Calculation of terminal velocity in transitional flow for spherical particle

The terminal velocity has been widely used in extensive fields, but the complexity of drag coefficient expression leads to the calculation of terminal velocity in transitional flow （1 〈 Re ≤ 1000） with much more difficulty than those in laminar flow （Re ≤ 1） and turbulent flow （Re ≥ 1000）. This paper summarized and compared 24 drag coefficient correlations, and developed an expression for calculating the terminal velocity in transitional flow, and also analyzed the effects of particle density and size, fluid density and viscosity on terminal velocity. The results show that 19 of 24 previously published correlations for drag coefficient have good prediction performance and can be used for calculating the terminal velocity in the entire transitional flow with higher accuracy. Adapting two dimensionless parameters （w＊, d＊）, a proposed explicit correlation, w＊=-25.68654 × exp （-d＊/77.02069）＋ 24.89826, is attained in transitional flow with good performance, which is helpful in calculating the terminal velocity.

Nonuniform Approach to Terminal Velocity for Single Mode Rayleigh-Taylor Instability

The temporal development of a single mode Rayleigh-Taylor instability consists of three stages: the linear, free fall and terminal velocity regimes. The purpose of this paper is to report on new phenomena observed in the approach to terminal velocity. Our numerical study shows an unexpected nonuniform approach to terminal velocity. The nonuniformity applies especially to the spikes, which are fingers of heavy fluid falling into the light fluid, but it also applies to the rising bubbles of light fluid. For spikes especially, our results call into question the meaningfulness of a terminal velocity for moderate values of the Atwood number A. After a short time period of pseudo-terminal plateau, the spike velocity increases to a significantly higher maximum, followed by a decrease. This phenomena appears to be due to a slow evolution in the shape of the spike and bubble. We find a relation between the spike (bubble) acceleration and the tip curvature. In correlation with an increase in the spike velocity, the main body of the spike becomes narrower and the tip curvature increases. Our numerical results are by the Front Tracking method. The very late time simulations considered here required stabilization by a small value for the viscosity, so that the compressible Navier-Stokes equations govern the dynamics.

Simulation and optimization for airdrop adaptability of overweight equipment

Airbag buffer process was analyzed with the aid of aerodynamic and thermodynamic methods.Based on the current structure of the airbag,the terminal velocity was too high.Therefore,the research on the diameter and height of the airbag was done and the feasible design area was found.With the optimized structure parameters,the airbag buffer experiment under normal conditions was conducted.Furthermore,the residual height and internal pressure of the airbag as well as the terminal velocity and acceleration of the airdrop were obtained.The experiment results show that the optimized airbag is feasible for 20 t cargo airdrop.

Effects of initial bubble size on geometric and motion characteristics of bubble released in water

To seek and describe the influence of bubble size on geometric and motion characteristics of the bubble,six nozzles with different outlet diameters were selected to inject air into water and to produce different bubble sizes.High-speed photography in conjunction with an in-house bubble image processing code was used.During the evolution of the bubble,bubble shape,traveling trajectory and the variation of bubble velocity were obtained.Bubble sizes acquired varied from0.25to8.69mm.The results show that after the bubble is separated from the nozzle,bubble shape sequentially experiences ellipsoidal shape,hat shape,mushroom shape and eventually the stable ellipsoidal shape.As the bubble size increases,the oscillation of the bubble surface is intensified.At the stabilization stage of bubble motion,bubble trajectories conform approximately to the sinusoidal function.Meanwhile,with the increase in bubble size,the bubble trajectory tends to be straightened and the influence of the horizontal bubble velocity component on the bubble trajectory attenuates.The present results explain the phenomena related to relatively large bubble size,which extends the existing relationship between the bubble terminal velocity and the equivalent bubble diameter.

Kinetic Optimal Midcourse Guidance Law for Air-to-Air Missiles

A new kinetic optimal midcourse guidance law is derived based on optimal control formulation. A new simplified Runge-Kutta grade numerical method is proposed to find the optimal trajectory. Real data of an Mr-to-air missile is referred to for comparing results using the kinetic optimal midcourse guidance law with those under both the kinematic optimal guidance law and singular perturbation sub-optimal guidance law, wherein the latter two laws are modified in this paper by adding a vertical g-bias command to each law for the sake of trajectory shaping. Simulation results show that using the new kinetic optimal mideourse guidance law can help save energy and maximize terminal velocity effectively.

A high precision model for the terminal settling velocity of drops in fluid medium

The terminal settling velocity(TSV)calcula-tion of drops and other spherical objects in fluid medium is a classical problem,which has important application values in many fields such as the study of cloud and precipitation processes,the evaluation of soil erosion,and the determination of fluid viscosity coefficient etc.In this paper,a new explicit approximation model of TSV is established,which combines the theoretical solution of N-S equation about fluid motion around spherical objects and the statistical regression of solution dimensionless coeffi-cients with measurement data.This new model can adapt to different values of drop parameters and medium parameters in a large range of Re.By this model,the relative and absolute calculation errors of TSV are in range of 3.42%+4.34%and 0.271 m/s-+0.128 m/s respec-tively for drop radius 0.005-2.9 mm.Their corresponding root mean square values are 1.77%and 0.084 rn/s respectively,which are much smaller than that of past theoretical and empirical models.

A Sedimentation-Dispersion Model for both Non-attached and Attached Particles in Three-Phase Batchwise Fluidized Beds

The axial concentration distribution of both particles with betterwetting (forming non-attached system) and poorer wetting (formingattached system) was investigated in a vertical gas-liquid-solidfluidized bed of 4.2 cm in diameters and 130 cm in height with thesolids holdup less than 0.05. The one-dimensionalsedimentation-dispersion model could be used satisfactorily todescribe the axial distribution of solids holdup by modifying only amodel parameter, i.e. by means of the terminal settling velocityminus a certain value, which is a functions of gas velocity andconsiders the effect of an additional drag force resulted fromattached rising bubbles.

Separation of shelled walnut particles using pneumatic method

Separation of shelled walnut particles was studied on two varieties of Persian walnut,Poost-Kaghazi and Poost-Sangi using pneumatic method.The moisture contents of the samples were determined.The particles were considered in three categories of shell,kernel and shell-kernel together.Each category was manually classified based on their size,in three portions of 1/8,1/4,and 1/2,as well as the whole kernel and whole walnut.The terminal velocity of each group was determined.The shelled walnuts were sieved and classified in three groups of small,medium and large.The effects of separation time(5,10 and 15 seconds),feeding value(50 to 80 gr)and air velocity on separation of the kernels and shells were studied for both varieties.The interaction effects were also studied for three walnut sizes(small,medium and large).The terminal velocity was the highest for the whole walnut and the whole kernel while it was lowest for 1/4 and 1/8 of the shell.The best separation was performed at air velocities of 9.20,10.04 and 10.94 m/s with 98.2%,98.9%and 98.2%,respectively.

Experimental study of sedimentation characteristics of spheroidal particles

The drag of non-spherical particles is a basic, important parameter for multi-phase flow. As the first step in research in this area, the terminal velocities, Ut, of hemispherical and spherical segment particles with maximal diameters of 6-21 mm were measured in static fluids by using a high-speed video camera. The drag coefficient, CD, measured for Reynolds number, Re of 10^1-10^5, has been obtained and compared with those for a sphere. The Re based on the terminal velocity has a logarithmic linear relationship with Ar number for both the facet facing upwards or downwards for the two experimental spheroidal particles, and their Co values are greater than those of spheres. A shape function that depends on the initial orientation of the particle facet is presented to correct for the shape effects.

Which factors have stronger explanatory power for primary wind dispersal distance of winged diaspores:the case of Zygophyllum xanthoxylon(Zygophyllaceae)?

Aims How seed dispersal distance is related to various factors is a major challenge for seed ecologists.However,there are different answers as to which factor is most important in determining wind dispersal distance.This study is to quantitatively describe the relationship between various factors and primary wind dispersal distance of winged diaspores.Methods The dispersal distances of five morphologies of winged diaspores in Zygophyllum xanthoxylum(Zygophyllaceae)were measured under controlled conditions in a wind tunnel.The explanatory power of environmental factor(i.e.wind speed),plant trait(i.e.release height)and diaspore attributes(i.e.wing loading(the ratio of diaspore mass to projected area),settlement-velocity,shape index(the variance of diaspore length,width and thickness))to the variation in dispersal distance was assessed by releasing diaspores at varying wind speeds and release heights.Important Findings Wind speed and seed release height were the strongest explanatory factors to dispersal distance,contributing 41.1%and 24.8%(P<0.01)to total variation in dispersal distance,respectively.Wind speed accounted more for relatively light disc-shaped seeds than for relatively heavy spherical seeds.Wing loading,shape index and settlement-velocity explained 9.0%(P<0.01),1.4%(P<0.01)and 0.9%(not significant)of the variation in dispersal distance,respectively.From disc-shaped to four-winged diaspores,relative contributions of wing loading and shape index decreased but contribution of settlementvelocity increased.The relative contributions of various factors to wind seed dispersal distance may change with the change in seed morphology.

Experimental study of settling and drag on cuboids with square base

The drag on non-spherical particles is an important basic parameter for multi-phase flows such as in biomass combustion, chemical blending, and mineral processing. Though there is much experimental research on such particles, there are few results for cuboids. This paper presents data for cuboids with a square base in static glycerin-water solutions of various volume concentrations. Complex motions were observed and characterized. A dimensionless expression is given for terminal velocity ut as a function of Archimedes number Ar which is used to develop an accurate correlation for friction factor CD. The accuracy of the correlation is 7.9% compared to experimental data in the literature. For both square plates and square rods, the terminal velocity per unit mass, ut/mp, was used to characterize the influence of narticle geometry on velocity, which was shown to be linear.

Three-dimensional analysis of relationship between relative orientation and motion modes

Target motion modes have a close relationship with the relative orientation of missile-totarget in three-dimensional highly maneuvering target interception. From the perspective of relationship between the sensor coordinate system and the target body coordinate system, a basic model of sensor is stated and the definition of relative angular velocity between the two coordinate systems is introduced firstly. Then, the three-dimensional analytic expressions of relative angular velocity for different motion modes are derived and simplified by analyzing the influences of target centroid motion, rotation around centroid and relative motion. Finally, the relationships of the relative angular velocity directions and values with motion modes are discussed. Simulation results validate the rationality of the theoretical analysis. It is demonstrated that there are significant differences of the relative orientation in different motion modes which include luxuriant information about motion modes. The conclusions are significant for the research of motion mode identification,maneuver detection, maneuvering target tracking and interception using target signatures.