bluuebunny/crossref_metadata_2025 huggingface dataset:
Axisymmetric particle-driven gravity currents
Authors: Bonnecaze Roger T. , Hallworth Mark A. , Huppert Herbert E. , Lister John R.
Published: April 2006

Axisymmetric gravity currents that result when a dense suspension intrudes under a lighter ambient fluid are studied theoretically and experimentally. The dynamics of and deposition from currents flowing over a rigid horizontal surface are determined for the release of either a fixed volume or a constant flux of a suspension. The dynamics of the current are assumed to be dominated by inertial and buoyancy forces, while viscous forces are assumed to be negligible. The fluid motion is modelled by the single-layer axisymmetric shallow-water equations, which neglect the effects of the overlying fluid. An advective transport equation models the distribution of particles in the current, and this distribution determines the local buoyancy force in the shallow-water equations. The transport equation is derived on the assumption that the particles are vertically well-mixed by the turbulence in the current, are advected by the mean flow and settle out through a viscous sublayer at the bottom of the current. No adjustable parameters are needed to specify the theoretical model. The coupled equations of the model are solved numerically, and it is predicted that after an early stage both constant-volume and constant-flux, particle-driven gravity currents develop an internal bore which separates a supercritical particle-free region upstream from a subcritical particle-rich region downstream near the head of the current. For the fixed-volume release, an earlier bore is also predicted to occur very shortly after the initial collapse of the current. This bore transports suspended particles away from the origin, which results in a maximum in the predicted deposition away from the centre.

To test the model several laboratory experiments were performed to determine both the radius of an axisymmetric particle-driven gravity current as a function of time and its deposition pattern for a variety of initial particle concentrations, particle sizes, volumes and flow rates. For the release of a fixed volume and of a constant flux of suspension, the comparisons between the experimental results and the theoretical predictions are fairly good. However, for the current of fixed volume, we did not observe the bore predicted to occur shortly after the collapse of the current or the resulting maximum in deposition downstream of the origin. This is unlike the previous study of Bonnecaze et al. (1993) on two-dimensional currents, in which a strong bore was observed during the slumping phase. The radial extent R of the deposit from a fixed-volume current is accurately predicted by the model, and for currents whose particles settle sufficiently slowly, we find that R = 1.9(g′0V3 / v2s)1/8, where V is the volume of the current, vs is the settling velocity of a particle in the suspension and g’0 is the initial reduced gravity of the suspension.
Interaction dynamics of solitary waves on a falling film
Authors: Chang H.-C. , Demekhin E. , Kalaidin E.
Published: April 2006

Beyond a short transition region near the inlet, waves on a falling film evolve into distinct pulse-like solitary waves that dominate all subsequent interfacial dynamics. Numerical and physical experiments indicate that these localized structures can attract and repel each other. Attractive interaction through the capillary ripples of the pulses causes two pulses to coalesce into a bigger pulse which accelerates and precipitates further coalescence. This binary interaction between an ‘excited’ pulse after coalescence and its smaller front neighbour is the key mechanism that drives the observed wave dynamics. From symmetry arguments, two dominant modes for a solitary pulse are obtained and used to develop an inelastic coherent structure theory for binary interaction between an excited pulse and its front neighbour. The theory offers a simple dynamical system that quantitatively describes the binary interaction and promises to elucidate the complex wave dynamics on a falling film.
Stability of the viscous flow of a fluid through a flexible tube
Authors: Kumaran V.
Published: April 2006

The stability of Hagen-Poiseuille flow of a Newtonian fluid of viscosity η in a tube of radius R surrounded by a viscoelastic medium of elasticity G and viscosity ηs occupying the annulus R < r < HR is determined using a linear stability analysis. The inertia of the fluid and the medium are neglected, and the mass and momentum conservation equations for the fluid and wall are linear. The only coupling between the mean flow and fluctuations enters via an additional term in the boundary condition for the tangential velocity at the interface, due to the discontinuity in the strain rate in the mean flow at the surface. This additional term is responsible for destabilizing the surface when the mean velocity increases beyond a transition value, and the physical mechanism driving the instability is the transfer of energy from the mean flow to the fluctuations due to the work done by the mean flow at the interface.

The transition velocity Γt for the presence of surface instabilities depends on the wavenumber k and three dimensionless parameters: the ratio of the solid and fluid viscosities ηr = (ηs/η), the capillary number λ = (T/GR) and the ratio of radii H, where T is the surface tension of the interface. For ηr = 0 and λ = 0, the transition velocity Γt diverges in the limits k [Lt ] 1 and k [Gt ] 1, and has a minimum for finite k. The qualitative behaviour of the transition velocity is the same for λ < 0 and ηr = 0, though there is an increase in λt in the limit k > 1. When the viscosity of the surface is non-zero (ηr < 0), however, there is a qualitative change in the λtvs. k curves. For ηr < 1, the transition velocity λt is finite only when k is greater than a minimum value kmin, while perturbations with wavenumber k < kmin are stable even for λ → ∞. For ηr > 1, λt is finite only for kmin < k < kmax, while perturbations with wavenumber k < kmin or k > kmax are stable in the limit λ → ∞. As H decreases or ηr increases, the difference kmax − kmin decreases. At a minimum value H = Hmin which is a function of ηr, the difference kmax − kmin = 0, and for H < Hmin, perturbations of all wavenumbers are stable even in the limit λ → ∞. The calculations indicate that Hmin shows a strong divergence proportional to exp (0.0832nr2) for ηr [Gt ] 1.
Forced convection and sedimentation past a flat plate
Authors: Pelekasis Nikolaos A. , Acrivos Andreas
Published: April 2006

The steady laminar flow of a well-mixed suspension of monodisperse solid spheres, convected steadily past a horizontal flat plate and sedimenting under the action of gravity, is examined. It is shown that, in the limit as Re → ∞ and ∈ → 0, where Re is the bulk Reynolds number and ∈ is the ratio of the particle radius a to the characteristic length scale L, the analysis for determining the particle concentration profile has several aspects in common with that of obtaining the temperature profile in forced-convection heat transfer from a wall to a fluid stream moving at high Reynolds and Prandtl numbers. Specifically, it is found that the particle concentration remains uniform throughout the O(Re−1/2) thick Blasius boundary layer except for two O(∈2/3) thin regions on either side of the plate, where the concentration profile becomes non-uniform owing to the presence of shear-induced particle diffusion which balances the particle flux due to convection and sedimentation. The system of equations within this concentration boundary layer admits a similarity solution near the leading edge of the plate, according to which the particle concentration along the top surface of the plate increases from its value in the free stream by an amount proportional to X5/6, with X measuring the distance along the plate, and decreases in a similar fashion along the underside. But, unlike the case of gravity settling on an inclined plate in the absence of a bulk flow at infinity considered earlier (Nir & Acrivos 1990), here the concentration profile remains continuous everywhere. For values of X beyond the region near the leading edge, the particle concentration profile is obtained through the numerical solution of the relevant equations. It is found that, as predicted from the similarity solution, there exists a value of X at which the particle concentration along the top side of the plate attains its maximum value ϕm and that, beyond this point, a stagnant sediment layer will form that grows steadily in time. This critical value of X is computed as a function of ϕs, the particle volume fraction in the free stream. In contrast, but again in conformity with the similarity solution, for values of X sufficiently far removed from the leading edge along the underside of the plate, a particle-free region is predicted to form adjacent to the plate. This model, with minor modifications, can be used to describe particle migration in other shear flows, as, for example, in the case of crossflow microfiltration.
Thermocapillary flow with evaporation and condensation at low gravity. Part 1. Non-deforming surface
Authors: Schmidt G. R. , Chung T. J. , Nadarajah A.
Published: April 2006

The problem of steady motion and thermal behaviour of a volatile, wetting liquid in an open cavity under low gravity is defined and examined. The domain geometrically approximates a two-phase pore of liquid on a wicking structure surface, and consists of a 1 to 102μu wide rectangular cavity bounded by a saturated vapour and liquid reservoir on its upper and lower surfaces, respectively. Thermal non-equilibrium and convection are established by symmetrically superheating or subcooling the pore boundaries by ∼ 1 K relative to the vapour. Numerical analyses show that although thermocapillary flow competes with interfacial phase change in dictating the circulation and flow structure, it tends to reinforce the convective effects of evaporation and condensation on surface temperature and heat transport. In addition, highly wetting fluids with curved menisci are characterized by greater circulation intensities and dynamic pressure gradients than a flat surface. The magnitude of these gradients suggests that the fixed menisci shapes assumed in this study are unrealistic, and that the influence of convection on surface morphology should be considered.
Thermocapillary flow with evaporation and condensation at low gravity. Part 2. Deformable surface
Authors: Schmidt G. R. , Chung T. J. , Nadarajah A.
Published: April 2006

The free surface behaviour of a volatile wetting liquid at low gravity is studied using scaling and numerical techniques. An open cavity model, which was applied in part 1 to investigate fluid flow and heat transfer in non-deforming pores, is used to evaluate the influence of convection on surface morphology with length scales and subcooling/superheating limits of 1 ≤ D ≤ 102 μm and ∼ 1 K, respectively. Results show that the menisci shapes of highly wetting fluids are sensitive to thermocapillary flow and to a lesser extent the recoil force associated with evaporation and condensation. With subcooling, thermocapillarity produces a suction about the pore centreline that promotes loss of mechanical equilibrium, while condensation exerts an opposing force that under some conditions offsets this destabilizing influence. With superheating, thermocapillarity and evaporation act in the same direction and mutually foster surface stability. All of these trends are magnified by high capillary and Biot numbers, and the stronger circulation intensities associated with small contact angles. These phenomena strongly depend on the thermal and interfacial equilibrium between the liquid and vapour, and have important ramifications for systems designed to maintain a pressure differential across a porous surface.
Kinetic-energy mass, momentum mass, and drift mass in steady irrotational subsonic flows
Authors: Yih Chia-Shun
Published: April 2006

Irrotational flows caused by a body moving with a constant velocity in an unbounded homentropic compressible fluid at rest at infinity are considered. Provided the (steady) flow relative to the body is everywhere subsonic, it is shown that the momentum mass is always equal to the drift mass, and the kinetic-energy mass is equal to the drift mass under certain conditions.
On the two-way interaction in two-dimensional particle-laden flows: the accumulation of particles and flow modification
Authors: Druzhinin O. A.
Published: April 2006

The evolution of two-dimensional regular flows laden with solid heavy particles is studied analytically and numerically. The particulate phase is assumed to be dilute enough to neglect the effects of particle-particle interactions. Flows with large Reynolds and Froude numbers are considered, when effects related to viscous dissipation and gravity are negligible. A Cauchy problem is solved for an initially uniform distribution of particles with Stokes (St) and Reynolds (Rep) numbers of order unity in several types of flows representing steady solutions of the two-dimensional Euler equations. We consider flows in the vicinity of the hyperbolic stagnation point (with a uniform strain and zero vorticity) and the elliptic stagnation point (where vorticity is uniform), a circular vortex (with vorticity depending on the radius) and Stuart vortex flow. Analytical solutions are obtained, for the case of sufficiently small St, describing the accumulation of particles and corresponding modification of the fluid flow. Solutions derived show that the concentration of particles, although remaining uniform, decreases at the elliptic stagnation point and grows at the hyperbolic point. Owing to the coupling between the particulate and fluid dynamics, the flow vorticity is reduced at the elliptic point, while flow strain rate is enhanced at the hyperbolic point. Solutions obtained for the circular vortex show that the accumulation of particles proceeds in the form of a travelling wave. The concentration grows locally, forming the crest of the wave which propagates away from the vortex centre. Owing to the influence of the particulate on the carrier flow, the vorticity is reduced in the vortex centre. At the location of the crest the gradient of the flow grows owing to the drag forces between the fluid and particles and a vorticity peak is generated. Analytical solutions are also obtained for a chain of particle-laden Stuart vortices. Owing to the coupling effects, the concentration is diminished and the vorticity is reduced at the centres of the vortices. A sheet of increased concentration and vorticity is formed extending from the braid region to the periphery of the vortices, and the flow strain in the braid region is enhanced. Results of numerical simulations performed for St = 0.5 show good agreement with analytical solutions.
Fundamental and subharmonic secondary instabilities of Görtler vortices
Authors: Li Fei , Malik Mujeeb R.
Published: April 2006

The nonlinear development of stationary Görtler vortices leads to a highly distorted mean flow field where the streamwise velocity depends strongly not only on the wall-normal but also on the spanwise coordinates. In this paper, the inviscid instability of this flow field is analysed by solving the two-dimensional eigenvalue problem associated with the governing partial differential equation. It is found that the flow field is subject to the fundamental odd and even (with respect to the Görtler vortex) unstable modes. The odd mode, which was also found by Hall & Horseman (1991), is initially more unstable. However, there exists an even mode which has higher growth rate further downstream. It is shown that the relative significance of these two modes depends upon the Görtler vortex wavelength such that the even mode is stronger for large wavelengths while the odd mode is stronger for short wavelengths. Our analysis also shows the existence of new subharmonic (both odd and even) modes of secondary instability. The nonlinear development of the fundamental secondary instability modes is studied by solving the (viscous) partial differential equations under a parabolizing approximation. The odd mode leads to the well-known sinuous mode of break down while the even mode leads to the horseshoe-type vortex structure. This helps explain experimental observations that Görtler vortices break down sometimes by sinuous motion and sometimes by developing a horseshoe vortex structure. The details of these break down mechanisms are presented.
Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow
Authors: Pozrikidis C.
Published: April 2006

The transient deformation of liquid capsules enclosed by elastic membranes subject to simple shear flow is studied numerically using a new implementation of the boundary element method. The numerical results for capsules with spherical unstressed shapes and varying degrees of surface elasticity are compared with the predictions of an asymptotic theory for small deformations due to Barthès-Biesel and coworkers, and the significance of nonlinear effects due to finite deformation is assessed. It is found that the capsules exhibit continuous elongation when the dimensionless shear rate becomes larger than a critical threshold, in agreement with recent experimental observations of capsules with polymerized interfaces. Membrane failure at large deformations is discussed with respect to membrane thinning and development of excessive elastic tensions, and it is argued that the location where the membrane is likely to rupture due to continued deformation is insensitive to the precise mechanism of rupture. The numerical results suggest that a dilute suspension of capsules behaves like shear-thinning medium with some elastic properties. Results of oblate spheroidal capsules suggest that the points of maximum membrane thinning and tension coincide but their location depends upon the unstressed capsule shape.
Fluid flow in loops driven by freshwater and heat fluxes
Authors: Dewar W. K. , Huang R. X.
Published: April 2006

Thermohaline convection in a salt water loop is discussed. Fluid temperature is affected by relaxation on the loop surface and fluid salinity by a freshwater flux through the loop surface. In addition, other boundary conditions on salinity, such as the equivalent virtual salt flux or salinity relaxation condition, are examined and the dynamic role of diffusion in thermohaline convection is analysed.

Both analytical and numerical analyses indicate that the system behaviour depends sensitively on the nature of the salinity boundary condition. For the saline-only loop model, analysis indicates that perturbations are advected by the mean flow, and flow stability is independent of the strength of the boundary forcing. In the full thermohaline loop problem, the virtual salt flux formulation accurately mirrors the freshwater flux results when the system is in the thermal mode. However, these formulations can differ substantially when the system is in the haline mode, especially in the strongly forced, weakly diffusive limit.

For both types of loop configuration, salinity profiles governed by freshwater flux have scales determined by the internal parameters, while virtual salt flux profiles necessarily reflect the lengthscales of applied boundary conditions. Negative salinities can also appear under virtual salt flux owing to the inaccuracies inherent in the approximation, while freshwater flux ensures positive-definite salinity values.

Our analysis supports the use of the physically more accurate freshwater flux boundary conditions when simulating thermohaline circulation.
Numerical study of the oscillations of axially excited liquid annuli with rotational symmetry enclosed in revolving circular cylindrical containers
Authors: Ehmann M. , Siekmann J.
Published: April 2006

In this paper we investigate numerically the periodic, axisymmetric response of a liquid annulus enclosed in a revolving cylinder and subject to a periodic axial excitation within the range of the natural frequencies. We use a description which employs as solution variables the transverse component of the vorticity vector, the scalar stream function and the transverse velocity component, as well as the position of the free surface. The acceleration due to gravity is neglected, whereas friction and surface tension are taken into account. At the fixed walls the no-slip condition is fulfilled except at points on the contact line. At the contact line the slip condition is applied. The solution of this problem is achieved using the spectral method in the time direction and finite differences in the space direction, whereby surface-adapted coordinates are utilized. Far away from the walls the computational results show good agreement with results obtained from a linearized theory assuming an inviscid liquid, while at the walls boundary layers are generated.
Hydrodynamical instabilities of thermocapillary flow in a half-zone
Authors: Levenstam Måarten , Amberg Gustav
Published: April 2006

The stability of the flow in a half-zone configuration is analysed with the aid of direct numerical simulation. The work is concentrated on the small Prandtl numbers relevant for typical semiconductor melts. The axisymmetric thermocapillary flow is found to be unstable to a steady non-axisymmetric state with azimuthal wavenumber 2, for a zone with aspect ratio 1. The critical Reynolds number for this bifurcation is 1960. This three dimensional steady solution loses stability to an oscillatory state at a Reynolds number of 6250. For small Prandtl numbers, both bifurcations are seen to be quite insensitive to changes in the Prandtl number, and are thus hydrodynamic in nature. An analogy to the instability of thin vortex rings is made. This analogy suggests a physical mechanism behind the instability and also gives an explanation of how the azimuthal wavenumber of the bifurcated solution is selected. The implications of this for the floating-zone crystal growth process are discussed.
Resistance functions for spherical particles, droplets and bubbles in cylindrical tubes
Authors: Higdon J. J. L. , Muldowney G. P.
Published: April 2006

Numerical computations are performed to evaluate the resistance functions for low Reynolds number flow past spherical particles, droplets and bubbles in cylindrical domains. Spheres of arbitrary radius a and radial position b move with arbitrary velocity U within a cylinder of radius R. The undisturbed fluid may be at rest, or subject to a pressure-driven flow with maximum velocity U0. The spectral boundary element method is employed to compute the resistance force for torque-free bodies in three cases: rigid solids, fluid droplets with viscosity ratio λ = 1, and bubbles with viscosity ratio λ = 0. A lubrication theory is developed to predict the limiting resistance of bodies near contact with the cylinder walls. Compact algebraic expressions are developed which accurately represent the numerical data over the entire range of particle positions 0 < b/(R − a) < 1 for all particle sizes in the range 0 < a/R < 0.9. The resistance functions are consistent with known analytical results and are presented in a form suitable for further studies of particle migration in cylindrical vessels.
Instability of a non-wetting film with interfacial viscous stress
Authors: Edwards David A. , Oron Alexander
Published: April 2006

The destabilization of a thin three-dimensional non-wetting film above a solid wall is examined for the special case in which surfactant is adsorbed onto the free surface of the film. Attention is restricted to the case of a Newtonian surface, with surfactant displaying rapid surface diffusion or exhibiting small Marangoni number, such that the dominant intrinsic interfacial stress is of a purely viscous origin. A surface-excess force approach is adopted for the purpose of incorporating into the analysis the attractive/repulsive dispersive forces acting between the solid wall and the film. Three coupled nonlinear partial differential equations are obtained that describe the ‘large-wavelength’ spatio-temporal evolution of the free film surface following a small initial disturbance. These equations are shown to reduce to results in the literature in the limit of zero interfacial viscosities. Employing linear stability analysis, an explicit dispersion equation is obtained relating the growth coefficient to interfacial viscosities. It is found, at least in the linear regime, that the sum of interfacial shear and dilatational viscosities – and not each separately – imparts a damping effect that in the most extreme case is four-fold relative to the case of no interfacial viscosities. Nonlinear stability analysis in the limiting case of a two-dimensional film indicates that interfacial viscosities may strongly hinder the onset of instability through large interfacial stresses that arise in the vicinity of trough and crest regions of the film.
Surface oscillations of electromagnetically levitated viscous metal droplets
Authors: Bratz A. , Egry I.
Published: April 2006

We investigate the oscillation spectrum of electromagnetically levitated metal droplets. In the case of electromagnetic levitation, gravity is compensated by a Lorentz force, which is generated by an external current. The oscillation spectrum contains information about the thermophysical properties of the liquid metal, namely surface tension and viscosity. For a correct interpretation of these spectra the influence of the external forces on the frequencies and the damping of the surface waves must be well understood. The external forces deform the droplet, so that the static equilibrium shape is aspherical. For a perfect conductor the effect of the Lorentz force and gravity on the oscillation spectrum is calculated for an arbitrary magnetic field and arbitrary values of the viscosity. The high Reynolds number limit is evaluated. Explicit results are obtained for a linear magnetic field, which describes the experimental situation well.
A wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support
Authors: Marušić Ivan , Perry A. E.
Published: April 2006

In Part 1 an extension of the attached eddy hypothesis was developed and applied to equilibrium pressure gradient turbulent boundary layers. In this paper the formulation is applied to data measured by the authors from non-equilibrium layers and agreement with the extended theory is encouraging. Also power spectra of the Reynolds stresses as developed from the extended theory compare favourably with experiment. The experimental data include a check of cone-angle effects by using a flying hot wire.
Transport processes in periodic porous media
Authors: Saeger R. B. , Scriven L. E. , Davis H. T.
Published: April 2006

The Stokes equation system and Ohm's law were solved numerically for fluid in periodic bicontinuous porous media of simple cubic (SC), body-centred cubic (BCC) and face-centred cubic (FCC) symmetry. The Stokes equation system was also solved for fluid in porous media of SC arrays of disjoint spheres. The equations were solved by Galerkin's method with finite element basis functions and with elliptic grid generation. The Darcy permeabilitykcomputed for flow through SC arrays of spheres is in excellent agreement with predictions made by other authors. Prominent recirculation patterns are found for Stokes flow in bicontinuous porous media. The results of the analysis of Stokes flow and Ohmic conduction through bicontinuous porous media were used to test the permeability scaling law proposed by Johnson, Koplik & Schwartz (1986), which introduces a length parameter Λ to relate Darcy permeabilitykand the formation factorF. As reported in our earlier work on the SC bicontinuous porous media, the scaling law holds approximately for the BCC and FCC families except when the porespace becomes nearly spherical pores connected by small orifice-like passages. We also found that, except when the porespace was connected by the small orifice-like passages, the permeability versus porosity curve of the bicontinuous media agrees very well with that of arrays of disjoint and fused spheres of the same crystallographic symmetry.
Absolute instability of the boundary layer on a rotating disk
Authors: Lingwood R. J.
Published: April 2006

This paper is concerned with the theoretical behaviour of the boundary-layer flow over a disk rotating in otherwise still fluid. The flow is excited impulsively at a certain radius at timet= 0. This paper analyses the inviscid stability of the flow and the stability with viscous, Coriolis and streamline curvature effects included. In both cases, within a specific range of the parameter space, it is shown that the flow isabsolutelyunstable, i.e. disturbances grow in time at every fixed point in space. Outside this range, the flow is convectively unstable or stable. The absolute or convective nature of the instabilities is determined by examining the branch-point singularities of the dispersion relation. Absolute instability is found for Reynolds numbers above 510. Experimentally observed values for the onset of transition from laminar to turbulent flow have an average value of 513. It is suggested that absolute instability may cause the onset of transition to turbulent flow. The results from the inviscid analysis show that the absolute instability is not caused by Coriolis effects nor by streamline curvature effects. This indicates that this mechanism may be possible on swept wings, where Coriolis effects are not present but the boundary layers are otherwise similar.
A gun tunnel investigation of hypersonic free shear layers in a planar duct
Authors: Buttsworth D. R. , Morgan R. G. , Jones T. V.
Published: April 2006

An experimental investigation of high Mach number free shear layers has been undertaken. The experiments were performed using a Mach 7 gun tunnel facility and a planar duct with injection from the base of a central strut producing a Mach 3 flow parallel to the gun tunnel stream. This configuration is relevant to the development of efficient scramjet propulsion, and the gun tunnel Mach number is significantly higher than the majority of previous supersonic turbulent mixing layer investigations reported in the open literature. Schlieren images and Pitot pressure measurements were obtained at four different convective Mach numbers ranging from 0 to 1.8. Only small differences between the four cases were detected, and the relatively large high-speed boundary layers at the trailing edge of the struct injector appear to strongly influence the shear layer development in each case. The Pitot pressure measurements indicated that, on average, the free shear layers all spread into the Mach 3 stream at an angle of approximately 1.4°, while virtually no spreading into the Mach 7 stream was detected until all of the low-speed stream was entrained. The free shear layers were simulated using a PNS code; however, the experimentally observed degree of spreading rate asymmetry could not be fully predicted with the k−ε turbulence model, even when a recently proposed compressibility correction was applied.
Particle motion in the stagnation zone of an impinging air jet
Authors: Anderson Steven L. , Longmire Ellen K.
Published: April 2006

This study investigated particle behaviour in the stagnation zone of natural and forced round impinging air jets using flow visualization, image analysis, and particle image velocimetry. The jet Reynolds number was 21000, and the nozzle to plate spacing was five diameters. Small mass loadings of glass beads with inertial time constants τp of 1.7 and 7 ms were examined. The Stokes number associated with the mean flow Stm = τpU0/D ranged from 0.6 to 2.4, and the Stokes number associated with vortices in the forced flow St′ = τpf ranged from 0.3 to 1.25 where f is the vortex passage frequency. Particle velocities near the wall deviated strongly from fluid velocities, resulting in rebound and non-Stokesian effects (i.e. significant particle Reynolds numbers Rep). The deceleration associated with rebounding caused long particle residence times in the stagnation zone and significant increases in particle number density above the plate. Rebound height and the height of the region of particle accumulation were well correlated and increased with Stm. Particles associated with lower Stm were accelerated in the radial direction more quickly, not only because of their decreased inertia, but also because of the larger fluid velocties encountered. Shear layer vortices produced spatial variations in particle concentration in the free jet which caused number density near the plate to fluctuate with time. The vortices had little effect on particle motion near the stagnation point, however. Only particles in the vicinity of vortex cores felt the influence of the vortex-induced velocity field. Hence, particle motion in the stagnation zone was most dependent on the mean flow (and thus Stm).
On steady columnar vortices under local compression
Authors: Verzicco Roberto , Jiménez Javier , Orlandi Paolo
Published: April 2006

Numerical simulations are presented of the long time behaviour of viscous columnar vortices subject to non-uniform axial stretching. The relevant result is that the vortices reach a steady state even when the axial average of the strain is zero, such that they are being compressed during half of their extent. The structure of the flow is analysed and shown to range from local Burgers equilibrium to massive separation. For an intermediate range of Reynolds numbers the vortices are more or less uniform and compact, and it is suggested that this condition is related to the strong vortices observed in turbulent flows. The reason for the survival of the vortices under compression is traced to induced axial pressure gradients and to the viscous cancellation of outgoing vorticity. Theoretical analyses of the linear Burgers’ regime and of the onset of separation are presented and compared to the numerical experiments. The results are related to the observation of intermittency in turbulence, and shown to be consistent both with the observed scaling of vortex diameter, and with the lack of intermittency of the velocity signal.
Non-equilibrium dissociating flow over spheres
Authors: Wen C.-Y. , Hornung H. G.
Published: April 2006

Previous work on the correlation of dissociative non-equilibrium effects on the flow field in front of blunt bodies considered the dependence of the dimensionless shock stand-off distance on the dimensionless dissociation rate immediately after the normal shock in the simple case of a diatomic gas with only one reaction. In this paper, the correlation is corrected to take into account the additional parameter of the dimensionless free-stream kinetic energy, and extended to the case of complex gas mixtures with many species and many reactions, by introducing a new reaction rate parameter that has a clear physical meaning, and leads to an approximate theory for the stand-off distance. Extensive new experimental results and numerical computations of air, nitrogen and carbon dioxide flow over spheres were obtained over a large range of total enthalpy. The results comprise surface heat flux measurements and differential interferograms. Both experimental results and numerical computations substantiate the approximate theory.
Impact of two bodies one of which is covered by a thin layer of liquid
Authors: Korobkin Alexander
Published: April 2006

The paper de als with the plane unsteady problem of the collision of two rigid undeformable and shallow surfaces, one of which is covered by a thin layer of an ideal incompressible liquid. At the initial instant of time, a dry surface touches the liquid free boundary at a single point and then starts to penetrate the liquid layer. The flow region is divided into four parts: the region beneath the entering surface, the jet root, the spray jet and outer region. Inside each of those subdomains the flow patterns have their own peculiarities and are analysed separately. The matching conditions allow us to obtain the uniformly valid asymptotic solution of the original problem. The relative body motion and the characteristics of the spray jets generated under the impact are determined. The condition on the shapes of the bodies, under which the velocity of the impact of the rigid surfaces is non-zero, is derived.
Free decay of shape oscillations of bubbles acoustically trapped in water and sea water
Authors: Asaki Thomas J. , Marston Philip L.
Published: April 2006

Asymptotic results for the free decay of shape oscillations of viscous liquid spheres have been extended to include higher-order terms in the ratios of the inner and outer viscous penetration lengths to the radius. The new expressions are shown to be important for studies in which the two fluids have dissimilar densities and viscosities such as air/liquid systems. The analysis also includes an expansion for the frequency of maximum response of driven oscillations. The calculations are supported by measurements of the small-amplitude quadrupole mode free decay of nearly spherical bubbles acoustically levitated in clean water. The bubble radii ranged from 400 μm to 1400 μm. The results are interpreted in light of the initial-value problem. The lack of excess damping suggests that the interface behaves ideally for times up to two hours after bubble injection. Measurements were also carried out on bubbles in 0.5 m NaCl solution and in sea water. Larger bubbles (radius > 800 μm) in clean water exhibit damping two to four times larger than predicted by theory. The transition from this anomalous damping to theoretical damping is a very abrupt function of radius. All observations were carried out with similar acoustic fields for counteracting buoyancy. The excess damping appears to be associated with some nonlinear response of the bubble.
Collective hydrodynamics of deformable drops and bubbles in dilute low Reynolds number suspensions
Authors: Manga Michael , Stone H. A.
Published: April 2006

Deformation due to hydrodynamic interactions between two deformable buoyant drops may result in the alignment and coalescence of horizontally offset drops. Three-dimensional boundary integral calculations are presented for systems containing two, three or four drops and it is argued that the interactions which occur between three drops or four drops may be characterized qualitatively by the two-drop interactions. In a dilute monodisperse suspension, the rate of coalescence of deformable drops is calculated using far-field analytical results and is found to be proportional to the Bond number. The rate of coalescence in a dilute polydisperse suspension of bubbles in corn syrup is determined by performing a large number of laboratory experiments for Bond numbers based on the larger bubble radius 15 < [Bscr ] < 120. The rate of coalescence is enhanced (by a factor of 10 for [Bscr ] = 10), owing to the effects of deformation, compared to the predictions of models which include hydrodynamic interactions and van der Waals forces among spherical bubbles. The rate of coalescence is greater than the rate predicted by the Smoluchowski model which ignores all hydrodynamic interactions. The experimental results are used to calculate the evolution of the bubble size distribution in suspensions using a standard one-dimensional population dynamics model; deformation affects the size distribution in suspensions, resulting in a wider range of bubble sizes.
An instability in supersonic boundary-layer flow over a compression ramp
Authors: Cassel K. W. , Ruban A. I. , Walker J. D. A.
Published: April 2006

Separation of a supersonic boundary layer (or equivalently a hypersonic boundary layer in a region of weak global interaction) near a compression ramp is considered for moderate wall temperatures. For small ramp angles, the flow in the vicinity of the ramp is described by the classical supersonic triple-deck structure governing a local viscous-inviscid interaction. The boundary layer is known to exhibit recirculating flow near the corner once the ramp angle exceeds a certain critical value. Here it is shown that above a second and larger critical ramp angle, the boundary-layer flow develops an instability. The instability appears to be associated with the occurrence of inflection points in the streamwise velocity profiles within the recirculation region and develops as a wave packet which remains stationary near the corner and grows in amplitude with time.
Nonlinear compressible magnetoconvection. Part 3. Travelling waves in a horizontal field
Authors: Brownjohn D. P. , Hurlburt N. E. , Proctor M. R. E. , Weiss N. O.
Published: April 2006

We present results of numerical experiments on two-dimensional compressible convection in a polytropic layer with an imposed horizontal magnetic field. Our aim is to determine how far this geometry favours the occurrence of travelling waves. We therefore delineate the region of parameter space where travelling waves are stable, explore the ways in which they lose stability and investigate the physical mechanisms that are involved. In the magnetically dominated regime (with the plasma beta,$\hat{\beta}$= 8), convection sets in at an oscillatory bifurcation and travelling waves are preferred to standing waves. Standing waves are stable in the strong-field regime ($\hat{\beta}$= 32) but travelling waves are again preferred in the intermediate region ($\hat{\beta}$= 128), as suggested by weakly nonlinear Boussinesq results. In the weak-field regime ($\hat{\beta}$≥ 512) the steady nonlinear solution undergoes symmetry-breaking bifurcations that lead to travelling waves and to pulsating waves as the Rayleigh number, $\circ{R}$, is increased. The numerical experiments are interpreted by reference to the bifurcation structure in the ($\hat{\beta}$, $\circ{R}$)-plane, which is dominated by the presence of two multiple (Takens-Bogdanov) bifurcations. Physically, the travelling waves correspond to slow magnetoacoustic modes, which travel along the magnetic field and are convectively excited. We conclude that they are indeed more prevalent when the field is horizontal than when it is vertical.
Singularity formation in three-dimensional motion of a vortex sheet
Authors: Ishihara Takashi , Kaneda Yukio
Published: April 2006

The evolution of a small but finite three-dimensional disturbance on a flat uniform vortex sheet is analysed on the basis of a Lagrangian representation of the motion. The sheet at time t is expanded in a double periodic Fourier series: R(λ1, λ2, t) = (λ1, λ2, 0) + Σn,mAn,m exp[i(nλ1 + δmλ2)], where λ1 and λ2 are Lagrangian parameters in the streamwise and spanwise directions, respectively, and δ is the aspect ratio of the periodic domain of the disturbance. By generalizing Moore's analysis for two-dimensional motion to three dimensions, we derive evolution equations for the Fourier coefficients An,m. The behaviour of An,m is investigated by both numerical integration of a set of truncated equations and a leading-order asymptotic analysis valid at large t. Both the numerical integration and the asymptotic analysis show that a singularity appears at a finite time tc = O(lnε−1) where ε is the amplitude of the initial disturbance. The singularity is such that An,0 = O(tc−1) behaves like n−5/2, while An,±1 = O(εtc) behaves like n−3/2 for large n. The evolution of A0,m(spanwise mode) is also studied by an asymptotic analysis valid at large t. The analysis shows that a singularity appears at a finite time t = O(ε−1) and the singularity is characterized by A0,2k ∝ k−5/2 for large k.
Steady compressible vortex flows: the hollow-core vortex array
Authors: Ardalan K. , Meiron D. I. , Pullin D. I.
Published: April 2006

We examine the effects of compressiblity on the structure of a single row of hollowcore, constant-pressure vortices. The problem is formulated and solved in the hodograph plane. The transformation from the physical plane to the hodograph plane results in a linear problem that is solved numerically. The numerical solution is checked via a Rayleigh-Janzen expansion. It is observed that for an appropriate choice of the parameters M∞ = q∞/c∞, and the speed ratio, a = q∞/qv, where qv is the speed on the vortex boundary, transonic shock-free flow exists. Also, for a given fixed speed ratio, a, the vortices shrink in size and get closer as the Mach number at infinity, M∞, is increased. In the limit of an evacuated vortex core, we find that all such solutions exhibit cuspidal behaviour corresponding to the onset of limit lines.
Reconsideration of oblique shock wave reflections in steady flows. Part 2. Numerical investigation
Authors: Vuillon J. , Zeitoun D. , Ben-Dor G.
Published: April 2006

The reflection of shock waves over straight reflecting surfaces in steady flows was investigated numerically with the aid of the LCPFCT algorithm. The findings completely supported the experimental results which were reported in Part 1 of this paper (Chpoun et al. 1995). In addition, the dependence of the resulting shock wave configuration on the distance between the trailing edge of the reflecting wedge and the bottom surface, inside the dual-solution domain, was studied. As a result of this study, as well as the one reported in Part 1, the state of the art of shock wave reflections in steady flows was reconsidered.
Direct measurements of slip in sheared polymer solutions
Authors: Archer L. A. , Larson R. G. , Chen Y.-L.
Published: April 2006

We report direct measurements of slip flow during and after plane-Couette shearing of poly(styrene) solutions between glass surfaces. Slip is studied by visualizing the microscopic motions of micron-sized silica spheres suspended in the solutions. Slip velocities as large as 4 μm s−1 are observed during shear, and recoil displacements of as much as 80 μm are observed at the glass surfaces after the driving surface stops moving. Significant slip is observed when the Weissenberg number $\lambda\dot{\gamma}$ exceeds 0.5 or so, where λ is the relaxation time and $\dot{\gamma}$ the shear rate. The magnitude of the slip correlates strongly with the fluid's birefringence, indicating that slip is induced by polymer stress or orientation. Away from the centre of the sample, toward the free edges, a secondary flow is observed, which appears to be driven by a normal-stress imbalance at these edges.
On spiral coordinates with application to wave propagation
Authors: Campos L. M. B. C. , Gil P. J. S.
Published: April 2006

We introduce a possibly new system of orthogonal curvilinear coordinates, whose coordinate curves are logarithmic spirals in the plane, supplemented by a cylindrical coordinate for three dimensions. It is shown that plane spiral coordinates form a oneparameter family, with equal scale factors along the two orthogonal coordinate curves, and constant Christoffel symbols. The equations of magnetohydrodynamics, which include those of fluid mechanics, are written in spiral coordinates and used to find a state of magnetohydrostatic equilibrium under a radial gravity field and spiral magnetic field, and to solve the equation of non-dissipative Alfvén waves in a spiral magnetic field in terms of Bessel functions. This exact solution specifies the evolution of wave perturbations (velocity and magnetic field) and energy variables (kinetic and magnetic energy densities and energy flux) with distance, for waves of arbitrary frequency. Both the frequency and the spiral angle are varied in plots of the waveforms, which show the effect on Alfvén wave propagation of three simultaneous effects: change in the mass density of the medium and in the strength and direction of the external magnetic field.