Drag Model Research Articles

A Simplified Bubble Size Relation Compatible with the Energy Minimization Multiscale Drag Model for Studying Hydrodynamics in a 2D Gas–Solid Tapered Fluidized Bed

Gas–solid fluidized bed reactors are extensively utilized in direct reduced iron production. In practice, these reactors will have a wide particle size distribution, which is better handled by tapered fluidized beds due to their vertical velocity gradient. Herein, a simplified bubble size relation is proposed to remove implicit interdependency between the bubble size and its drag coefficient in the bubble‐based energy minimization multiscale (EMMS) heterogeneous drag model. Further, the proposed drag model is coupled with the two‐fluid kinetic theory of granular flow model to investigate hydrodynamics. The heterogeneous flow structure predicted by the model is similar to experiments. Further, the bulk parameters such as bed expansion ratio and bubble fraction obtained from the simulations using a simplified EMMS drag model are compared and are found to be in good agreement with the experimental findings, with mean relative deviations of 3.95% and 14.64%, respectively. The time‐averaged bubble fraction and bed expansion ratio are found to increase with air velocity and decrease with taper angle, whereas a reverse trend is observed for the mean particulate fluidized area fraction. Based on the current study, the taper angle between 5° and 10° is found to be most suitable.

Experimental investigation of electrostatic capture of 1+ ions in charge breeder electron cyclotron resonance ion source plasma

We present comprehensive experimental data demonstrating that the capture process of the 1+ ions in charge breeder electron cyclotron resonance ion sources (ECRIS) is dominated by electrostatic deceleration by the ambipolar plasma potential, not by cumulative small-angle scattering of the incident ions in ion–ion collisions as postulated previously. To achieve this we varied the plasma potential of an ECRIS charge breeder by adjusting the microwave power applied to sustain the helium discharge and measured the corresponding shift in the optimum injection energy of the 1+ ions. The experiment was repeated with sodium, potassium, and cesium ions. It is shown that the optimum injection energy does not depend on the incident ion mass, which contradicts the collisional drag model. Conversely, the optimum injection energy (in eV) shifts in unison with the plasma potential (in V), which provides strong evidence for the electrostatic deceleration hypothesis.

Evaluation of Classification Possibility of Coke Breeze by Drag Force

Sintered ore used as blast furnace burden materials is produced by mixing iron ore, coke, and limestone, then burning the coke and sintering the iron ore with the combustion heat. Among the coke charged, A particle size of 0.25 mm or less has an insignificant effect as a heat source and adhere to the surface of other materials to inhibit the reaction between oxygen and raw materials, thereby decreasing the quality of sintered ore. Therefore, to increase combustion efficiency, it is necessary to reduce the ratio of coke breeze in the charged coke. In this study, theoretical calculation, experiment and simulation were conducted to investigate the possibility of size classification by drag force in the process of dropping coke after being transported through a belt conveyor. The height of belt conveyor was at 1m, and velocity of the belt was 1.5, 2.3, and 2.6 m/s, which were considered as experimental variables. After falling, the distribution of coke particle size according to the horizontal travel distance was confirmed, and a fall trajectory prediction formula model was created through the drag model of polydisperse system and compared with the experimental and analysis results.

Correction: A Stochastic Drag Model for Improved Uncertainty Realism of Select LEO Orbit Predictions

Correction: A Stochastic Drag Model for Improved Uncertainty Realism of Select LEO Orbit Predictions

A modified CFD-DEM method for accurate prediction of the minimum fluidization velocity

Monodisperse fluidized bed experiments have been carried out on 13 kinds of particles with different particle sizes in a cylindrical fluidized bed. The accuracy of nine commonly used monodisperse drag models, including the Gidsapow, BVK, and Zhou–Fan models is verified. It is found that the Zhou–Fan model is the most accurate at low and moderate values of the particle Reynolds number. It is found that with the traditional computational fluid dynamics–discrete element method (CFD-DEM) method it is difficult to obtain an accurate minimum fluidization velocity owing to difficulty in obtaining an accurate value of the minimum fluidization solid volume fraction. A modified method is proposed to increase the accuracy of prediction of the minimum fluidized solid volume fraction by using a virtual particle size in the calculation of the particle collision process. The effectiveness of the modified method is verified by comparing the CFD-DEM simulation results with experimental results for Geldart-D particles. The relative error of the minimum fluidization velocity is found to be reduced from 24.6% to 2%.

Design and hydraulic study of double‐partition dividing‐wall column

AbstractDividing‐wall column (DWC) provides tremendous advantages in terms of energy savings and capital costs for three‐component and even multi‐component separations. With increasing industrial application of three‐component DWCs, DWCs for separation of four‐component have received considerable research attention. The aim of this work is to investigate the design of the two‐staggered wall region and gas–liquid two‐phase flow behavior on the tray in a double‐partition DWC (DPDWC). The Aspen Plus was applied to simulate the steady state to obtain the gas–liquid‐phase flow rate in each region to serve as the basis for the tray design. In different task regions, the gas‐ and liquid‐phase flow varied in some ways. The drag models have variability for the study of fluid flow, and the Tomiyama model is more appropriate. Moreover, high‐velocity gradients and recirculating phenomenon can be discovered owing to the existence of multiple partitions in DPDWC.

Data-Driven Car Drag Prediction With Depth and Normal Renderings

Abstract Generative artificial intelligence (AI) models have made significant progress in automating the creation of 3D shapes, which has the potential to transform car design. In engineering design and optimization, evaluating engineering metrics is crucial. To make generative models performance-aware and enable them to create high-performing designs, surrogate modeling of these metrics is necessary. However, the currently used representations of 3D shapes either require extensive computational resources to learn or suffer from significant information loss, which impairs their effectiveness in surrogate modeling. To address this issue, we propose a new 2D representation of 3D shapes. We develop a surrogate drag model based on this representation to verify its effectiveness in predicting 3D car drag. We construct a diverse dataset of 4535 high-quality 3D car meshes labeled by drag coefficients computed from computational fluid dynamics simulations to train our model. Our experiments demonstrate that our model can accurately and efficiently evaluate drag coefficients with an R2 value above 0.84 for various car categories. Our model is implemented using deep neural networks, making it compatible with recent AI image generation tools (such as stable diffusion) and a significant step toward the automatic generation of drag-optimized car designs. Moreover, we demonstrate a case study using the proposed surrogate model to guide a diffusion-based deep generative model for drag-optimized car body synthesis.

Particle removal from solid surfaces via an impinging gas jet pulse: Comparison between experimental and CFD-DEM modeling results

Computational and experimental studies are performed to investigate the influence of a gas jet pulse impinging perpendicularly onto a flat solid surface seeded with a monolayer of spherical particles. A numerical resuspension model is derived to predict particle release into the gas phase during jet impingement. To this end, discrete particles are immersed in a continuous gas phase modeled via Large Eddy Simulation to capture the effect of jet turbulence on the particle detachment process. Two-way coupling between particulate and gas phase is established via a near-wall particle drag model and a lift model. Direct particle–wall interactions are captured with adhesion, rolling friction and sliding friction models. To validate the overall modeling approach, numerical results are compared with resuspension experiments for monodisperse polystyrene particles placed on a glass slide. Simulations show that the particles preferentially mobilize by rolling, followed to a limited extend by lift off from the solid surface driven by aerodynamic forces and particle–particle collisions. Resuspension occurs in the first instants after jet impingement. Computational and experimental results for removal efficiency Γ are in good agreement in terms of the location of their r50 parameter, i.e., the radial position where 50% of the particles have been removed by the jet; both results show a linear dependence between the r50 value and the jet Reynolds number of the impinging jet. However, experimental Γ(r) curves generally have a smooth sigmoidal shape whereas numerical results predict a sharp transition. Some model shortcomings are identified which lead to an underprediction of particle lift-off and which explain the observed differences. Furthermore, the experimental Γ curves nearly collapse onto each other when plotted over the predicted local wall-shear stress.

CFD‐ANN coupling model simulation of gas–solid feeding design for ternary biomass mixtures in bubbling fluidized bed gasifier

AbstractThe performance of continuous feeding fluidized bed reactors is significantly influenced by their design. These reactors can effectively operate with a wide range of biomass mixtures. Therefore, it is imperative to carefully design the gas distributor plate and solid tube inlet to ensure stable fluidization and uniform distribution of fluidizing gas and solid particles within the reactor. This study investigated the impact of gas–solid feeder design in bubbling fluidized bed gasifier for biomass mixtures on system hydrodynamics, employing a computational fluid dynamics–artificial neural network (CFD‐ANN) coupling model to achieve more realistic simulations. A 2k factorial experimental design was adopted to inquire the impact of gas and solid feeding systems. The responses under investigation included the gas–solid mixing index and the solid residence time, both of which hold pivotal roles in specific chemical processes related to biomass utilization in fluidized bed technology. All cases were successfully simulated, and the results uncovered that the position and length of the solid inlet tube wielded a significant influence on reactor performance, particularly concerning solid residence time. Furthermore, the designs of the gas distributor were identified as critical factors capable of enhancing system turbulence and mixing. In summary, the results showed the potential for enhancing reactor performance through the optimization of gas–solid feeding systems and underscored the efficacy of the ANN drag model in simulating continuous biomass gasification systems.

A Stochastic Drag Model for Improved Uncertainty Realism of Select LEO Orbit Predictions

A Stochastic Drag Model for Improved Uncertainty Realism of Select LEO Orbit Predictions

Novel drag and Nusselt number models based on direct numerical simulations of a bidisperse gas–solid system

AbstractFlow and heat transfer in a bidisperse gas–solid system with freely moving spheres are simulated by particle‐resolved direct numerical simulation (PR‐DNS). Gas–solid coupling is enforced by the direct‐forcing immersed boundary method. Compard with the DNS database, it is found that the existing polydisperse drag correction model developed from static systems combined with various monodisperse drag models underestimates the drag force on dynamic arrays of particles. The existing Nusselt number correction model developed from static systems combined with various monodisperse models overestimates the Nusselt number of dynamic arrays of particles. Sensitivity analysis indicates that the effects of the granular temperature on the drag force and Nusselt number are negligible. Novel polydisperse drag and Nusselt number models are derived based on the database. The advantages of the derived polydisperse drag and Nusselt number models are demonstrated and confirmed by comparing the results of the computational fluid dynamics–discrete element method using various drag and Nusselt number models with experimental or additional PR‐DNS data.

Modelling of cup anemometry and dynamic overspeeding in average wind speed measurements

Abstract. Cup anemometers measure average wind speed in the atmosphere and have been used for one and a half centuries by meteorologists. Within the last half century, cup anemometers have been used extensively in wind energy to measure wind resources and performance of wind turbines. Meteorologists researched cup anemometer behaviour and found dynamic overspeeding to be an inherent and significant systematic error. The wind energy community has strong accuracy requirements for power performance measurements on wind turbines, and this led in the last 2 decades to new research on cup anemometer characteristics, which was taken to a new level with the development of improved calibration procedures, cup anemometer calculation models and classification methods. Research projects in wind energy demonstrated, by field and wind tunnel measurements, that angular response was a significant contributor to uncertainty and that dynamic overspeeding was a significant but less important contributor. Earlier research was mainly made on cup anemometers with hemispherical cups on long arms, ​​​​​​​and dynamic overspeeding was considered an inherent and high uncertainty error for cup anemometers. Research on conical cups on short arms has now shown that zero or low overspeeding is present on a well-designed cup anemometer, providing a much lower overspeeding uncertainty error. Different cup anemometer calculation models were investigated in order to find derived overspeeding characteristics. The general and often used parabolic torque coefficient model showed that zero overspeeding is present when the speed ratio roots of the torque coefficient curve go through the equilibrium speed ratio and zero. The two-cup drag model is a special case of the parabolic torque coefficient model but with the second root being reciprocal to the equilibrium speed ratio. The drag model always results in a positive maximum overspeeding of the order of 1.1 times the turbulence intensity squared. A linear torque coefficient results in maximum overspeeding levels equal to the turbulence intensity squared. Torque characteristics of a cup anemometer with hemispherical cups fit slightly well to the drag model, but a cup anemometer with conical cups does not fit to the drag model nor the parabolic model; it fits better to a partial linear model and even better to an optimized torque model. The most accurate modelling of cup anemometer characteristics is at present made with the ACCUWIND model (Dahlberg et al., 2006). This model uses tabulated torque coefficient and angular response data measured in a wind tunnel. The ACCUWIND model is found in International Electrotechnical Commission (IEC) wind turbine power performance standards, where it is used in a classification system for estimation of operational uncertainties. For an actual comparison of two cup anemometers, with respectively hemispherical and conical cups, the influence of dynamic overspeeding was found to be relatively low compared to angular response, but for conical cups it was specifically low.

Probabilistic Short‐Term Solar Driver Forecasting With Neural Network Ensembles

AbstractSpace weather indices are used to drive forecasts of thermosphere density, which directly affects objects in low‐Earth orbit (LEO) through atmospheric drag force. A set of proxies and indices (drivers), F10.7, S10.7, M10.7, and Y10.7 are used as inputs by the JB2008, (https://doi.org/10.2514/6.2008‐6438) thermosphere density model. The United States Air Force (USAF) operational High Accuracy Satellite Drag Model (HASDM), relies on JB2008, (https://doi.org/10.2514/6.2008‐6438), and forecasts of solar drivers from a linear algorithm. We introduce methods using long short‐term memory (LSTM) model ensembles to improve over the current prediction method as well as a previous univariate approach. We investigate the usage of principal component analysis (PCA) to enhance multivariate forecasting. A novel method, referred to as striped sampling, is created to produce statistically consistent machine learning data sets. We also investigate forecasting performance and uncertainty estimation by varying the training loss function and by investigating novel weighting methods. Results show that stacked neural network model ensembles make multivariate driver forecasts which outperform the operational linear method. When using MV‐MLE (multivariate multi‐lookback ensemble), we see an improvement of RMSE for F10.7, S10.7, M10.7, and Y10.7 of 17.7%, 12.3%, 13.8%, 13.7% respectively, over the operational method. We provide the first probabilistic forecasting method for S10.7, M10.7, and Y10.7. Ensemble approaches are leveraged to provide a distribution of predicted values, allowing an investigation into robustness and reliability (R&R) of uncertainty estimates. Uncertainty was also investigated through the use of calibration error score (CES), with the MV‐MLE providing an average CES of 5.63%, across all drivers.

Maple samara flight is robust to morphological perturbation and united by a classic drag model

Winged, autorotating seeds from the genus Acer, have been the subject of study for botanists and aerodynamicists for decades. Despite this attention and the relative simplicity of these winged seeds, there are still considerable gaps in our understanding of how samara dynamics are informed by morphological features. Additionally, questions remain regarding the robustness of their dynamics to morphological alterations such as mass change by moisture or area change by damage. We here challenge the conventional approach of using wing-loading correlations and instead demonstrate the superiority of a classical aerodynamic model. Using allometry, we determine why some species deviate from interspecific aerodynamic behavior. We alter samara mass and wing area and measure corresponding changes to descent velocity, rotation rate, and coning angle, thereby demonstrating their remarkable ability to autorotate despite significant morphological alteration. Samaras endure mass changes greater than 100% while maintaining descent velocity changes of less than 15%, and are thus robust to changes in mass by moisture or damage. Additionally, samaras withstand up to a 40% reduction in wing area before losing their ability to autorotate, with the largest wings more robust to ablation. Thus, samaras are also robust to wing damage in their environment, a fact children joyfully exploit.

Influence of Frictional Stress Models on Simulation Results of High-Pressure Dense-Phase Pneumatic Conveying in Horizontal Pipe

Based on the two-fluid model, a three-zone drag model was developed, and the kinetic theory of granular flows and the Schneiderbauer solids wall boundary model were modified to establish a new three-dimensional (3D) unsteady mathematical model for high-pressure dense-phase pneumatic conveying in horizontal pipe. With this mathematical model, the influence of the three frictional stress models, namely Dartevelle frictional stress model, Srivastava and Sundaresan frictional stress model, and the modified Berzi frictional stress model, on the simulation result was explored. The simulation results showed that the three frictional stress models accurately predicted the pressure drop and its variations with supplementary gas in the horizontal pipe, with relative errors ranging from −4.91% to +7.60%. Moreover, the predicted solids volume fraction distribution in the cross-section of the horizontal pipe using these frictional stress models exhibited good agreement with the electrical capacitance tomography (ECT) images. Notably, the influence of the three frictional stress models on the simulation results was predominantly observed in the transition region and deposited region. In the deposited region, stronger frictional stress resulting in lower solids volume fraction and a higher pressure drop in the horizontal pipe were observed. Among the three frictional stress models, the simulation results with the modified Berzi frictional stress model aligned better with the experimental data. Therefore, the modified Berzi frictional stress model is deemed more suitable for simulating high-pressure dense-phase pneumatic conveying in horizontal pipe.

Numerical simulation and spray model development of liquid ammonia injection under diesel-engine conditions

Ammonia is regarded as a promising alternative fuel in internal combustion engine for its potential to reduce carbon emissions. Injection process of liquid ammonia will affect air-fuel mixture distribution and therefore combustion efficiency and NOx emissions. However, the experimental studies of liquid ammonia injection under engine conditions are limited, and the key impact factors of spray evolution are still unclear. This study aims to evaluate the applicability of numerical models for liquid ammonia spray, and numerically investigate spray characteristics under diesel-engine conditions (ambient temperature > 800K, ambient pressure > 2 MPa). Large eddy simulation coupled with Lagrangian particle tracking method were conducted, and the results show that the non equilibrium - Frössling phase change model coupled with Schiller-Naumann drag model can provide a good prediction of spray penetration. Liquid penetration increases with ambient pressure decreasing; vapor penetration increases with ambient density decreasing, but insensitive to ambient temperature. Temperature - mixture fraction distribution is sensitive to ambient temperature and superheat degree. Besides, a three-stage 0D model of spray tip penetration under diesel-engine conditions is developed firstly, which can reflect the key impact factors of ammonia spray evolution and provide theoretical support to optimize fuel injection strategy of liquid ammonia-fueled engines.

A CFD study on the start-up hydrodynamics of fluid catalytic cracking regenerator integrated with chemical looping combustion

ABSTRACT The integration of chemical looping combustion with fluid catalytic cracking (CLC-FCC) is an innovative concept that serves as a cost-effective method for CO2 capture in refineries. This approach has the potential to reduce refinery CO2 emissions by 25–35%, offering a promising solution. As in the conventional FCC unit, it is common for CLC-FCC regenerators to be exposed to an on-off process while they are being maintained and cleaned. The novelty of this research lies in its specific focus on a less-explored phase (start-up) of CLC-FCC regenerators, the application of advanced CFD modeling, and the comprehensive analysis of operational parameters that influence the system’s performance. To validate the CFD simulations of the different drag models for solid-gas granular, bed density profiles under steady-state conditions, collected from industrial processes, were used. For the flow period based on the start-up process of the drag models, the fluidization gas inlet geometry of the regenerator, flow regime (laminar and turbulent), and superficial gas velocity were comprehensively investigated to reveal their effects on hydrodynamic characteristics. The results show that Gidaspow and Syamlal-O’Brien drag models of the solid-gas multiphase granular flow exhibited a better fit with industrial data. The Syamlal-O’Brien and Gidaspow models closely align with industrial data under steady-state conditions, displaying similar bed densities in the dense phase region (230–310 kg/m3 for Syamlal-O’Brien and 235–300 kg/m3 for Gidaspow). During the initial stage (less than 0.2 seconds), both laminar and turbulent models yield comparable bed density profiles, approximately 510 kg/m3 in the dense phase. However, as the process progresses, the dense phase density decreases to about 250–350 kg/m3 at around 0.5 seconds, with laminar flow models showing a slightly better fit with industrial data. Notably, at 0.5 seconds of fluidization time, inlet geometries having better gas distribution achieve a highly diluted phase with bed densities of 10–20 kg/m3. Reaching a steady state, the bed density decreases from around 400 kg/m3 to 260–300 kg/m3, expanding into a higher section of the regenerator where it aligns well with industrial data. The increase in superficial gas velocity would result in the clarification of the difference and well mixing of the solid-gas multiphase flow.

Extended landslide velocity and analytical drag

The landslide velocity plays a dominant role in estimating the impact force and devastated area. Here, based on Pudasaini and Krautblatter (Earth Surf Dyn 10:165–189, 2022. https://doi.org/10.5194/esurf-10-165-2022), I develop a novel extended landslide velocity model that includes the force induced by the hydraulic pressure gradient, which was neglected by all the existing analytical landslide velocity models. By a rigorous conversion between this force and inertia, which facilitates constructing exact analytical solutions for velocity, I develop two peer systems expecting to produce the same result. However, this contradicts with our conventional wisdom. This raises a legitimate question of whether we should develop some new balance equations such that these phenomena can be better explained naturally. I compare the two velocity models that neglect and include the force induced by the hydraulic pressure gradient. Analytical solutions produced by the two systems are fundamentally different. The new model is comprehensive, elegant, and yet an extraordinary development as it reveals serendipitous circumstance resulting in a pressure–inertia paradox. Surprisingly, the mass first moves upstream for quite a while; then, it winds back and continues accelerating down slope. The difference between the extended and simple solution is significant, and widens strongly as the force associated with the hydraulic pressure gradient increases, demonstrating the importance of this force in the landslide velocity. The viscous drag is an essential dissipative force mechanism and plays an important role in controlling the landslide dynamics. However, no explicit mechanical and analytical model exists to date for this. The careful sagacity of the graceful form of new velocity equation results in a plain, yet mechanically extensive, analytical model for viscous drag, the first of this kind. It contains several physical and geometrical parameters, and evolves dynamically as it varies inversely with the flow depth. A dimensionless drag number is constructed characterizing the drag dynamics. Importance of the drag model is explained. In contrast with the prevailing practices, I have proved that drags are essentially different for the expanding and contracting motions. This is an entirely novel revelation. Drag coefficients are close to the empirical or numerical values often used in practice. But, now, I offer an innovative, physically founded analytical model for the drag that can be instantly applied in mass flow simulations.

Numerical Evaluation of Sodium Droplet Swarm Combustion and Its Modeling Optimization

Because of its superior thermal-hydraulic qualities, liquid sodium has been applied to a variety of industries, including energy storage, solar energy, sodium-cooled fast reactors, and aerospace. However, fires brought on by sodium leaks at high pressure can have major thermodynamic repercussions and put employees and equipment in use at risk directly or indirectly. As a result, a realistic and accurate forecast of the combustion behavior of sodium droplet swarm can offer technical backing for the use of liquid sodium in engineering as well as a way of sodium fire prevention and control. Spray dynamics (droplet settling, droplet particle size distribution, etc.), combustion kinetics (premixed combustion, gas phase combustion, etc.), sodium aerosol diffusion, and other specialized phenomena all contribute to the complex process of sodium droplet swarm combustion. The NACOM code created by Brookhaven National Laboratory for sodium droplet swarm combustion is utilized in this paper as a framework. The code is first validated using the benchmark of the sodium droplet swarm combustion tests carried out by prestigious institutions. The validation results demonstrate that the code’s drag model, droplet combustion model, and heat transfer model are to blame for the significantly overestimated thermodynamic effects of sodium droplet swarm combustion. NACOM is subsequently developed twice for the authors’ previously developed vapor-liquid two-layer-structure drag model, chemical kinetic combustion model, and suitable heat transfer coefficient. It is then thoroughly assessed for the separate-effects tests and integral-effects test. The evaluation results demonstrate that the optimized drag model accelerates the settling of sodium droplets due to the consideration of the sodium-vapor drag reduction effect, reducing the thermodynamic effects of liquid sodium combustion; the optimized premixed combustion model can accurately predict the low-temperature sodium droplet swarm combustion conditions, resolving the issue of serious misvaluation of the original version of NACOM. The associated research findings can serve as valuable resources and tools for deeper comprehension of the combustion effects and mechanisms of sodium droplet swarm under various operating settings (such as leakage rate and oxygen concentration).

Estimation of required power and energy for bicycle electrification using global positioning system

When designing an electric motor drive for a conversion of bicycle to an electric vehicle it is obligatory to determine the required power of the electric motor and the energy of a battery pack. By using a classical method, drive requirements can be established with speed and torque measurement on the drive wheel of the vehicle using a torque meter. The given traction profile is used for the design of the drive. This paper describes the method for estimation of power and required energy of vehicle only by means of global positioning system (GPS). When selecting a GPS device, it is necessary to take the resolution of the device and accuracy of vehicle speed and altitude into account. Using the measured track (speed and altitude profile) and the drag model of the vehicle it is possible to calculate both power that the vehicle develops, and energy consumed for a certain distance. The GPS device measurements, selection of electric drive, bicycle electrification and analysis of processed KTM Knoxville electric bicycle is presented.