Classification of instabilities in parallel two-phase flow

There is extensive literature on the stability of parallel two-phase flow, both in the context of liquid-liquid as well as gas-liquid flow. Aimed at making this literature more transparent, this paper presents a classification,scheme for the various instabilities arising in parallel two-phase flow. To achieve such a classification, the equation governing the rate of change of the linetic energy of the disturbances is evaluated for relevant values of the physical parameters. This shows the existence of five different ways of energy transfer from the primary to the disturbed flow, which have their origin in density stratification, velocity profile curvature, viscosity stratification or shear effects. Each class is discussed on the basis of references covering the developments over the last 35 years

Instability and dripping of electrified liquid films flowing down inverted substrates

We consider the gravity-driven flow of a perfect dielectric, viscous, thin liquid film, wetting a flat substrate inclined at a nonzero angle to the horizontal. The dynamics of the thin film is influenced by an electric field which is set up parallel to the substrate surface—this nonlocal physical mechanism has a linearly stabilizing effect on the interfacial dynamics. Our particular interest is in fluid films that are hanging from the underside of the substrate; these films may drip depending on physical parameters, and we investigate whether a sufficiently strong electric field can suppress such nonlinear phenomena. For a non-electrified flow, it was observed by Brun et al. [Phys. Fluids 27, 084107 (2015)] that the thresholds of linear absolute instability and dripping are reasonably close. In the present study, we incorporate an electric field and analyze the absolute and convective instabilities of a hierarchy of reduced-order models to predict the dripping limit in parameter space. The spatial stability results for the reduced-order models are verified by performing an impulse-response analysis with direct numerical simulations (DNS) of the Navier–Stokes equations coupled to the appropriate electrical equations. Guided by the results of the linear theory, we perform DNS on extended domains with inflow and outflow conditions (mimicking an experimental setup) to investigate the dripping limit for both non-electrified and electrified liquid films. For the latter, we find that the absolute instability threshold provides an order-of-magnitude estimate for the electric-field strength required to suppress dripping; the linear theory may thus be used to determine the feasibility of dripping suppression given a set of geometrical, fluid, and electrical parameters

A Local Condensation Analysis Representing Two-phase Annular Flow in Condenser/radiator Capillary Tubes

NASA's effort for the thermal environmental control of the Space Station Freedom is directed towards the design, analysis, and development of an Active Thermal Control System (ATCS). A two phase, flow through condenser/radiator concept was baselined, as a part of the ATCS, for the radiation of space station thermal load into space. The proposed condenser rejects heat through direct condensation of ATCS working fluid (ammonia) in the small diameter radiator tubes. Analysis of the condensation process and design of condenser tubes are based on the available two phase flow models for the prediction of flow regimes, heat transfer, and pressure drops. The prediction formulas use the existing empirical relationships of friction factor at gas-liquid interface. An attempt is made to study the stability of interfacial waves in two phase annular flow. The formulation is presented of a stability problem in cylindrical coordinates. The contribution of fluid viscosity, surface tension, and transverse radius of curvature to the interfacial surface is included. A solution is obtained for Kelvin-Helmholtz instability problem which can be used to determine the critical and most dangerous wavelengths for interfacial waves

Self-similarity of solitary waves on inertia-dominated falling liquid films

We propose consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers Re=20–120 and surface tension coefficients σ=0.0512–0.072Nm−1 on substrates with inclination angles β=19◦ − 90◦. Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e., height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by nonlinear effects and only driven by inertia, with surface tension and gravity having a negligible influence

Smoothed Dissipative Particle Dynamics model for mesoscopic multiphase flows in the presence of thermal fluctuations

Thermal fluctuations cause perturbations of fluid-fluid interfaces and highly nonlinear hydrodynamics in multiphase flows. In this work, we develop a novel multiphase smoothed dissipative particle dynamics model. This model accounts for both bulk hydrodynamics and interfacial fluctuations. Interfacial surface tension is modeled by imposing a pairwise force between SDPD particles. We show that the relationship between the model parameters and surface tension, previously derived under the assumption of zero thermal fluctuation, is accurate for fluid systems at low temperature but overestimates the surface tension for intermediate and large thermal fluctuations. To analyze the effect of thermal fluctuations on surface tension, we construct a coarse-grained Euler lattice model based on the mean field theory and derive a semi-analytical formula to directly relate the surface tension to model parameters for a wide range of temperatures and model resolutions. We demonstrate that the present method correctly models the dynamic processes, such as bubble coalescence and capillary spectra across the interface

Solitary waves on falling liquid films in the inertia-dominated regime

We offer new insights and results on the hydrodynamics of solitary waves on inertia-dominated falling liquid films using a combination of experimental measurements, direct numerical simulations (DNS) and low-dimensional (LD) modelling. The DNS are shown to be in very good agreement with experimental measurements in terms of the main wave characteristics and velocity profiles over the entire range of investigated Reynolds numbers. And, surprisingly, the LD model is found to predict accurately the film height even for inertia-dominated films with high Reynolds numbers. Based on a detailed analysis of the flow field within the liquid film, the hydrodynamic mechanism responsible for a constant, or even reducing, maximum film height when the Reynolds number increases above a critical value is identified, and reasons why no flow reversal is observed underneath the wave trough above a critical Reynolds number are proposed. The saturation of the maximum film height is shown to be linked to a reduced effective inertia acting on the solitary waves as a result of flow recirculation in the main wave hump and in the moving frame of reference. Nevertheless, the velocity profile at the crest of the solitary waves remains parabolic and self-similar even after the onset of flow recirculation. The upper limit of the Reynolds number with respect to flow reversal is primarily the result of steeper solitary waves at high Reynolds numbers, which leads to larger streamwise pressure gradients that counter flow reversal. Our results should be of interest in the optimisation of the heat and mass transport characteristics of falling liquid films and can also serve as a benchmark for future model development