Recursive and/or iterative estimation of the two-dimensional velocity field and reconstruction of three-dimensional motion

1989 ◽  
Vol 16 (1) ◽  
pp. 53-72 ◽  
Author(s):  
Georges Tziritas
Keyword(s):  
Velocity Field ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Iterative Estimation

Three-Dimensional Flow of a Newtonian Liquid Through an Annular Space with Axially Varying Eccentricity

2005 ◽  
Vol 128 (2) ◽  
pp. 223-231 ◽  
Author(s):  
Eduarda P. F. de Pina ◽  
M. S. Carvalho
Keyword(s):  
Velocity Field ◽  
Cross Section ◽  
Drill Pipe ◽  
Three Dimensional ◽  
Complete Analysis ◽  
Correct Prediction ◽  
Two Dimensional ◽  
Annular Space ◽  
Drilling Mud ◽  
Frictional Pressure Drop

Flow in annular space occurs in drilling operation of oil and gas wells. The correct prediction of the flow of the drilling mud in the annular space between the well wall and the drill pipe is essential to determine the variation in the mud pressure within the wellbore, the frictional pressure drop, and the efficiency of the transport of the rock drill cuttings. A complete analysis of this situation is extremely complex: the inner cylinder is usually rotating, the wellbore wall will depart significantly from cylindrical, the drill pipe is eccentric, and the eccentricity varies along the well. A complete analysis of this situation would require the solution of the three-dimensional momentum equation and would be computationally expensive and complex. Models available in the literature to study this situation do consider the rotation of the inner cylinder and the non-Newtonian behavior of the drilling fluids, but assume the relative position of the inner with respect to the outer cylinders fixed, i.e., they neglect the variation of the eccentricity along the length of the well, and the flow is considered to be fully developed. This approximation leads to a two-dimensional model to determine the three components of the velocity field in a cross-section of the annulus. The model presented in this work takes into account the variation of the eccentricity along the well; a more appropriate description of the geometric configuration of directional wells. As a consequence, the velocity field varies along the well length and the resulting flow model is three-dimensional. Lubrication theory is used to simplify the governing equations into a two-dimensional differential equation that describes the pressure field. The results show the effect of the variation of the eccentricity on the friction factor, maximum and minimum axial velocity in each cross section, and the presence of azimuthal flow even when the inner cylinder is not rotating.

On steady Stokes flow in a trihedral rectangular corner

2003 ◽  
Vol 476 ◽  
pp. 159-177 ◽  
Author(s):  
A. M. GOMILKO ◽  
V. S. MALYUGA ◽  
V. V. MELESHKO
Keyword(s):  
Velocity Field ◽  
Stokes Flow ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Stagnation Line ◽  
Stagnation Points ◽  
Boundary Velocity ◽  
Different Types ◽  
Spiral Shape ◽  
Induced Flow

Motivated by the recent paper of Hills & Moffatt (2000), we investigate the Stokes flow in a trihedral corner formed by three mutually orthogonal planes, induced by a non-zero velocity distribution over one of the walls of the corner. It is shown that the local behaviour of the velocity field near the edges of the corner, where a discontinuity of the boundary velocity is assumed, coincides with the Goodier–Taylor solution for a two-dimensional wedge. Analysis of the streamline patterns confirms the existence of eddies near the stationary edge in the flow, induced either by uniform translation of one of the walls of the corner in the direction perpendicular to its bisectrix or by uniform rotation of a side about the vertex of the corner. These flows are shown to be quasi-two-dimensional. If the wall rotates about a centre displaced from the vertex, the induced flow is essentially three-dimensional. In the antisymmetric velocity field, a stagnation line appears composed of stagnation points of different types. Otherwise the three-dimensionality manifests itself in a non-closed spiral shape of the streamlines.

scholarly journals Maximal heat transfer between two parallel plates

2018 ◽  
Vol 851 ◽  
Author(s):  
Shingo Motoki ◽  
Genta Kawahara ◽  
Masaki Shimizu
Keyword(s):  
Heat Transfer ◽  
Velocity Field ◽  
Large Scale ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Solution Branch ◽  
Search Range ◽  
Dimensional Solution

The divergence-free time-independent velocity field has been determined so as to maximise heat transfer between two parallel plates with a constant temperature difference under the constraint of fixed total enstrophy. The present variational problem is the same as that first formulated by Hassanzadeh et al. (J. Fluid Mech., vol. 751, 2014, pp. 627–662); however, the search range for optimal states has been extended to a three-dimensional velocity field. A scaling of the Nusselt number $Nu$ with the Péclet number $Pe$ (i.e., the square root of the non-dimensionalised enstrophy with thermal diffusion time scale), $Nu\sim Pe^{2/3}$, has been found in the three-dimensional optimal states, corresponding to the asymptotic scaling with the Rayleigh number $Ra$, $Nu\sim Ra^{1/2}$, expected to appear in an ultimate state, and thus to the Taylor energy dissipation law in high-Reynolds-number turbulence. At $Pe\sim 10^{0}$, a two-dimensional array of large-scale convection rolls provides maximal heat transfer. A three-dimensional optimal solution emerges from bifurcation on the two-dimensional solution branch at $Pe\sim 10^{1}$, and the three-dimensional solution branch has been tracked up to $Pe\sim 10^{4}$ (corresponding to $Ra\approx 2.7\times 10^{6}$). At $Pe\gtrsim 10^{3}$, the optimised velocity fields consist of convection cells with hierarchical self-similar vortical structures, and the temperature fields exhibit a logarithmic-like mean profile near the walls.

scholarly journals Turbulence in the Atmosphere of B-Type Stars

1980 ◽  
Vol 51 ◽  
pp. 170-171
Author(s):  
Keiichi Kodaira
Keyword(s):  
Surface Layer ◽  
Velocity Field ◽  
Differential Rotation ◽  
Meridional Circulation ◽  
Three Dimensional ◽  
Scale Height ◽  
Small Scale ◽  
Two Dimensional ◽  
Viscosity Term ◽  
Pressure Scale

AbstractThe stationary turbulent surface layer, whose depth is of the order of the pressure scale height in the subphotospheric layer, was investigated for B-type stars, using the momentum and the continuity equations with the inertia term neglected but the turbulence-viscosity term included. The mean velocity field is dominated by the horizontal component of the meridional circulation, driven by the pressure-density unbalance in the radiative envelope of the rotating star, and the differential rotation induced by the Coriolis force.The model calculation for a B3IV-V star with the equatorial rotational velocity of 200 km/s led to the conclusions that the velocity field due to the differential rotation is of the order of 0.1-1 km/s, the velocity field of the meridional circulation itself is negligible, the velocity field of the three-dimensional shear turbulence is of the order of 0.1 km/s, and i t s scale is comparable to or less than the pressure scale height, the velocity field of the horizontal two-dimensional turbulence is of the order of 1-10 km/s, and i t s maximum scale ranges from a few times the pressure scale height to one-fiftieth of the stellar radius. If the index of the energy density law is close to 3.5, the turbulent surface layer may be dominated by the large scale (two-dimensional) barotropic eddies whose energy is fed by the small scale (three-dimensional) baroclinic turbulence in a way similar to the planetary atmospheres. In this case we may expect the tangential macroturbulence of the order of 1-10 km/s, though the interaction between this and the small-scale three-dimensional turbulence still remains to be investigated.

scholarly journals The computation of the velocity field

1984 ◽  
Vol 221 (1223) ◽  
pp. 189-220 ◽  
Keyword(s):  
Velocity Field ◽  
Fundamental Problem ◽  
Empirical Studies ◽  
Three Dimensional ◽  
Human Motion ◽  
Dimensional Structure ◽  
Two Dimensional ◽  
Physical Assumption ◽  
Intensity Changes ◽  
Significant Intensity

The organization of movement in the changing retinal image provides a valuable source of information for analysing the environment in terms of objects, their motion in space, and their three-dimensional structure. A description of this movement is not provided to our visual system directly, however; it must be inferred from the pattern of changing intensity that reaches the eye. This paper examines the problem of motion measurement, which we formulate as the computation of an instantaneous two-dimensional velocity field from the changing image. Initial measurements of motion take place at the location of significant intensity changes. These measurements provide only one component of local velocity, and must be integrated to compute the two-dimensional velocity field. A fundamental problem for this integration stage is that the velocity field is not determined uniquely from information available in the changing image. We formulate an additional constraint of smoothness of the velocity field, based on the physical assumption that surfaces are generally smooth, which allows the computation of a unique velocity field. A theoretical analysis of the conditions under which this computation yields the correct velocity field suggests that the solution is physically plausible. Empirical studies show the predictions of this computation to be consistent with human motion perception.

Three-Dimensional Recirculation Flow in a Backward Facing Step

1994 ◽  
Vol 116 (2) ◽  
pp. 228-232 ◽  
Author(s):  
Chiang Shih ◽  
Chih-Ming Ho
Keyword(s):  
Velocity Field ◽  
Aspect Ratio ◽  
Recirculation Zone ◽  
Three Dimensional ◽  
Laser Doppler Anemometer ◽  
Separation Region ◽  
Two Dimensional ◽  
Small Aspect Ratio ◽  
Backward Facing Step ◽  
Recirculation Flow

The flow field behind a small aspect ratio (channel width/step height = 3) backward-facing step is examined using laser Doppler anemometer. All three velocity components inside the separation region are surveyed in detail. The velocity profile just upstream of the step is laminar and two-dimensional. The velocity field reveals that the reattachment and the flow in the recirculation zone are highly three-dimensional due to the small aspect ratio.

Rheology of a dilute two-dimensional suspension of vesicles

2010 ◽  
Vol 653 ◽  
pp. 489-518 ◽  
Author(s):  
GIOVANNI GHIGLIOTTI ◽  
THIERRY BIBEN ◽  
CHAOUQI MISBAH
Keyword(s):  
Velocity Field ◽  
Large Scale ◽  
Free Boundary Problems ◽  
Numerical Study ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Function Technique ◽  
Two Dimensional ◽  
Vesicle Membrane

The rheology of a dilute two-dimensional suspension of vesicles (closed bags of a lipid bilayer membrane) is studied by numerical simulations. The numerical methods used are based on the boundary integral formulation (Green's function technique) and the phase field approach, which has become a quite popular and powerful tool for the numerical study of free-boundary problems. The imposed flow is an unbounded linear shear. The goal of the present study is to elucidate the link between the rheology of vesicle suspensions and the microscopic dynamics of the constituent particles (tank-treading and tumbling motions). A comparison with emulsion rheology reveals the central role played by the membrane. In particular, at low viscosity ratio λ (defined as the viscosity of the internal fluid over that of the ambient one), the effective viscosity decreases with λ, while the opposite trend is exhibited by emulsions, according to the classical Taylor result. This fact is explained by considering the velocity field of the ambient fluid. The area-incompressibility of the vesicle membrane modifies the surrounding velocity field in a quite different manner than what a drop does. The overall numerical results in two dimensions are in reasonable agreement with the three-dimensional analytical theory derived recently in the small deformation limit (quasi-spherical shapes). The finding that the simulations in two dimensions capture the essential features of the three-dimensional rheology opens the way for extensive and large-scale simulations for semi-dilute and concentrated vesicle suspensions. We discuss some peculiar effects exhibited by the instantaneous viscosity in the tumbling regime of vesicles. Finally, the rheology is found to be relatively insensitive to shear rate.

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

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