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The paper is devoted to the analysis of a supersonic nozzle system effect in gas-cooled lances on the technological parameters of slag splashing in an oxygen converter. Simulation calculations were carried out, taking into account the parameters of nozzles used in the technological lines of converter steel plants in Ukraine and Brazil. The problems were solved in several stages. The simulation results of the first stage revealed the influence of different nozzle diameters dcr, dex and the inlet pressure before nozzle P0 on the nitrogen consumption of one nozzle Vн. Calculations also showed the influence of the critical dcr and output dex of the nozzle diameter and nitrogen flow through one nozzle Vн on the power of injected nitrogen N1 and the depth of penetration of the stream hx into the liquid slag. The second stage was dedicated to numerical simulation of the slag splashing process, including an array of results from the first stage. The thermodynamic and physical parameters were calculated using our own computer program, while 3D simulations were conducted using the ANSYS Fluent 2023 R2 program.

The interaction of droplets with a liquid film plays a central role in numerous scientific and engineering processes. While most existing studies have focused on spherical droplets, it is important to note that droplets can exhibit both spherical and nonspherical shapes at the moment of impact. This study numerically investigates the dynamics of nonspherical droplet impacts on a thin liquid layer, aiming to reveal the unique behaviors and phenomena arising from shape asymmetry. The results show that impact behaviors vary considerably with droplet shape (prolate, spherical, and oblate), even under identical impact conditions. Due to its flattened geometry, an oblate droplet expands more radially, making it more susceptible to splashing and secondary droplet formation. By contrast, a prolate droplet, with its elongated profile, distributes impact energy differently, suppresses lateral spreading, and exhibits greater resistance to splashing. Droplet shape also strongly influences crown geometry, particularly the upper external crown diameter. Notably, the difference in crown diameter between prolate and oblate droplets can reach 12%–15%. In addition, the complex dynamics of air entrapment and bubble bursting are examined in detail. The findings indicate that bubble bursting occurs earlier for prolate droplets than for oblate ones.

When a drop impacts a dry surface at high velocity, it atomises into secondary droplets. These small droplets are generated by one of two types of splashes: either by a prompt splash from the spreading rim at the surface or by a thin corona splash, which levitates from the surface. This study investigates the splashing mechanisms experimentally using multiple high-resolution cameras and characterises the outcome of both splashing types at high Weber and Reynolds numbers. We demonstrate that the prompt splash is well described by the Rayleigh–Taylor instability of the rapidly advancing liquid lamella and determine the boundaries defining this splashing regime, which allows us to distinguish the prompt from the corona splash. Furthermore, we provide an expression to estimate the elapsed time during which the secondary droplets are generated, which is then implemented in the theory of Riboux & Gordillo ( Phys. Rev. Lett. , vol. 113 (2), 2014, 024507). This theoretical approach together with detailed quantification of the splashing outcome allows us to completely predict the outcome of both splashing types, which includes the mean size, velocity and total ejected volume of the secondary droplets. The detailed model proposed here can be indeed used to understand, characterise and predict more accurately the underlying physics in several applications.

Here, we present experimental results of water and ethanol drops of radii $R$, density $\\rho$ and interfacial tension coefficient $\\sigma$, impacting with a velocity $V$ over different types of sandpapers containing particles of characteristic diameter $\\varepsilon$ embedded in their surfaces. It is shown that the transition from spreading to splashing at normal atmospheric conditions can be classified depending on the value of the parameter $\\varepsilon /H_t\\simeq We_\\varepsilon =We(\\varepsilon /R)$, with $We=\\rho V^2 R/\\sigma$ the Weber number and $H_t$ indicating the initial thickness of the thin film – the lamella – which is ejected along the substrate once the drop touches the solid. When $We_\\varepsilon \\lesssim 1$ and the liquid wets the substrate, the critical value of the Weber number above which the drop splashes, $We_c$, can be predicted using the results in Gordillo & Riboux (J. Fluid Mech., vol. 871, 2019, R3) once the angle the advancing rim forms with the substrate, $\\alpha$, is expressed as a decreasing function of the static advancing contact angle. The calculated values of $We_c$ for the case of water drops impacting over rough substrates are smaller than the corresponding ones for smooth substrates, in agreement with experimental observations. Moreover, if the liquid does not wet the substrate, it is also shown that the splash velocity can be predicted using the theory for superhydrophobic substrates in Quintero, Riboux & Gordillo (J. Fluid Mech., vol. 870, 2019, 175–188). For those cases in which $We_\\varepsilon \\gtrsim 1$ and the liquid wets the substrate, we demonstrate that the critical Weber number for splashing decreases with $\\varepsilon$ as $We_c\\propto (R\\cos \\theta _0 /\\varepsilon )^{3/5}$, with $\\theta _0$ the value of the Young contact angle.

The innovative slag splashing technology can significantly reduce CO 2 emissions in the steel industry. However, conventional oxygen lances are no longer sufficient due to the gas-slag reactions involved. Hence, the feasibility of applying nozzle-twisted oxygen lances to the innovative slag splashing process was investigated in this work. Numerical simulation was employed to compare the CO 2 jet, its impact characteristics on the slag, and the slag splashing performance of both the nozzle-twisted and conventional oxygen lances. It was found that the nozzle-twisted jet has higher radial and tangential velocities and a more significant impact region compared with the conventional jet. Furthermore, it exhibited superior stirring capability for the melt pool, enhancing the average velocity of the slag and reducing the size of dead zones. This facilitated the mixing of carbon powder and the interfacial reaction between CO 2 and the slag. However, the slag splashing performance deteriorated after the oxygen lance was replaced. Fortunately, the slag still reached the vicinity of the slag line. Furthermore, the addition of bottom blowing compensated for the disadvantages, elevating the slag mass flow rate and further enhancing the stirring of the slag. Therefore, utilizing nozzle-twisted oxygen lances is feasible in this scenario. Graphical Abstract

We experimentally determine the phase diagram for impacting ethanol droplets on a smooth, sapphire surface in the parameter space of Weber number $\\mathit{We}$ versus surface temperature $T$ . We observe two transitions, namely the one towards splashing (disintegration of the droplet) with increasing $\\mathit{We}$ , and the one towards the Leidenfrost state (no contact between the droplet and the plate due to a lasting vapour film) with increasing $T$ . Consequently, there are four regimes: contact and no splashing (deposition regime), contact and splashing (contact–splash regime), neither contact nor splashing (bounce regime), and finally no contact, but splashing (film–splash regime). While the transition temperature $T_{L}$ to the Leidenfrost state depends weakly, at most, on $\\mathit{We}$ in the parameter regime of the present study, the transition Weber number $\\mathit{We}_{C}$ towards splashing shows a strong dependence on $T$ and a discontinuity at $T_{L}$ . We quantitatively explain the splashing transition for $T

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