Rotational dynamics in dipolar colloidal suspensions: video microscopy experiments and simulations results

The dynamics of field-induced structures in very dilute dipolar colloidal suspensions subject to rotating magnetic fields have been experimentally studied using video microscopy. When a rotating field is imposed the chain-like aggregates rotate with the magnetic field frequency. We found that the size of the induced structures at small rotational frequencies is larger than at zero rotating frequency, i.e. when an uniaxial magnetic field is applied. At higher frequencies, the average size of the aggregates decreases with frequency following a power law with exponent −0.5 as the hydrodynamic friction forces overcome the dipolar magnetic forces, causing the chains break up. A non-thermal molecular dynamics simulations are also reported, showing good agreement with the experiments.     

Hybrid numerical method for wall-resolved large-eddy simulations of compressible wall-bounded turbulence

Acta Mechanica Sinica - Bogies are responsible for a significant amount of aerodynamic resistance and noise, both of which negatively affect high-speed train performance and passenger comfort. In...     

Effect of turbulence intensity on airfoil flow: numerical simulations and experimental measurements

The effect of the turbulence intensity of the oncoming stream on the aerodynamic characteristics of the NACA-0012 airfoil is investigated by a direct numerical simulation. The numerical results are found to be consistent with the experimental measurements. Based on the finite spectral QUICK scheme, the simulation gets the high accuracy results. Both the simulation and the experiment reveal that the airfoil stall does not exist for the low turbulence intensity, however, occurs when the turbulence intensity increases sufficiently. Besides, the turbulence intensity has a significant effect on both the airfoil boundary layer and the separated shear layer.     

Fluid dynamics in a bubble column: New experiments and simulations

New high quality experimental data for the fluid dynamics of a bubble column are used to validate a baseline set of closure relations for bubbly flows. Development and validation of such closure relations is an important and active area of research, since they facilitate CFD simulations on industrial scales by means of the Euler–Euler two-fluid model. The new dataset features in particular large spatial and temporal resolution and high accuracy for a comprehensive set of observables and a range of different conditions. The closure model, which has been validated previously for a range of different conditions, is shown to agree with the new data quite well. In this way, the confidence in the model for predictive applications, such as optimization and scale-up of chemical engineering processes, is further enhanced.     

Linear stability and dynamics of viscoelastic flows using time-dependent numerical simulations

Ultimately, numerical simulation of viscoelastic flows will prove most useful if the calculations can predict the details of steady-state processing conditions as well as the linear stability and non-linear dynamics of these states. We use finite element spatial discretization coupled with a semi-implicit θ-method for time integration to explore the linear and non-linear dynamics of two, two-dimensional viscoelastic flows: plane Couette flow and pressure-driven flow past a linear, periodic array of cylinders in a channel. For the upper convected Maxwell (UCM) fluid, the linear stability analysis for the plane Couette flow can be performed in closed form and the two most dangerous, although always stable, eigenvalues and eigenfunctions are known in closed form. The eigenfunctions are non-orthogonal in the usual inner product and hence, the linear dynamics are expected to exhibit non-normal (non-exponential) behavior at intermediate times. This is demonstrated by numerical integration and by the definition of a suitable growth function based on the eigenvalues and the eigenvectors. Transient growth of the disturbances at intermediate times is predicted by the analysis for the UCM fluid and is demonstrated in linear dynamical simulations for the Oldroyd-B model. Simulations for the fully non-linear equations show the amplification of this transient growth that is caused by non-linear coupling between the non-orthogonal eigenvectors. The finite element analysis of linear stability to two-dimensional disturbances is extended to the two-dimensional flow past a linear, periodic array of cylinders in a channel, where the steady-state motion itself is known only from numerical calculations. For a single cylinder or widely separated cylinders, the flow is stable for the range of Deborah number (De) accessible in the calculations. Moreover, the dependence of the most dangerous eigenvalue on De≡λV/R resembles its behavior in simple shear flow, as does the spatial structure of the associated eigenfunction. However, for closely spaced cylinders, an instability is predicted with the critical Deborah number De_c scaling linearly with the dimensionless separation distance L between the cylinders, that is, the critical Deborah number De_Lc≡λV/L is shown to be an O(1) constant. The unstable eigenfunction appears as a family of two-dimensional vortices close to the channel wall which travel downstream. This instability is possibly caused by the interaction between a shear mode which approaches neutral stability for De ≫ 1 and the periodic modulation caused by the presence of the cylinders. Nonlinear time-dependent simulations show that this secondary flow eventually evolves into a stable limit cycle, indicative of a supercritical Hopf bifurcation from the steady base state.     

Spectral structure of stratified turbulence: direct numerical simulations and predictions by large eddy simulation

Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series of direct numerical simulations (DNS) of stratified turbulence. To facilitate simulations of real-world problems, which are usually beyond the reach of DNS, we propose a subgrid-scale turbulence model for large eddy simulations of stratified flows based on the Adaptive Local Deconvolution Method (ALDM). Flow spectra and integral quantities predicted by ALDM are in excellent agreement with direct numerical simulation. ALDM automatically adapts to strongly anisotropic turbulence and is thus a suitable tool for studying turbulent flow phenomena in atmosphere and ocean.     

Some wave-propagation experiments in plasteline-clay rods

Compressional stress pulses have been propagated in plasteline-clay rods by detonating small charges of lead azide at one end. A capacitance gage at the other end was used to measure particle displacement associated with the pulses and the particle velocity was obtained by differentiation. The shapes and amplitudes of the pulses were determined in separate experiments using composite clay-steel rods where the steel acted, in effect, as a pressure transducer. The techniques employed permitted comparatively accurate determination of some aspects of the dynamic behavior of clay. On the basis of preliminary results, the behavior of clay has been compared to that of a linear viscoelastic solid with the tentative goal of studying the validity of a viscoelastic constitutive model.     

Large scale numerical simulations for multi-phase fluid dynamics with moving interfaces

This short communication presents our recent studies to implement numerical simulations for multi-phase flows on top-ranked supercomputer systems with distributed memory architecture. The numerical model is designed so as to make full use of the capacity of the hardware. Satisfactory scalability in terms of both the parallel speed-up rate and the size of the problem has been obtained on two high rank systems with massively parallel processors, the Earth Simulator (Earth simulator research center, Yokohama Kanagawa, Japan) and the TSUBAME (Tokyo Institute of Technology, Tokyo, Japan) supercomputers.     

Experimental and numerical investigation of the dynamics of uniform turbulence of a stably stratified fluid

The results of experimental and numerical studies of the dynamics of the parameters of uniform turbulence of a stably stratified fluid for different molecular Prandtl-Schmidt numbers over a wide range of buoyancy times Nτ are given. The tank, the measurement apparatus used, and the experimental procedure are briefly described. The numerical modeling used a second-order model of uniform turbulence of a stratified medium. The influence of fluctuations of the turbulent mass (heat) flux q(Nτ) on the evolution of the statistical parameters of the velocity and temperature fields is analyzed, and an invariant equation is found for the parameters of the strong turbulence of the stratified fluid. It is shown that the statistical parameters of the turbulence, being smoothed with respect to the amplitude of the fluctuations, vary self-similarly with time after the collapse point. Donetsk State University, Donetsk 340055.¹Institute of Heat and Mas Transfer, National Academy of Sciences of Belarusia, Minsk 220072. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 64–75, July–August, 1998.     

Non-linear dynamics of curved beams. Part 2, numerical analysis and experiments

The aim of this work is to formulate a model for the study of the dynamics of curved beams undergoing large oscillations. In Part 1, the interest was oriented to the formulation of a consistent analytical model and to obtain the equations of motion in weak form. In Part 2, a case-study is considered and the response for various initial curved configurations, obtained by varying the initial curvature, is analyzed. Both the free and the forced problems are considered: the linear free dynamics are studied to detect how the initial configuration affects the modal properties and to enlighten the typical phenomena of frequency coalescence and avoidance; the forced dynamics are then studied for different internal resonance conditions to enlighten the phenomenon of the dynamic instability under a shear periodic tip follower force and to describe the various classes of post-critical motion. The results of experimental tests conducted on a slightly imperfect straight beam prototype are eventually discussed.     

Chaos and direct numerical simulation in turbulence

We show that direct numerical simulation will yield turbulent flowfields which are strongly dependent upon computer hardware and software. A computed flow trajectory is apparently uncorrelated to the true solution of a flowfield if it is allowed to evolve over a long time, and hence is called a pseudo-orbit. This is due to the trajectory instability of chaotic turbulent flows. All is not lost, however; a long-time average of flow quantities can now be computed using a pseudo-orbit by invoking the shadowing lemma. For the inviscid flow, this time average tends to approach asymptotically the phase average as predicted by the classical ergodic theorem. Although the inviscid two-dimensional flow has no real physical importance, the existence of canonical (equilibrium) distribution permits us to examine the accuracy of time averaging based on the pseudo-orbit and its inherent limitations.This work was supported by AFOSR task 2304N1.     

A mesoscopic modelling approach for direct numerical simulations of transition to turbulence in hypersonic flow with transpiration cooling

A rescaling methodology is developed for high-fidelity, cost-efficient direct numerical simulations (DNS) of flow through porous media, modelled at mesoscopic scale, in a hypersonic freestream. The simulations consider a Mach 5 hypersonic flow over a flat plate with coolant injection from a porous layer with 42 % porosity. The porous layer is designed using a configuration studied in the literature, consisting of a staggered arrangement of cylinder/sphere elements. A characteristic Reynolds number ${\mathit{Re}}_c$ of the flow in a pore cell unit is first used to impose aerodynamic similarity between different porous layers with the same porosity, $∊$, but different pore size. A relation between the pressure drop and the Reynolds number is derived to allow a controlled rescaling of the pore size from the realistic micrometre scales to higher and more affordable scales. Results of simulations carried out for higher cylinder diameters, namely 24 μm, 48 μm and 96 μm, demonstrate that an equivalent Darcy-Forchheimer behaviour to the reference experimental microstructure is obtained at the different pore sizes. The approach of a porous layer with staggered spheres is applied to a 3D domain case of porous injection in the Darcy limit over a flat plate, to study the transition mechanism and the associated cooling performance, in comparison with a reference case of slot injection. Results of the direct numerical simulations show that porous injection in an unstable boundary layer leads to a more rapid transition process, compared to slot injection. On the other hand, the mixing of coolant within the boundary layer is enhanced in the porous injection case, both in the immediate outer region of the porous layer and in the turbulent region. This has the beneficial effect of increasing the cooling performance by reducing the temperature near the wall, which provides a higher cooling effectiveness, compared to the slot injection case, even with an earlier transition to turbulence.     

Vorticity dynamics in turbulence growth

The mechanisms of vorticity amplification in the formation of turbulence are investigated by means of direct numerical simulations of the Navier–Stokes equations with different initial conditions and Reynolds numbers. The simulations show good universality of the enstrophy evolution, that occurs in two stages. The first stage is dominated by the effect of vortex stretching, and it finishes with a k ^?3 power-law energy spectrum. The second stage is dominated by the action of viscosity on the small scales, and it finishes with a Kolmogorov k ^?5/3 energy spectrum.     

Statistics of particle dispersion in direct numerical simulations of wall-bounded turbulence: Results of an international collaborative benchmark test

In this paper the results of an international collaborative test case relative to the production of a direct numerical simulation and Lagrangian particle tracking database for turbulent particle dispersion in channel flow at low Reynolds number are presented. The objective of this test case is to establish a homogeneous source of data relevant to the general problem of particle dispersion in wall-bounded turbulence. Different numerical approaches and computational codes have been used to simulate the particle-laden flow and calculations have been carried on long enough to achieve a statistically steady condition for particle distribution. In such stationary regime, a comprehensive database including both post-processed statistics and raw data for the fluid and for the particles has been obtained. The complete datasets can be downloaded from the web at http://cfd.cineca.it/cfd/repository/. In this paper the most relevant velocity statistics (for both phases) and particle distribution statistics are discussed and benchmarked by direct comparison between the different numerical predictions.     

Conservation laws in the dynamics of rods

Conservation laws and associated integrals of motion for the dynamics of rods are derived. The classic conservation laws are those of total linear and angular momentum, and, for hyperelastic rods, conservation of energy. It will here be shown that an additional conservation law arises in each of two cases. The first case is that of uniform, hyperelastic rods, the second is that of a class of transversely isotropic rods. AMS(MOS) 73C50, 73K05.The research reported in this paper was partially supported by grants from the US Air Force Office of Scientific Research.     

Magnetic particle microrheometric dynamics in Newtonian fluids: numerical simulations on the early motion and beyond

Rotating magnetic particle microrheometry has been a promising technique in measuring material properties in limited-sample high-viscosity fluids. Experimental limitations in the early motion require further theoretical exploration. In this work, the rotation of a ferromagnetic particle is considered under the influence of an external uniform magnetic field in an infinite highly viscous Newtonian fluid. The motion is restricted at the very low Reynolds number limit. Early-time analytical approximations are utilised to initiate numerical calculations in an attempt to describe the azimuthal velocity dependency on scaled time and radius. The equation of motion is solved by implementing a Crank–Nicholson finite-difference scheme, while the driving time-dependent boundary condition is discretised according to a Lax–Wendroff scheme. Stability and convergence criteria for the PDE are also discussed. It is demonstrated that the step function form of the applied magnetic field does not cause finite displacement other than that expected from Newtonian fluid flow for the typical magnetic field magnitude ranges encountered in micro-rheometric studies. The numerical solution is compared against analytical values available for particle ‘zero-total-torque’ condition and it was found to be second-order accurate in time and radial dimension.     

A numerical study of supersonic turbulence

We report on simulations of nonstationary supersonic isotropic turbulent flow using the Piecewise-Parabolic Method on uniform grids of 2048² in two dimensions and 256³ in three dimensions. Intersecting shock waves initiate the transfer of energy from long to short wavelengths. Weak shocks survive for many acoustic times _ac. In two dimensions eddies merge over many _ac. In three dimensions vortex sheets break-up into short vortex filaments within two _ac. Entropy fluctuations, produced by strong shocks, are stretched into filaments over several _ac. These filaments persist and are mirrored in the density. We observe three temporal phases: onset, with the initial formation of shocks; quasi-supersonic, with strong density contrasts; and post-supersonic, with a slowly decaying root mean square Mach number. Compressive modes quickly establish a k ^–2 velocity power spectrum. In three dimensions solenoidal modes build-up during the supersonic phase delineating through time a Kolmogorov k ^–5/3 envelope and leaving a self-similarly decaying k ^–0.9 spectrum at lower wave numbers.This work was supported at the University of Minnesota by grants DE-FG02-87ER25035 from the Office of Energy Research of the Department of Energy, AST-8611404 from the National Science Foundation, and by equipment grants from Sun Microsystems, Gould Electronics, Seagate Technology, and the Air Force Office of Scientific Research (AFOSR-86-0239). Partial support for this work has also come from the Army Research Office Contract Number DAAL03-89-C-0038 funding the Army High Performance Computing Research Center (AHPCRC) at the University of Minnesota. At Nice this work was supported under DRET Contract 500-276, under the GdR CNRS-SPI Mécanique des Fluides, and under two special grants from the Observatoire de la Côte d'Azur.