Average Drag Force Research Articles

Effect of turbulent fluctuations on the drag and lift forces on a towed sphere and its boundary layer

AbstractThe impact of turbulent fluctuations on the forces exerted by a fluid on a towed spherical particle is investigated by means of high-resolution direct numerical simulations. The measurements are carried out using a novel scheme to integrate the two-way coupling between the particle and the incompressible surrounding fluid flow maintained in a high-Reynolds-number turbulent regime. The main idea consists of combining a Fourier pseudo-spectral method for the fluid with an immersed-boundary technique to impose the no-slip boundary condition on the surface of the particle. This scheme is shown to converge as the power $3/ 2$ of the spatial resolution. This behaviour is explained by the ${L}_{2} $ convergence of the Fourier representation of a velocity field displaying discontinuities of its derivative. Benchmarking of the code is performed by measuring the drag and lift coefficients and the torque-free rotation rate of a spherical particle in various configurations of an upstream-laminar carrier flow. Such studies show a good agreement with experimental and numerical measurements from other groups. A study of the turbulent wake downstream of the sphere is also reported. The mean velocity deficit is shown to behave as the inverse of the distance from the particle, as predicted from classical similarity analysis. This law is reinterpreted in terms of the principle of ‘permanence of large eddies’ that relates infrared asymptotic self-similarity to the law of decay of energy in homogeneous turbulence. The developed method is then used to attack the problem of an upstream flow that is in a developed turbulent regime. It is shown that the average drag force increases as a function of the turbulent intensity and the particle Reynolds number. This increase is significantly larger than predicted by standard drag correlations based on laminar upstream flows. It is found that the relevant parameter is the ratio of the viscous boundary layer thickness to the dissipation scale of the ambient turbulent flow. The drag enhancement can be motivated by the modification of the mean velocity and pressure profile around the sphere by small-scale turbulent fluctuations. It is demonstrated that the variance of the drag force fluctuations can be modelled by means of standard drag correlations. Temporal correlations of the drag and lift forces are also presented.

Particle-Cloud Drag Force in Dilute Particle Systems: Discrete Element Method versus Eulerian Simulations

The discrete element method (DEM) is utilized to calculate the drag force on big spherical objects exerted by the cloud of small particles as they are subjected to an initial relative velocity. The drag force is calculated as the average over single collisions within a certain time interval. Then it is comparable to the calculated values obtained from Eulerian simulations, which are performed on the same particulate system by keeping the big spherical objects in discrete form and turning the cloud of small particles into a continuum phase. The DEM simulations indicate that the average drag force on a big particle in a cluster is lower than that on a single big particle. The decrease in drag force is even larger when the big particles in the cluster are arranged in an ordered configuration such as a simple cubic array. In Eulerian simulations, it is found that the model for kinetic viscosity plays an influential role in the calculated drag force. The two models known as Syamlal–O’Brian and Gidaspow models ...

Dynamical properties of a condensate in a moving random potential

We study the dynamics of an inhomogeneous Bose-Einstein condensate subject to a one-dimensional harmonic trap and a moving random potential of finite extent. Above the critical velocity, a part of a condensate glues to the moving random potential with a consequent displacement of the condensate center-of-mass along the harmonic trap. We show that the center-of-mass turning point provides a direct measure of the average drag force acting on the condensate.

Flow-induced shear instabilities of cohesive granulates

In this work we use a multiscale framework to calculate the fluidization threshold of three-dimensional cohesive granulates under shear forces exerted by a creeping flow. A continuum model of flow through porous media provides an analytical expression for the average drag force on a single grain. The balance equation for the forces and a force propagation model are then used to investigate the effects of porosity and packing structure on the stability of the pile. We obtain a closed-form expression for the instability threshold of a regular packing of monodisperse frictionless cohesive spherical grains in a planar fracture. Our result quantifies the compound effect of structural (packing orientation and porosity) and dynamical properties of the system on its stability.

Simulation of mixed convection heat transfer in a horizontal channel with an open cavity containing a heated hollow cylinder

AbstractThe objective of this paper is to numerically investigate the mixed convective flow and heat transfer controlled by a heated hollow cylinder inside an open cavity attached with a horizontal channel. All the boundaries of the channel and cavity are perfectly insulated while the inner surface of the cylinder is heated uniformly by heat flux q. The equations of conservation of mass, momentum, and energy were solved using adequate boundary conditions by Galarkin's weighted residual finite element technique. The solution has been performed in the computational domain as a whole with proper treatment at the solid/fluid interface. Computations have been conducted for Ra = 103–105, Prandtl number Pr varying from 0.7 to 7 and ratio of solid to fluid thermal conductivities from 0.2 to 50. Results are presented in terms of streamlines, isotherms, heat transfer rate in terms of the average Nusselt number (Nuav), drag force (D), and maximum bulk temperature (θmax). © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21002

Optimization of Mixed Convection in a Lid-Driven Enclosure with a Heat Generating Circular Body

The physical model considered here is a lid-driven enclosure with bottom heating and top cooling conditions, and a heat generating circular body is placed at the center. The vertical walls of the cavity are kept thermally insulated, and the top lid moves at a constant speed. The steady two-dimensional governing equations for the physical problem are transformed in a dimensionless form with dimensionless governing parameters that decide the fluid flow and heat transfer characteristics in the system. The solution of these transport equations is obtained numerically with the finite element approach using the Galerkin method of weighted residuals. The parametric study has been carried out for variation of the heat generation parameters, the Reynolds numbers, solid-fluid thermal conductivity ratios as well as the Richardson numbers. The working fluid is assigned as air with a Prandtl number of 0.71 throughout the simulation. Results are presented in the form of streamlines, isotherms, average Nusselt number, bulk temperature, and drag force for the afore mentioned parameters. The numerical results indicate the strong influence of the mentioned parameters on the flow structure and heat transfer as well as average Nusselt number, average bulk temperature, and drag force. An optimum combination of the governing parameters would result in higher heat transfer and lower drag force.

Numerical Fluid-Dynamic Optimization of Microchannel-Provided Porous Scaffolds for the Co-Culture of Adherent and Non-Adherent Cells

Computational fluid dynamic (CFD) techniques were used to optimize the microenvironment inside scaffolds for hematopoietic stem cell (HSC) culture in a perfusion bioreactor. These matrices are meant to be seeded with adherent bone marrow stromal cells and then co-cultivated with HSCs; the scaffold micro-architecture and the fluid-dynamic conditions have to be optimized to avoid non-adherent stem cells being dragged away while ensuring adequate nutrient supply. The insertion of longitudinal microchannels was tested as a tool to improve perfusion in a homogeneous porous scaffold. Models of microchannel-provided scaffolds, characterized by different values of geometric parameters concerning pores and channels, were built, and numerical fluid-dynamic and oxygen-transfer analyses were carried out. The results of the computations indicated that the microchannels created preferential paths for culture medium flow, causing low shear stresses and drag forces within the pores; meanwhile, they improved oxygen delivery by forcing its penetration into the scaffold bulk. In particular, an 85% porous, 3-mm-thick scaffold with 175-microm-diameter pores was considered; at a constant average drag force guaranteeing stem cell suspension inside this porous bulk, the addition of approximately 260-microm-diameter, 700-microm-spaced channels resulted in 34% higher oxygen partial pressure at the exit (approximately 135 vs 101 mmHg), maintaining a wall shear stress median value of approximately 0.14 mPa. The present work demonstrates the capacity of microchannel-provided scaffolds to ensure suitable conditions for HSC culture and shows that CFD methods are a valuable tool to retrieve significant clues for the design of the culture environment.

Stroking Characteristics during Time to Exhaustion Tests

Race analyses during swimming reveal how exercise duration affects both clean swimming speed (v), stroke rate (SR), and stroke length (SL). The aim of this study is to provide an explanation for the change of SL and SR during paced exercise swimming the front crawl through an analysis of intracycle changes in motor organization. Trained swimmers (N = 10) swam three times to exhaustion (TTE in seconds) at predetermined velocities corresponding to 95%, 100%, and 110% of the mean speed attained in a 400-m race (V 400). During TTE tests, SR, SL, durations of the glide + catch, pull, push, and recovery phases (s) were measured. Assessment of arm coordination was made through the calculation of the index of coordination (IdC). The time allotted to propulsion per distance unit was estimated (T prop). For all tested speeds, fatigue development induced a gradual increase of SR with concomitant decrease of SL. The duration of the nonpropulsive phases decreased, whereas the duration of the propulsive phases per stroke remained constant. The IdC increased reflecting a reduction of the lag time between two consecutive propulsive actions. Consequently, T prop increased. Fatigue development induced an increase of the SR to compensate for the reduced capacity to generate a propulsive impulse per stroke. The change in arm coordination allows a better chain of the propulsive actions and leads to a greater time allotted to propulsion per distance unit. Such motor adaptation ensures that the overall propulsive impulse remained constant whereas average propulsive force per arm stroke is reduced.

Mechanical aspects of nitrile hydratase enzymatic activity. Steered molecular dynamics simulations of Pseudonocardia thermophila JCM 3095

Nitrile hydratase (NHase), an important biotechnological enzyme, has been investigated using a steered molecular dynamics computer modelling for the first time. An external force applied to the docked ligands was used to determine transport paths for acrylonitrile (substrate) and acrylamide (product). The average drag force of 120 pN within the enzyme channel is 50% higher than that in model water. The major hindrance of 500 pN is generated by βPhe37 residue. This region may be responsible for the stereoselectivity of NHases.

Simulation of the hydrodynamic drag of aggregated particles

The drag force on aggregates and partially sintered agglomerates is assessed using the lattice Boltzmann method (LBM) and accelerated Stokesian dynamics (ASD). Both methods have been compared in terms of accuracy and computational effort. It is shown that they give comparable results if all numerical parameters are controlled carefully. LBM requires a much higher computational effort, however, in contrast to ASD it is able to simulate partially sintered agglomerates as well. The results show that even a very small amount of sintering leads to a significant reduction in the drag force. The analysis of the drag force on agglomerates as well as on aggregates shows that there is no simple geometric quantity which is uniquely related to the drag force. Moreover, there is a significant variation in drag force for single aggregates at different orientations or for the orientation averaged drag force of different aggregates of the same size. This is explained by the structural effects which may lead to a variation in the drag force up to ± 20 % .

BINARY INTERACTION FORCE ON SPHERES I: LOW REYNOLDS NUMBER FLOW

A two-particle distribution function is derived to calculate the effect of the presence of the particles surrounding a test particle. The average drag force exerted on a particle accounting for binary particle- particle interactions is calculated assuming low particle-Reynolds number flow. The introduction of particle- particle interactions results in the prediction of forces that depend on particle concentration and concentration gradients, size gradients and second derivatives of the particle velocity field. Delta and Poisson size distributions were studied explicitly and some predictions compared with available experimental data, showing good agreement.

Fluidized bed in a confined volume

Coarse solid elastic enough particles form a packed bed in a vertical cylinder confined from below and from above by permeable elastic plates. A gas is forced through the lower plate with a velocity exceeding the terminal (transport) velocity. Adjacent to the lower plate the particles are entrained and impact on the upper plate. As a result, fluidization regimes of still unreported types take place in the confined cylinder. These regimes are analyzed qualitatively by a theoretical model proposed here. This model describes the mean motions of the gas and particles. It includes the mass and momentum equations for the gas and particle phases and the equation of the kinetic energy of particle fluctuations. The system of equations is supplemented by constitutive equations for the averaged drag force, granular pressure, kinetic energy dissipation due to inelastic particle collisions, and energy generation. It is assumed that generation of the kinetic energy is caused by the lateral Magnus force due to particle rotation. Steady state solutions of the equations are obtained, which describe the fluidization regimes in a confined cylinder, namely disperse for a fluidized bed with increasing or decreasing volume fraction and for an inverted packed bed. Experiments are performed to show the existence of the disperse regime of fluidization. Stability of the disperse bed with respect to small perturbations is considered. It is shown that a disperse fluidized bed is unstable for sufficiently concentrated dispersions where the bulk modulus of elasticity of the granular phase is negative. The effect of vibrations of the upper plate upon fluidization regimes is also studied. Resonant frequencies are detected in the concentration region where the bulk modulus of elasticity is positive.

CONVECTIVE HEAT TRANSFER FROM A CIRCULAR CYLINDER UNDER THE EFFECT OF A SOLID PLANE WALL

The purpose of this investigation is to study the convective heat transfer from a horizontal circular cylinder under the effect of a solid plane wall. The full Navier–Stokes and energy equations for two-dimensi onal steady flow are solved by a finite element method. The variations in surface shear stress, local pressure and Nusselt number around the surface of the cylinder as well as the predicted values of average Nusselt number, location of separation and some flow and temperature fields are presented. It is found that the average Nusselt number and drag force increase as the gap between the cylinder and the wall is increased.

The drag force on a moving dislocation, I. Zero temperature (lattice drag force)

The kinematics and equations of motion of an equivalent single-degree-of-freedom system for a moving dislocation in a modified Frenkel-Kontorova linear-chain model are derived and then used in conjunction with computer simulation runs. The average drag force on a moving dislocation at zero temperature (lattice drag force) is computed for a range of dislocation velocities. At a velocity comparable with the loss-free velocity, obtained by Earmme and Weiner from a steady-state solution, we obtain a minimum value for the lattice drag force. For velocities above the loss-free velocity the results agree with those obtained fom steady-state solutions by Earmme and Weiner. Below the loss-free velocity the lattice drag force is relatively small. It goes through a maximum which is of the order of 10−4 times the interatomic spring constant k1 of the model.

Drag on Baffle Walls in Hydraulic Jump

The drag force experienced by a two-dimensional baffle wall at different locations in a forced hydraulic jump has been measured. Both the average and fluctuating components of this force have been obtained using a drag frame with strain gages as the transducing element. A force coefficient using the free jump sequent depth pressure force has been used to correlate the drag force with the relevant parameters. The drag fluctuations have been analyzed using the root-mean-square value of the fluctuations as they are found to follow a normal distribution. A unified plot for the average drag force coefficient has been obtained using the data collected and some data available in literature. Results obtained have been compared with similar results available for three-dimensional baffle blocks.