Session F21: Flow Instability: Multiphase Flow

LInear stability analysis of granular Taylor-Couette flow

The linear stability analysis of the circular Couette flow of granular materials is carried out in the rapid shear regime. The kinetic-theory based continuum models, with a separate balance equation for granular/fluctuation energy, is employed, and the underlying rheological model is likely to be valid for a range of density from the dilute to dense regime. The steady base state equations for the case of rotating inner cylinder and stationary outer cylinder are solved numerically; it is found that the inelastic dissipation can make the flow radially inhomogeneous even in the narrow-gap limit. The linear stability equations are solved using spectral collocation method. The onset of Taylor-like vortices and the effects of inelastic dissipation and compressibility on them are analysed.   

Modulation of flow transition in microbubble Taylor-Couette flow

To examine the interaction mechanism of bubbles and flows that result in drag reduction, the effect of the presence of microbubbles on a flow state is experimentally investigated in a Taylor-Couette flow with azimuthal waves. The average diameter of the bubbles is 60 $\mu$m, which is smaller than the maximum length scale of vortices in the flow, and the maximum void fraction is $1.2 \times 10^{-4}$ at the maximum case. The modifications of the fluid properties, bulk density and effective viscosity are expected to have a small effect on modifying flow states. The power of the basic wave propagating in the azimuthal direction is enhanced; its modulation, however, is decreased by adding microbubbles in the flow regime corresponding to modulated Taylor vortex flow. Moreover, the gradient of the azimuthal velocity near the walls, source of the wall shear stress, decreases by 10\%. The modified velocity distribution by adding microbubbles is comparable to that obtained with a 20\% lower Reynolds number. Microbubbles in the wavy Taylor vortices are visualized and exhibit a preferential distribution and motion at the crests and troughs of the waviness. We discussed the effect of the extra buoyant force due to the inhomogeneously distributed microbubbles in wavy structures on the flow.   

Shock tube Multiphase Experiments

Shock driven multiphase instabilities (SDMI) are unique physical phenomena that have far-reaching practical applications in engineering and science. The instability is present in high energy explosions, scramjet combustors, and supernovae events. The SDMI arises when a multiphase interface is impulsively accelerated by the passage of a shockwave. It is similar in development to the Richtmyer-Meshkov (RM) instability however, particle-to-gas coupling is the driving mechanism of the SDMI. As particle effects such as lag and phase change become more prominent, the SDMI's development begins to significantly deviate from the RM instability. We have developed an experiment for studying the SDMI in our shock tube facility. In our experiments, a multiphase interface is created using a laminar jet and flowed into the shock tube where it is accelerated by the passage of a planar shockwave. The interface development is captured using CCD cameras synchronized with planar laser illumination. This talk will give an overview of new experiments conducted to examine the development of a shocked cylindrical multiphase interface. The effects of Atwood number, particle size, and a second acceleration (reshock) of the interface will be discussed.   

Effect of the boundary layer thickness on the hydrodynamic instabilities of coaxial atomization under harmonic flow rate and swirl ratio fluctuations

Break-up of a liquid jet by a high speed coaxial gas jet is a frequently-used configuration to generate a high quality spray. Despite its extended use in engineering and natural processes, the instabilities that control the liquid droplet size and their spatio-temporal distribution in the spray are not completely understood. We present an experimental measurements of the near field in a canonical coaxial gas-liquid atomizer. The liquid Reynolds number is constant at 10$^{\mathrm{3}}$, while the gas jet Reynolds number is varied from 10$^{\mathrm{4}}$-10$^{\mathrm{6}}$. The liquid injection rate and the swirl ratio are harmonically modulated to understand the effect of unsteadiness on the interfacial instability that triggers primary break-up. The gas velocity is measured using a combination of hot-wire anemometry and 3D PIV, resolving the gas boundary layer and the three-dimensionality of the flow, particularly in the cases with swirl. The development of the hydrodynamic instabilities on the liquid-gas interface is quantified using high speed visualizations at the exit of the nozzle and related to the frequency and growth rates predicted by stability analysis of this boundary layer flow. The resulting droplet size distribution is measured at the end of the break-up process via Particle Phase Doppler Anemometry and compared to stability analysis predictions statistics.   

Ultra-high speed visualization of the flashing instability under vacuum conditions

We investigated experimentally the flashing instability of a jet of perfluoro-n-hexane (PFnH) released into a low-pressure environment. Using a ultra-high speed camera we observed the jet fragmentation occurring close to the nozzle. Using a fixed total driving pressure, we decreased systematically the vacuum pressure, investigating the transition from a laminar jet to a fully flashing jet. Our high temporal resolution allowed to visualize the detailed dynamics of external flash-boiling for the first time. We identified different mechanisms of jet break-up. At chamber pressures lower than the vapor pressure the laminar jet evolves to a meandering stream. In this stage, bubbles start to nucleate and violently expand upstream the nozzle. At lower vacuum pressures the initially cylindrical jet elongates, forming a liquid sheet that breaks in branches and later in drops. At very low pressures both mechanisms are responsible for the jet breaking. We calculated the size distribution of the ejected droplets, their individual trajectories, velocities as well as the spray angle as a function of the dimensionless vacuum pressure.   

Direct numerical simulation of three-dimensional liquid jet breakup

We carry out direct numerical simulations of liquid jet dynamics and breakup using a high-performance code, {\it Blue}, which uses a hybrid technique based on the front-tracking and the level-set method; it defines the interface position through a marker function and a local triangular Lagrangian mesh. Liquid jet breakup is an example of interfacial complexity associated with multiphase flows because of the formation of ligaments and their pinch off to give rise to droplet formation. We consider the atomisation of a liquid jet released into a stagnant gas phase where the velocity is stimulated sinusoidally to promote the growth of Kelvin-Helmholtz instabilities, thus forming a flow system characterized by complex interfaces. The spread of cylindrical liquid jet into a coflowing external stream is also considered (essentially, a replication of the Marmottant and Villermaux experimental work).   

Direct numerical simulation of annular flows

Vertical counter-current two-phase flows are investigated using direct numerical simulations. The computations are carried out using Blue, a front-tracking-based CFD solver. Preliminary results show good qualitative agreement with experimental observations in terms of interfacial phenomena; these include three-dimensional, large-amplitude wave formation, the development of long ligaments, and droplet entrainment. The flooding phenomena in these counter current systems are closely investigated. The onset of flooding in our simulations is compared to existing empirical correlations such as Kutateladze-type and Wallis-type. The effect of varying tube diameter and fluid properties on the flooding phenomena is also investigated in this work.   

Direct numerical simulation of annular flows with surfactants

Vertical counter-current air-water surfactant-laden flows are investigated using direct numerical simulations. The computations are carried out using Blue, a front-tracking-based CFD solver. The presence of surfactants in the flow results in Marangoni stresses. At low gas and liquid flow rates, the Marangoni effect is found to be dominant over shear stresses, resulting in the suppression of wave perturbations and wave amplitudes. Marangoni stresses are found to dominate at low gas and liquid flow rates, resulting in lack of wave development and subsequent droplet detachment thus hindering flooding. It is also found that shear stresses dominate the flow at higher gas/liquid flow rates, ``trapping” surfactant in wave crests thus favouring droplet detachment and increasing the extent of flooding. In addition to the above, we also report on the results of a parametric study to observe the effect of varying surfactant surface concentration, maximum packing concentration, bulk and interface diffusivity, and adsorption and desorption rate on the interfacial dynamics.   

Flow characterization and stability analysis in rectangular lid-driven cavities with particle suspensions

Like the canonical, two-dimensional, square lid-driven cavity problem that serves as its cornerstone, the two-dimensional, rectangular lid-driven cavity is a well-studied extension that also generates dynamically stable, well-defined, flow structures within the laminar flow regimes. Mathematical time-dependent perturbations to these flow structures have been shown to generate a region of metastability as the system transitions towards a turbulent flow regime. By replacing the mathematically-generated, time-dependent perturbations of previous investigations into this phenomena with the particle-fluid and particle-particle interactions present within a multiphase flow, a unique perspective on the stability of these flow structures within the laminar flow regimes of the two-dimensional lid-driven cavity can be obtained. Therefore, the objective of this study is to investigate the effect varying area fractions and relative densities of suspended granular particles have on traditionally laminar and stable flows found at Reynolds numbers of 100, 400, and 1000 of a rectangular lid-driven cavity with an aspect ratio of 1.5. These studies and analyses will aid in the determination how granular materials can be used to enhance desirable flow characteristics of fluid behaviors.   

Morphological instabilities of rapidly solidified binary alloys under weak flow

Additive manufacturing, or three-dimensional printing, offers promising advantages over existing manufacturing techniques. However, it is still subject to a range of undesirable effects. One of these involves the onset of flow resulting from sharp thermal gradients within the laser melt pool, affecting the morphological stability of the solidified alloys. We examine the linear stability of the interface of a rapidly solidifying binary alloy under weak boundary-layer flow by performing an asymptotic analysis for a singular perturbation problem that arises as a result of departures from the equilibrium phase diagram. Under no flow, the problem involves cellular and pulsatile instabilities, stabilised by surface tension and attachment kinetics. We find that travelling waves appear as a result of flow and we map out the effect of flow on two absolute stability boundaries as well as on the cells and solute bands that have been observed in experiments under no flow.