Volume 16, Issue 11, November 2004
 LETTERS


A dynamic flame surface density model for large eddy simulation of turbulent premixed combustion
View Description Hide DescriptionA dynamic formulation for a previously developed coupled fractal–similarity model for large eddy simulation of premixed combustion is proposed. In this formulation, the fractal dimension is obtained dynamically from the resolved scales, leaving the inner cutoff scale, representative for the smallest flame structures, as the only parameter to be prescribed. The fractalmodel provides an accurate estimate for the mean flamesurface, whereas the similarity model predicts its spatial distribution.

Flow animation by unsteady temperature fields
View Description Hide DescriptionSimple mass conservation principles show that unsteady temperature fields in thermally expandable fluids are always accompanied by flow, even in the absence of gravity. This mechanism is demonstrated using several model problems, which exhibit its peculiar features. The thermally induced flows become substantial in smallscale systems, suggesting possibilities for microfluidic applications.

On the sensitivity of dynamo action to the system’s magnetic diffusivity
View Description Hide DescriptionAn experiment at the Karlsruhe dynamo test facility has shown that the intensity of the dynamo magnetic field decreases significantly with increasing temperature of the test fluid,liquidsodium, while keeping the other control parameters constant. This is explained by the increasing magnetic diffusivity with increasing temperatures utilizing results from a weakly nonlinear analysis of Tilgner and Busse [“Saturation mechanism in a model of the Karlsruhe dynamo,” in Dynamo and Dynamics, a Mathematical Challenge, NATO Science Series, II. Mathematics, Physics and Chemistry, Vol. 26, edited by P. Chossat, D. Armbruster, and I. Oprea (Kluwer, Dordrecht, 2001)] for the transcritical regime of the Karlsruhe dynamo experiment. The observations are also interpreted by dimensional reasoning utilizing previous experimental results.
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 ARTICLES


Numerical characterization of hydrothermal waves in a laterally heated shallow layer
View Description Hide DescriptionInstabilities of a buoyancythermocapillary flow in a threedimensional differentially heated layer have been examined by means of direct numerical simulations, in order to have a more detailed description of the flow field with respect to that obtained experimentally. The main aim of this work is the numerical modelization of some experiments performed by Riley and Neitzel [J. Fluid Mech. 359, 143 (1998)], considering a cavity filled with a silicone oil (Prandtl number equal to 13.9). Hydrothermal waves have been observed and examined in detail. Further simulations have been performed in order to describe also a basic unicellular flow and a steady multicellular flow. The numerical code is based on the vorticity–velocity formulation of the Navier–Stokes equations for an incompressible fluid, solved in time by means of a fully implicit approach.

Starting vortex dipoles in a viscous fluid: Asymptotic theory, numerical simulations, and laboratory experiments
View Description Hide DescriptionTranslational velocity of the starting vortex dipoles generated by the continuous or impulsive action of a localized force is obtained theoretically on simple physical grounds. Solutions of the diffusionequation for vorticity which take into account the translational motion of fluid particles are then obtained and compared with the results of direct numerical simulations of vortex dipoles as well as with the laboratory experiments. The comparison shows good quantitative agreement in both cases. Theoretical results for the translational velocity of the threedimensional (axisymmetric) flows such as starting jets or vortex rings are discussed as well.

On the computation of spacetime correlations by largeeddy simulation
View Description Hide DescriptionThe effect of subgridscale (SGS) modeling on velocity (space) time correlations is investigated in decaying isotropic turbulence. The performance of several SGS models is evaluated, which shows superiority of the dynamic Smagorinsky model used in conjunction with the multiscale largeeddy simulation(LES) procedure. Compared to the results of direct numerical simulation, LES is shown to underpredict the (unnormalized) correlation magnitude and slightly overpredict the decorrelation time scales. This can lead to inaccurate solutions in applications such as aeroacoustics. The underprediction of correlation functions is particularly severe for higher wavenumber modes which are swept by the most energetic modes. The classic sweeping hypothesis for stationary turbulence is generalized for decaying turbulence and used to analyze the observed discrepancies. Based on this analysis, the time correlations are determined by the wavenumber energy spectra and the sweeping velocity, which is the square root of the total energy. Hence, an accurate prediction of the instantaneous energy spectra is most critical to the accurate computation of time correlations.

Hydraulic jumps and standing waves in gravitydriven flows of viscous liquids in wavy open channels
View Description Hide DescriptionWe experimentally study the flow of a viscous liquid down an inclined channel with a sinusoidal bottom profile of moderate waviness. Depending on the film thickness, we find different flow regimes that are usually not observed in the same system. Besides characterizing these regimes, we study the transition from one regime to the other. At low inclination angles, basins form due to nonmonotonously falling bottom slopes. At the inflow of the basins, we observe the formation of stationary hydraulic jumps as shock fronts and surface rollers. We report on a bistable region in which both phenomena can occur. At the low end of the bistable region, an instationary regime of a shock with a fingering lateral modulation is found. The bistability of shocks and surface rollers is traced back to that of the shock front and the fingering. At higher volume flux or inclination angles, standing waves are created in resonance with the bottom contour. At the rising edge of the resonance curves, we observe humps that seem to be due to higher harmonics of the resonant wave number. There exists a small parameter region where stationary humps and shocks are bistable. At the transition between surface rollers and humps we observe a periodic switching between the two regimes.

Assessment of thermodynamic models for dense gas dynamics
View Description Hide DescriptionThe accuracy of thermodynamicmodels in the computation of nonclassical gasdynamic phenomena is discussed, to investigate their suitability in connection with the design of experimental apparatuses aimed at the observation of nonclassical wavefields. The Soave–Redlich–Kwong and the Peng–Robinson are preliminarily suggested as alternative thermodynamicmodels to the Martin–Hou usually considered in nonclassical gasdynamics of fluorinated substances. The validity of these models is assessed by comparisons to reference experimental data for fluorinated R13, R125, C318, FC72, FC75, and and to the Martin–Hou model itself. The three models are found to exhibit a comparable accuracy for reduced volumes ranging from 1.4 to 2.5 and near the critical isotherm, i.e., in the thermodynamic region where heavier fluorinated substances such as PP10 are expected to exhibit nonclassical gasdynamic phenomena. The Soave–Redlich–Kwong and the Peng–Robinson models are then used to supplement previous numerical results for a threediscontinuity nonclassical shocktube experiment with fluid PP10, which was designed under the Martin–Hou model. Under the initial conditions chosen for the experiment, the three models agree in predicting the formation of a supersonic nonclassical rarefaction wave, with wave Mach number in the range 1.01–1.02, thus providing further confidence on the possibility of experimentally observing nonclassical gasdynamic behavior in fluid PP10.

High Schmidt number scalars in turbulence: Structure functions and Lagrangian theory
View Description Hide DescriptionWe demonstrate the existence of Batchelor’s viscousconvective subrange using direct numerical simulation (DNS) results to confirm the logarithmic dependence of the scalar structure function on the separation for the scalar fieldgenerated by stationary isotropic turbulence acting on a uniform mean scalar gradient. From these data we estimate the Batchelor constant . By integrating a piecewise continuous representation of the scalar variance spectrum we calculate the steadystate scalar variance as a function of Reynolds number and Schmidt number. Comparison with DNS results confirms the behavior predicted from the spectral integration, but with a coefficient about 60% too small. In the large Reynolds number limit the data give a value of 2.5 for the mechanicaltoscalar time scale ratio. The dependence of the data for the scalar variance on Schmidt number agrees very well with the spectral integration using the values of the Batchelor constant estimated from the structure function. We also carry out an exact Lagrangian analysis of the scalar variance and structure function, explicitly relating the Batchelor constant to the Lyapunov exponent for the separation of pairs of fluid particles within the turbulence dissipation subrange. Our results, particularly for the scalar variance, illustrate explicitly the singular nature of the zero diffusivity limit. For finite values of the Schmidt number and Reynolds number the viscousconvective subrange contribution to the variance can be significant even at moderate values of the Reynolds number.

Unsteady flow field in a square tube junction
View Description Hide DescriptionThis work constitutes an extension of two previous experimental studies, examining the flow field in a square tube junction with a timedependent periodic inlet flow rate (zero to a maximum value) and equal branch flow rates. Based on numerical predictions, more details of the flow field are revealed, not being easily detectable by the experiment. Emphasis is given on the recirculation regions examining the velocity, pressure, and wall shear stress distributions as well as the limiting streamlines as a function of time. During acceleration an adverse pressure gradient builds up at the junction due to the streamlines curvature, causing flow separation before flow peak, which initiates at the corners of the tube cross section. Flow separation and reattachment lines, determined by the limiting streamline topology, move apart during deceleration. Streamwise crossflow vortices appear in both branches, being much stronger in the branch. The characteristics of the latter vortices, namely their circulation, swirl ratio, velocity distribution, as well as the process of their birth at the beginning of each cycle are examined in detail. Wall shear stress distributions exhibit maximum values at the entrance of the branch, taking values proportional to the inlet timedependent flow rate. Finally, comparisons with steady inlet conditions showed that in the unsteady case the flow can sustain much higher adverse pressure gradients before separating.

The formation and dynamics of a blob on free and wall sheets induced by a drop impact on surfaces
View Description Hide DescriptionA physical model for describing an inviscid motion of free and wall liquid sheets induced by drop impact is presented. This model takes into account the formation of thick borders at the edge of a spreading drop, and the influence of advancing and receding contact angles on the dynamics of blob formation and motion. It has been shown that the blob motion on a free liquid sheet is described by a universal relationship (independent of the Weber number) in terms of dimensionless blob coordinates at both advancing and receding stages. For the case of blob formation and motion on a wall sheet at high Weber numbers, only the advancing stage is described by a universal relationship. The receding stage depends on the ratio of advancing and receding contact angles, but not on the Weber number. At the instant when the drop is at its maximum extension, the blob speed becomes equal to the liquid sheet velocity and the total kinetic energy of the drop is greater than zero. It is shown that the ratio of the instantaneous capillary wavelength to the sheet thickness is a constant 2.619 for a free sheet, when the capillary wave propagates away from the blob.

Stable transport equations for rarefied gases at high orders in the Knudsen number
View Description Hide DescriptionAn approach is presented to derive transportequations for rarefied gases from the Boltzmann equation within higher orders of the Knudsen number. The method focuses on the order of magnitude of the moments of the phase density, and the order of accuracy of the transportequations, both measured in powers of the Knudsen number. The method is developed up to the third order, and it is shown that it yields the Euler equations at zeroth order, the Navier–Stokes–Fourier equations at first order, Grad’s 13 moment equations (with omission of a nonlinear term) at second order, and a regularization of these at third order. The method is discussed in detail, and compared with the classical methods of kinetic theory, i.e., Chapman–Enskog expansion and Grad moment method. The advantages of this method above the classical approaches are discussed conclusively. An important feature of the method presented is that the equations of any order are stable, other than in the Chapman–Enskog method, where the second and third approximation—Burnett and superBurnett equations—are unstable.

A new largeeddy simulation nearwall treatment
View Description Hide DescriptionTwo different types of instantaneous wall boundary conditions have been proposed for resolved large scale simulations that extend inside the viscous sublayer. These conditions transfer the physical noslip and impermeability/permeability information, which can only be rigorously applied to the unfiltered variables, to the filtered variables. The first condition is universal, while the second one specifies the wall stress and relevant distribution and can be used to treat inverse flow problems. The filter scale close to the wall is a function which varies according to its position and thus the problem of the noncommutation of the filter and differentiation operators arises. Used together with the explicit noncommutation procedure by Iovieno and Tordella, these boundary conditions constitute a wall treatment which could improve the use of the largeeddy methodology in relation to aspects that are independent of the modeling of the subgrid scale motion. When applied in the test case of the plane periodic channel, intentionally using the most crude subgrid scale model (Smagorinsky, with no dynamic procedure or wall damping function) to prove its efficacy, the proposed nearwall treatment yielded resolved largeeddy simulations which compare well with both direct numerical simulations and with experimental data. The effects of the Reynolds number on the structure of the flow are retained. Distributions of the noncommutation error on the turbulent solution are also reported.

Experimental analysis of the coalescence process via headon collisions in a timedependent flow
View Description Hide DescriptionThe present study experimentally investigates the mechanisms involved in the flowinduced coalescence process for two equalsized drops (polybutadiene drops suspended in a polydimethylsiloxane matrix), by taking advantage of the capability of the computercontrolled “fourroll mill” to carry out headon collisions. In this work, headon collision experiments have been carried out for a timedependent flow that is designed so that the force along the line of centers mimics the force history due to rotation of the two droplets in a glancing collision. One primary goal of these experiments is to assess the importance of global deformation of the drops in the coalescence process. Specifically, we seek to determine whether global deformation plays a role in the observation that coalescence often occurs during the portion of a glancing collision when the drops are actually being pulled apart by the external flow. By comparison of the results for headon and glancing collisions, we find that coalescence occurs in an apparently identical fashion in spite of the fact that the overall shape of the drops must be different since the velocity gradient is steady during the glancing collision but time dependent in the headon collision. Specifically, the (near) axisymmetric film drainage process achieved in a headon collision is apparently a very good approximation to the same process in a nonaxisymmetric glancing collision, suggesting that the coalescence process is dominated by the time history of the force along the line of centers and is at least approximately independent of the degree of asymmetry in the overall collision process.

Investigation of simplified thermal expansion models for compressible Newtonian fluids applied to nonisothermal plane Couette and Poiseuille flows
View Description Hide DescriptionIn this paper six different theories of a Newtonian viscous fluid are investigated and compared, namely, the theory of a compressible Newtonian fluid, and five constitutive limits of this theory: the incompressible theory, the limit where density changes only due to changes in temperature, the limit where density changes only with changes in entropy, the limit where pressure is a function only of temperature, and the limit of pressure a function only of entropy. The six theories are compared through their ability to model two test problems: (i) steady flow between moving parallel isothermal planes separated by a fixed distance with no pressure gradient in the flow direction, and (ii) steady flow between stationary isothermal parallel planes with a pressure gradient. The incompressible theory admits solutions to these problems of the plane Couette/Poiseuille flow form: a single nonzero velocity component in a direction parallel to the bounding planes, and velocity and temperature varying only in the direction perpendicular to the planes. The compressible theory admits a solution of this special form to problem (i) but not problem (ii). We find that the other four constitutive limits have Couetteform solutions to (i), but only the limits of density a function of temperature and pressure a function of entropy join the incompressible fluid in admitting the Poiseuilleform solutions to (ii); the limits of density a function only of entropy and pressure a function of temperature, as with the compressible theory, do not have solutions of that form. Based on the predictions of the fully compressible theory and its limits, we assess the usefulness of the limits as simplified models of thermal expansion.

Airdamping effects on developing velocity profiles in flowing soap films
View Description Hide DescriptionThe continuously running gravitydriven soapfilm tunnel is a device suitable for the study of twodimensional flows. In this innovative device, the films start from a reservoir, run over a vertical wire frame and get pulled by the gravity force. Despite its simple design and successful applications in twodimensional flows, its working mechanisms are not fully understood. In the present work, the laminar velocity profiles of freely suspended flowing soap films are examined theoretically and experimentally. A complete momentum integral analysis is performed including boundary layers developed within the channel on the film as well as beside the film in the air. The theoretical results are compared with the experimental measurements via laser Doppler velocimetry. Reasonable agreements are observed. Although the gravity force speeds up the filmmotion, the acceleration is significantly slowed down, but not completely, by the air friction. The growth of the boundary layers developed on the film is also damped by the air friction so that across the film channel the velocity profile is mostly uniform. Moreover, a saturated boundary layer thickness seemingly exists when the thinning due to acceleration and the thickening due to viscousdiffusion are in balance.

Development of boundarylayer flow in the presence of forced wavelength Görtler vortices
View Description Hide DescriptionHotwire measurements in the boundary layer developing on a concave surface of radius of curvature in the presence of forced wavelength Görtler vortices have been conducted for a freestream velocity of . The wavelengths of vortices were preset by vertical perturbation wires of diameter located upstream of the concave surface leading edge. The velocity contours in the crosssectional planes at several streamwise locations show the growth and breakdown of the vortices that are similar to those found in the transitional flow field. It shows the occurrence of the second instability mode that is indicated by the formation of small horseshoe eddies generated between the two neighboring vortices traveling in the streamwise direction to form mushroomlike structures as a consequence of the nonlinear growth of the Görtler vortices. The breakdown of these structures before the boundarylayer flow becomes turbulent is also shown to qualitatively predict the start of the transition in the flow. The Görtler number where the start of the transition was predicted is found to be within the range of transitional Görtler numbers previously reported for naturally developed Görtler vortices. The average of the spanwise wavelength after being normalized by is comparable with the generally quoted value of 100 for turbulent boundary layers.

Vortex models based on similarity solutions of the twodimensional diffusion equation
View Description Hide DescriptionIn this paper, a class of twodimensional (2D) vortexmodels is analyzed, which is based on similarity solutions of the diffusionequation. If the nonlinear advective term is neglected, the 2D NavierStokes equation reduces to a linear problem, for which a complete orthonormal set of eigenfunctions is known on an unbounded 2D domain. Some of the basic modes represent models for diffusing monopoles, dipoles, and tripolar vortices, which evolve selfsimilarly in time. Here, we mainly confine ourselves to an analysis of the dipole solution. In several respects, especially the decay and, to a lesser extent, the lateral expansion properties, the dipole model appears to be in fair agreement with the real evolution of dipolar vortices for finite Reynolds number, as obtained from numerical simulations of the full 2D NavierStokes equations. However, the simulations reveal that nonlinear effects result in small differences compared to the evolution according to the model. The most important nonlinear effect that was observed is the formation of “tails” of vorticity in the wake of the dipole. After a while, any initial condition leads to a vorticity distribution lying in between the viscous similarity solution and the Lamb dipole solution, which represents the limit of a stationary, inviscid flow. The exact form of the vorticity distribution is believed to be determined by an equilibrium between diffusion of vorticity through the separatrix and advection of vorticity into the wake of the dipole, which results in the formation of vorticity tails. A comparison revealed profound qualitative agreements between the model together with the simulations and dipolar vortex structures that were studied by laboratory experiments in stratified fluids.

On higher order passive scalar structure functions in grid turbulence
View Description Hide DescriptionThe scalar structure function scaling exponent is experimentally determined for in decaying, gridgenerated windtunnel turbulence with a constant mean temperature gradient. The Reynolds number is varied over the range by using static and active grids. The results show that up to the scaling exponent does not saturate although saturation is not precluded at higher orders. There appears to be no dependence of on Reynolds number and the values of are the same for the transverse (along the gradient) and the longitudinal (streamwise) structure functions. A compilation of previous work shows large variation in , with a few results indicating saturation and most not. Reasons for the scatter are attributed to convergence problems at high orders, effects of flow or computational domain size causing clipping of large rare fluctuations, and differences in initial and boundary conditions.

The spherical model of logarithmic potentials as examined by Monte Carlo methods
View Description Hide DescriptionWe examine Euler’s equations for inviscid fluid flow by a discretized version representing the fluid as a piecewise constant finite approximation based on Voronoi cells. The strengths of these cells are constrained to conserve circulation and enstrophy. With this model we examine by a Monte Carlo Metropolis–Hastings algorithm the dependence of the system on such parameters as the number of points, the statistical mechanics temperature, and the number of sweeps used in the simulation. Tools to examine the system include the mean nearest neighbor parity, energy, distance between extremevalued sites, and statistical study of an individual site or of all mesh site values. In negative statistical mechanics temperatures a solidbody rotation state is found. The positivetemperature state is not as strongly organized. Numerical evidence supports our expectation of a single phase transition, between positive and negative temperatures.
