Drag Coefficient Of Particles Research Articles

Special Issue on the 2022 Fluids Engineering Division Summer Meeting

The ASME Journal of Fluids Engineering (JFE) and the ASME Fluids Engineering Division (FED) present a Special Issue of papers that were presented at the 2022 Fluids Engineering Division Summer Meeting (FEDSM). The FED conference organizers were Professor Philipp Epple (chair) and Professor Kamran Siddiqui (co-chair), whose efforts helped the community assemble in the first in-person FED meeting since the pandemic. The conference was successful due to the hard work and dedication of the conference chairs, technical committee chairs, symposia organizers and other FED volunteers. The 2022 FEDSM was held August 3–5, 2022 at the Intercontinental Toronto Center, Toronto, ON, Canada and included three plenary speakers plus technical presentations and 145 attendees.The Special Issue is pleased to include the review paper by Professor Efstathios (Stathis) Michaelides (Texas Christian University) and Professor Zhigang Feng (University of Texas at San Antonio) titled “Drag Coefficients of Non-spherical and Irregularly-Shaped Particles.” The other paper topics include cardiovascular flow in the aorta, boundary layer response to plasma actuators, thermally stratified turbulent boundary layer flows, flapping foils, and unsteady propulsion.The Special Issue also presents the winners of the Flow Visualization competition, organized by Prof. Philipp Epple. The competition is an initiative that begin in 2017 and was expanded to include both still images and videos. The 2022 FEDSM winners in the video category were:In closing, my sincerest gratitude is extended to JFE Associate Editors, Professor Costanza Aricò, Professor Arindam Banerjee, Professor Luigi P. M. Colombo, Professor Philipp Epple, Professor Pierre Sullivan, and Professor Qianhong Wu, who shared in the responsibilities. I would also like to thank the JFE Editorial Assistant, Ms. Colette Montague, who helped ensure timely processing, and the support of the ASME staff, especially Ms. Beth Darchi, Ms. Erica Hodge, Ms. Tamiko Fung, and Ms. Jenna Seyer. Finally, thank you to our colleagues who served as reviewers and of course the authors.

High fidelity adaptive Cartesian octree grid computations of the flow past a Platonic polyhedron up to a Reynolds number of 200

We use a high fidelity non-boundary fitted Distributed Lagrange Multiplier/Fictitious Domain method implemented on an adaptive Cartesian octree grid to investigate the unbounded flow of a Newtonian fluid past a stationary Platonic polyhedron. We consider five Platonic polyhedrons and a sphere as an asymptotic polyhedron featuring an infinite number of faces. We explore the impact of angularity on the drag and lift coefficients for a range of Reynolds numbers Re∈[1,200] over which the flow is steady or only mildly unsteady. In order to reduce the parameter space, we consider three specific angular positions of the polyhedron: face facing the flow, edge facing the flow and vertex facing the flow. The effects of these angular positions, notably on drag and lift coefficients, are discussed. For low Reynolds numbers, the particle crosswise cross-sectional surface area has a prominent influence on the drag coefficient while for higher Reynolds numbers the impact of the particle angular position becomes more significant. We also observe that the change in the symmetry of the wake region and the corresponding regime transitions are strongly related to the lift coefficient evolution with Re. Finally, we evaluate the accuracy of various non-spherical particle drag coefficient correlations available in the literature and provide new insights into the understanding of unbounded laminar flows past a non-spherical angular particle.

Experimental Assessment of Drag Coefficient for Quasi-Radially-Symmetric Microplastic Particles Sinking in Water Stream

Microplastics (MPs) are found to be omnipresent in marine environments and their production and disposal are constantly increasing. In order to control and mitigate their negative effects on the environment, it is important to understand the processes involved in their transport and sinking. Most of the conducted experimental studies on MP in water have focused on exploring the settling behavior of MP particles under static flow conditions. This paper presents the results of an experimental study of MP particles in a horizontal stream of water. A series of laboratory experiments were carried out to measure the drag coefficient of quasi-radially-symmetric MP particles with different shapes (spheres, cubes, and crosses) and sizes (1.5 to 3.0 mm). In the study, the relationship between the drag coefficient and flow conditions represented by the local Reynolds number is investigated. The experimental procedure was validated, and a total of 400 measurements were performed. Values of the measured drag coefficient ranged from 0.8 to 2.5 for the values of Re from 40 to 300. The results show that the shape of MP particles in the water stream considerably influences the particle drag coefficient, with a rather complex relationship between the drag coefficient and flow conditions.

A Review of Drag Coefficient Models in Gas‐Liquid Two‐Phase Flow

AbstractAlthough great efforts have been made in modeling the drag force in gas‐liquid two‐phase flow, the research about that in both theory and method is at the stage of development due to its diversity and complexity, and previous summary work about drag is usually based on a certain aspect. In this review, a unified framework that guides the drag coefficient model in gas‐liquid two‐phase flow is provided. From simple to complex, this paper introduces the drag coefficient of solid particles, single bubbles, bubble swarms, and bubbles in turbulence moving in liquid in turn. The variables affecting the drag coefficient in each of the above situations and the relationship between the drag coefficient and these variables are mentioned.

Direct Numerical Simulation of Fluid Flow and Heat Transfer of a Reactive Particle Layer with Stefan Flow in Supercritical Water

Supercritical water gasification is an efficient and clean way of energy conversion. The research on different scales, such as the system, reactor, and particle, has different temporal and spatial significance. A study on particle–particle and particle–fluid–particle interaction on the particle scale has a fundamental guiding value for revealing gasification performance on the reactor scale. Reactive particles such as coal are pyrolyzed and gasified in a high-temperature and high-pressure reactor to form Stefan flow, which affects the mass, momentum, and energy transfer between particles and supercritical water. In this paper, a particle-resolved direct numerical simulation study of a reactive particle layer in supercritical water is carried out to investigate the effect of different particle layer solid holdups and Stefan flow intensities and distributions on the flow and heat transfer process between the particle layer and supercritical water. This work analyzes the pressure and friction drag coefficients to which the particles are subjected and specifies the flow, velocity, and temperature distribution inside and around the particle layer. The results show that the drag coefficient and Nusselt number of particles in the particle layer decrease gradually along the flow direction, and the presence of particle Stefan flow further reduces the drag force and Nusselt number of particles. With the increasing solid holdup of the particle layer, the particle–fluid–particle interaction becomes more intense, and the effect of Stefan flow cannot be negligible.

Experimental investigation of fluid flow around a porous cube for Reynolds numbers of 400–1400

Porous particles with different shapes are commonly used in chemical reactors. Flow characteristics and drag coefficients of these porous particles, affecting heat and mass transfers essentially, have received less attention at the single particle level. This work provides the particle image velocimetry investigation of flow around a porous cube with Darcy number Da=1.52×10-3 and Reynolds numbers Re=400-1400. It is found that the recirculation region behind the porous cube is significantly enlarged compared with that behind its solid counterpart owing to the strong push effect of penetration flow. Meantime, drag coefficients of the porous cube appear to be much higher than that of the solid cube at larger Re. This might be due to the transition of external flow to internal flow through the porous cube in the presence of permeability on the one hand, and the existence of rough surface of porous cube on the other hand.

Geometric descriptors for the prediction of snowflake drag

The dynamics of solid particles of complex shapes such as airborne snowflakes are governed by aerodynamic drag forces that are a function of the relative velocity of the particle in the flow and the particle drag coefficient, which depends on the particle geometry and its orientation. In this study, artificial snowflakes are produced by additive manufacturing and their drag coefficients are obtained by measuring the terminal velocity in a liquid container, matching the Reynolds number typically encountered in natural occurrences. The experimental results show that the convex hull of the particle is suitable to accurately predict the drag force with existing correlations. Since it is unfeasible to accurately measure the three-dimensional geometries of natural snowflakes, the approximation with the convex hull provides a useful simplification. Furthermore, the known shapes of the artificial snowflakes are used to develop correlations to estimate the most relevant three-dimensional descriptors to predict the drag of snowflakes from a two-dimensional projection onto an arbitrary plane.Graphic abstract

New model for predicting terminal settling velocity and drag coefficient of the Oncomelania

This paper presents a study of the terminal settling velocity and drag coefficient of the Oncomelanias with highly irregular shape in the range of particle Reynolds number (10 < Rep < 600). The movement characteristics of the Oncomelanias with horizontal and slant postures are revealed using image analysis and wavelet analysis. The shape features of Oncomelanias with different dimensions are quantified and formulated. The authors propose a new model for predicting the drag coefficient of the dormant and active Oncomelanias, which is proven to be better than several widely-used formulas. Further, a simple settling velocity model that can predict the terminal velocity of the Oncomelanias fairly with several easy-to-measure parameters is developed. These findings provide a basis for the further improvement for the hydraulic schistosomiasis control project and supply reference for the settling characteristics and drag coefficient of cone-shaped particles.

New Model for Non-Spherical Particles Drag Coefficients in Non-Newtonian Fluid

The settlement drag coefficient of non-spherical particles (SDCNPs) is a crucial parameter in the field of petroleum engineering. Accurately predicting the SDCNPs in the fluid is essential to the selection and design of proppant and hydraulic design in the fracturing scheme. Although many models for anticipating the SDCNPs have been proposed, none of them can be adopted for non-Newtonian fluid (NNF) and Newtonian fluid (NF). In the investigation, the SDCNPs in NF and NNF are studied experimentally, and the anticipation mode of the settlement drag coefficient of spherical particles (SDCSPs) in different fluids (including Newton, Herschel-Bulkley and power law) is proposed. On this basis, the shape depiction parameter circularity is introduced to develop the SDCNPs. The results exhibit that the predicted values of the SDCNPs model perfectly align with the experimental values, and the average relative errors are 5.70%, 6.24% and 6.72%, respectively. The mode can accurately describe the settlement behavior of non-spherical particles (NSPs) and provide a basis for the application of NSPs in petroleum engineering.

Virtual impaction in compressible flows with pressure recovery

Virtual impactors have been utilized towards classifying and increasing aerosol concentrations in sampling and measurement systems for half a century; in an ideal virtual impactor, sampled particles larger than a critical diameter (known as the cutsize) are directed inertially into a small fraction of the sample flow, known as the minor flow. Concentrating submicrometer particles with virtual impactors while maintaining near-atmospheric pressure downstream in the minor flow remains a challenge, due the low mass-to-drag ratios of these particles. Increased inertial behavior for small mass-to-drag ratio particles can be overcome by increasing flow velocities; however, in most prior work with virtual impaction of submicrometer particles, pressure recovery (keeping the aerosol outlet pressure similar to the inlet pressure) in the receiving tube at high sample flow rates was not investigated. Here, we describe the development and testing of virtual impactors functioning with flow velocities near the sonic limit, capable of submicrometer particle concentration, and with near-complete pressure recovery in the minor flow. We specifically designed, built, and tested two round-nozzle virtual impactors (denoted as VI-1 and VI-2) and evaluated their performances using fluorescent polystyrene latex particles and uranine-doped oleic acid particles with varying particle diameter. The results show that both virtual impactors, operating with 12 L per minute sample flow and a 10:1 sample flow-to-minor flow ratio, have submicrometer cutsizes (∼700 nm and 200 nm for VI-1 and VI-2, respectively) and near-complete pressure recovery. However, significant particle losses were observed in VI-2 with larger particle diameters. To understand such losses and particle trajectories in compressible flow virtual impactors, we also carried out computational fluid dynamics (CFD) simulations coupled with particle trajectory simulations. Importantly, trajectory calculations incorporated a recently developed drag model capable of predicting particle drag coefficients in a wide Mach number and Knudsen number (and hence Reynolds number) range. Trajectory calculations yielded cutsizes and large particle penetration curves in good agreement with experiments, indicating that large particle losses are due to overfocusing (radial inertial motion leading to deposition) within the nozzle and major flow chamber. Overfocusing always leads to an upper size limit in any virtual impactor system, but it is of greater concern in higher velocity systems. In addition to comparing simulations to measurements sampling at atmospheric pressure, we used trajectory calculations to examine compressible flow virtual impactor performance with variable sampling flow pressure and varying the driving pressure in the major flow. Such simulations reveal that sub-atmospheric pressure sampling leads to a reduced penetration “window” for virtual impaction, such that although it is possible for virtual impactor operation in reduced pressure environments, virtual impactors are applicable to a decreasing range of sizes at low pressure.

Experimental study and models of the settling of sand in heavy oil

In heavy crude oil, high viscosity exerts a large drag force on sand particles. In this paper, the influence of heavy oil viscosity on the natural settlement of sand is studied, and two models of settling velocity are established. These models have many practical applications such as calculating the time for sand to settle and designing separators and setting tanks. To visually observe and record the sand settlement process, transparent industrial white oil is used to simulate heavy oil in this study. The settling of individual particles of sand under the gravity force is experimentally studied, and drag coefficients are determined. Various models are used to predict drag coefficients of spherical and nonspherical particles, and predicted values are compared with experimental values. The results are analyzed to explore the influence of sand particle morphology on the prediction of drag coefficients. Two dimensionless settling velocity models are established and used to analyze the behavior of sand particles in heavy oil; the results prove the reliability and applicability of the settling velocity model. In this study, a nonspherical particle drag coefficient model has no advantage over a spherical particle drag coefficient model in terms of prediction accuracy. Thus, it is not necessary to consider the influence of sand particle morphology when making predictions of the characteristic parameters of sand sedimentation in heavy oil. An explicit settling velocity model is established on the basis of the Brown-Lawler drag coefficient model, and its prediction accuracy is greater than 90% for the settlement velocity of sand in heavy oil.

Comparison of hydrodynamic characteristics of Tulsion and Siran immobilised beads in a fluidised bed bioreactor

The fluidised bed reactors are successfully utilised in various bioprocesses to produce high value products using immobilised cells and enzymes. The present work aims at evaluating hydrodynamic characteristics of a three phase fluidised bed bioreactor using Tulsion® A-1X MP, Tulsion® ADS-400 and Tulsion® ADS-800, polystyrene and polyacrylic based three types of free and immobilised cells solid carriers viz. and comparing their performance with Siran® SIKUG41 glass beads. The hydrodynamic parameters such as particle density (cells and beads), drag coefficient, minimum and maximum fluidisation velocity, particle settling velocity were estimated and compared in water and biological media (E2 and MSM) having varying rheological properties. The relationships between drag coefficient (CD)–Reynolds numbers (NRe), superficial liquid velocity (Uf)–void fraction(ε), expansion index(n)–NRe were obtained.The scanning electron microscopy studies revealed that the pore sizes of Tulsion beads (20–300 nm) were significantly smaller compared to Siran carriers (7–120 μm) leading to cells growth only on the surface of the beads. The biomass grown was estimated to be 0.75–1.2 mgCDW/g for Tulsion beads and 1.27–1.3 mgCDW/g for Siran beads with immobilised cells of P. putida and R. erythropolis, respectively. As per the results obtained, the reactor could be operated as a fluidised bed reactor with Tulsion and Siran beads at ε>0.4 and ε>0.6. The cell immobilised Tulsion and Siran beads have shown higher drag co-efficient in E2 and MSM media compared to water. The empirical correlations describing beads properties in falling (NRe) and fluidisation conditions in the form of Archimedes Number (NAr) were developed for ε in the range of 0.3–0.8 at 0.3<NRe<100 and 10<NAr<1000. The experimental data was statistically analysed using percentage mean relative error ± standard deviation and values were found to be at 95% confidence level.The evaluation of hydrodynamic characteristics of Tulsion and Siran carriers could be used to set up an operating window for three phase fluidised bed reactor for a bioprocess.

A Novel Prediction Model of the Drag Coefficient of Shale Cuttings in Herschel–Bulkley Fluid

In the drilling industry, it is of great significance to accurately predict the drag coefficient and settling velocity of drill cuttings falling in the non-Newtonian drilling fluid. However, the irregular shape of drill cuttings and the non-Newtonian rheological properties of drilling fluid (e.g., shear-thinning and yield stress behavior) make it challenging to predict the settling velocity. In this study, the velocity of particle settlement was studied by a visual device and high-speed camera system. Experimental data of the free settlement of 224 irregular drilling cuttings and 105 spherical particles in the Herschel–Bulkley fluid were obtained. A mechanical model dependent on the force balance of settlement particles was adopted to conduct a detailed statistical analysis of the experimental results, and a prediction model of the drag coefficient of spherical particles in the Herschel–Bulkley fluid was established. A two-dimensional shape description parameter is introduced to establish a model for predicting the drag coefficient of irregular-shaped cuttings in a Herschel–Bulkley fluid. The model has high prediction accuracy for the settling velocity of irregular shale cuttings in Herschel–Bulkley fluid. The average relative error is 7.14%, verifying the model’s accuracy.

Microfluidic Rheometry and Particle Settling: Characterizing the Effect of Polymer Solution Elasticity.

The efficient transport of solid particles using polymeric fluids is an important step in many industrial operations. Different viscoelastic fluids have been designed for this purpose, however, the effects of elasticity have not been fully integrated in examining the particle-carrying capacity of the fluids. In this work, two elastic fluid formulations were employed to experimentally clarify the effect of elasticity on the particle drag coefficient as a proxy model for measuring carrying capacity. Fluids were designed to have a constant shear viscosity within a specific range of shear rates, , while possessing distinct (longest) relaxation times to investigate the influence of elasticity. It is shown that for dilute polymeric solutions, microfluidic rheometry must be practiced to obtain a reliable relaxation time (as one of the measures of viscoelasticity), which is on the order of milliseconds. A calibrated experimental setup, furnished with two advanced particle velocity measurement techniques and spheres with different characteristics, was used to quantify the effect of elasticity on the drag coefficient. These experiments led to a unique dataset in moderate levels of Weissenberg numbers, . The data showed that there is a subtle reduction in the drag coefficient at low levels of elasticity (), and a considerable enhancement at high levels of elasticity (). The experimental results were then compared with direct numerical simulation predictions yielding . These evaluations endorse the numerically quantified behaviors for the drag coefficient to be used to compare the particle-carrying capacity of different polymeric fluids under different flow conditions.

Drag and lift coefficients of ellipsoidal particles under rarefied flow conditions.

The capability to simulate a two-way coupled interaction between a rarefied gas and an arbitrary-shaped colloidal particle is important for many practical applications, such as aerospace engineering, lung drug delivery, and semiconductor manufacturing. By means of numerical simulations based on the direct-simulation Monte Carlo (DSMC) method, we investigate the influence of the orientation of the particle and rarefaction on the drag and lift coefficients, in the case of prolate and oblate ellipsoidal particles immersed in a uniform ambient flow. This is done by modeling the solid particles using a cut-cell algorithm embedded within our DSMC solver. In this approach, the surface of the particle is described by its analytical expression and the microscopic gas-solid interactions are computed exactly using a ray-tracing technique. The measured drag and lift coefficients are used to extend the correlations, based on the sine-squared drag law, available in the continuum regime to the rarefied regime, focusing on the transitional and free-molecular regimes. The functional forms of the correlations for the ellipsoidal particles are chosen as a generalization from the spherical case. We show that the fits over the data from numerical simulations can be extended to regimes outside the simulated range of Kn. Our approach allows to achieve a higher precision when compared with existing predictive models from the literature. Finally, we underline the importance of this work in providing correlations for nonspherical particles that can be used for point-particle Euler-Lagrangian simulations to address the problem of contamination from finite-size particles in high-tech mechanical systems.

Terminal velocity and drag coefficient for spherical particles

Empirical correlations and experimental works relating the drag coefficient (CD) of spheres to the Reynolds number (Re) and Re to the Archimedes number (Ar) were reviewed with a focus on the correlations applicable to the entire Re range. In addition, experiments with various spherical particles and fluids for the entire range of Re were conducted using high-speed video and added to the literature data. One of the correlations from the literature for Re-Ar and a modified correlation for CD–Re were found to best fit the experimental results. The analysis also established new correlations for Re–Ha (a non-dimensional number for velocity not including particle size) and CD–Ar. The latter is easier to use than the common CD–Re curve.

CFD study of drag and lift coefficients of non-spherical particles

The prediction of correct drag and lift forces acting on immersed bodies is vital for optimized efficiency and industrial economics. Particulate suspensions involving non-spherical particles are extensively used in the chemical and medical industry. In recent years, the hydrodynamics of non-spherical particles have attracted much attention. The hydrodynamic forces acting on these particles are the function of particle size, shape, orientation, and the physical properties of fluid. In the current research, the drag and lift coefficient of non-spherical particles of disc and prolate shapes at different inclination angles and Reynolds number (Re) is calculated using the simplified Eulerian approach of computational fluid dynamics (CFD). The method adopted for simulation is first validated for a simple case of sphere. The effect of orientation and Re on drag and lift coefficient (CD and CL, respectively) is studied and compared with the available data. It is found that CD and CL increase as the angle of inclination increases, but decrease with Re. CD and CL are smaller for prolate at given Re and orientation than for the case of disc. The effects of finite size geometry cause some deviation in results from the literature. The results obtained with this simple and less computationally intensive method agree well with highly resolved numerical simulations with minor deviations.

General Drag Coefficient for Flow over Spherical Particles

A generalized physics-based expression for the drag coefficient of spherical particles moving in a fluid is developed. The proposed correlation incorporates essential rarefied effects, low-speed hydrodynamics, and shock-wave physics to accurately model the particle-drag force for a wide range of Mach and Knudsen numbers (and therefore Reynolds number). Owing to the basis of the derivation in physics-based scaling laws, the proposed correlation embeds gas-specific properties and has explicit dependence on the ratio of specific heat capacities. The correlation is applicable for arbitrary particle relative velocity, particle diameter, gas pressure, gas temperature, and surface temperature. Compared with existing drag models, the correlation is shown to more accurately reproduce a wide range of experimental data. Finally, the new correlation is applied to simulate particle trajectories in high-speed dusty flows, relevant to a spacecraft entering the Martian atmosphere. The enhanced surface heat flux due to particle impact is found to be sensitive to the particle drag model.

Developing a standard platform to predict the drag coefficient of irregular shape particles

Irregular particles are very common in natural transport phenomena and industrial applications. Although numerous research studies have been conducted on irregular shape particles, there exist several issues like long list of CD correlations with numerous shape factors proposed for wide range of irregular particles. This research aimed at proposing a general CD correlation using a general shape factor applicable to various irregular shapes over a very wide range of Reynolds Number (Re). 60 reference model shapes were produced in SolidWorks® to achieve a very wide range of irregularity. A general shape factor was proposed and applied together with 16 previously proposed CD correlations to the 60 reference model shapes over a range of Re from 0.001 to 300,000 to derive a general CD correlation using nonlinear regression analysis. 60 reference model shapes were 3D printed and their CDs were experimentally measured and compared with estimated values using proposed general correlation.

Dynamics of freely rising spheres: the effect of moment of inertia

The goal of this study is to elucidate the effect the particle moment of inertia (MOI) has on the dynamics of spherical particles rising in a quiescent and turbulent fluid. To this end, we performed experiments with varying density ratios $\varGamma$ , the ratio of the particle density and fluid density, ranging from $0.37$ up to $0.97$ . At each $\varGamma$ the MOI was varied by shifting mass between the shell and the centre of the particle to vary $I^*$ (the particle MOI normalised by the MOI of a particle with the same weight and a uniform mass distribution). Helical paths are observed for low, and ‘three-dimensional (3-D) chaotic’ trajectories at higher values of $\varGamma$ . The present data suggest no influence of $I^*$ on the critical value for this transition $0.42&lt;\varGamma _{{crit}}&lt;0.52$ . For the ‘3-D chaotic’ rise mode, we identify trends of decreasing particle drag coefficient ( $C_d$ ) and amplitude of oscillation with increasing $I^*$ . Due to limited data it remains unclear if a similar dependence exists in the helical regime as well. Path oscillations remain finite for all cases studied and no ‘rectilinear’ mode is encountered, which may be the consequence of allowing for a longer transient distance in the present compared with earlier work. Rotational dynamics did not vary significantly between quiescent and turbulent surroundings, indicating that for the present configuration these are predominantly wake driven.