On the hydrodynamics of pairs of spheres falling along their line of centres in a viscous medium

1968 ◽  
Vol 34 (4) ◽  
pp. 809-819 ◽  
Author(s):  
E. H. Steinberger ◽  
H. R. Pruppacher ◽  
M. Neiburger
Keyword(s):  
Viscous Fluid ◽  
Drag Force ◽  
Reynolds Numbers ◽  
Viscous Medium ◽  
Force Coefficient ◽  
Stokes Approximation ◽  
Force Coefficients ◽  
Drag Forces

The velocities, accelerations and drag forces experienced by two equal spheres falling along their line of centres in a viscous fluid were determined for three groups of Reynolds numbers R in the range where it is commonly assumed that Stokes's approximation applies. For all groups, with R ranging between 0·060 and 0·216, both spheres continually acclerated as they fell, and the upper sphere fell faster and accelerated more than the lower one. In contrast to Stimson & Jeffery's (1926) theory, which is based on the Stokes approximation, and to most earlier experimenters, the drag-force coefficients of the upper sphere computed from the experiments were significantly smaller than those for the lower sphere. Oseen's theory for this case agreed with the experiments in some respects, but contrary to it the drag-force coefficient varied with R for the upper sphere as well as the lower sphere.

scholarly journals Simulation of Convection–Diffusion Transport in a Laminar Flow past a Row of Parallel Absorbing Fibers

Fibers ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 90 ◽  
Author(s):  
Vasily A. Kirsch ◽  
Alexandr V. Bildyukevich ◽  
Stepan D. Bazhenov
Keyword(s):  
Laminar Flow ◽  
Drag Force ◽  
Sherwood Number ◽  
Hollow Fiber Membrane ◽  
Reynolds Numbers ◽  
Regular System ◽  
Convection Diffusion ◽  
Drag Forces ◽  
Wide Range ◽  
Diffusion Mass

A numerical simulation of the laminar flow field and convection–diffusion mass transfer in a regular system of parallel fully absorbing fibers for the range of Reynolds numbers up to Re = 300 is performed. An isolated row of equidistant circular fibers arranged normally to the external flow is considered as the simplest model for a hollow-fiber membrane contactor. The drag forces acting on the fibers with dependence on Re and on the ratio of the fiber diameter to the distance between the fiber axes, as well as the fiber Sherwood number versus Re and the Schmidt number, Sc, are calculated. A nonlinear regression formula is proposed for calculating the fiber drag force versus Re in a wide range of the interfiber distances. It is shown that the Natanson formula for the fiber Sherwood number as a function of the fiber drag force, Re, and Sc, which was originally derived in the limit of high Peclet numbers, is applicable for small and intermediate Reynolds numbers; intermediate and large Peclet numbers, where Pe = Re × Sc; and for sparse and moderately dense rows of fibers.

scholarly journals Physical and Aerodynamic Properties of Lavender in relation to Harvest Mechanisation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Christos I. Dimitriadis ◽  
James L. Brighton ◽  
Mike J. O’Dogherty ◽  
Maria I. Kokkora ◽  
Anastasios I. Darras
Keyword(s):  
Surface Area ◽  
Drag Force ◽  
Aerodynamic Drag ◽  
Reynolds Numbers ◽  
Ultimate Tensile Stress ◽  
Flower Head ◽  
Drag Forces ◽  
Aerodynamic Properties ◽  
The Mean ◽  
Harvest Moisture

A laboratory study evaluated the physical and aerodynamic properties of lavender cultivars in relation to the design of an improved lavender harvester that allows removal of flowers from the stem using the stripping method. The identification of the flower head adhesion, stem breakage, and aerodynamic drag forces were conducted using an Instron 1122 instrument. Measurements on five lavender cultivars at harvest moisture content showed that the overall mean flower detachment force from the stem was 11.2 N, the mean stem tensile strength was 36.7 N, and the calculated mean ultimate tensile stress of the stem was 17.3 MPa. The aerodynamic measurements showed that the drag force is related with the flower surface area. Increasing the surface area of the flower head by 93% of the “Hidcote” cultivar produced an increase in drag force of between 24.8% and 50.6% for airflow rates of 24 and 65 m s−1, respectively. The terminal velocities of the flower heads of the cultivar ranged between 4.5 and 5.9 m s−1, which results in a mean drag coefficient of 0.44. The values of drag coefficients were compatible with well-established values for the appropriate Reynolds numbers.

Experimental Force Coefficients for a Parametric Series of Spinnakers

2003 ◽  
Author(s):  
William C. Lasher ◽  
James R. Sonnenmeier ◽  
David R. Forsman ◽  
Cheng Zhang ◽  
Kenton White
Keyword(s):  
Aspect Ratio ◽  
Thrust Force ◽  
Statistical Design ◽  
Navier Stokes ◽  
Statistical Design Of Experiments ◽  
Force Coefficient ◽  
Force Coefficients ◽  
Drag Forces ◽  
Parametric Series ◽  
Lift And Drag

A parametric series of eight spinnaker models was built and tested in a wind tunnel according to the theory of statistical Design of Experiments. In these models, three sail shape parameters were varied - cross section camber ratio, sail aspect ratio, and sweep. Lift and drag forces were measured for a range of angles of attack, and the thrust force coefficient was determined as a function of apparent wind angle for each of the eight sails. It was found that flat spinnakers are faster than full spinnakers and that spinnakers with low sweep (more vertical) are faster than spinnakers with high sweep. This is consistent with general sailing practice, which maximizes projected sail area by pulling the pole back and down. The influence of aspect ratio on drag coefficient was small and within experimental error. A description of the sail shapes and corresponding force coefficients is presented for future validation of Reynolds Averaged Navier-Stokes simulations.

On the drag force of bubbles in bubble swarms at intermediate and high Reynolds numbers

2011 ◽  
Vol 66 (14) ◽  
pp. 3204-3211 ◽  
Author(s):  
I. Roghair ◽  
Y.M. Lau ◽  
N.G. Deen ◽  
H.M. Slagter ◽  
M.W. Baltussen ◽  
...  
Keyword(s):  
Drag Force ◽  
Reynolds Numbers ◽  
High Reynolds Numbers ◽  
High Reynolds

Aerodynamics of Cyclist Posture, Bicycle and Helmet Characteristics in Time Trial Stage

2012 ◽  
Vol 28 (3) ◽  
pp. 317-323 ◽  
Author(s):  
Vincent Chabroux ◽  
Caroline Barelle ◽  
Daniel Favier
Keyword(s):  
Statistical Analysis ◽  
Wind Tunnel ◽  
Drag Coefficient ◽  
Drag Force ◽  
Time Trial ◽  
Frontal Area ◽  
Significant Gain ◽  
Upper Limbs ◽  
Force Coefficient ◽  
Coefficient Reduction

The present work is focused on the aerodynamic study of different parameters, including both the posture of a cyclist’s upper limbs and the saddle position, in time trial (TT) stages. The aerodynamic influence of a TT helmet large visor is also quantified as a function of the helmet inclination. Experiments conducted in a wind tunnel on nine professional cyclists provided drag force and frontal area measurements to determine the drag force coefficient. Data statistical analysis clearly shows that the hands positioning on shifters and the elbows joined together are significantly reducing the cyclist drag force. Concerning the saddle position, the drag force is shown to be significantly increased (about 3%) when the saddle is raised. The usual helmet inclination appears to be the inclination value minimizing the drag force. Moreover, the addition of a large visor on the helmet is shown to provide a drag coefficient reduction as a function of the helmet inclination. Present results indicate that variations in the TT cyclist posture, the saddle position and the helmet visor can produce a significant gain in time (up to 2.2%) during stages.

Drag Forces on, and Deformation of, Closed Flexible Bags

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Pål Lader ◽  
David W. Fredriksson ◽  
Zsolt Volent ◽  
Jud DeCew ◽  
Trond Rosten ◽  
...  
Keyword(s):  
Drag Force ◽  
Hydrodynamic Forces ◽  
Towing Tank ◽  
Drag Forces ◽  
Uniform Current ◽  
Salmon Production

The use of closed flexible bags is among the suggestions considered as a potential way to expand the salmon production in Norway. Few ocean structures exist with large, heavily compliant submerged components, and there is presently limited existing knowledge about how aquaculture systems with flexible closed cages will respond to external sea loads. The flexibility and deformation of the bag are coupled to the hydrodynamic forces, and the forces and deformation will be dependent on the filling level of the bag. In order to get a better understanding of the drag forces on, and deformation of, such bags, experiments were conducted with a series of closed flexible bags. The bags were towed in a towing tank in order to simulate uniform current. Four different geometries were investigated, cylindrical, cubical, conical, and pyramidal, and the filling levels were varied between 70% and 120%. The main findings from the experiments were that the drag force was highly dependent on the filling level, and that the drag force increases with decreasing filling level. Comparing the drag force on a deflated bag with an inflated one showed an increase of up to 2.5 times.

The Effects of Vibrations on Particle Motion in a Viscous Fluid Cell

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Samer Hassan ◽  
Masahiro Kawaji
Keyword(s):  
Viscous Fluid ◽  
Drag Force ◽  
Particle Motion ◽  
Fluid Model ◽  
Resonance Phenomenon ◽  
Fluid Viscosity ◽  
Mass Force ◽  
Amplitude Data ◽  
Viscous Fluid Model ◽  
Fluid Cell

The effects of small vibrations on particle motion in a viscous fluid cell have been investigated experimentally and theoretically. A steel particle was suspended by a thin wire at the center of a fluid cell, and the cell was vibrated horizontally using an electromagnetic actuator and an air bearing stage. The vibration-induced particle amplitude measurements were performed for different fluid viscosities (58.0cP and 945cP), and cell vibration amplitudes and frequencies. A viscous fluid model was also developed to predict the vibration-induced particle motion. This model shows the effect of fluid viscosity compared to the inviscid model, which was presented earlier by Hassan et al. (2004, “The Effects of Vibrations on Particle Motion in an Infinite Fluid Cell,” ASME J. Appl. Mech., 73(1), pp. 72–78) and validated using data obtained for water. The viscous model with modified drag coefficients is shown to predict well the particle amplitude data for the fluid viscosities of 58.5cP and 945cP. While there is a resonance frequency corresponding to the particle peak amplitude for oil (58.0cP), this phenomenon disappeared for glycerol (945cP). This disappearance of resonance phenomenon is explained by referring to the theory of mechanical vibrations of a mass-spring-damper system. For the sinusoidal particle motion in a viscous fluid, the effective drag force has been obtained, which includes the virtual mass force, drag force proportional to the velocity, and the Basset or history force terms.

The Effects of Fish Cages on Ambient Currents

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Lars C. Gansel ◽  
Thomas A. McClimans ◽  
Dag Myrhaug
Keyword(s):  
Drag Force ◽  
Particle Image ◽  
Reynolds Numbers ◽  
Strain Gauges ◽  
Metal Mesh ◽  
Image Velocimetry ◽  
Flow Through ◽  
Fish Cages ◽  
Ambient Currents ◽  
Wake Characteristics

Experiments were carried out to measure forces on and wake characteristics downstream from fish cages. Cylinders made from metal mesh with porosities of 0%, 30%, 60%, 75%, 82%, and 90% were tested in a towing tank. The drag force was measured with strain gauges, and the flow field downstream from the models was analyzed using particle image velocimetry. The Reynolds numbers ranged from 1000–20,000 based on the model diameter and 15–300 based on the diameter of the strings of the mesh as an independent obstacle. High porosities (here, 82% and 90%) lead to low water blockage and allow a substantial amount of water to flow through the model. The data indicate that the wake characteristics change toward the wake characteristics of a solid cylinder at a porosity just below 75%. The drag force is highly dependent on the porosity for high porosities of a cylinder.

Calculations of unsteady viscous flow past a circular cylinder

1958 ◽  
Vol 4 (1) ◽  
pp. 81-86 ◽  
Author(s):  
R. B. Payne
Keyword(s):  
Circular Cylinder ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Viscous Flow ◽  
Steady Flow ◽  
Reynolds Numbers ◽  
A Value ◽  
Unsteady Viscous Flow ◽  
Starting Flow ◽  
Forward Integration

A numerical solution has been obtained for the starting flow of a viscous fluid past a circular cylinder at Reynolds numbers 40 and 100. The method used is the step-by-step forward integration in time of Helmholtz's vorticity equation. The advantage of working with the vorticity is that calculations can be confined to the region of non-zero vorticity near the cylinder.The general features of the flow, including the formation of the eddies attached to the rear of the cylinder, have been determined, and the drag has been calculated. At R = 40 the drag on the cylinder decreases with time to a value very near that for the steady flow.

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