Modeling the evolution of droplet size distribution in two-phase flows

A theoretical model is developed in the present study to simulate droplet motion and the evolution of droplet size distribution (DSD) in two-phase air/dispersed water spray flows. The model takes into account several processes which influence DSD and droplet trajectory: droplet collision and coalescence, evaporation and cooling, gravitational settling, and turbulent dispersion of dispersed phase. The DSDs determined by the model at different locations in a two-phase flow are evaluated by comparing them to experimental observations obtained in an icing wind tunnel. The satisfactory coincidence between simulation and experimental results proves that the model is reliable when modeling two-phase flows under icing conditions. The model is applied for two particular examples in which the modification of DSD is calculated in two-phase flows under conditions describing in-cloud icing and freezing drizzle.     

Numerical simulations of nozzle starting process

The starting process of two-dimensional nozzle flow is investigated both experimentally and numerically. Discussions are made on the comparison between experimental and numerical results. Performances of two numerical methods which are used in the present study of unsteady flow problem are also discussed and indications for future development of numerical tools to study nozzle problems are obtained. Received 16 June 1998 / Accepted 17 August 1998     

Numerical investigation of transient nozzle flow

Abstract. The starting process of two-dimensional and axisymmetric nozzle flows has been investigated numerically. Special attention has been paid to the early phase of the starting process and to the appearance of a strong secondary shock wave. For both cases, shock intensities and velocities are obtained and discussed. The flow evolution in the axisymmetric case is proved to be more complex and the transient starting process is slower than in the plane case. Finally, the effects of changing the nozzle angle and the incident shock wave Mach number on the transient flow are addressed. It is shown that a faster start-up can be induced either by decreasing the nozzle angle or increasing the Mach number of the incident shock wave. Received 16 November 2001 / Accepted 24 September 2002 / Published online 4 December 2002 Correspondence to:A.-S. Mouronval (e-mail: mouronv@coria.fr)     

A model for droplet entrainment in heated annular flow

The ability to accurately predict droplet entrainment in annular two-phase flow is required to effectively calculate the interfacial mass, momentum, and energy transfer, which characterizes nuclear reactor safety, system design, analysis, and performance. Most annular flow entrainment models in the open literature are formulated in terms of dimensionless groups, which do not directly account for interfacial instabilities. However, many researchers agree that there is a clear presence of interfacial instability phenomena having a direct impact on droplet entrainment. The present study proposes a model for droplet entrainment, based on the underlying physics of droplet entrainment from upward co-current annular film flow that is characteristic to light water reactor safety analysis. The model is developed based on a force balance and stability analysis that can be implemented into a transient three-field (continuous liquid, droplet, and vapor) two-phase heat transfer and fluid flow systems analysis computer code.     

Delayed detached eddy simulation of the end-effect regime and side-loads in an overexpanded nozzle flow

The separated flow in an overexpanded nozzle featuring a restricted shock separation is investigated numerically using delayed detached eddy simulation and compared with the experimental data of Nguyen et al. (Int J Flow Turbul Combust 71(1):161–181, 2003). First, the enormous cost of a Large Eddy Simulation for such a nozzle flow is assessed before being performed to motivate the practical need for using an hybrid RANS/LES method. The calculation is then used to investigate the “end-effect” regime which involves a strong global unsteadiness with very large amplitude fluctuations of about 15–20% of nozzle divergent length. The flow regime is characterized by high wall pressure fluctuations which are hopefully nearly axisymmetric. The main properties (rms levels, amplitude of displacement of the separation) of the motion are rather well reproduced by DDES compared to the experiment. However, a major difference lies in the frequency of the computed motion which is higher than in the experiment. This major discrepancy is currently not explained by the author. The properties of the side-loads are also briefly discussed.      

A filtered mass density function approach for modeling separated two-phase flows for LES II: Simulation of a droplet laden temporally developing mixing layer

A two-phase velocity-scalar filtered mass density function (TVSFMDF) formulation developed for large eddy simulation (LES) is applied to a temporally developing counter-current mixing layer seeded with water droplets. Closure models for both the dispersed and carrier phases are developed and implemented that are self-consistent with the original TVSFMDF mathematical formulation developed by Carrara and DesJardin. Several simulation cases are conducted to examine the sensitivity of both evaporating and non-evaporating droplet dispersion on various levels of subgrid scale (SGS) modeling approximation – highlighting the importance of variations in composition space in the phase-coupling terms.     

Dynamic behaviors of droplet impact and spreading: A universal relationship study of dimensionless wetting diameter and droplet height

A notable universal relationship has been proposed in the literature for the evolution of dimensionless droplet height and wetting diameter during the initial spreading stage of droplet impingement. In this study, this universal relationship was investigated by employing three sets of measurements. Sequential images were recorded, and the whole droplet profile ensembles were plotted to facilitate this study. These sets of experiments were designed by changing impact velocity, surface hydrophobicity, or solution property. The experimental results illustrate that the importance of parameters causing the data variation is in the order of surface hydrophobicity > initial impact velocity > surfactant on wetting diameter, and surface hydrophobicity ≈ initial impact velocity > surfactant on droplet height. No universal relationship was observed for dimensionless droplet height and wetting diameter.     

Heat and mass transfer of a fuel droplet evaporating in oscillatory flow

A numerical study of the heat and mass transfer from an evaporating fuel droplet in oscillatory flow was performed. The flow was assumed to be laminar and axisymmetric, and the droplet was assumed to maintain its spherical shape during its lifetime. Based on these assumptions, the conservation equations in a general curvilinear coordinate were solved numerically. The behaviors of droplet evaporation in the oscillatory flow were investigated by analyzing the effects of flow oscillation on the evaporation process of a n-heptane fuel droplet at high pressure.The response of the time history of the square of droplet diameter and space-averaged Nusselt numbers to the main flow oscillation were investigated in frequency band of 1–75 Hz with various oscillation amplitudes. Results showed that, depending on the frequency and amplitude of the oscillation, there are different modes of response of the evaporation process to the flow oscillation. One response mode is synchronous with the main flow oscillation, and thus the quasi-steady condition is attained. Another mode is asynchronous with the flow oscillation and is highly unsteady. As for the evaporation rate, however, in all conditions is more greatly enhanced in oscillatory flow than in quiescent air.To quantify the conditions of the transition from quasi-steady to unsteady, the response of the boundary layer around the droplet surface to the flow oscillation was investigated. The results led to including the oscillation Strouhal number as a criteria for the transition. The numerical results showed that at a low Strouhal number, a quasi-steady boundary layer is formed in response to the flow oscillation, whereas by increasing the oscillation Strouhal number, the phenomena become unsteady.     

Investigation on a coupled Navier–Stokes–Direct Simulation Monte Carlo method for the simulation of plume flowfield of a conical nozzle

To assess the plume effects of space thrusters, the accurate plume flowfield is indispensable. The plume flow of thrusters involves both continuum and rarefied flow regimes. Coupled Navier–Stokes–Direct Simulation Monte Carlo (NS–DSMC) method is a major approach to the simulation of continuum‐rarefied flows. An axisymmetric coupled NS–DSMC solver, possessing adaptive‐interface and two‐way coupling features, is investigated in this paper for the simulation of the nozzle and plume flows of thrusters. The state‐based coupling scheme is adopted, and the gradient local Knudsen number is used to indicate the breakdown of continuum solver. The nitrogen flows in a conical nozzle and its plume are chosen as the reference case to test the coupled solver. The threshold value of the continuum breakdown parameter is studied based on both theoretical kinetic velocity sampling and coupled numerical tests. Succeeding comparisons between coupled and full DSMC results demonstrate their conformities, meanwhile, the former saves 58.8% computational time. The pitot pressure evaluated from the coupled simulation result is compared with the experimental data proposed in literatures, revealing that the coupled method makes precise predictions on the experimental pitot pressure. Copyright © 2014 John Wiley & Sons, Ltd.     

A lattice Boltzmann model for simulation of compressible flows

This paper presents a new model of lattice Boltzmann method for full compressible flows. On the basis of multi‐speed model, an extra potential energy distribution function is introduced to recover the full compressible Navier–Stokes equations with a flexible specific‐heat ratio and Prandtl number. The Chapman–Enskog expansion of the kinetic equations is performed, and the two‐dimension‐seventeen‐velocity density equilibrium distribution functions are obtained. The governing equations are discretized using the third order monotone upwind scheme for scalar conservation laws finite volume scheme. The van Albada limiter is used to avoid spurious oscillations. In order to verify the accuracy of this double‐distribution‐function model, the Riemann problems, Couette flows, and flows around a NACA0012 airfoil are simulated. It is found that the proposed lattice Boltzmann model is suitable for compressible flows, even for strong shock wave problem, which has an extremely large pressure ratio, 100,000. Copyright © 2014 John Wiley & Sons, Ltd.     

Downstream pressure and elastic wall reflection of droplet flow in a T-junction microchannel

This paper discusses pressure variation on a wall during the process of liquid flow and droplet formation in a T-junction microchannel. Relevant pressure in the chan-nel, deformation of the elastic wall, and responses of the droplet generation are analyzed using a numerical method. The pressure difference between the continuous and dis-persed phases can indicate the droplet-generation period. The pressure along the channel of the droplet flow is affected by the position of droplets, droplet-generation period, and droplet escape from the outlet. The varying pressures along the channel cause a nonuniform deformation of the wall when they are elastic. The deformation is a vibration and has the same period as the droplet generation arising from the process of droplet formation.     

Modelling and simulation of sprays in laminar flames

In the present paper we model and numerically simulate steady, laminar, premixed spray flames. The gasphase is described in Eulerian form by the equations governing the conservation of overall mass, momentum, energy and species mass. The liquid phase is described in Lagrangian form by the overall continuity equation, which reduces to an equation for the droplet size, the equations of motion, the energy equation and a droplet density function transport equation. The latter is the so-called spray equation, which, at any position in the chemically reacting flowfield, describes the joint distribution of droplet size, droplet velocity and droplet temperature. Herein the spray equation is solved using a Monte Carlo method. Detailed models of the exchange of mass, momentum and energy between the gaseous and the liquid phase are taken into account. The results presented in this paper are for an octane-air flame, where small amounts of liquid octane in form of a liquid spray are added to a fresh, unburnt gaseous octane-air mixture.Presented at Euromech Colloquium 324: The Combustion of Drops, Sprays and Aerosols, 25th–27th July 1994, Marseilles, France.     

Simulation of the starting flow in a wedge–like nozzle

The starting process of the flow in a wedge-like expansion nozzle of a shock tunnel is simulated by an unsplit 2-D GRP scheme on an unstructured grid. The scheme is briefly outlined and results are presented and discussed in comparison to the experimental (shadowgraph) findings obtained by Amann. The simulated pattern of reflected and transmitted shock waves in the nozzle inlet region and inside the nozzle is found to agree well with the experimental data. Received 5 April 1996 / Accepted 16 June 1997     

Experimental investigation of forced flow regime transition in a dual bell nozzle by secondary fluidic injection

Experiments on an axisymmetric dual-bell nozzle were performed at EDITH nozzle test facility of CNRS in Orléans, France. The main purpose of the study was to explore the possibility of controlling the flow regime transition by a secondary fluidic injection in the dual bell nozzle. The main focus of the present paper is to investigate the impact of the secondary injection parameters on the flow regimes transition in such nozzles. Secondary injection has been found to effectively control the flow regime transition and consequently to increase the propulsive performance of the device. It has also been pointed out that even a very low injected secondary mass flow rate leads to the control of the transition and contributes to reducing the lateral loads which can exist, moreover, when transitions are operated without injection.     

Numerical study on the dynamics of droplet passing through a cylinder obstruction in confined microchannel flow

The droplet dynamics passing through a cylinder obstruction was investigated with direct numerical simulations with FE-FTM (Finite Element-Front Tracking Method). The effect of droplet size and capillary number (Ca) was studied for both Newtonian and viscoelastic fluids. In the case of Newtonian droplet immersed in Newtonian medium, the droplet breakup induced by the geometric hindrance depends on the droplet size. As Ca increases, the short droplets (1.3 times longer than the channel width) break up while passing through the obstruction. However, the breakup does not occur for longer droplets (1.8 times longer than the channel width). When the viscoelastic fluid characterized by the Oldroyd-B model is considered, the Newtonian droplet immersed in viscoelastic medium breaks up into two smaller droplets while passing through the cylinder obstruction with increasing De_m (Deborah number of the medium). We also show that the normal stress difference plays a key role on the droplet breakup and the droplet extension. The normal stress difference is enhanced in the negative wake region due to the droplet flow, which also promotes droplet extension in that region. This numerical study provides information not only on underlying physics of the droplet flows passing through a cylinder obstruction but also on the useful guidelines for microfluidic applications.     

BGK-equation simulation of the exhaust plume formed by a manoeuvre thruster in outer space

The general principle of utilizing the BGK equation to simulate a macroscopic gas flow is illustrated. Two typical examples, i.e., a low-speed axisymmetric submerged jet and the Prandtl-Meyer expansion to a vacuum, are presented for validating the feasibility and accuracy of the BGK-equation simulation in continuum and non-continuum flow regimes. This approach is then used to simulate the exhaust plume formed by a small manoeuvre thruster of an artificial satellite in the outer space. The plume impingement on a flat surface perpendicular to the nozzle axis is also simulated by the same method. In the latter case the impingement force acting on the flat surface is calculated. When the flow reaches to the steady state the calculated impingement force is reasonably compared with the theoretical value of the nozzle thrust. The project supported by Beijing Institute of Spacecraft Overall Design     

Numerical study on the effect of nozzle pressure and yarn delivery speed on the fiber motion in the nozzle of Murata vortex spinning

Murata vortex spinning (MVS) is a recently developed spinning technology which utilizes high speed swirling airflow to insert twist into the yarn. The motional characteristics of the flexible fibers in the airflow inside the MVS nozzle are of vital importance to the yarn formation mechanism and properties. The fiber motion in the MVS nozzle involves fluid-structure interaction (FSI) and contact problems. In this paper, a two-dimensional FSI model combined with the fiber-wall contact is introduced to simulate a single fiber moving in the airflow inside the MVS nozzle. The model is solved using a finite element code ADINA. Based on the model, the motional characteristics of the fiber are analyzed and the effect of two process parameters - the nozzle pressure and yarn delivery speed - on the fiber motion and, in turn, the yarn tenacity is discussed. The results indicate that the fiber firstly undergoes a false-twisting process. Subsequently, its trailing end splays out and whirls within the nozzle chamber for several turns to helically wrap and make the spun yarn. The results also show that the effect of the nozzle pressure on the tenacity of the produced MVS yarn is not obvious. The increased yarn delivery speed leads to the decreased MVS yarn tenacity. The numerical results show good agreement with the experimental results provided by other researchers.     

Experimental analysis of unsteady separated flows in a supersonic planar nozzle

The unsteady aspects of shock-induced-separation patterns have been investigated inside a Mach 2 planar nozzle. The mean location of the shock can vary by changing, relatively to the nozzle throat, the height of the second throat which is positioned downstream of the square test section. This study focuses on the wall pressure fluctuations spectra and the unsteady behaviour of the shock. Symmetric shock configurations appear both for the largest openings of the second throat, and for the smallest openings. For an intermediate opening the shock system exhibits asymmetrical configurations. A coating with roughnesses sticked on the throat part of the nozzle in order to modify the state of the incoming boundary layers (from smooth to rought turbulent statement) is a driver for the asymmetry. The fluctuating displacements of the shock patterns were analysed by using an ultra fast shadowgraph visualization technique. A spectral analysis of the unsteady wall pressure measurements has revealed low frequency phenomena governed by large structure dynamics in the separated flows. Communicated by K. Takayama PACS 02.60.Cb; 05.10.Ln; 47.11.+j; 47.15.Cb; 47.40.Nm     

Application of a droplet cluster to visualize microscale gas and liquid flows

The possibility of using microdroplets, which form a dissipative droplet-cluster structure, as tracers localized in the boundary layer of a gas adjoining a liquid-gas interface is experimentally demonstrated. Examples of the visualization of boundary layer flow fields generated by both processes in the gaseous phase and liquid convection are considered.     

High-throughput generation of uniform droplets from parallel microchannel droplet generators and the preparation of polystyrene microsphere material

To prepare uniform polystyrene particles with ten microns of diameter, a parallel scaling-up strategy for the capillary-assembled stepwise microchannel was developed, which created uniform droplets with high-throughput and formed a large amount of emulsion templates for the polymerization of styrene and cross-linker. The microchannel droplet generator was robust for the flow rate deviation of the continuous phase in the jetting flow, and droplet generation frequency up to 2.8 × 10⁴ Hz was achieved with only four parallel droplet generators, which were much more efficient than the parallelly scaled microfluidic devices working in dripping flow. 32–52 μm average diameter droplets with 4.5%–8.4% diameter variation coefficients were successfully prepared from the microchannel device fabricated by low-cost 3D-print method, and the droplets were subsequently turned to solid particles via a two-step polymerization in the platform. The polystyrene particles were further reduced to 16.9–23.5 μm with 5.0%–8.6% diameter variation coefficients due to the accompanying emulsion polymerization, and the working capacity of the platform reached hundred milligrams of particles per hour.