Flow Between Eccentric Rotating Cylinders

1984 ◽  
Vol 51 (4) ◽  
pp. 869-878 ◽  
Author(s):  
A. San Andres ◽  
A. Z. Szeri
Keyword(s):  
Reynolds Number ◽  
Perturbation Theory ◽  
Numerical Methods ◽  
Numerical Study ◽  
Separation Point ◽  
Test Functions ◽  
B Spline ◽  
First Order ◽  
Eccentric Cylinders ◽  
Galerkin's Procedure

In this numerical study of flow between eccentric cylinders, the size of the separation eddy and the position of the points of separation and reattachment are found to be Reynolds number dependent. The separation point moves in the direction of rotation upon increasing the Reynolds number, in contradiction to the first-order inertial perturbation theory of Ballal and Rivlin [1]. The numerical methods employed in this study include Galerkin’s procedure with B-spline test functions.

Stretched vortices – the sinews of turbulence; large-Reynolds-number asymptotics

1994 ◽  
Vol 259 ◽  
pp. 241-264 ◽  
Author(s):  
H. K. Moffatt ◽  
S. Kida ◽  
K. Ohkitani
Keyword(s):  
Reynolds Number ◽  
Numerical Study ◽  
Large Reynolds Number ◽  
Order Problem ◽  
First Order ◽  
Contour Maps ◽  
Constant Rate ◽  
The Family ◽  
Positive Rate ◽  
Long Time

A large-Reynolds-number asymptotic theory is presented for the problem of a vortex tube of finite circulation [Gcy ] subjected to uniform non-axisymmetric irrotational strain, and aligned along an axis of positive rate of strain. It is shown that at leading order the vorticity field is determined by a solvability condition at first-order in ε = 1/R[Gcy ] where R[gcy ] = [gcy ]/ν. The first-order problem is solved completely, and contours of constant rate of energy dissipation are obtained and compared with the family of contour maps obtained in a previous numerical study of the problem. It is found that the region of large dissipation does not overlap the region of large enstrophy; in fact, the dissipation rate is maximal at a distance from the vortex axis at which the enstrophy has fallen to only 2.8% of its maximum value. The correlation between enstrophy and dissipation fields is found to be 0.19 + O(ε2). The solution reveals that the stretched vortex can survive for a long time even when two of the principal rates of strain are positive, provided R[gcy ] is large enough. The manner in which the theory may be extended to higher orders in ε is indicated. The results are discussed in relation to the high-vorticity regions (here described as ‘sinews’) observed in many direct numerical simulations of turbulence.

A numerical study of the transition of jet diffusion flames

1990 ◽  
Vol 431 (1882) ◽  
pp. 301-314 ◽  
Keyword(s):  
Reynolds Number ◽  
Diffusion Coefficient ◽  
Large Scale ◽  
Numerical Study ◽  
Small Scale ◽  
Surface Model ◽  
Flame Surface ◽  
Transition Mechanism ◽  
Air Stream ◽  
Scale Fluctuation

A numerical study on the transition from laminar to turbulent of two-dimensional fuel jet flames developed in a co-flowing air stream was made by adopting the flame surface model of infinite chemical reaction rate and unit Lewis number. The time dependent compressible Navier–Stokes equation was solved numerically with the equation for coupling function by using a finite difference method. The temperature-dependence of viscosity and diffusion coefficient were taken into account so as to study effects of increases of these coefficients on the transition. The numerical calculation was done for the case when methane is injected into a co-flowing air stream with variable injection Reynolds number up to 2500. When the Reynolds number was smaller than 1000 the flame, as well as the flow, remained laminar in the calculated domain. As the Reynolds number was increased above this value, a transition point appeared along the flame, downstream of which the flame and flow began to fluctuate. Two kinds of fluctuations were observed, a small scale fluctuation near the jet axis and a large scale fluctuation outside the flame surface, both of the same origin, due to the Kelvin–Helmholtz instability. The radial distributions of density and transport coefficients were found to play dominant roles in this instability, and hence in the transition mechanism. The decreased density in the flame accelerated the instability, while the increase in viscosity had a stabilizing effect. However, the most important effect was the increase in diffusion coefficient. The increase shifted the flame surface, where the large density decrease occurs, outside the shear layer of the jet and produced a thick viscous layer surrounding the jet which effectively suppressed the instability.

scholarly journals Chiral perturbation theory for GR

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Kirill Krasnov ◽  
Yuri Shtanov
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation ◽  
Perturbative Calculation ◽  
New Formalism ◽  
Yang Mills ◽  
First Order ◽  
Starting Point ◽  
Gauge Fixing ◽  
New Perturbation ◽  
Effective Description

Abstract We describe a new perturbation theory for General Relativity, with the chiral first-order Einstein-Cartan action as the starting point. Our main result is a new gauge-fixing procedure that eliminates the connection-to-connection propagator. All other known first-order formalisms have this propagator non-zero, which significantly increases the combinatorial complexity of any perturbative calculation. In contrast, in the absence of the connection-to-connection propagator, our formalism leads to an effective description in which only the metric (or tetrad) propagates, there are only cubic and quartic vertices, but some vertex legs are special in that they cannot be connected by the propagator. The new formalism is the gravity analog of the well-known and powerful chiral description of Yang-Mills theory.

Radial lift on a suspended finite-sized sphere due to fluid inertia for low-Reynolds-number flow through a cylinder

2013 ◽  
Vol 722 ◽  
pp. 159-186 ◽  
Author(s):  
Sukalyan Bhattacharya ◽  
Dil K. Gurung ◽  
Shahin Navardi
Keyword(s):  
Reynolds Number ◽  
Particle Diameter ◽  
Axial Direction ◽  
Perturbation Scheme ◽  
Fluid Inertia ◽  
Regular Perturbation ◽  
Cross Sectional ◽  
First Order ◽  
Reynolds Number Flow ◽  
Freely Suspended

AbstractThis article describes the radial drift of a suspended sphere in a cylinder-bound Poiseuille flow where the Reynolds number is small but finite. Unlike past studies, it considers a circular narrow conduit whose cross-sectional diameter is only $1. 5$–$6$ times the particle diameter. Thus, the analysis quantifies the effect of fluid inertia on the radial motion of the particle in the channel when the flow field is significantly influenced by the presence of the suspended body. To this end, the hydrodynamic fields are expanded as a series in Reynolds number, and a set of hierarchical equations for different orders of the expansion is derived. Accordingly, the zeroth-order fields in Reynolds number satisfy the Stokes equation, which is accurately solved in the presence of the spherical particle and the cylindrical conduit. Then, recognizing that in narrow vessels Stokesian scattered fields from the sphere decrease exponentially in the axial direction, a simpler regular perturbation scheme is used to quantify the first-order inertial correction to hydrodynamic quantities. Consequently, it is possible to obtain two results. First, the sphere is assumed to follow the axial motion of a freely suspended sphere in a Stokesian condition, and the radial lift force on it due to the presence of fluid inertia is evaluated. Then, the approximate motion is determined for a freely suspended body on which net hydrodynamic force including first-order inertial lift is zero. The results agree well with the available experimental results. Thus, this study along with the measured data would precisely describe particle dynamics inside narrow tubes.

Vortex-Induced Vibrations of a Cylinder at Subcritical Reynolds Number

2011 ◽  
Author(s):  
Yoann Jus ◽  
Elisabeth Longatte ◽  
Jean-Camille Chassaing ◽  
Pierre Sagaut
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Numerical Study ◽  
Damping Ratio ◽  
Experimental Studies ◽  
Cross Flow ◽  
Physical Analysis ◽  
Arbitrary Lagrangian Eulerian ◽  
Vortex Induced Vibrations ◽  
Low Mass

The present work focusses on the numerical study of Vortex-Induced Vibrations (VIV) of an elastically mounted cylinder in a cross flow at moderate Reynolds numbers. Low mass-damping experimental studies show that the dynamic behavior of the cylinder exhibits a three-branch response model, depending on the range of the reduced velocity. However, few numerical simulations deal with accurate computations of the VIV amplitudes at the lock-in upper branch of the bifurcation diagram. In this work, the dynamic response of the cylinder is investigated by means of three-dimensional Large Eddy Simulation (LES). An Arbitrary Lagrangian Eulerian framework is employed to account for fluid solid interface boundary motion and grid deformation. Numerous numerical simulations are performed at a Reynolds number of 3900 for both no damping and low-mass damping ratio and various reduced velocities. A detailed physical analysis is conducted to show how the present methodology is able to capture the different VIV responses.

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