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Due to current and future environmental and safety issues in space propulsion, typical propellants for upper stage or satellite rocket engines such as the toxic hydrazine are going to be replaced by green propellants like the combination of liquid oxygen and hydrogen or methane. The injection of that kind of cryogenic fluids into the vacuum atmosphere of space leads to a superheated state, which results in a sudden and eruptive atomization due to flash boiling. For a detailed experimental investigation of superheated cryogenic fluids, the new cryogenic test bench M3.3 with a temperature controlled injection system was built at DLR Lampoldshausen. After a first test campaign with high-speed shadowgraphy of flash boiling liquid nitrogen sprays, a laser-based Phase Doppler system was set-up to determine the spatial distributions of droplet velocities and diameters in highly superheated sprays. The spatial distributions revealed a core region with high mean velocities close to the injector orifice. With increasing distance from the injector orifice, the sprays develop a more and more monodisperse pattern. These distributions also showed that atomization due to flash boiling generates finer sprays with growing degrees of superheat. In certain spray regions, two droplet populations varying in their direction of motion, velocity and diameter due to possible recirculation zones were observed. The experimental data of flash boiling liquid nitrogen generated within this study provide a comprehensive data base for the validation of numerical models and further numerical investigations., Deutsche Forschungsgemeinschaft, Projekt DEAL

Mixing and evaporation processes play an important role in fluid injection and disintegration. Laser-induced thermal acoustics (LITA) also known as laser-induced grating spectroscopy (LIGS) is a promising four-wave mixing technique capable to acquire speed of sound and transport properties of fluids. Since the signal intensity scales with pressure, LITA is effective in high-pressure environments. By analysing the frequency of LITA signals using a direct Fourier analysis, speed of sound data can be directly determined using only geometrical parameters of the optical arrangement no equation of state or additional modelling is needed at this point. Furthermore, transport properties, like acoustic damping rate and thermal diffusivity, are acquired using an analytical expression for LITA signals with finite beam sizes. By combining both evaluations in one LITA signal, we can estimate mixing parameters, such as the mixture temperature and composition, using suitable models for speed of sound and the acquired transport properties. Finally, direct measurements of the acoustic damping rate can provide important insights on the physics of supercritical fluid behaviour., Deutsche Forschungsgemeinschaft, Projekt DEAL

Physics of supercritical fluids is extremely complex and not yet fully understood. The importance of the presented investigations into the physics of supercritical fluids is twofold. First, the presented approach links the microscopic dynamics and macroscopic thermodynamics of supercritical fluids. Second, free falling droplets in a near to supercritical environment are investigated using spontaneous Raman scattering and a laser induced fluorescence/phosphorescence thermometry approach. The resulting spectroscopic data are employed to validate theoretical predictions of an improved evaporation model. Finally, laser induced thermal acoustics is used to investigate acoustic damping rates in the supercritical region of pure fluids.

Collisions between a stream of drops and a continuous jet of a different liquid are experimentally investigated. In contrast to previous studies, our work focuses on the effects of liquid miscibility and wettability on the collision outcomes. Thus, miscible and immiscible liquids providing total and partial wetting are used. We show that, as long as the jet surface tension is smaller than the drop surface tension, the drops can be encapsulated by the jet, providing the so-called drops-in-jet structure. The transitions between the different regimes remain similar in nature with a capillary fragmentation responsible for the jet break-up and an inertial fragmentation causing the drops (and then possibly the jet) to break up. The dimensionless numbers proposed in the literature to model the inertial fragmentation thresholds do not bring the results obtained with different liquids at the same critical value. We explain the reason via a detailed analysis of the collisions, accounting for the drop and jet extensions and their kinetics. The drop fragmentation is found to occur during the recoil phase, leading us to propose a new dimensionless parameter that successfully reproduced all our experimental data obtained with immiscible liquids. Finally we demonstrate that the most dramatic change of the collision outcomes is produced by using drops that totally wet the jet. In this case, the encapsulation of the drops cannot be achieved, constituting a true limit to some applications based on the solidification of the drops-in-jet structure., Comment: 34 pages, 15 figures

The existence of large-scale turbulent structures within a porous medium, generated through the interaction with a turbulent outer flow, is a highly debated topic, albeit most of the analysis is based on computational studies. This study contributes to the ongoing discussion by providing detailed point-measurements of the velocity in both regions by means of Particle Image Velocimetry (PIV). Two porous models of different porosity are investigated at three Reynolds numbers. The design of the experiments is based on theoretical studies to guarantee the presence of an unperturbed viscous layer at the interface (alias permeability Reynolds numbers of order one). Under these conditions and in compliance with theoretical predictions, the PIV data show the rapid dumping of turbulent fluctuations within the first pore cavities and can be used to validate closure models for volume-averaged computational studies. A point-data analysis is applied in the interfacial region by requiring continuity of tangential velocity and shear stress. The presence of the attached viscous layer implies that the coupling condition for momentum transfer must be controlled by shear, leading to the well-known Beavers and Joseph coupling condition. PIV data corroborate this statement and show the close interdependency between the penetration depth of the outer flow in the porous media and the characteristics of the vortical secondary flows induced by the strain rate at the pore scale. Consequently, the Beavers and Joseph-slip coefficient depends only upon the topology of the porous medium, at least as long as no transition to a perturbed mixing layer occurs at the interface.

The rapid implementation of Selective-Catalytic-Reduction (SCR) technologies into light passenger and commercial vehicles, led to the omission of fundamental research creating several reliability issues that are largely related to the research field of droplet dynamics. In this study, the splashing behaviour of an AdBlue droplet impacting onto thin urea-water solution films is experimentally investigated over a range of impact parameters. In particular, the crown-type splashing threshold, the number of fingers and the characteristics of the ejected secondary droplets are evaluated for various drop impact velocities, wall-film thicknesses and urea concentrations in the liquid film. The results show that impact parameters that are able to enhance the energy dissipation in the wall-film, e.g. film thickness and viscosity, influence negatively the intensity of splashing. On the other hand, as the droplet kinetic energy increases or the wall-film thickness decreases, more energy is available to intensify the splashing outcome, and consequently, the upward ejected secondary droplet volume. The obtained trends are correlated in simple empirical expressions providing a remarkable industrial design tool, and they are also compared to the state-of-the-art literature of single- and binary-droplet/wall-film interactions aiming to draw generalised theories and paradigms that will support the connection between SCR applications and academic research.

The International Research Training Group GRK 2160 (DROPIT), active since Oct. 2016, focuses on droplet interaction technologies, which have a large number of applications in a variety of technological processes. The main objective of DROPIT is to identify and to investigate the mechanisms through which small-scale interactions at the interface couple with and influence large scale features in the main flow. DROPIT is a joint initiative of the University of Stuttgart in Germany, the University of Bergamo and the University of Trento in Italy. The project consists of 17 subprojects, which are structured into three main research areas, involving researchers from a large number of different disciplines. The project consists of an extensive qualification program which aims at fostering the education of young scientists and providing them the knowledge and skills to conduct independent research. This paper provides an overview of the structure and the research activities within DROPIT as well as on the qualification program implemented. Selected research results are shown and discussed. The main purpose of this paper is to familiarize colleagues with this extensive research effort in the area of droplet interaction technologies and to exchange ideas and promote future collaboration with others in this field.

The influence of wettability on the morphology of droplet impacts onto dry surfaces is often neglected in the literature, despite its significant effect on the resulting morphology. In this work, the role of wettability is investigated systematically by considering droplet impact processes on smooth dry surfaces of two different materials. The wetting behavior is varied not only by employing two different fluids, but most importantly by varying the surface properties by plasma activation and polymerization. Overall, this leads to four different wetting behaviors for each surface. The changes in impact morphology are visualized by means of a three-perspective experimental facility. In particular, the bottom view employs a total internal reflection-configuration for visualizing the exact droplet contact area and contact time. This enables us to characterize the main features of the different wetting behaviors. Overall, we found that surface wettability mainly influences the receding phase, resulting in higher receding rates with decreasing wettability but also the maximum spreading diameter., Fundação para a Ciência e a Tecnologia e Deutsche Forschungsgemeinschaft (DFG)

Mixing characteristics of supercritical injection studies were analyzed with regard to the necessity to include diffusive fluxes. Therefore, speed of sound data from mixing jets were investigated using an adiabatic mixing model and compared to an analytic solution. In this work, we show that the generalized application of the adiabatic mixing model may become inappropriate for subsonic submerged jets at high-pressure conditions. Two cases are discussed where thermal and concentration driven fluxes are seen to have significant influence. To which extent the adiabatic mixing model is valid depends on the relative importance of local diffusive fluxes, namely Fourier, Fick and Dufour diffusion. This is inter alia influenced by different time and length scales. The experimental data from a high-pressure n-hexane/nitrogen jet injection were investigated numerically. Finally, based on recent numerical findings, the plausibility of different thermodynamic mixing models for binary mixtures under high pressure conditions is analyzed.

The influence of miscibility and liquid wettability during droplet impact onto thin wall films is investigated experimentally. Despite similar liquid properties and impact conditions, differences in the splashing limit, the crown extension and the duration of the ascending phase are observed. These differences are related to the interfacial tension of the droplet/wall-film liquid pairs, which is linked to their miscibility and wettability. More precisely, by calculating the crown surface energy, we show that the energy stored in the interface between droplet and wall-film (if any) is not negligible and leads to smaller crown extensions and the need of more kinetic energy to initiate splashing. Similarly, by calculating a modified capillary time taking into account all surface and interfacial tensions, we show that the interfacial tension acts as a non-negligible recoiling force, which reduces the duration of the ascending phase. The dynamics of this ascending phase is well captured for different wall-film thicknesses if accounting for the variations of the liquid masses in movement. Overall, droplet/wall-film interactions can be seen as inertio-capillary systems where the interfacial tension between droplet and wall film plays a significant role in the storage of energy and in the crown kinetics during the impact process. Besides, this analysis highlights that viscous losses have already a significant effect during the crown extension phase, by dissipating almost half of the initial energies for droplet impact onto thin wall films, and most likely by influencing the capillary time scale through damping., 24 pages, 10 figures, submitted to the Journal of Fluid Mechanics

This study is the first to provide a comprehensive speed of sound database for multi-component jet mixing at high pressure. It serves as a unique reference for numerical simulations of mixture preparation processes in future liquid rocket engines and internal combustion engines. We performed quantitative speed of sound measurements in jet mixing zones for five configurations with well-defined experimental conditions. The database covers three different injectant fluids (two alkanes and a fluoroketone) that were brought beyond their critical temperature and pressure prior to injection and discharged into cold nitrogen at supercritical pressure (with respect to the pure injectant properties). Here, we chose the conditions such that subsonic jets were obtained and re-condensation due to cooling of the injected fluid was prevented. Hence, we provide speed of sound data for single-phase jet mixing for three different binary systems. Quantitative data are presented along the jet centerline with sufficiently high spatial resolution to properly resolve the axial decay. In addition, two radial profiles at a position close to the nozzle allow for an assessment of the transversal mixing characteristics. The experimental speed of sound data show consistent trends, which corroborate that mixture effects are correctly resolved in the measurement.

The present work summarises the main findings of a systematic study on the behaviour of liquid droplets embedded in a high pressure and temperature environment. Thanks to the availability of quantitative temperature data, it was possible for the first time to assess the conceptual soundness of different theoretical approaches. In all cases, the predictions from non-equilibrium models agree fairly well with Raman-extracted temperatures. By performing a thermodynamic analysis of interfacial transport in the framework of the Onsager theory, the following was found. Models that assume vapour-liquid equilibrium fail to provide a good estimation of the droplet temperature. This is due to the description of the interfacial fluxes that does not include the interdependency between heat and mass transfer, as prescribed by the Onsager theorem. Under non-equilibrium conditions, interfacial temperature jumps may exist without leading to the disintegration of the immiscible interface, as corroborated by several theoretical and experimental studies. The inception of thermal losses is controlled by the interfacial resistivities rather than by the Knudsen number. With decreasing droplet size and increasing ambient temperatures, the inclusion of local non-equilibrium effects in the modelling of the interfacial fluxes from the vapour side leads to higher interfacial temperature jumps.

In this study, n-hexane was compressed beyond six times its critical pressure and discharged into argon at subcritical pressure (with respect to the injectant). The injection temperature systematically varied from sub- to supercritical values to investigate near-critical disintegration phenomena of retrograde jets. Here, the ratio of the pressure in the nozzle reservoir and chamber was always above 14 leading to highly-expanded injections. We analyzed the breakup process in terms of combined shadowgraphy and light scattering measurements. Close to the critical point, different physical mechanisms have been observed. Their occurrence is predominantly determined by the expansion process resulting from the thermodynamic conditions in nozzle reservoir and chamber in combination with thermodynamic properties of the injectant. The experimental images for near- but subcritical injection temperatures imply that a fluid in liquid state expands in the nozzle and atomizes downstream of it. For sufficiently low backpressures, high liquid superheats trigger rapid vapor formation across a thin transition layer inside the nozzle that leads to a choked two-phase flow. A thermodynamic model that assumes a discontinuous phase transition layer and uses metastable fluid properties provides a physical explanation of the resulting underexpanded two-phase disintegration downstream of the nozzle exit . An increase to supercritical injection temperatures increases the compressibility of the fluid within the nozzle. An isentropic flow analysis showed that this triggers choking at thermodynamic states in the supercritical pressure regime resulting in the discharge of a sonic single-phase fluid. The expansion within the Mach barrel can lead to a supersaturated fluid state at near-critical temperature. In this case, a sharp phase transition front established approximately half a nozzle diameter downstream of the exit. We defined a dimensionless parameter to characterize the two-phase extent in underexpanded jets with near-critical phase transition based on initial injection conditions and retrograde fluid properties. We deduced the axial extent of the two-phase region from light scattering signals for a wide parameter range and demonstrate that it features a clear dependency upon the proposed parameter, which demonstrates its feasibility.

An electrohydrodynamic model for the simulation of droplet formation, detachment and motion in an electrically driven droplet generator is introduced. The numerical approach is based on the coupled solution of the multiphase flow problem with the charge continuity equation. For the latter, a modified convection-conduction model is applied, taking into account conductive, capacitive as well as convective electrical currents in the fluid. This allows for a proper description of charge relaxation phenomena in the moving fluid. In particular, the charge received by the droplet after detachment is an important parameter influencing the droplet dynamics in the test chamber. Simulation results are shown for highly conductive acetone droplets and for low conductivity pentane droplets, respectively. The operation characteristic of the droplet generator is investigated by computing droplet sizes and detachment times with respect to the applied voltage.

The relationship between ‘microscopic’ velocity field and ‘macroscopic’ outcomes of liquid droplet impact on wall-films is not yet fully understood. This article reports a preliminary experimental investigation to measure the velocity field within wall-film when a droplet impacts on it, using micro-Particle Image Velocimetry (μ-PIV). The challenges associated with measuring the velocity field within the wall-film are outlined. In this context, the limitations of the traditional μ-PIV technique are discussed, leading to the adoption of high-speed μ-PIV as the suitable technique for measuring the spatio-temporal evolution of velocity within wall-film. The salient features of the high-speed μ-PIV set-up are discussed. Further, results from preliminary experimental investigations on water droplet impacting on water wall-film at moderate impact velocities are presented. It is seen that the current high-speed μ-PIV set-up can be used to obtain reliable measurements of in-plane radial velocity, V, at ‘intermediate’ values of radial, r, and temporal, t, coordinates. Within the measurement range of the current set-up, it is observed that V scales with r and t as V ∝ r/t, which is similar to that reported in literature based on analytical considerations. The limitations of the current set-up, and the requirements for further experiments and validation are highlighted.

Drop impact onto wetted surfaces is of relevance to any spray coating application since the maximum spreading diameter and the residual film thickness of the applied liquid droplets affect the efficient distribution of the coating materials. In this paper, we propose a modification to existing models for crown propagation during single drop impact onto a wall-film based on the stagnation-point flow solution of Hiemenz. This offers two main advantages: a simple estimation of the film thickness decay rate, induced by the impulse transfer from impacting droplet to resting wall-film. Besides, the self-similarity of Hiemenz’s solution allows a straightforward estimation of the momentum losses during radial liquid spreading along the wall. The incorporation of these estimations into existing inviscid models provides an excellent agreement with experiments over the entire crown elevation phase. Additionally, the effect of fluid viscosity and initial film thickness on the momentum transfer from droplet to wall-film is highlighted.

Droplet impact on wall-films are typical examples where ‘splashing’, the fragmentation of the crown rim during its expansion, takes place. The triggering instability mechanisms are directly linked to crown rim kinematics. This experimental study analyses which geometrical parameter is physically the most suited for studying crown rim kinematics during expansion. The problems associated with the classical geometrical parameters rim radius \(R_{R}\) and height \(H_{R}\) (often considered separately) are presented. First, the radial and axial rim expansions have different durations which prevents the definition of rim expansion in a unified way. Second, considering separately \(H_{R}\) and \(R_{R}\) leads to an incomplete picture of the impact process in terms of momentum transfer to the rim since the crown aspect ratio Open image in new window varies strongly with the impact conditions. We show that considering the crown rim displacement instead solves these problems: a single peak during the impact process enables a clear definition of rim expansion (duration and magnitude). Furthermore, the temporal evolution of the rim displacement during expansion could systematically be fitted by a quadratic curve with high accuracy, which indicates a constant deceleration process. Thus, considering the rim displacement reveals important features of the crown rim kinematics.

The evaporation of liquid drops in stagnant gaseous environment is modelled, accounting for the effect of drop curvature and size at the macro- and microscopic scales. At the macro-scale level, the validity of the conjectured dependence of the local fluxes on the drop surface curvature is analysed. Analytical solutions to the gas-phase conservation equations for five drop shapes (sphere, oblate and prolate spheroids and inverse oblate and prolate spheroids), under uniform Dirichlet boundary conditions, are used to calculate the local vapour and heat fluxes. The analysis shows that in general non-dimensional fluxes do not solely depend on local curvature, but possibly the effect of the whole drop shape must be taken into account. At the micro-scale level, the equilibrium vapour pressure at a convex curved surface is higher than that at a flat surface, thus leading to a considerable enhancement of the evaporation rate for nanometre sized droplets. To model the increase in equilibrium vapour pressure, we consider the Kelvin correction. Our analysis shows that the Kelvin correction is strictly required for droplet radii below 20 A, as typically encountered for modelling the growth of critical clusters in phase transition processes initiated by homogeneous nucleation. At these conditions, it is mandatory to consider also the repartition of molecules in the different phases, in order to prevent a significant overestimation of the equilibrium vapour pressure.

This book provides a selection of contributions to the DIPSI workshop 2019 (Droplet Impact Phenomena & Spray Investigations) as well as recent progress of the Int. Research Training Group “DROPIT”. The DIPSI workshop, which is now at its thirteenth edition, represents an important opportunity to share recent knowledge on droplets and sprays in a variety of research fields and industrial applications. The research training group “DROPIT” is focused on droplet interaction technologies where microscopic effects influence strongly macroscopic behavior. This requires the inclusion of interface kinetics and/or a detailed analysis of surface microstructures. Normally, complicated technical processes cover the underlying basic mechanisms, and therefore, progress in the overall process modelling can hardly be gained. Therefore, DROPIT focuses on the underlying basic processes. This is done by investigating different spatial and/or temporal scales of the problems and by linking them through a multi-scale approach. In addition, multi-physics are required to understand e.g. problems for droplet-wall interactions, where porous structures are involved.

This work analyses whether the inclusion of interfacial temperature jumps is necessary in the modelling of droplet evaporation at high pressure. The analysis is divided into two parts. First, we revise the major findings from theoretical models and molecular dynamics simulations on the conditions leading to the inception of interfacial jumps and the main parameters affecting them. Second, an evaporation model is considered that includes a diffuse transition layer (Knudsen layer), in the order of a few mean free paths around the droplet, where transport processes are described by kinetic molecular theory. The analysis shows that discontinuities in temperature and chemical potential across the interface are important when molecular collisions control transport processes and result in large heat and mass fluxes. This may occur not only at low pressures, but also at high pressures and temperatures for conditions sufficiently far from global thermodynamic equilibrium and/or for sufficiently small droplets. On a macroscopic scale, the resulting correction to the boundary conditions for classical diffusion-controlled models may be significant at high evaporation rates.

The development of new upper orbit thrusters using cryogenic propellants requires an improved understanding of the dynamics of oxidizer and fuel injection at near vacuum conditions before ignition. Due to the low ambient pressure, the propellants enter a superheated state and flash evaporation occurs. Flash boiling of cryogenic liquid nitrogen is studied experimentally on the newly developed test bench at DLR Lampoldshausen and numerically with a newly developed OpenFOAM© solver. Here, a one-fluid approach is selected where phase properties, such as density, enthalpy and saturation conditions are determined with the thermodynamic library CoolProp and tabulated before runtime. The phase change is modeled by the homogeneous relaxation model. For highly superheated jets the flow becomes supersonic and forms a shock after the injector outlet. The solver is validated with the aid of flashing acetone spray experiments where the shock structures are more clearly visible. The results show that the developed solver is capable to predict the all important gas dynamics by matching shock structure and spray angle to the experiment. The experiments using cryogenic liquid, however, do not reveal any shock structures but regions with low negative axial velocities can be identified on the jet centerline. A comparison with the simulations now demonstrates that shocks continue to persist but the respective shadowgraph signals may be obscured in these flows. The joint experimental and numerical study thus provides a consistent understanding of the observed flow features that govern the fluid dynamics and jet breakup of cryogenic flashing flows.

Cryogenic supercritical fluids represent an intriguing category of fluids that combine mechanical and thermophysical properties of both ultralow temperature conditions and phenomena taking place well above the critical point. Recent research has demonstrated that it is a common misconception to consider the supercritical state as one homogeneous state. Instead, these fluids consist of two to four liquid and gas like phases, each with their own unique characteristics. In our work, we investigate numerically single-specie cryogenic fluid jets—initially at subcritical temperatures—which are injected into a supercritical environment (both the pressure and temperature exceed the thermodynamic critical state). For the investigation, a new solver, namely, “CoolFoam,” has been developed, which is designed for compressible non-isothermal two-fluid simulations where diffusive transport of heat and/or mass is accounted for. Real fluid thermodynamics are modeled using a polynomial fitting approach developed in our previous work. We introduce also a new phase characterization framework based on the association of phases with specific temperature ranges (rather than using a single line like the Widom line), which allowed us to better identify the similarity effects between the various conditions. We analyze the inter-dependence of the underlying phenomena: density gradient and diffusive mass transport [molecular and thermo(Soret)-diffusion] and turbulence. We also compared supercritical N2 with subcritical liquid and gas jets to highlight potential differences with respect to how these jets behave. We find that the jet dynamics are largely dictated by the thermodynamic transition of the injected fluid and the associated variation in thermophysical properties.

Rising pressures in modern combustion systems lead to conditions that can be supercritical for the injected liquid fuels. Quantitative measurement data is required for a better understanding of this complex process and for validation of corresponding simulations. The present study focusses on the evaporation of single free-falling droplets to reduce the complexity of the problem. The species concentration field in the wake of n- heptane droplets is measured with 2D Raman imaging. The atmosphere consists of nitrogen at conditions that are sub- to super-critical with regards to pure n -heptane. The concentration fields of all droplets at one set of operation conditions are overlaid to allow statistical interpretation. Additionally, data points for the correlation between n -heptane concentration and the relative number density are determined from the Raman signals. These data points are fitted by a model based on the adiabatic mixing assumption and a Virial equation of state for mixtures. The fitted model is used to calculate the correlation between fuel concentration and temperature. As suggested by the temperature results the droplet is cooled due to evaporation rather than being heated up towards its critical temperature. The data is available for the validation of numerical simulations.

Transcritical injection is of relevance to many areas of science and engineering. In all applications, one of the most controversial issue is the prediction of the transition point from two-phase to single phase mixing. In this work, we have analysed the applicability of recent transition models, e.g. the Knudsen criterion developed originally for propulsion applications, to analyse the formation and development of mixing layers of carbon dioxide and different organic solvents. Results show that global equilibrium models fail to predict the experimental behaviour reported in the literature and exhibit an inconsistent trend among the different organic solvents/CO2 mixtures. This implies that initial conditions alone are not sufficient to determine the evolution of the mixing layer. As a consequence, research efforts should be directed to the accurate description of the coupled energy and mass diffusive fluxes both at the liquid–gas interface and in the surrounding gaseous mixing layer.

The present work provides an overview on the possible phase transitions associated with supercritical fluid injection and a detailed evaluation of the mixing process between injectant fluid and quiescent ambience. The experiments cover superheated liquid disintegration, pseudo-boiling transition and single-phase jets under different nozzle pressure ratios. Pseudo-boiling effects emerge when rapid, subsequent changes in pressure/temperature interact with the non-linear behavior of thermodynamic response functions across the Widom line. The associated density fluctuations cause a significant increase in the scattering cross section and may lead to thermo-convective instabilities. Our analysis of the mixing process demonstrates the limited applicability of the adiabatic mixing model, which is often restricted to short residence times even in highly turbulent jets ( Re = O ( 10 5 ) ). Specifically, our findings show the importance of considering all coupled transport processes in the analysis of mixing problems at high pressures, in particular in presence of large mass concentration and temperature gradients.

Mean temperatures of acetone, millimeter-sized, freely falling droplets in a nitrogen atmosphere are studied at two different locations downstream a capillary-type injector. Injection and ambient temperatures have been varied independently between 433 and 513 K and pressures from 2 to 6 MPa. The ratio of simultaneously measured laser-induced phosphorescence (LIP) and fluorescence (LIF) is shown to be a suitable approach for measuring temperatures in the given conditions. Cumulated uncertainties (2 σ) of mean droplet temperatures of ±3 K are estimated. The temperatures measured in this study are partly compared to results of previous investigations where droplet temperatures have been estimated by an extrapolation of temperature mixture fraction data in the gas phase obtained from spontaneous Raman scattering. Overall a reasonable agreement has been observed which indicates the applicability of the previous approach for estimations based on the adiabatic mixing assumption and the extrapolation of the Raman-measured data.

During droplet impact on thin wall-films, a liquid lamella, the so-called ‘crown’, expands radially and vertically away from the impact point. This phenomenon is often associated with the growth of fingers at the crown rim, leading to the fascinating crown-type splashing. The present study reports an experimental investigation on droplet impact on wall-films, where the droplet and wall-film are made of different silicone oils. The focus is to characterize the crown rim kinematics in terms of relevant length, velocity, and acceleration scales during the expansion phase. The analysis showed that the crown rim displacement is a physically meaningful parameter to characterize the rim expansion. From this parameter, it is possible to clearly define the maximum expansion of the crown rim as well as the average velocity and the constant deceleration of crown rim expansion. The effects of droplet and wall-film properties (especially, their viscosities), droplet impact velocity, and wall-film thickness on these length, time, velocity, and acceleration scales associated with crown rim expansion are studied. Furthermore, the experimental data extracted from our vast database are systematically compared with the theoretical predictions from relevant models reported in literature to discuss their range of applicability.

Understanding suitable boundary conditions for vapor-liquid interfaces is important for the development of physically realistic simulations of evaporation and condensation processes. This work addresses the question whether the inclusion of interfacial temperature jumps is necessary in the modeling of droplet evaporation or condensation. The analysis is divided into two parts. First, a model for coupled heat and mass transfer resistivities for sharp vapor-liquid interfaces is derived from a diffuse interface model. Local resistivities within the interface of n-alkane/nitrogen mixtures are predicted for diffuse interfaces by means of classical density functional theory (DFT) in combination with the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. Integration over different domains of the local resistivities yields integral resistivities for sharp, or diffuse, interfaces. This allows computation of temperature jumps projected onto sharp interfaces under non-equilibrium conditions. Using this projection we found that interfacial jumps across the vapor-liquid interface are typically small, even for large temperature differences between droplet and ambient vapor. Second, an evaporation model is considered that includes a diffuse transition layer (Knudsen layer) in the order of a few mean free paths around the droplet, where transport processes are described by kinetic molecular theory. The analysis shows that discontinuities in temperature and chemical potential across the interface are important when heat and mass transfer are dominated by molecular collisions. This may occur not only at low pressures, but also at high pressures and temperatures for conditions sufficiently far from global thermodynamic equilibrium, resulting in large heat and mass fluxes and/or for sufficiently small droplets. On a macroscopic scale, the resulting correction to the boundary conditions for classical diffusion-controlled models may be significant at high evaporation or condensation rates.

Non-resonant laser-induced thermal acoustics (LITA), a four-wave mixing technique, was applied to post-shock flows within a shock tube. Simultaneous single-shot determination of temperature, speed of sound and flow velocity behind incident and reflected shock waves at different pressure and temperature levels are presented. Measurements were performed non-intrusively and without any seeding. The paper describes the technique and outlines its advantages compared to more established laser-based methods with respect to the challenges of shock tube experiments. The experiments include argon and nitrogen as test gas at temperatures of up to 1000 K and pressures of up to 43 bar. The experimental data are compared to calculated values based on inviscid one-dimensional shock wave theory. The single-shot uncertainty of the technique is investigated for worst-case test conditions resulting in relative standard deviations of 1, 1.7 and 3.4 % for Mach number, speed of sound and temperature, respectively. For all further experimental conditions, calculated values stay well within the 95 % confidence intervals of the LITA measurement.

We report a comprehensive speed of sound database for multi-component mixing of underexpanded fuel jets with real gas expansion. The paper presents several reference test cases with well-defined experimental conditions providing quantitative data for validation of computational simulations. Two injectant fluids, fundamentally different with respect to their critical properties, are brought to supercritical state and discharged into cold nitrogen at different pressures. The database features a wide range of nozzle pressure ratios covering the regimes that are generally classified as highly and extremely highly underexpanded jets. Further variation is introduced by investigating different injection temperatures. Measurements are obtained along the centerline at different axial positions. In addition, an adiabatic mixing model based on non-ideal thermodynamic mixture properties is used to extract mixture compositions from the experimental speed of sound data. The concentration data obtained are complemented by existing experimental data and represented by an empirical fit.

The electrohydrodynamics of millimetric droplets under the influence of slowly varying electric fields is considered. Strong electric fields applied on liquids induce forces driving fluid motion. This effect can be used, among others, in on-demand droplet generators. In this work, we discuss a convection-conduction model for the simulation of droplet motion in strong electric fields. The model focuses on robustness with respect to topology changes and on dynamic charging effects in liquids. We illustrate the model with the simulation of electrically driven droplet generation. The simulated dynamics for droplets with different conductivities are compared with experiments.

The present paper investigates experimentally the impact dynamics of crown-type splashing for miscible two- and one-component droplet wall–film interactions over a range of Weber numbers and dimensionless film thicknesses. The splashing outcome is parametrised in terms of a set of quantifiable parameters, such as crown height, top and base diameter, wall inclination, number of fingers, and secondary droplet properties. The results show that the outcome of a splashing event is not affected by the choice of similar or dissimilar fluids, provided the dimensionless film thickness is larger than 0.1. Below this threshold, distinctive features of two-component interactions appear, such as hole formation and crown bottom breakdown. The observation of different crown shapes (e.g. V-shaped, cylindrical, and truncated-cone) confirms that vorticity production induces changes in the crown wall inclination, thus affecting the evolution of the crown height and top diameter. The evolution of the crown base diameter, instead, is mainly dependent on the relative importance of liquid inertia and viscous losses in the wall-film. The maximum number of liquid fingers decreases with increasing wall, film thickness, due to the enhanced attenuation of the effect of surface properties on the fingering process. The formation of secondary droplets is also affected by changes in the crown wall inclination. In particular, for truncated-cone shapes the occurrence of crown rim contraction induces a large scatter in the secondary droplet properties. Consequently, empirical models for the maximum number and mean diameter of the secondary droplets are derived for V-shaped crowns, as observed for the hexadecane-Hyspin interactions.

[EN] Single drop impacts on thin liquid layers are of particular interest because of the ejection of secondary droplets, the so-called splashing. Only a few studies handle the deposition/splashing limit for two-component interaction, where the liquid properties of the impacting drop and wall film differ significantly. This study aims at identifying a unified approach for one- and two-component interactions to determine the deposition/splashing limit. Therefore, a large database of both interactions is considered, which includes data from literature for one-component interactions plus the following binary combinations: hyspin-hexadecane, diesel-hexadecane and diesel-motor oil. Furthermore, a systematic study of two-component interactions with several silicon oils and hexadecane is performed. To map the outcomes, the Ohnesorge number Oh and the Reynolds number Re calculated with arithmetically averaged fluid properties between droplet and wall film fluid are chosen. The dimensionsless film thickness δ is added to form a 3D plot, where one- and two-component experiments are combined. Existing correlations from the literature are revised regarding both interactions and their consistency is checked. The investigated range of high viscosity fluids allow us to propose an improvement of the correlation for high Oh. Our results show that the arithmetically averaged fluid properties lead to a good repartition of both one- and twocomponents interactions toward the deposition/splashing limit. They also corroborate the previous findings that an increase of δ inhibits splashing but its influence is decreasing with increasing Oh., The authors kindly acknowledge the financial support of this work by the Deutsche Forschungsgemeinschaft (DFG) in the frame of the International Research Training Group "Droplet Interaction Technologies" (DROPIT)

[EN] Experiments and numerical simulations were carried out in order to contribute to a better understanding and prediction of high-pressure injection into a gaseous environment. Specifically, the focus was put on the phase separation processes of an initially supercritical fluid due to the interaction with its surrounding. N-hexane was injected into a chamber filled with pure nitrogen at 5 MPa and 293 K and three different test cases were selected such that they cover regimes in which the thermodynamic non-idealities, in particular the effects that stem from the potential phase separation, are significant. Simultaneous shadowgraphy and elastic light scattering experiments were conducted to capture both the flow structure as well as the phase separation. In addition, large-eddy simulations with a vaporliquid equilibrium model were performed. Both experimental and numerical results show phase formation for the cases, where the a-priori calculation predicts two-phase flow. Moreover, qualitative characteristics of the formation process agree well between experiments and numerical simulations and the transition behaviour from a dense-gas to a spray-like jet was captured by both, The authors gratefully acknowledge the German Research Foundation (Deutsche Forschungsgemeinschaft) for providing financial support in the framework of SFB/TRR 40. Financial support was also provided by Munich Aerospace (www.munich-aerospace.de). Furthermore, the authors thank the Gauss Centre for Supercomputing e.V. (GCS) (www.gauss-centre.eu) for supporting this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (www.lrz.de).

This paper presents a systematic study on flashing atomisation, which includes both standards and retrograde fluids. A novel data reduction method is proposed in terms of the controlling parameters for (bubble) nucleation. The analysis indicates that bubble nucleation is the rate-controlling process for both the transition to fully flashing and for the spray lateral spreading. Specifically, the onset condition coincides with the surmount of the energy barrier to nucleation. The spray lateral spreading, instead, is directly linked to the population of bubble clusters: the larger the population the wider the spray angle. Theoretical aspects of bubble nucleation theory are also reviewed. An interesting conclusion of the analysis is that the experimental trends observed in fully flashing jets are compliant with recent advances in nucleation theory. At very high initial superheat, a complex shock wave structure appears around the flashing jets. The novel aspect of this work is that such shock-systems are observed consistently in both standard and retrograde substances. This similarity indirectly confirms that, far from the critical temperature, the phase transition mechanism is the same for all substances, independently from their degree of retrogradicity.