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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.

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...

In a vast number of industrial applications, particle-laden flows consist of irregularly-shaped particles with various sizes and shapes and thus, the drag coefficient is strongly affected and different for each particle. The key issue is to incorporate these characteristics within numerical calculations. Therefore, a sample-set of irregularly-shaped combustion residues or rather clinker flakes, with sizes between 50 μm and 250 μm was experimentally and numerically investigated. Particle geometry, terminal velocity measurements and drag analysis were carried out within the present work. Areflected-light microscope and an optical particle analyzer were used for geometry analysis. Terminal velocities were measured in a water filled glass column with a commercially available digital camera with a recording rate of 1000 frames per second and a frame-by-frame tracking method. At first a simple particle classification method based on this geometrical analysis and terminal velocity measurements in a static fluid was introduced. As a result, several particle groups were defined based on the obtained data. As a second step, this data were used as input parameters for two simple drag models from literature. The required particle shape parameters were determined by velocity recalculations and data fitting. Furthermore, the applicability of these drag models in combination with the experimentally determined particle shape descriptors was evaluated within a simple test rig, where freely falling particles are exposed to a lateral compressed airflow. The particles would be deflected and settle at different positions at the bottom of the test rig. Numerical calculations of the test rig were performed using a commercial Computational Fluid Dynamics (CFD) code and a numerically efficient Euler-Lagrangian approach in order to predict the accurate motion of particles. The particle mass dispersion at the bottom of the test rig was compared to numerical results. It was shown that the used drag models in combination with the experimentally determined particle shape descriptors improved the prediction of particle drag coefficients and trajectories significantly without an increase of computational cost and time.

The OMNI-Max anchor, a newly developed gravity installed anchor, offers a cost effective anchoring solution with improved reliability for deep-water mooring facilities. However, the anchor final penetration depth is relatively shallow in the soil with high strength gradient. A booster, which can be attached at the tail of the OMNI-Max anchor, is designed with the aim to improve both the anchor directional stability and terminal velocity, such that the anchor can penetrate deeper into the seabed and consequently gain higher holding capacity. The objective of this paper is to investigate the directional stability and terminal velocity of the OMNI-Max anchor and hybrid anchor (i.e. an OMNI-Max anchor with a booster) based on the computational fluid dynamics (CFD) approach. The numerical simulation results demonstrated that the booster is beneficial in moving the position of the hydrodynamic centre towards the anchor rear, hence the directional stability of the hybrid anchor is improved. Moreover, the anchor terminal velocity was increased from 22.44 m/s to 32.01 m/s by the aid of a booster. Finally, an optimised design on the booster geometry was performed to ensure that the hybrid anchor can obtain high terminal velocity and maintain directional stability at the same time.

Ground-based freefall facilities are to create microgravity environment on earth for studying the space-related or fundamental sciences, which have been widely used in the field of combustion, fluid, physics and material sciences. Aiming to serve for the broader microgravity science and preliminary tests for projects onboard the upcoming assembly of Chinese Space Station, a 2.2 second freefall facility was designed and built in the Lee Shau Kee Science and Technology Building on the campus of Tsinghua University in Beijing. This facility is composed of five systems: (I) freefall tunnel and safety cables; (II) release and retrieve system; (III) the capsule; (IV) brake system; (V) electrical control and safety interlock system. The capsule consists of an outer drag shield and an inner rig of which the total weight is 280 kg. The capsule is released by a pneumatic chuck that minimizes disturbance of the release operation. The eddy current brake modules made of several permanent magnets are applied to decelerate the capsule without power supply. This paper primarily discusses the tests designed and conducted to characterize the performance of such facility in many aspects. The results show that during freefall, the microgravity level of 10-3 g can be achieved for 2.2 second. Concerning movement of the inner rig relative to the drag shield during freefall, the clearance of 0.43 m and relative velocity of 0.62 m/s were specified. The deceleration can be controlled within 15 g. The terminal velocity of capsule in the brake system ranges from 0.4 to 0.5 m/s depending on the actual weight of capsule. The noise level in the entrance section of brake system is about 75.6 dB. The duration of this noise is very short (

Particle Image Velocimetry (PIV) is a proven technique for the observation of flow or particle motion in fluids. A pulsed laser is used to create a thin plane of light in the fluid, which typically...

A new type of liquid–solid circulating fluidized bed, the conventional circulating fluidized bed (CCFB), which operates at a superficial liquid velocity lower than the particle terminal velocity, was numerically studied by the Eulerian-Eucerin two-fluid model. The flow structures in the upward CCFB where the liquid and solids flow upward by using heavy particles with a density higher than the liquid, and in the inverse CCFB where liquid and solids flow downward with light particles are compared in this work. Time-averaged axial and radial profiles of the liquid velocity, particle velocity, and solid holdup from the numerical results are presented. Instantaneous profiles representing the local flow structures are also provided.

In this work, we present an alternative methodology to solve the particle-fluid interaction in the resolved CFDEM ® coupling framework. This numerical approach consists of coupling a Discrete Element Method (DEM) with a Computational Fluid Dynamics (CFD) scheme, solving the motion of immersed particles in a fluid phase. As a novelty, our approach explicitly accounts for the body force acting on the fluid phase when computing the local momentum balance equations. Accordingly, we implement a fluid-particle interaction computing the buoyant and drag forces as a function of local shear strain and pressure gradient. As a benchmark, we study the Stokesian limit of a single particle. The validation is performed comparing our outcomes with the ones provided by a previous resolved methodology and the analytical prediction. In general, we find that the new implementation reproduces with very good accuracy the Stokesian dynamics. Complementarily, we study the settling terminal velocity of a sphere under confined conditions.

The hydrodynamics of the binary mixture system in the multisolid pneumatic transport bed (MPTB), where a fine-particle laden gas flows through a coarse particle bed, was investigated by computational fluid dynamics (CFD) simulation. A pseudo-homogeneous method, which considers the gas phase and the fine particle phase as one pseudo-homogeneous dilute phase, was proposed to predict the coarse particle terminal velocity. In the second approach, the fine particle and coarse particle are treated separately, with the structure-based drag model developed in our previous study being used to simulate the coarse particle terminal velocity and fine particle holdup in the coarse particle bed. The simulation results of the two methods showed reasonable agreement with the experimental data under different operating conditions. As observed in the experiment, the terminal velocity of coarse particles decreases with increasing the fine particle flow rate, and the reduction is more significant for larger coarse particles. Besides, the fine particle holdup increases with the decrease of the diameter of coarse particles. These results demonstrated that the multisolid pneumatic transport system can serve as a simple binary system, with its coarse particle terminal velocity and fine particle holdup being used for the verification and validation of binary-particle CFB models.

This work included the experimental studies of the Newtonian fluid flow over hollow frustum both in the normal and inclined channel. It encompasses terminal velocity and drag coefficient, CD data for 0.13 ≤ Re ≤ 8.41, 0.19 ≤ do/D ≤ 0.33, 0.22 ≤ di/do ≤ 0.83 and 40° ≤ θ ≤ 90o. The effect of inner diameter to outer diameter ratio, di/do and the outer diameter to the flow channel diameter ratio, do/D on terminal velocity is reported for the specified range of angle of inclination, θ for several hollow frustums in a series of high viscous Newtonian fluids. The terminal velocity shows an increasing trend with increasing and decreasing do/D and di/do ratios, respectively. The terminal velocity also increases with increasing the angle of inclination, θ of the flow channel. Predictive equations are developed for the estimation of CD as a combined function of Re, di/do, do/D and θ. The statistical sensitivity analysis shows a large variation of the drag coefficient of the hollow frustum with the Reynolds number than with di/do and do/D ratios. The dependency of CDRe term on the fluid viscosity and θ are expressed in terms of the developed correlations. Linear variation of CD with 1/Re confirms that flow regime is laminar in the present study. The experimental drag coefficients are then predicted excellently through numerical approximation using Reynolds Stress Model (RSM) available in Ansys-15.

A novel multiple constrained adaptive gliding guidance method which is independent of quasi-equilibrium gliding condition (QEGC) and standard trajectory is proposed in this paper. The gliding guidance task is decomposed into longitudinal and lateral directions. In longitudinal direction, an altitude control model is established independent of QEGC, a hierarchical adaptive guidance strategy is introduced to control the vehicle to achieve equilibrium flight state and to meet the terminal altitude and flight-path angle constraints. In lateral direction, a heading error control model is constructed and the optimal control is employed to eliminate the heading error in real time with minimum energy consumption. In addition, the terminal velocity magnitude is predicted and corrected analytically based on lift–drag ratio, and the coordination strategy between guidance and velocity control is proposed to realize multi-constraint gliding guidance. This algorithm can generate angle-of-attack and bank angle commands which can meet the given terminal constraints with high precision based on the current flight states analytically, and has strong robustness to the initial deviation and environmental deviation.

This work presents a multiscale three-dimensional CFD model for the simulation of two-phase gas-liquid flows with different interface length scales, with focus on slug flow pattern. The model is based on the coupling of the Volume-of-Fluid (VOF) method, used to model the large-scale interface dynamics, and the Discrete Bubble Model (DBM) for modeling the small-scale bubbles, which allows to simulate two-phase flows with different interface length scales. A validation study is conducted independently for the VOF and DBM methods, by comparing the numerical results with experimental data from the literature, showing a very good agreement. A model for the collision between the VOF interface and Lagrangian bubbles is proposed and also independently validated. The coupled VOF-DBM model is used to study a liquid-gas two-phase flow with different interface length scales, where large Taylor bubbles and small dispersed bubbles are present. The results demonstrate that the presence of the small dispersed bubbles alters the flow structure around the Taylor bubble, increases the terminal velocity of the Taylor bubble and affects the flow structure in the wake region, which is directly related to heat and mass transfer rates in slug flow.

Reliable and accurate prediction of the transition from spherical cap bubble to slug flow is crucial not only to the operation of industrial facilities such as the crude oil pipelines, bubble column, and nuclear reactors but also for model development for computational fluid dynamics (CFD) studies. The present paper presents a review of the transition mechanics from spherical cap bubble flow to slug flow in vertical pipes. The bubble flow was split into sub-regions, bubbles and spherical cap bubbles and the mechanisms to classify them (i.e., bubble terminal velocity and cap bubble velocity) was analysed. For now, the literature review does not present some important previous works. This paper presents an original data set of gas–silicone oil in vertical pipes to support the new findings. The experimental two-phase data classifies the flow patterns using the probability density function (PDF) and shows the important flow variables such as average void fraction, pressure gradient, slug body void fraction, liquid slug, Taylor bubble and slug unit lengths, structural velocity and frequency obtained by electrical capacitance tomography (ECT) and a wire mesh sensor (WMS).

The expanding fracture of an explosively driven 1045 steel cylinder was studied. The fracture process and the expanding velocity of the cylinder were recorded by a high-speed camera and a Photonic Doppler Velocimetry (PDV) probe in real time. The fragments were recovered and analyzed by metallurgical examinations. The fracture mechanism, expanding velocity and fragment size were analyzed respectively. We found that the adiabatic shear band (ASB) plays a key role in the fracture process of an expanding 1045 steel cylinder. As the deformation of the cylinder increases, multiple ASBs firstly initiate near the inner surface of the cylinder and then propagate outward along the maximum shear stress direction. After the ASBs arrive at the outer surface of the cylinder, all of the plastic deformation is concentrated in the ASBs, and meanwhile the cracks initiate near the outer surface of the cylinder and propagate inwardly along the developed ASBs. The terminal velocity of the cylinder was accurately predicted by the Gurney model and was found to be little influenced by the fracture mode. The width and thickness of the fragments were measured and found to be controlled by the momentum diffusion. Furtherly, we modeled the expanding fracture process of the cylinder. A three dimensional simulation results suggested that the propagation of the shock wave along the radial direction can't be neglected although the cylinder is very thin. At an early stage, the material near the inner and outer surface is in a compressive and tensile state, respectively, and the material in the middle of the cross-section is alternately in a tensile and compressive state due to the propagation of the shock waves. At a late stage, the whole cylinder is in a tensile state. In a two dimensional plane strain simulation, the initiation and propagation of multiple ASBs in the expanding cylinder were successfully replicated.

Electrohydrodynamic motion and deformation of a sedimenting drop in the presence of a uniform alternating electric field is investigated experimentally. Application of an electric field causes a drop to deform to an ellipsoidal shape. As a result of this deformation, the terminal velocity of the drop is affected. In this study, a detailed experimental investigation of the effect of a horizontally directed uniform alternating electric field on the sedimentation velocity and deformation characteristics of deionized water drop and silicone oil drop falling in castor oil medium is presented. Both water and silicone oil drops are found to deform to a prolate shape on application of electric field, which retards the drop motion in the vertical direction. There is a marked decrease in drop velocity with increase in strength of the alternating electric field.

Liquid metal is an important type of energy transport carrier in nuclear reactors, such as in accelerator-driven sub-critical systems, fusion reactors and spallation neutron source devices. It is necessary to conduct research for bubbles rising in a liquid metal under different magnetic field intensities. The Perspex container is positioned concentrically inside a transverse magnetic field, which provides a homogeneous DC longitudinal magnetic field that passes through the fluid district. The coils are supplied with maximum field strength of 1.97 T. The equivalent diameter of the bubble is 3.1–5.6 mm. The Ultrasonic Doppler Velocimetry (UDV) method is used to evaluate the internal flow velocity of opaque liquid metals. Research shows that the influence of the Lorenz force on the bubble ascension velocity is not simply positive or negative. The magnetic field inhibits the ascension velocity of small bubbles with diameters of 3.1 mm and 3.4 mm. The terminal velocity for large bubbles with diameters of 4.57 mm, 5.15 mm and 5.6 mm is higher under a weak magnetic field than without a magnetic field. The positive effect happens under strong magnetic intensity. The target is to obtain the hydro-dynamical relationships between the terminal velocity, drag coefficient, the Eotvos number, Reynolds number, and Stuart number in a strong magnetic field using a multiple regression method to reveal that the mechanism of the induced current's restraining influence determines the ascension velocity of the bubble in viscous electric liquids with a strong magnetic field.

The present study aims to investigate the characteristics of airflow inside the room through 5-blade square louver face ceiling diffuser using CFD. Several diffuser models are installed inside 3D room model by changing blade angles (60°, 65° and 45°) and lip angles (0°, 5°, 10° and 15°). Besides, the model with 60° blade angle and 0° lip angle is installed inside different room models with various return air inlet positions. The realizable k–e turbulence model is used in simulation process. The results indicated that the diffuser model with 65° blade angle provide jet and terminal air velocities beside airflow patterns cling with ceiling higher than the models 60° and 45°. Therefore, it is suitable to install in the space with larger size and relatively higher noise level to reaches to the comfort criteria faster than the other models to reduce the energy consumption. On the other hand the model with 45° blade angle is applicable to installed in the spaces with larger height due to airflow patterns out in cone shape. In addition, increasing lip angle to 15° leads to relatively reduce the cling of airflow patterns with room ceiling, and reach to comfort conditions with less energy consumption faster than 0° lip angle. Moreover, the room geometry model with two return air inlets on the ceiling with adequate size is produced ideal design of a fully mixed air distribution system with relatively constant temperature gradient.

The present study aims to modify and develop a small, simple, and cheep machine for cleaning and grading Egyptian crop seeds by using both mechanical and aerodynamic methods, suitable for the small village. The developed machine was constructed locally from available material which purchased from domestic market and fabricated to ensure low initial cost and availability of spare parts and ease cleaning and repair. The parameters involved in grading machine and analysis the behavior of particles and forces acting during grading process, to achieve the optimum conditions for cleaning, grading and conveying operations. To evaluate the performance of the modified cleaning and grading machine, a series of experiments were carried out to study some parameters, such as the effect of screen oscillation speed inclination, Broad beans (Giza 461); grading operations. The main results obtained from the experiments were summarized in the following main points:- Te average mas of 1000 kernels 7579, Length 14.7 mm, width 11 mm, thickness 6 mm, specific density 1.28 g/cm3, projected area 2.15 cm2, terminal velocity 12.4 drag coefficient 0.396, Reynolds number 1170, and spherically 0.66 at M.C 14-18%. Separation efficiency was 98% at screen oscillation 2/5 rpm, Zero deg. feed rate 250 kg/h. Grain recovery was 99%, grain loss was 0.70%, and grain clean lines was 98% at the same conditions.

Traditional air classifiers produce binary splits based on the terminal velocity rather than the density of the feed. In this study, a pulsating air with a sine-like shape wave was introduced into a vertical column air classifier to achieve the density dominant separation on −6+3 mm fine coal. A lab-scale separation device was used to investigate the effects of pulsating characteristics (amplitude and frequency) and particles volumetric concentration on pulsating airflow separation in a batch process. The optimum operating conditions of 34.1 cm pulsation amplitude, 2.45 Hz frequency and 500 g feed amount achieved 48.08% separation efficiency, 68.22% combustible matter recovery and produced a clean coal with 17.98% ash (from a feed containing 42.02% ash), 47.73% yield and Ep value of 0.17. The results showed that the pulsating air classifier has a potential for fine coal dry beneficiation. The motion of particles in a pulsating airflow field under a hindered settling condition has been presented.

Taylor bubble velocity in slug flow is a closure relation which significantly affects the prediction of liquid holdup (or void fraction) and pressure gradient in mechanistic models of slug flow for oil and gas pipe applications. In this work, we use a validated Computational Fluid Dynamics (CFD) approach to simulate the motion of Taylor bubbles in pipes; the interface is tracked with a Level-Set method implemented in a commercial code. A large numerical database is generated covering the most ample range of fluid properties and pipe inclination angles explored to date (Eo ∈ [10, 700], M o ∈ [ 1 × 10 − 6 , 5 × 10 3 ] , andθ ∈ [0°, 90°]). A unified Taylor bubble rise velocity correlation is extracted from that database. The new correlation predicts the numerical database with 8.6% absolute average relative error and a coefficient of determination R 2 = 0.97 , and other available experimental data with 13.0% absolute average relative error and R 2 = 0.84 outperforming existing correlations and models.

Purpose This research aims to investigate the effects of manipulation of a torpedo’s geometries to attain higher terminal velocity. The parameters of interest include geometric changes of the original design, as well as sea water properties that reflect water depth in South China Sea. Design/methodology/approach The research make use of computational fluid dynamics (CFD) software, FLUENT, to solve viscous incompressible Navier–Stokes equations with two equations k-epsilon turbulent model. The calculated drag coefficient is subsequently used to calculate the maximum attainable terminal velocity of the torpedo. Findings It was found that the terminal velocity can be improved by sharper tip angle, greater aspect ratio, greater diameter ratio and optimum rear angle at 30°. Sensitivity of drag coefficient toward each of the parameters is established in this paper. Originality/value The paper, in addition to verifying the importance of aspect ratio, has also established the tip angle, diameter ratio and rear angle of the torpedo as important geometric aspects that could be tuned to improve its terminal velocity.

The basis of a novel braking technique by using the Phobos sands for landing large payloads on Mars is outlined. Here consideration is given to the utilization of the Phobos or Deimos regolith as material for aerobraking by discharging a load of sand at certain distance in front of the spacecraft during the descent manoeuver. Although immediately after getting rid the load of sand in front of the spacecraft they have a null relative velocity with the spacecraft, however, because the stronger atmospheric drag acting on the tiny particles of sand they will be promptly decelerated. As a result, the particles of sand will impact onto the front of the spacecraft with a velocity close to the terminal velocity of the spacecraft itself. By using a pusher-disc – or akin damping system, in front of the spacecraft the momentum exchange from the sand collisions will result in a braking force acting on the spacecraft. Due to the very small delta-v budget required to lift material from the surface of Phobos or Deimos to their transfer orbits, then a small amount of dedicated rocket chemical propellant brought from Earth could be transformed into a huge amount of sand lifted from the surface of Phobos of Deimos to their transfer orbits. The large thrust generated by the Sandbraking makes this technique propitious for landing of planetary bodies struggling against gravity.

The aerodynamic characteristics of high-speed trains operating in severe environment have gained an increasing interest in the past few years. As rain is a common weather phenomenon, understanding its effects on the aerodynamic characteristics of the high-speed train provides valuable information for the design of a train. In the present paper, the aerodynamic model of a high-speed train operating in a dry condition is first set up, and the simulation results are compared with the existing wind tunnel test data to validate accuracy of the mesh resolution and CFD technique. For the simulation of raindrops, the applicability of spherical raindrop assumption in numerical simulations is discussed in this paper. The results demonstrate that, when the equivalent spherical diameters are greater than 2 ​mm, the simulation errors of terminal velocity of raindrops exceed 3%. The non-spherical characteristics of raindrops need to be considered for large particle sizes, and the particle sphericity for various equivalent spherical diameters is investigated. After that, a two-way coupled Euler-Lagrange approach is developed to evaluate the aerodynamic characteristics of a high-speed train in heavy rain environment based on non-spherical raindrop assumption. The flow around the train, pressure coefficient distribution, skin friction coefficient distribution, and aerodynamic force coefficients of the high-speed train exposed to heavy rain environment are then investigated. It is found that the aerodynamic coefficients of the high-speed train increase approximately linearly with the rainfall intensity. The explicit equations for predicting the aerodynamic force coefficient which is correlated with train speed and rainfall intensity are proposed in this study.

Terminal rising velocity of a single bubble in stagnant water and glycerol aqueous solution was studied by the techniques of high-speed photography and digital image analysis. The results can be summarized as follows: In water, bubble terminal velocity increases while aspect ratio decreases almost linearly in the region where d 6 mm. In the surface-tension-dominated regime, the aspect ratio of a single bubble varies significantly with the value fluctuating from 0.4 to 0.99. The aspect ratio should be taken into account with the bubble diameter when predicting the terminal velocity. In the inertia-dominated regime, the terminal velocity increases gradually with increasing the bubble diameter while their aspect ratios vary between 0.4 and 0.7. In the glycerin aqueous solution, as a whole, the terminal velocity increases with bubble diameter and the trend of the bubble velocity does not show a scattered behavior. In water, the most accurate model for predicting terminal velocity throughout the investigated range is given by Tomiyama et al. (2002), and then followed by Ishii and Chawla (1979).

Slurry systems in mineral processing processes often behave as pseudo-plastic fluids, where the viscosity of the slurry changes as a function of the shear imparted. Thus, characterizing motion of macroscopic objects through such systems is a challenging task because the viscous forces on it vary rapidly. In this paper, we have studied motion of falling spherical particles in non-Newtonian fluid using a novel macroscopic particle model (MPM). The simulation results were compared with the available experimental data and analytical correlations, where MPM was found to be effective in accurately determining the forces acting on particle during fluid–particle interaction. Thus, it was concluded that MPM is a computationally viable solution for resolving hydrodynamics of macroscopic particles in slurries, especially for its ability to accurately capture the acceleration of particles, which is significantly lower when compared with that in Newtonian fluids. The validated MPM model was used to investigate the effect of particle properties on the motion of particle and yield-structure of fluid. For low Reynolds number, the well-known toroidal yielded structure of fluid was observed with particle equator as centre and √2dp diameter. Beyond the Reynolds number to Bingham number ratio of 10, a wake was formed behind the particle that increased with increasing Reynolds number. Copyright © 2016 Curtin University of Technology and John Wiley & Sons, Ltd.

Summary In this paper, a method is proposed for modeling explosive-driven fragments as spherical particles with a point-particle approach. Lagrangian particles are coupled with a multimaterial Eulerian solver that uses a three-dimensional finite volume framework on unstructured grids. The Euler–Lagrange method provides a straightforward and inexpensive alternative to directly resolving particle surfaces or coupling with structural dynamics solvers. The importance of the drag and inviscid unsteady particle forces is shown through investigations of particles accelerated in shock tube experiments and in condensed phase explosive detonation. Numerical experiments are conducted to study the acceleration of isolated explosive-driven particles at various locations relative to the explosive surface. The point-particle method predicts fragment terminal velocities that are in good agreement with simulations where particles are fully resolved, while using a computational cell size that is eight times larger. It is determined that inviscid unsteady forces are dominating for particles sitting on, or embedded in, the explosive charge. The effect of explosive confinement, provided by multiple particles, is investigated through a numerical study with a cylindrical C4 charge. Decreasing particle spacing, until particles are touching, causes a 30–50% increase in particle terminal velocity and similar increase in gas impulse. Copyright © 2015 John Wiley & Sons, Ltd.

In this work, the transient regime of motion of a sphere, that falls along an inclined smooth plane, submerged in still water, is studied experimentally and analytically. Several experiments were performed, with spheres of different diameters and densities, and two slope angles. The measurements show that the motion of the sphere presents two well defined stages: a transitional regime, where the sphere rapidly accelerates from rest, and an asymptotic regime, where the sphere moves with constant velocity. Closed expressions, for the position and velocity of the sphere as functions of time, are obtained by direct integration of the motion equations. This theoretical analysis is based on the empirical correlation for the drag coefficient as a function of the Reynolds number of the sphere, that was proposed by Chhabra and Ferreira [2] for the experimental data set of Jan and Chen [1]. The analytical solution shows good agreement with experimental results, for a wide range of experimental conditions. Fil: Martino, Román Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; Argentina Fil: Paterson, Agnes. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Hidráulica; Argentina Fil: Piva, Marcelo Fabian. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; Argentina

To improve the separation efficiency of a conventional Teetered Bed Separator (TBS) in beneficiation of fine coal with a wide size range, an Aeration TBS (A-TBS) was proposed in this investigation. The bubbles were introduced to A-TBS by a self-priming micro-bubble generator. This study theoretically analyzed the effect of bubbles on the difference in hindered settling terminal velocity between different density particles, investigated the impact of superficial water velocity (VSW) and superficial gas velocity (VSG) on bed fluidization, and compared the performance of the TBS and A-TBS in treating 1–0.25 mm size fraction particles. The results show that the expansion degree of fluidized bed which was formed by different size particles or has different initial height, is increased by the introduction of bubbles. Compared with the TBS, at the same level of clean coal ash content, the A-TBS shows an increase in the combustible recovery of clean coal, ash content of tailings, and practical separation density by 5.26%, 6.56%, and 0.088 g/cm3 respectively, while it shows a decrease in the probable error (Ep) and VSW by 0.031 and 3.51 mm/s, respectively. The addition of bubbles at a proper amount not only improves the separation performance of TBS, but also reduces the upward water velocity. Keywords: Teetered bed separator, Fine coal, Bubbles, Superficial water velocity, Superficial gas velocity

Development of an Earth entry vehicle and the methodology created to evaluate the vehicle’s impact landing response when returning to Earth is reported. NASA’s future Mars Sample Return Mission requires a robust vehicle to return Martian samples back to Earth for analysis. The Earth entry vehicle is a proposed solution to this Mars mission requirement. During Earth reentry, the vehicle slows within the atmosphere and then impacts the ground at its terminal velocity. To protect the Martian samples, a spherical energy absorber called an impact sphere is under development. The impact sphere is composed of hybrid composite and crushable foam elements that endure large plastic deformations during impact and cause a highly nonlinear vehicle response. The developed analysis methodology captures a range of complex structural interactions and much of the failure physics that occurs during impact. Numerical models were created and benchmarked against experimental tests conducted at NASA Langley Research Center. The...

Wind turbines are subject to a wide range of environmental conditions during a lifespan that can conceivably extend beyond 20 years. Hailstone impact is thought to be a key factor in the leading edge erosion and damage of wind turbine blades. Along with the size and density of the hailstone, the aggregated impact velocity components are crucial variables that characterise the kinetic energy associated with singular impact. These components include: the terminal velocity of the hailstone, the mean wind speed and the rotational speed of the turbine. Theorised values for the impact velocity may not truly reflect the conditions experienced by wind turbine blades. Using UK meteorological data, a greater representation of hail characteristics, occurrence probabilities and realistic impact component velocities is proposed, which will assist in the development of a realistic damage model for hailstone impact.

The dual pulse rocket motor(DPRM) distributes the propellant energy effectively via pulse separation device(PSD) to improve the range and terminal velocity of the missile. There are two types of PSD such as bulk head type and thermal barrier type. A subscale thermal barrier type DPRM was designed, manufactured, and tested. The results showed good understanding of the characteristics of the PSD and will be applied to the design of the full scale DPRM.

Simulations of single droplets rising in a quiescent liquid were performed for various initial droplet diameters. The continuous phase was water and the dispersed phase was either n-butanol, n-butyl acetate or toluene, thus resulting in three standard test systems for liquid–liquid extraction. For the simulations, a level set based code was developed and implemented in the open-source computational fluid dynamics (CFD) package OpenFOAM®. To prevent volume (or mass) loss during the reinitialisation of the level set function, two methods published recently were used in the code. The continuum surface force (CSF) model and the ghost fluid method (GFM) were applied to model interfacial forces, and their influence on grid convergence, droplet shapes and rise velocities was investigated. Grid convergence studies show a reasonable behaviour of the GFM, whereas the CSF model is less reliable, especially for systems with high interfacial tension. The results for droplet shape and terminal rise velocity are in excellent agreement with experimental and numerical investigations from literature. The onset of oscillations is correctly predicted, and the influence of the smoothing of interfacial forces on velocity oscillations is studied. Simulations of oscillating droplets remain stable, but the frequencies of the velocity oscillations differ from experimental results.

The study and modelling of two-phase flow, even the simplest ones such as the bubbly flow, remains a challenge that requires exploring the physical phenomena from different spatial and temporal resolution levels. CFD (Computational Fluid Dynamics) is a widespread and promising tool for modelling, but nowadays, there is no single approach or method to predict the dynamics of these systems at the different resolution levels providing enough precision of the results. The inherent difficulties of the events occurring in this flow, mainly those related with the interface between phases, makes that low or intermediate resolution level approaches as system codes (RELAP, TRACE, ...) or 3D TFM (Two-Fluid Model) have significant issues to reproduce acceptable results, unless well-known scenarios and global values are considered. Instead, methods based on high resolution level such as Interfacial Tracking Method (ITM) or Volume Of Fluid (VOF) require a high computational effort that makes unfeasible its use in complex systems.In this thesis, an open-source simulation framework has been designed and developed using the OpenFOAM library to analyze the cases from microescale to macroscale levels. The different approaches and the information that is required in each one of them have been studied for bubbly flow. In the first part, the dynamics of single bubbles at a high resolution level have been examined through VOF. This technique has allowed to obtain accurate results related to the bubble formation, terminal velocity, path, wake and instabilities produced by the wake. However, this approach has been impractical for real scenarios with more than dozens of bubbles. Alternatively, this thesis proposes a CFD Discrete Element Method (CFD-DEM) technique, where each bubble is represented discretely. A novel solver for bubbly flow has been developed in this thesis. This includes a large number of improvements necessary to reproduce the bubble-bubble and bubble-wall interactions, turbulence, velocity seen by the bubbles, momentum and mass exchange term over the cells or bubble expansion, among others. But also new implementations as an algorithm to seed the bubbles in the system have been incorporated. As a result, this new solver gives more accurate results as the provided up to date.Following the decrease on resolution level, and therefore the required computational resources, a 3D TFM have been developed with a population balance equation solved with an implementation of the Quadrature Method Of Moments (QMOM). The solver is implemented with the same closure models as the CFD-DEM to analyze the effects involved with the lost of information due to the averaging of the instantaneous Navier-Stokes equation. The analysis of the results with CFD-DEM reveals the discrepancies found by considering averaged values and homogeneous flow in the models of the classical TFM formulation. Finally, for the lowest resolution level approach, the system code RELAP5/MOD3 is used for modelling the bubbly flow regime. The code has been modified to reproduce properly the two-phase flow characteristics in vertical pipes, comparing the performance of the calculation of the drag term based on drift-velocity and drag coefficient approaches., El estudio y modelado de flujos bifásicos, incluso los más simples como el bubbly flow, sigue siendo un reto que conlleva aproximarse a los fenómenos físicos que lo rigen desde diferentes niveles de resolución espacial y temporal. El uso de códigos CFD (Computational Fluid Dynamics) como herramienta de modelado está muy extendida y resulta prometedora, pero hoy por hoy, no existe una única aproximación o técnica de resolución que permita predecir la dinámica de estos sistemas en los diferentes niveles de resolución, y que ofrezca suficiente precisión en sus resultados. La dificultad intrínseca de los fenómenos que allí ocurren, sobre todo los ligados a la interfase entre ambas fases, hace que los códigos de bajo o medio nivel de resolución, como pueden ser los códigos de sistema (RELAP, TRACE, etc.) o los basados en aproximaciones 3D TFM (Two-Fluid Model) tengan serios problemas para ofrecer resultados aceptables, a no ser que se trate de escenarios muy conocidos y se busquen resultados globales. En cambio, códigos basados en alto nivel de resolución, como los que utilizan VOF (Volume Of Fluid), requirieren de un esfuerzo computacional tan elevado que no pueden ser aplicados a sistemas complejos.En esta tesis, mediante el uso de la librería OpenFOAM se ha creado un marco de simulación de código abierto para analizar los escenarios desde niveles de resolución de microescala a macroescala, analizando las diferentes aproximaciones, así como la información que es necesaria aportar en cada una de ellas, para el estudio del régimen de bubbly flow. En la primera parte se estudia la dinámica de burbujas individuales a un alto nivel de resolución mediante el uso del método VOF (Volume Of Fluid). Esta técnica ha permitido obtener resultados precisos como la formación de la burbuja, velocidad terminal, camino recorrido, estela producida por la burbuja e inestabilidades que produce en su camino. Pero esta aproximación resulta inviable para entornos reales con la participación de más de unas pocas decenas de burbujas. Como alternativa, se propone el uso de técnicas CFD-DEM (Discrete Element Methods) en la que se representa a las burbujas como partículas discretas. En esta tesis se ha desarrollado un nuevo solver para bubbly flow en el que se han añadido un gran número de nuevos modelos, como los necesarios para contemplar los choques entre burbujas o con las paredes, la turbulencia, la velocidad vista por las burbujas, la distribución del intercambio de momento y masas con el fluido en las diferentes celdas por cada una de las burbujas o la expansión de la fase gaseosa entre otros. Pero también se han tenido que incluir nuevos algoritmos como el necesario para inyectar de forma adecuada la fase gaseosa en el sistema. Este nuevo solver ofrece resultados con un nivel de resolución superior a los desarrollados hasta la fecha.Siguiendo con la reducción del nivel de resolución, y por tanto los recursos computacionales necesarios, se efectúa el desarrollo de un solver tridimensional de TFM en el que se ha implementado el método QMOM (Quadrature Method Of Moments) para resolver la ecuación de balance poblacional. El solver se desarrolla con los mismos modelos de cierre que el CFD-DEM para analizar los efectos relacionados con la pérdida de información debido al promediado de las ecuaciones instantáneas de Navier-Stokes. El análisis de resultados de CFD-DEM permite determinar las discrepancias encontradas por considerar los valores promediados y el flujo homogéneo de los modelos clásicos de TFM. Por último, como aproximación de nivel de resolución más bajo, se investiga el uso uso de códigos de sistema, utilizando el código RELAP5/MOD3 para analizar el modelado del flujo en condiciones de bubbly flow. El código es modificado para reproducir correctamente el flujo bifásico en tuberías verticales, comparando el comportamiento de aproximaciones para el cálculo del término d, L'estudi i modelatge de fluxos bifàsics, fins i tot els més simples com bubbly flow, segueix sent un repte que comporta aproximar-se als fenòmens físics que ho regeixen des de diferents nivells de resolució espacial i temporal. L'ús de codis CFD (Computational Fluid Dynamics) com a eina de modelatge està molt estesa i resulta prometedora, però ara per ara, no existeix una única aproximació o tècnica de resolució que permeta predir la dinàmica d'aquests sistemes en els diferents nivells de resolució, i que oferisca suficient precisió en els seus resultats. Les dificultat intrínseques dels fenòmens que allí ocorren, sobre tots els lligats a la interfase entre les dues fases, fa que els codis de baix o mig nivell de resolució, com poden ser els codis de sistema (RELAP,TRACE, etc.) o els basats en aproximacions 3D TFM (Two-Fluid Model) tinguen seriosos problemes per a oferir resultats acceptables , llevat que es tracte d'escenaris molt coneguts i se persegueixen resultats globals. En canvi, codis basats en alt nivell de resolució, com els que utilitzen VOF (Volume Of Fluid), requereixen d'un esforç computacional tan elevat que no poden ser aplicats a sistemes complexos. En aquesta tesi, mitjançant l'ús de la llibreria OpenFOAM s'ha creat un marc de simulació de codi obert per a analitzar els escenaris des de nivells de resolució de microescala a macroescala, analitzant les diferents aproximacions, així com la informació que és necessària aportar en cadascuna d'elles, per a l'estudi del règim de bubbly flow. En la primera part s'estudia la dinàmica de bambolles individuals a un alt nivell de resolució mitjançant l'ús del mètode VOF. Aquesta tècnica ha permès obtenir resultats precisos com la formació de la bambolla, velocitat terminal, camí recorregut, estela produida per la bambolla i inestabilitats que produeix en el seu camí. Però aquesta aproximació resulta inviable per a entorns reals amb la participació de més d'unes poques desenes de bambolles. Com a alternativa en aqueix cas es proposa l'ús de tècniques CFD-DEM (Discrete Element Methods) en la qual es representa a les bambolles com a partícules discretes. En aquesta tesi s'ha desenvolupat un nou solver per a bubbly flow en el qual s'han afegit un gran nombre de nous models, com els necessaris per a contemplar els xocs entre bambolles o amb les parets, la turbulència, la velocitat vista per les bambolles, la distribució de l'intercanvi de moment i masses amb el fluid en les diferents cel·les per cadascuna de les bambolles o els models d'expansió de la fase gasosa entre uns altres. Però també s'ha hagut d'incloure nous algoritmes com el necessari per a injectar de forma adequada la fase gasosa en el sistema. Aquest nou solver ofereix resultats amb un nivell de resolució superior als desenvolupat fins la data. Seguint amb la reducció del nivell de resolució, i per tant els recursos computacionals necessaris, s'efectua el desenvolupament d'un solver tridimensional de TFM en el qual s'ha implementat el mètode QMOM (Quadrature Method Of Moments) per a resoldre l'equació de balanç poblacional. El solver es desenvolupa amb els mateixos models de tancament que el CFD-DEM per a analitzar els efectes relacionats amb la pèrdua d'informació a causa del promitjat de les equacions instantànies de Navier-Stokes. L'anàlisi de resultats de CFD-DEM permet determinar les discrepàncies ocasionades per considerar els valors promitjats i el flux homogeni dels models clàssics de TFM. Finalment, com a aproximació de nivell de resolució més baix, s'analitza l'ús de codis de sistema, utilitzant el codi RELAP5/MOD3 per a analitzar el modelatge del fluxos en règim de bubbly flow. El codi és modificat per a reproduir correctament les característiques del flux bifàsic en canonades verticals, comparant el comportament d'aproximacions per al càlcul del terme de drag basades en velocitat de drift flux model i de les basades en coe, Peña Monferrer, C. (2017). Computational fluid dynamics multiscale modelling of bubbly flow. A critical study and new developments on volume of fluid, discrete element and two-fluid methods [Tesis doctoral no publicada]. Universitat Politècnica de València. doi:10.4995/Thesis/10251/90493, TESIS

52 Pags.- 1 Tabl.- 13 Figs. The definitive version is available at: https://link.springer.com/journal/271, Numerous methodologies have been developed to characterize sprinkler irrigation drops with the purpose of improving irrigation efficiency and controlling soil erosion and compaction. This paper presents the laboratory characterization of the morphology and velocity of drops in their free-falling trajectory as influenced by drop diameter and wind speed. For this purpose, a particle tracking velocimetry technique with in-line volumetric illumination was implemented. Hypodermic needles were used to produce droplets of uniform size. Two needle diameters resulted in drops with average diameters of 1.94 and 2.94 mm. Drops were illuminated with a double-pulsed laser beam or an LED lamp. Drop characterization reached an elevation of 4.28 m and occasionally attained terminal velocity. Motion blur was suppressed using a deconvolution filter. Drop equivalent diameter, velocity, chord ratio, canting angle and trajectory angle were determined using an ad-hoc software. The experimental approach led to the measurement of real drop size by illuminating a volume in the capture zone; drop shape ranged from quasi-sphere to ellipsoid. Drop deformation was more intense under high wind speeds. Ballistic simulations of drop fall were performed using sphere and ellipsoid drag force models. Both models resulted in excellent agreement with measured drop velocity, with the ellipsoid model performing marginally better. The robustness of the experimental equipment, particularly in combination with the developed LED lamp, announces future outdoor applications in real sprinkler irrigated fields. Such applications will provide insight on the governing processes, and data sets for the improvement of sprinkler simulation models., Thanks are due to the Centro Interamericano de Recursos del Agua from the Universidad Autónoma del Estado de México, to the Universidad Autónoma de Zacatecas and to Aula Dei from the Consejo Superior de Investigaciones Científicas for the collaboration and support provided for the publication of this paper. Thanks are also due to CONACYT for providing a scholarship to Jesús Ramiro Félix-Félix to pursue doctoral studies.

Spatial Digital Image Correlation (DIC) was used to measure the bubble rising terminal velocity to obtain the bubble size distribution generated by a mixing pump. This method provides non-contact and low cost measurement of bubble size. The digital image correlation setup is designed using low-cost line laser-diode as light source, and a consumer pocket digital camera to record the light scattered from the rising bubble inside the chamber. The measured terminal velocity distribution is proportional to the square radius of the microbubble according to the Hadamard-Rybczynski equation. DIC analysis from multiple interrogation windows was performed to obtain the bubble velocity distribution. Therefore the bubble size distribution can be estimated by calculating the radius from the Hadamard-Rybczynski equation. Evaluation of multiple frame pairs over time was performed to see the effect of the geometrical shape of the impeller to the size distribution of the bubble radius.

This paper proposes a novel approach to solve the complex optimal train control problems that so far cannot be perfectly tackled by the existing methods, including the optimal control of a fleet of interacting trains, and the optimal train control involving scheduling. By dividing the track into subsections with constant speed limit and constant gradient, and assuming the train’s running resistance to be a quadratic function of speed, two different methods are proposed to solve the problems of interest. The first method assumes an operation sequence of maximum traction – speedholding – coasting – maximum braking on each subsection of the track. To maintain the mathematical tractability, the maximum tractive and maximum braking functions are restricted to be decreasing and piecewise-quadratic, based on which the terminal speed, travel distance and energy consumption of each operation can be calculated in a closed-form, given the initial speed and time duration of that operation. With these closed-form expressions, the optimal train control problem is formulated and solved as a nonlinear programming problem. To allow more flexible forms of maximum tractive and maximum braking forces, the second method applies a constant force on each subsection. Performance of these two methods is compared through a case study of the classic single-train control on a single journey. The proposed methods are further utilised to formulate more complex optimal train control problems, including scheduling a subway line while taking train control into account, and simultaneously optimising the control of a leader-follower train pair under fixed- and moving-block signalling systems.

The influence of ultrasonic waves on hydrodynamics and mass transfer of circulating drops in liquid-liquid extraction process was studied. The recommended chemical systems of toluene-acetic acid-water with mass transfer resistance mainly in the organic phase, and cumene-isobutyric acid-water in the aqueous phase were used. An extraction column, equipped with an ultrasonic emitter of 35.40kHz real frequency and 0.37mW/cm2 intensity, was employed. The ultrasound properties were measured using the hydrophone standard method. Drops terminal velocity was comparable with the Grace model. In mass transfer study, significant enhancement was revealed in overall mass transfer coefficient for different drop sizes and for the both mass transfer directions by using ultrasonic waves. The average and maximum enhancements were, respectively, 20.8 and 31.7% for toluene-acetic acid-water, and 40.3 and 55.1% for cumene-isobutyric acid-water. Small drops exhibited a higher enhancement percentage. Regarding the mass transfer direction, the system of cumene-isobutyric acid-water with continuous to dispersed phase direction, was benefited more as the consequence of creating effective agitation in continuous phase than in dispersed phase.

Two full-scale passive Earth Entry Vehicles (EEV) with realistic structure, surrogate sample container, and surrogate Thermal Protection System (TPS) were built at NASA Langley Research Center (LaRC) and tested at the Utah Test and Training Range (UTTR). The main test objective was to demonstrate structural integrity and investigate possible impact response deviations of the realistic vehicle as compared to rigid penetrometer responses. With the exception of the surrogate TPS and minor structural differences in the back shell construction, the two test vehicles were identical in geometry and both utilized the Integrated Composite Stiffener Structure (ICoSS) structural concept in the forward shell. The ICoSS concept is a lightweight and highly adaptable composite concept developed at NASA LaRC specifically for entry vehicle TPS carrier structures. The instrumented test vehicles were released from a helicopter approximately 400 m above ground. The drop height was selected such that at least 98% of the vehicles terminal velocity would be achieved. While drop tests of spherical penetrometers and a low fidelity aerodynamic EEV model were conducted at UTTR in 1998 and 2000, this was the first time a passive EEV with flight-like structure, surrogate TPS, and sample container was tested at UTTR for the purpose of complete structural system validation. Test results showed that at a landing vertical speed of approximately 30 m/s, the test vehicle maintained structural integrity and enough rigidity to penetrate the sandy clay surface thus attenuating the landing load, as measured at the vehicle CG, to less than 600 g. This measured deceleration was found to be in family with rigid penetrometer test data from the 1998 and 2000 test campaigns. Design implications of vehicle structure/soil interaction with respect to sample container and sample survivability are briefly discussed.

Droplets spawn and perish continuously. The splashing of rain or the generation of aerosols during the breaking of waves are examples of drop formation in nature. In industry, droplets serve the need for controlled delivery of material. In agriculture, e.g. in pesticides crop spraying, drop impact and the subsequent splashing and droplet rebound is important. Drop impact occurs in e.g. metal spray deposition and direct fuel injection internal combustion engines. In many of these applications, splashing is an unwanted side effect after impact; it decreases deposition efficiency and may lead to widespread contamination. We show that the superposition of two Rayleigh-Plateau-unstable modes is an efficient and robust method to generate a periodic stream of droplets, that allows for control of the droplet sizes and distances. The method is efficient because it uses the available surface energy of the continuous jet to induce the coalescence. The method is robust because the wave numbers of the employed Rayleigh-Plateau-unstable modes are close to the fastest growing mode. By tuning the phase difference between the two modes, the coalescence pattern is controlled. We show experimental, numerical and modeling results of perpendicular droplet impact on a deep pool. We have extended the work of Oguz and Prosperetti to the regime beyond the terminal velocity under ambient conditions for droplets smaller than a millimeter in size. The dynamics of the cavity are well described by a 1D Rayleigh-Plesset model including surface tension of the cavity. The cavity is closed by a capillary wave which has a velocity set only by the droplet size. Next to the observed regular bubble entrainment, there also exists a region in which the second to last wave entrains a bubble, this is also confirmed experimentally. We present an experimental study of oblique drop impact onto a quiescent deep liquid pool. We performed quantitative experiments where oblique drops impact onto a deep liquid pool for a wide range of We and impact angles α and analyzed the splashing behavior, the cavity formation and the cavity collapse.

Estimates show that skydivers in free-fall displace a mass of air downwards equal to their own mass every second, in order to maintain a constant terminal velocity. This is also demonstrated at indoor skydiving centers where air blown upwards can suspend skydivers in mid-air. Like a boat floating in water, the skydiver is floating on air. Consequently, Archimedes principle of buoyancy can be used to explain the physics of terminal velocity in skydiving. Conventional physics explains that drag, the force needed to push air out of a skydiver’s path, sets a limit to a skydiver’s velocity. Which is correct but incomplete. It is more accurate to add that according to buoyancy, the skydiver’s velocity will increase until a mass of air equal to his own mass is displaced each second. Drag on a skydiver is defined by the equation: Drag = 0.5 (Velocity2 × Air Density × Surface Area × Drag Coefficient) This equation has severe limitations as It relies on a drag coefficient which must be already known in order to calculate terminal velocity. Worse, this drag coefficient cannot be directly measured and changes constantly. Why is this important? This demonstrates that buoyancy applies to objects that move and is measured over a one second time period. At present, buoyancy is only applied to stationary objects, such as boats or balloons. Also, buoyancy provides a simpler and more accurate method to estimate terminal velocity, without having to know the drag coefficient. This paper predicts that all objects falling at terminal velocity will displace a mass of fluid equal to their own mass each second to maintain buoyancy and a constant terminal velocity. An explanatory video: “Buoyancy explains terminal velocity in skydiving,” is available on youtube, on channel of ‘N Landell’ (the author of this paper).

One proposed method for spacecraft to reach nearby stars is by accelerating sails using either solar radiation pressure or directed energy. This idea constitutes the thesis behind the Breakthrough Starshot project, which aims to accelerate a gram-mass spacecraft up to one-fifth the speed of light towards Proxima Centauri. For such a case, the combination of the sail's low mass and relativistic velocity render previous treatments formally incorrect, including that of Einstein himself in his seminal 1905 paper introducing special relativity. To address this, we present formulae for a sail's acceleration, first in response to a single photon and then extended to an ensemble. We show how the sail's motion in response to an ensemble of incident photons is equivalent to that of a single photon of energy equal to that of the ensemble. We use this 'principle of ensemble equivalence' for both perfect and imperfect mirrors, enabling a simple analytic prediction of the sail's velocity curve. Using our results and adopting putative parameters for Starshot, we estimate that previous relativistic treatments underestimate the spacecraft's terminal velocity by ~50m/s for the same incident energy, sufficient to miss a target by several Earth radii. Additionally, we use a simple model to predict the sail's temperature and diffraction beam losses during the laser firing period, allowing us to estimate that for firing times of a few minutes and operating temperatures below 300C (573K), Starshot will require a sail of which absorbs less than 1 in 260,000 photons., Comment: Accepted to AJ. This version corrects the comparison in Figure 4 between our prediction and that of previous works, by accounting for finite light travel time effects. Other results are unchanged

Experiments at low gravities are typically performed within very expensive projects: “zero G” planes and space stations, to put two examples. In this chapter, I show how experiments in controlled gravities smaller (and also bigger) than that of the Earth can be performed using a very inexpensive device. We have studied, for example, how a spherical intruder penetrates granular matter from gravities as smaller as that on Mars, to gravities as big as that on Neptune. We plan to investigate, in the same scenarios, how a replica of the wheels of a “Mars Rover” performs. This might help avoiding misfunctioning of man-made vehicles sent to other bodies of the Solar system as they move onto sandy soils.

Horizontal gas drilling has been considered as an innovative technique for tight gas reservoir development. Given currently there are few effective models to determine the exact minimum required gas injection rate in a wide range of ROP of horizontal gas drilling, in this work a new method for determining the minimum required gas injection rate for hole cleaning in horizontal gas drilling is developed, meanwhile a new terminal velocity model and a new required minimum gas velocity model are developed in the “build” section of horizontal well based on the widely used Gray's model to extend the minimum velocity criteria to be applied in horizontal gas drilling. Analysis using field data in the published article demonstrates that the new method can accurately determine the minimum required gas injection rate of horizontal gas drilling in a wide range of ROP (or cuttings size) and provides drilling engineers a practical tool for designing the appropriate gas injection rate in horizontal gas drilling.

Purpose – This paper aims to find methods to enhance position estimates for mobile terminals by cooperating with each other. Design/methodology/approach – The main methods used are, on the one hand, mathematical modelling of the system, drone mobility, communication and positioning errors, and on the other hand, detailed discrete event simulation, which the author uses to evaluate the positioning errors. In the simulation runs, important parameters like signal speed, terminal velocity, area size and error correlation were varied. The author details the influence of these parameters on the theoretically possible error enhancement with respect to the traditional non-cooperative method. Findings – Simulation results show that using cooperation is useful and can indeed significantly enhance the accuracy of position estimates, even in difficult situations. However, there are limits and the accuracy cannot always be enhanced. Research limitations/implications – Future research might use more sophisticated processing methods to further enhance position estimates. Limitations are given by the use of discrete time models in an inherently continuous system. Discretization errors are, however, kept low by using small time steps. Practical implications – It has been shown that the positioning of drone swarms can be significantly enhanced once drones cooperate with each other. This might improve maneuverability of drones in all situations where drone swarms are used. Originality/value – It has been proven by using simulation that cooperative positioning can yield positioning enhancements, even in difficult situations, when using wireless communication. In this light, future research can come up with practical implementations of such a cooperative approach.

With water mist regarded as a promising fire-extinguishing agent in spacecraft, it is necessary to investigate characteristics of water mist in microgravity. In this paper, FDS 6.0 is used to measure the centerline velocity of water mist with various initial velocities and the spray distance. The droplets will approach their terminal velocity after leaving the nozzle in normal-gravity, which agrees with the theoretical calculation. The velocity of water mist declines in microgravity. The polynomials of the velocity change are given in microgravity, which makes it possible to obtain the velocity with the spray distance increase when arbitrary initial velocity is given.

Augmented design of a guidance algorithm previously developed for intercepting target in a missile-target engagement scenario, but catering to powered descent soft landing on lunar surface is the main focus of this paper. When it comes to lunar soft landing guidance formulation, it is required that the Lander reach the desired position with terminal velocity constraints. An existing circular guidance law developed for missile guidance is modified to be applied for the fine braking phase of lunar powered descent. Presently in the algorithm, at the beginning of each guidance cycle, there will be an assumed varying circular path from missile to target and the guidance solution lies in finding the acceleration towards the centre of the circle so that the missile moves towards the target. The design augmentation proposed for lunar landing introduces a quadratic acceleration term opposite to the instantaneous tangential velocity vector to ensure terminal conditions. Coefficients of the quadratic acceleration profile are determined by the length of the circle as well as the magnitude of instantaneous tangential velocity. Finally a simple compensation scheme based on comparison of actual velocity from sensors and expected velocity from the algorithm is also proposed to take care of the variation in gravity and error in initial mass estimate.

Dividing the guidance stages into two main phases, a midcourse phase and a terminal phase, is a common practice in long-range interceptions. The midcourse guidance task is to keep the interceptor on an optimal trajectory under various problem constraints toward a predicted interception point, whereas the terminal guidance task is to hit the target. This study develops a novel near-optimal spatial midcourse guidance to the predicted interception point under a terminal angular constraint. The angular constraint is formulated in terms of a required difference between the interceptor and the target flight directions at impact. The paper consists of two main parts: the planar case and the spatial case. The first part revisits the linear planar guidance problem with a terminal angular constraint between the velocities. Then, a nonlinear optimal control problem is solved numerically, either by minimizing the total squared acceleration or by maximizing the total terminal energy. Finally, a new closed-loop guidanc...