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.

Effect of wall-mounted V-baffle position in a turbulent flow through a channel

2019 ◽  
Vol 29 (10) ◽  
pp. 3908-3937 ◽  
Author(s):  
Younes Menni ◽  
Ahmed Azzi ◽  
Ali J. Chamkha ◽  
Souad Harmand
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Simple Algorithm ◽  
Two Dimensions ◽  
Large Reynolds Number ◽  
Constant Property ◽  
Content Type

Purpose The purpose of this paper is to carry out a numerical study on the dynamic and thermal behavior of a fluid with a constant property and flowing turbulently through a two-dimensional horizontal rectangular channel. The upper surface was put in a constant temperature condition, while the lower one was thermally insulated. Two transverse, solid-type obstacles, having different shapes, i.e. flat rectangular and V-shaped, were inserted into the channel and fixed to the top and bottom walls of the channel, in a periodically staggered manner to force vortices to improve the mixing, and consequently the heat transfer. The flat rectangular obstacle was put in the first position and was placed on the hot top wall of the channel. However, the second V-shaped obstacle was placed on the insulated bottom wall, at an attack angle of 45°; its position was varied to find the optimum configuration for optimal heat transfer. Design/methodology/approach The fluid is considered Newtonian, incompressible with constant properties. The Reynolds averaged Navier–Stokes equations, along with the standard k-epsilon turbulence model and the energy equation, are used to control the channel flow model. The finite volume method is used to integrate all the equations in two-dimensions; the commercial CFD software FLUENT along with the SIMPLE-algorithm is used for pressure-velocity coupling. Various values of the Reynolds number and obstacle spacing were selected to perform the numerical runs, using air as the working medium. Findings The channel containing the flat fin and the 45° V-shaped baffle with a large Reynolds number gave higher heat transfer and friction loss than the one with a smaller Reynolds number. Also, short separation distances between obstacles provided higher values of the ratios Nu/Nu0 and f/f0 and a larger thermal enhancement factor (TEF) than do larger distances. Originality/value This is an original work, as it uses a novel method for the improvement of heat transfer in completely new flow geometry.

Numerical Study on the Heat Transfer Characteristic in Periodical Variable Cross-Section Channel

2011 ◽  
Vol 243-249 ◽  
pp. 4935-4938
Author(s):  
Li Li ◽  
Xiao Ze Du
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Cross Section ◽  
Heat Transfer Characteristic ◽  
Numerical Study ◽  
Transfer Characteristic ◽  
Variable Cross Section ◽  
Central Line ◽  
Large Reynolds Number ◽  
Variable Cross

The heat transfer characteristic through periodical variable cross-section passage is studied with numerical scheme. The results in multi-period variable cross-section channel show that the heat transfer enhancement can be obtained by forming flow destabilization at large Reynolds number. The parameters include pressure, velocity, temperature in the channel are symmetric about central line at low Reynolds number, then change to asymmetric at high Reynolds number. The variations occur firstly at the downstream near outlet of the channel and move upstream, which could improve the fluid mixing to increase the enhancement of heat transfer in channel.

scholarly journals When is high Reynolds number shear flow not turbulent?

2017 ◽  
Vol 824 ◽  
pp. 1-4 ◽  
Author(s):  
Steven A. Balbus
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
High Reynolds Number ◽  
Laboratory Experiments ◽  
Numerical Study ◽  
Accretion Discs ◽  
Large Reynolds Number ◽  
Rotating Flow ◽  
General Tendency ◽  
High Reynolds

Rotating flow in which the angular velocity decreases outward while the angular momentum increases is known as ‘quasi-Keplerian’. Despite the general tendency of shear flow to break down into turbulence, this type of flow seems to maintain stability at very large Reynolds number, even when nonlinearly perturbed, a behaviour that strongly influences our understanding of astrophysical accretion discs. Investigating these flows in the laboratory is difficult because secondary Ekman flows, caused by the retaining Couette cylinders, can become turbulent on their own. A recent high Reynolds number numerical study by Lopez & Avila (J. Fluid Mech., vol. 817, 2017, pp. 21–34) reconciles apparently discrepant laboratory experiments by confirming that this secondary flow recedes toward the axial boundaries of the container as the Reynolds number is increased, a result that enhances our understanding of nonlinear quasi-Keplerian flow stability.

Numerical study of three-dimensional Kolmogorov flow at high Reynolds numbers

1996 ◽  
Vol 306 ◽  
pp. 293-323 ◽  
Author(s):  
Vadim Borue ◽  
Steven A. Orszag
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Large Reynolds Number ◽  
Kolmogorov Flow ◽  
Turbulence Decay ◽  
High Reynolds

High-resolution numerical simulations (with up to 2563 modes) are performed for three-dimensional flow driven by the large-scale constant force fy = F cos(x) in a periodic box of size L = 2π (Kolmogorov flow). High Reynolds number is attained by solving the Navier-Stokes equations with hyperviscosity (-1)h+1Δh (h = 8). It is shown that the mean velocity profile of Kolmogorov flow is nearly independent of Reynolds number and has the ‘laminar’ form vy = V cos(x) with a nearly constant eddy viscosity. Nevertheless, the flow is highly turbulent and intermittent even at large scales. The turbulent intensities, energy dissipation rate and various terms in the energy balance equation have the simple coordinate dependence a + b cos(2x) (with a, b constants). This makes Kolmogorov flow a good model to explore the applicability of turbulence transport approximations in open time-dependent flows. It turns out that the standard expression for effective (eddy) viscosity used in K-[Escr ] transport models overpredicts the effective viscosity in regions of high shear rate and should be modified to account for the non-equilibrium character of the flow. Also at large scales the flow is anisotropic but for large Reynolds number the flow is isotropic at small scales. The important problem of local isotropy is systematically studied by measuring longitudinal and transverse components of the energy spectra and crosscorrelation spectra of velocities and velocity-pressure-gradient spectra. Cross-spectra which should vanish in the case of isotropic turbulence decay only algebraically but somewhat faster than corresponding isotropic correlations. It is verified that the pressure plays a crucial role in making the flow locally isotropic. It is demonstrated that anisotropic large-scale flow may be considered locally isotropic at scales which are approximately ten times smaller than the scale of the flow.

Effect of large bulk viscosity on large-Reynolds-number flows

2014 ◽  
Vol 751 ◽  
pp. 142-163 ◽  
Author(s):  
M. S. Cramer ◽  
F. Bahmani
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Bulk Viscosity ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Large Reynolds Number ◽  
Steady Flows ◽  
Outer Flow ◽  
First Order ◽  
Large Bulk

AbstractWe examine the inviscid and boundary-layer approximations in fluids having bulk viscosities which are large compared with their shear viscosities for three-dimensional steady flows over rigid bodies. We examine the first-order corrections to the classical lowest-order inviscid and laminar boundary-layer flows using the method of matched asymptotic expansions. It is shown that the effects of large bulk viscosity are non-negligible when the ratio of bulk to shear viscosity is of the order of the square root of the Reynolds number. The first-order outer flow is seen to be rotational, non-isentropic and viscous but nevertheless slips at the inner boundary. First-order corrections to the boundary-layer flow include a variation of the thermodynamic pressure across the boundary layer and terms interpreted as heat sources in the energy equation. The latter results are a generalization and verification of the predictions of Emanuel (Phys. Fluids A, vol. 4, 1992, pp. 491–495).

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.

A higher order theory for compressible turbulent boundary layers at moderately large Reynolds number

1973 ◽  
Vol 57 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Noor Afzal
Keyword(s):  
Reynolds Number ◽  
Viscous Dissipation ◽  
Order Theory ◽  
Higher Order ◽  
Second Order ◽  
Large Reynolds Number ◽  
Law Of The Wall ◽  
First Order ◽  
The Law ◽  
Higher Order Theory

A higher order theory for two-dimensional turbulent boundary-layer flow of a compressible fluid past a plane wall is formulated, for moderately large values of the Reynolds number, by the method of matched asymptotic expansions. The parameters (γ − 1) M2∞and the molecular Prandtl number are assumed to be of order unity. The analysis deals with the set of Reynolds equations of mean motion (which are underdetermined without an additional set of closure hypotheses) and assumes that the non-dimensional fluctuations in velocity, temperature and density are of orderU*, (friction velocity divided by free-stream velocity a t some designation point), while fluctuations in pressure are of orderU2*.The first-order results of the present study lead to asymptotic laws for velocity and temperature distributions which correspond to the law of the wall, logarithmic law and defect law, and also to skin friction and heat-transfer laws. It turns out that the first-order defect law depends upon the gradient of entropy and stagnation enthalpy and the law of the wall is independent of viscous dissipation. The second-order terms of the present work (accounting for mean convection due to turbulent mass flux, viscous dissipation in the inner flow and displacement effects in the outer flow) describe the necessary corrections to first-order terms due to low Reynolds number effects. In the overlap region the second-order results, for the law of the wall and the defect law, show bilogarithmic terms along with logarithmic terms.

scholarly journals Elliptic instability in a strained Batchelor vortex

2007 ◽  
Vol 577 ◽  
pp. 341-361 ◽  
Author(s):  
LAURENT LACAZE ◽  
KRIS RYAN ◽  
STÉPHANE LE DIZÈS
Keyword(s):  
Reynolds Number ◽  
Strain Field ◽  
Flow Parameter ◽  
Numerical Study ◽  
Normal Modes ◽  
Axial Flow ◽  
Base Flow ◽  
Large Reynolds Number ◽  
Resonant Coupling ◽  
Flow Parameters

The elliptic instability of a Batchelor vortex subject to a stationary strain field is considered by theoretical and numerical means in the regime of large Reynolds number and small axial flow. In the theory, the elliptic instability is described as a resonant coupling of two quasi-neutral normal modes (Kelvin modes) of the Batchelor vortex of azimuthal wavenumbers m and m + 2 with the underlying strain field. The growth rate associated with these resonances is computed for different values of the azimuthal wavenumbers as the axial flow parameter is varied. We demonstrate that the resonant Kelvin modes m = 1 and m = −1 which are the most unstable in the absence of axial flow become damped as the axial flow is increased. This is shown to be due to the appearance of a critical layer which damps one of the resonant Kelvin modes. However, the elliptic instability does not disappear. Other combinations of Kelvin modes m = −2 and m = 0, then m = −3 and m = −1 are shown to become progressively unstable for increasing axial flow. A complete instability diagram is obtained as a function of the axial flow parameter for several values of the strain rate and Reynolds number.The numerical study considers a system of two counter-rotating Batchelor vortices in which the strain field felt by each vortex is due to the other vortex. The characteristics of the most unstable linear modes developing on the frozen base flow are computed by direct numerical simulations for two axial flow parameters and compared to the theory. In both cases, a very good agreement is obtained for the most unstable modes. Less unstable modes are also identified in the numerics and shown to correspond to peculiar resonances involving Kelvin modes from branches of different labels.

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