Drag Model Research Articles

Enhancement investigation of mass transfer and mixing performance in the static mixers with three twisted leaves

Abstract The mass transfer and mixing performance in the static mixers with three twisted leaves (TKSM) were investigated by the computational fluid dynamics coupled population balance model. A high-precision and efficient gas-liquid two phase model were evaluated by considering several drag models based on experimental bubble size distributions. The bubble size prediction matched well with experimental data and the mean relative error of Sauter mean diameter (d 32) between the prediction and experiment values is 4.93 %. The drag correction factor considering hindering effect of small bubbles can improve the accuracy of cumulative probability distribution (CPD) prediction by 10.06 %. Bubble breakup capacity is quantized via gas-liquid interfacial area, and an empirical correlation between Eo and bubble aspect ratio (γ) have been proposed to predict morphological characteristics of bubble swarms. The effect of liquid Re on the mass transfer rate is much more significant than that of gas volume fraction (α d). The coefficients of variation profiles show that RL-TKSM has better mixing efficiency compared with LL-TKSM and perfect mixing could be achieved after seven mixing elements. The micro mixing efficiency of RL-TKSM is 1.06–1.14 times that of LL-TKSM, which indicates that RL-TKSM has excellent mixing and mass transfer performances.

Numerical study of the wall-retardation effect on proppant transport in rough fractures

Proppant transport and distribution in fractures is critical to evaluate the effectiveness of hydraulic fracturing of unconventional reservoirs such as shale and tight sandstone. This study reproduced the process of proppant transport in rough fractures by two fluid method (TFM) and investigated the wall-retardation effect on proppant migration and settlement. Based on our previous work, the solid–liquid drag model considering wall-retardation effect was further discussed by Lattice Boltzmann method (LBM). The characteristics of rough surfaces of shale and tight sandstone samples were analyzed, and the 4 m × 0.3 m (length × height) rough fracture models were constructed based on these characteristics. The proppant transport and distribution in smooth fractures, sheared fractures and joint fractures were compared, and then the effects of fracture morphology, aperture and mated state on the retarded proppant transport were explored. In smooth fractures, the effect of wall retardation will disappear when the eccentric factor is more than 2.5. In rough fractures, the wall-retardation effect on proppant transport is further enhanced by the unevenly distributed fracture aperture. Both vertical and horizontal velocity of proppant decrease in rough fractures, and this phenomenon is strengthened when the wave-shaped texture or stratification is vertical to the flow direction. The none-flow zones formed by the contact of fracture surfaces will even destroy the continuity of flow filed and block up the proppant transport. However, the morphology of rough fractures will produce little impact on proppant transport when the mean fracture aperture overs the critical fracture aperture. For sheared fractures, the critical fracture aperture is around 6 mm, while for joint fractures, the critical fracture aperture is much less than 4 mm.

3D CFD-PBM simulation of gas–solid bubbling beds of Geldart A particles with sub-grid drag correction

The importance of bubble dynamics in fluidized beds is underscored by the efforts undertaken over the past decades through experimental and numerical studies. Nonetheless, the bubble dynamic evolution and its effects on sub-grid closures were neglected in previous coarse-grid CFD models, particularly for Geldart A particles. In this article, a population balance model with improved kernels was employed to describe the bubble dynamic evolution in three-dimensional bubbling beds, whereby the EMMS drag model was closedto be incorporated into an Eulerian continuum model . Furthermore, the Extended Quadrature Method of Moments (EQMOM) was utilized to reconstruct the number density function of bubble size once their lower moments were obtained. The simulation results showed that the hydrodynamics including bed expansion characteristics, solids concentration and bubble size distribution can be well predicted by the model, indicating its capability to capture the heterogeneous structures in three-dimensional bubbling beds of fine particles.

Experimental validation of the screw compressor oil drag model for various rotor profiles

Injecting oil inside the compressor chambers of the oil-flooded, twin-screw compressors has several advantages. Oil cools the compressing fluid upon mixing with it and hence the compression process is brought nearer to the ideal isothermal compression process. The oil also serves as a lubricant between the meshing rotors and other clearance gaps in the compressor. The thin film of oil formed in the clearance gaps prevents internal leakages too; enhancing the volumetric efficiency of the compressor. Among these desirable effects of injecting oil in screw compressors, there is an undesirable effect too. The interaction (friction) of oil films formed in various clearance gaps with the rotors leads to a drag power loss. Recent studies such as Abdan et al. have proposed more detailed and accurate methods to estimate the oil drag losses in screw compressors. These methods enable the modelling of the effect of even minor changes in rotor profile on the drag loss power. Predictions of this model were hence used to tweak the screw rotor profiles with an objective to reduce the oil drag losses. Such profiles were then retrofitted in the existing machines and tested. Comparing the differences in power consumption of these machines, the component of oil drag loss was deduced. The experimental results show close agreement with the oil drag loss prediction model. The reduction of oil drag losses through profile modifications led to an improvement in the specific power of oil-flooded screw compressor.

Modeling Microplastic Transport in the Marine Environment: Testing Empirical Models of Particle Terminal Sinking Velocity for Irregularly Shaped Particles.

Microplastic (mP) pollution has been indicated as an area of concern in the marine environment. However, there is no consensus on their potential to cause significant ecological harm, and a comprehensive risk assessment of mP pollution is unattainable due to gaps in our understanding of their transport, uptake, and exchange processes. This research considers drag models that have been proposed to calculate the terminal settling velocity of regularly and irregularly shaped particles to assess their applicability in a mP modeling context. The evaluation indicates three models that predict the settling velocity of mPs to a high precision and suggests that an explicit model is the most appropriate for implementation in a mP transport model. This research demonstrates that the mP settling velocity does not vary significantly over time and depth relevant to the scale of an ocean model and that the terminal settling velocity is independent of the initial particle velocity. These findings contribute toward efforts to simulate the vertical transport of mPs in the ocean, which will improve our understanding of the residence time of mPs in the water column and subsequently their availability for uptake into the marine ecosystem.

Self-Attenuation of Drillstring Torsional Vibrations Using Distributed Dampers

Summary During drilling operations, drillstring vibrations cause many downhole dysfunctions, resulting in underperformance, equipment failure, and possibly wellbore damage. Current drillstring vibration mitigation solutions are generally located at a single site, either at the topdrive or close to the bit. However, because the sources of vibration excitation are distributed along the whole drillstring, these single-point vibration damping solutions do not succeed in removing all vibration modes. A distributed vibration damping solution is investigated, wherein damping subs are placed at intervals along the drillstring. The drillpipe rotates on bearings inside the damping subs, thereby reducing mechanical torque. The damping sub has a slightly larger diameter than the neighboring tool joints, lifting the drillstring off the borehole wall and thus eliminating most of the mechanical friction between the damping subs. Viscous friction is introduced in the form of rotary eddy current brakes within the damping subs, which cause the damping of torsional oscillations. The damping sub moves axially on spur wheels supported by bearings, thereby reducing drag forces. The decoupling of rotary and axial movement is a key element for removing a source of excitation. Simulations made with a 4n degree-of-freedom (DOF) transient torque and drag model confirm the expected results. The results of simulations for a use case based on a complex 3D trajectory are presented. With damping subs every 30 m and a damping coefficient of 20 N·s/rd, the topdrive torque is reduced to 40% of that of a plain drillstring, and torsional stability is obtained across the topdrive speed range of 60 to 180 rev/min. By comparison, conventional nonrotating pipe protectors (NRPPs) would have reduced the topdrive torque to 30%, but torsional stability would have not been achieved because the expected damping coefficient was less than 0.02 N·s/rd. The design of the damping sub relies on readily available technological components that can sustain very high pressures and temperatures. The damping subs are therefore compatible with high-pressure/high-temperature applications, including geothermal drilling.

A unified CFD methodology for Gas-Solid fluidized beds based on the Quasi-Three-Fluid approach

This work aims on developing a unified numerical methodology which can be utilized for addressing the challenge of accurately describing mesoscale structures in the simulation of gas–solid fluidization systems. To achieve this goal, a dependable and unified model is established to correct the simulation results under diverse fluidization through adjusting the drag models or initial emulsion phase state, and several correction methods that are applicable to a variety of fluidizations are proposed. The developed quasi-three-fluid method can be used to accurately predict the mesoscale structures of bubbles and particle clusters in gas–solid fluidized beds with particle type of Geldart A or B. Furthermore, the unified analysis capability for gas–solid fluidized beds is improved via reasonable application of quasi-three-fluid approach.

A Tensile Rotary Airborne Wind Energy System—Modelling, Analysis and Improved Design

A unique rotary kite turbine designed with tensile rotary power transmission (TRPT) is introduced in this work. Power extraction, power transmission and the ground station are modelled in a modular framework. The TRPT system is the key component of power transmission, for which three models with different levels of complexity are proposed. The first representation is based on the stationary state of the system, in which the external and internal torques of a TRPT section are in equilibrium, referred to as the steady-state TRPT model. The second representation is a simplified spring-disc model for dynamic TRPT, and the third one is a multi-spring model with higher degrees of freedom and more flexibility in describing TRPT dynamics. To assess the torque loss on TRPT, a simple tether drag model is written for the steady-state TRPT, followed by an improved tether drag model for the dynamic TRPT. This modular framework allows for multiple versions of the rotor, tether aerodynamics and TRPT representations. The developed models are validated by laboratory and field-testing experimental data, simulated over a range of modelling options. Model-based analysis are performed on TRPT design, rotor design and tether drag to understand any limitations and crucial design drivers. Improved designs are explored through multi-parameter optimisation based on steady-state analysis.

Particle-scale and sub-grid drag models coupled CFD for simulating the CO methanation in a CFB riser

The diffusion and chemical reactions inside the catalyst particles and the heterogeneous flow structure in the computational cells are key factors to affect the accuracy of the coarse-grid simulation in circulating fluidized bed (CFB) methanation reactors. In this work, a particle-scale model is developed to calculate the effective reaction rate considering the transient diffusion and chemical reactions in the particle scale, i.e., the scale of the single catalyst particle. A modified sub-grid drag model is proposed to consider the effects of the meso-scale and chemical reactions on the heterogeneous gas-solid interaction, where the meso-scale is between the single particle and the whole reactor and featured with the particle cluster. Subsequently, a coupled model is developed by integrating the particle-scale and modified sub-grid drag models into CFD. Moreover, the coupled model is validated to achieve accurate predictions on the CO methanation process in a CFB riser. Notably, the coupled model can be performed with a coarse grid (∼58 times particle diameter) and a large time step (0.005 s) to accelerate the simulation. By simply changing the reaction kinetics, different gas-solid catalytic reaction systems can be simulated by using the coupled model.

A high‐order stabilized solver for the volume averaged Navier‐Stokes equations

AbstractThe volume‐averaged Navier‐Stokes equations are used to study fluid flow in the presence of fixed or moving solids such as packed or fluidized beds. We develop a high‐order finite element solver using both forms A and B of these equations. We introduce tailored stabilization techniques to prevent oscillations in regions of sharp gradients, to relax the Ladyzhenskaya–Babuska–Brezzi inf‐sup condition, and to enhance the local mass conservation and the robustness of the formulation. We calculate the void fraction using the particle centroid method. Using different drag models, we calculate the drag force exerted by the solids on the fluid. We implement the method of manufactured solution to verify our solver. We demonstrate that the model preserves the order of convergence of the underlying finite element discretization. Finally, we simulate gas flow through a randomly packed bed and study the pressure drop and mass conservation properties to validate our model.

Ground Risk Estimation of Unmanned Aerial Vehicles Based on Probability Approximation for Impact Positions with Multi-Uncertainties

In this paper, a methodology to assess ground risk with multi-uncertainties is introduced, which is associated with a major unmanned aerial vehicle (UAV) in-flight incident. In the assessment model, random factors are taken into account including uncertainty in the drag force, uncertainty in the UAV velocity, and the random effects of local wind. The probability distribution of impact positions is first estimated by using a second-order drag model with probabilistic assumptions regarding the least well-known parameters. Then, an approach for modeling and estimating the ground risks is presented, in which the ground casualties are set as the safety index. In the multifactor risk estimation model, ground casualty areas covered by the UAVs’ debris are determined. Correspondingly, the probability of fatal injuries to people is derived by addressing the protection effects, impact energy, and energy threshold a person can sustain. Further, four kinds of sheltering effects are defined. Finally, the affected area on the ground is partitioned into six zones, taking into consideration the density and distribution of the local population. Case studies are conducted for fixed-wing and rotary-wing UAVs. Risk levels on the ground are obtained and compared with the widely accepted target safety level of manned aircrafts.

Remediation of lindane contaminated soil by fluidization-like dielectric barrier discharge.

This study proposed the fluidization-like dielectric barrier discharge (DBD) plasma for the remediation of lindane contaminated soil and integrated physical and chemical reaction pathway. Soil particle distribution within the reactor was simulated with Euler-Euler and Gidaspow drag models, and a bipolar pulsed power supply was applied to energize the DBD reactor after full fluidized. The effect of soil particles movement on electric features was discussed in terms of voltage waveforms and Lissajous figures. Lindane degradation was found to be related to electrics parameters and soil properties. Soil samples before and after treatment were analyzed by XRD and SEM methods. A 95.98% lindane decomposition and 0.66mgLindane/h average reaction rate were obtained with 3wt% CaO injection by pulse power drove fluidization-like DBD after 32min treatment. Ozone was proved to play a major role during lindane degrading by plasma. The reaction potential pathway of lindane decomposition contains 4 steps, including dehydrogen, dehydrochlorination, and dechlorination, respectively.

Implementation and study of a drag model for an N-body problem simulator

Implementation and study of a drag model for an N-body problem simulator

Modeling particle collisions in moderately dense curtain impacted by an incident shock wave

The interactions between an incident shock and a moderately dense particle curtain are simulated with the Eulerian–Lagrangian method. A customized solver based on OpenFOAM is extended with an improved drag model and collision model and then validated against two benchmark experiments. The results show that the collision model has a limited impact on curtain morphology compared with the improved drag model. In this work, parametric studies are performed considering different particle sizes, volume fractions, and curtain thicknesses. Smaller particle sizes and larger volume fractions lead to stronger reflected shock and weaker transmitted shock. Attention is paid to the particle collision effects on the curtain evolution behaviors. According to our results, for the mono-dispersed particle curtain, the collision effects on curtain front behaviors are small, even when the initial particle volume fraction is as high as 20%. This is due to the positive velocity gradient across the curtain after the shock wave passage, leading to the faster motion of downstream particles than the upstream ones, and hence, no collision occurs. For the bi-dispersed particle curtain, the collision effects become important in the mixing region of different-size particles. Collisions decelerate small particles while accelerating large ones and cause velocity scattering. Moreover, increasing the bi-dispersed curtain thickness leads to multiple collision force peaks, which is the result of the delayed separation of different particle groups. Our results indicate that the collision model may be unnecessary to predict curtain fronts in mono-dispersed particles, but in bi-dispersed particles, the collision effects are important and, therefore, must be modeled.

A bubble-based drag model of rough sphere for the simulation of bubbling fluidized bed

A bubble-based drag model of rough sphere for the simulation of bubbling fluidized bed

Modeling of a detailed bow spring centralizer description in stiff-string torque and drag calculation

Flexible bow spring centralizers are commonly used in the drilling industry to ensure a good centralization of casings inside the borehole. A bow spring centralizer consists of multiple bows evenly spaced around the tubular. They are attached to the casing at multiple locations via connections or rings, and run-in hole such that the bows are sliding against the borehole. To provide a good centralization, the bows must be stiff enough to push the casing away from the borehole. Also, it must be flexible enough to avoid large contact forces and consequently friction forces that can cause excessive drag. This paper aims to present a theoretical model for bow-spring centralizers and its implementation in a stiff-string torque and drag model based on the finite element method.Our modeling approach assumes that the flexible centralizer bows are identical. Each bow acts independently from the others and could be in contact with the borehole or not, depending on the lateral displacement and orientation of the centralizer. The bow force follows a power law based on a constant stiffness and a stiffness power coefficient that are computed based on test measurements provided by the manufacturer.When introduced in a stiff-string torque and drag model, the contact forces are computed on each individual bow. For drag forces, the bows are assumed to be non-rotating inside the borehole, so the axial friction force at a bow spring is related to the algebraic sum of all bow contacts. When the casing is rotating inside the centralizer, a tangential friction force is generated between the casing and bow spring rings. It is related to the resultant contact force i.e., the vector sum of all bow contacts.An example of the calibration for a bow-spring centralizer is studied in this paper. The theoretical bow-spring model showed its capacity to have a good interpretation of the measurements. It also showed the importance of specifying the testing condition with regards to the possible clearance between the casing and centralizer rings. The finite element torque and drag model is firstly validated against another model. When applied to a case study of running in hole a casing string with bow-spring centralizers, the model shows its effectiveness to describe the casing centralization along the wellbore as well as the tension variations at the surface.

Quantum Solid Phase and Coulomb Drag in 2D Electron–Electron Bilayers of MoS2

AbstractCoulomb drag experiments can give information about the interaction state of double‐layer systems. Here, anomalous Coulomb drag behaviors are demonstrated in a 2D electron–electron bilayer system constructed by stacking atomically thin MoS2 on opposite sides of thin dielectric layers of boron nitride. In the low‐temperature regime, the measured drag resistance does not follow the behavior predicted by the Coulomb drag models of exchanging momenta and energies with the particles in Fermi‐liquid bilayer systems. Instead, it shows an upturn to higher and higher values. Quantum solid/fluid phases and the Kosterlitz–Thouless/Wigner 2D quantum melting transition are investigated in this bilayer system and this interesting phenomenon is described based on thermally activated carriers of quantum defects from the formation of the correlation‐induced electron solid phases, with enhanced stabilization by the potential due to the boron nitride dielectric layers.

Point-particle drag, lift, and torque closure models using machine learning: Hierarchical approach and interpretability

Point-particle closure models that are utilized in Euler-Lagrange simulations play an important role in replicating true dynamics of particle-laden flows. The accuracy of these point-particle models depends on how well they incorporate the local microstructural information of neighboring particles. The current work presents a physics-based hierarchical machine learning approach for developing robust N-body closures. The inclusion of ternary interactions, in addition to binary interactions, enabled by the hierarchical approach leads to improved predictions.

Impact of Limited Degree of Freedom Drag Coefficients on a Floating Offshore Wind Turbine Simulation

The worldwide effort to design and commission floating offshore wind turbines (FOWT) is motivating the need for reliable numerical models that adequately represent their physical behavior under realistic sea states. However, properly representing the hydrodynamic quadratic damping for FOWT remains uncertain, because of its dependency on the choice of drag coefficients (dimensionless or not). It is hypothesized that the limited degree of freedom (DoF) drag coefficient formulation that uses only translational drag coefficients causes mischaracterization of the rotational DoF drag, leading to underestimation of FOWT global loads, such as tower base fore-aft shear. To address these hydrodynamic modeling uncertainties, different quadratic drag models implemented in the open-source mid-fidelity simulation tool, OpenFAST, were investigated and compared with the experimental data from the Offshore Code Comparison Collaboration, Continued, with Correlation (OC5) project. The tower base fore-aft shear and up-wave mooring line tension were compared under an irregular wave loading condition to demonstrate the effects of the different damping models. Two types of hydrodynamic quadratic drag formulations were considered: (1) member-based dimensionless drag coefficients applied only at the translational DoF (namely limited-DoF drag model) and (2) quadratic drag matrix model (in dimensional form). Based on the results, the former consistently underestimated the 95th percentile peak loads and spectral responses when compared to the OC5 experimental data. In contrast, the drag matrix models reduced errors in estimates of the tower base shear peak load by 7–10% compared to the limited-DoF drag model. The underestimation in the tower base fore-aft shear was thus inferred be related to mischaracterization of the rotational pitch drag and the heave motion/drag by the limited-DoF model.

A Sea Surface–Based Drag Model for Large-Eddy Simulation of Wind–Wave Interaction

Abstract Monin–Obukhov similarity theory (MOST) is a well-tested approach for specifying the fluxes when the roughness surfaces are homogeneous. For flow over waves (inhomogeneous surfaces), phase-averaged roughness length scales are often prescribed through models based on the wave characteristics and the wind speed. However, such approaches lack generalizability over different wave ages and steepnesses due to the reliance on model coefficients tuned to specific datasets. In this paper, a sea surface–based hydrodynamic drag model applicable to moving surfaces is developed to model the pressure-based surface drag felt by the wind due to the waves. The model is based on the surface gradient approach of Anderson and Meneveau applicable to stationary obstacles and extended here to the wind–wave problem. The wave drag model proposed specifies the hydrodynamic force based on the incoming momentum flux, wave phase speed, and the surface frontal area. The drag coefficient associated with the wind–wave momentum exchange is determined based on the wave steepness. The wave drag model is used to simulate turbulent airflow above a monochromatic wave train with different wave ages and wave steepnesses. The mean velocity profiles and model form stresses are validated with available laboratory-scale experimental data and show good agreement across a wide range of wave steepnesses and wave ages. The drag force is correlated with the wave surface gradient and out-of-phase with the wave height distribution by a factor of π/2 for the sinusoidal wave train considered. These results demonstrate that the current approach is sufficiently general over a wide parameter space compared to wave phase-averaged models with a minimal increase in computational cost. Significance Statement Understanding the physics of wind waves plays an important role in the context of numerous geophysical and engineering applications. A drag-based model is developed that characterizes the effect of the sea surface waves on the wind above. The model is validated with existing experimental datasets and is shown to be effective in predicting the average wind velocity and stress over waves with varied steepnesses and phase speeds. The ease of implementation and low computational cost of the model make it useful for studying turbulent atmospheric-scale flows over the sea surface important in offshore wind energy research as well as for modeling air–sea fluxes of momentum, heat, and mass.