bluuebunny/crossref_metadata_2025_split huggingface dataset:
A critical-layer analysis of the resonant triad in boundary-layer transition: nonlinear interactions
Authors: Mankbadi Reda R. , Wu Xuesong , Lee Sang Soo 
Published: April 2006

A systematic theory is developed to study the nonlinear spatial evolution of the resonant triad in Blasius boundary layers. This triad consists of a plane wave at the fundamental frequency and a pair of symmetrical, oblique waves at the subharmonic frequency. A low-frequency asymptotic scaling leads to a distinct critical layer wherein nonlinearity first becomes important, and the critical layer's nonlinear, viscous dynamics determine the development of the triad.The plane wave initially causes double-exponential growth of the oblique waves. The plane wave, however, continues to follow the linear theory, even when the oblique waves’ amplitude attains the same order of magnitude as that of the plane wave. However, when the amplitude of the oblique waves exceeds that of the plane wave by a certain level, a nonlinear stage comes into effect in which the self-interaction of the oblique waves becomes important. The self-interaction causes rapid growth of the phase of the oblique waves, which causes a change of the sign of the parametric-resonance term in the oblique-waves amplitude equation. Ultimately this effect causes the growth rate of the oblique waves to oscillate around their linear growth rate. Since the latter is usually small in the nonlinear regime, the net outcome is that the self-interaction of oblique waves causes the parametric resonance stage to be followed by an ‘oscillatory’ saturation stage.
The one-dimensional adiabatic flow of equilibrium gas–particle mixtures in variable-area ducts with friction
Authors: Buresti Guido , Casarosa Claudio 
Published: April 2006

A general one-dimensional model for the steady adiabatic motion of gas-particle mixtures in arbitrarily oriented ducts with gradually varying cross-section and wall friction is presented. The particles are assumed to be incompressible and in thermomechanical equilibrium with a perfect gas phase, and the effects of their finite volume and of gravity are also taken into account.The equations of motion are written in a form that allows a theoretical analysis of the behaviour of the solutions to be carried out. In particular, the results of the application to the model of a procedure that permits the identification and the topological classification of the singular points of the trajectories representing, in a suitable phase space, the solutions of the set of equations defining the problem are described. This characterization of the singular points is useful in order to overcome difficulties in the numerical integration of the equations.Subsequently, a geometrical analysis is carried out which allows a study of the signs of the local variations of the flow quantities, and shows that some unusual behaviour may occur if certain geometrical and fluid dynamic conditions are fulfilled. For instance, in an upward motion it is possible to have a simultaneous decrease of velocity, pressure and temperature, while in a downward flow an increase of all these quantities may be found. It is also shown that conditions exist in which expansion and heating of the mixture may take place simultaneously, both in accelerating and decelerating flows.The model is applied to the study of upward motion in particular ducts, having converging-diverging and constant-diverging cross-sections; to this end the equations are integrated numerically by using the Mach number as the independent variable. The results show that even limited variations of the duct diameter may give rise to significant qualitative and quantitative variations in the flow conditions inside the duct and in the mass flow rate. Finally, an example is given of a subsonic downward flow in which a simultaneous increase of pressure, temperature and velocity occurs even in the case of a pure perfect gas.
A new mechanism for oblique wave resonance in the ‘natural’ far wake
Authors: Williamson C. H. K. , Prasad A. 
Published: April 2006

There has been some debate recently on whether the far-wake structure downstream of a cylinder is dependent on, or ‘connected’ with, the precise details of the near-wake structure. Indeed, it has previously been suggested that the far-wake scale and frequency are unconnected with those of the near wake. In the present paper, we demonstrate that both the far-wake scale and frequency are dependent on the near wake. Surprisingly, the characteristic that actually forges a ‘connection’ between the near and far wakes is the sensitivity to free-stream disturbances. It is these disturbances that are also responsible for the regular three-dimensional patterns that may be visualized. Observations of a regular ‘honeycomb’-like three-dimensional pattern in the far wake is found to be caused by an interaction between oblique shedding waves from upstream and large-scale two-dimensional waves, amplified from the free-stream disturbances. The symmetry and spanwise wavelength of Cimbala, Nagib & Roshko's (1988) three-dimensional pattern are precisely consistent with such wave interactions. In the presence of parallel shedding, the lack of a honeycomb pattern shows that such a three-dimensional pattern is clearly dependent on upstream oblique vortex shedding.With the deductions above as a starting point, we describe a new mechanism for the resonance of oblique waves, as follows. In the case of two-dimensional waves, corresponding to a very small spectral peak in the free stream (fT) interacting (quadratically) with the oblique shedding waves frequency (fK), it appears that the most amplified or resonant frequency in the far wake is a combination frequency fFW = (fK–fT), which corresponds physically with ‘oblique resonance waves’ at a large oblique angle. The large scatter in (fFW/fK) from previous studies is principally caused by the broad response of the far wake to a range of free-stream spectral peaks (fT). We present clear visualization of the oblique wave phenomenon, coupled with velocity measurements which demonstrate that the secondary oblique wave energy can far exceed the secondary two-dimensional wave energy by up to two orders of magnitude. Further experiments show that, in the absence of an influential free-stream spectral peak, the far wake does not resonate, but instead has a low-amplitude broad spectral response. The present phenomena are due to nonlinear instabilities in the far wake, and are not related to vortex pairing. There would appear to be distinct differences between this oblique wave resonance and the subharmonic resonances that have been previously studied in channel flow, boundary layers, mixing layers and airfoil wakes.
Axially invariant laminar flow in helical pipes with a finite pitch
Authors: Liu Shijie , Masliyah Jacob H. 
Published: April 2006

Steady axially invariant (fully developed) incompressible laminar flow of a Newtonian fluid in helical pipes of constant circular cross-section with arbitrary pitch and arbitrary radius of coil is studied. A loose-coiling analysis leads to two dominant parameters, namely Dean number, Dn = Reλ½, and Germano number, Gn = Reη, where Re is the Reynolds number, λ is the normalized curvature ratio and η is the normalized torsion. The Germano number is embedded in the body-centred azimuthal velocity which appears as a group in the governing equations. When studying Gn effects on the helical flow in terms of the secondary flow pattern or the secondary flow structure viewed in the generic (non-orthogonal) coordinate system of large Dn, a third dimensionless group emerges, γ = η/(λDn)½. For Dn < 20, the group γ* = Gn Dn-2 = η/(λRe) takes the place of γ.Numerical simulations with the full Navier-Stokes equations confirmed the theoretical findings. It is revealed that the effect of torsion on the helical flow can be neglected when γ ≤ 0.01 for moderate Dn. The critical value for which the secondary flow pattern changes from two vortices to one vortex is γ* > 0.039 for Dn < 20 and γ > 0.2 for Dn ≥ 20. For flows with fixed high Dean number and A, increasing the torsion has the effect of changing the relative position of the secondary flow vortices and the eventual formation of a flow having a Poiseuille-type axial velocity with a superimposed swirling flow. In the orthogonal coordinate system, however, the secondary flow generally has two vortices with sources and sinks. In the small-γ limit or when Dn is very small, the secondary flow is of the usual two-vortex type when viewed in the orthogonal coordinate system. In the large-γ limit, the appearance of the secondary flow in the orthogonal coordinate system is also two-vortex like but its orientation is inclined towards the upper wall. The flow friction factor is correlated to account for Dn, A and γ effects for Dn ≤ 5000 and γ < 0.1.
Instability of stratified fluid in a vertical cylinder
Authors: Batchelor G. K. , Nitsche J. M. 
Published: April 2006

In a previous paper we analysed the stability to small disturbances of stationary stratified fluid which is unbounded. Various forms of the undisturbed density distribution were considered, including a sinusoidal profile and a function of the vertical coordinate z which is constant outside a central horizontal layer. Both these types of stratification are so unstable that the critical Rayleigh number is zero. In this sequel we make the study more complete and more useful by taking account of the effect of a vertical circular cylindrical boundary of radius a which is rigid and impermeable. As in the previous paper we assume that the undisturbed density distribution is steady.The case of fluid in a vertical tube with a uniform density gradient is useful for comparison, and so we review and extend the available results, in particular obtaining growth rates for a disturbance which is neither z-independent nor axisymmetric. A numerical finite-difference method is then developed for the case in which dρ/dz = ρ0kA cos kz. When ka [Lt ] 1 the relation between growth rate and Rayleigh number approximates to that for a uniform density gradient of magnitude ρ0kA; and when ka [Gt ] 1 the tilting-sliding mechanism identified in the previous paper is relevant and the results approximate to those for an unbounded fluid, except that the smallest Rayleigh number for a neutral disturbance is not zero but is of order (ka-1. In the case of an undisturbed density which varies only in a central layer of thickness l, the same mechanism is at work when the horizontal lengthscale of the disturbance is large compared with l, resulting in high growth rates and a critical Rayleigh number which vanishes with l/a. Estimates of the growth rate are given for some particular density profiles.
The diode-array velocimeter
Authors: Devenport William J. , Smith Edward J. 
Published: April 2006

Diode-array velocimetry is an optical technique for measuring turbulent flows. It involves timing the passage of seed particles through a small section of a light beam by imaging the light they scatter onto one or more photodiode arrays. The arrays have a few carefully shaped elements, the shapes and positions of which are used to control the measurement-volume geometry and thus select the measurement made. Measurement volumes sensitive to velocity, position and acceleration may be designed. Measurements in highly turbulent and reversing flows are possible.A diode-array velocimeter (DAV) for one-component velocity measurements has been developed to demonstrate this concept. This uses a single laser beam to illuminate particles and a photodiode array with two rectangular elements to sense their motion. The sensitivity of this DAV to electrical noise in the photodiode circuitry decreases with reduction in measurement-volume size. The angle response is closely cosinusoidal to about 60°. Changes to the photodiode-array design could substantially increase this limit.Measurements of mean velocity, normal turbulence stress and velocity skewness made with this DAV in two attached boundary-layer flows compare well with hot-wire measurements. Useful DAV measurements were made as close as 0.2 mm from the wall. DAV measurements made in a separated flow formed downstream of a fence are also presented. These show all the expected features of the separated shear layer and recirculation including the sub-boundary layer formed beneath the backflow. Histograms measured in the reversing part of this flow show a hole near zero velocity that is a consequence of the imperfections in the DAV angle response and limitations on the maximum transit time. These are not fundamental problems, however, and the hole could be minimized or eliminated by using a different photodiode array design and/or measurement strategy.
The motion generated by a slowly rising disk in an unbounded rotating fluid for arbitrary Taylor number
Authors: Vedensky D. , Ungarish M. 
Published: April 2006

The motion of a disk rising steadily parallel to the axis of rotation in a uniformly rotating unbounded liquid is considered. In the limit of zero Rossby number the linear viscous equations of motion are reduced to a system of dual integral equations which renders an ‘exact’ solution for arbitrary values of the Taylor number, Ta. The investigation is focused on the drag and the flow field. In the limits of small and large Ta the asymptotic results of the present formulation agree with – and extend – previous investigations by different approaches.A particular novel feature, for large Ta, is the contribution of the Ekman-layer flux to the outer motion. New insight into the structure of the Taylor column is gained; in particular, it is shown that the main part of the column is a ‘bubble’ of recirculating fluid, detached from the body and not communicating with the Ekman layer. However, it turns out that the essential discrepancy in drag between experiments (Maxworthy 1970) and previous theories cannot be attributed to the Ekman-layer suction effect.
Electrophoretic motion of an arbitrary prolate body of revolution toward an infinite conducting wall
Authors: Feng Jian-Jun , WU Wang-YI 
Published: April 2006

The electrophoretic motion of an arbitrary prolate body of revolution perpendicular to an infinite conducting planar wall is investigated by a combined analytical–numerical method. The electric field is exerted normal to the conducting planar wall and parallel to the axis of revolution of the particle. The governing equations and boundary conditions are obtained under the assumption of electric double layer thin compared to the local particle curvature radius and the spacing between the particle and the boundary. The axisymmetrical electrostatic and hydrodynamic equations are solved by the method of distribution of singularities along a certain line segment on the axis of revolution inside the particle. The analytical expressions for fundamental singularities both of electrostatic and hydrodynamic equations in the presence of the infinite planar wall are derived. Employing a piecewise parabolic approximation for the density function and applying the boundary collocation method to satisfy the boundary conditions on the surface of the particle, a system of linear algebraic equations is obtained which can be solved by matrix reduction technique.Solutions for the electrophoretic velocity of the colloidal prolate spheroid are presented for various values ofa/banda/d, whereaandbare the major and minor axes of the particle respectively anddis the distance between the centre and the wall. Numerical tests show that convergence to at least four digits can be achieved. For the limiting cases ofa=bord→ ∞, our results agree quite well with the exact solutions of electrophoresis of a sphere moving perpendicularly to an infinite planar wall or of a prolate spheroid in an unbounded fluid. As expected, owing to the effect of the wall, the electrophoretic mobility of the particle decreases monotonically for a given spheroid as it gets closer to the wall. Another important feature is that the wall effect on electrophoresis will reduce with the increase of slenderness ratio of the prolate spheroid at the same value ofa/d. The boundary effect on the particle mobility and flow pattern in electrophoresis differ significantly from those of the corresponding sedimentation problem and the wall effect on the electrophoresis is much weaker than that on the sedimentation. In order to demonstrate the generality of the proposed method, the convergent results for prolate Cassini ovals are also given in the present paper.
An experimental investigation of concentrated suspension flows in a rectangular channel
Authors: Koh Christopher J. , Hookham Philip , Leal L. G. 
Published: April 2006

An experimental adaptation of the well-known laser-Doppler anemometry technique is developed for measuring the velocity and concentration profiles in concentrated suspension flows. To circumvent the problem of optical turbidity, the refractive indices of the solid and liquid phases are closely matched. The residual turbidity, owing to small mismatches of the refractive indices, as well as impurities in the particles, allows a Doppler signal to be detected when a particle passes through the scattering volume. By counting the number of Doppler signals in a period of time, the local volume fraction is also measured.This new technique is utilized to study concentrated suspension flows in a rectangular channel. The general behavior of the suspension is that the velocity profile is blunted while the concentration profile has a maximum near the centre. Comparisons are made with theoretical predictions based on the shear-induced particle migration theory.
On one-dimensional flow of a conducting gas between electrodes – with application to MHD thrusters
Authors: Cowley M. D. , Horlock J. H. 
Published: April 2006

Inviscid, adiabatic, one-dimensional flow of a conducting gas in the presence of crossed electric and magnetic fields is investigated for the case where the magnetic field is generated by the current being supplied to the gas. The electrode geometry and the connections to the electrical power supply are such that the magnetic field falls to zero at the downstream end of the MHD duct. The analysis allows for magnetic Reynolds number rm to be anywhere in the range 0 to ∞ The main part of the investigation is restricted to consideration of ducts with constant spacing between electrodes.The way in which the density of the gas varies along the duct with the changing magnetic field is analysed generally and the results are then applied to the case where gas is fed to the MHD duct from high pressure in a plenum chamber and where the duct exhausts to a region of negligible pressure. If the flow is choked by the converging entry to the duct and the magnetic Reynolds number is moderate to high, the main electromagnetic effect is for the j × B forces to accelerate the gas to supersonic speeds. As rm is reduced, ohmic heating becomes more important, and it may cause the flow to be choked at exit from the duct, giving rise to a reduction in mass flow. For certain ranges of rm and ratio of initial magnetic pressure to plenum-chamber pressure the flow may choke at a sonic point within the duct itself, while accelerating from subsonic to supersonic through the point.Some illustrative examples of how properties vary with distance along the duct have been computed and the consequences of the analysis for MHD thrusters are explored. The magnetic forces will augment thrust per unit cross-sectional area, the essential measure of this being the drop in magnetic pressure along the duct, but there is an upper limit on the ratio of magnetic pressure to plenum-chamber pressure for flows to be possible. Flow at low magnetic Reynolds number is favoured if the object is to increase specific thrust by reducing mass flow through the duct.
Evolution and breakup of vortex rings in straining and shearing flows
Authors: Marshall J. S. , Grant J. R. 
Published: April 2006

A study of the effect of external straining and shearing flows on the evolution and form of breakup of vortex rings has been performed. Two orientations each of straining and shearing flows are considered. A theoretical analysis of the ring motion for small strain and shear rates is performed, and it is found that for shearing and straining flows in the plane of the ring, the ring may oscillate periodically. For a straining flow with compression normal to the initial plane of the ring, the linear theory predicts that the ring radius will expand with time. For shearing flow normal to the initial plane of the ring, the linear theory predicts tilting of the ring in the direction of the shear flow rotation.Numerical calculations are performed with both single vortex filaments and with a three-dimensional discrete vortex element method. The numerical calculations confirm the predictions of the linear theory for values of strain and shear rates below a certain critical value (which depends on the ratio R/σ0 of initial ring to core radii), whereas for strain and shear rates above this value the ring becomes very elongated with time and eventually pinches off. Three distinct regimes of long-time behaviour of the ring have been identified. Regime selection depends on initial ring geometry and orientation and on values of strain and shear rates. These regimes include (i) periodic oscillations with no pinching off, (ii) pinching off at the ring centre, and (iii) development of an elongated vortex pair at the ring centre and wider ‘heads’ near the ends (with pinching off just behind the heads). The boundaries of these regimes and theoretical reasons for the vortex behaviour in each case are described. It is also shown that the breakup of stretched vortex rings exhibits a self-similar behaviour, in which the number and size of ‘offspring’ vortices, at the point of pinching-off the ring, may be scaled by the product of the strain rate e (or shear rate s) and the oscillation period τ of a slightly elliptical ring with mean radius R.
A theory of steady breakers
Authors: Cointe Raymond , Tulin Marshall P. 
Published: April 2006

The mechanics of the quasi-steady breaking wave created above a submerged hydrofoil, first studied experimentally by Duncan (1981), is elucidated here. It is an example of a flow wherein the resistance of the body manifests itself in a detached separation eddy located away from the body (i.e. on the free surface). As we show, the conditions for inception of separation and the prediction of the breaking configuration follow from simple considerations, without extensive calculation.The physical model of the breaker, based on observations, consists of an essentially stagnant eddy riding on the forward face of the leading wave in the wave train behind the hydrofoil. This eddy is sustained by turbulent stresses acting in the shear zone separating the eddy and the underlying flow. These stresses result in a trailing turbulent wake just beneath the water surface. The breaker eddy contains air entrained at breaking, and the degree of aeration is a parameter of the problem.The eddy—breaker model is quantified utilizing independent measurements of turbulent shear stress in shear zones. It is then shown that the hydrostatic pressure acting on the dividing streamline underneath the eddy creates a trailing wave which largely cancels the trailing wave that would exist in the absence of breaking. The ‘wave’ resistance of the hydrofoil then manifests itself in the momentum flux of the residual trailing wave, plus the momentum flux in the breaker wake, i.e. the breaker resistance.For a fixed hydrofoil speed the total momentum flux, or resistance, in the presence of breaking is shown to have a minimum corresponding to a particular value of the trailing-wave steepness. It is thus concluded that the wave resistance must exceed this value for breaking to ensue. For hydrofoil resistance in excess of this minimum, both a weak and strong breaker would seem to exist. It is shown, however, that the weak breaker is unstable. It is also shown that a maximum steady breaking resistance exists, limited by the size of the breaker and dependent on the extent of its aeration.Good quantitative comparisons between theory and experiments are shown.