It is thus concluded that theimplementation of this model is an effective approach for overcoming the need of a pre-defined dynamic contact angle law, frequently adopted as an approximate boundary condition for such simulations. Clearly, this model is mostly influential during the spreading phase for the cases of low We number impacts (We<˜80) since for high impact velocities, inertia dominates significantly over capillary forces in the initial phase of spreading.

This paper presents CFD predictions for the evaporation of nearly spherical suspended droplets for ambient temperatures in the range 0.56 up to 1.62 of the critical fuel temperature, under atmospheric pressures. The model solves the Navier-Stokes equations along with the energy conservation equation and the species transport equations; the Volume of Fluid (VOF) methodology has been utilized to capture the liquid-gas interface using an adaptive local grid refinement technique aiming to minimize the computational cost and achieve high resolution at the liquid-gas interface region. A local evaporation rate model independent of the interface shape is further utilized by using the local vapor concentration gradient on the droplet-gas interface and assuming saturation thermodynamic conditions. The model results are compared against experimental data for suspended droplet evaporation at ambient air cross flow including single-and multi-component droplets as well as experiments for non-convective conditions. It is proved that the detailed evaporation process under atmospheric pressure conditions can be accurately predicted for the wide range of ambient temperature conditions investigated.

This is the accepted version of the paper.This version of the publication may differ from the final published version. The Navier-Stokes equations, energy and vapor transport equations coupled with the VOF 14 methodology and a vaporization rate model are numerically solved to predict aerodynamic 15 droplet breakup in a high temperature gas environment. The numerical model accounts for 16 variable properties and uses an adaptive local grid refinement technique on the gas-liquid 17 interface to enhance the accuracy of the computations. The parameters examined include Weber 18 (We) numbers in the range 15 -90 and gas phase temperatures in the range 400 -1000K for a 19 volatile n-heptane droplet. Initially isothermal flow conditions are examined in order to assess 20 the effect of Weber (We) and Reynolds (Re) number. The latter was altered by varying the gas 21 phase properties in the aforementioned temperature range. It is verified that the We number is 22 2 the controlling parameter, while the Re number affects the droplet breakup at low We number 23 conditions. The inclusion of droplet heating and evaporation mechanisms has revealed that 24 heating effects have generally a small impact on the phenomenon due to its short duration 25 except for low We number cases. Droplet deformation enhances heat transfer and droplet 26 Permanent repository linkevaporation. An improved 0-D model is proposed, able to predict the droplet heating and 27 vaporization of highly deformed droplets. 28

This is the accepted version of the paper.This version of the publication may differ from the final published version.Permanent repository link: http://openaccess.city.ac.uk/15666/ Link to published version: http://dx. AbstractThe impact of liquid droplets onto spherical stationary solid particles under isothermal conditions is simulated. The CFD model solves the Navier-Stokes equations in three dimensions and employs the Volume of Fluid Method (VOF) coupled with an adaptive local grid refinement technique able to track the liquid-gas interphase. A fast-marching algorithm suitable for the quick computation of distance functions required during the grid refinement in large 3-D computational domains is proposed. The numerical model is validated against experimental data for the case of a water droplet impact onto a spherical particle at low We number and room temperature conditions. Following that, a parametric study is undertaken examining (a) the effect of Weber number (=ρu 2 Do/σ) in the range of 8 to 80 and (b) the droplet to particle size ratio ranging in-between 0.31 and 1.24, on the impact outcome. This has resulted to the identification of two distinct regimes that form during droplet-particle collisions: the partial/full rebound and the coating regimes; the latter results to the disintegration of secondary satellite droplets from elongated expanding liquid ligaments forming behind the impinging droplet. Additionally, the temporal evolution of variables of interest, such as the maximum dimensionless liquid film thickness and the average wetting coverage of the solid particle by the liquid, have been quantified. The present study assists the understanding of the physical processes governing the impact of liquids onto solid spherical surfaces occurring in industrial applications, including fluid catalytic cracking (FCC) reactors.

1 Highlights  CFD simulation of bi-axial droplet motion in continuous air jet experiment  Comparison against detailed experimental data for droplet breakup  Capturing of droplet breakup regimes for a wide range of Weber numbers  Effect of numerical parameters in predicting droplet breakup  The gas phase recirculation affects the breakup outcome  The pressure interpolation scheme affects the predicted flow field Abstract The present work examines numerically the deformation and breakup of free falling droplets subjected to a continuous cross flow. The model is based on the solution of the Navier-Stokes equations coupled with the Volume of Fluid (VOF) methodology utilized for tracking the droplet-air interface; an adaptive local grid refinement is implemented in order to decrease the required computational cost. Neglecting initially the effect of the vertical droplet motion, a 2D axisymmetric approximation is adopted to shed light on influential numerical parameters. Following that, 3D simulations are ACCEPTED MANUSCRIPT A C C E P T E D M A N U S C R I P T 3 performed which include inertial, surface and gravitational forces. The model performance is assessed by comparing the results against published experimental data for the bag breakup and the sheet thinning breakup regimes. Furthermore, a parametric study reveals the model capabilities for a wider range of Weber numbers.It is proved that the model is capable of capturing qualitatively the breakup process, while the numerical parameters that best predict the experimental data are identified.

Citation: Malgarinos, I., Nikolopoulos, N. and Gavaises, M. (2015). Coupling a local adaptive grid refinement technique with an interface sharpening scheme for the simulation of two-phase flow and free-surface flows using VOF methodology. Journal of Computational Physics, 300, pp. 732-753. doi: 10.1016/j.jcp.2015.08.004 This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractThis study presents the implementation of an interface sharpening scheme on the basis of the Volume of Fluid (VOF) method, as well as its application in a number of theoretical and real cases usually modelled in literature. More specifically, the solution of an additional sharpening equation along with the standard VOF model equations is proposed, offering the advantage of "restraining" interface numerical diffusion, while also keeping a quite smooth induced velocity field around the interface. This sharpening equation is solved right after volume fraction advection; however a novel method for its coupling with the momentum equation has been applied in order to save computational time. The advantages of the proposed sharpening scheme lie on the facts that a) it is mass conservative thus its application does not have a negative impact on one of the most important benefits of VOF method and b) it can be used in coarser grids as now the suppression of the numerical diffusion is grid independent. The coupling of the solved equation with an adaptive local grid refinement technique is used for further decrease of computational time, while keeping high levels of accuracy at the area of maximum interest (interface).The numerical algorithm is initially tested against two theoretical benchmark cases for interface tracking methodologies followed by its validation for the case of a free-falling water droplet accelerated by gravity, as well as the normal liquid droplet impingement onto a flat substrate. Results indicate that the coupling of the interface sharpening equation with the HRIC discretization scheme used for volume fraction flux term, not only decreases the interface numerical diffusion, but also allows the induced velocity field to be less perturbed owed to spurious velocities across the liquid-gas interface. With the use of the proposed algorithmic flow path, coarser grids can replace finer ones at the slight expense of accuracy.

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractThe present paper investigates the collisions between heavy gasoil droplets and solid catalytic particles taking place at conditions realized in Fluid Catalytic Cracking reactors (FCC). The computational model utilizes the Navier-Stokes equations along with the energy conservation and transport of species equations. The VOF methodology is used in order to track the liquid-gas interface, while a dynamic local grid refinement technique is adopted, so that high accuracy is achieved with a relative low computational cost. Phase-change phenomena (evaporation of the heavy gasoil droplet), as well as catalytic cracking surface reactions are taken into account. Physical properties of heavy and light molecular weight hydrocarbons are modeled by representative single component species, while a 2-lump scheme is proposed for the catalytic cracking reactions. The numerical model is firstly validated for the case of a single liquid droplet evaporation inside a hot gaseous medium and impingement onto a flat wall for droplet heating and film boiling conditions. Afterwards, it is utilized for the prediction of single droplet-catalyst collisions inside the FCC injection zone. The numerical results indicate that droplets of similar size to the catalytic particles tend to be levitated more easily by hot catalysts, thus resulting in higher cracking reaction rates/cracking product yield, and limited possibility for liquid pore blocking. For larger sized droplets, the corresponding results indicate that the production of cracking products is not favored, while solid-liquid contact increases. Hotter catalysts promote catalytic cracking reactions and droplet levitation over the catalytic particle, owed to the formation of a thin vapour layer between the liquid and the solid particle.