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An analysis has been completed for a comprehensive set of vertical, dilute-phase pneumatic conveying pressure drop data from an investigation by Flatow. The data were collected in the established flow region for eight different materials conveyed in 0.05-, 0.10-, 0.20-m internal diameter, 20-m tall steel risers. Particle velocities derived from the pressure drop data were used to develop an equation of motion that includes terms for pipe diameter, terminal velocity, coefficient of restitution, and particle shape. The best data fit was achieved using the actual gas density and the actual gas velocity adjusted for voidage. Adjusting the terminal velocity for voidage, an approach recommended by many investigators, did not improve the fit for reasons identified by the present research. Using the equation of motion, particle velocities were predicted and used to calculate total pressure drops that are within ±15% of the measured values. The calculated values also produce the characteristic trough-shaped total pressure drop curves allowing the minimum pressure drop gas velocity to be determined without recourse to a separate correlation. A comparison with other studies using shorter risers indicates that data from these studies likely include acceleration effects. A separate study will investigate this observation further.

In the present paper, the three dimensional (3D) settlement process of two side-by-side free-falling spheres in a water tank was numerically investigated using coupled Smoothed Particle Hydrodynamics (SPH) - Discrete Element Method (DEM) method. The maximum particle Reynolds number, calculated based on the terminal velocity and sphere diameter, is R e m = 2 . 4 × 1 0 4 . The accuracy of the model was firstly validated by simulating the single sphere water-entry, settlement of two circular cylinders arranged in series and two identical spheres settlement side by side problems, respectively. The simulation results exhibited a satisfactory agreement with the available numerical and experimental data in the literatures. Then, the settlement process of two spheres with different sizes and transverse distances were simulated. In particular, the motion patterns of two interacting spheres with different initial gaps and diameter ratios, including motion trajectory, vertical falling distance and flow field, were systematically investigated. The results demonstrate that when initial gap S 0 ∗ S 0 ∗ > 0.75, the interaction between the two spheres are negligible. In addition, the interaction between particles would slow down the settling velocity and affect the terminal settling distance.

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.

The management of fluids in space is complicated by the absence of relevant buoyancy forces. This raises significant technical issues for two-phase flow applications. Different approaches have been...

To enable the mechanistic description of the mixing of larger particles in gas-fluidized beds in models (e.g. fuel particles in combustors), knowledge about the rheology of the bed emulsion is required. Here, it is crucial to determine the drag on large fuel-alike particles. This work presents the experimental work on the fate of 13 different solid spheres falling or rising through a bed of air and glass beads at minimum fluidization. The trajectories of the tracer are highly resolved (sampling rate of 200 Hz) by means of magnetic particle tracking, this previously unmet accuracy allows disclosing the complex rheological behavior of gas-solids fluidized bed emulsions in terms of drag on immersed objects. The trajectories reveal that none of the tracers reach terminal velocity during their fall and rise through the bed. The shear stress is obtained through the drag force by solving the equation of motion for the tracer. The data reveal particularities of the bed rheology and clear differences of its effect on rising and falling particles. When studying the shear stress over the characteristic shear rate of each tracer, it can be seen that the stress of the bed on the tracers is dominated by a yield stress, with a somewhat smaller contribution of the shear stress. For rising tracers this last contribution is almost negligible. The falling tracers show strong interaction with the bed emulsion, resulting in a fluctuating shear stress, which increases with tracer size and density. The stagnation of some tracers at low shear rates reveals a viscoplastic behavior of the bed emulsion, exhibiting a typical yield stress that showing a clear dependence on the tracer diameter and buoyant density. The concept of yield gravity is used in order to introduce a normalized shear stress which provides additional verification of the experimental observations in relation to the influence of tracer size and relative density on the shear stress.

This numerical study investigates the dynamics around a single Taylor bubble rising with small-dispersed bubbles in a vertical pipeline. The Volume-of-fluid (VOF) method in Ansys Fluent 18.1 is used to track the Taylor bubble, and the Discrete Particle Method (DPM) is used to track the small-dispersed bubbles, for the following parameter range; $$812 \leqslant \text{Re} \leqslant 5684$$ , $${\kern 1pt} Eo = 94$$ and $$\log (Mo) = - 10.6$$ . The coupling strategies for both the continuous gas–liquid phase as well as the discrete bubble phase are all accounted for in the numerical calculations. The dispersed bubbles significantly affect the behaviour of the rising Taylor bubble in numerous ways. The terminal velocity increases with an increase in the number of dispersed bubbles. The rise velocity is, however directly correlated with the deformation of the nose of the bubble. The flow dynamics around the nose of the Taylor bubble are stronger for low velocities due to lower inertia. The computations also demonstrated that there are both acceleration and deceleration effects on the Taylor bubble. Our predictions are in quantitative agreement with published experimental results by Cerqueira and Paladino (Int. J. Multiph. Flow, vol. 133, p. 103,450, Dec. 2020).

In particle-laden flows, a turbulent field can be produced in the carrier phase by the movement of the particle/spray cloud. In this study, the intensity and the integral length scale of the particle-induced turbulence are studied using a simple mechanistic model with comparison to experimental data and numerical simulations for large-scale numerical applications. The experimental results of DynAsp are investigated with numerical simulation results. Out of the spray nozzle, two regions can be distinguished for the spray dynamics: an inertial zone and an equilibrium zone. It is found that the initial injection velocity of the cloud has little effect on the terminal slip-velocity of the particles in the equilibrium zone far from the injection region. The turbulent kinetic energy is closely related to the particle slip-velocity and shows a maximal value when particles reach their terminal velocity inside the equilibrium zone. The integral length scale depends mainly on three parameters: particle slip-velocity, particle size and volume fraction. Combined with the terminal slip-velocity correlation, the reduced-order mechanistic model can give a reasonable estimation of the turbulent kinetic energy as well as the integral length scale of the particle-laden flow in large-scale configurations.

In this study, the interaction between a spherical solid particle descending in a fine-bubble plume and the fine-bubbles around the particle is investigated experimentally. The fine-bubbles, which are formed by water electrolysis and have an average diameter of 0.037 mm, rise via buoyancy to form bubble plumes. The average bubble velocity in the conduit is 0.05 mm/s. A spherical solid particle with a diameter of 11.1 mm and a density of 1130 kg/m3 is dropped into the fully-developed bubble plume. The particle falls in a meandering motion in the fine-bubble plume. In this process, the terminal velocity of the particles falling in the fine-bubble plume is almost identical to that of a particle falling in the quiescent water. Additionally, after the fine-bubbles have been separated from the particle surface, they flow into the wake of the particle, forming a stagnant region. The particle wake diameter increases threefold, as compared with its value in the downstream direction of the fine-bubble plume.

Study of drag force on dendritic particles in highly viscous fluids is essential for understanding the dynamic sinking/floating behavior of particles in metallurgical systems. In this study, experiments were carried out to investigate the drag coefficient of simplified three-dimensional dendritic particles in silicone oil with a range of viscosities (20, 100 and 500 cSt). The experimental system was designed to represent the basic oxygen steelmaking (BOS) slag system based on a dynamic similarity approach. The drag coefficient of each dendritic particle was calculated from the measured terminal velocity based on a force balance and the known drag coefficient of its volume equivalent sphere. The drag coefficients were determined over a range of Reynolds numbers (~ 0.035 to 84) differing by two orders of magnitude accounting for various particle shape factors that included aspect ratio, sphericity, and particle orientation. Correlations between the drag coefficient and the shape factors were proposed for each viscosity.

Liquid–solid fluidized bed separators (LSFBS) are particles handling equipment where solid particles are caused to exhibit liquid-like behavior. Segregation and separation of suspended particles are achieved by maintaining superficial velocity of upward flowing fluid between settling velocity and terminal velocity of particles. Rapid increase in the consumption rate of metals and ores in the last few decades necessitates effective utilization of marginal, low-grade ores. This work focuses on the ability of LSFBS in upgrading lean-grade banded magnetite quartzite (BMQ) ore. To gain an understanding of segregation, separation, and layer inversion phenomena inside the fluidization column, hydrodynamics characteristics, process efficiency, and misplacement of solid particles have been studied qualitatively and quantitatively. Feed, concentrate, and tailing samples were analyzed using wet chemical method, scanning electron microscopy (SEM), and X-ray diffraction (XRD) analysis. Taguchi-based grey relational analysis (GRA) and one-way ANOVA were employed to statistically analyze the fluidization process and provide ranking of input parameters for individual and multiple responses synchronically. In order to characterize misplacement, fractions of iron-phase minerals and gangue minerals reporting in overflow (tailings) and underflow (concentrate) have been calculated. The best rank indicating multi-response optimization and the highest normalized misplacement index were obtained at superficial velocity: 1.41 cm/s, mean particle size: 125 µm, overflow tap height: 62 cm, and bed height: 20 cm. The highest values of normalized misplacement index and misplacement index obtained are 28.82975% and − 0.5979, respectively. This suggests that minimum misplacement and maximum process efficiency can be achieved at this optimized set of experimental conditions.

This work demonstrates that an additional resistance term should be included in the Navier–Stokes equation when fluids and objects are in relative motion. This is based on an observation that the effect of the microscopic molecular random velocity component parallel to the macroscopic flow direction is neglected. The two components of the random velocity perpendicular to the local mean flow direction are accounted for by the viscous resistance, e.g., by Stokes’ law for spherical objects. The relationship between the mean- and the random velocity in the longitudinal direction induces differences in molecular collision velocities and collision frequency rates on the up- and downstream surface areas of the object. This asymmetry therefore induces flow resistance and energy dissipation. The flow resistance resulting from the longitudinal momentum transfer mode is referred to as thermal resistance and is quantified by calculating the net difference in pressure up- and downstream the surface areas of a sphere using a particle velocity distribution that obeys Boltzmann’s transport equation. It depends on the relative velocity between the fluid and the object, the number density and the molecular fluctuation statistics of the fluid, and the area of the object and the square root of the absolute temperature. Results show that thermal resistance is dominant compared to viscous resistance considering water and air in slow relative motion to spherical objects larger than nanometer-size at ambient temperature and pressure conditions. Including the thermal resistance term in the conventional expression for the terminal velocity of spherical objects falling through liquids, the Stokes–Einstein relationship and Darcy’s law, corroborates its presence, as modified versions of these equations fit observed data much more closely than the conventional expressions. The thermal resistance term can alternatively resolve d’Alembert’s paradox as a finite flow resistance is predicted at both low and high relative fluid–object velocities in the limit of vanishing fluid viscosity.

This paper addresses the problem of midcourse guidance of dual-pulse rocket motor interceptors with seeker field-of-view constraints using singular perturbation technique. The guidance law consider...

Ballistic missiles often require the terminal velocity and impact angle to be confined to a certain region around a desired value considering a wide variety of uncertain initial conditions and operational ranges. This study presents a design framework to determine optimum waypoints that satisfy constraints for given launch conditions and mission profiles. As a systematic approach to this kinodynamic motion planning problem, the proposed framework deterministically samples the waypoints. The trajectory generated by the determined waypoints in consideration of various conditions satisfies the terminal constraint. Numerical simulations are performed to demonstrate the effectiveness of the proposed method.

An experimental study for the drag of solid spheres in drag reducing Fluids is presented. Polyacrylamide solutions of different concentrations are considered. The drag coefficient is measured by tie terminal velocity of the spherical particle falling in stagnant fluid using high speed camera, Compared to Newtonian Fluid results, the drag of solid particle in polymer solutions exhibit reduced values. However, a drag increase Is exhibited at low Reynolds number. Analysis of the data show the presence of a critical Reynolds number that distinguish between the drag increase and drag reduction regions. It has been postulated that the measured drag is a result of two opposing effects of polymer additives. One is flow resistance increase due to increased extensional viscosity. The other, is the reduction in the form drag due to the influence of these additives on vortex shedding and boundary layer separation. It has been found that the experimental data of drag coefficient is best correlated with the polymer -particle parameter ᴓ or Weissenberg number Ws as well as Reynolds number.

The behavior of the terminal velocity of gas-liquid compound drops was studied experimentally. The eect of the size of the internal bubble was analyzed, covering a wide range of relative sizes. The bubble signicantly increased the buoyancy eects, particularly for denser external uids. The terminal velocity increases with the size of the internal bubble, suggesting that the motion is governed by the geometry of the compound drop. A mechanistic model was proposed, and it showed a good agreement with the measurements., El comportamiento de la velocidad terminal de las gotas compuestas gas-líquido se estudió experimentalmente. Se analizó el efecto del tamaño de la burbuja interna, cubriendo un amplio rango de tamaños relativos. La burbuja aumentó signicativamente los efectos de otabilidad, particularmente para uidos externos más densos. La velocidad terminal aumenta con el tamaño de la burbuja interna, lo que sugiere que el movimiento está gobernado por la geometría de la gota compuesta. Se propuso un modelo mecanicista que mostró una buena concordancia con las mediciones. Palabras clave : Flotación, Gota compuesta, Velocidad terminal, Eciencia.

This paper addresses an impact angle control guidance problem for nose-dive missiles to achieve the maximum terminal speed against a fixed target in the same vertical plane. By modeling the aerodynamic drag as a drag polar, we set up the nonlinear system equations needed to pursue an analytic closed-form solution. This paper shows that maximizing the terminal speed is equivalent to minimizing a weighted quadratic cost of the curvature of trajectory, and can be used as an equivalent problem to the original problem. Applying Pontryagin’s maximum principle to the equivalent problem, we obtained a closed-form optimal guidance law, described in terms of air density parameters as well as heading error angle, flight path angle, range-to-go, and time-varying speed.

Fine kaolinite particles are mineral particles that are found in mine wastewater. The particles' shape is one of the parameters that causes a significant change in the sedimentation dynamics in water environments. In this work, experimental methods and Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) methods served to investigate the dynamic characteristics of fine kaolinite particle sedimentation. The Results of statistical analyses show that the length-width ratio of fine kaolinite particles is 1–3 and the average simplified spherical coefficient is 0.625 in the 50–500 μm particle size range. The simplified spherical coefficient formula proved to be effective according to experimentation and simulations. Moreover, the effects of particle size, liquid viscosity, and liquid velocity on kaolinite particle sedimentation dynamic characteristics were numerically studied in detail by using the modified spherical coefficient. The simulation revealed that an increase in liquid viscosity resulted in a declining particle terminal velocity. However, the sensitivity of the particle terminal velocity affected by liquid viscosity fell when the particle size also declined. When an increase in particle size occurred, the sensitivity of the particle terminal velocity to the influence of upwelling water decreased.

The terminal velocity of cloud drops and raindrops used in numerical model calculations can significantly affect weather predictions. Current formulations rely on laboratory experiments made in the 1940s and 1960s. Because these experiments were performed only at typical environmental conditions of 20°C and 1013 hPa, parameterizations have been introduced to deduce the terminal velocity aloft without rigorous evaluation. In this study, an incompressible two-phase flow direct numerical simulation model is used to calculate the free-falling motion of axisymmetric drops with diameters between 0.025 and 0.5 mm to study the terminal fall velocity. Simulated terminal fall velocities of free-falling drops at 20°C and 1013 hPa agree within 3.2% with the previous empirical parameterization (Beard formula), and 4.5% with existing laboratory data in the diameter range between 0.3 and 0.5 mm. The velocities converge to the analytic Hadamard–Rybczynski solution within 2% for small Reynolds numbers, demonstrating the robustness of our simulations. Simulations under various atmospheric conditions show that existing empirical parameterizations that account for the air density dependence of the terminal velocity have errors up to 11.8% under the conditions examined in this study. We propose a new empirical formula that describes the air density dependence of the terminal velocity. It is also shown that the falling speed of a small drop is not sensitive to shape oscillation, and the terminal velocity decreases by only less than 1.3% when the axis ratio increases by 12% with reduced surface tension. Internal circulation within falling drops is also presented and compared with previous studies.

Single bubbles rising in a confined geometry – a parallelepidic bubble column with a 4 mm thickness – in the presence of a non-Newtonian liquid phase are studied using a shadowgraphy technique. The context is the cultivation of microalgae at high cell concentrations. In fact, it necessitates the reduction of the bioreactor thickness to allow light penetration through the whole culture. In the same time, the medium becomes shear-thinning for biomass concentrations higher than 30 g L−1. A 2 g L−1 carboxymethyl cellulose (CMC) and a 1 g L−1 Xanthan Gum (XG) aqueous solutions are studied to mimic the behavior of 42 g L−1 Chlorella vulgaris cultures. Besides, a comparison with water, representing the Newtonian liquid phase at low culture concentrations, is proposed. The bubble equivalent diameter is varied between 1.34 and 3.36 mm using different capillary sizes to generate the bubbles. Results show the complex and coupled effects of confinement and shear-thinning behavior of the liquid phase on bubbles terminal velocity, shape and trajectory. In fact, compared to the case of an infinite liquid medium, confinement increases wall friction on the bubbles, while reduces the liquid phase apparent viscosity in its neighborhood due to increased shear rate. This is why, depending on the bubble size, the bubble terminal velocity in shear-thinning fluids can be higher or lower than in unconfined conditions. For bubbles rising in shear-thinning fluids, contrary to water, it is observed that confinement induces a transition from spherical shape to ellipsoidal shape that occurs sooner in terms of bubbles diameter or Eo number. A correlation for the bubble drag coefficient in confined conditions in presence of shear-thinning fluids is also proposed for confinement ratios db/e between 0.34 and 0.84.

The basic physical properties of hemp seeds were measured to determine the correlations between these properties to facilitate the planning of seed sorting operations. The basic dimensions (length, width, and thickness), terminal velocity, angle of external friction, and mass were determined in the selected seeds. The seeds were subjected to a uniaxial compressive strength test to determine the force required to damage a seed, the corresponding displacement, and the energy consumed during the trial. The seed sorting was based on the basic dimensions of the seeds in order to divide the seeds into groups with similar average mass. The hemp seeds were most effectively sorted with the use of a screen with slotted apertures. The optimal set of screens should separate approximately 11% to 24% of the seeds into a fraction with the lowest seed thickness, and approximately 16% to 21% of the seeds into a fraction with the highest seed thickness. The basic seed dimensions significantly influenced the specific mass of the individual hemp seeds, and the corresponding correlations are most effectively described by power functions.

This paper presents a new two-phase zero-effort-miss/zero-effort-velocity (ZEM/ZEV) feedback guidance strategy for Mars precision landing, which directly accommodates a variety of constraints and r...

Highlights Physical properties of whole rough rice and empty kernels of five short-grain rice varieties were measured. Geometric traits of kernels could not be used for the separation of empty kernels from whole kernels. Separation of kernels can be achieved based on weight difference between whole and empty kernels. Air velocity in pre-cleaners should be set between the terminal velocities of whole and empty kernels. Abstract . The key factors required to separate empty kernels (EKs) from whole kernels (WKs) were investigated in rough rice varieties. The geometric properties and 1000-grain weight of rough rice WKs and EKs of five varieties of short-grain rice with varying moisture content were measured. The terminal velocities for floating and dropping of WKs and EKs were tested in a vertical air column to identify the aerodynamic separation characteristics. The separation of EKs from WKs based on kernel geometric characteristics was not possible because of insignificant differences between WKs and EKs in terms of length, width, roundness, and other geometric characteristics. The 1000-grain weight of WKs and EKs ranged from 23.7 to 29.2 g and from 3.9 to 8.5 g, respectively. Linear regression equations were used to determine the relationship between terminal velocity and moisture content in both floating and dropping phase. The allowable floating and dropping terminal velocity range for separating WKs and EKs ranged from 5.0 to 7.6 m s-1 and from 2.1 to 4.1 m s-1, respectively. Moisture content, and especially, kernel type and terminal velocity type had significant effects on the terminal velocity. Keywords: Empty kernel, Physical property, Rough rice, Separating, Terminal velocity.

Two identical objects are simultaneously projected vertically upward with the same initial speed in a uniform gravitational field and then return to their starting point. One object is subject to a resistive force proportional to the nth power of its speed where n ≥ 0, such as linear (Stokes) drag for n = 1 or quadratic (Newtonian) drag for n = 2. The other object moves through vacuum with no resistance. Which object returns to its starting point first? It is shown analytically that the object subject to drag always wins the race if n ≥ 1, but that either object can win otherwise, depending on the ratio of the launch speed to the terminal speed of the object subject to drag if 0 < n < 1 or depending on the ratio of the frictional acceleration to the gravitational acceleration if n = 0. These analytical results are confirmed by Euler–Cromer numerical integration of the equations of motion.

Bagasse particle is used in energy generation, and the usual method for determining their size distribution is sieving. Traditional methods for measuring the bagasse particle size distribution, such as sieving, do not evaluate the effect of the irregular particle shape, producing results that are not always applicable to the prediction of fluid dynamic behavior. This work determined size distribution of bagasse particles considering their aerodynamic behavior. Physical-chemical characterization was performed in different particle sizes of the bagasse. A particulate elutriation and settling system was developed to determine the terminal velocity distribution of particles. Drag coefficients and terminal velocities measured were compared with literature correlations. Almost all the correlations analyzed showed significant deviations from the values obtained experimentally. Haider and Levenspiel’s correlation showed the smallest average deviation. Two types of particles were observed in bagasse: fibers and spongy pith. The apparent density of the particles depends on the particle size, and the ash concentration in smaller fractions is 3 times larger than the average. The method of aerodynamic separation for the characterization of bagasse particle allowed to obtain information that cannot be found by the traditional method of separation by sieving.

Due to the lack of information about the engineering properties of okra seeds in Egypt. Some physical, mechanical and aerodynamic characteristics of okra seeds were studied to set a database for properties related to grading, separating, handling, cleaning, storage and other future processing units. The study of experiments conducted on okra seeds at 6.31 % moisture content dry basis. The study revealed that the average value of length, width, thickness, geometrical and arithmetic mean diameters, volume, sphericity, coefficient of contact surface and surface area of okra seed were 5.85, 4.40, 4.04, 4.68, 4.75 mm, 56.12 mm3, 80.43%, 30.77% and 69.77 mm2, respectively. While; the mean value of bulk and true densities, individual seed mass, one thousand seed, porosity and projected area were 0.633g/cm3, 0.898g/cm3, 0.067 g, 61.27 g, 33.81 % and 22.46 mm2, respectively. The study also revealed that the average value of repose angle was 29.15°. While; the lowest values of static friction coefficient for okra seeds were on stainless steel sheet followed by galvanized iron, plywood and the highest on rubber were 0.271, 0.328, 0.402 and 0.466, respectively. The study also concluded that the rupture force and deformation ratio of okra seeds were 82.89 N and 4.33 %. The mean values of terminal velocity and coefficient of drag were 8.40 m/s and 0.70, respectively. Also; the mean value of Reynolds number was 2621 therefore; the pattern of air flow is in the range of transitional flow.

In a traditional teaching approach, a physics course begins with mechanics, and generally the braking effect due to magnetic interactions is not mentioned among the various types of friction presented (static, sliding, rolling) because students will discover magnetism only in later chapters. In our didactic experience this traditional choice is only partially effective for two reasons. First of all it does not distinguish between the nature of the interactions involved in friction processes and the way in which their effects appear, allowing students to believe erroneously, for example, that sliding friction (due ultimately to electrical interactions) is intrinsically “more mechanical” than the braking force produced by magnets moving over a metal surface. Secondly, the traditional approach doesn’t consider that Newtonian dynamics is sufficient to get a quantitative albeit empirical description of a magnetic braking force, without any introduction to magnetism, exactly as it is traditionally done, for example, for sliding friction, described as a force without discussing its complex electrical nature.

The results of experimental studies of the terminal velocity of peat dust in an air flow with different size distributions of dust particles are presented, and the particle sizes and shapes were examined by microscopic methods. The aerodynamic drag of peat particles of various sizes in an air flow was studied, and a criterion relationship between the drag coefficient CD and the Reynolds number (Re) was determined. The experimental results on the terminal velocity of peat dust were compared with data calculated using well-known methods, and recommendations for their application in the design of pneumatic fuel supply systems were given.

Ember transport and the subsequent development of spot fires is a significant mode of wildfire spread, particularly in extreme conditions. An important simplifying assumption made in early research into ember transport is the terminal-velocity assumption, in which embers are assumed to always fly at their terminal velocity relative to the wind field. With increases in computational power, it is now possible to directly simulate the atmospheric conditions resulting from wildfires and such simulations can resolve the larger of the turbulent processes involved. Because of the time-scales at which these processes occur, the terminal-velocity assumption may not be justified when modelling ember transport using these simulations. In this study we use a large eddy simulation of a turbulent plume to examine the validity of the terminal-velocity assumption when modelling the long-range transport of non-combusting embers. The results indicate that the use of the terminal-velocity assumption significantly overestimates the density of ember landings at long range, particularly for embers with higher terminal fall speeds.

One of the most important design parameters for the inkjet printing device is the inkjet drop velocity, which changes along the falling path from the ejection out of a nozzle to the impact on a substrate. Therefore, in this study, the droplet velocity of the piezoelectric drop-on-demand inkjet was measured. The nozzle diameter was 70 µm and polyethylene glycol aqueous solution was used as ink. The inkjet droplets were generated within a range from 500 to 10000 Hz of frequencies at a reference piezoelectric input voltage. The successive inkjet droplets were captured by the high-speed camera with 100000 fps, then the inkjet droplet velocities were analyzed visually at each falling location. The velocity change of a drop up to its terminal velocity was calculated theoretically to be compared with the experimental results. This study found that the velocity of the continuously ejected droplets depended on the interval of the droplets, as well as the density and diameter of the droplet which are essential factors of the general velocity change of a falling drop. The inkjet droplets with the long interval can be considered as an independent droplet so that it can follow the terminal velocity curve of the general drop. However, the inkjet droplets with short interval have the higher velocity than the general terminal velocity curve. It is considered that each droplet gets into the wake field of the former droplet so that its drag force can decrease and the velocity can increase.

This paper provides an alternative Lambert solution based on the terminal velocity vector. The chordal terminal velocity component is selected as the independent variable since it is the final requ...

Mineral dry density separation behavior (mineral beneficiation) involves segregation of high density particles and low density particles in the feed, i.e., in nutshell, mineral dry density beneficiation is density segregation in physics terms. In dry beneficiation, this density segregation is achieved using air as fluidized medium. Density segregation on dry separators can be achieved in two ways: (1) using minimum fluidization velocity differences and (2) using terminal velocity difference between different density particles. Dry separators based on minimum fluidization velocities follow two steps for dry beneficiation: (1) vertical density stratification and (2) horizontal segregation. Particles due to buoyancy, drag and gravitational forces get vertically density stratified and later frictional, gravity and external (vibrational, etc.) forces horizontally segregate different density particles. Dry separators based on terminal velocities follow single step for dry beneficiation of mineral, and air velocity in this type of dry density separators is maintained between terminal velocity of high density and low density particles. Velocity of air is higher for low density particles, which leads to higher drag and buoyancy forces to get pushed out of system with air and get collected at further distance than high density particles leading to density segregation. Mathematical models have been developed using force balance on particles and simulated in MATLAB for both type of separators to explain the physics of separation. Solutions to the simulated mathematical model equations are the particle trajectories of different density particles in the two dry separators. Iron ore is used as feed for studying separation futures in mathematical modeling on dry separators.

This paper proposes generalized polynomial guidance for controlling the terminal velocity vector (speed and flight path angle), which could be critical for the effectiveness of the warhead of tactical ballistic missiles. A polynomial reference trajectory satisfying the initial and terminal altitudes and flight path angles is introduced with a guidance parameter that can be chosen to change the terminal speed. A single differential equation of the speed along the reference trajectory is then derived and an iterative search method for determining the guidance parameter to satisfy the prescribed terminal speed is proposed. Numerical simulation study with various impact angle and terminal speed constraints is conducted to demonstrate the performance of the proposed guidance method for terminal velocity control. Robustness of the proposed method to drag variations is also investigated to check the feasibility of generalized polynomial guidance for a practical purpose.

A novel theoretical model which takes into account the particle property, equipment parameters, particle terminal velocity and Reynolds number was established to describe the separation of particles under critical conditions. Meanwhile, this established model was used to predict the superficial velocity of particle separation in the different spacing of inclined channels. A system was developed to test and verify the model. The correlation coefficient (R2) and Sum of Squares for Error (SSE) were adopted to evaluate the experimental results. When the ratio of fluid Reynolds number to particle Reynolds number was less than 43, the novel model was proved to be highly accurate in the prediction of the superficial velocity. The results suggested that the novel model provided much better conclusions than does a tradition empirical model. This study provides a theoretical and experimental foundation for the design of industrial inclined channel structure and operating parameters.

Aerodynamic properties of solid materials have long been used to convey and separate seeds during harvest and postharvest operations. In this study, the terminal velocities of chickpea (Cicer arietinum L.) and dry bean (Phaseolus vulgaris L.) seeds as a function of seed mass and projected area were determined and also it was predicted by the fuzzy knowledge-based model. The results showed that the terminal velocity increased non linearly from 6.46 to 7.567m s -1 for chickpea and from 5.224 to 6.463 m s -1 for dry bean with an increase in seed mass and projected area. In this paper, a sophisticated intelligent model, based on Mamdani approach fuzzy modeling principles, was developed to predict the terminal velocities of chickpea and dry bean seeds. The verification of the proposed model is achieved via various numerical error criteria. The relative error of predicted values was found to be less than the acceptable limits (10%).

The terminal constraints in entry guidance design are generally position and velocity constraints. In this study, the terminal time constraint is also taken into account. The estimates of time-to-go and range-to-go are discussed based on the quasi-equilibrium glide condition. Further analysis reveals that only two among the time-to-go, range-to-go, and terminal velocity are independent. Based on this observation, a guidance method is designed, which provides a new aspect to exploit the potential of entry guidance.

Engineering properties aid in the design and construction of equipment for post processing of cashew kernels. In this study, the engineering properties of cashew kernels from different locations were evaluated. The physical, mechanical and thermal properties of the kernels at a moisture content of 5% (wet basis) were investigated. The samples used for the study were randomly selected from four different plantation locations across two basic agro-ecological zones of Nigeria. The experiments were carried out in three replicates for each of the properties examined in any location in order to get average values. The physical properties considered were length, width, sphericity, bulk density, true density and specific gravity while the mechanical properties evaluated were porosity, angle of repose, terminal velocity, coefficient of friction, compression force, stress and deformation. The thermal properties examined were specific heat capacity and thermal conductivity. The results showed no significant difference (p

Numerical simulations are performed to investigate the effect of electric field and electrification process on dynamic, microphysical, and precipitation in thunderclouds. A three-dimension (3D) convective cloud model with electrification and discharge scheme is used to explore the differences between kinematic, microphysical process, precipitation, and lightning activity. The results show that the electrification process significantly enhances the updraft before the first discharge in thundercloud, but the electric field force has a significant effect on the updraft after the first discharge. The influence of electric field force on the formation of precipitation is greater than that of electrification process, and the increase of ice crystal terminal velocity is helpful to the formation of liquid precipitation, and then the increase of graupel terminal velocity is beneficial to the development of solid precipitation. The results also suggest that the new scheme of graupel terminal velocity enhances the high-concentration region of graupel before the first discharge, and the region lasts as long as 10 min, which effectively promotes the production of raindrop in the whole troposphere at specific time. Additionally, the electric field has the most significant effect on the velocity of smaller particles, and an increasing of ice crystal fall speed above 0 °C is also helpful to the formation of lightning. Moreover, it is found that the electric field force enhances the collision and coalescence between cloud droplets/raindrops and graupel during the mature period of thundercloud.

Knowledge on regime transition from conventional to circulating fluidization is important to scale-up and operation of liquid-solid fluidized systems in industrial applications. Previous experimental studies reported that the onset velocity measured by bed empty time test is pertinent to the physical properties of particle and liquid, and independent of solid inventory, bed geometry, and configuration. The effect of liquid properties is, however, not clear yet since tap water is usually used as the working fluid in laboratory test for convenience. To address this problem, a Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) model is applied to numerically measure the onset velocity of particles in different liquid media. The model is first validated in terms of the experimental data of bed expansion in literature. Then several kinds of particles and three kinds of liquid media of different densities and viscosities are further simulated. We find that the Reynolds number based on onset velocity and Archimedes number follows a power-law relationship. With the decrease of Archimedes number, the discrepancy of Reynolds number based on onset velocity and that on particle terminal velocity becomes highly significant. The ratio of the onset velocity to particle terminal velocity for various particles in one liquid medium is not a constant, and instead dependent on both the particle and liquid properties.

The paper presents an analysis of the effect of collisions between coarse and fine particles in the vertical flow of a stream of fine particles suspended in gas on the exchange of momentum in these conditions. It was found that the phenomenon of double collisions of fine particles with the surface of coarse particles can be observed during the flow of a stream of fine particles suspended in gas around moving and stationary coarse particles. This phenomenon changes the nature of the relationship between the force of mutual interactions and mass flow rate of fine particles. The proposed corrective relationship significantly improved the consistency of the value of coarse particle terminal velocity depending on mass flow rate of fine particles suspended in the gas flowing around coarse particles. The range of importance of the relationships concerning the terminal velocity of coarse particles was determined.

Motion of droplets in liquid –liquid extraction column is of importance for many industrial processes. This study aims at evaluation of hydrodynamic behavior of a nanofluid particle moving through an immiscible liquid. Toluene based nanofluids were used as referral systems in this study. Nanoparticles of ZnO, Al2O3, SiO2 and TiO2 have been used to synthesize stable nanofluids. The experiments were carried out using different concentrations of nanoparticles to study the variation in terminal velocity, drag coefficient and eccentricity of the nanofluid droplet. Observations show enhancement in terminal velocity and reduction in drag coefficient of the droplets, for all nanofluids up to optimum concentration of nanoparticles. With increase in concentration of nanofluid beyond the optimum concentration, the droplet terminal velocity decreases and drag coefficient increases due to deformation in shape and an increase in oscillation that could be due to nanoparticle aggregation in nanofluid. The eccentricity of...

The settling of well-characterised fractal aggregates has been investigated numerically. The Immersed Boundary Method coupled with the Lattice Boltzmann Method (IBM-LBM) was developed to fully solve the liquid flow passing through the porous aggregate. Aggregates with prescribed structures covering the large spectrum of fractal dimension were fabricated and the benchmark experimental data have been collected to extensively validate the numerical model. Subsequently, the settling dynamics of fractal aggregates in liquid in terms of orientation evolution, time dependent drag force and terminal orientation was investigated and correlated to their morphological characteristics. Different equations have been developed for predicting the terminal settling velocity of fractal aggregates. A correlation that only requires inputs of primary particle size and fractal dimension is proposed for predicting the terminal velocity of fractal aggregates. Deviations less than 7% were obtained when applying the model for aggregates with the primary particle size ranging between 1.5 mm and 5 mm. The model's applicability to small aggregates comprised of primary particles less than 1 mm has also been demonstrated and discussed.

Industrial processes do not often deal with a pure fluid. Impurities can affect physical properties of gas-liquid systems, resulting in change of gas bubbles velocity. Purpose of the study ...

An accurate and convenient method is essential for measuring the terminal velocity of seeds dispersed by wind. Systematic and random errors produced by existing methods lower the accuracy and convenience in determining seed terminal velocity. In this study, a video camera was used to record the falling process of forty-one species of wind-borne seed with eight appendage structures and seven aerodynamic behaviors in a settling tower at a speed of 50 frames per second (fps). The videos were analyzed by Quick Time Player to determine seed acceleration height, acceleration time, and terminal velocity. The results showed that acceleration height and time, terminal velocity, and the difference between terminal velocity and descent velocity (DTD) increased with wing loading. Compared with dropping methods, the camera recording method eliminated the effect of acceleration and corrected seed terminal velocity. Based on wing loading, release heights were determined for accurate measurement of terminal velocity of different seeds. This method, due to its inexpensive equipment, high accuracy, easy observation and operation, can be applied to measure the terminal velocity of wind dispersed seeds, and provides a promising method in exploring the dispersal process of seeds.

Porous particles are widely used in liquid–solid and gas-liquid-solid reactors, and accurate prediction of drag coefficients ( C D ) for porous particles is essential for designing and optimizing these reactors. The drag coefficients for porous particles, however, have been mainly obtained via theoretical analysis and numerical simulations. Only three experimental studies were carried out to study the drag force on porous spherical particles due to the difficulties in the preparation of model porous spheres with a homogeneous porosity and homogeneous surface properties. In this paper, a method to prepare model porous spheres which have a homogeneous porosity and homogeneous surface properties with a good sphericity for a wider range of relative permeability β has been presented. The details of this method were documented, and it showed that the porous spheres constructed could withstand rigid collisions at the maximum terminal velocity of 1 m/s and keep the structure intact with a negligible quantity of binders. Then gravity-driven settling experiments of a single porous sphere by use of particle tracking velocimetry (PTV) method were carried out to evaluate the feasibility of the use of the prepared porous spheres. Experimental results for 12 porous spheres, with particle Reynolds number ( R e ) ranging from 1 to 108 and relative permeability β from 21.6 to 315.6, agreed well with the previous results in the literature. The porous particles prepared by our proposed method can be potentially used for measuring drag coefficients of the porous permeable spheres in a wider range of particle Reynolds number and permeability and studying the complex interaction between the porous particles and the surrounding fluid.

A lateral guidance method is presented to satisfied long lateral maneuver range for reentry vehicle. The conventional technique for lateral guidance is based on reference trajectory, and the bank sign is determined by the relative position from destination area. A new automated guidance method of lateral maneuver is given based on coverage zone profile, which steers the vehicle to destination without reference trajectory. Database of possible flight paths are calculated off line, the bank angle is related to lateral and longitudinal range. The guidance law predicts position at restrained terminal velocity with different bank angles, and determines one with minimum distance from destination. Simulation in nominal case indicates that lateral maneuver range over half of longitudinal range can be satisfied. Monte Carlo simulations are taken for aerodynamic dispersions. The lateral guidance method is proved with good interference capacity, and taps the potential of lateral maneuver capability by reaching target beyond nominal range.

The present investigation shows a kinematic analysis of Baumgartner’s stratospheric jump, based on a scientific report by Red Bull. The modeling was carried out using the different forces that intervened in the event (velocity, acceleration, etc.), making it possible to generate a mathematical model capable of extrapolating data and allowing us a better appreciation of such scientific achievement. All the mathematical exploration has been carried out with ten decimal places; however, they will be rounded to four in writing. The action plan was based on obtaining the velocities by placing points on a velocity model belonging to an approximate graph of a Red Bull scientific report, which was put into the GeoGebra Classic 5 program to find the velocities. After this, we proceeded to find the accelerations and the formula of the function that models them. Finally, this formula was integrated to acquire the mathematical model of the velocities.

The motion of solids in a viscous fluid with nonlinear complex behavior has important applications in different industries and engineering sciences. This work experimentally investigated the free-fall behavior of rotating and non-rotating spherical particles in a viscous fluid. The effects of physical parameters, including particle size, particle density, fluid viscosity, and rotational velocity, on the terminal velocity of the falling spherical particles were examined. A high-speed camera was employed to capture the phenomena and study the free-fall behavior of the spherical solid particles in a viscous fluid. The studied spherical particles had five different densities of 2800, 7800, 7900, 8660, and 8960 kg/m3 and three varying dimensions of 4, 5, and 6 mm. To explore the effect of fluid viscosity on the terminal velocity of particles, two types of fluids with the viscosities of 0.012 and 0.014 Pa.s were used. The initial rotational velocities were 0, 600, 900, and 1200 rpm for the falling particles. The obtained results revealed that increases in the particle diameter, density, and rotational velocity, along with a decrease in fluid viscosity, accelerated the terminal velocity and shortened the time of reaching this velocity. Furthermore, an increase in the Reynolds number gave rise to a decrease in the lift coefficient. On the other hand, the accelerated dimensionless rotational velocity increased the lift coefficient.