Showing papers in "Physics of Fluids in 1998"

The formation and evolution of synthetic jets

Abstract: A nominally plane turbulent jet is synthesized by the interactions of a train of counter-rotating vortex pairs that are formed at the edge of an orifice by the time-periodic motion of a flexible diaphragm in a sealed cavity. Even though the jet is formed without net mass injection, the hydrodynamic impulse of the ejected fluid and thus the momentum of the ensuing jet are nonzero. Successive vortex pairs are not subjected to pairing or other subharmonic interactions. Each vortex of the pair develops a spanwise instability and ultimately undergoes transition to turbulence, slows down, loses its coherence and becomes indistinguishable from the mean jet flow. The trajectories of vortex pairs at a given formation frequency scale with the length of the ejected fluid slug regardless of the magnitude of the formation impulse and, near the jet exit plane, their celerity decreases monotonically with streamwise distance while the local mean velocity of the ensuing jet increases. In the far field, the synthetic jet i...

Filtered density function for large eddy simulation of turbulent reacting flows

Abstract: A methodology termed the “filtered density function” (FDF) is developed and implemented for large eddy simulation (LES) of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of subgrid scale (SGS) scalar quantities. A transport equation is derived for the FDF in which the effect of chemical reactions appears in a closed form. The influences of scalar mixing and convection within the subgrid are modeled. The FDF transport equation is solved numerically via a Lagrangian Monte Carlo scheme in which the solutions of the equivalent stochastic differential equations (SDEs) are obtained. These solutions preserve the Ito-Gikhman nature of the SDEs. The consistency of the FDF approach, the convergence of its Monte Carlo solution and the performance of the closures employed in the FDF transport equation are assessed by comparisons with results obtained by direct numerical simulation ...

Large deformation of red blood cell ghosts in a simple shear flow

Abstract: Red blood cells are known to change shape in response to local flow conditions. Deformability affects red blood cell physiological function and the hydrodynamic properties of blood. The immersed boundary method is used to simulate three-dimensional membrane-fluid flow interactions for cells with the same internal and external fluid viscosities. The method has been validated for small deformations of an initially spherical capsule in simple shear flow for both neo-Hookean and the Evans-Skalak membrane models. Initially oblate spheroidal capsules are simulated and it is shown that the red blood cell membrane exhibits asymptotic behavior as the ratio of the dilation modulus to the extensional modulus is increased and a good approximation of local area conservation is obtained. Tank treading behavior is observed and its period calculated.

A dynamic model for subgrid-scale variance and dissipation rate of a conserved scalar

Abstract: The dynamic procedure is applied to the problem of modeling the subgrid-scale variance and dissipation rate of a conserved scalar in large eddy simulations of turbulent reacting flows. A simple scaling relation for the subgrid-scale variance is proposed, and the coefficient of the scaling law is obtained using the dynamic procedure. The variance dissipation rate is modeled by assuming equilibrium with the local variance production rate, which is obtained using a dynamic model. Example model predictions are obtained using actual large eddy simulation data, and the subgrid variance predicted by the dynamic model is compared to results obtained using a scale similarity model. Generalization of the approach to multiple scalars and nonconserved scalars is briefly discussed.

Proper orthogonal decomposition and low-dimensional models for driven cavity flows

Abstract: A proper orthogonal decomposition (POD) of the flow in a square lid-driven cavity at Re=22,000 is computed to educe the coherent structures in this flow and to construct a low-dimensional model for driven cavity flows. Among all linear decompositions, the POD is the most efficient in the sense that it captures the largest possible amount of kinetic energy (for any given number of modes). The first 80 POD modes of the driven cavity flow are computed from 700 snapshots that are taken from a direct numerical simulation (DNS). The first 80 spatial POD modes capture (on average) 95% of the fluctuating kinetic energy. From the snapshots a motion picture of the coherent structures is made by projecting the Navier–Stokes equation on a space spanned by the first 80 spatial POD modes. We have evaluated how well the dynamics of this 80-dimensional model mimics the dynamics given by the Navier–Stokes equations. The results can be summarized as follows. A closure model is needed to integrate the 80-dimensional system ...

A numerical investigation on the effect of the inflow conditions on the self-similar region of a round jet

Abstract: In this paper we consider the direct numerical simulation (DNS) of a spatially developing free round jet at low Reynolds numbers. Simulation of a spatially evolving flow such as the jet requires boundary conditions, which allow entrainment into the turbulent flow across the lateral boundaries of the computational domain. The boundary conditions which satisfy this requirement are so-called traction free boundary conditions. After showing that these boundary conditions lead to a correct behavior of the velocity near the lateral boundary of the jet, we will consider the DNS of the jet flow at a Reynolds number of 2.4×103 and compare the results with experimental data obtained by Hussein et al. [J. Fluid Mech. 258, 31 (1994)] and by Panchapakesan and Lumley [J. Fluid Mech. 246, 197 (1993)]. The results of our numerical simulations agree very well with the experimental data. Next we use the DNS to investigate the influence of the shape of the velocity profile at the jet orifice on the self-similarity scaling f...

A new Strouhal–Reynolds-number relationship for the circular cylinder in the range 47<Re<2×105

Abstract: Based on experiments a new law is proposed for the vortex shedding from a circular cylinder which describes in a consistent way the Strouhal–Reynolds-number dependency as Sr=Sr*+m/Re from the beginning of the vortex shedding at Re=47 up to the laminar–turbulent transition of the cylinder boundary layer at Re>2×105. The various vortex shedding processes, occurring with increasing Reynolds number, are described by different coefficients Sr* and m.

An update on the energy dissipation rate in isotropic turbulence

Abstract: Direct numerical simulations of homogeneous turbulence in a periodic box are examined here to support the traditional expectation that the dissipation rate at high Reynolds numbers is independent of fluid viscosity, and is a constant of order unity when scaled on the integral scale and root-mean-square velocity. However, the numerical value of the constant appears to depend on details of forcing at low wavenumbers, or, perhaps, the structure of the large scale itself.

Capillary breakup of a viscous thread surrounded by another viscous fluid

Abstract: Previous long-wavelength analyses of capillary breakup of a viscous fluid thread in a perfectly inviscid environment show that the asymptotic self-similar regime immediately prior to breakup is given by a balance between surface tension, inertia, and extensional viscous stresses in the thread. In contrast, it is shown here that if viscosity in the external fluid, however small, is included then the asymptotic balance is between surface tension and viscous stresses in the two fluids while inertia is negligible. Scaling estimates for this new balance suggest that both axial and radial scales decrease linearly with time to breakup, so that the aspect ratio remains O(1) with time but scales with viscosity ratio like (μint/μext)1/2 for μint≫μext, where μint and μext are the internal and external viscosities. Numerical solutions to the full Stokes equations for μint=μext confirm the scalings with time and give self-similar behavior near pinching. However, the self-similar pinching region is embedded in a logari...

Simulation of flow through bead packs using the lattice Boltzmann method

Abstract: The lattice Boltzmann method (LBM) is used to simulate viscous fluid flow through a column of glass beads. The results suggest that the normalized velocity distribution is sensitive to the spatial resolution but not the details of the packing. With increasing spatial resolution, simulation results converge to a velocity distribution with a sharp peak near zero. A simple argument is presented to explain this result. Changes in the shape of the distribution as a function of flow rate are determined for low Reynolds numbers, and the large-velocity tail of the distribution is shown to depend on the packing geometry. The effect of a finite Reynolds number on the apparent permeability is demonstrated and discussed in relation to previous results in the literature. Comparison with velocity distributions from NMR (nuclear magnetic resonance) spectroscopy finds qualitative agreement after adjusting for diffusion effects in the NMR distributions.

Intermittency in the two-dimensional inverse cascade of energy: Experimental observations

Abstract: An extensive experimental study of the two-dimensional inverse energy cascade is presented. The experiments are performed in electromagnetically driven flows, using thin, stably-stratified layers. Complete instantaneous velocity fields are measured using particle imaging velocimetry techniques. Depending on the bottom-wall friction, two different regimes are observed: when the friction is low, the energy transferred from the forcing scale towards large scales accumulates in the lowest accessible mode, leading to a mean rotation of the flow and to an energy spectrum displaying a sharp peak at the minimum wave-number. This condensation is accompanied by the emergence of a very strong vortex around which the rotation is organized. At higher frictions, the inverse energy cascade conjectured by Kraichnan [Phys. Fluids 10, 1417 (1967)] is observed and is found to be stationary, homogeneous and isotropic, with a Kolmogorov constant consistent with numerical estimates. This inverse cascade does not appear to be c...

Cell size dependence of transport coefficients in stochastic particle algorithms

Abstract: Using the Green–Kubo theory, the dependence of the viscosity and thermal conductivity on cell size is obtained explicitly for stochastic particle methods such as direct simulation Monte Carlo (DSMC) and its generalization, the consistent Boltzmann algorithm (CBA). These analytical results confirm empirical observations that significant errors occur when the cell dimensions are larger than a mean free path.

Evolution of the fingering pattern of an impacting drop

Abstract: The impact of a drop on a solid surface generates a rapidly expanding thin jet traveling along the surface. We study the evolution of the fingering pattern at the edge of this jet during the impact of a water drop on a glass plate. Multiple-flash photography shows that systematic changes in frontal shapes take place during the expansion. The initial fingers widen and split in two. This splitting is in many cases limited to the development of a double peak on each finger. The subsequent interaction of two such adjacent undulations often results in merging which produces three pronounced fingers. Despite the significant changes in the frontal shapes, the number of fundamental undulations remains approximately constant during the expansion. The progenitors of these azimuthal disturbances are observed right at first contact. Some heuristic arguments based on capillary waves are put forth to explain the splitting and merging. The main focus of this study is on impacts having Reynolds numbers of about 15 000, b...

A model for universal time scale of vortex ring formation

Abstract: An analytical model for predicting the universal time scale for formation of vortex rings generated through impulsively started jets is considered. The model is based on two assumptions, namely the validity of the slug model in simulating the discharge process of the fluid out of the cylinder and the approximation of the vortex at the pinch off moment by a vortex in the Norbury family. The nondimensional stroke length L/D (referred to as "formation number," following Gharib et al. [J. Fluid Mech. 360, 121 (1998)]) predicted by the model satisfactorily matches the experimental observation of Gharib et al. The model introduces two nondimensional parameters that govern the limiting formation number: nondimensional energy End and circulation Gammand. The predicted value of End matches very well with the experimental data. It is also predicted that there is a limiting value for the nondimensional circulation in the range 1.77 <~ Gammand <~ 2.07.

Lagrangian acceleration measurements at large Reynolds numbers

Abstract: We report experimental measurements of Lagrangian accelerations in a turbulent water flow between counter-rotating disks for Taylor–Reynolds numbers 900

Trajectory and entrainment of a round jet in crossflow

Abstract: This paper examines the trajectory and entrainment characteristics of a round jet in crossflow. A series of large eddy simulations was performed at Reynolds numbers of 1050 and 2100 and at jet to crossflow velocity ratios of 2.0 and 3.3. Trajectories, which are defined based on the mean streamlines on the centerplane, all collapse to a single curve far from the jet exit, and this curve can be represented with a power law fit. Within this power law region, entrainment of crossflow fluid is shown to be the primary mechanism by which the jet trajectory is determined. Upstream of the power law region, near the jet exit, jet trajectory varies from changes in pressure drag and from differences in the turbulence intensities in the incoming pipe flow.

Direct excitation of small-scale motions in free shear flows

Abstract: The conventional approach to small-scale mixing enhancement in free shear flows by the manipulation of global flow instabilities and the ensuing large-scale vortical structures depends on the classical cascading mechanism to transfer the control influence to the scales at which molecular mixing takes place. Thus the manipulation of mixing at the smallest scales is indirect and only weakly coupled to the control input. The present work focuses on direct excitation of the small scales within the dissipation range of a free shear flow. This approach is demonstrated in a shear layer segment of an air jet emanating from a square conduit. The flow is forced at a frequency that is approximately an order of magnitude lower than the passage frequency of eddies at the Kolmogorov scale using cantilevered piezoelectric actuators. Cross-stream distributions of the streamwise velocity component are measured at a number of streamwise stations downstream of the actuator using hot wire anemometry. Direct small scale excitation results in enhanced energy transfer from the large to the small scales and in a substantial increase in the dissipation and in the decay rate of turbulent kinetic energy.

Surface tension force on a partly submerged body

Abstract: The vertical component of the surface tension force on a body partly submerged in a liquid is shown to equal the weight of liquid displaced by the meniscus. It is upward if the meniscus is depressed and downward if the meniscus is elevated. Previously this was known for vertical axially symmetric bodies and for two-dimensional vertical plates. The vertical component of the pressure force on the body is shown to equal the weight of liquid which would fill the volume bounded by the wetted surface of the body, a vertical cylinder through the waterline, and the original horizontal free surface.

Numerical study of hypersonic reacting boundary layer transition on cones

Abstract: Hypersonic gas flow over cones is solved using computational fluid dynamics to obtain accurate boundary layer profiles A linear stability analysis is performed on the profiles to determine the amplification rates of naturally occurring disturbances, and this information is used with the eN method to predict the boundary layer transition location The effects of free-stream total enthalpy and chemical composition on transition location are studied to give a better understanding of recent experimental observations Namely, there is an increase in transition Reynolds number with increasing free-stream total enthalpy, and this increase is greater for gases with lower dissociation energies The results show that linear stability predicts the same trends that were observed in the experiments, but with N=10, it consistently overpredicts the transition Reynolds numbers by about a factor of 2 The results of numerical experiments are presented which show the effect of reaction endo- or exothermicity on disturbanc

Small‐scale structures in Boussinesq convection

Abstract: Two‐dimensional Boussinesq convection is studied numerically using two different methods: a filtered pseudospectral method and a high‐order accurate eno scheme. The issue whether finite time singularity occurs for initially smooth flows is investigated. In contrast to the findings of Pumir and Siggia who reported finite time collapse of the bubble cap, the present numerical results suggest that the strain rate corresponding to the intensification of the density gradient across the front saturates at the bubble cap. Consequently, the thickness of the bubble decreases exponentially. On the other hand, the bubble experiences much stronger straining and intensification of gradients at its side. As the bubble rises, a secondary front also forms from its tail. Together with the primary front, they constitute a pair of tightly bound plus and minus double vortex sheet structure which is highly unstable and vulnerable to viscous dissipation.

Drop breakup in three-dimensional viscous flows

Abstract: A new three-dimensional boundary integral algorithm is presented that is capable of simulating the process of drop breakup in viscous flows. The surface discretization is fully adaptive, thus providing accurate resolution of the highly deformed drop shapes that are characteristic of breakup events. Our algorithm is used to study drop breakup in shear flow and in buoyancy; the predictions are compared with experimental observations.

A large-scale control strategy for drag reduction in turbulent boundary layers

Abstract: Using direct numerical simulations of turbulent channel flow, we present a new method for skin friction reduction, enabling large-scale flow forcing without requiring instantaneous flow information. As proof-of-principle, x-independent forcing, with a z wavelength of 400 wall units and an amplitude of only 6% of the centerline velocity, produces a significant sustained drag reduction: 20% for imposed counterrotating streamwise vortices and 50% for colliding, z-directed wall jets. The drag reduction results from weakened longitudinal vortices near the wall, due to forcing-induced suppression of an underlying streak instability mechanism. In particular, the forcing significantly weakens the wall-normal vorticity ωy flanking lifted low-speed streaks, thereby arresting the streaks’ sinuous instability which directly generates new streamwise vortices in uncontrolled flows. These results suggest promising new drag reduction techniques, e.g., passive vortex generators or colliding spanwise jets from x-aligned sl...

Shear sheltering and the continuous spectrum of the orr-sommerfeld equation

Abstract: The expansion into eigenfunctions of a general disturbance in a viscous flow is possible only when both the discrete and continuous modes of the Orr–Sommerfeld equation are employed. Proper implementation of the boundary conditions and a method for computation of the continuous modes are developed. The unique phenomenon known as shear sheltering is discussed and illustrated. It is shown that the penetration depth of disturbances into the boundary layer has a dependence on frequency and Reynolds number similar to that of a Stokes layer. A simple model that captures this dependence is developed.

On the collision rate of small particles in isotropic turbulence. II. Finite inertia case

Abstract: Numerical experiments have been performed to study the geometric collision rate of finite-size particles with zero inertia (i.e., fluid elements) in isotropic turbulence. The turbulent flow was generated by the pseudospectral method. We argue that the formulation of Saffman and Turner [J. Fluid Mech. 1, 16 (1956)] for the average collision kernel is correct only under the assumptions that the particles are kept in the system after collision and allowed to overlap in space. This was confirmed, for the first time, by numerical experiments to within a numerical uncertainty as small as 1%. Finite corrections to the Saffman and Turner result must be made if one applies the theory to actual coagulation process where particles are not allowed to overlap before collision and particles are removed from a given size group after collision. This is due to the fact that Saffman and Turner assumed a uniform, time-independent concentration field in their formulation of the average collision kernel, while in the actual modeling of population evolution the particle number concentration changes in time and may be locally nonuniform as a result of a biased removal process due to spatially nonuniform coagulation rates. However, the quantitative level of the deviations from the Saffman and Turner result remain to be explained. Numerical experiments in simple shear flow were also conducted to elaborate our findings.

Large eddy simulation of a nonpremixed reacting jet: Application and assessment of subgrid-scale combustion models

Abstract: Results from large eddy simulations (LES) and direct numerical simulations (DNS) of a two-dimensional, spatially developing, compressible planar free jet undergoing an idealized, exothermic, chemical reaction of the type F+rOx→(1+r)P are presented in order to assess several subgrid-scale (SGS) combustion models. Both a priori and a posteriori assessments are conducted. The SGS turbulence model used is the dynamic Smagorinsky model (DSM). Two classes of SGS combustion models are employed in this study. These include the conserved scalar approach and the direct closure approach. Specifically, the SGS combustion models involve several forms of direct filtered reaction rate closures, including a scale similarity filtered reaction rate model (SSFRRM), and a mixing controlled strained laminar flamelet model (SLFM) in the form of thermochemical state relationships, obtained from the DNS, and two assumed forms for the subgrid mixture fraction filtered density function (FDF). In general, LES results are in reasonable agreement with DNS results and highlight the performance of the various SGS combustion models. In particular, in the context of the present study, it is found that: (1) the SLFM cases overpredict product formation due to their inability to capture finite-rate chemistry effects; (2) due to the relatively low values of the SGS mixture fraction variance in the flow under study, the SLFM results are not sensitive to the form of the assumed FDF; and (3) in comparison to the other models investigated, the SSFRRM combustion model provides the best agreement with the DNS for product formation.

Mechanism of elastic instability in Couette flow of polymer solutions: Experiment

Abstract: Experiments on flow stability and pattern formation in Couette flow between two cylinders with highly elastic polymer solutions are reported. It is found that the flow instabilities are determined by the elastic Deborah number, De, and the polymer concentration only, while the Reynolds number becomes completely irrelevant. A mechanism of such “purely elastic” instability was suggested a few years ago by Larson, Shaqfeh, and Muller [J. Fluid Mech. 218, 573 (1990)], referred to as LMS. It is based on the Oldroyd-B rheological model and implies a certain functional relation between De at the instability threshold and the polymer contribution to the solution viscosity, ηp/η, that depends on the polymer concentration. The elastic force driving the instability arises when perturbative elongational flow in radial direction is coupled to the strong primary azimuthal shear. This force is provided by the “hoop stress” that develops due to stretching of the polymer molecules along the curved streamlines. It is found experimentally that the elastic instability leads to a strongly nonlinear flow transition. Therefore, the linear consideration by LMS is expanded to include finite amplitude velocity perturbations. It is shown that the nature of the elastic force implies major asymmetry between inflow and outflow in finite amplitude secondary flows. This special feature is indeed exhibited by the experimentally observed flow patterns. For one of the flow patterns it is also shown that the suggested elastic force should be quite efficient in driving it, which is important evidence for the validity of the mechanism proposed by LMS. Further, the predicted relation between De and ηp/η is tested. At fixed ηp/η the elastic instability is found to occur at constant Deborah number in a broad range of the solution relaxation times in full agreement with the theoretical prediction. The experimentally found dependence of the Deborah number on ηp/η also agrees with the theoretical prediction rather well if a proper correction for the shear thinning is made. This provides further support to the proposed instability mechanism.

Spatial instability of planar channel flow with fluid injection through porous walls

Abstract: The present paper deals with the stability properties of a planar channel flow driven by air injection through porous walls. Experimental investigations have been carried out in the so-called VECLA facility and a theoretical linear stability analysis has been performed. The nonparallel effects are studied by using three different stability approaches. They appear to be very significant for this particular flow. This study provides indeed an interesting example of an instability mechanism strongly related to the vertical component (usually negligible) of the mean flow. The obtained results finally agree very well with the measurements with respect to the amplified frequency range and to the streamwise amplification of the instability waves.

The viscous drag force on a spherical bubble with a time-dependent radius

Abstract: The expression of the hydrodynamic force experienced by a spherical bubble having a variable radius and moving in a viscous incompressible liquid is derived analytically in two different asymptotic situations. The solution is obtained by rewriting the initial problem in a frame of reference where the bubble has a fixed radius and where the relevant dimensionless parameters are conserved. It is shown that when the assumption of unsteady creeping motion is valid, the bubble radius variation combined with a constant rise velocity produces a nonzero history force. This contribution can have a significant effect on the bubble motion, especially for a collapsing bubble.

Direct numerical simulations of bubble-laden turbulent flows using the two-fluid formulation

Abstract: Direct numerical simulations (DNS) of bubble-laden isotropic decaying turbulence are performed using the two-fluid approach (TF) instead of the Eulerian–Lagrangian approach (EL). The motivation for the study is that EL requires considerable computational resources, especially for the case of two-way coupling, where the instantaneous trajectories of a large number of individual bubbles need to be computed. The TF formulation is developed by spatially averaging the instantaneous equations of the carrier flow and bubble phase over a scale of the order of the Kolmogorov length scale, which, in our case, is much larger than the bubble diameter. On that scale, the bubbles are treated as a continuum (without molecular diffusivity) characterized by the bubble phase velocity field and concentration (volume fraction). The bubble concentration, C, is assumed small enough (C⩽10−3) to neglect the bubble–bubble interactions. As a test case, direct simulation of a bubble-laden Taylor–Green vortex with one-way coupling i...

Steady particulate flows in a horizontal rotating cylinder

Abstract: Results of discrete element method (DEM) simulation and magnetic resonance imaging (MRI) experiments are compared for monodisperse granular materials flowing in a half-filled horizontal rotating cylinder. Because opacity is not a problem for MRI, a long cylinder with an aspect ratio ∼7 was used and the flow in a thin transverse slice near the center was studied. The particles were mustard seeds and the ratio of cylinder diameter to particle diameter was approximately 50. The parameters compared were dynamic angle of repose, velocity field in a plane perpendicular to the cylinder axis, and velocity fluctuations at rotation rates up to 30 rpm. The agreement between DEM and MRI was good when the friction coefficient and nonsphericity were adjusted in the simulation for the best fit.