Homogeneous Two-phase Mixture Research Articles

Prandtl and Ohnesorge numbers dependent of ultrasonic horn energy in Newtonian liquid under batch and continuous flow

The level of knowledge on the non-thermal contribution of ultrasonic wave’s energy to perform physico-chemical phenomena is one of the bottlenecks for the commercialization purposes. Under constant nominal power of transducer (Pn), the input electrical power (Pin) is less and sensitive to the medium’s physical properties. This study attempts to assess the conversion of acoustic to thermal power experimentally and numerically using COMSOL Multiphysis@ for a 24 kHz horn-type sonicator through a medium without any sono-chemical effect. Single- and homogeneous two-phase Newtonian mixtures of sunflower oil and water (o/w) with a relatively wide range of density (914–998 kg/m3) and viscosity (0.5–63.5 mPa.s) were irradiated in a lab-scale vessel (1 L) under batch and continuous flow configuration. The direct influence of Pn (80–400 W) and o/w ratio (0–1) on temperature rise and subsequent thermo-physical properties of liquid and the indirect influence on Pin and thermal energy conversion (TEC) were investigated employing calorimetric method. A new engineering concept including a power factor correlation was proposed and validated for prediction of Pin as a function of liquid space velocity (ϑ), temperature, Prandtl (Pr) and Ohnesorge (Oh) dimensionless groups. The results showed that under constant temperature and Pn, increasing Pr and Oh increased Pin with a similar trend for both modes of operation. An increase in temperature directly led to a decrease in Pin with a power factor closed to “-1”. The Pin in continuous flow was higher compared to batch configuration at similar temperature, liquid properties, and Pn. This effect was more significant with increasing ϑ. An increase in ϑ at constant Pn led to a decrease in the inlet/outlet temperature difference in continuous flow and an increase in Pin. Increasing Pn resulted in higher TEC for both configurations; however, TEC was relatively lower in continuous flow than batch configuration indicating more efficient sonication in continuous flow.

An Analytical Two-Phase Flow Model for Prediction of Leakage in Wet Gas Labyrinth Seals and Pocket Damper Seals. Is Simplicity Still Desired?

Abstract Current and upcoming two-phase pump and compression systems in subsea production facilities must demonstrate long-term operation and continuous availability. Annular pressure seals, limiting secondary flow, also influence the dynamic stability of turbomachinery. Hence, it becomes paramount to quantify the leakage and dynamic force coefficients of annular seals operating with two-phase flow, a liquid in gas mixture or wet gas. Until now, a simple model for labyrinth seals (LSs) and the more modern pocket damper seals (PDSs) is not available, though these seal types find wide applications in subsea machinery. The paper develops a simple analytical model predicting the leakage and cavity pressures for LSs and PDSs operating with two-phase flow. The model adapts Neumann’s leakage equation for use with the physical properties of a homogeneous two-phase flow mixture. Predictions of leakage for a four-blade, eight-pocket, fully partitioned PDS operating under a low supply pressure (PS = 2.3 bar and 3.2 bar) and a low rotor speed equal to 5250 rpm (surface speed = 35 m/s) agree well with experimental results procured for both a pure gas and a wet gas conditions (2.2% in liquid volume). Predicted leakage and cavity pressures also agree with those found by a multimillion node computational fluid dynamics (CFD) model. For an eight-blade, sixteen-pocket PDS supplied with air at PS = 62.1 bar, discharge pressure Pa = 31.1 bar, and rotor speed of 15 krpm (surface speed = 91 m/s), the analytical model predicts leakage that is just 2% larger than a published CFD prediction. For the PDS supplied with an oil in gas mixture having gas volume fraction βS = 0.92–0.98, the simple model delivers leakage that is up to ∼6% lower than published CFD results. An analysis of the two-phase leakage predictions via a modified flow factor reveals a loss coefficient (cd) impervious to the range of supply and discharge pressures considered and growing in proportion to the liquid volume fraction (LVF). Throughout the life of an oil well that sees radical changes in gas and liquid composition as well as pressure conditions, the expedient model, quick and accurate to estimate leakage in wet gases seals, can be readily integrated into an engineering routine or practice.

Effects of the Cross-Sectional Area of a Volute on Suction Recirculation and Cavitation in a Centrifugal Pump

Abstract The effects of the cross-sectional area of a volute on suction recirculation and cavitation in a centrifugal pump were investigated. The pump performance and fluid flow were analyzed using both steady and unsteady three-dimensional Reynolds-averaged Navier–Stokes analyses. The shear stress transport (SST) model was adopted as a turbulence closure model, and a simplified Rayleigh–Plesset cavitation model and a homogeneous two-phase mixture model were used to simulate the cavitating flow inside the pump. A constant to determine the designed circumferential velocity of the volute was selected as the geometric parameter for a parametric study. The hydraulic efficiency, head coefficient, blockage in front of the impeller, and critical cavitation number for a head-drop of 3% were selected as the performance parameters to evaluate the hydraulic performance. The results show that unlike the blockage, the hydraulic and suction performances were affected significantly by the volute shape. Both steady and unsteady flow analyses showed that the onset and development of suction recirculation were relatively unaffected by the volute geometry and the best efficiency point of the pump.

Numerical and experimental investigation of shedding mechanisms from leading-edge cavitation

Leading-edge cavitation is responsible of the generation of transient cavities, usually made of clouds of bubbles. These transient cavities travel downstream to high-pressure regions and collapse violently, leading to noise and vibration as well as erosion. In the present paper, the focus is on the mechanisms generating transient cavities to better understand the starting point of the erosion process. The case studied is the cavitating flow over a NACA0009 hydrofoil which is investigated using experiments and numerical simulation. In the experimental part, which is conducted in EPFL high-speed cavitation tunnel, the shedding behavior is studied using high-speed visualization (HSV). In the numerical part, the cavitating flow is simulated using an incompressible solver coupled with isothermal homogeneous two-phase mixture cavitation model and Implicit Large Eddy Simulation (ILES) turbulence modelling. Owing to high speed visualization and numerical simulations, we identified two shedding mechanisms of transient cavities: (i) A primary shedding, characterized by a periodic generation of large cloud cavities and (ii) a secondary shedding of small-scale horse-shoe vortices, which are revealed for the first time. These small-scale structures, which are believed to play a major role in the erosion process, result from a complex interaction between the sheet cavity, the cloud cavity and re-entrant jets of different types. Furthermore, the detailed comparison between HSV and simulation confirms that the current numerical approach is capable of capturing the two types of shedding mechanisms very well.

Evaluation of Rotor–Stator Interface Models for the Prediction of the Hydraulic and Suction Performance of a Centrifugal Pump

The effects of a rotor–stator interface model on the hydraulic and suction performance of a single-stage centrifugal pump have been evaluated. A three-dimensional Reynolds-averaged Navier–Stokes (RANS) analysis was performed using the shear-stress transport turbulence model. The cavitating flow was simulated using a homogeneous two-phase mixture model and a simplified Rayleigh–Plesset cavitation model. Three performance parameters were selected to compare different cases: the hydraulic efficiency, head coefficient, and critical cavitation number for a head-drop of 3%. Frozen-rotor and stage models were evaluated for the rotor–stator interface. The evaluation was done using three different computational domains: one with a single passage of the impeller with a vaneless diffuser, one with a single passage of the impeller with the whole shape of volute casing, and another with the whole passage of the impeller with the whole shape of volute casing. Two different volute shapes were also tested. The results show that it is desirable to use the whole domain of the impeller and volute with the frozen-rotor model for accurate prediction of the suction performance. The stage model is not recommended for the prediction of the suction performance of the centrifugal pump with the volute in severe off-design conditions.

Numerical investigation on the collapse of a bubble cluster near a solid wall.

This paper studies numerically the collapse of a cluster of cavitation bubbles (as a primitive model for a bubble cloud) near a solid wall. The homogeneous two-phase mixture model is used, with the liquid-vapor interface resolved by volume of fluid method. The liquid is treated as compressible, allowing the propagation of pressure waves at the speeds determined by a state equation. This cluster consists of 27 identical bubbles, evenly distributed in a cubic region, with various bubble-wall and bubble-bubble distances considered. Our simulations suggest that the bubble-wall distance plays a more significant role. The maximum impulsive pressure of 41MPa is achieved when the cluster is very close to the wall. The inward progress of collapse is observed by examining the evolutions of bubble shapes and flow fields, with two distinctly different sequences of collapse identified between the small and large bubble-wall distances. At a large bubble distance, the centermost bubble is the last to collapse, while at a small bubble distance, it is the central bubble nearest to the wall which collapses lastly. This difference can also explain the more intensive impulsive pressure for the smaller bubble-wall distances. The proposed numerical approach is of special interest because it can resolve the details of bubble-bubble and bubble-wall interactions, which are significant to the study of the collapse of a cavitation cloud, and its potential damage to hydraulic systems.

Experimental and Theoretical Research into Dynamic Loading of Tungsten Porous Alloy with Reinforcing Agent

The paper studies the behavior of ceramic porous tungsten alloy with reinforcing agents under the shock-wave loading conditions. Penetrating capacity of tungsten kinetic energy projectiles is calculated and experimentally investigated during their high-speed impacts on steel plates. It is shown that the increased penetration depth of tungsten projectiles exceeds that of the prototype with relevant weight and size, made of tungsten-nickel-iron cast alloy. A mathematical model is developed together with the design technique of the behavior of tungstennickel-iron-cobalt metal foams alloyed with boron carbide, tungsten titanium carbide and tungsten carbide during the high-speed impact interaction. The composite ceramic material is described here as a porous medium. The matrix of this medium is a homogeneous two-phase mixture of the tungsten-nickel-iron-cobalt system and reinforcing agents added in the required proportions.

Numerical investigation of the impact of computational resolution on shedding cavity structures

In this paper, three-dimensional cavitation is analysed, and in particular how its dynamics is influenced by computational resolution. Cavitation-vorticity interactions are investigated in several spatial resolutions to address impact of the mesh resolution on cavitating vortical flow predictions. Three-dimensional, fully turbulent, cavitating flow around the Delft Twist11 foil is simulated and investigated numerically with particular focus on cavitation structures, shedding dynamics, and vorticity distribution. Implicit Large Eddy Simulation is employed along with the iso-thermal homogeneous two-phase mixture model to conduct the cavitation simulation in OpenFOAM. The paper clarifies the importance of capturing small scales of the flow, and their impact on the cavitation shedding behaviour, especially for flows where the shed cavity is affected significantly by flow vortices. It is shown that the mesh requirement for vortical cavitating flows is governed by the minimum spatial resolution needed to transport vorticity in the flow rather than the resolution needed to simulate the phase change. Better predictions of the mechanisms driving the shed cavity, and its collapse location, will provide a better control over nuisance behaviour in cavitating flows, which is a critical key for design improvements.

A Simulation of the Liquid Shock and Cavitation Based on a Multi-Equation Model

In this paper, an unsteady preconditioning formulation for multi-phase flows with arbitrary equation of state based on the approximated Riemann solver is developed for multi-phase flows at all speed. This paper considers a homogeneous two-phase multi-equation mixture model with the assumption of kinematics and thermodynamics equilibriums. The thermodynamics behaviors of liquid phase, vapor phase and their phase transitional process are described by a temperature-dependent hybrid equation of state. Benchmark test cases, including one-dimensional (1D) condensation shock in the cavitated nozzle and two-dimensional (2D) cavitated blunt body problem, demonstrate accurate capturing of interfaces, shock waves and cavitation zones.

Study about the influence of cavitation on the dynamic characteristics for the sliding bearing

Sliding bearings are employed to support the rotor system and limit the vibration amplitude. In high speed rotor system, cavitation often occurs in the oil film and affects the dynamic characteristics of the sliding bearing greatly. In this paper, numerical method is adopted to simulate the cavitation in the oil film with homogeneous two-phase mixture flow using Singhal-et-al cavitation model in the commercial code FLUENT-solver. Cases without cavitation model were also calculated at the same time. Many computations with different frequency ratios were conducted. Then the rotor dynamic characteristics of the sliding bearing were retrieved. The results show that the cavitation has great influences on the pressure distribution in the oil film. As the rotational speed or whirling speed of the journal increases, the cavitation will become prominent. The dynamic coefficients of the bearing such as stiffness and damping with cavitation model considered are quite different from that without cavitation. So it is worth to pay attention to and do further study about the cavitation in the sliding bearing in the high speed rotor system.

Phase equilibrium and mechanisms of crystallization in liquid–liquid phase separating system

The influence of liquid–liquid phase separation (LLPS) in a crystallizing system is examined, and the liquid–liquid tie lines are determined in the ternary system of butyl paraben, water and ethanol. Crystallization by evaporation in droplets (solution of butyl paraben in ethanol and water mixtures) of homogeneous solution and two-phase liquid mixtures on plates of different materials: glass, plastic, steel, and tin were investigated by microscopy. Different crystallization and liquid–liquid phase separation behaviour are observed depending on initial droplet composition and the surface material. This work reveals that crystallization in the LLPS solution of butyl paraben in ethanol–water mixtures starts in the butyl paraben rich phase as can be explained by a higher butyl paraben concentration, and a lower solid–liquid interfacial energy.

Experimental Investigations of Pressure Wave Propagation by the Inception of a Laser-Induced Bubble in Bubbly Flows

The pressure wave propagation caused by the breakdown of a focused laser beam in a bubbly channel flow is investigated experimentally. Measurements were conducted in the downstream of a convergent-divergent channel with rectangular cross-section; microbubbles are generated downstream the constriction of the channel. Optical observation and pressure measurement were conducted using a high-speed video camera and a hydrophone, respectively. There are two major pressure waves: one which propagates with the speed of sound in water known as a precursor wave, another which propagates more slowly. The slower pressure wave is associated with the volume elasticity of gas-liquid mixture which depends on the local void fraction and bubble oscillations. The propagation speed of the slower wave is calculated from the image processing, and decreases down to 60 m/s. The influence of wave length, bubble size, and surface tension on the void fraction evaluated from the propagation speed of the slower wave is discussed. As a result, the void fraction is quantitatively estimated from luminance value and the propagation speed of slower wave in an isothermal homogeneous two-phase mixture. It was shown that with increasing the void fraction, the amplitude of the precursor wave decreases drastically while that of the slower wave decreases weakly.

Damping and added mass coefficients for a squeeze film damper using the full 3-D Navier–Stokes equation

Direct and cross-coupled damping coefficients are developed for the 2π-film, π-film (Gumbel cavitation condition) and homogeneous two-phase mixture films in a squeeze film damper. The numerical simulation uses the CFD-ACE+ commercial software, which employs a finite volume method for the discretization of the Navier–Stokes equations (NSE). In order to determine the dynamic coefficients, the NSE is combined with a finite perturbation method applied to the ‘equivalent journal’ of the damper. It was found that for the 2π-film and the Gumbel conditions, the damping coefficients exhibit linear characteristics, while the homogeneous cavitation model yields nonlinear coefficients. Using the CFD-ACE+, the inertia/added mass coefficients are derived for the limiting cases of the short and long dampers, respectively. The first set of forces is calculated by setting the fluid density to its actual value. The second set of forces is calculated when the density of the fluid is set close to zero (1E-10 kg/m 3), thus practically eliminating the effects of the inertia terms. Subtracting the two sets of forces from each other, allows the determination of the inertia component contribution and the corresponding inertia coefficients. By varying the density, dynamic viscosity and whirling speed, it was found that the inertia coefficients follow a single curve represented by a function dependent on the modified Reynolds number, Re*. The inertia coefficients presented in this study are compared with the ones reported by other researchers that used the modified Reynolds equation. Some differences were found between the NSE based results and the Reynolds equation based outcomes. This is attributed to the three-dimensional effects introduced by the totality of the terms comprised in the full NSE.

Comparative Studies On Bovine And Rat Pulmonary Surfactants Using AFM

Recent studies employing a variety of microscopic techniques have revealed that phospholipid (PL) phase separations and transitions may play important roles in determining the biophysical properties of pulmonary surfactant. Most of these microscopic studies used model systems which were composed of simple mixtures of PL with or without hydrophobic surfactant proteins and cholesterol. The present work compared modified natural (lipid extract) bovine and rat surfactants using atomic force microscopy (AFM). AFM revealed PL phase separation upon compression of both surfactant monolayers, and a monolayer-to-multilayer transition at surface pressure 40-50 mN/m. Similar to bovine surfactant, the tilted-condensed (TC) phase in rat surfactant consisted of domains both on micrometer and nanometer scales. Upon film compression, the microdomains were dissociated into nanodomains, thus forming a more homogeneous two-phase mixture. Differences between rat and bovine surfactants were: (1) more TC domains were formed at lower surface pressures in rat than in bovine surfactant; and (2) an interesting domain-in-domain structure was exclusively observed in rat surfactant. These structural differences were attributed to the higher cholesterol content of rat surfactant (∼ 10 vs ∼2.5 wt%). To further investigate the effects of cholesterol on the structure of surfactant films, we have studied cholesterol-depleted bovine surfactant (∼ 0%) prepared by repetitive acetone extraction. Removal of cholesterol from bovine surfactant induced significant variations in film structure. More importantly, the film structure can be effectively restored by recombining cholesterol with the cholesterol-depleted bovine surfactant. Recombinant bovine surfactant with 10% cholesterol showed domain-in-domain structures similar to those found with rat surfactant. These interspecies studies of the micro- and nano- structures of natural pulmonary surfactants add insight into the biophysical interpretation of phospholipid phase transition and separation, in particular the role of cholesterol.

Analysis of pulsating spray flames propagating in lean two-phase mixtures with unity Lewis number

Pulsating (or oscillatory) spray flames have recently been observed in experiments on two-phase combustion. Numerical studies have pointed out that such front oscillations can be obtained even with very simple models of homogeneous two-phase mixtures, including elementary vaporization schemes. The paper presents an analytical approach within the simple framework of the thermal-diffusive model, which is complemented by a vaporization rate independent of gas temperature, as soon as the latter reaches a certain thermal threshold ( θ v in reduced form). The study involves the Damköhler number (Da), the ratio of chemical reaction rate to vaporization rate, and the Zeldovich number (Ze) as essential parameters. We use the standard asymptotic method based on matched expansions in terms of 1 / Ze . Linear analysis of two-phase flame stability is performed by studying, in the absence of differential diffusive effects (unity Lewis number), the linear growth rate of 2-D perturbations added to steady plane solutions and characterized by wavenumber k in the direction transverse to spreading. A domain of existence is found for the pulsating regime. It corresponds to mixture characteristics often met in air–fuel two-phase systems: low boiling temperature ( θ v ≪ 1 ) , reaction rate not higher than vaporization rate ( Da < 1 , i.e., small droplets), and activation temperature assumed to be high compared with flame temperature ( Ze ⩾ 10 ) . Satisfactory comparison with numerical simulations confirms the validity of the analytical approach; in particular, positive growth rates have been found for planar perturbations ( k = 0 ) and for wrinkled fronts ( k ≠ 0 ) . Finally, comparison between predicted frequencies and experimental measurements is discussed.

On the Application of the Method of Landau and Lifshitz to Sonic Velocities in Homogeneous Two-Phase Mixtures

A theoretical sonic velocity correlation for homogeneous two-phase mixtures under thermal equilibrium is proposed. By application of the method of Landau and Lifshitz, a dimensionless correlating parameter ω is found whereby different fluid properties and vapor mass fraction (quality) can be adequately accounted for by the simple correlation.

Concentration/density shocks in an inertially-coupled two-phase dispersion

We analyze a plane shock wave propagating into a homogeneous two-phase mixture in which the gas density is small compared with the liquid density. Inertial effects are assumed to govern the mechanics and “added mass” effects are represented by the methods of Geurst and Wallis. Expressions are obtained for the shock speed, as well as void fraction, pressure and density jumps across small-amplitude shocks. A method is presented for predicting the behavior of large-amplitude shocks; their characteristics and conditions for their existence are discussed.

On Rayleigh and Fanno flows of homogeneous equilibrium two-phase fluids

This article introduces a model fluid that has ideal liquid and perfect gas phases and a homogeneous two-phase mixture region. The thermodynamic-state properties of the model compare favorably with those of three common fluids. A gas dynamic study of Rayleigh and Fanno flows is discussed using one approach similar to the classical work of Shercliff and another based on the proposed model. The role of the isentropic and Newtonian and other new “sound speeds” are discussed. The relevance of these sound speeds in relation to critical speeds of the fluid is examined. It is concluded that in the two-phase region, a Rayleigh flow exhibits a maximum enthalpy at a point where the flow velocity reaches the isenthalpic speed of sound. This third speed of sound a h is defined by the relation a h 2 = ( δp/ δπ) h.

Density and Viscosity Models for Two-Phase Homogeneous Hydrodynamic Damper Fluids

Theoretical cavitation models previously adopted in analyzing dynamically loaded hydrodynamic bearings or squeeze-film dampers are inconsistent with experimental observations in that bubbles, once formed, in many instances do not completely redissolve upon the reappearance of high pressure. A more representative approach could be to model the lubricant as a homogeneous two-phase gas-liquid mixture. The density and viscosity of such a homogeneous mixture are developed as functions of the pressure and the known mole fraction of the noncondensable gas to the liquid at supply entry. Omitting the possible effects of surface tension, it is shown that if the vapor pressure of the lubricant is of the order of 10−3 atm or less, it has only a minimal effect on the density of the mixture and may be ignored. On the other hand, solubility effects may be significant, though it is unknown to what extent gases, once drawn out of solution, will redissolve in the short time of the cycle period of the dynamic loading. Hence...

Investigation of hydrodynamics in appartus with aerating devices

One way of intensifying processes in multiphase systems is the use of self-priming aerating devices in reactors. The investigation of processes of hydrodynamics in the liquid phase, in particular the regularities of the change of power requirements for the mixing of gas-liquid systems, has not been treated sufficiently. The present article submits the results of the calculation of the expended power of an aerating device of optimum design. Investigations have shown that the power expended on the hydraulic resistances with developed turbulent flow of a homogeneous two-phase mixture is close to the power expended with flow of such a pure liquid whose density is equal to the mean density of the mixture. Since with intense mixing a gas is distributed evenly throughout the entire volume and since the size of the bubbles is small compared with the dimensions of the apparatus and the aerator mixer, the gas-liquid system in this case may be regarded as homogeneous. Being lower than the density of the liquid, the density of the gas is neglected. Equations are derived for obtaining the power required by an aerating device with different geometric dimensions.