Drag Equation Research Articles

Kinematic Properties of Slow ICMEs and an Interpretation of a Modified Drag Equation for Fast and Moderate ICMEs

We report kinematic properties of slow interplanetary coronal mass ejections (ICMEs) identified by SOHO/LASCO, interplanetary scintillation, and in situ observations and propose a modified equation for the ICME motion. We identified seven ICMEs between 2010 and 2011 and compared them with 39 events reported in our previous work. We examined 15 fast (V SOHO−V bg>500 km s−1), 25 moderate (0 km s−1≤V SOHO−V bg≤500 km s−1), and 6 slow (V SOHO−V bg<0 km s−1) ICMEs, where V SOHO and V bg are the initial speed of ICMEs and the speed of the background solar wind. For slow ICMEs, we found the following results: i) They accelerate toward the speed of the background solar wind during their propagation and reach their final speed by 0.34±0.03 AU. ii) The acceleration ends when they reach 479±126 km s−1; this is close to the typical speed of the solar wind during the period of this study. iii) When γ 1 and γ 2 are assumed to be constants, a quadratic equation for the acceleration a=−γ 2(V−V bg)|V−V bg| is more appropriate than a linear one a=−γ 1(V−V bg), where V is the propagation speed of ICMEs, while the latter gives a smaller χ 2 value than the former. For the motion of the fast and moderate ICMEs, we found a modified drag equation a=−2.07×10−12(V−V bg)|V−V bg|−4.84×10−6(V−V bg). From the viewpoint of fluid dynamics, we interpret this equation as indicating that ICMEs with 0 km s−1≤V−V bg≤2300 km s−1 are controlled mainly by the hydrodynamic Stokes drag force, while the aerodynamic drag force is a predominant factor for the propagation of ICME with V−V bg>2300 km s−1.

H-2-2 アメンボを規範とした水面移動ロボットの研究 : 脚の撥水性が水面移動に及ぼす影響

This paper describes water-repellency and drag forces of hydrophobic wire legs for water-walking robots inspired by a water strider. Recently, many researchers developed bio-inspired water-walking robots. However, the supporting legs of these robots are inferior to those of water striders in water repellency. In this study, helical grooves with various depths were fabricated on the surface of a brass wire using femtosecond laser machining to increase water repellency. Effects of the grooves on contact angles and drag forces were investigated. The experimental results showed that the wire with deep grooves exhibits high water repellency. The drag force acting on the leg was found to obey the drag equation when the reference area was determined considering a dimple and a bump of the surface of water.

Heat Transfer and Pressure Drop Through Nano-Fin Arrays in the Free-Molecular Flow Regime

Gas flow through arrays of rectangular nanofins is modeled using the linearized free-molecular drag and heat transfer equations. These are combined with the one-dimensional equations for conservation of mass, momentum, and energy, and the ideal gas law, to find the governing equations for flow through the array. The results show that the pressure gradient, temperature, and local velocity of the gas are governed by coupled ordinary differential equations. The system of equations is solved for representative arrays of nanofins to find the total heat transfer and pressure drop across a 1 cm chip.

Transit Time of Coronal Mass Ejections under Different Ambient Solar Wind Conditions

The speed [v(R)] of coronal mass ejections (CMEs) at various distances from the Sun is modeled (as proposed by Vrsnak and Gopalswamy in J. Geophys. Res. 107, 2002, doi: 10.1029/2001/JA000120 ) by using the equation of motion a drag=γ(v−w) and its quadratic form a drag=γ(v−w)|v−w|, where v and w are the speeds of the CME and solar wind, respectively. We assume that the parameter γ can be expressed as γ=αR β , where R is the heliocentric distance, and α and β are constants. We extend the analysis of Vrsnak and Gopalswamy to obtain a more detailed insight into the dependence of the CME Sun–Earth transit time on the CME speed and the ambient solar-wind speed, for different combinations of α and β. In such a parameter-space analysis, the results obtained confirm that the CME transit time depends strongly on the state of the ambient solar wind. Specifically, we found that: i) for a particular set of values of α and β, a difference in the solar-wind speed causes larger transit-time differences at low CME speeds [v 0], than at high v 0; ii) the difference between transit times of slow and fast CMEs is larger at low solar-wind speed [w 0] than at high w 0; iii) transit times of fast CMEs are only slightly influenced by the solar-wind speed. The last item is especially important for space-weather forecasting, since it reduces the number of key parameters that determine the arrival time of fast CMEs, which tend to be more geo-effective than the slow ones. Finally, we compared the drag-based model results with the observational data for two CME samples, consisting of non-interacting and interacting CMEs (Manoharan et al. in J. Geophys. Res. 109, 2004). The comparison reveals that the model results are in better agreement with the observations for non-interacting events than for the interacting events. It was also found that for slow CMEs (v 0<500 km s−1), there is a deviation between the observations and the model if slow-wind speeds (≈ 300 – 400 km s−1) are taken for the model input. On the other hand, the model values and the observed data agree for both the slow and the fast CMEs if higher solar-wind speeds are assumed. It is also found that the quadratic form of the drag equation reproduces the observed transit times of fast CMEs better than the linear drag model.

That's a Drag: The Effects of Drag Forces

Drag is a force that opposes motion due to an object's shape, material, and speed. This project defined what drag force is, derived the governing equation for drag and listed some applications of drag forces. Derivation of the drag equation was achieved using the Buckingham π theorem, a dimensional analysis tool. Lastly, this project explored the problem of how long and how far a dragster takes to stop once its parachute is deployed.

Impact experiments of exotic dust grain capture by highly porous primitive bodies

Small primitive bodies were presumably highly porous when they formed and some still have low densities that are indicative of a high pore content. Therefore, after their formation, interplanetary dust impacting on their surface may have been captured because of their porous structure. The mechanism of dust penetration is thus of importance to understand the evolution of small bodies and the origin of their internal dust particles. Impact experiments of sintered glass-bead targets characterized by 80%, 87%, and 94% bulk porosity were conducted using metal and basalt projectiles at impact velocities ranging from 1.6 to 7.2kms−1. Track morphology and penetration processes were analyzed using both X-ray tomography and a flash X-ray system. Two types of track were observed, as previously also found in the Stardust aerogel: a thin and long track (carrot-shaped track), and a “bulb” with tails (bulb-shaped track). The track shape changed with initial dynamic pressure. We found that the transition between “carrot” and “bulb” occurred at a pressure of roughly 20 times the projectile’s tensile strength. The deceleration process of projectiles without severe deformation and fragmentation was reproduced by a drag equation composed of an inertia drag that was proportional to the square of the projectile’s velocity and a constant drag proportional to the target’s compressive strength. We applied this deceleration equation to silicate dust penetrating into hypothetical porous icy bodies which were homogeneous on much smaller scales than the impacting dust particles. The penetration depth was approximately 100 times the projectile diameter for the bodies with 90% porosity.

A novel kinematic model for drag anchors in seabed soils

The penetration behavior and trajectory of drag anchors in seabed soils is not only a complicated engineering problem, but also an interesting topic with lots of scientific meanings. Nearly all the previous methods that are capable of predicting the trajectory of drag anchors need a numerical incremental computation. Based on a kinematic model and mathematical derivations, a theoretical framework for predicting the trajectory of drag anchors is established. The concepts put forward and described in detail in the paper are not only necessary for the theoretical framework but also meaningful to further understanding of the engineering problem due to clear physical background. A comparative study has proved the effectiveness and veracity of the kinematic model and theoretical framework for predicting the trajectory. The proposed model and developed drag equations, which combine the anchor, the drag line and the anchor handling vessel being an interactional system, may provide a new angle of view to understand the anchor behaviors in soils, and be valuable for deterministic and theoretical analysis of drag anchors.

Solutions to Buoyancy—Drag Equation for Dynamical Evolution of Rayleigh—Taylor and Richtmyer—Meshkov Mixing Zone

With a self-similar parameter b(At) = Hi/λi, where At is the Atwood number, Hi and λi are the amplitude and wavelength of bubble (i = 1) and spike (i = 2) respectively, we derive analytically the solutions to the buoyancy—drag equation recently proposed for dynamical evolution of Rayleigh—Taylor and Richtmyer—Meshkov mixing zone. Numerical solutions are obtained with a simple form of b(At) = 1/(1 + At) and comparisons with recent LEM (linear electric motor) experiments are made, and an agreement is found with properly chosen initial conditions.

Observations of canonical flow resistance in fast-flowing sand bed rivers

Field data are here re-interpreted using the Vortex–Drag equation for evaluating the alluvial resistance in a sand bed river. The Vortex–Drag equation introduces the Rossiter resonance concept into alluvial hydraulics. It appears that this equation is more consistent than the Manning approach for the lower alluvial regime since a ripple configuration effectively induces a lower flow resistance coefficient than a duned configuration. A systematic decrease in the control factor down to a canonical value during the transition from the lower to the upper alluvial regime is found for well-contrasted freshet events. It results that during high stream power events with maximum river bed reshaping, the flow pattern is reproduced by simply imposing this canonical value. This is most welcome in alluvial hydraulic routing, because peak-discharge events are generally these which are the most difficult to characterize in a straightforward way, both experimentally and numerically.

Small intestinal model for electrically propelled capsule endoscopy

The aim of this research is to propose a small intestine model for electrically propelled capsule endoscopy. The electrical stimulus can cause contraction of the small intestine and propel the capsule along the lumen. The proposed model considered the drag and friction from the small intestine using a thin walled model and Stokes' drag equation. Further, contraction force from the small intestine was modeled by using regression analysis. From the proposed model, the acceleration and velocity of various exterior shapes of capsule were calculated, and two exterior shapes of capsules were proposed based on the internal volume of the capsules. The proposed capsules were fabricated and animal experiments were conducted. One of the proposed capsules showed an average (SD) velocity in forward direction of 2.91 ± 0.99 mm/s and 2.23 ± 0.78 mm/s in the backward direction, which was 5.2 times faster than that obtained in previous research. The proposed model can predict locomotion of the capsule based on various exterior shapes of the capsule.

Investigation of catalyst particle hydrodynamic and heat transfer in three phase flow circulating fluidized bed

Vaporization of gas oil droplets has significant effects on the gas–solid flow hydrodynamic and heat transfer characteristic. A three dimensional CFD model of the riser section of a CFB have been developed considering three phase flow hydrodynamic, heat transfer and evaporation of the feed droplets. Several experiments were performed in order to obtain the data needed to evaluate the model using a pilot scale CFB unit. The Eulerian approach was used to model both gas and catalyst particle phases comprising of continuity, momentum, heat transfer and species equations as well as an equation for solid phase granular temperature. The flow field and evaporating liquid droplet characteristics were modeled using the Lagrangian approach. The catalyst particle velocity and volume fraction were measured using a fiber optic probe. The comparison between model predictions of catalyst particle velocity and volume fraction with the experimental data indicated that they were in good agreements and the Syamlal-O'Brien was the most accurate drag equation. The CFD model was capable of predicting the main characteristic of the complex gas–solids flow hydrodynamic and heat transfer, including the cluster formation of the catalyst particles near the reactor wall. In addition, the simulation results showed droplet vaporization caused reduction of catalyst particle residence time. Moreover, the higher ratios of the feed to catalyst flow rates led to the lower values of the catalyst temperature profile minimum.

Roll and Pitch Motion Analysis of a Biologically Inspired Quadruped Water Runner Robot

In this paper, the roll and pitch dynamics of a biologically inspired quadruped water runner robot are analyzed, and a stable robot design is proposed and tested. The robot’s foot—water interaction force is derived using drag equations. Roll direction instability is attributed to a small roll moment of inertia and large instantaneous roll moments generated by the foot—water interaction forces. Roll dynamics are modeled by approximating the water as a linear spring. Using this model, estimates on the roll moment of inertia that can endure moments generated by water interactions are derived. Instability in the pitch direction is caused by the thrust force the four feet exert on the water. To correct this, a circular tail which can negate the pitch moment around the center of mass is proposed. Both passive and active tail designs which can cope with disturbances are introduced. Based on these analyses, a stable water runner is designed, and built. Experimental high-speed video footage demonstrates the stable roll and pitch motion of the robot. Simulations are used to estimate robustness against disturbances, waves, and leg running frequency variations. It is found that roll motion is more sensitive to disturbances when compared with the pitch direction.

Stabilization of nanostructured materials using fine inert ceramic particles

Modified versions of the Zener drag equation were obtained by evaluating a non-random distribution of incoherent ceramic particles in a nano-crystalline material. Analytical investigation of particle-boundary correlation indicates that the limiting grain size would be proportional to f V −1/3 for f V larger than 2.96%. The limiting grain size can be obtained by a combination of random and non-random Zener drag pressure in the case of volume fractions smaller than 2.96%.

Numerical Modeling of Multidirectional Flow and Heat Transfer in Graphitic Foams

To investigate the feasibility of the use of foams with an interconnected spherical pore structure in heat transfer applications, models for heat transfer and pressure drop for this type of porous materials are developed. Numerical simulations are carried out for laminar multidirectional thermofluid flow in an idealized pore geometry of foams with a wide range of geometry parameters. Semiheuristic models for pressure drop and heat transfer are developed from the results of simulations. A simplified solid-body drag equation with an extended high inertia term is used to develop the hydraulic model. A heat transfer model with a nonzero asymptotic term for very low Reynolds numbers is also developed. To provide hydraulic and heat transfer models suitable for a wide range of porosity, only a general form of the length-scale as a function of pore structure is defined a priori, where the parameters of the function were determined as part of the modeling process. The proposed ideal models are compared to the available experimental results, and the source of differences between experimental results and the ideal models is recognized and then calibrated for real graphitic foam. The thermal model is used together with volume-averaged energy equations to calculate the thermal dispersion in graphitic foam. The results of the calculations show that the linear models for thermal dispersion available in literature are oversimplified for predicting thermal dispersion in this type of porous material.

Drag on Freely Falling Cones in Newtonian and in Power Law Fluids

New extensive data on the terminal falling velocities of conical shaped bodies in scores of Newtonian and power law fluids are reported. Altogether, 11 Newtonian and 11 non-Newtonian test liquids together with 33 cones made from four different materials and 14 spheres of three different materials have been used to gather 486 individual data points covering wide ranges of conditions as follows: Reynolds number 0.0019 to 507; power law flow behaviour index 0.4 to 1, the value of sphericity 0.59 to 0.79; and the cone-to-fall tube diameter ratios up to 0.264 to assess the extent of wall effects. A simple expression is developed to estimate the terminal falling velocity of a cone from a knowledge of its dimensions, and the terminal velocity of an equivalent sphere. A generalized drag equation applicable to both Newtonian and power law liquids is also presented.

DEVELOPMENT OF NEW EMPIRICAL EQUATIONS FOR ESTIMATION OF DRAG COEFFICIENT, SHAPE DEFORMATION, AND RISING VELOCITY OF GAS BUBBLES OR LIQUID DROPS

Some new correlations are derived to estimate the drag coefficient, the shape deformation, and the rising velocity of particles moving in an infinite liquid medium. The correlations are derived in terms of the dimensionless groups such as Reynolds number (Re), Morton number (Mo), and Weber number (We). The derivations are based on the experimental data or some other correlations given in the literature. A single statement is proposed to estimate the drag coefficient for the spherical solid particles that may be applicable in the range of 0.5 < Re < 105. Similarly, some other equations are also derived to estimate the drag coefficient, the shape deformation, or the rising velocity for gas bubbles or liquid drops. The drag equation is applicable in the range of 0.5 < Re < 100 and 9 × 10−7 ≤ Mo ≤ 7; the shape deformation equation is applicable in the range of 0.5 < Re < 100 and 1.1 × 10−5 ≤ Mo ≤ 7; and the rising velocity equation is applicable in the range of 0.1 < Re < 100 and 9 × 10−7 ≤ Mo ≤ 80. The model predictions are compared with the experimental data and with the other correlations given in the literature. The results indicated that the model predictions are in a good agreement with the literature data.

Analytical study of the buoyancy–drag equation

AbstractThe buoyancy–drag equation (BDE) is used for describing the time evolution of the mixing zone, between two fluids, due to Rayleigh–Taylor instabilities in a highly non‐linear regime. The BDE is similar to an equation of motion for each fluid and, in addition to the inertial term, it contains a buoyancy term (proportional to the external acceleration experienced by the system) and a friction proportional to the square of the velocity. In this paper, the integrability of the BDE is studied using Lie point symmetries. Two relevant situations are studied analytically. First, for a constant acceleration, the general solution with two arbitrary constants is derived. On the other hand, for accelerations varying like a power of time, we obtain a one‐parameter family of solutions. These theoretical results can be compared with the various experimental results published in the current literature. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Swing-up Control of Mass Body Interlinked Tether

The tethered system, which composed with a mother ship and satellite connected with tether, is an example of recent satellites. In the analysis and modeling of tether, large deformation and large displacements must be considered. The Absolute Nodal Coordinate Formulation can describe the motion of tether. In the modeling method, internal damping and fluid resistance are not considered, and the identification for such parameters is still problem to be solved. In this study, the effect of damping and fluid resistance based on strain energy and drag equation are formulated while considering a parameter identification method. These parameter and number of elements are identified by the experiment at the same time. In order to verify the modeling method, an example of swing-up control using a genetic algorithm is performed in simulation and experiment. Validity of model and availability of motion control based on multibody dynamics are shown comparison between experiment and simulation.

Backwater effect due to a single spur dike

Spur dikes are river engineering structures that project from the bank of a stream at some angle to the main flow direction. They are principally used for river training and protection of the riverbank from erosion. A spur dike might be considered a form of macroscale boundary roughness, which produces a backwater effect upstream from the spur dike location. Despite this impact, spur dike design often proceeds without regard to the effect that the spur dike might have on the stream system. The work presented herein is on the backwater effect due to a single, vertical-walled spur dike. It is based on a momentum analysis in which the resistance offered by the spur dike is represented by a drag equation, for which the key parameter is the spur dike drag coefficient. Experimental data acquired for various configurations of a single spur dike within fixed-bed flumes have been used to calibrate and validate the proposed backwater model. The results show that the spur dike drag coefficient, hence the computed backwater effect, depends on the channel contraction caused by the spur dike, the degree of spur dike submergence, the aspect ratio of the spur dike, and the Froude number of the flow.Key words: spur dike, backwater effect, physical model, momentum principle, drag force, drag coefficient, river engineering.

Buoyancy-drag mix model obtained by multifluid interpenetration equations

In this paper, a buoyancy drag equation for describing the motion of the edges of a mixing zone driven by Rayleigh-Taylor or Richtmyer-Meshkov instabilities is derived from the multifluid interpenetration mix model equations of Scannapieco and Cheng [Phys. Letters A 299, 49 (2002)]. This derivation provides a physics foundation for a large class of phenomenological buoyancy-drag mix models and also establishes a physical connection between the microscopic collision frequency and the macroscopic fluid drag coefficient. The predicted values for model parameter a(ss') in the multifluid interpenetration mix model, from the Rocket-Rig experiments, is in the range of 0.043-0.125 depending upon the Atwood number. The results are also in good agreement with inertial confinement fusion capsule implosions.