bluuebunny/crossref_metadata_2025_split huggingface dataset:
Hot-wire and hot-film anemometry and conditional measurements: A report on Euromech 132
Authors: Comte-Bellot G. , Charnay G. , Sabot J. 
Published: April 2006

The European Mechanics Colloquium, Euromech 132, was held at the Ecole Centrale de Lyon from 2 to 4 July 1980. Specific areas of hot-wire or hot-film anemometry were presented and discussed, more especially the effect of the finite time constant of the wire supports, the use of yawed hot wires in supersonic flows, the possible improvement of vorticity meters, and multi-point measurements of wall-shear-stress fluctuations. Other subjects described during the meeting included a new technique for concentration measurements in flames, developments and new uses of digitization and conditional sampling, pattern recognition analysis of fluid flow from multi-point, multi-time velocity measurements, and new turbulence measurements in complex flows and in fluid-flow machinery.An exhibition of hot-wire and hot-film anemometers and associated equipment was held during the colloquium.
Stokes flow past a sphere coated with a thin fluid film
Authors: Johnson Robert Edward 
Published: April 2006

The present study examines the steady, axisymmetric Stokes flow past a sphere coated with a thin, immiscible fluid layer. Inertial effects are neglected for both the outer fluid and the fluid film, and surface tension forces are assumed large compared with the viscous forces which deform the fluid film. Furthermore, the present analysis assumes that the mechanism driving the fluid circulation within the film is not too large. From force equilibrium on the film we find that a steady fluid film can only partially cover the sphere, i.e. the film must be held to the sphere by surface tension forces at the contact line. The extent of the sphere covered by the film is specified, in terms of the solid–fluid contact angle, by the condition of global force equilibrium on the fluid film.Using a perturbation scheme based on the thinness of the fluid layer the solution to the flow field is obtained analytically, except for the fluid-film profile (i.e. the fluid–fluid interface) which requires numerical calculations. One of the principal results is an expression for the drag force on the fluid-coated particle. In particular, we find that the drag on a sphere is reduced by the presence of a fluid coating when the ratio of the film fluid viscosity to the surrounding fluid viscosity is less than ¼. Detailed numerical computations are conducted for a few typical cases. The calculations show that a film of prescribed areal extent, i.e. specified contact angle, is only possible when the magnitude of the driving force on the film is below some maximum value. A simple experiment was also performed, and photographs, which qualitatively illustrate the fundamental fluid-film configurations predicted by the theory, are presented.
Enhanced sedimentation in narrow tilted channels
Authors: Herbolzheimer Eric , Acrivos Andreas 
Published: April 2006

The analysis of Acrivos & Herbolzheimer (1979) is extended to describe the sedimentation of dilute suspensions in tilted two-dimensional channels in which the spacing between the plates is small compared with their length. The theory assumes that the flow is laminar and that the suspension consists of monodisperse spherical beads having small particle Reynolds number. Expressions for the flow fields in the clearfluid region and in the suspension, as well as for the location of the interface separating these two regions, are obtained asymptotically in the limit of Λ [Gt ] 1 with $R\Lambda^{-\frac{1}{3}}\ll 1$, where R and A are as defined in the previous work. The present analysis differs from that given earlier in that the aspect ratio, i.e. the ratio of the height of the suspension to the channel width, is now taken to be O(A1/3) rather than O(1) as was the case before. Under these conditions, the solution of the time-dependent equations leads to the surprising prediction that the clear-fluid layer which forms beneath the downward-facing plate attains a steady shape only along the lower portion of the channel while, in contrast, its thickness increases with time for locations along the channel that are above some critical point. Because of this transient behaviour, the well-known Ponder-Nakamura-Kuroda (PNK) formula overestimates the rate at which the top of the suspension region falls with time; however, the PNK results for the volumetric settling rate still hold under the conditions considered in this paper. It is shown that this discontinuity in the interface shape can be suppressed in continuous settling systems but only if the feed and withdrawal locations are chosen properly.Batch sedimentation experiments were conducted in a channel with parallel flat walls under the following sets of conditions: H0/b ≈ 90, 5° ≤ θ ≤ 45°, 0·01 ≤ c0 ≤ 0·025, 1·7 × 107 < Λ < 3·5 × 107, and 1·8 < R < 2·1, where θ is the angle of inclination of the vessel from the vertical, and c0 is the initial volume fraction of solids in the suspension. The experimental observations were found to be in excellent agreement with the theoretical predictions.
The continuous spectrum of the Orr-Sommerfeld equation. Part 2. Eigenfunction expansions
Authors: Salwen Harold , Grosch Chester E. 
Published: April 2006

The expansion of an arbitrary two-dimensional solution of the linearized stream-function equation in terms of the discrete and continuum eigenfunctions of the Orr-Sommerfeld equation is discussed for flows in the half-space, y ε [0, ∞). A recent result of Salwen is used to derive a biorthogonality relation between the solution of the linearized equation for the stream function and the solutions of the adjoint problem.For the case of temporal stability, the orthogonality relation obtained is equivalent to that of Schensted for bounded flows. This relationship is used to carry out the formal solution of the initial-value problem for temporal stability. It is found that the vorticity of the disturbance at t = 0 is the proper initial condition for the temporal stability problem. Finally, it is shown that the set consisting of the discrete eigen-modes and continuum eigenfunctions is complete.For the spatial stability problem, it is shown that the continuous spectrum of the Orr-Sommerfeld equation contains four branches. The biorthogonality relation is used to derive the formal solution to the boundary-value problem of spatial stability. It is shown that the boundary-value problem of spatial stability requires the stream function and its first three partial derivatives with respect to x to be specified at x = 0 for all t. To be applicable to practical problems, this solution will require modification to eliminate disturbances originating at x = ∞ and travelling upstream to x = 0.For the special case of a constant base flow, the method is used to calculate the evolution in time of a particular initial disturbance.
Quadrupoles in potential flow: two model problems
Authors: Blackburn H. W. 
Published: April 2006

The Ffowcs Williams-Hawkings formulation of the sources of the acoustic analogy is examined by reference to two compressible inviscid flows whose density and velocity fields are known exactly. The purpose of this exercise is to generate some feel for the importance of the various source terms in determining the sound of moving surfaces with shocks, and to help quantify the errors involved in approximating those sources. Practical applications of the theory involve flows that cannot be known exactly and the errors of approximation cannot be checked directly. Progress must start with simple cases, and these model problems represent a first move. The flows considered are the one-dimensional flow caused by a plane boundary impulsively accelerated into a fluid, and the two-dimensional flow due to a wedge moving supersonically and supporting a plane attached shock.For each of these flows, a system of analogous acoustic sources is developed, the fields of which, when superposed, produce a density field (an acoustic field) identical with that of the original flow. The acoustic fields generated by the component source terms are calculated and compared. This suggests that the volume quadrupoles of potential flow play only a minor role as sound generators. When properly viewed the field is generated entirely on the bounding surfaces of the flow. A general argument shows that volume quadrupoles in steady rectilinear motion only influence the sound field through propagation effects.
Kinematic-wave theory of sedimentation beneath inclined walls
Authors: Schneider W. 
Published: April 2006

The two-phase flow in settling vessels with walls that are inclined to the vertical is investigated. By neglecting inertial effects and the viscosity of the suspension i t is shown that the particle concentration remains constant on kinematic-wave fronts. The wave fronts are horizontal and propagate in a quasi-one-dimensional manner, but are imbedded in a two-dimensional or three-dimensional basic flow which, in turn, depends on the waves via the boundary conditions. Concentration discontinuities (interfaces) are described by kinematic-shock theory. The kinematic shocks are shown to be horizontal, with the possible exception of discontinuities that separate the suspension from the sediment.At downward-facing inclined walls conservation of mass enforces the existence of a boundary-layer flow with relatively large velocity. As G/R2→∞ and G/R4→ 0, where G and R are respectively a sedimentation Grashof number and a sedimentation Reynolds number, the entrainment of suspended particles into the boundary-layer flow of clear liquid is negligibly small. This provides an appropriate boundary condi- tion for the basic flow of the suspension. Thus, in the double limit considered, a kine- matic theory suffices to determine the convective flow of the suspension due to the presence of inclined walls.As an example batch sedimentation in vessels with inclined plane or conical walls is investigated. The settling process is terminated after a time that can be considerably smaller than the time required in a vertical vessel under the same conditions.Depending on the initial particle concentration, there are centred kinematic waves that are linked to a continuous increase of the particle concentration in the suspension. In an appendix, the flow in the boundary layer at a downward facing, inclined wall is investigated. With G/R2→∞ and G/R4→ 0, the boundary layer consists of an inviscid particle-free main part, a viscous sublayer at the wall, and a free shear sublayer at the liquid/particle interface.
Rising bubbles
Authors: Miksis Michael J. , Vanden-Broeck Jean-Marc , Keller Joseph B. 
Published: April 2006

The shape of a rising bubble, or of a falling drop, in an incompressible viscous fluid is computed numerically, omitting the condition on the tangential traction at the bubble or drop surface. When the bubble is sufficiently distorted, its top is found to be spherical and its bottom is found to be rather flat. Then the radius of its upper surface is in fair agreement with the formula of Davis & Taylor (1950). This distortion occurs when the effect of gravity is large while that of surface tension is small. When the effect of surface tension is large, the bubble is nearly a sphere.The shape is found, together with the flow of the surrounding fluid, by assuming that both are steady and axially symmetric, with the Reynolds number being large. The flow is taken to be a potential flow. The boundary condition on the normal component of normal stress, including the viscous stress, is satisfied, but not that on the tangential component. The problem is converted into an integro-differential set of equations, reduced to a set of algebraic equations by a difference method, and solved by Newton's method together with parameter variation.
A vortex-street model of the flow in the similarity region of a two-dimensional free turbulent jet
Authors: Oler J. W. , Goldschmidt V. W. 
Published: April 2006

The mean-velocity profiles and entrainment rates in the similarity region of a two-dimensional jet are generated by a simple superposition of Rankine vortices arranged to represent a vortex street. The spacings between the vortex centres, their two-dimensional offsets from the centreline, as well as the core radii and circulation strengths, are all governed by similarity relationships and based upon experimental data.Major details of the mean flow field such as the axial and lateral mean-velocity components and the magnitude of the Reynolds stress are properly determined by the model. The sign of the Reynolds stress is, however, not properly predicted.
Some aspects of the fluid dynamics of laser welding
Authors: Dowden John , Davis Michael , Kapadia Phiroze 
Published: April 2006

When a laser beam is used as the energy source for welding two pieces of metal together, a hole is formed perpendicular to the plane of the workpiece. The latter is moved relative to the laser and metal is transferred from the front to the rear by fluid flow round the hole. The equations governing the process are set out and the conditions at the two boundaries in the problem (one between the hole and the molten metal, and the other between the liquid and the solid states of the metal) are considered.Approximate solutions of the problem for low welding speeds are obtained for four different models. The first is one in which the viscosity is taken to be constant. In the second, the viscosity is allowed to depend linearly on temperature. The third model divides the liquid into a region in which the cooler part is taken to be viscous and the hotter part inviscid; the fourth model is then constructed as a limit, with the liquid motion considered as wholly inviscid. It is found that the motion is not irrotational in this last model. The models all display a downstream displacement of the boundary between the solid and liquid states, in agreement with observations. An expression for the minimum power of the laser is calculated.
Stokes flow past bubbles and drops partially coated with thin films. Part 2. Thin films with internal circulation – a perturbation solution
Authors: Johnson Robert E. , Sadhal S. S. 
Published: April 2006

In the present study we examine the steady axisymmetric creeping flow due to the motion of a liquid drop or a bubble which is partially covered by a thin immiscible fluid layer or film. The analysis is based on the assumption that surface-tension forces are large compared with viscous forces which deform the drop, and that the circulation in the film is weak. The latter assumption is satisfied provided that the film-fluid viscosity is not too small. A perturbation scheme based on the thinness of the fluid layer is used to construct the solution.One of the principal results is an expression for the drag force on the complex drop. We also find that the extent to which the drop or bubble is covered the film has a maximum value depending on the magnitude of the driving force on the film. In addition, we find the rather interesting result that when the ratio of the primary drop viscosity and bulk fluid viscosity is greater than ½, the circulation within the film may have a double-cell structure.
Flow past a liquid drop with a large non-uniform radial velocity
Authors: Sadhal S. S. , Ayyaswamy P. S. 
Published: April 2006

In this analysis, the translation of a liquid drop experiencing a strong non-uniform radial velocity has been investigated. The situation arises when a moving liquid drop experiences condensation, evaporation or material decomposition at the surface. By simultaneously treating the flow fields inside and outside the drop, we have obtained physical results relevant to the problem. The magnitude of the radial velocity is allowed to be very large, but the drop motion is restricted to slow translation. The solution to the problem has been developed by considering a uniform radial flow with the translatory motion introduced as a perturbation. The role played by the inertial terms due to the strong radial field has been clearly delineated. The study has revealed several interesting features. An inward normal velocity on a slowly moving drop increases the drag. An increasing outward normal velocity decreases the drag up to a minimum beyond which it increases. The total drag force not only consists of contributions from the viscous and the form drags but also from the momentum transport at the interface. Since the liquid drop admits a non-zero tangential velocity, the tangential momentum convected by the radial velocity forms a part of this drag force. The circulation inside the drop decreases (increases) with an outward (inward) normal velocity. A sufficiently large non-uniform outward velocity causes the circulation to reverse.In the limit of the internal viscosity becoming infinite, our analysis collapses to the simple case of a translating rigid sphere experiencing a large non-uniform radial velocity. By letting the radial velocity become vanishingly small the Stokes-flow solution is recovered.An important contribution of the present study is the identification of a new singularity in the flow description. It accounts for both the inertial and the viscous forces and displays Stokeslet-like characteristics at infinity.
The mixing layer: deterministic models of a turbulent flow. Part 2. The origin of the three-dimensional motion
Authors: Corcos G. M. , Lin S. J. 
Published: April 2006

Experimental evidence suggests that in the turbulent mixing layer the fundamental mechanism of growth is two-dimensional and little affected by the presence of vigorous three-dimensional motion. To quantify this apparent property and study the growth of streamwise vorticity, we write for the velocity field
\[
{\boldmath V}(x, t) = {\boldmath U}(x, z, t) + {\boldmath u}(x, y, z, t),
\]
where U is two-dimensional and u is three-dimensional. In a first version of the problem U is independent of u, while in the second U is the spanwise average of V. In both cases the equation for u is linearized around U. The equations for U and u are solved simultaneously by a finite-difference calculation starting with a slightly disturbed parallel shear layer.The solutions provide a detailed description of the growth of the three-dimensional motion. They show that its characteristics are dictated by the distribution of spanwise vorticity which results from roll-up and pairing. Pairing inhibits its growth. The solutions also demonstrate that even when the three-dimensional flow attains large amplitudes it has a negligible effect on the interaction of spanwise vortices and thus on the growth of the layer.
Organized structures in turbulent Taylor-Couette flow
Authors: Barcilon A. , Brindley J. 
Published: April 2006

A simple mathematical model is constructed to describe the regime of flow, extending over a wide range of values of Taylor number, in which turbulent Taylor–Couette flow in the annular region between two coaxial circular cylinders is characterized by the coexistence of steady coherent motion on two widely separated scales. These scales of motion, corresponding to the gap width of the annular region and to a boundary-layer thickness, are each identified as the consequence of a centrifugal instability, and are described as Taylor vortices and Görtler vortices respectively.The assumption that both scales of motion are near marginal stability gives a closure to a pair of coupled eigenvalue problems, and the results of a linear analysis are shown to be in good agreement with many features of experimental observations.
Theoretical study of the transonic flow past wedge profiles with detached shock waves
Authors: Abboud Michel 
Published: April 2006

This report presents a numerical study of the two-dimensional, steady and inviscid flow of a perfect gas past wedge profiles with detached shock waves for free-stream Mach numbers between 1.05 and 1.44.Utilizing the hodograph transformation, a boundary-value problem for the mixed flow is formulated in the hodograph plane and subsequently solved by a finite-difference scheme, iterating respectively between the elliptic and hyperbolic regions. The use of boundary-fitted coordinates and a graded lattice failed to achieve satisfactory results, owing to either convergence difficulties or numerical inaccuracies introduced through the coordinate generator. On the other hand, Cartesian coordinates presented no convergence problems and yielded accurate results.After transforming the solution back to the physical plane, the flow field between the shock wave and the limiting Mach wave is determined. A comparison of the results with experiments and other theories shows a good agreement both for the pressure distribution on the wedge and for the shock stand-off distance.Also of special interest is a quantitative comparison of the results with the small-disturbance theory (solution of the Tricomi equation) and the limiting case of the free-stream Mach number 1.Moreover, an example of the flow past round-nosed wedges, with and without an angle of attack, is treated using the inverse method.
Forces on cylinders in viscous oscillatory flow at low Keulegan-Carpenter numbers
Authors: Bearman P. W. , Downie M. J. , Graham J. M. R. , Obasaju E. D. 
Published: April 2006

This paper presents a comparison between theory and experiment for the in-line forces on cylinders of general cross-section in planar oscillatory flows of small amplitude. The theoretical analysis evaluates corrections to the standard inviscid inertial force at low Keulegan-Carpenter numbers which arise from the presence of viscous laminar boundary layers and from the development of vortex shedding. The boundary-layer contribution due to both skin friction and displacement effects is calculated to first order in the Stokes parameter β−½. The contribution to the in-line force from separation and vortex shedding, for which the results presented only apply to sharp-edged bodies, is taken from previous work on vortex shedding from isolated edges using the discrete vortex modelling technique. The resulting force has components both in phase with the fluid acceleration (inertia) and in phase with the velocity (drag).The theoretical results are compared to measurements taken in a [xcup ]-tube water channel on a number of cylinders of different cross-section including circular cylinders and sharp-edged sections. The comparisons suggest that the theory is valid for Keulegan–Carpenter numbers below about 3 and for moderately high values of the β parameter.
Transient axisymmetric motion of a floating cylinder
Authors: Newman J. N. 
Published: April 2006

A linear theory is developed in the time domain for vertical motions of an axisymmetric cylinder floating in the free surface. The velocity potential is obtained numerically from a discretized boundary-integral-equation on the body surface, using a Galerkin method. The solution proceeds in time steps, but the coefficient matrix is identical at each step and can be inverted at the outset.Free-surface effects are absent in the limits of zero and infinite time. The added mass is determined in both cases for a broad range of cylinder depths. For a semi-infinite cylinder the added mass is obtained by extrapolation.An impulse-response function is used to describe the free-surface effects in the time domain. An oscillatory error observed for small cylinder depths is related to the irregular frequencies of the solution in the frequency domain. Fourier transforms of the impulse-response function are compared with direct computations of the damping and added-mass coefficients in the frequency domain. The impulse-response function is also used to compute the free motion of an unrestrained cylinder, following an initial displacement or acceleration.