Influence of hydrogen concentration on Fe_2O_3 particle reduction in fluidized beds under constant drag force

The fixed-gas drag force from a model calculation method that stabilizes the agitation capabilities of different gas ratios was used to explore the influence of temperature and hydrogen concentration on fluidizing duration, metallization ratio, utilization rate of reduction gas, and sticking behavior. Different hydrogen concentrations from 5vol%to 100vol%at 1073 and 1273 K were used while the drag force with the flow of N2 and H2 （N2：2 L·min^-1;H2：2 L·min^-1） at 1073 K was chosen as the standard drag force. The metallization ratio, mean reduc-tion rate, and utilization rate of reduction gas were observed to generally increase with increasing hydrogen concentration. Faster reduction rates and higher metallization ratios were obtained when the reduction temperature decreased from 1273 to 1073 K. A numerical relation among particle diameter, particle drag force, and fluidization state was plotted in a diagram by this model.

Optimization of the Drag Forces of Shell Janus Micromotor:A Study Based on Hydrodynamical Analysis and Numerical Simulation

Micromotors are widely used in cell operation,drug delivery and environmental decontamination due to their small size,low energy consumption and large propelling power.Compared to traditional Janus micromotor,the shell Janusmicromotor has better motion performance.However,the structural optimization of itsmotion performance is still unclear.The main factor restricting the motion performance of shell Janus micromotors is the drag forces.In the current work,theoretical analysis and numerical simulation were applied to analyze the drag forces of shell Janus micromotors.This study aims to design the optimum structure of shell Janus micromotors with minimum drag forces and obtain the magnitude of drag forces considering both the internal and external fluids of the shell Janus micromotors.Moreover,the influence of the motor geometry and Reynolds number on the drag coefficient was analyzed using numerical simulations.The results provide guidance for the optimum flow velocity,opening diameter and shell thickness to achieve minimum drag force.

Spectral Analysis of Nonlinear Drag Forces

The spectral properties of nonlinear drag forces of random waves on vertical circular cylinders are analyzed in this paper by means of nonlinear spectral analysis. The analysis provides basic parameters for estimation of the characteristic drag forces. Numerical computation is also performed for the investigation of the effects of nonlinearity of the drag forces. The results indicate that the wave drag forces calculated by linear wave theory are larger than those calculated by the third order Stokes wave theory for given waves. The difference between them increases with wave height. The wave drag forces calculated by use of linear approximation are about 5% smaller than their actual values when measured in the peak values of spectral densities. This will result in a safety problem for the design of offshore structures. Therefore, the nonlinear effect of wave drag forces should be taken into consideration in design and application of important offshore structures.

In situ calibrating optical tweezers with sinusoidal-wave drag force method

We introduce a corrected sinusoidal-wave drag force method （SDFM） into optical tweezers to calibrate the trapping stiffness of the optical trap and conversion factor （CF） of photodetectors. First, the theoretical analysis and experimental result demonstrate that the correction of SDFM is necessary, especially the error of no correction is up to 11.25% for a bead of 5μm in diameter. Second, the simulation results demonstrate that the SDFM has a better performance in the calibration of optical tweezers than the triangular-wave drag force method （TDFM） and power spectrum density method （PSDM） at the same signal-to-noise ratio or trapping stiffness. Third, in experiments, the experimental standard deviations of calibration of trapping stiffness and CF with the SDFM are about less than 50% of TDFM and PSDM especially at low laser power. Finally, the experiments of stretching DNA verify that the in situ calibration with the SDFM improves the measurement stability and accuracy.

Numerical investigation on the drag force of a single bubble and bubble swarm Authors

The bubble drag force correlation plays an important role in the numerical simulation accuracy of gas/liquid flows.In order to systematically investigate the interphase drag force of non-buoyancy driven bubbly flows,a dynamic-positioning body force(DPBF)method is developed in this study.It is proved that this method has an enough computation precision.Using this method,a series of direct numerical simulation(DNS)cases of a single bubble with low-intermediate Re(1≤Re≤200)and a bubble swarm with low Re(5.6≤Re≤45)are carried out and the bubble drag coefficients are calculated.Based on all the DNS data,the drag correlations with dimensionless parameters(Re,We for a single bubble and Re,We,gas fraction for bubble swarm)are systematically investigated and reported in this paper,which can provide a reference to the development of drag force closure model for non-buoyancy driven bubbly flows.

Estimation of drag forces caused by natural woody vegetation of different scales

To reliably estimate water levels and velocities in vegetated rivers and floodplains, flow resistance models based on physical plant properties are advantageous. The purpose of this study is （1） to assess the suitable parameterization of woody riparian vegetation in estimating the drag forces, （2） to address the effect of plant scale on the drag estimates and reconfiguration, and （3） to evaluate the applicability of three recently developed flow resistance models. Experiments on four tree species in a towing tank together with detailed characterization of tree properties were carried out to establish a novel dataset. Despite the variability in the tree height （0.9 m-3.4 m）, the stem, leaf and total areas proved to be suitable characteristic dimensions for estimating the flow resistance at different scales. Evaluations with independent data revealed that the tested models produced reasonable results. The performance of the models was controlled by the parameter values used rather than the model structure or the plant scale.

A drag force formula for heterogeneous granular flow systems based on finite average statistical method

The existing drag models are mostly based on the assumption of homogenous fluidization.However,the use of a homogeneous drag model to predict a heterogeneous granular flow system will cause a deviation.In this study,we developed a drag force model based on the assumption of heterogeneous fluidization.To prevent weakening of the heterogeneous characteristics in the drag force formula,we propose a finite average statistical method to filter the information of the heterogeneous granular cluster.The filtered information was used to fit the modified drag formula,which can reflect the heterogeneity of the granular cluster considering different configurations.A comparison shows that the new proposed drag formula filtered by the finite average statistical method fits well with energy minimization multi-scale simulation results.

Evaluation of drag force on a nonuniform particle distribution with a meshless method

A meshless Element-Free Galerkin （EFG） method was used to directly simulate the fluidization process in two dimensions. The drag force on particles was obtained by integrating the stress and shear forces on the particle surfaces. The results show that meshless methods are capable of dealing with real particle collisions, thus are superior to most mesh-based methods in reflecting the fluidization process with frequent particle collisions and suitable void fractions. Particle distribution greatly influences the drag coefficients even for the same voidage, that is, there are large differences in the average drag coefficients between nonuniform and uniform particle distributions. Different compacting directions also have different regu- larities, so conventional formulas such as ＇Wen and Yu＇ and ＇Felice＇ models have some deviations in such nonuniform distributions. To evaluate the influence of the nonuniformity, the drag force in multiple particle systems was simulated by using nonuniformity coefficients, Cvx and Cvy, to quantitatively describe the nonuniform distribution in different directions. Drag force during fluidization can be successfully evaluated by the use of Cvx alone.

Theory of superfluidity and drag force in the one-dimensional Bose gas

The one-dimensional Bose gas is an unusual superfluid. In contrast to higher spatial dimensions, the existence of non-classical rotational inertia is not directly linked to the dissipationless motion of infinitesimal impurities. Recently, experimental tests with ultracold atoms have begun and quanti- tative predictions for the drag force experienced by moving obstacles have become available. This topical review discusses the drag force obtained from linear response theory in relation to Lan- dau＇s criterion of superfluidity. Based upon improved analytical and numerical understanding of the dynamical structure factor, results for different obstacle potentials are obtained, including single impurities, optical lattices and random potentials generated from speckle patterns. The dynamical breakdown of superfluidity in random potentials is discussed in relation to Anderson localization and the predicted superfluid-insulator transition in these systems.

Drag force on a moving heavy quark with deformed string configuration

To study drag force on a moving heavy quark through a plasma,we use a deformed AdS spacetime,in which deformation parameter c describes non-conformality in AdS/QCD.In this case,the quark is mapped to a probe string in the AdS space.Considering the probable contribution of the deformation parameter in the probe string,we apply a general form of c-dependent string ansatz in the drag force computation.Then,we find the acceptable value of this parameter as it satisfies QCD calculations.Using this result,we also discuss the diffusion constant which is in agreement with the phenomenological result for the non-relativistic limit.Also,we show that while in absence of a deformation parameter,the probe string is a strictly increasing function of radial coordinate,the c-dependent probe string has a maximum value versus z.

Computational Solution to the Problems of Projectile Motion under Significant Linear Drag Effect

This paper investigates the computational solution to the problem of projectile motion under a significant linear drag effect. The drag force acting on the particle within the medium of propagation is proportional to the cross-section area of the projectile, the velocity of the particle, and the medium’s density. From zero air resistance force (vacuum) the problems are well known with solutions, but with air resistance (drag force) the problems have no exact analytical solutions which lead to most of the significant scientific research works using numerical methods. Therefore, this study aims to present the analysis of the computational modelling of drag force exerted by the surrounding medium on the linear motion. However, the horizontal and vertical components of differential equations of motion were derived and characterized from the solutions governed by Newton’s 2nd law of motion. The baseball features were presented as the projectile (object) in this work. In addition, the numerical computational results were received from FreeMat. The results were discussed and compared with those from the vacuum. Moreover, the displacements, velocities, range, and trajectories of the projectile were all discussed and a conclusion was made.

EFFECT OF INTERPHASE LIFT FORCE ON THE FLUID FLOW IN AN AIR-STIRRED CYLINDRICAL VESSEL

In the present paper, based on the two-phase model (Eulerian model), the two dimensional fluid flow liz air-stirred water systems is simulated, and the effect of interphase lift force on the fluid flow is specially discussed. In the Eulerian two-phase model, gas and liquid phase are considered to be two different continuous fluids interacting with each other through the finite inter-phase areas. The exchange between the phases is represented by source terms in conversation equations. Turbulence is assumed to be a property of the liquid phase, k - ε model is used to describe the behavior of the liquid phase. The dispersion of phases due to turbulence is represented by introducing a diffusion term in mass consecrvation equation. The contribution of bubble movement to the turbulent energy and its dissipation rate is taken into accounted by adding extra volumetric source terms to the equations of turbulent enemy and its dissipation rate. The comparison between the mathematical simulation and experiment data indicates that the interphase lift force has a big effect on the flow behavior, and considering both drug force and lift force as interphase forces is important to accurately simulate the gas-water two-phase fluid flow in air-stirred systems. The interphase lift force makes bubbles move away from the centerline, the gas concentration is decreased near the centerline, and increased near the wall. The lift force is smaller than drug force at the same place, especially far away from the centerline.

Numerical Study on Characteristics of Supercavitating Flow Around the Variable-Lateral-Force Cavitator

A control scheme named the variable-lateral-force cavitator, which is focused on the control of lift force, drag force and lateral forces for underwater supercavity vehicles was proposed, and the supercavitating flow around the cavitator was investigated numerically using the mixture multiphase flow model. It is verified that the forces of pitching, yawing, drag and lift, as well as the supercavity size of the underwater vehicle can be effectively regulated through the movements of the control element of the variable-lateral-force cavitator in the radial and circumferential directions. In addition, if the control element on either side protrudes to a height of 5% of the diameter of the front cavitator, an amount of forces of pitching and yawing equivalent to 30% of the drag force will be produced, and the supercavity section appears concave inwards simultaneously. It is also found that both the drag force and lift force of the variable-lateral-force cavitator decline as the angle of attack increases.

Numerical investigation of turbulent channel flow controlled by spatially oscillating spanwise Lorentz force

A formulation of the skin-friction drag related to the Reynolds shear stress in a turbulent channel flow is derived. A direct numerical simulation （DNS） of the turbulent control is performed by imposing the spatially oscillating spanwise Lorentz force. Under the action of the Lorentz force with several proper control parameters, only the periodi- cally well-organized streamwise vortices are finally observed in the near-wall region. The Reynolds shear stress decreases dramatically, especially in the near-wall area, resulting in a drag reduction.

Two-dimensional analytical solution for compound channel flows with vegetated floodplains

This paper presents a two-dimensional analytical solution for compound channel flows with vegetated floodplains. The depth-integrated N-S equation is used for analyzing the steady uniform flow. The effects of the vegetation are considered as the drag force item. The secondary currents are also taken into account in the governing equations, and the preliminary estimation of the secondary current intensity coefficient K is discussed. The predicted results for the straight channels and the apex cross-section of meandering channels agree well with experimental data, which shows that the analytical model presented here can be applied to predict the flow in compound channels with vegetated floodplains.

Two dimensional analytical solution for a partially vegetated compound channel flow

The theory of an eddy viscosity model is applied to the study of the flow in a compound channel which is partially vegetated. The governing equation is constituted by analyzing the longitudinal forces acting on the unit volume where the effect of the vegetation on the flow is considered as a drag force item, The compound channel is divided into 3 sub-regions in the transverse direction, and the coefficients in every region＇s differential equations were solved simultaneously. Thus, the analytical solution of the transverse distribution of the depth-averaged velocity for uniform flow in a partially vegetated compound channel was obtained. The results can be used to predict the transverse distribution of bed shear stress, which has an important effect on the transportation of sediment. By comparing the analytical results with the measured data, the analytical solution in this paper is shown to be sufficiently accurate to predict most hydraulic features for engineering design purposes.

Numerical simulation of low-Reynolds number flows past two tandem cylinders of different diameters

The flow past two tandem circular cylinders of different diameters was simulated using the finite volume method. The diameter of the downstream main cylinder （D） was kept constant, and the diameter of the upstream control cylinder （d） varied from 0.1D to D. The studied Reynolds numbers based on the diameter of the downstream main cylinder were 100 and 150. The gap between the control cylinder and the main cylinder （G） ranged from 0.1D to 4D. It is concluded that the gap-to-diameter ratio （G/D） and the diameter ratio between the two cylinders （d/D） have important effects on the drag and lift coefficients, pressure distributions around the cylinders, vortex shedding frequencies from the two cylinders, and flow characteristics.

Normalization of Hydrodynamic Coefficients in Morison Equation

The hydrodynamic coefficients C-d and C-m are not only dependent on the size of slender cylinder, its location in water, KC number and Re number, but also vary with environmental conditions, i.e., in regular waves or in irregular waves, in pure waves or in wave-current coexisting field. In this paper, the normalization of hydrodynamic coefficients for various environmental conditions is discussed. When a proper definition of KC number and proper characteristic values of irregular waves are used, a unified relationship between C-d, C-m and KC number for regular waves, irregular waves, pure waves and wave-current coexisting field can be obtained.

Hybrid Analysis Approach for Stochastic Response of Offshore Jacket Platforms

The dynamic response of offshore platforms is more serious in hostile sea environment than in shallow sea. In this paper, a hybrid solution combined with analytical and numerical method is proposed to compute the stochastic response of fixed offshore platforms to random waves, considering wave-structure interaction and non-linear drag force. The simulation program includes two steps: the first step is the eigenanalysis aspects associated the structure and the second step is response estimation based on spectral equations. The eigenanalysis could be done through conventional finite element method conveniently and its natural frequency and mode shapes obtained. In the second part of the process, the solution of the offshore structural response is obtained by iteration of a series of coupled spectral equations. Considering the third-order term in the drag force, the evaluation of the three-fold convolution should be demanded for nonlinear stochastic response analysis. To demonstrate this method, a numerical analysis is carried out for both linear and non-linear platform motions. The final response spectra have the typical two peaks in agreement with reality, indicating that the hybrid method is effective and can be applied to offshore engineering.

Analytical solution of velocity distribution for flow through submerged large deflection flexible vegetation

An analytical solution for predicting the vertical distribution of streamwise mean velocity in an open channel flow with submerged flexible vegetation is proposed when large bending occurs. The flow regime is separated into two horizontal layers： a vegetation layer and a free water layer. In the vegetation layer, a mechanical analysis for the flexible vegetation is conducted, and an approximately linear relationship between the drag force of bending vegetation and the streamwise mean flow velocity is observed in the case of large deflection, which differes significantly from the case of rigid upright vegetation. Based on the theoretical analysis, a linear streamwise drag force-mean flow velocity expression in the momentum equation is derived, and an analytical solution is obtained. For the free water layer, a new expression is presented, replacing the traditional logarithmic velocity distribution, to obtain a zero velocity gradient at the water surface. Finally, the analytical predictions are compared with published experimental data, and the good agreement demonstrates that this model is effective for the open channel flow through the large deflection flexible vegetation.