bluuebunny/crossref_metadata_2025 huggingface dataset:
Dynamics of linear and T-shaped Ar–I2 dissociation upon B←X optical excitation: A dispersed fluorescence study of the linear isomer
Authors: Stevens Miller Amy E. , Chuang Cheng-Chi , Fu Henry C. , Higgins Kelly J. , Klemperer William
Published: July 2002

We report the dispersed fluorescence spectra of the linear and the previously well-studied T-shaped isomers of Ar–I2 following B←X optical excitation for vpump=16–26, below the I2 dissociation limit. The linear isomer has a continuum excitation spectrum. For excitation at the highest pumping energy (vpump=26), the product vibrational state distribution is nearly identical to that observed for excitation above the I2(B) dissociation limit; it shows a broad, nearly Gaussian distribution of I2(B) vibrational states, with about 22% of the available excess energy deposited in translation of the Ar+I2. This gives direct evidence that the “one-atom cage” effect seen above the I2(B) dissociation limit is attributable to the linear Ar–I2 isomer. The product vibrational state distribution becomes increasingly Poisson for decreasing excitation energies, and only about 7% of the excess energy is deposited in translation for vpump=16. The bond energy in the linear isomer is determined from the spectra, 170(±1.5)⩽D0″(linear Ar–I2(X))⩽174(±1.5) cm−1. A bond energy of D0″(T-shaped Ar–I2(X))=142±15 cm−1 is estimated based on the linear to T-shaped population ratio observed in the beam, which is about 90 cm−1 smaller than that determined from fluorescence spectra. We suggest that electronic quenching in the T-shaped isomer is nearly 100% for the highest vibrational level produced by vibrational predissociation.
Simple physical model of liquid water
Authors: Tanaka Hajime
Published: July 2002

We propose a simple two-state model of water to explain the unusual thermodynamic and dynamic behavior of liquid water. Our model is based on a physical picture that there exist two competing orderings in water, namely, density ordering and bond ordering. Short-range bond ordering leads to the formation of a rather stable locally favored structure (in a ground state) in a sea of disordered normal-liquid structures (in an excited state). Its fraction increases with decreasing temperature, obeying a Boltzmann factor. The concept of a “symmetry (or volume) element” is introduced to specify such locally favored structures in an unambiguous manner. The most probable candidate of such locally favored structures is an “octameric unit,” which is an elementary structural unit of ice Ih. According to this picture, the uniqueness of water comes from that below the crossover pressure Pc (∼2  kbar) the short-range bond order can develop into the long-range order (crystallization into ice Ih). Note that in ordinary liquids crystallization is induced only by density ordering, while in water it is induced by bond ordering below Pc, while by density ordering above Pc. Our model predicts that the anomalous parts of density ρ, isothermal compressibility KT, heat capacity at constant pressure CP, and the activation energy of viscosity η should all be proportional to the Boltzmann factor in the temperature region, where “bulk water” is in a liquid state. It is found that this prediction well explains not only the thermodynamic anomaly of ρ, KT, and CP, but also the dynamic anomaly of η, including their pressure dependencies. This demonstrates that the anomaly of “bulk water” is a direct consequence of short-range bond ordering and it is not due to the thermodynamic singularity, at least above −20 to −30° C. Our model indicates a new possibility that the viscosity anomaly of water may also be explained by the same mechanism as that of the thermodynamic anomaly; namely, neither critical anomaly nor slow dynamics associated with a glass transition may be a major cause of the dynamic anomaly of water above −20 °C. We also point out that the water’s thermodynamic and dynamic anomaly is not necessarily related to the low-temperature phase behavior of liquid water in an obvious manner, contrary to the common belief.
Cahn–Hilliard theory with triple-parabolic free energy. II. Nucleation and growth in the presence of a metastable crystalline phase
Authors: Gránásy László , Oxtoby David W.
Published: July 2002

Nucleation and growth of stable and metastable crystalline phases are described in the framework of a single-order parameter Cahn–Hilliard theory. A piecewise parabolic free-energy order parameter relationship composed of three parabolas of positive curvature coefficient has been adopted. The analytical solution of the problem is presented. It is found that above a critical (bifurcation) temperature the interface is layered; a metastable layer is sandwiched between the initial and the stable phases. Above the bifurcation point, two solutions exist, one with a sharper interface and another with an extended metastable layer, of which the latter has a larger free energy of formation. The two solutions converge to each other at the bifurcation temperature. At lower temperatures only the metastable phase is able to nucleate from the liquid. In the parameter space we investigated, the growth rate of the stable phase exceeds that of the metastable one. The nucleation and growth rates are sensitive to the features (curvature and position) of the parabola for the metastable phase.
The effect of the underlying substrate on the crystallization kinetics of dense amorphous solid water films
Authors: Dohnálek Z. , Kimmel Greg A. , Ciolli Ryan L. , Stevenson K. P. , Smith R. Scott , Kay Bruce D.
Published: July 2002

The crystallization kinetics of thin, dense amorphous solid water films deposited on crystalline ice and Pt(111) substrates are investigated. A dramatic acceleration of the crystallization rate is observed for amorphous films on crystalline ice substrates. The acceleration originates from the absence of the nucleation process on the crystalline ice substrate which serves as a two-dimensional nucleus for the growth of the crystalline phase. This contrasts with the crystallization on a Pt(111) substrate which proceeds via bulk nucleation and three-dimensional growth. Activation energies for growth and nucleation are determined to be 56 and 140 kJ/mol, respectively, using the apparent activation energies measured on crystalline ice and Pt(111) substrates. For amorphous films deposited on crystalline ice substrates, the crystallization rate decreases rapidly with increasing distance from the crystalline ice substrate most probably due to crystallization-induced cracking of the films.
Ultrafast excited-state proton transfer and subsequent coherent skeletal motion of 2-(2′-hydroxyphenyl)benzothiazole
Authors: Lochbrunner S. , Wurzer A. J. , Riedle E.
Published: July 2002

The excited-state intramolecular proton transfer of 2-(2′-hydroxyphenyl)benzothiazole was investigated with 30 fs temporal resolution. The proton takes 60 fs to arrive at its S1 equilibrium position and the electron distribution changes on the same time scale. The molecule cannot adjust to the new structure of the H-chelate ring equally fast and starts to strongly vibrate in four low-frequency skeletal modes. This coherent wave packet motion is the cause of the experimentally observed strong signal oscillations that are only weakly damped despite the solvent environment.
Some multivariable orthogonal polynomials of the Askey tableau—Continuous families
Authors: Tratnik M. V.
Published: July 2002

A multivariable generalization is presented for all the continuous families of the Askey tableaux. This significantly extends some previously known multivariable Jacobi polynomials. The latter are recovered as a limit case from a family of multivariable continuous Hahn polynomials which in turn are obtained as a limit of some multivariable Wilson polynomials. A continuous analog of the single variable Charlier polynomials is also introduced.
Algebraic structures of quantum projective field theory related to fusion and braiding. Hidden additive weight
Authors: Juriev Denis
Published: July 2002

The interaction of various algebraic structures describing fusion, braiding, and group symmetries in quantum projective field theory is the object of investigation in this article. Structures of projective Zamolodchikov algebras, their representations, spherical correlation functions, correlation characters and enveloping quantum projective field theory (QPFT)-operator algebras, projective Ẅ-algebras, shift algebras, infinite-dimensional R matrices Rproj(u) and Rproj*(u) of the QPFT, braiding admissible QPFT-operator algebras, and projective G hypermultiplets are explored. It is proven (in the formalism of shift algebras) that sl(2,C)-primary fields are characterized by their projective weights and by the hidden additive weight, a hidden quantum number discovered in this article. Special attention is paid to various constructions of projective G hypermultiplets (QPFT-operator algebras with G symmetries).
On Fock-space representations of quantized enveloping algebras related to noncommutative differential geometry
Authors: Jurčo B. , Schlieker M.
Published: July 2002

In this paper explicitly natural (from the geometrical point of view) Fock-space representations (contragradient Verma modules) of the quantized enveloping algebras are constructed. In order to do so, one starts from the Gauss decomposition of the quantum group and introduces the differential operators on the corresponding q-deformed flag manifold (assumed as a left comodule for the quantum group) by a projection to it of the right action of the quantized enveloping algebra on the quantum group. Finally, the representatives of the elements of the quantized enveloping algebra corresponding to the left-invariant vector fields on the quantum group are expressed as first-order differential operators on the q-deformed flag manifold.
Statistical properties of eigenvectors in non-Hermitian Gaussian random matrix ensembles
Authors: Mehlig B. , Chalker J. T.
Published: July 2002

Statistical properties of eigenvectors in non-Hermitian random matrix ensembles are discussed, with an emphasis on correlations between left and right eigenvectors. Two approaches are described. One is an exact calculation for Ginibre’s ensemble, in which each matrix element is an independent, identically distributed Gaussian complex random variable. The other is a simpler calculation using N−1 as an expansion parameter, where N is the rank of the random matrix: this is applied to Girko’s ensemble. Consequences of eigenvector correlations which may be of physical importance in applications are also discussed. It is shown that eigenvalues are much more sensitive to perturbations than in the corresponding Hermitian random matrix ensembles. It is also shown that, in problems with time evolution governed by a non-Hermitian random matrix, transients are controlled by eigenvector correlations.
AC transport losses in multifilamentary (Bi, Pb)2Sr2Ca2Cu3Ox/Ag tapes
Authors: Rudnev I. A. , Khodot A. E. , Eremin A. V. , Akimov I. I.
Published: July 2002

The results of ac transport losses measurements are presented for multifilamentary HTSC composite Bi-2223/Ag tapes with the number of filaments N=7, 19, 37, 61, 91, 127, 169, and 703. The measurements have been made under the self-field conditions as well as in a constant magnetic field applied to the tapes at different angles. The dependence of AC losses on the amplitude and frequency of the alternating transport current have been obtained. It is found that the dependence of the AC losses on the current amplitudes for all the tapes are in accord with the Norris theoretical predictions for an elliptical or strip geometry of the wire. The external magnetic field increases the magnitude of the AC losses. It is concluded that transport AC losses in multifilamentary HTSC composites are “saturation losses.”
Dynamics of vortex lattice in the current state in high-temperature superconductors: Monte Carlo method
Authors: Gracheva M. E. , Kashurnikov V. A. , Rudnev I. A.
Published: July 2002

The current–voltage characteristics (IVC) of real defective high-temperature layered superconductors are calculated by simulating the vortex lattice by means of the Monte Carlo method. The temperature dependence of the defect activation energy is obtained. It is shown that IVC singularities in different temperature ranges are due to the change in the phase conditions of the vortex system and, in particular, the presence of the “rotating lattice” phase in a wide temperature range.
A lower bound on the third virial coefficient for a system of arbitrary hard convex particles
Authors: Jansons Kalvis M.
Published: July 2002

In this Brief Communication a lower bound on the third virial coefficient for a system of arbitrary hard convex particles is determined, using a result from integral geometry. The bound is a simple function of the volumes, surface areas, and integrals of the mean curvature of the particles. Applied to a system of identical balls, the ratio of the exact result to the lower bound is 1.1298... . The bound does not become trivial (i.e., zero or negative) for systems of particles of zero volumes provided that they have positive surface areas.
Asymptotic solution of the Enskog equation
Authors: Kuszell A. , Makowski K.
Published: July 2002

An asymptotic solution of the Enskog equation is obtained by an expansion in two parameters: ε, estimating the deviation from equilibrium and ε1, the Knudsen number. It is shown that different relations between these parameters imply that the different versions of approximate hydrodynamic equations are consistent. A second-order approximated solution of the Enskog equation in the case of ε≈ε1 provides nonlinear hydrodynamic equations for dissipative incompressible flows as the most appropriate approximation.
Side wall effects in centrifugal separation of mixtures
Authors: Ungarish Marius
Published: July 2002

The flow of a centrifugally separating mixture of particles (droplets) and fluid is considered, with emphasis on the azimuthal no-slip requirement on the side wall of the cylindrical container. In the framework of the ‘‘mixture’’ averaged equations—when the Ekman number E, particle Taylor number β, and relative density difference ε are small—a single partial differential nonhomogeneous parabolic equation is obtained for the angular velocity ω(r,t) (relative to the rotating vessel). Analytical and numerical solutions are presented for the dilute limit and for the more general case, respectively. It is shown that, during the separation process, ω develops a quasisteady boundary layer of thickness δ(λ/(λ−1))1/2 on r=1, only if λ>1, where δ=H1/2E1/4 is the typical Stewartson layer scale, λ=E1/2/εβH, and H is the dimensionless height of the container. If λ≤1, however, the side wall affects ω in an unsteady, diffusing viscous domain. Correspondingly significant variations in the axial flux are induced by the Ekman layers. Comparisons to numerical results (produced by a code discussed elsewhere) of the full two-fluid equations display a favorable agreement.
The spreading of self-excited hot jets by side jets
Authors: Monkewitz Peter A. , Lehmann Bernhard , Barsikow Bernd , Bechert Dietrich W.
Published: July 2002

A transitional, heated, axisymmetric air jet is investigated in the regime in which it is self-excited and develops a regular sequence of intense vortex ring structures. Seeding of the jet fluid and laser illumination reveals a star-shaped jet cross section with between two and six radial fingers. Each finger thereby represents a cut through a strong quasisteady side jet that is directed away from the main jet axis and is approximately planar. It is suggested that these side jets contribute prominently to the entrainment of all jets with strong primary vortex ring structures.
Passive scalar tagging for the study of coherent structures in the plane mixing layer
Authors: Ramaprian B. R. , Sandham N. D. , Mungal M. G. , Reynolds W. C.
Published: July 2002

Data obtained from the two-dimensional numerical simulation of a plane mixing layer have been used to study the feasibility of tagging one side of the flow by a passive scalar and using the instantaneous concentration of the scalar to detect the typical coherent events in the flow. The study has shown that this technique works quite satisfactorily and yields results similar to those obtained by using the instantaneous vorticity as a detection criterion. The contribution from the coherent events to the time-averaged turbulent momentum and scalar transport has been estimated. It is found that this contribution is of the same order as the time-mean transport during most of the dynamical evolution of the coherent structure. However, it may attain very large values for short periods of time in the neighborhood of pairing. The increase is particularly spectacular in the case of the Reynolds shear stress. While the present findings obtained from a two-dimensional simulation seem to support earlier results obtained from actual experiments, it is desirable to conduct additional studies with three-dimensional simulations when they become available.
A model for Stokes flow through a stenotic channel
Authors: Davis A. M. J. , Ranger K. B.
Published: July 2002

A model for Stokes flow through a channel with a stenosis is presented for both two-dimensional motion and three-dimensional flow with axial symmetry. Expressions are found for both the axial velocity and wall stress on the boundary.
Analysis of a rapidly distorted, supersonic, turbulent boundary layer
Authors: Jayaram M. , Donovan J. F. , Dussauge J.-P. , Smits A. J.
Published: July 2002

Rapid distortion concepts are used to calculate the evolution of turbulent stresses in the flow of a compressible boundary layer through a short region of concave curvature. Different models for the rapid part of strain were tested. For all models used, the calculations in the curved region agree well with experimental data. Downstream, however, the discrepancies between experiment and calculation increase, probably because of the increased importance of the mean shear and the nonlinear terms.
The effects of streamwise vortices on transition in the plane channel
Authors: Singer Bart A. , Reed Helen L. , Ferziger Joel H.
Published: July 2002

The effect of streamwise vorticity on the three-dimensional breakdown of two-dimensional Tollmien–Schlichting waves in a plane-channel flow is studied via direct numerical simulation. Streamwise vortices of the strength inherent to most transition experiments are shown to alter the relative importance of the subharmonic and fundamental modes and to explain discrepancies observed between theory, previous computations, and experiments in both the plane channel and in the flat-plate boundary layer. It is shown that without the inclusion of the vortices, the computations support the theory; with inclusion of the vortices, the computations support the experiments. This work demonstrates the importance of combining theory, experiments, and computations in the study of transition in both internal and external applications.
Tensorial volume of turbulence revisited
Authors: Kassinos S. C. , Reynolds W. C.
Published: July 2002

A corrected tensorial turbulent volume transport equation, which is exact for uniform density flows, is derived from the Navier–Stokes equations. For homogeneous turbulence, the new terms appearing in the correct equation account for the effect of the pressure velocity correlation and of the mean velocity gradient. The correct tensorial volume equation is closed only for the case of isotropic homogeneous turbulence. To solve the equation for the anisotropic case a model for the velocity spectrum is required. When applied to the cases of isotropic expansion, incompressible axisymmetric contraction, and shearing of initially isotropic turbulence, the correct equation predicts the same time evolution for the tensorial volume that rapid distortion theory does.
Lattice gas method based on the Chapman–Enskog expansion
Authors: Higuera F. J.
Published: July 2002

A new lattice gas is introduced based on the Chapman–Enskog expansion for small Knudsen numbers of a model Boltzmann equation. This kind of discrete dynamical system is intended to narrow the gap between ordinary lattice gases and the macroscopic incompressible Navier–Stokes equations, and to increase the efficiency and flexibility of lattice gas methods. The large scale evolution of the gas is shown to obey the Navier–Stokes equations. The linear stability of the system, considered as a finite-difference scheme, is studied.
A note on the effects of polymer additives on the formation of Goertler vortices in an unsteady flow
Authors: Ikeda E. , Maxworthy T.
Published: July 2002

The addition of a polymer to a fluid has been observed to delay the transition to turbulence. The question then arises: Can the polymer delay the appearance of a hydrodynamic instability, such as the one that leads to Goertler vortices? The experimental technique was the same as that used in Maxworthy [Turbulence Measurements in Liquids (Univ. of Missouri—Rolla, Rolla, MO, 1971), pp. 32–38], where a cylindrical container of fluid in solid body rotation was suddenly brought to rest. The diffusing boundary layer on the curved side wall became unstable to a Goertler vortex pattern after a time that could be related to the initial rotation rate and the critical Goertler number (Gc). For small concentrations of polymer, the increase in Gc was linear in concentration for both Separan AP30 and polyethylene oxide. This number seemed to asymptote to a value of 9.5 for the Separan AP30 above a concentration of 0.10% by weight and to a value of 7.5 for the polyethylene oxide above a concentration of 0.07%. The wavelength of the instabilities increased due to the presence of the polymer; for a 0.1% concentration, the increase was 50% to 90%, depending on the initial rotation speed.
A rising bubble in a tube
Authors: Levine Herbert , Yang Yumin
Published: July 2002

The rise of an infinitely long bubble in a vertical cylindrical tube full of inviscid fluid is studied. It is demonstrated numerically that the rising velocity of the bubble is determined by the surface tension through a solvability mechanism. The numerical results are in good agreement with the experimental ones.
A demonstration of the suppression of turbulent cascades by coherent vortices in two-dimensional turbulence
Authors: McWilliams James C.
Published: July 2002

The role of coherent vortices in suppressing the rates of cascade (i.e., spectrum evolution through scale transfer and dissipation) is demonstrated in numerical solutions of decaying two-dimensional turbulence at high Reynolds number. The demonstration is made by comparing the evolution of a primary solution that has well-developed vortices with other solutions that initially have equivalent wavenumber spectra but lack vortices because of an imposed phase scrambling. The solutions without vortices have substantially greater cascade rates. Furthermore, when the primary solution is compared with other solutions whose initial conditions are constructed only from isolated, axisymmetric vortices, their spectrum evolution is qualitatively similar. This demonstrates the control of cascade rates by coherent vortices.
Lagrangian correlations and scales in uniformly sheared turbulence
Authors: Karnik U. , Tavoularis S.
Published: July 2002

The present study focuses on the relationship between dispersion and Lagrangian statistics in a flow with uniform shear and with turbulent stresses and scales that are nearly transversely homogeneous but grow exponentially in the streamwise direction. Based on the assumption that the Lagrangian velocity field is self-preserving, an expression is derived for the Lagrangian autocoreelation coefficient in terms of the mean-square particle dispersion. Estimates of the mean-square particle dispersion, obtained from measurements of the mean temperature field downstream of a thin heated line source in uniformly sheared turbulence, are subsequently used to evaluate the Lagrangian autocorrelation coefficient and the corresponding integral scale and microscale. The ratios of the estimated Lagrangian scales and the Eulerian scales measured in a convected frame are found comparable to the estimates of previous investigators in other flows.
Multigroup solutions of the nonlinear Boltzmann equation
Authors: Kügerl Georg , Schürrer Ferdinand
Published: July 2002

The nonlinear Boltzmann equation is solved numerically to examine the Maxwellization of spatially homogeneous gases, using the multigroup method. By applying the Krook–Wu scattering model, an exact solution of the Boltzmann equation (BKW mode) is reproduced with high accuracy. The numerical code is also used for hard-sphere molecules. Initial distributions are a Maxwellian with tail cutoff and distributions composed of two δ peaks. For the latter class, a strong transient overpopulation of the distribution function is observed, which may amount to several orders of magnitude.
Creeping flow of a conducting fluid past axisymmetric bodies in the presence of an aligned magnetic field
Authors: Kyrlidis A. , Brown R. A. , Walker J. S.
Published: July 2002

The use of strong magnetic fields for the control of particle settling in metallic systems is investigated in the limit of small inertial and magnetic Reynolds numbers. Finite element calculations of flow around axisymmetric bodies show that the drag increases proportional to the intensity of the magnetic field B or the Hartmann number Ha. The flow field forms boundary layers, which thin with increasing Ha, along surfaces parallel to the flow. For axisymmetric bodies, the boundary layer separates as the poles of the surface are approached and encloses regions of almost stagnant fluid. These regions spread upstream and downstream along the body with increasing Ha, thereby trapping the particle in a column of stagnant fluid. The pressure difference between the leading and trailing fluid columns is responsible for the increased particle drag. Asymptotic analysis with Ha≫1 confirms the scalings from the computations and clarifies the flow structure near the body.
Numerical simulation of flow structures and instabilities occurring in a liquid-encapsulated Czochralski process
Authors: Fontaine J. P. , Randriamampianina A. , Bontoux P.
Published: July 2002

This paper concerns the prediction and the analysis of the steady and time-dependent flow regimes that develop in liquid-encapsulated Czochralski (LEC) systems for material processing. The combined effects of temperature gradient and rotation on the flow and the temperature field, and especially the influence of the encapsulant layer (of Prandtl number 10≤Pre≤3270 ) on the melt (Prm=0.015), are investigated using axisymmetric modeling. The accuracy of the solutions based on a finite element method is discussed. The effects of the Grashof number (up to Gr=1.9×107 ) and of the rotation Reynolds numbers of the crystal (up to ‖Res‖=104 ) and of the crucible (up to Rec=1.5×104) are analyzed.
Semiempirical theories of turbulent diffusion in a neutrally stratified atmospheric surface layer
Authors: Tsarenko V. M. , Yaglom A. M.
Published: July 2002

Four different models of pressure-concentration-gradient correlations are considered. These models, together with the local equilibrium approximation in the corresponding second-order closure formulation, permit one to determine all the components of the eddy-diffusivity tensor Kij(z) for steady plane-parallel turbulent flows. Computations of the eddy diffusivities Kij are performed for a homogeneous turbulent flow with constant shear and for an atmospheric surface layer (ASL) in neutral stratification. The results obtained by different models differ only slightly and agree satisfactorily with the available experimental data. Characteristics of the diffusion from an instantaneous point source in the neutral atmospheric surface layer are computed from the considered local equilibrium second-order closures and then are compared with the characteristics obtained from two other second-order closures that are not local equilibrium ones. This comparison shows that more complex theories give results that are close to those obtained from the local equilibrium approximation.
Scaling properties of the viscous-convective scalar spectral subrange in turbulent jets
Authors: Kerstein Alan R.
Published: July 2002

A recent analysis by Dimotakis and Miller [Phys. Fluids A 2, 1919 (1990)] of the power spectrum of a diffusive scalar in turbulent flow identified a difficulty with the k−1 viscous-convective scaling in the limit of very large Schmidt number for finite-Reynolds-number flows with bounded scalar fluctuations. Here, a modified scaling of the form k−1−p is derived for the self-similar round jet, where p∼Re−1/2 for Re≫1.
Comments on ‘‘Rayleigh–Taylor instability of a continuously stratified magnetofluid under a general rotation field’’ [Phys. Fluids A 1, 1600 (1989)]
Authors: Chakraborty B. B. , Tuteja G. S.
Published: July 2002

Rayleigh–Taylor instability of a continuously stratified magnetofluid under a general rotation field, earlier studied by Dávalos-Orozco and Aguilar-Rosas [Phys. Fluids A 1, 1600 (1989)] is reconsidered. Some corrections in their analysis are made and the discrepancies between their results in some special cases and those obtained by Chakraborty [Phys. Fluids 25, 743 (1982)] and Hide [J. Fluid Mech. 39, 283 (1969)] are removed.
Source function approach to turbulence bulk properties
Authors: Canuto V. M. , Cheng Y. , Hartke G. J. , Schilling O.
Published: July 2002

A turbulence model to compute bulk properties is presented in which a prescribed source function is used to provide the rate of energy input into the turbulent flow, and the EDQNM model is used to treat the nonlinear transfer in the Navier–Stokes equations. The predictions of the model are tested against (1) the measured Nusselt number versus Rayleigh number relation in turbulent laboratory convection, and (2) the measured bulk kinetic energies and dissipation rates in turbulent channel flow for Reynolds numbers Re=12 300 and 30 800. In addition, a sensitivity study is performed with respect to the choice of Kolmogorov constant. Generally, the predictions of the model are in reasonable accord with the available experimental data.
Observations of pattern evolution in thermal convection with high-resolution quantitative schlieren imaging
Authors: Irvin Benjamin R. , Ross John
Published: July 2002

High-resolution measurements of the mean temperature gradient field of a fluid undergoing thermal convection in a vertical slot were made. The detection method employs schlieren optics with a linear photodiode array detector. With proper calibration the schlieren signals permit quantitative reconstruction of the varying temperature field along one dimension in the fluid, with a relative temperature resolution of ±0.02 K. The critical applied temperature difference, ΔTb,c, is determined by extrapolation of the measured convection pattern amplitudes. The measurements permit detailed monitoring of the wave number distribution and its development in time as well as harmonic analysis of the temperature waveform. The stability limits of convective patterns are investigated as a function of forcing and wave number and the observed limits are compared to theoretical predictions. The details of the transitions from conduction to convection and from one convective spatial pattern to another are observed and analyzed as the degree of forcing is varied. The creation and destruction of convective roll cells is observed as is the propagation of convective flow across the slot.
Influence of viscous stresses on shock wave stability in gases
Authors: Bashkirov A. G.
Published: July 2002

New shock jump conditions and the effect of curvature are derived, including viscous stresses within the shock layer and in the downstream gas flow. The main difference from the well-known Rankine–Hugoniot conditions is the existence of surface tension due to an anisotropy of viscous stresses in the layer. The classical problem of shock wave instability in gases has been solved with the new jump conditions. The surface tension is found to stabilize the shock wave generally whereas the viscous stresses in downstream flow destabilize it. The destabilizing effect dominates in the mode of spontaneous sound emission resulting in an absolute instability of the shock wave. This mode was previously considered to be neutrally stable.
Shear-thinning duct flow characteristics of relevance to stirred reactors
Authors: Pinho F. T. , Whitelaw J. H.
Published: July 2002

Improvements in the performance of stirred reactors operating with non-Newtonian fluids under turbulent flow conditions require detailed knowledge of their fluid-mechanic properties. The complexity of stirred vessel flows, the large variety of flow configurations, and possible non-Newtonian fluids indicate that such an undertaking should be preceded by an investigation aimed at selecting the fluids and to assess transitional Reynolds number and non-Newtonian effects in the flows with characteristics of relevance to the process of stirring tanks. Mean and turbulent velocity characteristics of the flow of aqueous solutions of CMC (carboxymethyl cellulose) in a 25.4 mm diam duct, with and without a 50% area blockage disk located on its axis, were measured with a laser velocimeter. The polymer solutions at concentrations of 0.1% to 0.4% by weight were weakly elastic and shear-thinning. Water and a viscous Newtonian fluid were also investigated for comparison. The pipe flow measurements encompassing a range of Reynolds numbers from 240 to 111 000 quantify the delay in transition from laminar to turbulent flow caused by shear-thinning, the suppression of turbulence fluctuations particularly in the radial and tangential directions, and the reduction in the drag coefficient.

The baffle flow of Newtonian and non-Newtonian fluids was increasingly dependent on Reynolds numbers below 50 000 with the dampening of the normal Reynolds stresses also dependent on polymer concentration. At a Reynolds number 8000, the maximum values of turbulent kinetic energy with the 0.2% CMS and 0.4% CMC solutions were 35% and 45% lower than for water, respectively. Non-Newtonian effects are important in regions of low strain rates at low Reynolds numbers, and are represented by a decrease of turbulent diffusion and an increase of viscous diffusion, which would be enlarged by the effect of the elongational viscosity if higher than three times the viscometric viscosity. The performance of stirred vessel flows is likely to be impaired by the suppression of small-scale turbulence over the boundary layer of the blades and its possible early separation. A deterioration in the quality of micromixing is also likely to arise because of lower turbulence production in the shear layer of the jet emanating from the impeller. With strong shear-thinning fluids, the high viscosity in the large regions of low mean shear rate far from the impeller further contribute to turbulence suppression so that laminarizations of the flow may occur. However, the strong three-dimensionality of the mixer flow means that turbulence damping will occur for all Reynolds stresses rather than in preferential directions.
Vortices interacting with nonslip walls: Stirring and mixing of primary and secondary vorticity
Authors: Orlandi Paolo
Published: July 2002

The interaction of vortices with fixed boundaries is an important problem in many areas of practical interest. During the approach of the vortices to the wall, vorticity is created at the wall, and then mixing and stirring of primary and secondary vorticity lead to different scenarios that depend on the Re number. This problem is relevant to bursting in turbulent boundary layers, which is responsible for turbulence production. In the near-wall region of turbulent flows, vortex stretching plays a fundamental role. As a prelude to attempting the solution by direct simulation of 3-D Navier–Stokes equations, it is convenient to describe the mechanism associated with 2-D or axisymmetric flows. In the present study, axisymmetric vortex rings and vortex dipoles approaching a nonslip flat wall have been considered. In both cases, experimental results based on flow visualization are available.1,2 The purpose of the present paper is to do a numerical simulation with the same conditions used in the real experiments and follow the flow evolution for a much longer time than has been possible in such experiments. Both for axisymmetric and 2-D cases the numerical simulation shows, as revealed by the experiments, that, at the initial stage, very thin layers of vorticity of sign opposite to that of the primary vortex are generated at the wall.

This mechanism is almost independent of Re. This thin and intense layer immediately becomes unstable and rolls up creating a secondary vortex. This vortex interacts with the primary vortex and different flow structures are generated, depending on Re. The location where these structures form depends, in large measure, on whether vortex stretching is present or not. Particularly relevant to the bursting phenomenon is the case at intermediate Re (e.g., Re=1600). Here, a new dipole is created near the wall after multiple rebounding and pairing of secondary vortices. This new structure has sufficient strength to move itself away from the wall. We conclude that mixing and stirring of vorticity are the relevant mechanisms influencing the whole process in a two-dimensional simulation. This ejection of a new structure was previously noticed in the interaction of vortex rings with a wall. From flow visualization, Walker et al., at Re=Γ/ν>3500, observed the occurrence of azimuthal instabilities and, immediately after that, they noticed a new vortex ring was rapidly ejected away from the wall.2 From these observations, those authors argued that the ejection was due to the azimuthal instabilities. In the present paper, axisymmetric calculations have been done in the same range of numbers used in the experiment of Walker et al.2 From the time evolution of the vorticity distribution, we argue that vortex pairing is the main mechanism that contributes to the generation of the new ring rather than azimuthal instabilities. The numerical simulations clearly show that this new ring is created above the primary ring and not at its interior.
Superdiffusion transport in stratified porous media
Authors: Koplik Joel
Published: July 2002

We discuss the convective dispersion of passive tracer in a stratified porous medium consisting of an infinite number of parallel layers, an idealization of geologically heterogeneous oil and water reservoirs first discussed by Matheron and de Marsily. There is assumed to be a random, horizontal velocity in each layer, reflecting variations in permeability, and the tracer undergoes molecular diffusion between layers coupled to convection plus diffusion in the horizontal direction. The resulting tracer motion is superdiffusive, 〈X2(t)〉→t3/2 at large times, with analogous behavior for higher moments, and a non-Gaussian probability distribution. We discuss the origin of this effect using both intuitive and exact arguments, give an asymptotic estimate for the tracer concentation distribution, and consider the first-passage-time aspects of the problem. [This work was done in collaboration with A. Georges, J.-P. Bouchaud, F. Leyvraz, A. Provata, and S. Redner.]
The dispersion of particles in a separated backward-facing step flow
Authors: Ruck B. , Makiola B.
Published: July 2002

Flows in technical and natural circuits often involve a particulate phase. To measure the dynamics of suspended, naturally resident or artificially seeded particles in the flow, optical measuring techniques, e.g., laser Doppler anemometry (LDA) can be used advantageously. In this paper the dispersion of particles in a single-sided backward-facing step flow is investigated by LDA. The investigation is of relevance for both, two-phase flow problems in separated flows with the associated particle diameter range of 1–70 μm and the accuracy of LDA with tracer particles of different sizes. The latter is of interest for all LDA applications to measure continuous phase properties, where interest for experimental restraints require tracer diameters in the upper micrometer range, e.g., flame resistant particles for measurements inside reactors, cylinders, etc. For the experiments, a closed-loop wind tunnel with a step expansion was used. Part of this tunnel, the test section, was made of glass.

The step had a height H=25 mm (channel height before the step 25 mm, after 50 mm, i.e., an expansion ratio of 2). The width of the channel was 500 mm. The length of the glass test section was chosen as 116 step heights. The wind tunnel, driven by a radial fan, allowed flow velocities up to 50 m/sec which is equivalent to ReH=105. Seeding was performed with particles of well-known size: 1, 15, 30, and 70 μm in diameter. As 1 μm tracers oil droplets were used, whereas for the upper micron range starch particles (density 1.500 kg/m3) were chosen. Starch particles have a spherical shape and are not soluble in cold water. Particle velocities were measured locally using a conventional 1-D LDA system. The measurements deliver the resultant ‘‘flow’’ field information stemming from different particle size classes. Thus, the particle behavior in the separated flow field can be resolved. The results show that with increasing particle size, the particle velocity field differs increasingly from the flow field of the continuous phase (inferred from the smallest tracers used). The velocity fluctuations successively decrease with increasing particle diameter. In separation zones, bigger particles have a lower mean velocity than smaller ones.

The opposite holds for the streamwise portions of the particle velocity field, where bigger particles show a higher velocity. The measurements give detailed insight into the particle dynamics in separated flow regions. LDA-measured dividing streamlines and lines of zero velocity of different particle classes in the recirculation region have been plotted and compared. In LDA the use of tracer particles in the upper micrometer size range leads to erroneous determinations of continuous phase flow characteristics. It turned out that the dimensions of the measured recirculation zones are reduced with increasing particle diameter. The physical reasons for these findings (relaxation time of particles, Stokes numbers, etc.) are explained in detail.
The kinematics of quasi-2-D freely decaying turbulence in a stratified fluid
Authors: Caperan Ph. , Maxworthy T. , Spedding G.
Published: July 2002

We have studied experimentally the dynamics of freely decaying turbulence in a stratified fluid. At low Froude number this flow has a quasi-2-D behavior1 that modifies the mixing (Fr=0.004, Re=1000; based on the integral scales). We characterize the vorticity evolution in the range scales where the enstrophy cascade is taking place. The quasi-2-D period of this turbulence is studied by photographic analysis of the velocity field V, which is interpolated on a regular grid (128×128). We are able to decompose it into its internal wave and turbulent component, and to compute its derivative fields up to the vector η=curlHΩV (related to the enstrophy cascade; where ΩV is the vertical vorticity). An enstrophy transfer model is developed by generalizing the model of Weiss to slightly divergent flows: the tensor F=∇HVH−DivH VHI2 (where H denotes the horizontal component, and I2 is the identity tensor of order 2) enters the equation of evolution for η as dtη=ηF+ΩV curlH (DivHVH). (1) An elongation of η corresponds to an increase of the local vorticity gradient, which is the mechanism of the enstrophy cascade to small scales.

We neglect the second term of (1) since it occurs at the measurement noise scale. Thus eigenvalues λi and eigenvectors of F characterize Eq. (1) and we present maps of these functions. The analysis of these eigenvalues of F gives us the ‘‘coherent’’ zones of the flow where λ is complex, i.e., where the local effect of rotation counteracts the local strain induced by the whole vorticity field. In the remaining zones the λi are generally of opposite sign. Under this condition, the histogram of the angle α between the elongating (V+) and the contracting (V−) eigenvectors shows broad peaks centered on ±π/2, Where the separating curve of ΩV=0 on an Ω map corresponds to α=±π/2. In these regions the strain provokes a deformation of the vorticity field, which corresponds to the enstrophy cascade phenomenon. Statistics on the angles β±=∠(η,V±) reveals a mean alignment of η with V+ (elongation) and a mean right angle with V−. Thus, the relations between F and η are clearly shown in our experimental case.

The main effect of vertical compression or expansion at every point of the field, due for instance to a weak internal wave, is to modify the eigenvalues of F, thus inhibiting or favoring the local enstrophy cascade. In some cases, it is able to impose its sign onto the two eigenvalues: this is observed at the border of the coherent zone.
Turbulent mixing and the selectivity of fast chemical reactions
Authors: Bourne J. R.
Published: July 2002

Assuming that complete information is available about (a) the chemical reactions (mechanism, stoichiometry, thermodynamics, and kinetics) and (b) the turbulent flow field in a reactor (mean velocities and turbulence parameters), we would like to calculate directly the time evolution of the temperature and the concentrations of all species present. No general method is yet available to satisfy this goal. Starting from the phenomena of reaction, molecular diffusion, and laminar deformation in laminated structures, which are formed by the action of vorticity, mixing in liquids at sub-Kolmogorov scales can be quantitatively described. This approach requires the compositions of the fluids incorporated into the vortices to be known. Thus, for example, when a reagent solution (B) is slowly added to a huge volume of a second reagent solution (A) in a stirred tank reactor, fresh B mixes with the average A composition. (Slowly means that the addition time is much greater than the time needed for turbulent and molecular transport to homogenize the tank contents.) Progress of the reactions is then determined essentially by the interaction between the fine-scale mixing (near the Batchelor concentration scale) and the chemical kinetics.

A convenient way to evaluate this modeling compares predicted and measured product distributions (or selectivities) for fast multiple reactions. (Up to now, this has been done for dilute solutions, which exhibited concentration, rather than also temperature segregation.) Advantages compared to working with single reactions can include enhanced sensitivity, inclusion of a wider range of flow fields than turbulent pipe flow, e.g., well-stirred systems, and practical relevance of controlling product distributions in the manufacture of chemicals. The effects on the product distributions of fast reactions of operating parameters such as stoichiometric and volumetric feed ratios, reagent concentrations, feed location, impeller speed, size and shape, viscosity, and type of reaction can be well described. Present efforts concentrate on relaxing the assumption of slow feed addition and of describing reactors where not only fine-scale, but also coarse-scale inhomogeneities occur. A simplified model for the engulfment frequency between fluids having different compositions is being evaluated. Some progress has been made, but the way in which fluid elements mix with each other is still not fully known.