scholarly journals Path oscillations and enhanced drag of light rising spheres

2018 ◽  
Vol 841 ◽  
pp. 228-266 ◽  
Author(s):  
Franck Auguste ◽  
Jacques Magnaudet
Keyword(s):  
Density Ratio ◽  
Reynolds Numbers ◽  
Relative Magnitude ◽  
The Body ◽  
Sphere Diameter ◽  
Viscous Effects ◽  
Flow Parameters ◽  
Route To Chaos ◽  
Set Up ◽  
Equivalent Conditions

The dynamics of light spheres rising freely under buoyancy in a large expanse of viscous fluid at rest at infinity is investigated numerically. For this purpose, the computational approach developed by Mougin & Magnaudet (Intl J. Multiphase Flow, vol. 28, 2002, pp. 1837–1851) is improved to account for the instantaneous viscous loads induced by the translational and rotational sphere accelerations, which play a crucial role in the dynamics of very light spheres. A comprehensive map of the rise regimes encountered up to Reynolds numbers (based on the sphere diameter and mean rise velocity) of the order of $10^{3}$ is set up by varying independently the body-to-fluid density ratio and the relative magnitude of inertial and viscous effects in approximately 250 distinct combinations. These computations confirm or reveal the presence of several distinct periodic regions on the route to chaos, most of which only exist within a finite range of the sphere relative density and Reynolds number. The wake structure is analysed in these various regimes, evidencing the existence of markedly different shedding modes according to the style of path. The variation of the drag force with the flow parameters is also examined, revealing that only one of the styles of path specific to very light spheres yields a non-standard drag behaviour, with drag coefficients significantly larger than those measured on a fixed sphere under equivalent conditions. The outcomes of this investigation are compared with available experimental and numerical results, evidencing points of consensus and disagreement.

scholarly journals Falling styles of disks

2013 ◽  
Vol 719 ◽  
pp. 388-405 ◽  
Author(s):  
Franck Auguste ◽  
Jacques Magnaudet ◽  
David Fabre
Keyword(s):  
Complex Dynamics ◽  
Three Dimensional ◽  
Relative Magnitude ◽  
The Body ◽  
Fluid Inertia ◽  
Viscous Effects ◽  
Fluid Medium ◽  
Body Experiences ◽  
Set Up ◽  
Thin Disks

AbstractWe numerically investigate the dynamics of thin disks falling under gravity in a viscous fluid medium at rest at infinity. Varying independently the density and thickness of the disk reveals the influence of the disk aspect ratio which, contrary to previous belief, is found to be highly significant as it may completely change the route to non-vertical paths as well as the boundaries between the various path regimes. The transition from the straight vertical path to the planar fluttering regime is found to exhibit complex dynamics: a bistable behaviour of the system is detected within some parameter range and several intermediate regimes are observed in which, although the wake is unstable, the path barely deviates from vertical. By varying independently the body-to-fluid inertia ratio and the relative magnitude of inertial and viscous effects over a significant range, we set up a comprehensive map of the corresponding styles of path followed by an infinitely thin disk. We observe the four types of planar regimes already reported in experiments but also identify two additional fully three-dimensional regimes in which the body experiences a slow horizontal precession superimposed onto zigzagging or tumbling motions.

scholarly journals Core mechanisms of drag enhancement on bodies settling in a stratified fluid

2019 ◽  
Vol 875 ◽  
pp. 622-656 ◽  
Author(s):  
Jie Zhang ◽  
Matthieu J. Mercier ◽  
Jacques Magnaudet
Keyword(s):  
Scaling Laws ◽  
Relative Magnitude ◽  
Stratified Fluid ◽  
The Body ◽  
Lower Atmosphere ◽  
Governing Equations ◽  
Flow Parameters ◽  
Induced Drag ◽  
Widespread Belief ◽  
Living Organisms

Stratification due to salt or heat gradients greatly affects the distribution of inert particles and living organisms in the ocean and the lower atmosphere. Laboratory studies considering the settling of a sphere in a linearly stratified fluid confirmed that stratification may dramatically enhance the drag on the body, but failed to identify the generic physical mechanism responsible for this increase. We present a rigorous splitting scheme of the various contributions to the drag on a settling body, which allows them to be properly disentangled whatever the relative magnitude of inertial, viscous, diffusive and buoyancy effects. We apply this splitting procedure to data obtained via direct numerical simulation of the flow past a settling sphere over a range of parameters covering a variety of situations of laboratory and geophysical interest. Contrary to widespread belief, we show that, in the parameter range covered by the simulations, the drag enhancement is generally not primarily due to the extra buoyancy force resulting from the dragging of light fluid by the body, but rather to the specific structure of the vorticity field set in by buoyancy effects. Simulations also reveal how the different buoyancy-induced contributions to the drag vary with the flow parameters. To unravel the origin of these variations, we analyse the different possible leading-order balances in the governing equations. Thanks to this procedure, we identify several distinct regimes which differ by the relative magnitude of length scales associated with stratification, viscosity and diffusivity. We derive the scaling laws of the buoyancy-induced drag contributions in each of these regimes. Considering tangible examples, we show how these scaling laws combined with numerical results may be used to obtain reliable predictions beyond the range of parameters covered by the simulations.

scholarly journals Particles, Drops, and Bubbles Moving Across Sharp Interfaces and Stratified Layers

2020 ◽  
Vol 52 (1) ◽  
pp. 61-91 ◽  
Author(s):  
Jacques Magnaudet ◽  
Matthieu J. Mercier
Keyword(s):  
Relative Magnitude ◽  
Immiscible Fluids ◽  
The Body ◽  
Body Motion ◽  
Physical Parameters ◽  
Viscous Effects ◽  
Fluid Resistance ◽  
Wide Range ◽  
Deformable Bodies ◽  
Sharp Interfaces

Rigid or deformable bodies moving through continuously stratified layers or across sharp interfaces are involved in a wide variety of geophysical and engineering applications, with both miscible and immiscible fluids. In most cases, the body moves while pulling a column of fluid, in which density and possibly viscosity differ from those of the neighboring fluid. The presence of this column usually increases the fluid resistance to the relative body motion, frequently slowing down its settling or rise in a dramatic manner. This column also exhibits specific dynamics that depend on the nature of the fluids and on the various physical parameters of the system, especially the strength of the density/viscosity stratification and the relative magnitude of inertia and viscous effects. In the miscible case, as stratification increases, the wake becomes dominated by the presence of a downstream jet, which may undergo a specific instability. In immiscible fluids, the viscosity contrast combined with capillary effects may lead to strikingly different evolutions of the column, including pinch-off followed by the formation of a drop that remains attached to the body, or a massive fragmentation phenomenon. This review discusses the flow organization and its consequences on the body motion under a wide range of conditions, as well as potentialities and limitations of available models aimed at predicting the body and column dynamics.

Hypersonic flow over spherically blunted cone capsules for atmospheric entry. Part 1. The sharp cone and the sphere

2019 ◽  
Vol 871 ◽  
pp. 1097-1116 ◽  
Author(s):  
H. G. Hornung ◽  
Jan Martinez Schramm ◽  
Klaus Hannemann
Keyword(s):  
Hypersonic Flow ◽  
Functional Form ◽  
Cone Angle ◽  
Density Ratio ◽  
The Body ◽  
Normal Shock ◽  
Viscous Effects ◽  
Atmospheric Entry ◽  
Shock Density ◽  
Sharp Cone

Depending on the cone half-angle and the inverse normal-shock density ratio $\unicode[STIX]{x1D700}$, hypersonic flow over a spherically blunted cone exhibits two regimes separated by an almost discontinuous jump of the body end of the sonic line from a point on the spherical nose to the shoulder of the cone, here called sphere behaviour and cone behaviour. The inflection point of the shock wave in sphere behaviour is explained. In Part 1 we explore the two elements of the capsule shape, the sphere and the sharp cone with detached shock, theoretically and computationally, in order to put the treatment of the full capsule shape on a sound basis. Starting from the analytical expression for the shock detachment angle of a cone given by Hayes & Probstein (Hypersonic Flow Theory, 1959, Academic Press) we make a hypothesis for the sharp cone, about the functional form of the dependence of dimensionless quantities on $\unicode[STIX]{x1D700}$ and a cone angle parameter, $\unicode[STIX]{x1D702}$. In the critical part of atmospheric entry the shock shape and drag of the capsule are insensitive to viscous effects, so that much can be learned from inviscid studies. Accordingly, the hypothesis is tested by making a large number of Euler computations to cover the parameter space: Mach number, specific heat ratio and cone angle. The results confirm the hypothesis in the case of the dimensionless shock stand-off distance as well as for the drag coefficient, yielding accurate analytical functions for both. This reduces the number of independent parameters of the problem from three to two. A functional form of the shock stand-off distance is found for the transition from the $90^{\circ }$ cone to the sphere. Although the analysis assumes a calorically perfect gas, the results may be carried over to the high-enthalpy real-gas situation if the normal-shock density ratio is replaced by the density ratio based on the average density along the stagnation streamline (see e.g. Stulov, Izv. AN SSSR Mech. Zhidk. Gaza, vol. 4, 1969, pp. 142–146; Hornung, J. Fluid Mech., vol. 53, 1972, pp. 149–176; Wen & Hornung, J. Fluid Mech., vol. 299, 1995, pp. 389–405).

scholarly journals Fish larvae exploit edge vortices along their dorsal and ventral fin folds to propel themselves

2016 ◽  
Vol 13 (116) ◽  
pp. 20160068 ◽  
Author(s):  
Gen Li ◽  
Ulrike K. Müller ◽  
Johan L. van Leeuwen ◽  
Hao Liu
Keyword(s):  
Larval Fish ◽  
Fish Larvae ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Bony Fish ◽  
The Body ◽  
Functional Explanation ◽  
Image Velocimetry ◽  
Median Fins

Larvae of bony fish swim in the intermediate Reynolds number ( Re ) regime, using body- and caudal-fin undulation to propel themselves. They share a median fin fold that transforms into separate median fins as they grow into juveniles. The fin fold was suggested to be an adaption for locomotion in the intermediate Reynolds regime, but its fluid-dynamic role is still enigmatic. Using three-dimensional fluid-dynamic computations, we quantified the swimming trajectory from body-shape changes during cyclic swimming of larval fish. We predicted unsteady vortices around the upper and lower edges of the fin fold, and identified similar vortices around real larvae with particle image velocimetry. We show that thrust contributions on the body peak adjacent to the upper and lower edges of the fin fold where large left–right pressure differences occur in concert with the periodical generation and shedding of edge vortices. The fin fold enhances effective flow separation and drag-based thrust. Along the body, net thrust is generated in multiple zones posterior to the centre of mass. Counterfactual simulations exploring the effect of having a fin fold across a range of Reynolds numbers show that the fin fold helps larvae achieve high swimming speeds, yet requires high power. We conclude that propulsion in larval fish partly relies on unsteady high-intensity vortices along the upper and lower edges of the fin fold, providing a functional explanation for the omnipresence of the fin fold in bony-fish larvae.

Boundaries Influence on the Flow Field Around an Oscillating Sphere

2013 ◽  
Author(s):  
Domenica Mirauda ◽  
Antonio Volpe Plantamura ◽  
Stefano Malavasi
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Boundary Conditions ◽  
Damping Ratio ◽  
Water Channel ◽  
Open Water ◽  
Free Surface Flows ◽  
The Body ◽  
Sphere Diameter ◽  
Oscillating Sphere

This work analyzes the effects of the interaction between an oscillating sphere and free surface flows through the reconstruction of the flow field around the body and the analysis of the displacements. The experiments were performed in an open water channel, where the sphere had three different boundary conditions in respect to the flow, defined as h* (the ratio between the distance of the sphere upper surface from the free surface and the sphere diameter). A quasi-symmetric condition at h* = 2, with the sphere equally distant from the free surface and the channel bottom, and two conditions of asymmetric bounded flow, one with the sphere located at a distance of 0.003m from the bottom at h* = 3.97 and the other with the sphere close to the free surface at h* = 0, were considered. The sphere was free to move in two directions, streamwise (x) and transverse to the flow (y), and was characterized by values of mass ratio, m* = 1.34 (ratio between the system mass and the displaced fluid mass), and damping ratio, ζ = 0.004. The comparison between the results of the analyzed boundary conditions has shown the strong influence of the free surface on the evolution of the vortex structures downstream the obstacle.

Effect of Buoyancy and Density Ratio on Heat Transfer in a Smooth Cooling Channel of a Gas Turbine Blade

2018 ◽  
Author(s):  
Mandana S. Saravani ◽  
Saman Beyhaghi ◽  
Ryoichi S. Amano
Keyword(s):  
Heat Transfer ◽  
Rotational Speed ◽  
Cfd Simulation ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Buoyancy Effect ◽  
Square Channel ◽  
First Case ◽  
Computational Fluid Dynamics Cfd ◽  
The Impact

The present work investigates the effects of buoyancy and density ratio on the thermal performance of a rotating two-pass square channel. The U-bend configuration with smooth walls is selected for this study. The channel has a square cross-section with a hydraulic diameter of 5.08 cm (2 inches). The lengths of the first and second passes are 514 mm and 460 mm, respectively. The turbulent flow enters the channel with Reynolds numbers of up to 34,000. The rotational speed varies from 0 to 600 rpm with the rotational numbers up to 0.75. For this study, two approaches are considered for tracking the buoyancy effect on heat transfer. In the first case, the density ratio is set constant, and the rotational speed is varied. In the second case, the density ratio is changed in the stationary case, and the effect of density ratio is discussed. The range of Buoyancy number along the channel is 0–6. The objective is to investigate the impact of Buoyancy forces on a broader range of rotation number (0–0.75) and Buoyancy number scales (0–6), and their combined effects on heat transfer coefficient for a channel with aspect ratio of 1:1. Several computational fluid dynamics (CFD) simulation are carried out for this study, and some of the results are validated against experimental data.

External work in level and grade walking on a motor-driven treadmill

1960 ◽  
Vol 15 (5) ◽  
pp. 759-763 ◽  
Author(s):  
J. W. Snellen
Keyword(s):  
Heat Loss ◽  
Heat Production ◽  
Total Energy Expenditure ◽  
The Body ◽  
External Work ◽  
Thermal Exchange ◽  
Level Walking ◽  
The Subject ◽  
Set Up ◽  
Physical Laws

When studying a walking subject's thermal exchange with the environment, it is essential to know whether in level walking any part of the total energy expenditure is converted into external mechanical work and whether in grade walking the amount of the external work is predictable from physical laws. For this purpose an experiment was set up in which a subject walked on a motor-driven treadmill in a climatic room. In each series of measurements a subject walked uphill for 3 hours and on the level for another hour. Metabolism was kept equal in both situations. Air and wall temperatures were adjusted to the observed weighted skin temperature in order to avoid any heat exchange by radiation and convection. Heat loss by evaporation was derived from the weight loss of the subject. All measurements were carried out in a state of thermal equilibrium. In grade walking there was a difference between heat production and heat loss by evaporation. This difference equaled the caloric equivalent of the product of body weight and gained height. In level walking the heat production equaled heat loss. Hence it was concluded that in level walking all the energy is converted into heat inside the body. Submitted on April 26, 1960

Determination of Discharge Coefficient for Ball Valves With Calibrated Inserts

2004 ◽  
Author(s):  
Gino James Rouss ◽  
William S. Janna
Keyword(s):  
Discharge Coefficient ◽  
Polynomial Equation ◽  
The Body ◽  
Orifice Diameter ◽  
Flow Parameters ◽  
Dimensionless Groups ◽  
Order Polynomial ◽  
Experimental Process ◽  
Power Law Equation

The valve coefficient was measured for 1, 1-1/4, 1-1/2 and 2 nominal ball valves. A recently designed orifice insert was used with these valves to obtain smaller valve coefficients. Orifice inserts were threaded into the body of a ball valve just upstream of the ball itself. The valve coefficient was measured for every insert used with these valves, and an expression was determined to relate the orifice diameter to other pertinent flow parameters. Two dimensionless groups were chosen to correlate the collected data, and expressions were developed that can be used as aids in sizing the orifice insert needed to obtain the desired valve coefficient. The study has shown that a 2nd order polynomial equation as well as a power law equation can both be used to predict the desired results. Knowing pipe size and schedule, the diameter of the orifice insert needed to obtain the required valve coefficient can be approximated with minimum error. An error analysis performed on the collected data shows that the results are highly accurate, and that the experimental process is repeatable.

On one-dimensional unsteady flow at infinite Mach number

1968 ◽  
Vol 304 (1478) ◽  
pp. 255-273 ◽  
Keyword(s):  
Asymptotic Expansion ◽  
Blast Wave ◽  
Outer Part ◽  
The Body ◽  
Viscous Boundary Layer ◽  
Outer Flow ◽  
Hypersonic Speeds ◽  
Set Up ◽  
Viscous Boundary ◽  
Infinite Set

The use of the blast-wave analogy, as an aid to the interpretation of experimental data on the motion of a fluid past an obstacle at hypersonic speeds, has led to the theoretical study of its role in an asymptotic expansion of the solution to the governing equations at large distances downstream of the body. In all attempts to set up such an expansion it has proved necessary to divide the flow régime into two parts, an outer part dominated by the blast wave and an inner part consisting of streamlines which, originally, pass close by the body. The matching of these two regions is apparently only possible if a certain integral vanishes. In the present paper a numerical integration, in one particular set of circumstances, is carried out to test the validity of the asymptotic expansion proposed. Formally, an unsteady problem is tackled, for ease of computation, but the steady analogue follows immediately and is of exactly the form discussed in the earlier investigations. It is found that the main results are in line with the theory and that the integral in question is indistinguishable from zero. However, a deeper investigation of the asymptotic expansion shows that, for an expansion of the type envisaged, an infinite set of integrals must each vanish. The next integral does not appear to be zero according to our computations but this result is not believed to be conclusive. Assuming that all the integrals do vanish, then it appears that the inner layer, which although inviscid, has many of the characteristics of a viscous boundary layer, has the addi­tional, surprising property that it can exert no direct influence on the outer flow at large distances downstream of the body.

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