scholarly journals Unsteady low Reynolds number flow in a heated tube of slowly varying section

1988 ◽  
Vol 30 (2) ◽  
pp. 179-202 ◽  
Author(s):  
A. R. Bestman
Keyword(s):  
Fluid Motion ◽  
The Body ◽  
Axial Component ◽  
Axial Distance ◽  
Mean Flow ◽  
Steady Streaming ◽  
Reynolds Number Flow ◽  
Number Flow ◽  
The Mean ◽  
Oscillatory Pressure

AbstractFluid motion established by an oscillatory pressure gradient superimposed on a mean, in a tube of slowly varying section, is studied when the temperature of the tube wall varies with axial distance. Particular attention is focussed on the mean flow and steady streaming components of the oscillatory flow of higher approximation. For the velocity components, the axial component takes the pride of place, since this component is responsible for convection of nutrients to various parts of the body of a mammal in systematic circulation. A salient point in the paper concerns consequences of free convection currents at a constriction (stenosis).

The drag on a cloud of spherical particles in low Reynolds number flow

1969 ◽  
Vol 38 (3) ◽  
pp. 537-546 ◽  
Author(s):  
Christopher K. W. Tam
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
Fluid Motion ◽  
Spherical Particles ◽  
Mean Flow ◽  
Flow Equations ◽  
Low Reynolds Number Flow ◽  
Reynolds Number Flow ◽  
Number Flow ◽  
Low Reynolds

A formula for the drag exerted on a cloud of spherical particles of a given particle size distribution in low Reynolds number flow is derived. It is found that the drag experienced by a particle depends only on the first three moments of the distribution function. A treatment of viscous interaction betweenNparticles to the lowest order is carried out systematically. By appealing to the concept of ‘randomness’ of the particle cloud, equations describing the averaged properties of the fluid motion are derived. The averages are formed over a statistical ensemble of particle configurations. These mean flow equations so obtained are in a form resembling a generalized version of Darcy's empirical equation for the motion of fluid in a porous medium. The physical meaning of these equations is discussed.

Unsteady disturbances of streaming motions around bodies

1989 ◽  
Vol 209 ◽  
pp. 385-403 ◽  
Author(s):  
H. M. Atassi ◽  
J. Grzedzinski
Keyword(s):  
Wave Equation ◽  
Body Surface ◽  
Source Term ◽  
The Body ◽  
Entire Body ◽  
Two Dimensional ◽  
Mean Flow ◽  
Inhomogeneous Wave ◽  
Inhomogeneous Wave Equation ◽  
The Mean

For small-amplitude vortical and entropic unsteady disturbances of potential flows, Goldstein proposed a partial splitting of the velocity field into a vortical part u(I) that is a known function of the imposed upstream disturbance and a potential part ∇ϕ satisfying a linear inhomogeneous wave equation with a dipole-type source term. The present paper deals with flows around bodies with a stagnation point. It is shown that for such flows u(I) becomes singular along the entire body surface and its wake and as a result ∇ϕ will also be singular along the entire body surface. The paper proposes a modified splitting of the velocity field into a vortical part u(R) that has zero streamwise and normal components along the body surface, an entropy-dependent part and a regular part ∇ϕ* that satisfies a linear inhomogeneous wave equation with a modified source term.For periodic disturbances, explicit expressions for u(R) are given for three-dimensional flows past a single obstacle and for two-dimensional mean flows past a linear cascade. For weakly sheared flows, it is shown that if the mean flow has only a finite number of isolated stagnation points, u(R) will be finite along the body surface. On the other hand, if the mean flow has a stagnation line along the body surface such as in two-dimensional flows then the component of u(R) in this direction will have a logarithmic singularity.For incompressible flows, the boundary-value problem for ϕ* is formulated in terms of an integral equation of the Fredholm type. The theory is applied to a typical bluff body. Detailed calculations are carried out to show the velocity and pressure fields in response to incident harmonic disturbances.

scholarly journals The Effect of Surface Roughness of a Body in the High Reynolds-Number Flow

1995 ◽  
Vol 2 (1) ◽  
pp. 23-32
Author(s):  
Tsutomu adachi
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
The Body ◽  
Reynolds Number Flow ◽  
Flow Phenomena ◽  
Number Flow ◽  
High Reynolds ◽  
Cryogenic Wind Tunnel ◽  
Effect Of Surface

In this paper, first, the principle, structures, operations, and performances of the cryogenic wind tunnel are described. By changing the pressure, temperature and velocity of gas a high Reynolds-number flow(5×104<Re<107)can be obtained. From the research results, a high Reynolds-number flow with comparatively low power, LN consumptions was attained. It was with Mach-number independent of each other, o show some examples of high Reynolds-number flow, the effects of surface roughness and grooves on the surface of a cylinder on the flow are measured using models with various values of roughness and size. A model test of an airship was also conducted. With the high Reynolds-number flow, the thickness of the boundary layer becomes thinner. Then the surface conditions of a body have great effect on the flow phenomena and on the drag of the body. Some attempts to reduce the drag of the body were shown.

Effect of Upstream Flow Processes on Hydrodynamic Development in a Duct

1977 ◽  
Vol 99 (3) ◽  
pp. 556-560 ◽  
Author(s):  
E. M. Sparrow ◽  
C. E. Anderson
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Center Line ◽  
Viscous Effects ◽  
Mean Velocity ◽  
Inertia Effects ◽  
Reynolds Number Flow ◽  
Compact Size ◽  
Number Flow ◽  
The Mean

Consideration is given to the developing laminar flow in a parallel plate channel, with the fluid being drawn from a large upstream space. The flow fields upstream and downstream of the channel inlet were solved simultaneously. A finite-difference technique was employed which was facilitated by a coordinate transformation that telescoped the broadly extended flow domain into a more compact size. For the solutions, the Reynolds number was assigned values from 1 to 1000, covering the range from viscous-dominated flows to those where both viscous and inertia effects are relevant. Streamline maps indicate that whereas a low Reynolds number flow glides smoothly into the channel, a high Reynolds number flow has to turn sharply to enter the channel, with the result that the sharply turning fluid tends to overshoot at first and then readjust. A significant amount of upstream predevelopment occurs at low and intermediate Reynolds numbers. Thus, for example, at Re = 1 and 100, the center-line velocities at inlet are, respectively, 1.37 and 1.13 times the mean velocity (the fully developed center-line velocity is 1.5 times the mean). The upstream pressure drop, measured in terms of the velocity head, is substantially increased by viscous effects at low and intermediate Reynolds numbers.

The hybrid Euler–Lagrange procedure using an extension of Moffatt's method

2010 ◽  
Vol 661 ◽  
pp. 45-72 ◽  
Author(s):  
A. M. SOWARD ◽  
P. H. ROBERTS
Keyword(s):  
Fluid Dynamic ◽  
Fluid Motion ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Constant Density ◽  
Mean Flow ◽  
Tensor Calculus ◽  
Inviscid Incompressible Fluid ◽  
Large Eddy ◽  
The Mean

The hybrid Euler–Lagrange (HEL) description of fluid mechanics, pioneered largely by Andrews & McIntyre (J. Fluid Mech., vol. 89, 1978, pp. 609–646), has had to face the fact, in common with all Lagrangian descriptions of fluid motion, that the variables used do not describe conditions at the coordinate x, upon which they depend, but conditions elsewhere at some displaced position xL(x, t) = x + ξ(x, t), generally dependent on time t. To address this issue, we employ ‘Lie dragging’ techniques of general tensor calculus to extend a method introduced by Moffatt (J. Fluid Mech., vol. 166, 1986, pp. 359–378) in the fluid dynamic context, whereby the point x is dragged to xL(x, t) by a ‘fictitious steady flow’ η*(x, t) in a unit of ‘fictitious time’. Whereas ξ(x, t) is a Lagrangian concept intimately linked to the location xL(x, t), the ‘dragging velocity’ η*(x, t) has an essentially Eulerian character, because it describes the fictitious velocity at x itself. For the case of constant-density fluids, we show, using solenoidal η*(x, t) instead of solenoidal ξ(x, t), how the HEL theory can be cast into Eulerian form. A useful aspect of this Eulerian development is that the mean flow itself remains solenoidal, a feature that traditional HEL theories lack. Our method realizes the objective sought by Holm (Physica D, vol. 170, 2002, pp. 253–286) in his derivation of the Navier–Stokes–α equation, which is the basis of one of the methods currently employed to represent the sub-grid scales in large-eddy simulations. His derivation, based on expansion to second order in ξ, contained an error which, when corrected, implied a violation of Kelvin's theorem on the constancy of circulation in inviscid incompressible fluid. We show that this is rectified when the expansion is in η* rather than ξ, Kelvin's theorem then being satisfied to all orders for which the expansion converges. We discuss the implications of our approach using η* for the Navier–Stokes–α theory.

On the theory of unsteady high Reynolds number flow through a circular aperture

1979 ◽  
Vol 366 (1725) ◽  
pp. 205-223 ◽  
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
High Reynolds Number ◽  
Circular Aperture ◽  
Mean Flow ◽  
Reynolds Number Flow ◽  
Contraction Ratio ◽  
Number Flow ◽  
Flow Through ◽  
High Reynolds

This paper examines the theory of the unsteady motion caused by fluctuations in the driving pressure of a high Reynolds number mean flow through a circular aperture in a thin rigid plate. A theoretical model is proposed which is amenable to exact analytical treatment, and involves the shedding of vorticity from the rim of the aperture. The theory determines the dependence of the Rayleigh conductivity of the aperture on the Strouhal number, and provides quantitative estimates for the rate of dissipation of large scale ordered structures as a result of the generation of turbulence at the apertures in a perforated liner. The limit of zero Strouhal number yields a description of steady high Reynolds number flow, the contraction ratio of the emerging jet being predicted to be equal to the minimum theoretical value of ½. Application is made to the problem of sound trans­mission through a uniformly perforated screen in the presence of a low Mach number bias flow.

Trapped-wave modes of bodies in channels

2016 ◽  
Vol 812 ◽  
pp. 178-198 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Fluid Motion ◽  
Open Water ◽  
The Body ◽  
Finite Width ◽  
Trapped Waves ◽  
Trapped Mode ◽  
Trapped Wave ◽  
Different Types ◽  
Body Shapes ◽  
Oscillatory Pressure

Trapped waves can exist in the presence of bodies in open water, and also in channels of finite width. Various examples are found for bodies that support trapped waves in channels, including floating and submerged bodies and bottom-mounted cylinders. Different types of trapping are considered where the body is fixed or free to move in response to the oscillatory pressure. In some cases both types are supported by the same body. In most cases for fixed bodies the fluid motion is antisymmetric about the centreline of the channel, but special body shapes exist where the trapped mode is asymmetric. For free bodies the trapping modes and body motions are symmetric about the centreline if the body is floating or antisymmetric if it is submerged.

scholarly journals Bluff bodies in deep turbulent boundary layers: Reynolds-number issues

2007 ◽  
Vol 571 ◽  
pp. 97-118 ◽  
Author(s):  
HEE CHANG LIM ◽  
IAN P. CASTRO ◽  
ROGER P. HOXEY
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Delta Wing ◽  
Body Height ◽  
Turbulent Boundary Layers ◽  
The Body ◽  
Bluff Bodies ◽  
Mean Flow ◽  
Order Of Magnitude ◽  
The Mean

It is generally assumed that flows around wall-mounted sharp-edged bluff bodies submerged in thick turbulent boundary layers are essentially independent of the Reynolds number Re, provided that this exceeds some (2–3) × 104. (Re is based on the body height and upstream velocity at that height.) This is a particularization of the general principle of Reynolds-number similarity and it has important implications, most notably that it allows model scale testing in wind tunnels of, for example, atmospheric flows around buildings. A significant part of the literature on wind engineering thus describes work which implicitly rests on the validity of this assumption. This paper presents new wind-tunnel data obtained in the ‘classical’ case of thick fully turbulent boundary-layer flow over a surface-mounted cube, covering an Re range of well over an order of magnitude (that is, a factor of 22). The results are also compared with new field data, providing a further order of magnitude increase in Re. It is demonstrated that if on the one hand the flow around the obstacle does not contain strong concentrated-vortex motions (like the delta-wing-type motions present for a cube oriented at 45° to the oncoming flow), Re effects only appear on fluctuating quantities such as the r.m.s. fluctuating surface pressures. If, on the other hand, the flow is characterized by the presence of such vortex motions, Re effects are significant even on mean-flow quantities such as the mean surface pressures or the mean velocities near the surfaces. It is thus concluded that although, in certain circumstances and for some quantities, the Reynolds-number-independency assumption is valid, there are other important quantities and circumstances for which it is not.

Sign in / Sign up

Export Citation Format

Share Document