ALBERT

Description: The classical gravitational instability of a layer of denser fluid overlying a layer of less dense fluid, commonly known as the Rayleigh-Taylor instability, has been studied for well over a hundred years. In this article, we present the results of numerical simulations of a variant of this instability in which a plug of dense fluid is released from rest in a thin channel between two flat, vertical walls, causing a downward acceleration of the entire fluid column and formation of boundary layers near the walls. The plug of dense fluid undergoes distinctly different evolution near the walls and in the fluid interior. The instability in the interior, which we label the “hammerhead” instability based on its shape, is robust over a range of physical parameters, but disappears below a threshold Schmidt number. Fluid near the wall is slowed, and thin tendrils that link the near wall fluid to the main body of the fluid plug form, and in some cases undergo their own instability. We characterize the fully three-dimensionalized state, finding that while bulk measures of kinetic energy three-dimensionalization do not discriminate between low and high Schmidt number cases, the geometric distributions of the dynamical parameters Q and R from the turbulence literature are profoundly different in the high Schmidt number case. Finally, we consider the role of shear in situations in which the two plates are not exactly vertical, demonstrating that shear diminishes the importance of three-dimensionalization, while the hammerhead instability remains relevant.

Description: Flow past two cylinders of different diameters in close proximity is simulated numerically for a constant diameter ratio of 0.45, a gap ratio of 0.0625, and a Reynolds number of 1000 (defined using the diameter of the main cylinder). The effect of the position angle α of the small cylinder relative to the large one on force coefficients and wake flow patterns are studied. Depending on the position angle α of the small cylinder, four wake flow modes are identified: the upstream interference mode for α = 0°, 22.5°, and 45°, the intermittent attached gap flow mode for α = 67.5° and 90°, the attached gap flow mode for α = 112.5° and 135°, and the wake interference mode for α = 157.5° and 180°. The RMS lift coefficients of both cylinders are reduced significantly compared with that of a single cylinder, regardless of the position angle of the small cylinder. Although the variation trends of the mean drag and lift coefficients with the position angle of the small cylinder obtained from the two-dimensional (2D) and three-dimensional (3D) simulations are similar, the 2D simulations overestimate the mean drag coefficient, the RMS drag and lift coefficients compared with those obtained from the 3D simulations.

Description: This paper investigates the effects of particle shape and Stokes number on the behaviour of non-spherical particles in turbulent channel flow. Although there are a number of studies concerning spherical particles in turbulent flows, most important applications occurring in process, energy, and pharmaceutical industries deal with non-spherical particles. The computation employs a unique and novel four-way coupling with the Lagrangian point-particle approach. The fluid phase at low Reynolds number ( Re τ = 150) is modelled by direct numerical simulation, while particles are tracked individually. Inter-particle and particle-wall collisions are also taken into account. To explore the effects of particles on the flow turbulence, the statistics of the fluid flow such as the fluid velocity, the terms in the turbulence kinetic energy equation, the slip velocity between the two phases and velocity correlations are analysed considering ellipsoidal particles with different inertia and aspect ratio. The results of the simulations show that the turbulence is considerably attenuated, even in the very dilute regime. The reduction of the turbulence intensity is predominant near the turbulence kinetic energy peak in the near wall region, where particles preferentially accumulate. Moreover, the elongated shape of ellipsoids strengthens the turbulence attenuation. In simulations with ellipsoidal particles, the fluid-particle interactions strongly depend on the orientation of the ellipsoids. In the near wall region, ellipsoids tend to align predominantly within the streamwise ( x ) and wall-normal ( y ) planes and perpendicular to the span-wise direction, whereas no preferential orientation in the central region of the channel is observed. Important conclusions from this work include the effective viscosity of the flow is not affected, the direct dissipation by the particles is negligible, and the primary mechanism by which the particles affect the flow is by altering the turbulence structure around the turbulence kinetic energy peak.

Description: Reynolds Averaged Navier Stokes (RANS) models are widely used in industry to predict fluid flows, despite their acknowledged deficiencies. Not only do RANS models often produce inaccurate flow predictions, but there are very limited diagnostics available to assess RANS accuracy for a given flow configuration. If experimental or higher fidelity simulation results are not available for RANS validation, there is no reliable method to evaluate RANS accuracy. This paper explores the potential of utilizing machine learning algorithms to identify regions of high RANS uncertainty. Three different machine learning algorithms were evaluated: support vector machines, Adaboost decision trees, and random forests. The algorithms were trained on a database of canonical flow configurations for which validated direct numerical simulation or large eddy simulation results were available, and were used to classify RANS results on a point-by-point basis as having either high or low uncertainty, based on the breakdown of specific RANS modeling assumptions. Classifiers were developed for three different basic RANS eddy viscosity model assumptions: the isotropy of the eddy viscosity, the linearity of the Boussinesq hypothesis, and the non-negativity of the eddy viscosity. It is shown that these classifiers are able to generalize to flows substantially different from those on which they were trained. Feature selection techniques, model evaluation, and extrapolation detection are discussed in the context of turbulence modeling applications.

Description: The energy spectrum contains information not only on the intensity but also on the scale dependence of the turbulent fluctuations; the spectrum is commonly used to describe the dynamics of homogeneous isotropic turbulence. On the other hand, one-point statistical quantities such as the turbulent kinetic energy are mainly treated for inhomogeneous turbulence. Although the energy spectrum must be useful in describing the scale dependence of inhomogeneous turbulence, the Fourier transform cannot be performed in general cases. In this work, instead of the energy spectrum in the wavenumber space, the energy density in the scale space was introduced on the basis of the two-point velocity correlation in the physical space. The transport equation for the energy density was derived for inhomogeneous turbulence. Direct numerical simulation (DNS) data of homogeneous isotropic turbulence were first used to evaluate the energy transfer in the scale space. The energy density equation was compared with the energy spectrum equation to assess the role of the energy density. DNS data of turbulent channel flow were also used to evaluate the energy density equation for inhomogeneous turbulence. The energy transport in the physical and scale spaces was examined in different regions of channel flow. It was shown that the transport equation for the energy density adequately describes the energy transfer in the scale space. The energy flux from the large to the small scales was observed for both turbulent flows in a similar manner to the conventional energy cascade in the wavenumber space.

Description: The variable hard sphere and related models have proven to be accurate and computationally convenient replacements for the inverse power law model of classical kinetic theory in direct simulation Monte Carlo calculations. We attempt to provide theoretical support for this remarkable success by comparing the relaxation rates in the linearized Boltzmann equation for the Maxwellian collision model with those of its variable hard sphere surrogate. The comparison demonstrates that the linearized collision operator with variable hard sphere interactions can accurately approximate the linearized collision operator with Maxwellian inverse power law interactions under well-defined and broadly applicable conditions. Extensions of the analysis to the general inverse power law model and to more realistic intermolecular potentials are briefly discussed.

Description: We present an investigation of the stability of liquid metal flow under the influence of an imposed magnetic field by means of a laboratory experiment as well as a linear stability analysis of the setup using the finite element method. The experimental device ZUrich Cylindrical CHannel INstability Investigation is a modified cylindrical annulus with electrically driven flow of liquid GaInSn operating at Hartmann and Reynolds numbers up to M = 2022 and Re = 2.6 ⋅ 10 5 , respectively. The magnetic field gives rise to a free shear layer at the prominent inner electrode. We identify several flow regimes characterized by the nature of the instabilities. Above a critical current I c = O ( 0 . 1 A ) , the steady flow is destabilized by a Kelvin-Helmholtz mechanism at the free shear layer. The instability consists of counterrotating vortices traveling with the mean flow. For low forcing, the vortices are restricted to the free shear layer. Their azimuthal wave number m grows with M and decreases with Re . At Re / M ≈ 25, the instability becomes container-filling and energetically significant. It enhances the radial momentum transport which manifests itself in a broadening of the free shear layer width δ S . We propose that this transition may be related to an unstable Hartmann layer. At R e / M 2 = O ( 1 ) , an abrupt change is observed in the mean azimuthal velocity 〈 u ϕ ¯ 〉 and the friction factor F , which we interpret as the transition between an inertialess and an inertial regime.

Description: The immiscible displacement of one viscous liquid by another in a capillary tube is experimentally and numerically analyzed in the low inertia regime with negligible buoyancy effects. The dimensionless numbers that govern the problem are the capillary number Ca and the viscosity ratio of the displaced to the displacing fluids N μ . In general, there are two output quantities of interest. One is associated to the relation between the front velocity, U b , and the mean velocity of the displaced fluid, U ̄ 2 . The other is the layer thickness of the displaced fluid that remains attached to the wall. We compute these quantities as mass fractions in order to make them able to be compared. In this connection, the efficiency mass fraction, m e , is defined as the complement of the mass fraction of the displaced fluid that leaves the tube while the displacing fluid crosses its length. The geometric mass fraction, m g , is defined as the fraction of the volume of the layer that remains attached to the wall. Because in gas–liquid displacement, these two quantities coincide, it is not uncommon in the literature to use m g as a measure of the displacement efficiency for liquid–liquid displacements. However, as is shown in the present paper, these two quantities have opposite tendencies when we increase the viscosity of the displacing fluid, making this distinction a crucial aspect of the problem. Results from a Galerkin finite element approach are also presented in order to make a comparison. Experimental and numerical results show that while the displacement efficiency decreases, the geometrical fraction increases when the viscosity ratio decreases. This fact leads to different decisions depending on the quantity to be optimized. The quantitative agreement between the numerical and experimental results was not completely achieved, especially for intermediate values of Ca . The reasons for that are still under investigation. The experiments conducted were able to achieve a wide range of Ca . We show that in the range 1 〈 N μ 〈 2, wavy shape instabilities appear at the interface and that increasing capillary number the amplitude of those waves increases. A deeper investigation on the operation window where these instabilities occur is in order.

Description: We employ a barotropic two-phase/two-fluid model to study the primary break-up of cavitating liquid jets emanating from a rectangular nozzle, which resembles a high aspect-ratio slot flow. All components (i.e., gas, liquid, and vapor) are represented by a homogeneous mixture approach. The cavitating fluid model is based on a thermodynamic-equilibrium assumption. Compressibility of all phases enables full resolution of collapse-induced pressure wave dynamics. The thermodynamic model is embedded into an implicit large-eddy simulation (LES) environment. The considered configuration follows the general setup of a reference experiment and is a generic reproduction of a scaled-up fuel injector or control valve as found in an automotive engine. Due to the experimental conditions, it operates, however, at significantly lower pressures. LES results are compared to the experimental reference for validation. Three different operating points are studied, which differ in terms of the development of cavitation regions and the jet break-up characteristics. Observed differences between experimental and numerical data in some of the investigated cases can be caused by uncertainties in meeting nominal parameters by the experiment. The investigation reveals that three main mechanisms promote primary jet break-up: collapse-induced turbulent fluctuations near the outlet, entrainment of free gas into the nozzle, and collapse events inside the jet near the liquid-gas interface.