Showing papers in "Journal of Fluid Mechanics in 1994"
TL;DR: In this article, a general technique for simulating solid-fluid suspensions is described, which combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping flow regime and at higher Reynolds numbers.
Abstract: A new and very general technique for simulating solid–fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping-flow regime and at higher Reynolds numbers. Brownian motion of the solid particles arises spontaneously from stochastic fluctuations in the fluid stress tensor, rather than from random forces or displacements applied directly to the particles. In this paper, the theoretical foundations of the technique are laid out, illustrated by simple analytical and numerical examples; in a companion paper (Part 2), extensive numerical tests of the method, for stationary flows, time-dependent flows, and finite-Reynolds-number flows, are reported.
2,073 citations
TL;DR: In this paper, extensive numerical tests of the method are described; results are presented for creeping flows, both with and without Brownian motion, and at finite Reynolds numbers, and the short-time dynamics of random dispersions of up to 1024 colloidal particles have been simulated.
Abstract: A new and very general technique for simulating solid–fluid suspensions has been described in a previous paper (Part 1); the most important feature of the new method is that the computational cost scales linearly with the number of particles. In this paper (Part 2), extensive numerical tests of the method are described; results are presented for creeping flows, both with and without Brownian motion, and at finite Reynolds numbers. Hydrodynamic interactions, transport coefficients, and the short-time dynamics of random dispersions of up to 1024 colloidal particles have been simulated.
1,331 citations
TL;DR: In this article, structural features resulting from the interaction of a turbulent jet issuing transversely into a uniform stream are described with the help of flow visualization and hot-wire anemometry.
Abstract: Structural features resulting from the interaction of a turbulent jet issuing transversely into a uniform stream are described with the help of flow visualization and hot-wire anemometry. Jet-to-crossflow velocity ratios from 2 to 10 were investigated at crossflow Reynolds numbers from 3800 to 11400. In particular, the origin and formation of the vortices in the wake are described and shown to be fundamentally different from the well-known phenomenon of vortex shedding from solid bluff bodies. The flow around a transverse jet does not separate from the jet and does not shed vorticity into the wake. Instead, the wake vortices have their origins in the laminar boundary layer of the wall from which the jet issues. It is argued that the closed flow around the jet imposes an adverse pressure gradient on the wall, on the downstream lateral sides of the jet, provoking 'separation events’ in the wall boundary layer on each side. These result in eruptions of boundary-layer fluid and formation of wake vortices that are convected downstream. The measured wake Strouhal frequencies, which depend on the jet-crossflow velocity ratio, match the measured frequencies of the separation events. The wake structure is most orderly and the corresponding wake Strouhal number (0.13) is most sharply defined for velocity ratios near the value 4. Measured wake profiles show deficits of both momentum and total pressure.
1,186 citations
TL;DR: In this article, the turbulent flow resulting from a top-hat jet exhausting into a large room was investigated and the Reynolds number based on exit conditions was approximately 105 Velocity moments to third order were obtained using flying and stationary hot-wire and burstmode laser-Doppler anemometry (LDA) techniques.
Abstract: The turbulent flow resulting from a top-hat jet exhausting into a large room was investigated The Reynolds number based on exit conditions was approximately 105 Velocity moments to third order were obtained using flying and stationary hot-wire and burst-mode laser-Doppler anemometry (LDA) techniques The entire room was fully seeded for the LDA measurements The measurements are shown to satisfy the differential and integral momentum equations for a round jet in an infinite environmentThe results differ substantially from those reported by some earlier investigators, both in the level and shape of the profiles These differences are attributed to the smaller enclosures used in the earlier works and the recirculation within them Also, the flying hot-wire and burst-mode LDA measurements made here differ from the stationary wire measurements, especially the higher moments and away from the flow centreline These differences are attributed to the cross-flow and rectification errors on the latter at the high turbulence intensities present in this flow (30% minimum at centreline) The measurements are used, together with recent dissipation measurements, to compute the energy balance for the jet, and an attempt is made to estimate the pressure-velocity and pressure-strain rate correlations
1,056 citations
TL;DR: In this paper, hot-wire measurements of the velocity fluctuations in the test-section-ceiling boundary layer of the 80×120 foot Full-Scale Aerodynamics Facility at NASA Ames Research Center, the world's largest wind tunnel, were taken to test the localisotropy predictions of Kolmogorov's universal equilibrium theory.
Abstract: To test the local-isotropy predictions of Kolmogorov's universal equilibrium theory, we have taken hot-wire measurements of the velocity fluctuations in the test-section-ceiling boundary layer of the 80×120 foot Full-Scale Aerodynamics Facility at NASA Ames Research Center, the world's largest wind tunnel. The maximum Reynolds numbers based on momentum thickness, R θ , and on Taylor microscale, R λ , were approximately 370 000 and 1450 respectively. These are the largest ever attained in laboratory boundary-layer flows. The boundary layer develops over a rough surface, but the Reynolds-stress profiles agree with canonical data sufficiently well for present purposes
820 citations
TL;DR: In this paper, it was shown that the structure of a micro-joint becomes independent of electrostatic parameters such as V or the electrode configuration, being governed mostly by the liquid properties and flow rate Q. In the limit e [Gt ] 1, an upper bound was found for the convected current at the virtual cone apex, which accounts for only one quarter of the total measured spray current.
Abstract: When a liquid meniscus held at the exit of a metallic capillary tube is charged to a high voltage V, the free surface often takes the form of a cone whose apex emits a steady microjet, and thus injects a certain charge I and liquid volume Q per unit time into the surrounding gas. This work deals with liquids with relatively large conductivities K, for which the jet diameter dj is much smaller than the diameter dn of the capillary tube. In the limit dj/dn → 0, the structure of the jet (dj and I, in particular) becomes independent of electrostatic parameters such as V or the electrode configuration, being governed mostly by the liquid properties and flow rate Q. Furthermore, the measured current is given approximately by I = f(e) (γQK/e)½ for a wide variety of liquids and conditions (e, and γ are, respectively, the dielectric constant of the liquid and the coefficient of interfacial tension; f(e) is shown in figure 11). The following explanation is proposed for this behaviour. Convection associated with the liquid flow Q transports the net surface charge towards the cone tip. This upsets the electrostatic surface charge distribution slightly at distances r from the apex large compared to a certain charge relaxation length λ, but substantially when r ∼ λ. When the fluid motion is modelled as a sink flow, λ is of the order of r* = (Qee0/K) (e0 is the electrical permittivity of vacuum). If, in addition, the surface charge density is described through Taylor's theory, the corresponding surface current convected towards the apex scales as Is ∼ (γQK/e)½, as observed for the spray current. The sink flow hypothesis is shown to be realistic for sufficiently small jet Reynolds numbers. In a few photographs of ethylene glycol cone jets, we find the rough scaling dj ∼ 0.4r* for the jet diameter, which shows that the jet forms as soon as charge relaxation effects set in. In the limit e [Gt ] 1, an upper bound is found for the convected current at the virtual cone apex, which accounts for only one-quarter of the total measured spray current. The rest of the charge must accordingly reach the head of the jet by conduction through the bulk.
804 citations
TL;DR: In this paper, the properties of turbulence subgrid-scale stresses are studied using experimental data in the far field of a round jet, at a Reynolds number of Rλ ≈ 310.
Abstract: The properties of turbulence subgrid-scale stresses are studied using experimental data in the far field of a round jet, at a Reynolds number of Rλ ≈ 310. Measurements are performed using two-dimensional particle displacement velocimetry. Three elements of the subgrid-scale stress tensor are calculated using planar filtering of the data. Using a priori testing, eddy-viscosity closures are shown to display very little correlation with the real stresses, in accord with earlier findings based on direct numerical simulations at lower Reynolds numbers. Detailed analysis of subgrid energy fluxes and of the velocity field decomposed into logarithmic bands leads to a new similarity subgrid-scale model. It is based on the ‘resolved stress’ tensor Lij, which is obtained by filtering products of resolved velocities at a scale equal to twice the grid scale. The correlation coefficient of this model with the real stress is shown to be substantially higher than that of the eddy-viscosity closures. It is shown that mixed models display similar levels of correlation. During the a priori test, care is taken to only employ resolved data in a fashion that is consistent with the information that would be available during large-eddy simulation. The influence of the filter shape on the correlation is documented in detail, and the model is compared to the original similarity model of Bardina et al. (1980). A relationship between Lij and a nonlinear subgrid-scale model is established. In order to control the amount of kinetic energy backscatter, which could potentially lead to numerical instability, an ad hoc weighting function that depends on the alignment between Lij and the strain-rate tensor, is introduced. A ‘dynamic’ version of the model is shown, based on the data, to allow a self-consistent determination of the coefficient. In addition, all tensor elements of the model are shown to display the correct scaling with normal distance near a solid boundary.
790 citations
TL;DR: In this article, the authors explore concepts for active control of turbulent boundary layers leading to skin-friction reduction using the direct numerical simulation technique and show that significant drag reduction is achieved when the surface boundary condition is modified to suppress the dynamically significant coherent structures present in the wall region.
Abstract: The objective of this study is to explore concepts for active control of turbulent boundary layers leading to skin-friction reduction using the direct numerical simulation technique. Significant drag reduction is achieved when the surface boundary condition is modified to suppress the dynamically significant coherent structures present in the wall region. The drag reduction is accompanied by significant reduction in the intensity of the wall-layer structures and reductions in the magnitude of Reynolds shear stress throughout the flow. The apparent outward shift of turbulence statistics in the controlled flows indicates a displaced virtual origin of the boundary layer and a thickened sublayer. Time sequences of the flow fields show that there are essentially two drag-reduction mechanisms. Firstly, within a short time after the control is applied, drag is reduced mainly by deterring the sweep motion without modifying the primary streamwise vortices above the wall. Consequently, the high-shear-rate regions on the wall are moved to the interior of the channel by the control schemes. Secondly, the active control changes the evolution of the wall vorticity layer by stabilizing and preventing lifting of the spanwise vorticity near the wall, which may suppress a source of new streamwise vortices above the wall.
756 citations
TL;DR: In this paper, a model for suspension flow is proposed in which macroscopic mass, momentum and energy balances are constructed and solved simultaneously, and the concept of the suspension temperature is introduced in order to provide a nonlocal description of suspension behaviour.
Abstract: Dynamic simulations of the pressure-driven flow in a channel of a non-Brownian suspension at zero Reynolds number were conducted using Stokesian Dynamics. The simulations are for a monolayer of identical particles as a function of the dimensionless channel width and the bulk particle concentration. Starting from a homogeneous dispersion, the particles gradually migrate towards the centre of the channel, resulting in an homogeneous concentration profile and a blunting of the particle velocity profile. The time for achieving steady state scales as (H/a)3a/[left angle bracket]u[right angle bracket], where H is the channel width, a the radii of the particles, and [left angle bracket]u[right angle bracket] the average suspension velocity in the channel. The concentration and velocity profiles determined from the simulations are in qualitative agreement with experiment.
A model for suspension flow has been proposed in which macroscopic mass, momentum and energy balances are constructed and solved simultaneously. It is shown that the requirement that the suspension pressure be constant in directions perpendicular to the mean motion leads to particle migration and concentration variations in inhomogeneous flow. The concept of the suspension ‘temperature’ – a measure of the particle velocity fluctuations – is introduced in order to provide a nonlocal description of suspension behaviour. The results of this model for channel flow are in good agreement with the simulations.
733 citations
TL;DR: In this paper, the authors investigated the differences between fully developed turbulent flow in an axisymmetric pipe and a plane channel geometry, and compared the results obtained from a channel flow simulation.
Abstract: Direct numerical simulations (DNS) and experiments are carried out to study fully developed turbulent pipe flow at Reynolds number Rec ≈ 7000 based on centreline velocity and pipe diameter The agreement between numerical and experimental results is excellent for the lower-order statistics (mean flow and turbulence intensities) and reasonably good for the higher-order statistics (skewness and flatness factors) To investigate the differences between fully developed turbulent flow in an axisymmetric pipe and a plane channel geometry, the present DNS results are compared to those obtained from a channel flow simulation Beside the mean flow properties and turbulence statistics up to fourth order, the energy budgets of the Reynolds-stress components are computed and compared The present results show that the mean velocity profile in the pipe fails to conform to the accepted law of the wall, in contrast to the channel flow This confirms earlier observations reported in the literature The statistics on fluctuating velocities, including the energy budgets of the Reynolds stresses, appear to be less affected by the axisymmetric pipe geometry Only the skewness factor of the normal-to-the-wall velocity fluctuations differs in the pipe flow compared to the channel flow The energy budgets illustrate that the normal-to-the-wall velocity fluctuations in the pipe are altered owing to a different ‘impingement’ or ‘splatting’ mechanism close to the curved wall
732 citations
TL;DR: In this article, the Strouhal number and the mean base suction coefficient were measured at the mid-span position Reynolds numbers from about 50 to 4 × 104 were investigated.
Abstract: The investigation is concentrated on two important quantities – the Strouhal number and the mean base suction coefficient, both measured at the mid-span position Reynolds numbers from about 50 to 4 × 104 were investigated Different aspect ratios, at low blockage ratios, were achieved by varying the distance between circular end plates (end plate diameter ratios between 10 and 30) It was not possible, by using these end plates in uniform flow and at very large aspect ratios, to produce parallel shedding all over the laminar shedding regime However, parallel shedding at around mid-span was observed throughout this regime in cases when there was a slight but symmetrical increase in the free-stream velocity towards both ends of the cylinder At higher Re, the results at different aspect ratios were compared with those of a ‘quasi-infinite cylinder’ and the required aspect ratio to reach conditions independent of this parameter, within the experimental uncertainties, are given For instance, aspect ratios as large as L/D = 60–70 were needed in the range Re ≈ 4 × 103–104 With the smallest relative end plate diameter and for aspect ratios smaller than 7, a bi-stable flow switching between regular vortex shedding and ‘irregular flow’ was found at intermediate Reynolds number ranges in the subcritical regime (Re ≈ 2 × 103)
TL;DR: In this article, two models based on Rapid Distortion Theory (RDT) are investigated to model the complete second-order structure of homogeneous, neutrally stratified atmospheric boundary-layer turbulence, including spectra of all velocity components and cross-spectra of any combination of velocity components at two arbitrarily chosen points.
Abstract: Modelling of the complete second-order structure of homogeneous, neutrally stratified atmospheric boundary-layer turbulence, including spectra of all velocity components and cross-spectra of any combination of velocity components at two arbitrarily chosen points, is attempted. Two models based on Rapid Distortion Theory (RDT) are investigated. Both models assume the velocity profile in the height interval of interest to be approximately linear. The linearized Navier–Stokes equation together with considerations of ‘eddy’ lifetimes are then used to modify the spatial second-order structure of the turbulence. The second model differs from the first by modelling the blocking by the surface in addition to the shear. The resulting models of the spectral velocity tensor contain only three adjustable parameters: a lengthscale describing the size of the largest energy-containing eddies, a non-dimensional number used in the parametrization of ‘eddy’ lifetime, and the third parameter is a measure of the energy dissipation.Two atmospheric experiments, both designed to investigate the spatial structure of turbulence and both running for approximately one year, are used to test and calibrate the models. Even though the approximations leading to the models are very crude they are capable of predicting well the two-point second-order statistics such as cross-spectra, coherences and phases, on the basis of measurements carried out at one point. The two models give very similar predictions, the largest difference being in the coherences involving vertical velocity fluctuations, where the blocking by the surface seems to have a significant effect.
TL;DR: In this paper, the interactions between small dense particles and fluid turbulence have been investigated in a downflow fully developed channel in air, at particle mass loadings up to 80% by laser Doppler anemometry.
Abstract: The interactions between small dense particles and fluid turbulence have been investigated in a downflow fully developed channel in air. Particle velocities of, and fluid velocities in the presence of, 50 μm glass, 90 μm glass and 70 μm copper spherical beads were measured by laser Doppler anemometry, at particle mass loadings up to 80%. These particles were smaller than the Kolmogorov lengthscale of the flow and could respond to some but not all of the scales of turbulent motion. Streamwise mean particle velocity profiles were flatter than the mean fluid velocity profile, which was unmodified by particle loading. Particle velocity fluctuation intensities were larger than the unladen-fluid turbulence intensity in the streamwise direction but were smaller in the transverse direction. Fluid turbulence was attenuated by the addition of particles; the degree of attenuation increased with particle Stokes number, particle mass loading and distance from the wall. Turbulence was more strongly attenuated in the transverse than in the streamwise direction, because the turbulence energy is at higher frequencies in the transverse direction. Streamwise turbulence attenuation displayed a range of preferred frequencies where attenuation was strongest.
TL;DR: In this article, the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel is solved for the Navier-Stokes equations for moderate Reynolds numbers in the hundreds.
Abstract: This paper reports the result of direct simulations of fluid–particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel. The fluid motion is computed from the Navier–Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved according to the equations of motion of a rigid body under the action of gravity and hydrodynamic forces arising from the motion of the fluid. The solutions are as exact as our finite-element calculations will allow. As the Reynolds number is increased to 600, a circular particle can be said to experience five different regimes of motion: steady motion with and without overshoot and weak, strong and irregular oscillations. An elliptic particle always turn its long axis perpendicular to the fall, and drifts to the centreline of the channel during sedimentation. Steady drift, damped oscillation and periodic oscillation of the particle are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered structure, a periodic wake-action regime and an active drafting–kissing–tumbling scenario are realized at increasing Reynolds numbers. The non-linear effects of particle–fluid, particle–wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, steady and unsteady wakes and wake interactions. The results are compared to experimental and theoretical results previously published.
TL;DR: In this article, the results of a two-dimensional finite element simulation of the motion of a circular particle in a Couette and a Poiseuille flow were reported, and the authors compared the results with pertinent experimental data and perturbation theories.
Abstract: This paper reports the results of a two-dimensional finite element simulation of the motion of a circular particle in a Couette and a Poiseuille flow. The size of the particle and the Reynolds number are large enough to include fully nonlinear inertial effects and wall effects. Both neutrally buoyant and non-neutrally buoyant particles are studied, and the results are compared with pertinent experimental data and perturbation theories. A neutrally buoyant particle is shown to migrate to the centreline in a Couette flow, and exhibits the Segre-Silberberg effect in a Poiseuille flow. Non-neutrally buoyant particles have more complicated patterns of migration, depending upon the density difference between the fluid and the particle. The driving forces of the migration have been identified as a wall repulsion due to lubrication, an inertial lift related to shear slip, a lift due to particle rotation and, in the case of Poiseuille flow, a lift caused by the velocity profile curvature. These forces are analysed by examining the distributions of pressure and shear stress on the particle. The stagnation pressure on the particle surface are particularly important in determining the direction of migration.
TL;DR: In this article, a detailed numerical study of the interaction of a weak shock wave with an isolated cylindrical gas inhomogeneity is presented, focusing on the early phases of interaction process which are dominated by repeated refractions and reflections of acoustic fronts at the bubble interface.
Abstract: We present a detailed numerical study of the interaction of a weak shock wave with an isolated cylindrical gas inhomogeneity. Such interactions have been studied experimentally in an attempt to elucidate the mechanims whereby shock waves propagating through random media enhance mixing. Our study concentrates on the early phases of the interaction process which are dominated by repeated refractions and reflections of acoustic fronts at the bubble interface. Specifically, we have reproduced two of the experiments performed by Haas and Sturtevant.
TL;DR: In this paper, the equations constituting the stability problem for the interface of two viscous fluids subjected to sinusoidal forcing are derived and a Floquet analysis is presented and a method for the measurement of the interfacial tension, and the sum of densities and dynamic viscosities of two phases of a fluid near the liquid-vapour critical point is proposed.
Abstract: The flat interface between two fluids in a vertically vibrating vessel may be parametrically excited, leading to the generation of standing waves. The equations constituting the stability problem for the interface of two viscous fluids subjected to sinusoidal forcing are derived and a Floquet analysis is presented. The hydrodynamic system in the presence of viscosity cannot be reduced to a system of Mathieu equations with linear damping. For a given driving frequency, the instability occurs only for certain combinations of the wavelength and driving amplitude, leading to tongue-like stability zones. The viscosity has a qualitative effect on the wavelength at onset: at small viscosities, the wavelcngth decreases with increasing viscosity, while it increases for higher viscosities. The stability threshold is in good agreement with experimental results. Based on the analysis, a method for the measurement of the interfacial tension, and the sum of densities and dynamic viscosities of two phases of a fluid near the liquid-vapour critical point is proposed.
TL;DR: In this article, a direct numerical simulation (DNS) is used to estimate the different terms appearing in the Σ-equation of the flame surface density, where basic physical mechanisms like production by hydrodynamic straining and destruction by propagation effects are described explicitly.
Abstract: One basic effect of turbulence in turbulent premixed combustion is for the fluctuating velocity field to wrinkle the flame and greatly increase its surface area. In the flamelet theory, this effect is described by the flame surface density. An exact evolution equation for the flame surface density, called the Σ-equation, may be written, where basic physical mechanisms like production by hydrodynamic straining and destruction by propagation effects are described explicitly. Direct numerical simulation (DNS) is used in this paper to estimate the different terms appearing in the Σ-equation. The numerical configuration corresponds to three-dimensional premixed flames in isotropic turbulent flow. The simulations are performed for various mixture Lewis numbers in order to modify the strength and nature of the flame-flow coupling. The DNS-based analysis provides much information relevant to flamelet models. In particular, the flame surface density, and the source and sink terms for the flame surface density, are resolved spatially across the turbulent flame brush. The geometry as well as the dynamics of the flame differ quite significantly from one end of the reaction zone to the other. For instance, contrary to the intuitive idea that flame propagation effects merely counteract the wrinkling due to the turbulence, the role of flame propagation is not constant across the turbulent brush and switches from flame surface production at the front to flame surface dissipation at the back. Direct comparisons with flamelet models are also performed. The Bray-Moss-Libby assumption that the flame surface density is proportional to the flamelet crossing frequency, a quantity that can be measured in experiments, is found to be valid. Major uncertainties remain, however, over an appropriate description of the flamelet crossing frequency. In comparison, the coherent flame model of Marble & Broadwell achieves closure at the level of the Σ-equation and provides a more promising physically based description of the flame surface dynamics. Some areas where the model needs improvement are identified.
TL;DR: In this article, a large-scale large-aspect-ratio system with a viscous fluid and two simultaneous forcing frequencies is investigated, and the asymptotic pattern observed just above the threshold for the first instability of the flat surface is found to depend strongly on the frequency ratio and the amplitudes and phases of the two sinusoidal components of the driving acceleration.
Abstract: Parametric excitation of surface waves via forced vertical oscillation of a container filled with fluid (the Faraday instability) is investigated experimentally in a small-depth large-aspect-ratio system, with a viscous fluid and with two simultaneous forcing frequencies. The asymptotic pattern observed just above the threshold for the first instability of the flat surface is found to depend strongly on the frequency ratio and the amplitudes and phases of the two sinusoidal components of the driving acceleration. Parallel lines, squares, and hexagons are observed. With viscosity 100 cS, these stable standing-wave patterns do not exhibit strong sidewall effects, and are found in containers of various shapes including an irregular shape. A ‘quasi-pattern’ of twelvefold symmetry, analogous to a two-dimensional quasi-crystal, is observed for some even/odd frequency ratios. Many of the experimental phenomena can be modelled via cubic-order amplitude equations derived from symmetry arguments.
TL;DR: In this article, the modification of the mean and fluctuating characteristics of a flat-plate boundary layer subjected to nearly isotropic free stream turbulence (FST) is studied experimentally using hot-wire anemometry.
Abstract: The modification of the mean and fluctuating characteristics of a flat-plate boundary layer subjected to nearly isotropic free stream turbulence (FST) is studied experimentally using hot-wire anemometry. The study is focussed on the region upstream of the transition onset, where the fluctuations inside the boundary layer are dominated by elongated flow structures which grow downstream both in amplitude and length. Their downstream development and scaling are investigated and the results are compared with those obtained by previous authors. This allows some conclusions about the parameters which are relevant for the modelling of the transition process. The mechanisms underlying the transition process and the relative importance of the Tollmien–Schlichting wave instability in this flow are treated in an accompanying paper (part 2 of the present report).
TL;DR: In this article, it was shown that there exists at least one mode of oscillation, antisymmetric about the centreline, that corresponds to a local oscillation at a particular frequency, in the absence of excitation, which decays with distance down the waveguide away from the obstruction.
Abstract: A two-dimensional acoustic waveguide of infinite extent described by two parallel lines contains an obstruction of fairly general shape which is symmetric about the centreline of the waveguide. It is proved that there exists at least one mode of oscillation, antisymmetric about the centreline, that corresponds to a local oscillation at a particular frequency, in the absence of excitation, which decays with distance down the waveguide away from the obstruction. Mathematically, this trapped mode is related to an eigenvalue of the Laplace operator in the waveguide. The proof makes use of an extension of the idea of the Rayleight quotient to characterize the lowest eigenvalue of a differential operator on an infinite domain.
TL;DR: In this article, the development of anisotropic states from initially isotropic ones is investigated numerically for fully three-dimensional incompressible MHD turbulence, and it is found that when an external d.c. magnetic field (B0) is imposed on viscous and resistive MHD systems, excitations are preferentially transferred to modes with wavevectors perpendicular to B0.
Abstract: Building on results from two-dimensional magnetohydrodynamic (MHD) turbulence (Shebalin, Matthaeus & Montgomery 1983), the development of anisotropic states from initially isotropic ones is investigated numerically for fully three-dimensional incompressible MHD turbulence. It is found that when an external d.c. magnetic field (B0) is imposed on viscous and resistive MHD systems, excitations are preferentially transferred to modes with wavevectors perpendicular to B0). The anisotropy increases with increasing mechanical and magnetic Reynolds numbers, and also with increasing wavenumber. The tendency of B0 to inhibit development of turbulence is also examined.
TL;DR: In this article, a theoretical analysis of the turbulent stress tensor in large-eddy simulation is presented from a theoretical point of view, where realizability conditions for the components of this tensor are derived, which hold if and only if the filter function is positive.
Abstract: The turbulent stress tensor in large-eddy simulation is examined from a theoretical point of view. Realizability conditions for the components of this tensor are derived, which hold if and only if the filter function is positive. The spectral cut-off, one of the filters frequently used in large-eddy simulation, is not positive. Consequently, the turbulent stress tensor based on spectrally filtered fields does not satisfy the realizability conditions, which leads to negative values of the generalized turbulent kinetic energy k. Positive filters, e. g. Gaussian or top-hat, always give rise to a positive k. For this reason, subgrid models which require positive values for k should be used in conjunction with e. g. the Gaussian or top-hat filter rather than with the spectral cutoff filter. If the turbulent stress tensor satisfies the realizability conditions, it is natural to require that the subgrid model for this tensor also satisfies these conditions. With respect to this point of view several subgrid models are discussed. For eddy-viscosity models a lower bound for the generalized turbulent kinetic energy follows as a necessary condition. This result provides an inequality for the model constants appearing in a ‘Smagorinsky-type’ subgrid model for compressible flows.
TL;DR: In this article, the effective viscosity for the Brinkman-Forchheimer flow (BFF) model has been determined experimentally for steady flow through a wall-bounded porous medium.
Abstract: The effective viscosity mu{sub e} for the Brinkman-Forchheimer flow (BFF) model has been determined experimentally for steady flow through a wall-bounded porous medium. Nuclear magnetic resonance (NMR) techniques were used to measure non-invasively the ensemble-average velocity profile of water flowing through a tube filled with an open-cell rigid foam of high porosity (phi = 0.972). By comparing these data with the BFF model, for which all remaining parameters were measured independently, it was determined that mu{sub e} = (7.5{sub -2.4}{sup +3.4}) mu{sub f}, where mu{sub f} was the viscosity of the fluid. The Reynolds number, based upon the square root of the permeability, was 17. 14 refs.
TL;DR: In this article, the authors analyzed the energy flows that are connected to the dynamical behaviour of coherent structures in a transitional flat-plate boundary layer and showed that the occurrence of a spike must be attributed to an autonomous event and cannot be interpreted as just an epiphenomenon of the passage of a Λ-vortex.
Abstract: An investigation is presented that analyses the energy flows that are connected to the dynamical behaviour of coherent structures in a transitional flat-plate boundary layer. Based on a mathematical description of the three-dimensional coherent structures of this flow as provided by the Karhunen–Loeve procedure, energy equations for the coherent structures are derived by Galerkin projection of the Navier–Stokes equations in vorticity transport formulation onto the corresponding basis of eigenfunctions. In a first step, the time-averaged energy balance – showing the energy flows that support the different coherent structures and thus maintain the fluctuations of the velocity field – is considered. In a second step, the instantaneous power budget is investigated for the particularly interesting case of a coherent structure providing a prime contribution to the characteristic spike events of the transitional boundary layer. As this structure shows a strong variation in energy, the question about which mechanisms cause these variations is addressed. Our results show that the occurrence of a spike must be attributed to an autonomous event and cannot be interpreted as just an epiphenomenon of the passage of a Λ-vortex.
TL;DR: In this paper, an experimental adaptation of the well-known laser-Doppler anemometry technique is developed for measuring the velocity and concentration profiles in concentrated suspension flows in a rectangular channel.
Abstract: An experimental adaptation of the well-known laser-Doppler anemometry technique is developed for measuring the velocity and concentration profiles in concentrated suspension flows. To circumvent the problem of optical turbidity, the refractive indices of the solid and liquid phases are closely matched. The residual turbidity, owing to small mismatches of the refractive indices, as well as impurities in the particles, allows a Doppler signal to be detected when a particle passes through the scattering volume. By counting the number of Doppler signals in a period of time, the local volume fraction is also measured. This new technique is utilized to study concentrated suspension flows in a rectangular channel. The general behaviour of the suspension is that the velocity profile is blunted while the concentration profile has a maximum near the centre. Comparisons are made with theoretical predictions based on the shear-induced particle migration theory.
TL;DR: In this paper, the authors present a reduced integrodifferential Hamiltonian reduced equation for weakly nonlinear surface waves, called five-wave, where the non-resonant quadratic, cubic and fourth-order nonlinear terms are eliminated by suitable canonical transformation.
Abstract: Many studies of weakly nonlinear surface waves are based on so-called reduced integrodifferential equations. One of these is the widely used Zakharov four-wave equation for purely gravity waves. But the reduced equations now in use are not Hamiltonian despite the Hamiltonian structure of exact water wave equations. This is entirely due to shortcomings of their derivation. The classical method of canonical transformations, generalized to the continuous case, leads automatically to reduced equations with Hamiltonian structure. In this paper, attention is primarily paid to the Hamiltonian reduced equation describing the combined effects of four- and five-wave weakly nonlinear interactions of purely gravity waves. In this equation, for brevity called five-wave, the non-resonant quadratic, cubic and fourth-order nonlinear terms are eliminated by suitable canonical transformation. The kernels of this equation and the coefficients of the transformation are expressed in explicit form in terms of expansion coefficients of the gravity-wave Hamiltonian in integral-power series in normal variables. For capillary–gravity waves on a fluid of finite depth, expansion of the Hamiltonian in integral-power series in a normal variable with accuracy up to the fifth-order terms is also given.
TL;DR: In this paper, a direct numerical simulation of turbulent homogeneous shear flow is performed in order to clarify compressibility effects on the turbulence growth in the flow, and the stabilizing effect of compressibility on the turbulent energy growth rate is observed to be substantially larger in the DNS series where the initial value of M_g is changed.
Abstract: Direct numerical simulation of turbulent homogeneous shear flow is performed in order to clarify compressibility effects on the turbulence growth in the flow. The two Mach numbers relevant to homogeneous shear flow are the turbulent Mach number M_t and the gradient Mach number M_g. Two series of simulations are performed where the initial values of M_g and M_t are increased separately. The growth rate of turbulent kinetic energy is observed to decrease in both series of simulations. This `stabilizing'' effect of compressibility on the turbulent energy growth rate is observed to be substantially larger in the DNS series where the initial value of M_g is changed. A systematic comparison of the different DNS cases shows that the compressibility effect of reduced turbulent energy growth rate is primarily due to the reduced level of turbulence production and not due to explicit dilatational effects. The reduced turbulence production is not a mean density effect since the mean density remains constant in compressible homogeneous shear flow. The stabilizing effect of compressibility on the turbulence growth is observed to increase with the gradient Mach number M_g in the homogeneous shear flow DNS. Estimates of M_g for the mixing layer and the boundary layer are obtained. These estimates show that the parameter M_g becomes much larger in the high-speed mixing layer relative to the high-speed boundary layer even though the mean flow Mach numbers are the same in the two flows. Therefore, the inhibition of turbulent energy production and consequent `stabilizing'' effect of compressibility on the turbulence (over and above that due to the mean density variation) is expected to be larger in the mixing layer relative to the boundary layer in agreement with experimental observations.
TL;DR: In this article, a large-Reynolds number asymptotic theory is presented for the problem of a vortex tube of finite circulation subjected to uniform non-axisymmetric irrotational strain, and aligned along an axis of positive rate of strain.
Abstract: A large-Reynolds-number asymptotic theory is presented for the problem of a vortex tube of finite circulation [Gcy ] subjected to uniform non-axisymmetric irrotational strain, and aligned along an axis of positive rate of strain. It is shown that at leading order the vorticity field is determined by a solvability condition at first-order in e = 1/R[Gcy ] where R[gcy ] = [gcy ]/ν. The first-order problem is solved completely, and contours of constant rate of energy dissipation are obtained and compared with the family of contour maps obtained in a previous numerical study of the problem. It is found that the region of large dissipation does not overlap the region of large enstrophy; in fact, the dissipation rate is maximal at a distance from the vortex axis at which the enstrophy has fallen to only 2.8% of its maximum value. The correlation between enstrophy and dissipation fields is found to be 0.19 + O(e2). The solution reveals that the stretched vortex can survive for a long time even when two of the principal rates of strain are positive, provided R[gcy ] is large enough. The manner in which the theory may be extended to higher orders in e is indicated. The results are discussed in relation to the high-vorticity regions (here described as ‘sinews’) observed in many direct numerical simulations of turbulence.
TL;DR: In this paper, it is shown that free shear flows can be substantially altered through direct control of the large coherent vortices present in the flow by placing a foil in the wake of a D-section cylinder, sufficiently far behind the cylinder so that it does not interfere with the vortex formation process.
Abstract: It is shown experimentally that free shear flows can be substantially altered through direct control of the large coherent vortices present in the flow.First, flow-visualization experiments are conducted in Kalliroscope fluid at Reynolds number 550. A foil is placed in the wake of a D-section cylinder, sufficiently far behind the cylinder so that it does not interfere with the vortex formation process. The foil performs a heaving and pitching oscillation at a frequency close to the Strouhal frequency of the cylinder, while cylinder and foil also move forward at constant speed. By varying the phase of the foil oscillation, three basic interaction modes are identified. (i) Formation of a street of pairs of counter-rotating vortices, each pair consisting of one vortex from the initial street of the cylinder and one vortex shed by the foil. The width of the wake is then substantially increased. (ii) Formation of a street of vortices with reduced or even reverse circulation compared to that of oncoming cylinder vortices, through repositioning of cylinder vortices by the foil and interaction with vorticity of the opposite sign shed from the trailing edge of the foil. (iii) Formation of a street of vortices with circulation increased through merging of cylinder vortices with vortices of the same sign shed by the foil. In modes (ii) and (iii) considerable repositioning of the cylinder vortices takes place immediately behind the foil, resulting in a regular or reverse Karman street. The formation of these three interaction patterns is achieved only for specific parametric values; for different values of the parameters no dominant stable pattern emerges.Subsequently, the experiments are repeated in a different facility at larger scale, resulting in Reynolds number 20000, in order to obtain force and torque measurements. The purpose of the second set of experiments is to assess the impact of flow control on the efficiency of the oscillating foil, and hence investigate the possibility of energy extraction. It is found that the efficiency of the foil depends strongly on the phase difference between the oscillation of the foil and the arrival of cylinder vortices. Peaks in foil efficiency are associated with the formation of a street of weakened vortices and energy extraction by the foil from the vortices of the vortex street.