Average Drag Force Research Articles

Spacing effects on flows around two square cylinders in staggered arrangement via LBM

This study presents a computational analysis of fluid flow characteristics around two staggered arranged square cylinders using the Lattice Boltzmann Method (LBM). With Reynolds number (Re) fixed at 200, numerical simulations explore the influence of varying gap ratios (G) ranging from 0 to 10 times the cylinder size. Emphasis is placed on understanding the impact of cylinders spacing on flow structure mechanisms and induced forces. Investigation of fluid flow parameters includes vorticity behavior, pressure streamlines, and variations in drag and lift coefficients alongside the Strouhal number under different values of G. From the results, four distinct flow patterns emerge: single bluff body flow, flip flopping flow, modulated synchronized flow, and synchronized flow, each exhibiting unique characteristics. This study reveals the strong dependence of fluid forces on G, with low spacing values leading to complex vortex structures and fluctuating forces influenced by jet flow effects. At higher spacing values, proximity effects between cylinders diminish, resulting in a smoother periodic flow. The Strouhal number, average drag force and the rms values of drag and lift force coefficients vary abruptly at narrow gaps and become smooth at higher gap ratios. Unlike the tandem and side-by-side arrangements the staggered cylinders arrangement is found to have significant impact on the pressure variations around both cylinders. Overall, this research could contribute to a comprehensive understanding of staggered cylinder arrangements and their implications for engineering applications.

Neural-network-based drag force model for polydisperse assemblies of irregular-shaped particles

In this study, a drag force model of irregular-shaped particles in gas-solid flows is investigated using neural network approaches. Pre-developed variational autoencoder, multi-layer perceptron model, and transpose convolutional neural-network model are utilized to obtain intermediate parameters of a pair-wise interaction point-particle (PIEP) model. These parameters are utilized to predict individual drag force coefficients of polydisperse, particulate flows. To apply the PIEP-based model to medium-concentration flows, the average drag force coefficients are obtained through an in-house particle-resolved direct numerical simulation, and a regressed model is developed to predict solid volume fraction factors. With the regression model, the PIEP-based model using the neural-network approaches shows good prediction in particulate systems from low to intermediate concentrations. This study provides computationally efficient models of practical, realistic particulate systems for large scale fluid dynamics simulation, in that it allows predicting the drag forces of polydisperse particles with a small amount of data.

Microstructure-based prediction of hydrodynamic forces in stationary particle assemblies

In this work, we derive novel hydrodynamic force models to describe the interaction of a flow with particles in an assembly when only an averaged resolution of the flow is available. These force models are able to predict the average drag on the particle assembly, as well as the deviations from the average drag force and the lift force for each individual particle in the assembly. To achieve this, PR-DNS of various particle assemblies and flow regimes are carried out, varying the particle volume fraction up to 0.6, and the mean particle flow Reynolds number up to 300. To characterize the structure of the particles in the assembly, a Voronoi tessellation is carried out, and a number of scalars, vectors and tensors are defined based upon this tessellation. The microstructure informed hydrodynamic force models are based on symbolic regressions of these quantities derived from the Voronoi tessellation, the global particle volume fraction of the particle assembly and the flow regime represented by the Reynolds number, and the forces on the individual particles in the assembly.The resulting hydrodynamic force models are single expressions and can be directly employed in a Lagrangian particle tracking (LPT) or computational fluid dynamics/discrete element model (CFD/DEM) framework. By comparing the results of the newly proposed hydrodynamic force models with an averaged force model, as is usually adopted in Lagrangian particle tracking simulations, we show that, potentially, a significant increase in accuracy can be achieved, with only a relatively small increase in computational cost, compared to the cost of the CFD/DEM simulation.

Aerodynamic and Flow Characteristics of a Rough Airfoil: A Numerical Study

A computational study explores the aerodynamic and flow properties of rough-surfaced NACA-0018 airfoils using turbulent K-omega SST methodology and the control volume method. Ansys Fluent 2022 R2 was used to do the simulations, and Reynolds numbers between 5000 and 10000 were used. The analysis of how the rough surface affects the performance of the airfoil was the main goal of the study. The skin friction coefficient, drag force, lift force, pressure contours, and stream functions were among the many variables assessed. To have a thorough understanding of the flow behavior, these parameters were studied at various Reynolds numbers. The findings revealed a clear pattern: along the wall of the airfoil, the average drag force, lift force, and skin friction coefficient all increased linearly as the Reynolds number rose from 5000 to 10000. This discovery sheds important light on how the rough surface affects the overall aerodynamic performance of the airfoil. This study advances knowledge of the aerodynamic behavior of rough airfoils by illuminating the flow characteristics and their relationship to surface roughness. Significant results impact aeronautics, wind turbine design, and other airfoil applications.

Effect of the shape of flapping airfoils on aerodynamic forces

The rapid exhaustion of fossil fuels and the ozone depletion caused by the excessive usage of the fossil fuels has prompted researchers to look towards bioinspired designs for both propulsion and energy extraction purposes. Limited amount of work has been done to present the effects of airfoil shape on the aerodynamic forces on flapping foils. In this paper, we examine in detail the effect of airfoil camber and its position on flapping foil performance in both energy extraction and propulsion regimes. We also examine the effect of reflex camber on flapping foil performance in both flow regimes. In total, 42 airfoils are analyzed using the NACA 4 and 5-series cross-sections. The man objective of this research is to identify a trend, between airfoil shape and aerodynamic forces. The database created as a result will be used in the future work for designing a hydrokinetic turbine and a bio-inspired unmanned aerial vehicle. The results from the numerical simulations indicate that the airfoil shape has significant effects on the time averaged drag force on the airfoil in both flow regimes. However, the time averaged lift force remains negligible for all cases.

A Drag Force Model of Vertical Penetration into a Granular Medium Based on DEM Simulations and Experiments

The force exerted on a cylindrical intruder as it penetrates a granular medium was analyzed utilizing both experiments and the discrete element method (DEM). In this work, a series of penetration experiments were performed, considering cylindrical intruders with different nose shapes. We found that the drag force of the intruder with a hemispherical nose is close to that of those with conical noses with apex angles of 53° and 90°. The drag force of the blunt-nosed intruder is bigger; the drag force of the conical-nosed intruder with an apex angle of 37° is the smallest. We studied the interplay between the drag force on an intruder with a hemispherical nose and key variables—the penetration velocity (V), penetrator’s diameter (di), and friction coefficient (μ). From this analysis, two piecewise functions were derived: one for the average drag force versus the penetration velocity, and the other for the scaled drag force versus the friction coefficient. Furthermore, the average drag force per contact point, Fa/P, can be succinctly represented by two linear relationships: Fa/P = 0.232μ + 0.015(N) for μ<0.9, and Fa/P = 0.225(N) for μ≥0.9.

Analysis of the wake mechanism in external flow around tandem bluff bodies with different aspect ratios

The interaction mechanism of external flow with two inline rectangular cylinders having different aspect ratios under the impact of gap spacing (G) is the subject of this research. The gap spacing between the cylinders was varied from 0.25 to 20 times their size. Both cylinders were vertically mounted, with the first having a higher aspect ratio than the second. The results revealed five distinct flow patterns under the influence of G: single slender body, shear layer reattachment, intermittent shedding, binary vortex street, and single-row vortex street. The mean pressure on both cylinders was found to vary due to changes in flow patterns. Both cylinders bore the same shedding frequency but had different pressure variations. The second cylinder placed in the wake of first experienced negative average drag force for some spacing values, while the first cylinder had positive average drag values for all chosen G. Due to the change in flow pattern from shear layer reattachment to intermittent shedding flow, the negative drag force on the second cylinder jumped to a positive drag. It was also observed that the rms values of drag and lift force coefficients, as well as their amplitudes for the second cylinder, were mostly higher than corresponding values for the first cylinder at all selected G. This study revealed that G = 4 and 8 are the critical gap spacing values due to sudden changes in fluid force parameters.

Numerical simulations of suspensions of rigid spheres in shear-thinning viscoelastic fluids

In multiphase flows, accurately modeling the interaction between the liquid phase of complex fluids and a porous medium of solid spheres poses a fundamental challenge. The dynamics of moderately dense non-colloidal suspensions constituted by static random arrays of mono-disperse spherical particles in non-linear viscoelastic fluids is studied numerically. This numerical study consists of about 9000 different systems, in which the volume fraction ϕ (0.04≤ϕ≤0.2) of the dispersed solid phase, the Reynolds number Re(5≤Re≤50), the solvent viscosity ratio β(0.05≤β≤0.9), the Weissenberg number Wi(0.5≤Wi≤4), and the mobility parameter of the Giesekus model α (0.1≤α≤0.5) were varied to understand the particle's interactions with the viscoelastic suspending fluid. We aim to investigate the relationship between the volume fraction of the dispersed solid phase and the non-linear rheology of shear-thinning viscoelastic fluids with the normalized average drag force ⟨F⟩. In addition, by assessing the flow patterns predicted numerically, we were able to provide a characterization of the velocity and stress fields as a function of the simulation parameters.

Local Scour Mechanism of Offshore Wind Power Pile Foundation Based on CFD-DEM

The local scour around offshore pile foundations often seriously affects the normal operation of offshore wind power. The most widely used numerical simulation method in the study of local scour is the Euler two-fluid model (TFM). However, the contact effect between sediment particles is neglected in this model. Thus, the momentum and energy transfer between sediment particles and the fluid is not realistically reflected, which limits its significance in revealing the mesoscopic mechanism of local scour. Therefore, the computational fluid dynamics-discrete element method (CFD-DEM) numerical model was applied in this study, which fully considers the contact between solid particles and momentum transfer between two phases. The model was first verified by experimental data of a local scour test under clear water scour. Then, the mechanism of local scour was further discussed from macro and micro perspectives. The results showed that CFD-DEM could be effectively used to study the local scour around a pile foundation. The local scour was comprehensively affected by flow velocity, gravity, fluid force, drag force, and interaction between particles, etc. Although the maximum average drag force happened in the area about 90° from the direction of incoming flow, the maximum scour depth always occurred at about 45°. Corresponding findings and conclusions can be used for future reference when designing and protecting the offshore wind power pile.

Numerical Study of The Effects of Vehicle Arrangement on Aerodynamics Resistance

The cause of drag force vehicle accounts high fuel losses. Fuel consumption is adversely affected due to aerodynamic forces, which specially is the drag force. Vehicles that are moving in certain arrangement allows for a significant decrease in fuel consumption at highway speeds by reducing the aerodynamic drag on the moving vehicles. In this paper, the effect of vehicle arrangement on the aerodynamic resistance was numerically investigated. The vehicle models were arranged back-to-back with difference distances between each other. The distance was varied with 1.5 m, 2.0 m and 2.5 m. Computational Fluid Dynamics (CFD) was performed using ANSYS-Fluent software. The results in terms of drag coefficient were obtained for each of distance setting. There are nine different arrangements were studied. It was found out that the lowest average drag force of which 0.1857 experienced by vehicle model that are arranged at the distance of 1.5m and 2.5 m. This average drag coefficient shows a reduction of 26.8%. Consequently, the aerodynamics resistance can be significantly reduced by having a proper arrangement of vehicle cruising in highways.

Trajectory simulations by the numerical solution of the point-mass equations of motion for 7.62 mm/.308” rifle bullets

BACKGROUND: The understanding of the dynamics of the trajectory is important in ballistics to estimate the values of various flight variables accurately. The paper deals with the study of the fundamental principles of external ballistics, which allows to delve into the trajectory characteristics of the free flight trajectory of seven. 308 caliber bullets by numerically solving the point-mass equations of motion. Numerical solutions were performed by writing scripts in the Python programming language and using the Matplotlib library to plot simulated trajectories.
 AIM: the three aims of the study were to observe the variation of CD with Mach number (Ma) of flight and calculate an average CD for each bullet under consideration. Further, solving the 3-DoF (Degrees-of-Freedom) Point-Mass trajectory equations of motion for the given bullets (along side observing the effects of range winds on the trajectory behaviour as a variable). And finally, solving the flat-fire approximation with analysis of the effects of a crosswind.
 MATERIALS AND METHODS: Simulations of free-flight trajectories of seven different 7.62 mm/.308 rifle bullets (designated B0B6) have been carried out by the numerical solution of the equations of motion. The average drag force coefficients (CD) for B0B6 have been calculated by scaling the variation of CD with the Mach number of flight with reference to the G7 standard projectile. The Point-Mass trajectory model and its Flat-Fire approximation have been studied with and without the effect of range winds. The solutions of the systems of equations have been carried out by writing scripts in the Python programming language.
 RESULTS: It is observed that an increase in the bullet weight and consequently the sectional density lowers the CD. As expected, it is seen that the bullet with the highest drag (B0) has the shortest range and lowest apogee, while lower drag bullets fly further and higher. The crossover of trajectories is observed at ~30 angle of gun elevation, which implies that the maximum range is not achieved when fired at 45, as is the case with vacuum trajectories. Flat-fire approximation of the point-mass model was also solved to observe trajectories and crosswind deflections of the bullets when fired at 5 angles of elevation.
 CONCLUSION: This project presents the numerical solution of equations of motion of the Point-Mass model for a bullet fired from a gun to computationally simulate its trajectory. A group of seven 7.62 mm/.308 rifle bullets were chosen as samples to simulate free-flight trajectories. The programming language Python is well-equipped to carry out numerical solutions of systems of differential equations owing to its library of in-built functions which assists in writing an efficient script and reduces computational load. This method of solution can be applied with suitable modifications in the field of forensic ballistics for the reconstruction of bullet trajectories and to form a conclusion based on the available evidence from a crime scene.

Micromechanical schemes for Stokes to Darcy homogenization of permeability based on generalized Brinkman inhomogeneity problems

Mean field homogenization schemes are formulated for the Stokes to Darcy upscaling of the permeability on the basis of generalized inhomogeneity problems in which flow is described by Brinkman equations. The average velocity and drag force concentrations for flow in a potentially composite inclusion are characterized in terms of a permeability contribution tensor and an equivalent permeability, which allow for the direct transposition to Stokes to Darcy upscaling of most homogenization schemes available in elasticity (self-consistent, differential, Mori–Tanaka, Maxwell, …). The unified framework extends existing effective medium and cell model permeability estimates. Its flexibility is illustrated on a panel of microstructures of porous media: granular or fibrous materials, materials with spanning cylindrical or crack-like pores, double porosity materials with disconnected or connected meso-porosity and compared with existing or newly produced full field simulation results.

Numerical Investigation Aerodynamic Characteristic Installation I-65° Cylinder Type Upstream Bluffbody as Airflow Passive Control

This report is the basic research that focuses on efforts to reduce the drag force of a cylindrical pipe by placing an interfering cylinder in the area of the incoming flow direction. The aerodynamic behavior of the central cylinder and its disturbances were modeled in 2D are discretized in laminar flow by Finite Volume Methode using Ansys Fluent®. Efforts to reduce the drag force are carried out with the main cylinder diameter D=60 mm and the interfering cylinder type I-65° with diameter d/D = 0.125. The distance between the center points of the two cylinders being s/D=1,4 and Reynold number Re = 5.3 x 10 4 at a speed of U∞=14 m/s. Numerical simulation using variations of turbulent models k-epsilon (2eq), k-omega (2eq), and transition k-kl-omega (3eq). The results of this research can show better aerodynamic performance. Placing the cylinder I-65° in tandem can reduce the average drag force coefficient by 68% at 700-800 timesteps. In contrast, the average lift coefficient decreased by 13% at the same timestep. The results were obtained with transition k-kl-omega (3eq) turbulence models that have been validated and able to approach the referenced experimental data.

Hydrodynamic regimes and drag on horizontally pulled floating spheres

We use high-speed imaging to investigate the movement of a floating sphere pulled horizontally along a water surface. The model sphere is 10 cm in diameter and has half of the water density resulting in a half-submerged static sphere. By varying the pulling force, we investigate the flow dynamics in the subcritical Reynolds number range, of Re ≈ 2 × 104 to 2 × 105. We characterize three hydrodynamic regimes with the increase in the pulling force, to which we refer to as: low Froude number, Fr < 0.6, intermediate, 0.6 < Fr < 1.2 and high Froude number, Fr > 1.2 regimes. In the low Fr regime, the sphere moves with little disturbance of the water surface and the drag is close to half of the drag on a fully submerged sphere. In the intermediate Fr regime, a pronounced wave pattern is developed which together with the dipping of the sphere below the water level leads to an increase in the drag force. Based on a potential flow approximation for the downward force on the sphere moving along the surface, we derive a semiempirical relation for the sphere dipping as a function of the Froude number. Finally, in the high Fr regime, the sphere movement switches to a mode of periodic dipping below and surfacing above the water surface. The periodic vertical motion portrays a decrease in the average drag force.

DEM – CFD coupling simulation and optimization of a self-suction wheat shooting device

Planting performance is essential for wheat seeders and reliable seed germination. The seed-filling effect is also important in the sowing performance. In this study, a self-suction wheat shooting device was developed to improve the seed-filling performance. In specific, the shooting device structure was optimized, in which negative pressure was generated in the inner cavity of the device. A DEM-CFD coupling simulation experiment was conducted to investigate the seed-filling and shooting performance. The effect of three working parameters (rotational speed of shooting device, window length and window width of directional seed delivery wheel) on the coefficient of variation of the seed-filling performance (CVSF), average shooting speed (ASS), average shooting depth (ASD) and drag force (DF) were analyzed. Afterward, a validation experiment was conducted to investigate the shooting performance of the self-suction shooting device. The results showed that the shooting performance of the self-suction device under optimized operation parameters could fully meet the shooting requirements of winter wheat in the North China plain. In specific, the coefficient of variation of the seed amount (CVSA), ASD and ASS of self-suction shooting device were 7.1%, 30.9 mm and 33.5 m/s at the rotational speed, window length and window width were 1200 rpm, 35 mm and 60 mm, respectively.

Particle-resolved simulation of freely evolving particle suspensions: Flow physics and modeling

The objective of this study is to understand the dynamics of freely evolving particle suspensions over a wide range of particle-to-fluid density ratios. The dynamics of particle suspensions are characterized by the average momentum equation, where the dominant contribution to the average momentum transfer between particles and fluid is the average drag force. In this study, the average drag force is quantified using particle-resolved direct numerical simulation in a canonical problem: a statistically homogeneous suspension where an imposed mean pressure gradient establishes a steady mean slip velocity between the phases. The effects of particle velocity fluctuations, particle clustering, and mobility of particles are studied separately. It is shown that the competing effects of these factors could decrease, increase, or keep constant the drag of freely evolving suspensions in comparison to fixed beds at different flow conditions. It is also shown that the effects of particle clustering and particle velocity fluctuations are not independent. Finally, a correlation for interphase drag force in terms of volume fraction, Reynolds number, and density ratio is proposed. Two different approaches (symbolic regression and predefined functional forms) are used to develop the drag correlation. Since this drag correlation has been inferred from simulations of particle suspensions, it includes the effect of the motion of the particles. This drag correlation can be used in computational fluid dynamics simulations of particle-laden flows that solve the average two-fluid equations where the accuracy of the drag law affects the prediction of overall flow behavior.

Mechanisms of particle preferential concentration induced by secondary motions in a dilute turbulent square duct flow

Particle-laden turbulent square duct flows at Reτ = 300 (based on the duct half-width and the mean friction velocity) are investigated using direct numerical simulation with one-way coupled Lagrangian particle tracking. Four particle-to-fluid density ratios are considered with the corresponding shear Stokes number St+ = 0.31, 25, 125, and 260. Particle motion is governed by drag, lift, added-mass, and pressure gradient forces. The main purpose of this work is to examine the effect of the turbulence-driven secondary flows on particle preferential accumulation and their dependence on the Stokes number. Results obtained indicate that the cross-stream secondary motions encourage inertial particles to accumulate preferentially in the duct corners, where the maximum of the cross-sectional particle concentration occurs. The extent of accumulation here is strongly dependent on the Stokes number, with the greatest accumulation found at St+ = 25. Interestingly, the maximum of the intensity of the secondary particle velocity along the corner bisector is also achieved at St+ = 25, whereas in the region adjacent to the wall, it is found to decrease with a particle Stokes number. Additionally, it is observed that the higher inertia particles are more easily trapped in the stagnation zone of secondary flows with low turbulence intensity in the corner region. In the near-wall region, the heavier particles (St+ ≥ 25) are prone to reside and form elongated clusters along the low-speed streamwise velocity streaks, with this trend less pronounced with the increasing Stokes number. Along the wall, away from the corner where the secondary motion is attenuated, particle accumulation is dominated by the near-wall coherent vortices. This phenomenon is further discussed using a region-based correlation analysis between the particle spatial distribution and local flow topology. An in-depth particle dynamic analysis determines that the average cross-sectional drag force resulting from the secondary flow is mainly responsible for the particle motion throughout the duct cross section, which tends to push particles away from the walls in the near-wall region but shows the exact opposite trend in the bulk flow region. Moreover, the pressure gradient force also plays an important role for low-inertia particles. As the Stokes number is increased, the lift force becomes progressively dominant in the viscous sublayer, acting to pull particles toward the corners and walls of the duct.

A Model to Improve Granular Temperature in CFD-DEM Simulations

CFD-DEM (computational fluid dynamic-discrete element method) is a promising approach for simulating fluid–solid flows in fluidized beds. This approach generally under-predicts the granular temperature due to the use of drag models for the average drag force. This work develops a simple model to improve the granular temperature through increasing the drag force fluctuations on the particles. The increased drag force fluctuations are designed to match those obtained from PR-DNSs (particle-resolved direct numerical simulations). The impacts of the present model on the granular temperatures are demonstrated by posteriori tests. The posteriori tests of tri-periodic gas–solid flows show that simulations with the present model can obtain transient as well as steady-state granular temperature correctly. Moreover, the posteriori tests of fluidized beds indicated that the present model could significantly improve the granular temperature for the homogenous or slightly inhomogeneous systems, while it showed negligible improvement on the granular temperature for the significantly inhomogeneous systems.

Analysis of the different sources of stress acting in fully rough turbulent flows over geometrical roughness elements

The discrete element roughness method is considered in this article for the prediction of turbulent flows over rough walls. This approach is derived by ensemble- and volume-averaging the Navier–Stokes equations, providing double-averaged Navier–Stokes equations, and yielding three unknown terms in the momentum equation: the Reynolds stress and dispersive stress tensors and the average drag force acting on the roughness elements. This work aims at analyzing these different terms, quantifying their respective contributions to the near-wall momentum budget, and providing guidance for their modeling. For this purpose, relevant data of turbulent flows are required. Roughness-resolved Reynolds-averaged Navier–Stokes simulations of transitionally and fully rough channel flows over academic roughness configurations are performed at high friction Reynolds numbers ranging from 3500 to 8000. Comparisons with existing and new velocity measurements performed in rough-wall turbulent boundary layers provide support to the simulation results, a particular emphasis being given on the validity of the numerical results in the wake of the roughness elements. These numerical results highlight the influence of roughness elements geometry and density on the roughness drag coefficient and the dispersive stress. It is particularly suggested that the standard roughness drag closure model should be revisited for double-averaged flows. Furthermore, the dispersive stress is shown to mainly originate from the wake of the roughness elements, an observation that could be leveraged for its modeling. However, since this stress contributes only marginally to the global stress and to the skin friction coefficient, such a modeling may not be critical at first order.

Gas-solid heat transfer in assemblies of cubes for ReV ≤ 100

The thermal lattice Boltzmann method using an immersed moving boundary condition was employed to calculate the particle-to-fluid heat transfer in an assembly of super-quadric cubes. The simulations were performed for Reynolds numbers 1–100 (based on the volume equivalent diameter) and solid volume fractions ϕ = 0.1–0.45. The simulation results show that the Nusselt numbers for assemblies of super-quadric cubes are larger than those for assemblies of spheres, in particular for high solid volume fractions. A relationship between the average Nusselt number and the drag force (Chen & Müller, 2018) for assemblies of cubes was developed. It was found that the average drag force acting on cubes increases faster with increasing solid volume fraction than the average Nusselt number. Defining the Reynolds number and the Nusselt number using the hydraulic diameter of the packing system (Reh) and the Sauter diameter of the cube, respectively, the Nusselt number correlation of Chen & Müller (2019), that was proposed for assemblies of spheres, can be applied for assemblies of non-spherical particles. We also demonstrate that the proposed Nusselt number correlation predicts well the heat transfer between a gas and ellipsoidal or cylindrical particles.