Breakup Model Research Articles

Effects of drive amplitude on continuous jet break-up

We develop a one-dimensional model of jet breakup in continuous inkjet printing to explore the nonlinear behavior caused by finite-amplitude modulations in the driving velocity, where jet stability deviates from classic (linear) “Rayleigh” behavior. At low driving amplitudes and high Weber numbers, the spatial instability produces drops that pinch-off downstream of the connecting filament, leading to the production of small satellite droplets between the main drops. On the other hand, we identify a range of driving amplitudes where pinching becomes “inverted,” occurring upstream of the filament connecting the main drops, rather than downstream. This inverted breakup is preferable in printing, as it increases the likelihood of satellite drops merging with the main drops. We find that this behavior can be controlled by the addition of a second harmonic to the driving signal. This model is in quantitative agreement with a full axisymmetric simulation, which incorporates nozzle geometry.

Influence of corium composition on ex-vessel steam explosion

The worst event that could happen in a nuclear power plant is a severe accident. If during such accident the corium melt comes into contact with the coolant water, a steam explosion may occur. At some stage of the accident progression, the primary system and the containment integrity of the nuclear power plant are jeopardized.In the article, the material influence of the oxide and metal corium on the ex-vessel steam explosion is investigated. The main purpose of the research work was a comparative analysis of different scenarios of steam explosion in the flooded reactor cavity. The purpose was to determine the influence of the material properties of the melt (comparison of oxide and metallic melt) and the oxidation of the metallic melt on the steam explosion strength. A PWR ex-vessel steam explosion study was carried out with the MC3D computer code. A premixing simulation and an explosion simulation were performed for each type of the corium. The explosion was triggered at the time of melt bottom contact. The global jet breakup model was used to simulate the premixing simulations.In the first part comparative calculations with oxide corium and oxide corium with prescribed thermal properties of metal corium are presented to find the isolated influence of thermal properties. The analysis of PWR ex-vessel steam explosion with oxide corium was already performed in the past (Leskovar and Uršič, 2014), but in this paper the comparative calculations with oxide corium and oxide corium with prescribed thermal properties of metal corium are presented for the first time. The purpose was to determine the differences in premixing and the steam explosion strength at simulations considering solely the different thermal properties of the oxide and metal corium.In the second part of the paper the influence of the metal corium oxidation on the ex-vessel steam explosion is presented. Due to the focusing effect the reactor vessel would most likely fail at the side and the outflow of metal corium would occur. First of all it was necessary to collect material properties of metal corium. The ex-vessel steam explosion was investigated and discussed by varying the metal corium oxidation rate. Additionally, based on experimental findings, the hydrogen film hypothesis for oxidation is presented. In this paper the calculations with properties of metal corium are presented for the first time. With the comparison of the simulation results the influence of the corium composition on the strength of the steam explosion is analysed. The simulation results revealed that with metal corium the strength of the steam explosion is in some cases higher than with oxide corium.

On the breakup of Taylor length scale size bubbles and droplets in turbulent dispersions

This work explores the mechanism of bubble and droplet breakup caused by turbulence in turbulent dispersions. Considering the deformation properties of the particle during the particle-eddy interaction process, a breakup model for bubbles and droplets of the Taylor length scale size is developed. The particle-eddy interaction frequency is modeled based on bubbles/droplets interacting with both larger and smaller eddies, in contrast with the usual collision frequency. Breakup criteria are demonstrated to depend on the degree of surface deformation prior to breakup. The relationship between the local characteristics of surrounding flows, such as the turbulent eddies’ variance and dissipation rate and the breakage rate as well as the daughter size distribution is then established and quantified. In particular, the contribution of turbulent eddies to the total breakage rate is clarified. This work provides a further understanding of breakup observations in complex turbulent fields and offers a more fundamental breakup kernel for the population balance model.

A High-Efficiency Two-Stroke Engine Concept: The Boosted Uniflow Scavenged Direct-Injection Gasoline (BUSDIG) Engine with Air Hybrid Operation

Abstract A novel two-stroke boosted uniflow scavenged direct-injection gasoline (BUSDIG) engine has been proposed and designed in order to achieve aggressive engine downsizing and down-speeding for higher engine performance and efficiency. In this paper, the design and development of the BUSDIG engine are outlined discussed and the key findings are summarized to highlight the progress of the development of the proposed two-stroke BUSDIG engine. In order to maximize the scavenging performance and produce sufficient in-cylinder flow motions for the fuel/air mixing process in the two-stroke BUSDIG engine, the engine bore/stroke ratio, intake scavenge port angles, and intake plenum design were optimized by three-dimensional (3D) computational fluid dynamics (CFD) simulations. The effects of the opening profiles of the scavenge ports and exhaust valves on controlling the scavenging process were also investigated. In order to achieve optimal in-cylinder fuel stratification, the mixture-formation processes by different injection strategies were studied by using CFD simulations with a calibrated Reitz–Diwakar breakup model. Based on the optimal design of the BUSDIG engine, one-dimensional (1D) engine simulations were performed in Ricardo WAVE. The results showed that a maximum brake thermal efficiency of 47.2% can be achieved for the two-stroke BUSDIG engine with lean combustion and water injection. A peak brake toque of 379 N·m and a peak brake power density of 112 kW·L−1 were achieved at 1600 and 4000 r·min−1, respectively, in the BUSDIG engine with the stoichiometric condition.

CST: A new semi-empirical tool for simulating spacecraft collisions in orbit

This paper provides a general description of a new Collision Simulation Tool (CST) to model the consequences of orbital impacts involving large debris and satellites, with the aim to predict fragments distributions in case of sub-catastrophic and catastrophic impacts. The new tool is being developed in the framework of the ESA contract “Numerical simulations for spacecraft catastrophic disruption analysis”, carried out by the Center of Studies and Activities for Space CISAS “G. Colombo” of the University of Padova (prime contractor) and etamax space GmbH.The CST makes possible to model a large variety of collision scenarios involving complex systems, such as entire satellites with many design details included, and provides statistically accurate results with a computational effort orders of magnitude lower than hydrocodes. To this end, the simulation approach is based on a hybrid modelling strategy, in which every colliding object is described as a gross net of Macroscopic Elements (ME) representing spacecraft elementary building blocks. On one hand, individual fragmentation of Macroscopic Elements is addressed through the use of semi-empirical breakup models applied, at element level, only to those spacecraft parts which are involved in the collision. On the other hand, structural distortion, fracture, and separation of satellite broken parts are modelled with a discrete-element approach through the simulation of momentum transfer to Macroscopic Elements through the net, taking into account energy dissipation inside elements and across links.This paper provides a description of the CST simulation methodology and framework; preliminary results are also shown with respect to the tool validation process. Validation is done by comparing the tool predictions with empirical data from ground-based impact tests on simple targets (simple plates and Whipple Shields) as well as sub-scale spacecraft models. In the first case, the tool capability of predicting fragments distributions from plates and ballistic limit equations of shields is verified. In the second case, fragments distributions calculated by the software are compared with those derived from published experiments on a micro-satellite.

Development and assessment of an improved droplet breakup model for numerical simulation of spray in a turbulent flow field

The present article proposes an improved spray breakup model considering the effect of carrier phase turbulence on both the critical Weber number and the breakup rate. For this aim, the effective surface tension as a new concept was introduced to combine the effects of turbulent and aerodynamic induced breakup. A simple analytical expression has been developed for calculating the effective surface tension according to the local turbulence characteristics of the carrier phase. Afterwards, the proposed effective surface tension was used for calculating the critical Weber number in turbulent flow fields and an excellent agreement was shown in comparison with the available experimental data. In the following, an improved secondary atomization model was developed by implementation of the effective surface tension in the classic Pilch-Erdman model. To assess the capabilities of the new breakup model, it was implemented into a CFD code and the results compared with experimental data and those obtained by the previous breakup models. The present model showed a better agreement with experimental data in predicting the spray tip penetration length and local Sauter mean diameter (SMD). It is concluded that the improved model is effectively more reliable for simulation of spray droplet breakup in turbulent gaseous environments.

Three-dimensional flow structures and droplet-gas mixing process of a liquid jet in supersonic crossflow

The mixing process of a liquid jet in supersonic crossflow with a Mach number of 2.1 was investigated numerically using large eddy simulation (LES) based on the Eulerian-Lagrangian method. The gas phase was described using the Navier-Stokes equations and the liquid phase was represented using discrete droplets, which were injected and tracked in the computational domain individually according to Newton's second law of motion. The KH (Kelvin-Helmholtz) breakup model was used to calculate the droplet stripping process, and the secondary breakup process was simulated by coupling the RT (Rayleigh-Taylor) breakup model and the TAB (Taylor Analogy Breakup) model. Two-way coupling was enforced to consider the momentum and energy exchange between the gas and the droplets. It was found that the LES predicted spray characteristics, including spray penetration and cross-sectional distribution, agree reasonably well with the experiment. The major gas flow structures such as the bow shock, the large-scale vortices, and the recirculation zones were replicated successfully in the simulations. It was found that the gas flow structures have a significant effect on the mixing process of the droplets. The simulation results revealed that two sets of counter-rotating vortex pair (CVP) exist in the gas-liquid mixing region. Under the influence of CVP, part droplets were transported to the near wall region and subsequently to both sides of the core spray region. The formation mechanism of the CVP was analyzed by comparing the pressure gradient and the source term of droplets in the Navier-Stokes equations. Differences of the mixing process of liquid jet in supersonic crossflow, gas jet in supersonic crossflow and liquid jet in incompressible crossflow were identified.

Microscopic and macroscopic atomization characteristics of a pressure-swirl atomizer, injecting a viscous fuel oil

Abstract Combustion of heavy fuels is one of the main sources of greenhouse gases, particulate emissions, ashes, NOx and SOx. Gasification is an advanced and environmentally friendly process that generates combustible and clean gas products such as hydrogen. Some entrained flow gasifiers operate with Heavy Fuel Oil (HFO) feedstock. In this application, HFO atomization is very important in determining the performance and efficiency of the gasifiers. The atomization characteristics of HFO (Mazut) discharging from a pressure-swirl atomizer (PSA) are studied for different pressures difference (Δp) and temperatures in the atmospheric ambient. The investigated parameters include atomizer mass flow rate ( m ), discharge coefficient (CD), spray cone angle (θ), breakup length (Lb), the unstable wavelength of undulations on the liquid sheet (λs), global and local SMD (sauter mean diameter) and size distribution of droplets. The characteristics of Mazut sheet breakup are deduced from the shadowgraph technique. The experiments on Mazut film breakup were compared with the predictions obtained from the liquid film breakup model. Validity of the theory for predicting maximum unstable wavelength was investigated for HFO (as a highly viscous liquid). A modification on the formulation of maximum unstable wavelength was presented for HFO. SMD decreases by getting far from the atomizer. The measurement for SMD and θ were compared with the available correlations. The comparisons of the available correlations with the measurements of SMD and θ show a good agreement for Ballester and Varde correlations, respectively. The results show that the experimental sizing data could be presented by Rosin-Rammler distributions very well at different pressure difference and temperatures.

Comparison of secondary breakup models for droplet-laden compressor flows

Different secondary breakup models are assessed to simulate gas-droplet flows that involve large velocity gradients and yield relative velocities between both phases (e.g. wet compression flows). For the simulation of such two-phase flows, the Euler-Lagrange approach is employed, using a commercial flow solver and an in-house FORTRAN source code. The droplet deformation models: Taylor Analogy Breakup (TAB) and a simplified implementation of the Non-linear TAB (NLTAB3) are each tested with two different breakup criteria to evaluate the adequacy for considered droplet-laden compressor flows. A detailed atomization model is applied to account for a temporal fragmentation process. By contrast with experimental results good agreements are found for Weber number distributions in the inter blade flow. Though, different sensitivities and locations for secondary breakup occurrence are observed in dependence of applied droplet deformation model and breakup criterion. In spite of incisive model simplifications to reduce its computational effort, the non-linear droplet deformation model (NLTAB3) in combination with a physically substantiated breakup criterion showed good agreements with qualitative experimental data.

AUSM scheme: its application to a realistic combustor configuration, the Energy Efficient Engine

Highlights of work inspired by Liou and performed in the last few years with the ultimate goal of simulating combustor–turbine interactions are presented. First, we have updated the Open National Combustion Code (OpenNCC) by implementing the advection upstream splitting method (AUSM) and the extended version of the AUSM-family scheme (AUSM$$^+$$-up) and then performed a series of verification tests. The AUSM$$^+$$-up scheme and the standard Jameson–Schmidt–Turkel scheme are compared in terms of accuracy and convergence. Next, the second-order AUSM$$^+$$-up scheme is applied to model unsteady flow fields inside a combustor sector from the Energy Efficient Engine ($${\hbox {E}}^3$$) program, in conjunction with a sensitivity analysis of turbulent combustion models. Three different turbulent combustion models are considered: the eddy break-up model, the linear eddy model, and the probability density function model, as well as the laminar finite-rate chemistry model. A comprehensive comparison of the flow fields and the flame structures is provided. Our main interest here is not to select the best model out of four different models with lack of data under the exact same conditions, but to understand how different turbulent combustion models impact thermal variation along the surface of first-stage vanes (i.e., hot streaks). Considering that these models are often used in combustor/turbine communities, the intent of this study is to provide some guidelines on numerical modeling of combustor–turbine interactions and, thus, help improve future designs of the combustor and high-pressure turbine.

An improved bubble breakup model in turbulent flow

An improved bubble breakup model has been developed by adequately describing the internal flow inside the deformed bubble, to account for the significant effect of pressure on the bubble breakup behaviors and hydrodynamics in a bubble column. In this new model, several significant conditions and experimental findings, such as static stress analysis, interfacial stress of bubble neck, viscous flow resistance, were taken into account. These issues were not considered and led to under-predictions of the bubble breakup rate in our previous model. The bubble breakup rate and daughter bubble size distribution predicted by this improved model were consistent with available experimental data. Moreover, this bubble breakup model was directly used in the CFD-PBM model to numerically simulate a bubble column operated at different pressures. A good agreement between the simulated and experimental results was obtained under complex operating conditions.

Dual mechanism model for fluid particle breakup in the entire turbulent spectrum

AbstractThis work provides an in‐depth understanding of different breakup mechanisms for fluid particles in turbulent flows. All the disruptive and cohesive stresses are considered for the entire turbulent energy spectrum and their contributions to the breakup are evaluated. A new modeling framework is presented that bridges across turbulent subranges. The model entails different mechanisms for breakup by abandoning the classical limitation of inertial models. The predictions are validated with experiments encompassing both breakup regimes for droplets stabilized by internal viscosity and interfacial tension down to the micrometer length scale, which covers both the inertial and dissipation subranges. The model performance ensures the reliability of the framework, which involves different mechanisms. It retains the breakup rate for inertial models, improves the predictions for the transition region from inertia to dissipation, and bridges seamlessly to Kolmogorov‐sized droplets.

Collision risk prediction for constellation design

INDEMN is an object-oriented program dedicated to the modeling of the evolution of the densities of space objects. Following the work achieved by D. Kessler (1978) and by other authors more recently (G. L. Somma, IAC 2016, A6-IP3; A. Rossi, DPPS 2004, 197), the dynamical model is based on a source and sink approach for various altitudes. The source terms represent the future launches, the explosion of intact spacecrafts, and the collision between objects. Different collision cross sections are used for the various types of objects and the number of debris generated is based on the NASA break-up model. The sink terms are the drag and the end-of-life de-orbitation for the satellites launched after 2009, with a controllable success rate. The code was validated against former simulations performed with statistical and semi-deterministic models. In addition to the classical object types featured in several statistical codes, which are intact objects, explosion debris, and collision debris, a new type representing the satellites of a specific constellation is included. These satellites orbit with altitudes close to 1200 km and they can perform collision avoidance maneuvers as long as they are fully operational. It is shown that, under realistic assumptions, if only one primary collision occurs at an altitude of 800 km, the probability of a collision involving a constellation satellite becomes larger than 2% by 2035, which highly jeopardizes the satellite constellation as a whole.

Coupled CFD-PBM simulation of bubble size distribution in a 2D gas-solid bubbling fluidized bed with a bubble coalescence and breakup model

A coupled model of computational fluid dynamics and population balance model (CFD-PBM) scheme was developed to simulate bubble size distribution in gas-solid bubbling fluidized beds. The bubbling gas fluidized bed was divided into a discrete bubble phase and a dense emulsion including a pseudo solids continua modeled by the kinetic theory of granular flow (KTGF). A modified bubble coalescence and breakup model was proposed and implemented in the population balance model. A pseudo bubble-emulsion drag force model was derived based on the bubble size distribution and used for simulating the gas-solid momentum exchanges between gas bubbles and the solids belong to the emulsion phase. By taking into account the effects of bubble coalescence and breakup, the coupled CFD-PBM model was capable of predicting the hydrodynamic behavior of a bubbling gas-solid fluidized bed. A benchmark simulation showed good agreements between the computation results and the literature experimental data. Particularly, the predicted time-averaged bubble local hold-up maps, bubble size distributions and their evolution agreed well with the measurement data. Grid convergence simulation results demonstrated that the present model is able to predict the major hydrodynamic behavior of a 2D bubbling fluidized bed using coarse computational grids, which makes the present model a promising tool for applications in large-scale fluidized bed reactors.

Droplet size prediction model based on the upper limit log-normal distribution function in venturi scrubber

Abstract Droplet size and distribution are important parameters determining venturi scrubber performance. In this paper, we proposed physical models for a maximum stable droplet size prediction and upper limit log-normal (ULLN) distribution parameters. For the proposed maximum stable droplet size prediction model, a Eulerian-Lagrangian framework and a Reitz-Diwakar breakup model are solved simultaneously using CFD calculations to reflect the effect of multistage breakup and droplet acceleration. Then, two ULLN distribution parameters are suggested through best fitting the previously published experimental data. Results show that the proposed approach provides better predictions of maximum stable droplet diameter and Sauter mean diameter compared to existing simple empirical correlations including Boll, Nukiyama and Tanasawa. For more practical purpose, we developed the simple, one dimensional (1-D) calculation of Sauter mean diameter.

Improved hybrid model applied to liquid jet in crossflow

Spray formation in a liquid jet in air crossflow is investigated numerically using a hybrid approach for two cases: We=11 and We=53, where We is the air Weber number. The VOF method was used to solve the interaction between the liquid jet column and the air flow up to the primary breakup. The Eulerian liquid portion is converted to discrete Lagrangian drops by the use of source terms of mass and momentum and according to empirical correlations. The effects of two secondary breakup models, as well as two-way coupling with droplet-to-droplet collisions were evaluated in this work, in order to establish an improved hybrid model suitable to solve liquid jet in crossflow at low computational cost. The results were very satisfactory relating droplet velocity and mass fraction distribution for the lower Weber number case. For the higher Weber number case, the deviation of the numerical mass fraction distribution in comparison with the experimental one was less than 14×10−2. Improvement to the droplet size distribution was observed by using a new secondary breakup model, specially for the higher Weber number case.

Revisiting and improving models for the breakup of compact dry powder agglomerates in turbulent flows within Eulerian–Lagrangian simulations

The present study is concerned with breakup models for agglomerates in turbulent flows. First, a brief literature review is provided describing the state of the art concerning the description and modeling of breakup of agglomerates with special emphasis on the role of fluid forces. That comprises turbulent and drag (inertia) stresses. Furthermore, the breakup by rotary stresses is taken into account. Based on the idea to describe these processes using first principles within an Eulerian–Lagrangian approach relying on the large-eddy simulation methodology, modeling ideas from the literature are revisited and extended in order to be applied in a four-way coupled simulation. Building on a deterministic collision and agglomeration model, the breakup process is tackled in a similar manner leading to a highly efficient procedure, which allows to track a huge number of agglomerates and particles but with the restriction to compact dry powder agglomerates. For this kind of agglomerates an enhanced evaluation of the strength is derived relying on an improved determination of the average porosities and coordination number. Furthermore, special emphasis is put on the post-breakup treatment, i.e., models for the sizes and velocities of the generated fragments. Finally, the proposed models are applied to a test case inspired by the experimental study of Weiler [1] for the deagglomeration in a dry powder disperser. The effect of the different physical mechanisms (turbulence, drag, rotation) is analyzed concerning breakup rates and resulting size distributions. Furthermore, the dominant breakup regions are identified separately. Since agglomeration processes are simultaneously taken into account, re-agglomeration of the fragments is found to play a non negligible role. Finally, the effect of the properties of the powder on the breakup and re-agglomeration processes is investigated.

Improved droplet breakup models for spray applications

The current study examines the performance of two zero-dimensional (0D) aerodynamically-induced breakup models, utilized for the prediction of droplet deformation during the breakup process in the bag, multi-mode and sheet-thinning regimes. The first model investigated is an improved version of the widely used Taylor analogy breakup (TAB) model, which compared to other models has the advantage of having an analytic solution. Following, a model based on the modified Navier–Stokes (M-NS) is examined. The parameters of both models are estimated based upon published experimental data for the bag breakup regime and CFD simulations with Diesel droplets performed as part of this work for the multi-mode and sheet-thinning regimes, for which there is a scarcity of experimental data. Both models show good accuracy in the prediction of the temporal evolution of droplet deformation in the three breakup regimes, compared to the experimental data and the CFD simulations. It is found that the best performance of the two is achieved with the M-NS model. Finally, a unified secondary breakup model is presented, which incorporates various models found in the literature, i.e. TAB, non-linear TAB (NLTAB), droplet deformation and breakup (DDB) and M-NS, into one equation using adjustable coefficients, allowing to switch among the different models.

Large Eddy Simulation-Based Turbulent Combustion Models for Reactive Sprays: Recent Advances and Future Challenges

Numerical simulations of turbulent reactive sprays are challenging owing to the presence of multiple timescales and multiphysics phenomena involving complex turbulence spray and turbulence-chemistry interactions. In turbulent spray flames, several physical phenomena such as primary and secondary atomization, droplet dispersion, interparticle collisions, evaporation, mixing, and combustion occur simultaneously, and hence it becomes a formidable task to model these complex interactions. To gain fundamental knowledge and advance current modeling capabilities, it may be appropriate to aim for progress in individual modeling of breakup, dispersion, mixing and combustion, which however cannot be viewed in complete isolation. A brief review of the development of state-of-the-art turbulent combustion models applicable to the dilute spray regime is presented. Therefore, complexities associated with the dense regime, including interparticle collisions as well as primary and secondary atomization, are not covered. Further, we restrict ourselves to a brief discussion on large eddy simulation, which has found applications in both laboratory and industrial applications of turbulent combustion without a change in phase. The gas phase-based turbulent combustion models such as flamelet, conditional moment closure and transported filtered density function methods have been developed and extensively used for combustion without a phase change. However, careful adaptation and extension of these models are necessary toward modeling of turbulent combustion with phase change. This article presents a review of recent advances and directions of future research on modeling of turbulent combustion for dilute sprays.

Breakup prediction under uncertainty: Application to upper stage controlled reentries from GTO orbit

More and more human-made space objects re-enter the atmosphere, and yet the risk for human populations remains often unknown because predicting their reentry trajectories is formidably complex. While falling back on Earth, the space object absorbs large amounts of thermal energy that affects its structural integrity. It undergoes strong aerodynamic forces and heating that lead to one or several breakups. Breakup events have a critical influence on the rest of the trajectory but are extremely challenging to predict and subject to uncertainties. In this work, we present an original model for robustly predicting the breakup of a reentering space object. This model is composed of a set of individual solvers that are coupled together such as each solver resolves a specific aspect of this multiphysics problem. This paper deals with two levels of uncertainties. The first level is the stochastic modeling of the breakup while the second level is the statistical characterization of the model input uncertainties. The framework provides robust estimates of the quantities of interest and quantitative sensitivity analysis. The objective is twofold: first to compute a robust estimate of the breakup distribution and secondly to identify the main uncertainties in the quantities of interest. Due to the significant computational cost, we use an efficient framework particularly suited to multiple solver predictions for the uncertainty quantification analysis. Then, we illustrate the breakup model for the controlled reentry of an upper stage deorbited from a Geosynchronous Transfer Orbit (GTO), which is a classical Ariane mission.