepping, vortex-blob rediscretization, and the use of a “vortex curtain” preventing vortex mergers within a predetermined distance from the rotor. Finite span and spoke drag corrections are applied to account for three-dimensional effects in addition to a formulation for extending the two-dimensional model to arbitrary three-dimensional geometries. The two-dimensional free vortex model is validated against unswept and swept-bladed vertical axis wind turbine experimental data, with allowances for the effects of wind-tunnel walls made within the free vortex model in the case of the swept-bladed data set.

Small UAV Design Using an Integrated Design Tool

A numerical design tool was developed that greatly facilitates the design process of small UAVs. The integrated approach of the method makes it highly suitable for the aerodynamic needs of such small aircraft. Traditional design tools and methodologies are typically tailored for the design of larger aircraft, such as for general aviation, whose aerodynamics generally exhibit more linear behaviors. Building on this motivation, a user friendly integrated design tool was developed and validated in order to provide a more tailored approach to designing low Reynolds number aircraft. At the heart of the tool is a performance prediction that relies on a higher-order free wake potential flow aerodynamic code that employs viscous drag corrections. Subsequently, the method provides accurate characteristics for a wide range of Reynolds numbers and aspect ratio wings. In a validation process, the flight performance results of the method are compared with the results of other prediction methods as well as with several experimental flight test results. In general good agreement exists. The utility of the integrated design tool is demonstrated with the design application of a small UAV for a heavy lift competition. The design tool greatly streamlined the design process, limiting it to two weeks rather than the typical several months.

Shear-induced Electrokinetic Lift at Large Péclet Numbers

We analyze the problem of shear-induced electrokinetic lift on a particle freely suspended near a solid wall, subject to a homogeneous (simple) shear. To this end, we apply the large-Peclet-number generic scheme recently developed by Yariv et al. (J. Fluid Mech. , Vol. 685, 2011, p. 306). For a force- and torque-free particle, the driving flow comprises three components, respectively describing (i) a particle translating parallel to the wall; (ii) a particle rotating with an angular velocity vector normal to the plane of shear; and (iiii) a stationary particle in a shear flow. Symmetry arguments reveal that the electro-viscous lift, normal to the wall, is contributed by Maxwell stresses accompanying the induced electric field, while electro-viscous drag and torque corrections, parallel to the wall, are contributed by the Newtonian stresses accompanying the induced flow. We focus upon the near-contact limit, where all electro-viscous contributions are dominated by the intense electric field in the narrow gap between the particle and the wall. This field is determined by the gap-region pressure distributions associated with the translational and rotational components of the driving Stokes flow, with the shear-component contribution directly affecting only higher-order terms. Owing to the similarity of the corresponding pressure distributions, the induced electric field for equal particle–wall zeta potentials is proportional to the sum of translation and rotation speeds. The electro-viscous loads result in induced particle velocities, normal and tangential to the wall, inversely proportional to the second power of particle–wall separation.

Streaming-potential phenomena in the thin-Debye-layer limit. Part 1. General theory

AbstractElectrokinetic streaming-potential phenomena are driven by imposed relative motion between liquid electrolytes and charged solids. Owing to non-uniform convective ‘surface’ current within the Debye layer Ohmic currents from the electro-neutral bulk are required to ensure charge conservation thereby inducing a bulk electric field. This, in turn, results in electro-viscous drag enhancement. The appropriate modelling of these phenomena in the limit of thin Debye layers $\delta \ensuremath{\rightarrow} 0$ ($\delta $ denoting the dimensionless Debye thickness) has been a matter of ongoing controversy apparently settled by Cox’s seminal analysis (J. Fluid Mech., vol. 338, 1997, p. 1). This analysis predicts electro-viscous forces that scale as ${\delta }^{4} $ resulting from the perturbation of the original Stokes flow with the Maxwell-stress contribution only appearing at higher orders. Using scaling analysis we clarify the distinction between the normalizations pertinent to field- and motion-driven electrokinetic phenomena, respectively. In the latter class we demonstrate that the product of the Hartmann & Péclet numbers is $O({\delta }^{\ensuremath{-} 2} )$ contrary to Cox (1997) where both parameters are assumed $O(1)$. We focus on the case where motion-induced fields are comparable to the thermal scale and accordingly present a singular-perturbation analysis for the limit where the Hartmann number is $O(1)$ and the Péclet number is $O({\delta }^{\ensuremath{-} 2} )$. Electric-current matching between the Debye layer and the electro-neutral bulk provides an inhomogeneous Neumann condition governing the electric field in the latter. This field, in turn, results in a velocity perturbation generated by a Smoluchowski-type slip condition. Owing to the dominant convection, the present analysis yields an asymptotic structure considerably simpler than that of Cox (1997): the electro-viscous effect now already appears at $O({\delta }^{2} )$ and is contributed by both Maxwell and viscous stresses. The present paradigm is illustrated for the prototypic problem of a sphere sedimenting in an unbounded fluid domain with the resulting drag correction differing from that calculated by Cox (1997). Independently of current matching, salt-flux matching between the Debye layer and the bulk domain needs also to be satisfied. This subtle point has apparently gone unnoticed in the literature, perhaps because it is trivially satisfied in field-driven problems. In the present limit this requirement seems incompatible with the uniform salt distribution in the convection-dominated bulk domain. This paradox is resolved by identifying the dual singularity associated with the limit $\delta \ensuremath{\rightarrow} 0$ in motion-driven problems resulting in a diffusive layer of $O({\delta }^{2/ 3} )$ thickness beyond the familiar $O(\delta )$-wide Debye layer.

Evaluation of drag correction factor for spheres settling in associative polymers

Drag correction factors are calculated for the creeping motion of spheres descending in various associative polymers of different concentration with various sphere-container ratios and Weissenberg numbers. The simple-shear rheology and linear viscoelasticity of these polymeric fluids have been previously presented and modeled with the BMP (Bautista–Manero–Puig) equation of state (Mendoza-Fuentes et al., Phys Fluids 21:033104, 2009). The drag on the sphere is initially kept nearly constant for small Weissenberg numbers, We < 0.1. As the Weissenberg number increases, We < 0.1, a reduction in drag is found. Experimental results show the presence of a critical Weissenberg number at which a drag reduction occurs. The reduction in the drag correction factor is associated to the onset of extension-thinning, which coincides with the formation of a negative wake. No increase in the drag correction factor was observed, due to the simultaneous opposing effects of extension-thickening and shear-thinning viscosity. The shape of the drag correction factor curve may be predicted considering the extensional properties of the solutions, as suggested elsewhere (Chen and Rothstein, J Non-Newton Fluid Mech 116:205–215, 2004).

Comparison of Faxén’s correction for a microsphere translating or rotating near a surface

Boundary walls in microfluidic devices have a strong influence on the fluid flow and drag forces on moving objects. The Stokes drag force acting on a sphere translating in the fluid is increased by the presence of a neighboring wall by a factor given by Faxén's correction. A similar increase in the rotational drag is expected when spinning close to a wall. We use optical tweezers to confirm the translational drag correction and report the hitherto unmeasured rotational equivalent. We find that the corrections for the rotational motion is only required for particle-wall separations an order of magnitude shorter than that for the translational cases. These results are particularly significant in the use of optical tweezers for measuring viscosity on a picolitre scale.

CFD simulation of gas–liquid flows in stirred vessel equipped with dual rushton turbines: influence of parallel, merging and diverging flow configurations

Computational fluid dynamics (CFD) was used to investigate the influence of parallel, merging and diverging flow configurations on the gas dispersion operation in stirred vessel. The simulation was based on the two-fluid model along with the standard k– ε turbulence model along with an appropriate drag correction to account for bulk turbulence [Khopkar, A.R., Ranade, V.V., 2006. CFD simulation of gas–liquid stirred vessel: VC, S33 and L33 flow regimes. A.I.Ch.E. Journal 52, 1654–1671]. The model predictions were compared with the published experimental data of Bombac, Zun [2000. Gas-filled cavity structures and local void fraction distribution in vessel with dual-impellers. Chemical Engineering Science 55, 2995–3001] for parallel flow configuration. The predicted results show reasonably good agreement with the experimental data. The computational model was then used to simulate the gas–liquid flows for the other two flow configurations. The results of this work provide ‘a priory’ information on the implications of flow configuration on the vessel performance.