scholarly journals Time-dependent lift and drag on a rigid body in a viscous steady linear flow

2019 ◽  
Vol 864 ◽  
pp. 554-595 ◽  
Author(s):  
Fabien Candelier ◽  
Bernhard Mehlig ◽  
Jacques Magnaudet
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Rigid Body ◽  
Slip Velocity ◽  
Fluid Velocity ◽  
The Body ◽  
Time Dependent ◽  
Leading Order ◽  
Linear Flow ◽  
Force Components

We compute the leading-order inertial corrections to the instantaneous force acting on a rigid body moving with a time-dependent slip velocity in a linear flow field, assuming that the square root of the Reynolds number based on the fluid-velocity gradient is much larger than the Reynolds number based on the slip velocity between the body and the fluid. As a first step towards applications to dilute sheared suspensions and turbulent particle-laden flows, we seek a formulation allowing this force to be determined for an arbitrarily shaped body moving in a general linear flow. We express the equations governing the flow disturbance in a non-orthogonal coordinate system moving with the undisturbed flow and solve the problem using matched asymptotic expansions. The use of the co-moving coordinates enables the leading-order inertial corrections to the force to be obtained at any time in an arbitrary linear flow field. We then specialize this approach to compute the time-dependent force components for a sphere moving in three canonical flows: solid-body rotation, planar elongation, and uniform shear. We discuss the behaviour and physical origin of the different force components in the short-time and quasi-steady limits. Last, we illustrate the influence of time-dependent and quasi-steady inertial effects by examining the sedimentation of prolate and oblate spheroids in a pure shear flow.

Flow past a sphere undergoing unsteady rectilinear motion and unsteady drag at small Reynolds number

2001 ◽  
Vol 446 ◽  
pp. 95-119 ◽  
Author(s):  
EVGENY S. ASMOLOV
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Slip Velocity ◽  
Diffusion Length ◽  
Time Limit ◽  
Large Displacement ◽  
Small Displacement ◽  
Rectilinear Motion ◽  
Small Reynolds Number ◽  
Long Time

The flow induced by a sphere which undergoes unsteady motion in a Newtonian fluid at small Reynolds number is considered at distances large compared with sphere radius a. Previous solutions of the unsteady Oseen equations (Ockendon 1968; Lovalenti & Brady 1993b) for rectilinear motion are refined. Three-dimensional Fourier transforms of the disturbance field are integrated over Fourier space to derive new concise equations for the velocity field and history force in terms of single history integrals.Various slip-velocity profiles are classified by the ratio A of the particle relative displacement, z′p(t′) − z′p(τ′), to the diffusion length, l′D = 2[v(t′ − τ′)]1/2, where v is the kinematic viscosity of the fluid. Most previous studies are concerned with large-displacement motions for which the ratio is large in the long-time limit. It is shown using asymptotic calculations that the flow at any point at large distance z past a sphere for arbitrary large-displacement and non-reversing motion is the same as the steady-state laminar wake if z is expressed in terms of the time elapsed since the particle was at that point in the laboratory frame. The point source solution for the remainder of the far flow is also valid for the unsteady case.A start-up motion with slip velocity V′p = γ′(t′)−1/2, t′ > 0, is investigated for which A is finite. A self-similar solution for the flow field is obtained in terms of space coordinates scaled by the diffusion length, u′ = auss(η)/t′ where η = r′/2(vt′)1/2. The unsteady Oseen correction to the drag is inversely proportional to time.When A is small in the long-time limit (a small-displacement motion) the flow field also depends on the space coordinates in terms of η. The distribution of the streamwise velocity uz is symmetrical in z.

scholarly journals The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number

1993 ◽  
Vol 256 ◽  
pp. 561-605 ◽  
Author(s):  
Phillip M. Lovalenti ◽  
John F. Brady
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Stokes Flow ◽  
Slip Velocity ◽  
Hydrodynamic Force ◽  
Time Dependent ◽  
Rigid Particle ◽  
Flowing Fluid ◽  
Arbitrary Time ◽  
Unsteady Stokes Flow

The hydrodynamic force acting on a rigid spherical particle translating with arbitrary time-dependent motion in a time-dependent flowing fluid is calculated to O(Re) for small but finite values of the Reynolds number, Re, based on the particle's slip velocity relative to the uniform flow. The corresponding expression for an arbitrarily shaped rigid particle is evaluated for the case when the timescale of variation of the particle's slip velocity is much greater than the diffusive scale, a2/v, where a is the characteristic particle dimension and v is the kinematic viscosity of the fluid. It is found that the expression for the hydrodynamic force is not simply an additive combination of the results from unsteady Stokes flow and steady Oseen flow and that the temporal decay to steady state for small but finite Re is always faster than the t-½ behaviour of unsteady Stokes flow. For example, when the particle accelerates from rest the temporal approach to steady state scales as t-2.

scholarly journals The disappearance of laminar and turbulent wakes in complex flows

2002 ◽  
Vol 457 ◽  
pp. 111-132 ◽  
Author(s):  
J. C. R. HUNT ◽  
I. EAMES
Keyword(s):  
Flow Field ◽  
Rigid Body ◽  
The Body ◽  
Viscous Drag ◽  
Total Force ◽  
Far Field ◽  
Volume Flux ◽  
Wake Region ◽  
Complex Flows ◽  
Turbulent Wakes

The singular effects of steady large-scale external strain on the viscous wake generated by a rigid body and the overall flow field are analysed. In an accelerating flow strained at a positive rate, the vorticity field is annihilated owing to positive and negative vorticity either side of the wake centreline diffusing into one another and the volume flux in the wake decreases with downwind distance. Since the wake disappears, the far-field flow changes from monopolar to dipolar. In this case, the force on the body is no longer proportional to the strength of the monopole, but is proportional to the strength of the far field dipole. These results are extended to the case of strained turbulent wakes and this is verified against experimental wind tunnel measurements of Keffer (1965) and Elliott & Townsend (1981) for positive and negative strains. The analysis demonstrates why the total force acting on a body may be estimated by adding the viscous drag and inviscid force due to the irrotational straining field.Applying the analysis to the wake region of a rigid body or a bubble shows that the wake volume flux decreases even in uniform flows owing to the local straining flow in the near-wake region. While the wake volume flux decreases by a small amount for the flow over streamline and bluff bodies, for the case of a clean bubble the decrease is so large as to render Betz's (1925) drag formula invalid.To show how these results may be applied to complex flows, the effects of a sequence of positive and negative strains on the wake are considered. The average wake width is much larger than in the absence of a strain field and this leads to diffusion of vorticity between wakes and the cancellation of vorticity. The latter mechanism leads to a net reduction in the volume flux deficit downstream which explains why in calculations of the flow through groups of moving or stationary bodies the wakes of upstream bodies may be ignored even though their drag and lift forces have a significant effect on the overall flow field.

On Detached Shocks for Blunt Bodies at Small Angles of Attack

1965 ◽  
Vol 32 (2) ◽  
pp. 271-276
Author(s):  
Hsuan Yeh ◽  
Raymond Doby
Keyword(s):  
Flow Field ◽  
Rigid Body ◽  
Blunt Body ◽  
Subsonic Flow ◽  
The Body ◽  
Body Rotation ◽  
Numerical Computations ◽  
Primary Flow ◽  
Perturbation Procedure ◽  
Blunt Bodies

This paper is addressed to the problem of determining the subsonic flow field that exists between the shock and the associated blunt body at small angles of attack. An inverse perturbation procedure is used whereby the shock itself is caused to rotate and the body that supports the perturbed shock is determined. It is found that the perturbed body does not possess a rigid-body-rotation relation relative to the primary flow body. Curves and tables are presented which represent the results of the numerical computations.

The deformation of a viscous particle surrounded by an elastic shell in a general time-dependent linear flow field

1983 ◽  
Vol 126 ◽  
pp. 533-544 ◽  
Author(s):  
P. O. Brunn
Keyword(s):  
Flow Field ◽  
Shell Thickness ◽  
Elastic Shell ◽  
Time Dependent ◽  
Linear Flow ◽  
Special Cases ◽  
Arbitrary Thickness ◽  
Elastic Membranes ◽  
Freely Suspended ◽  
General Time

The dynamics of a viscous particle surrounded by an elastic shell of arbitrary thickness freely suspended in a general linear flow field is investigated. Assuming the unstressed shell to be spherical, an analysis is presented for the case in which the flow-induced deformation leads to small departures from sphericity. The general time-dependent evolution of shape is derived and various special cases (purely elastic sphere, rigid and gaseous interior, elastic membranes) are discussed in detail. It is found that for steady-state flows the equilibrium deformations are absolutely stable and depend only upon the shell thickness, although the rates at which they are attained show the effect of the inside viscosity, too.

Generalized Kirchhoff equations for a deformable body moving in a weakly non-uniform flow field

1994 ◽  
Vol 446 (1926) ◽  
pp. 169-193 ◽  
Keyword(s):  
Flow Field ◽  
Rigid Body ◽  
Degrees Of Freedom ◽  
Surface Deformation ◽  
Nonlinear Differential Equations ◽  
Deformable Body ◽  
Equations Of Motion ◽  
First Integral ◽  
Uniform Flow ◽  
The Body

The classical Kirchhoff’s method provides an efficient way of calculating the hydrodynamical loads (forces and moments) acting on a rigid body moving with six-degrees of freedom in an otherwise quiescent ideal fluid in terms of the body’s added-mass tensor. In this paper we provide a versatile extension of such a formulation to account for both the presence of an imposed ambient non-uniform flow field and the effect of surface deformation of a non-rigid body. The flow inhomogeneity is assumed to be weak when compared against the size of the body. The corresponding expressions for the force and moment are given in a moving body-fixed coordinate system and are obtained using the Lagally theorem. The newly derived system of nonlinear differential equations of motion is shown to possess a first integral. This can be interpreted as an energy-type conservation law and is a consequence of an anti-symmetry property of the coefficient matrix reported here for the first time. A few applications of the proposed formulation are presented including comparison with some existing limiting cases.

Hydrodynamic arrest of a flat body moving towards a parallel surface at arbitrary Reynolds number

1988 ◽  
Vol 186 ◽  
pp. 285-301 ◽  
Author(s):  
C. J. Lawrence ◽  
S. Weinbaum
Keyword(s):  
Reynolds Number ◽  
Initial Velocity ◽  
Stokes Equations ◽  
The Body ◽  
Applied Force ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Gap Height ◽  
Body Inertia

The motion of a flat body towards a parallel plane surface in incompressible fluid is considered both in the presence and absence of an applied force for a non-vanishing initial velocity. In the inviscid limit, a first integral of the equations is obtained and analytic solutions are presented for the cases of finite body inertia with zero applied force and finite applied force with negligible body inertia. In the former case when the ratio of body inertia to fluid inertia is large, a singular behaviour is observed in the arrest of the body before impact wherein the time-dependent pressure and radial velocity of the fluid exhibit a sharp peak and there is a large transfer of kinetic energy from the body to the thin fluid layer. For a real fluid, a general procedure is described to obtain solutions at arbitrary Reynolds number for naturally occurring initial velocity conditions. Solutions to the full Navier-Stokes equations are obtained for an arbitrary Reynolds number based on gap height which are valid provided the flow remains laminar and the gap height is small. In general, the equations of motion of the body and fluid are both dynamically and kinematically coupled. The dynamic coupling, however, is removed when the body inertia is neglected. In particular, the cases of hydrodynamic arrest with zero applied force, and draining of the fluid under a constant applied force are considered. The natural initial conditions lead to a new exact similarity solution of the Navier-Stokes equations which is valid for an instantaneous time-dependent Re based on gap height of greater than approximately 100, wherein the top and bottom boundary layers remain distinct. The longer time portions of the motion and the final arrest are described by a numerical calculation for intermediate Reynolds number and a low-Reynolds-number analysis.

The motion of long slender bodies in a viscous fluid. Part 2. Shear flow

1971 ◽  
Vol 45 (4) ◽  
pp. 625-657 ◽  
Author(s):  
R. G. Cox
Keyword(s):  
Shear Flow ◽  
Viscous Fluid ◽  
Fluid Velocity ◽  
Axial Rotation ◽  
Axisymmetric Body ◽  
The Body ◽  
Total Force ◽  
Axis Ratio ◽  
Linear Flow ◽  
Slender Bodies

A long slender axisymmetric body is considered placed at rest in a general linear flow in such a manner that the undisturbed fluid velocity is identically zero on the body axis. Formulae for the total force and torque on the body are found as an expansion in terms of a small parameter κ defined as the radius-to-length ratio of the body. These general results are used to determine the resistance to axial rotation of the body and also the equivalent axis ratio of the body for motion in a shear flow.

Transient Motion of a Rigid Body Through a Narrow Tube and Characteristics of Surrounding Fluid Flow

2008 ◽  
Author(s):  
Tatsuya Otsuka ◽  
Daichi Ishii ◽  
Toru Maeda ◽  
Masatsugu Yoshizawa
Keyword(s):  
Rigid Body ◽  
Fluid Velocity ◽  
Small Diameter ◽  
Flow Characteristics ◽  
Viscous Friction ◽  
The Body ◽  
Axial Component ◽  
Transient Motion ◽  
Viscous Friction Force ◽  
Micro Machine

A multibody transportation system that moves with fluid inside a small-diameter tube has been studied by a lot of researchers. It is expected to be developed for future engineering applications such as a micro machine that transports medicines to a certain part of a body. This paper deals with the flow characteristics around a single rigid body and transient motion of the body when a body is influenced by pressure force from upstream. The model considered a body smaller than a diameter of a tube so that the force on the body can be numerically and analytically estimated as viscous friction force. It was assumed that the flow is axisymmetric, laminar and taken to be Newtonian and incompressible. It was obtained that the axial component of the fluid velocity decreases and pressure increases near the body like stagnation flow. Moreover, the pressure rapidly increases behind the body and decreases in front of the body with increasing diameter of the body.

scholarly journals Detection of Acetaminophen and Its Glucuronide in Fingerprint by SALDI Mass Spectrometry Using Zeolite and Study of Time-Dependent Changes in Detected Ion Amount

Analytica ◽  
2021 ◽  
Vol 2 (3) ◽  
pp. 66-75
Author(s):  
Toshiki Horikoshi ◽  
Chihiro Kitaoka ◽  
Yosuke Fujii ◽  
Takashi Asano ◽  
Jiawei Xu ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Glucuronic Acid ◽  
Laser Desorption ◽  
The Body ◽  
Time Dependent ◽  
Laser Desorption Ionization ◽  
Fingerprint Analysis ◽  
Desorption Ionization ◽  
Acid Conjugate ◽  
Over Time

The ingredients of an antipyretic (acetaminophen, AAP) and their metabolites excreted into fingerprint were detected by surface-assisted laser desorption ionization (SALDI) mass spectrometry using zeolite. In the fingerprint taken 4 h after AAP ingestion, not only AAP but also the glucuronic acid conjugate of AAP (GAAP), caffeine (Caf), ethenzamide (Eth), salicylamide (Sala; a metabolite of Eth), and urea were detected. Fingerprints were collected over time to determine how the amounts of AAP and its metabolite changed with time, and the time dependence of the peak intensities of protonated AAP and GAAP was measured. It was found that the increase of [GAAP+H]+ peak started later than that of [AAP+H]+ peak, reflecting the metabolism of AAP. Both AAP and GAAP reached maximum concentrations approximately 3 h after ingestion, and were excreted from the body with a half-life of approximately 3.3 h. In addition, fingerprint preservation was confirmed by optical microscopy, and fingerprint shape was retained even after laser irradiation of the fingerprint. Our method may be used in fingerprint analysis.

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