Similarity solutions for the evolution of polydisperse droplets in vortex flows

A new mathematical analysis of the dynamics of evaporating sprays in the vicinity of a vortex flow field is presented. The governing equations for a polydisperse spray evaporating in an unsteady viscous vortex flow are formulated using the sectional approach. First, new similarity solutions are found for the dynamics of the spray in a mono-sectional framework. It is shown that similarity for the droplets’ drag term exists, and an explicit model for the drag is found using perturbation theory. Numerical simulations are conducted to validate the main assumptions of the analytic approach adopted in this study. An extension of the mono-sectional solution of the spray equations to a polydisperse spray solution is then derived and the dynamics of polydisperse spray in an Oseen type vortex are presented. It is shown that for a given radial location, the droplets in each section reach a maximal radial velocity due to the effect of vorticity. A simple model is derived for the prediction of this maximal radial velocity of the droplets using perturbation theory, which agrees very well with the full similarity solution. The present study shows that spray dynamics is highly affected by the droplets’ size, but also by the spray initial size distribution, even when the same Sauter mean diameter is considered. This may have far reaching implications, especially in spray combustion applications.     

Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques

A new approach for simultaneous planar measurement of droplet velocity and size with gas phase velocities is reported, which combines the out-of-focus imaging technique ‘Interferometric Laser Imaging Droplet Sizing’ (ILIDS) for planar simultaneous droplet size and velocity measurements with the in-focus technique ‘Particle Image Velocimetry’ (PIV) for gas velocity measurements in the vicinity of individual droplets. Discrimination between the gas phase seeding and the droplets is achieved in the PIV images by removing the glare points of focused droplet images, using the droplet position obtained through ILIDS processing. Combination of the two optical arrangements can result in a discrepancy in the location of the centre of a droplet, when imaging through ILIDS and PIV techniques, of up to about 1 mm, which may lead to erroneous identification of the glare points from droplets on the PIV images. The magnitude of the discrepancy is a function of position of the droplet’s image on the CCD array and the degree of defocus, but almost independent of droplet size. Specifically, it varies approximately linearly across the image along the direction corresponding to the direction of propagation of the laser sheet for a given defocus setting in ILIDS. The experimental finding is supported by a theoretical analysis, which was based on geometrical optics for a simple optical configuration that replicates the essential features of the optical system. The discrepancy in the location was measured using a monodisperse droplet generator, and this was subtracted from the droplet centres identified in the ILIDS images of a polydisperse spray without ‘seeding’ particles. This reduced the discrepancy between PIV and ILIDS droplet centres from about 1 mm to about 0.1 mm and hence increased the probability of finding the corresponding fringe patterns on the ILIDS image and glare points on the PIV image. In conclusion, it is shown that the proposed combined method can discriminate between droplets and ‘seeding’ particles and is capable of two-phase measurements in polydisperse sprays.     

A moment method for splashing and evaporation processes of polydisperse sprays

A new moment method for the modelling of polydisperse sprays is proposed that simultaneously takes into account the dispersion in droplet size and droplet velocity. For the derivation of this Eulerian method the kinetic spray equation is used which constitutes a partial differential equation for the probability density function of droplets. To reduce the complex kinetic spray equation to a form that can be managed with the available numerical procedures, moment transforms with respect to the droplet velocity and the droplet size are conducted. The resulting moment equations are closed by choosing an approximate probability density function which applies to polydisperse sprays. The method is successfully tested for configurations in which a polydisperse spray is either splashed, evaporated or effected by a Stokes drag force. The tests are organised in such a way that crossing of two spray distributions is always included. The new method is able to capture the polydisperse nature of sprays as well as the bi-(or multi-) modal character of the droplet velocity distribution function, for example, when droplets cross each other.     

Effects of Turbulence, Evaporation and Heat Release on the Dispersion of Droplets in Dilute Spray Jets and Flames

The dispersion characteristics of a selection of non-evaporating non-reacting, evaporating non-reacting, and reacting dilute spray jets issuing in ambient air (Gounder et al, Combust Sci Technol 182:702–715, 2010; Masri and Gounder, Combust Flame 159:3372–3397, 2010) and in a hot coflow (Oloughlin and Masri, Flow Turbul Combust 89:13–35, 2012) are analysed. Other than the cases found in those contributions, two additional sprays of kerosene have been investigated in order to systematically study the effects of evaporation. The burners are well designed such that boundary conditions may be accurately measured for use in numerical simulations. The dynamics and dispersion characteristics are analysed by conditioning results on the droplet Stokes numbers and by systematically investigating changes in dispersion and dynamics as a function of carrier air velocity, liquid loading, ignition method, and location within the flame or spray jet. The tendency for droplet dispersion defined by the ratio of radial rms velocity to axial mean velocity varies significantly between reacting and non-reacting flows. However, dispersion is found to be largely unaffected by evaporation. The total particle concentration, or number density of droplets within the spray has also been used as a direct measure of spray dispersion with the effect of evaporation on a turbulent polydisperse spray being isolated by investigating acetone and kerosene sprays with similar boundary conditions. The rate of change of droplet size with radial position is almost identical for the kerosene and acetone cases. The dispersion characteristics, closely related to the ‘fan spreading’ phenomenon are dependant on the carrier air velocity and axial location within the spray.     

Experimental study on effect of relative humidity on heat transfer of an evaporating water droplet in air flow

Dispersed water droplets are often seen in environmental air flows in rain, cloud, mist, sea spray and so on. It is therefore of great importance to precisely estimate heat transfer between water droplets and atmospheric air in developing a reliable climate model. The purpose of this study is to fabricate the measurement system for the temperature of a small water droplet in air flow under the controlled relative humidity condition and to investigate the effect of relative humidity on heat transfer across the surface of an evaporating water droplet in air flow. The results show that the droplet temperature decreases in the low-relative-humidity condition, whereas it increases in the high-relative-humidity condition. Nusselt number on the droplet surface is not affected by the relative humidity.     

Large Eddy Simulation of a Polydisperse Ethanol Spray Flame

Ethanol is identified as an interesting alternative fuel. In this regards, the predictive capability of combustion Large Eddy Simulation approach coupled to Lagrangian droplet dynamic model to retrieve the turbulent droplet dispersion, droplet size distribution, spray evolution and combustion properties is investigated in this paper for an ethanol spray flame. Following the Eulerian-Lagrangian approach with a fully two way coupling, the Favre-filtered low Mach number Navier-Stokes equations are solved on structured grids with dynamic sub-grid scale models to describe the turbulent carrier gas phase. Droplets are injected in polydisperse manner and generated in time dependent boundary conditions. They evaporate to form an air-fuel mixture that yields spray flame. Part of the ethanol droplets evaporates within the prevaporization area before reaching the combustion zone, making the flame to burn in a partially premixed regime. The chemistry is described by a tabulated detailed chemistry based on the flamelet generated manifold approach. The fuel, ethanol, is modeled by a detailed reaction mechanism consisting of 56 species and 351 reversible reactions. The simulation results including excess gas temperature, droplet velocities and corresponding fluctuations, droplet mean diameters and spray volume flux at different distances from the exit plane show good agreement with experimental data. Analysis of combustion spray features allows gaining a deep insight into the two-phase flow process ongoing.     

Accurate analysis of multicomponent fuel spray evaporation in turbulent flow

The aim of this paper is to perform an accurate analysis of the evaporation of single component and binary mixture fuels sprays in a hot weakly turbulent pipe flow by means of experimental measurement and numerical simulation. This gives a deeper insight into the relationship between fuel composition and spray evaporation. The turbulence intensity in the test section is equal to 10%, and the integral length scale is three orders of magnitude larger than the droplet size while the turbulence microscale (Kolmogorov scales) is of same order as the droplet diameter. The spray produced by means of a calibrated droplet generator was injected in a gas flow electrically preheated. N-nonane, isopropanol, and their mixtures were used in the tests. The generalized scattering imaging technique was applied to simultaneously determine size, velocity, and spatial location of the droplets carried by the turbulent flow in the quartz tube. The spray evaporation was computed using a Lagrangian particle solver coupled to a gas-phase solver. Computations of spray mean diameter and droplet size distributions at different locations along the pipe compare very favorably with the measurement results. This combined research tool enabled further investigation concerning the influencing parameters upon the evaporation process such as the turbulence, droplet internal mixing, and liquid-phase thermophysical properties.     

Measuring particle size distribution using LED-illumination

A particle/droplet image analysis (PDIA) system employing LED-illumination was designed. Freezing the moving droplets using high speed camera instead of stroboscopic illumination, the system had no requirement to synchronize the backlight and the camera. It featured low cost, low power consumption and simple optical configuration in comparison to laser-based systems. Only focused droplets in images were counted. Given the sample size of the system was relatively small, an upper-limit lognormal distribution was used to fit the actual data to represent the spray patterns. The accuracy of the diameter measurement was verified using precisely manufactured balls. Comparisons with two laser-based systems were given and the system’s capacity to distinct spray patterns were demonstrated in nozzle classification experiments.     

Evaporating and combusting droplet temperature measurements using two-color laser-induced fluorescence

 The paper presents a new technique based on laser-induced fluorescence, allowing droplet temperature measurement of evaporating and combusting droplets to be performed. The liquid spray is seeded with a low concentration of rhodamine B. The fluorescence, induced by the green line of an argon laser, is measured on two separated color bands. It is demonstrated that two color bands can be selected for their strong difference in the temperature sensitivity of the fluorescence quantum yield. The determination of the fluorescence ratio between the fluorescence intensity corresponding to each color band allows the tracer concentration and the droplet size dependences to be eliminated. The technique was applied on a monodisperse spray: the effect of a thermal impulse on the distribution of the droplet temperature is studied and, the temperature of combusting droplets is investigated. Received: 16 June 2000/Accepted: 10 November 2000     

Transient fuel spray impingement at atmospheric and elevated ambient conditions

This study analyses detailed temporally resolved full flow field data for pre- and post-impingement fuel sprays under atmospheric and elevated ambient conditions. A comprehensive suite of diagnostic techniques is utilised comprising of phase-resolved Phase Doppler Interferometry—employing a very fine grid and velocity signature to differentiate between pre- and post-impingement droplets—high-speed imaging (utilising Mie-scattering), high-magnification shadowgraphy and an adapted instantaneous mass-rate tube. Raised ambient conditions are achieved in a high-temperature, high-pressure constant volume rig affording large optical access. Temporal data for the free and impinging sprays is compared and analysed within three phases—early, mid and late injection—defined by the mass-rate tube data. All experimental techniques employed present consistent temporal and spatial trends at atmospheric and elevated ambient conditions, and global trends are consistent with the phenomenological flow structure originally proposed by Ozdemir and Whitelaw. Detailed analysis close to the piston surface reveals approximately a threefold increase in the D₅₀ mean spray diameter for the post-impingement droplet size distribution at the wall spray tip. It is suggested that this is due to droplet coalescence, with some supporting evidence from high-speed imaging. Comparison of transient mass deposited on the surface with model predictions show reasonable agreement with the ‘Wet’ model assumption.     

EFFECT OF NOZZLE FAN ANGLE ON SPRAYS IN GAS-SOLID RISER FLOW

A three-dimensional simulation study is performed for investigating the hydrodynamic behaviors of a cross-flow liquid nitrogen spray injected into an air-fluidized catalytic cracking (FCC) riser of rectangular cross-section. Rectangular nozzles with a fixed aspect ratio but different fan angles are used for the spray feeding. While our numerical simulation reveals a generic three-phase flow structure with strong three-phase interactions under rapid vaporization of sprays, this paper tends to focus on the study of the effect of nozzle fan angle on the spray coverage as well as vapor flux distribution by spray vaporization inside the riser flow. The gas-solid (air-FCC) flow is simulated using the multi-fluid method while the evaporating sprays (liquid nitrogen) are calculated using the Lagrangian trajectory method, with a strong two-way coupling between the Eulerian gas-solid flow and the Lagrangian trajectories of spray. Our simulation shows that the spray coverage is basically dominated by the spray fan angle. The spray fan angle has a very minor effect on spray penetration. The spray vaporization flux per unit area of spray coverage is highly non-linearly distributed along the spray penetration. The convection of gas-solid flow in a riser leads to a significant downward deviation of vapor generated by droplet vaporization, causing a strong recirculating wake region in the immediate downstream area of the spray.     

The Effect of Droplets Evaporation on Turbulence Modification and Heat Transfer Enhancement in a Two-Phase Mist Flow Downstream of a Pipe Sudden Expansion

Turbulent droplet-laden flow downstream of a sudden pipe expansion is numerically studied using an Eulerian two-fluid model. The model is used to investigate the effect of droplet evaporation on the particle dispersion and on the gas phase turbulence modification. Turbulence suppression in the case of evaporating droplets is hardly observed near the wall, and the level of turbulence tends to the corresponding value for the single-phase flow regime. In the flow core, where evaporation is insignificant, a decrease in the level of gas turbulence (to 20 % as compared to a single-phase flow) can be observed. The maximal effect of droplet evaporation is obtained in the wall region of the tube. A considerable increase in the maximal value of heat exchange on adding the evaporating droplets to the separated flow is shown (more than 1.5-fold as compared to the single-phase flow at a small value of droplet mass concentration of M _L1≤ 0.05). The addition of the solid non-evaporating particles causes a slight increase in the maximum value of heat transfer in the case of small particles and a decrease in heat transfer in the case of large particles.     

Measurements of droplet size in shear-driven atomization using ultra-small angle x-ray scattering

Measurements of droplet size in optically-thick, non-evaporating, shear-driven sprays have been made using ultra-small angle x-ray scattering (USAXS). The sprays are produced by orifice-type nozzles coupled to diesel injectors, with measurements conducted from 1 – 24 mm from the orifice, spanning from the optically-dense near-nozzle region to more dilute regions where optical diagnostics are feasible. The influence of nozzle diameter, liquid injection pressure, and ambient density were examined. The USAXS measurements reveal few if any nanoscale droplets, in conflict with a popular computational model of diesel spray breakup. The average droplet diameter rapidly decreases with downstream distance from the nozzle until a plateau value is reached, after which only small changes are seen in droplet diameter. This plateau droplet size is consistent with the droplets being small enough to be stable with respect to further breakup. Liquid injection pressure and nozzle diameter have the biggest impact on droplet size, while ambient density has a smaller effect.     

A laser extinction based sensor for simultaneous droplet size and vapor measurement

Multiphase flows involving liquid droplets in association with gas flow occur in many industrial and scientific applications. Recent work has demonstrated the feasibility of using optical techniques based on laser extinction to simultaneously measure vapor concentration and temperature and droplet size and loading. This work introduces the theoretical background for the optimal design of such laser extinction techniques, termed WMLE (wavelength-multiplexed laser extinction). This paper focuses on the development of WMLE and presents a systematic methodology to guide the selection of suitable wavelengths and optimize the performance of WMLE for specific applications. WMLE utilizing wavelengths from 0.5 to 10 μm is illustrated for droplet size and vapor concentration measurements in an example of water spray, and is found to enable unique and sensitive Sauter mean diameter measurement in the range of ～1–15 μm along with accurate vapor detection. A vapor detection strategy based on differential absorption is developed to extend accurate measurement to a significantly wider range of droplet loading and vapor concentration as compared to strategies based on direct fixed-wavelength absorption. Expected performance of the sensor is modeled for an evaporating spray. This work is expected to lay the groundwork for implementing optical sensors based on WMLE in a variety of research and industrial applications involving multi-phase flows.     

Interaction phenomena between liquid droplets and hot particles—Captured via high-speed camera

The interaction of evaporating droplets and hot catalyst particles plays a major role in heterogeneously catalysed reactions. The liquid feed is injected into a gas–solid flow and is mixed with the catalyst. The interaction phenomena determine the evaporation time which should be minimised to keep the reactor vessel small. First measurements with a bed of fixed hot FCC-particles (fluid catalytic cracking) and two model fluids have been conducted. The interactions of ethanol and water droplets with the hot bed surface were captured via a high-speed camera. While the ethanol droplet developed a stable steam cushion due to Leidenfrost phenomena, water showed intense interaction and steam explosions which induced repulsion and atomisation of the droplet.