Drag Model Research Articles

Modelling of filtered drag force for clustered particle-laden flows based on interface-resolved simulation data

Interface-resolved direct numerical simulations (DNS) of clustered settling suspensions in a periodic domain are performed to study the filtered drag force for clustered particle-laden flows. Our results show that, for the homogeneous system, the filtered drag is independent of the filter size, whereas for the clustered particle-laden flows, the averaged drag becomes smaller than the homogeneous drag at the filter size above 4 particle diameters. The drag reduction saturates at the filter size being comparable to the cluster size in the horizontal direction in our simulations. A new correlation is proposed to account for the mesoscale effect on the filtered drag force by using drift velocity and variance of the solid volume fraction, based on the modification of existing subgrid drag models for the inhomogeneous system. The existing models for the drift velocity and the variance of the solid volume fraction are assessed using our DNS data. A new model for the drift velocity and the variance of the solid volume fraction is proposed, based on the combination and modification of the previous models. All mesoscale models considered can predict well the filtered drag with comparable accuracy, and are superior to the homogeneous drag model for the clustered system. Our models with the same parameter values obtained from the large-scale system can also predict well the filtered drag for smaller computational domain sizes.

Prediction of vertical transport of microplastics: Shape- and aging-dependent drag models

The prediction of vertical transport of microplastics (MPs) is essential for understanding their multidimensional transport, fate, and environmental risks, but drag models applicable to aging MPs are currently understudied. In this study, pristine and UV-aged polyethylene terephthalate (PET) and polystyrene (PS) MPs were used for settling experiments. Combining physicochemical properties and transport data, a shape-dependent drag model based on the Corey shape factor was optimized with average errors of 9.73% and 10.42% and coefficients of determination of 0.6878 and 0.8359 for predicting the settling terminal velocities (ut) for PET and PS MPs, respectively. Meanwhile, aging-dependent drag models were constructed by incorporating the carbonyl index as functional forms of the newly defined aging index, which can be used to differentiate the effects of shape and aging characteristics on the vertical transport of MPs. These aging-dependent models showed better predictive abilities with average errors of 3.97% and 4.56% in predicting ut for PET MPs, and of 5.89% and 6.91% for PS MPs. Additionally, the drag models in this study improved applicability to predict vertical transport of environmentally-collected weathered MPs. With the continuous improvement of the transport database of diverse MPs, this study is expected to provide scientific support for predicting the environmental behaviors of MPs and formulating targeted pollution control strategies.

Comparative Planetology of Magnetic Effects in Ultrahot Jupiters: Trends in High-resolution Spectroscopy

Ultrahot Jupiters (UHJs), being the hottest class of exoplanets known, provide a unique laboratory for testing atmospheric interactions with internal planetary magnetic fields at a large range of temperatures. Thermal ionization of atmospheric species on the dayside of these planets results in charged particles becoming embedded in the planet’s mostly neutral wind. The charges will resist flow across magnetic field lines as they are dragged around the planet and ultimately alter the circulation pattern of the atmosphere. We model this process to study this effect on high-resolution emission and transmission spectra in order to identify observational signatures of the magnetic circulation regime that exist across multiple UHJs. Using a state-of-the-art kinematic MHD/active drag approach in a 3D atmospheric model, we simulate three different UHJs with and without magnetic effects. We postprocess these models to generate high-resolution emission and transmission spectra and explore trends in the net Doppler shift as a function of phase. In emission spectra, we find that the net Doppler shift before and after secondary eclipse can be influenced by the presence of magnetic drag and the wavelength choice. Trends in transmission spectra show our active drag models consistently produce a unique shape in their Doppler shift trends that differs from the models without active drag. This work is a critical theoretical step to understanding how magnetic fields shape the atmospheres of UHJs and provides some of the first predictions in high-resolution spectroscopy for observing these effects.

Up, Up, and Away: Winds and Dynamical Structure as a Function of Altitude in the Ultrahot Jupiter WASP-76b

Due to the unprecedented signal strengths offered by the newest high-resolution spectrographs on 10 m class telescopes, exploring the 3D nature of exoplanets is possible with an unprecedented level of precision. In this paper, we present a new technique to probe the vertical structure of exoplanetary winds and dynamics using ensembles of planet absorption lines of varying opacity, and apply it to the well-studied ultrahot Jupiter WASP-76b. We then compare these results to state-of-the-art global circulation models (GCMs) with varying magnetic drag prescriptions. We find that the known asymmetric velocity shift in Fe i absorption during transit persists at all altitudes, and observe tentative trends for stronger blueshifts and more narrow line profiles deeper in the atmosphere. By comparing three different model prescriptions (a hydrodynamical model with no drag, a magnetic drag model, and a uniform drag model) we are able to rule out the uniform drag model due to inconsistencies with observed trends in the data. We find that the magnetic model is slightly favored over the the hydrodynamic model, and note that this 3-Gauss kinematic magnetohydrodynamical GCM is also favored when compared to low-resolution data. Future generation high-resolution spectrographs on extremely large telescopes will greatly increase signals and make methods like these possible with higher precision and for a wider range of objects.

A novel treatment of solute drag and solute trapping at a solid–liquid interface during rapid solidification of multicomponent alloys

AbstractIn response to the renewed interest in solute drag and solute trapping models fueled by their applications to additive manufacturing, a novel treatment is proposed to describe the diffusional behaviors of solute at a migrating solid–liquid interface during rapid solidification of multicomponent alloys. While the treatment is still built on irreversible thermodynamics and linear kinetic law, its novelty lies in breaking up the classical trans‐interface diffusional flux into two separate fluxes one is the transferred‐back flux with its ending point at the interface and the other is the bumping‐back flux with its starting point at the interface. This novel treatment entails three significant improvements in reference to the existing models. Firstly, it reveals that the degree of solute drag is dependent on the ratio of liquid diffusive speed over interface diffusive speed. Secondly, a novel relation between the distribution coefficient and interface velocity is derived. It amends the confusing behavior seen in Aziz’s without‐drag continuous growth model. Thirdly, the proposed treatment eliminates the need of prescribing the degree of solute drag parameter for the kinetic phase diagram calculation. The numerical solution to the proposed model is presented, and it is ready to be used for the kinetic phase diagram calculation.

A universal drag model for liquid-solid fluidization: Experiment, data-driven modeling, CFD modeling and simulation

Various industrial applications are performed in liquid-solid fluidized beds where drag force plays a significant role in affecting the expansion characteristics of granular-bed, and then determines the mass/heat transfer performance. This study employs dimensionless learning data-driven modeling method, which is derived from the principle of dimensional invariance, to automatically discover the relationship between the drag coefficient and hydraulic dimensionless numbers from the liquid-solid fluidization data. It is found that the Fr number (=ul2/gds) also plays important role in improving the prediction accuracy of drag model except for Re number (=dsulρl/μl). The proposed data-driven modeling method has desired robustness, and the yielded drag model can be applicable to other liquid-solid systems, such as water-polystyrene spheres and water-coal particles, although it is derived from the fluidization of spherical glass beads in rising tap-water. The proposed drag model can also provide good CFD simulation results that agree very well with the experiment data with the relative error less than 5 %.

A modified drag model for the fluidization of nano-modulated Group C particles

Geldart Group C powders are inherently cohesive due to the strong interparticle forces, leading to severe agglomeration and poor fluidization capability. In this study, fluidization of nano-modulated Group C particles was investigated numerically. These particles, also known as Group C+ particles, were obtained through the nanoparticle modulation technique, with which a small fraction of nanoparticles were vigorously mixed with Group C particles so that they are adhered to the surface of the much larger Group C particles. After modification, the cohesiveness of Group C+ particle was significantly weakened, and therefore these particles could exhibit much better fluidization quality. However, the still existing cohesion resulted in the formation of small agglomerates within the system. To understand the internal agglomeration mechanisms of Group C+ particles and their impact on fluidization behaviors, a new drag model was proposed based on experimental results and the postulation of particle agglomeration. The numerical results of the cases employing the new drag model agreed well with the experimental data in terms of total and dense phase expansion. These findings revealed the drag mechanism associated with modified Group C particles, contributing to the understanding of ultrafine particle fluidization.

Numerical investigation of turbulent mass transfer processes in turbulent fluidized bed by computational mass transfer

Turbulent fluidized bed possesses a distinct advantage over bubbling fluidized bed in high solids contact efficiency and thus exerts great potential in applications to many industrial processes. Simulation for fluidization of fluid catalytic cracking (FCC) particles and the catalytic reaction of ozone decomposition in turbulent fluidized bed is conducted using the Eulerian–Eulerian approach, where the recently developed two-equation turbulent (TET) model is introduced to describe the turbulent mass diffusion. The energy minimization multi-scale (EMMS) drag model and the kinetic theory of granular flow (KTGF) are adopted to describe gas–particles interaction and particle–particle interaction respectively. The TET model features the rigorous closure for the turbulent mass transfer equations and thus enables more reliable simulation. With this model, distributions of ozone concentration and gas–particles two-phase velocity as well as volume fraction are obtained and compared against experimental data. The average absolute relative deviation for the simulated ozone concentration is 9.67% which confirms the validity of the proposed model. Moreover, it is found that the transition velocity from bubbling fluidization to turbulent fluidization for FCC particles is about 0.5 m·s–1 which is consistent with experimental observation.

Development of the gas–liquid drag model for flows on sieve plates in distillation columns via direct numerical simulation

Development of the gas–liquid drag model for flows on sieve plates in distillation columns via direct numerical simulation

Numerical Investigation into Gas-Solid Fluidized Bed Reactors for Activating the Iron-based Fischer-Tropsch Synthesis Catalyst

Abstract The present work conducted experimental and computational fluid dynamics simulation studies on the hydrodynamic characteristics of gas-solid fluidized bed reactors for activating the iron-based Fischer-Tropsch synthesis catalyst. In order to provide reliable guidance for the design and scale-up of the reactor, the present study applied experimental data from a pilot fluidized bed device to verify the accuracy of the drag force model used in the two-fluid model and further used the validated drag force model to simulate an industrial-scale fluidized bed activation reactor. It was found that the bubbling-EMMS drag model can accurately simulate the pilot-scale fluidized bed in the flow regimes ranging from bubbling to turbulent fluidization. Simulation studies on the industrial-scale fluidized bed activation reactor showed that the reactor was in a turbulent fluidization regime under the designed operating gas velocity, with high gas-solid dispersion efficiency, reasonable utilization of reactor space, and low gas-solid separation load.

Simulation analysis of gas-solid two-phase flow and reaction in a novel catalytic cracking reactor

A gas-solid two-phase flow reaction model was developed to evaluate the performance of a novel catalytic cracking reactor in the residue-to-chemicals (RTC) process. Coupled TFM, EMMS drag, and 12-lump kinetic models were employed to simulate the flow reaction process. The reaction temperature and product yields at the reactor exit aligned well with real industrial RTC reactor test results, indicating the reliability and effectiveness of the coupling model. Catalyst particles formed an internal circulation structure in the reactor, increasing the instantaneous catalyst-to-oil ratio. The reactor exhibited low axial and radial temperature gradients with higher reaction temperatures, accelerating the catalytic cracking rate and enhancing the selectivity for high-value products. The effects of the catalyst-to-oil ratio, catalyst inlet temperature, and feedstock mass flow rate on the flow reaction process were optimized. Results showed that both the catalyst-to-oil ratio and catalyst inlet temperature influenced the overall catalyst velocity distribution. Within the limit range, increasing the catalyst-to-oil ratio increased feedstock conversion, gasoline, LPG, dry gas, and coke yields, but decreased diesel yield. Conversely, increasing the feedstock mass flow rate showed opposite trends. Different trends in product yields were observed with varying inlet catalyst temperatures, with optimal product distribution at 973.15 K.

CFD modeling of gas–solid flow in a two‐stage jetting fluidized bed with an overflow standpipe

AbstractThe two‐fluid model–kinetic theory of granular flow (TFM–KTGF) model and the sub‐grid‐scale (SGS) model are used to conduct a three‐dimensional numerical simulation study on the hydrodynamic characteristics of a two‐stage fluidized bed with an integrated overflow pipe. Using various drag models, the gas–solid flows, bed expansions, pressure drop distributions, and equilibrium conditions in the two‐stage bed are compared, and the conditions for the formation of a stable overflow in the two‐stage bed are thoroughly investigated. In addition, during the simulation of the secondary distribution in the bed, the porous media model simulates the momentum loss caused by the redistribution plate to avoid the direct simulation of the redistribution plate, which requires extensive grid division work and calculation costs. This work can provide technical direction for the industrialization of one‐step coal to multistage fluidized bed natural gas technology.

Development of a CFD-DEM Model for a 1 MWth Chemical Looping Gasification Pilot Plant Using Biogenic Residues as Feedstock.

Chemical looping gasification (CLG) is a novel dual fluidized bed gasification process that enables the conversion of solid feedstocks to a nitrogen-free syngas through in situ air separation, avoiding a costly air separation unit. While there have been recent advances in experimental studies, modeling of CLG is almost exclusively restricted to lab-scale units or 1D models. In this study, a 3D CFD-DEM model of a 1 MWth fuel reactor for the conversion of solid biomass was developed. Due to the high computational demand of the DEM method, a coarse-grained approach was used in combination with a simplified reaction network. The hydrodynamics were modeled with an EMMS drag model. Simulations were conducted for two woody biomasses and wheat straw based on experimental data of a 1 MWth CLG reactor. The model was able to predict the pressure profile over the reactor accurately, with a mean error below 10%. Carbon conversion and oxygen carrier oxidation were in good agreement with the experimental data with mean deviations below 5%, while reasonable values below 8 mol % mean error were achieved for the gas composition. Discrepancies in the gas composition as well as temperature profile indicate that further work is needed in the pyrolysis step of the model.

A simple EMMS drag model for the simulation of bubbling fluidized beds using mesoscience-based structural model

State-of-the-art EMMS drag model for bubbling fluidization needs an empirical correlation for bubble diameter. In this short communication, an EMMS drag model is developed to predict the effective drag coefficient without the use of an empirical correlation for bubble diameter. The model is then coupled with mesoscience-based structural model to simulate the hydrodynamics of three bubbling fluidized beds, it is shown that the bed hydrodynamics can be predicted reasonably well, in terms of axial and radial solid concentration profiles. Present study establishes an effective and simple model for simulating bubbling fluidization using mesoscience-based structural model.

Drag Modeling Effects on Simulations of Supersonic Jet-Induced Cratering in a Soil

The impact of the drag model in the simulation of turbulent granular flows is studied using databases here created through simulations of supersonic jet-induced cratering in granular soil. The simulations are based on a previously developed model, which was shown to be hyperbolic, thus permitting the unhindered propagation of pressure waves critical to craters produced by supersonic plumes. The goal is to identify predicted quantities from these simulations that show sufficient differences among simulations performed with different drag models; these quantities would warrant future experimental investigations determining which model is correct. Among all drag models examined, only two models are found applicable to the regime of investigation. Examination of the databases is conducted from the viewpoint of global quantities and detailed quantities. The results show that isocontours and characteristic length scales are minimally affected by the employed drag law. In contrast, azimuthally averaged and root mean square ejecta-related quantities are more sensitive to the drag model employed, but only in the central part of the crater. This sensitivity is much larger for shallow craters having a parabolic cross section than for deep craters having a conical cross section, thus indicating the experimental configuration best suited to experimentally evaluating drag models.

Investigation of models to estimate flight performance of gliding birds from wakes.

Mathematical models based on inviscid flow theory are effective at predicting the aerodynamic forces on large-scale aircraft. Avian flight, however, is characterized by smaller sizes, slower speeds, and increased influence of viscous effects associated with lower Reynolds numbers. Therefore, inviscid mathematical models of avian flight should be used with caution. The assumptions used in such models, such as thin wings and streamlined bodies, may be violated by birds, potentially introducing additional error. To investigate the applicability of the existing models to calculate the aerodynamic performance of bird flight, we compared predictions using simulated wakes with those calculated directly from forces on the bird surface, both derived from computational fluid dynamics of a high-fidelity barn owl geometry in free gliding flight. Two lift models and two drag models are assessed. We show that the generalized Kutta-Joukowski model, corrected by the streamwise velocity, can predict not only the lift but also span loading well. Drag was predicted best by a drag model based on the conservation of fluid momentum in a control volume. Finally, we estimated force production for three raptor species across nine gliding flights by applying the best lift model to wake flow fields measured with particle tracking velocimetry.

Modeling of Dual‐Factor Drag Correction Model for Bubbly Flow under Elevated Pressure

AbstractA pressure correction method is proposed considering the influence of a dual factor. The applicability of a pressure correction method coupled with a drag model is discussed along with the accuracy of the simulation results obtained by such a pressure correction method. It is found that the present pressure correction method combined with the DBS (dual bubble size) drag model can accurately reflect the changing trend of gas holdup distribution with pressure. It is also established that results from this model applied to a bubble column match well with the experimental data. Finally, when compared with other pressure correction models, the proposed model shows better robustness in three‐dimensional simulations and can predict radial gas holdup distributions with better accuracy.

A new controllable weak recycling inflow turbulence generator for evaluating wind effects on building in LES

The weak recycling method, known as the “rescaling-recycling” method, has been extended to simulate micro-scale turbulent atmospheric boundary layers (ABL) by employing staggered blocks in the developing section, replicating physical ABL wind tunnel setups. However, this method faces challenges, such as the need to re-evaluate the sizes and configurations of roughness elements when addressing different objective structures, computational domain sizes, or ground exposures. To address these issues, we propose a controllable weak recycling (CWR) method for generating turbulent ABL flows over rough surfaces in large eddy simulation (LES). This method can directly produce a turbulent boundary layer with arbitrary target characteristics in a single simulation, significantly enhancing generation efficiency and reducing computational resource consumption. Our refinement method incorporates a feedback proportional control algorithm into the “rescaling” procedure to minimize errors between simulated and targeted turbulence intensities. Besides, an existing drag model is utilized in the near-ground region to maintain horizontal homogeneous ABL flows over rough surfaces. The proposed CWR method is validated by simulating three turbulent ABL flows over various rough terrains using LES. Results confirm that the generated inflow turbulence adheres to prescribed mean velocities and turbulence intensities, demonstrating consistent self-sustainability along the flow direction. Furthermore, the generated wind spectra closely align with the anisotropic von-Kármán spectrum. When applying the extracted wind time histories at the main domain’s inlet, we find that the mean and fluctuating wind pressures on a high-rise building closely match specified wind tunnel test results.

Investigating Proppant Transport in Slickwater Fractures using Direct Numeriacl Simulations (DNS) and Two-Fluid Models (TFM)

Proppant / fracturing fluid two-phase separation always occurs in proppant-slickwater systems, especially in fractures with small width created by low-viscosity slickwater. Forces acting on the proppant include drag from the fluid, body force and force due to inter-particles impede / improve proppant settling. In this paper, lattice Boltzmann method (LBM) using direct numerical simulation (DNS) scheme presented is motivated to resolve lightweight and regular-weight proppant carried by slickwater. DNS simulations have investigated Archimedes number (Ar), proppant volume fraction (ϕ), wall effect (W/dp), horizontal crossflow (Rex) and proppant-slickwater density ratio (ρp/ρf). It is observed that Rex and ρp/ρfhave little effect on proppant settlement as the balance between proppant weight and slickwater viscosity is fixed at a constant Ar. Thus, the proppant carried by slickwater relevant drag correlation series have been derived using small-scale DNS, which is a look-up table that takes fracture aperture, amount of proppant and rheology of fracturing fluid into account. Furthermore, the performances of proppant transport were evaluated by the rate of formation of proppant bank quantitatively and the length and height of proppant bank formed in fractures qualitatively. The drag correlations derived from DNS and Beestra Van der Hoef Kuipers (BVK) were then substituted into MFIX Two Fluid Model (TFM). Proppant bank propagation and equilibrium height in the experiments have validated this DNS derived drag model. Finally, it is to apply DNS-derived drag correlations to characterize proppant settling and transport by slickwater.

Numerical study on Fe3O4 nanoparticle separation from water flow using magnetic field: A 3D simulation

The development of magnetic separation technology using magnetic nanoparticles offers a promising avenue for targeted drug delivery and dealing with the upcoming water crises, environmental pollution and the gradual mineral resource depletion. In this study, a three-dimensional Lagrangian Discrete Phase Model (DPM) is carried out to simulate the performance of Fe3O4 nanoparticles to improve the separation process under the influence of an external magnetic field within a horizontal pipe. The crucial role of the drag force in capture efficiency (CE) prompted its examination, simulating various drag models for groups of particles. The Stokes-Cunningham model, showing a 3.59% average error is a suitable choice compared to experimental results. The research examines the impact of effective parameters, including flow velocity, magnetic field intensity, wire location, particle size and mass flow rate, and pipe diameter on CE and flow pattern. The results show that increasing nanoparticle concentration reshapes the flow pattern due to secondary flows without significantly changing separation efficiency. Moreover, decreasing flow velocity, diminishes drag force and enhances magnetic force impact. Specifically, reducing the velocity to a third increases CE by 37%. Furthermore, capture capacity varies approximately linearly with electric current. Due to the magnetic force’s role as a volumetric force in interphase momentum transfer, the increase in particle size from 200 to 500 nm at 3 × 105 A enhances CE by nearly 50%. However, increasing the pipe diameter diminishes particle capture, attributed to higher Reynolds numbers. According to the results, the impact of increasing magnetic field intensity and particle size on CE improvement is notably more pronounced compared to the effect of flow velocity reduction. A comparative analysis of three injection types reveals that using the group injection type helps to select an appropriate injection location to increase CE and identify the final positions of nanoparticles.