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In the current study, an Immersed Boundary Method for simulating cavitating flows with complex or moving boundaries is presented, which follows the discrete direct forcing approach. Although the Immersed Boundary Methods are widely used in various applications of single phase, multiphase and particulate flows, either incompressible or compressible, and numerous alternative formulations exist, to the best of the authors' knowledge, a handful of computational works employ such methodologies on cavitating flows. The herein proposed method, following the works of the author's group1,2,3, tries to fill this gap and to solidify the development of a computational tool of a simple formulation capable to tackle complex numerical problems of cavitation modelling. The method aims to be used in a wide range of applications of industrial interest and treat flows of engineering scales. Therefore, a validation of the method is performed by numerous benchmark test-cases, of progressively increasing complexity, from incompressible low Reynolds number to compressible and highly turbulent cavitating flows.

The present work describes a numerical methodology and its experimental validation of the flow development inside and outside of the orifices during a pilot injection, dwelt time and the subsequent start of injection cycle. The compressible Navier-Stokes equations are numerically solved in a six-hole injector imposing realistic conditions of the needle valve movement and considering in addition a time-dependent eccentric motion. The valve motion is simulated using the immersed boundary method; this allows for simulations to be performed at zero lift during the dwelt time between successive injections, where the needle remains closed. Moreover, the numerical model utilises a fully compressible two-phase (liquid, vapour) two-component (fuel, air) barotropic model. The air’s motion is simulated with an additional transport equation coupled with the VOF interface capturing method able to resolve the near-nozzle atomisation and the resulting impact of the injected liquid on the oleophilic nozzle wall surfaces. The eccentric needle motion is found to be responsible for the formation of strong swirling flows inside the orifices, which not only contributes to the breakup of the injected liquid jet into ligaments but also to their backwards motion towards the external wall surface of the injector. Model predictions suggest that such nozzle wall wetting phenomena are more pronounced during the closing period of the valve and the re-opening of the nozzle, due to the residual gases trapped inside the nozzle, and which contribute to the poor atomisation of the injected fluid upon re-opening of the needle valve in subsequent injection events.

This work investigates the effect of liquid fuel viscosity, as specific by the European Committee for Standardization 2009 (European Norm) for all automotive fuels, on the predicted cavitating flow in micro-orifice flows. The wide range of viscosities allowed leads to a significant variation in orifice nominal Reynolds numbers for the same pressure drop across the orifice. This in turn, is found to affect flow detachment and the formation of large-scale vortices and microscale turbulence. A pressure-based compressible solver is used on the filtered Navier-Stokes equations using the multifluid approach; separate velocity fields are solved for each phase, which share a common pressure. The rates of evaporation and condensation are evaluated with a simplified model based on the Rayleigh-Plesset equation; the coherent structure model is adopted for the subgrid scale modeling in the momentum conservation equation. The test case simulated is a well-reported benchmark throttled flow channel geometry, referred to as "I-channel"; this has allowed for easy optical access for which flow visualization and laser-induced fluorescence measurements allowed for validation of the developed methodology. Despite its simplicity, the I-channel geometry is found to reproduce the most characteristic flow features prevailing in high-speed flows realized in cavitating fuel injectors. Subsequently, the effect of liquid viscosity on integral mass flow, velocity profiles, vapor cavity distribution, and pressure peaks indicating locations prone to cavitation erosion is reported.

In this work, a Rolling-Ball Viscometer/Densimeter is used to measure high-pressure, hightemperature (HPHT) density and viscosity data from 298.2 to 532.6 K and pressures up to 300.0 MPa for three different diesel fuels. The densities and viscosities have combined expanded uncertainties of 0.6% and 2.5%, respectively, with a coverage factor, k = 2. Two of the diesels, Highly Paraffinic (HPF) and Highly Aromatic (HAR), contain a larger paraffinic and aromatic content relative to the others, and are standard engine test fuels. The third is a Ultra-Low Sulfur Diesel (ULSD) that resembles an unfinished commercial diesel. Detailed compositional information is also reported for each diesel that provides a basis for interpreting the impact of composition on density and viscosity at high pressures. Both density and viscosity data are correlated to Tait-type equations with uncertainties of 0.6% and 4.0%, respectively. The Tait\ud equations provide a facile means to compare observed differences in the density-pressure and viscosity-pressure profiles of the three different diesels. Density data are modeled with the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS) with pure component parameters calculated representing diesel as a single, pseudo-component only requiring average molecular weight (Mave) and hydrogen to carbon ratio (RH/C) as inputs. Viscosity data are modeled reasonably well using entropy scaling coupled with the PC-SAFT EoS and\ud information on the diesel Mave and RH/C. The HPHT viscosity data are also modeled reasonably well with Free Volume Theory (FVT) with model parameters correlated to Mave and RH/C.

The two-phase flow of liquid oxygen in a converging-diverging nozzle has been numerically predicted at conditions resembling those that prevail in the lower-stage boosters of rocket engines realising lift off, as well as in the respective upper stages operating in sub-atmospheric pressures. A comparative evaluation of the predictive capability of a pressure and a density-based solver with various approaches regarding the imposed phase-change rate and thermodynamics closure have been performed. The departure from thermodynamic equilibrium during phase-change has been taken into account via implementation of a bubble-dynamics model employing the Hertz-Knudsen equation in the pressure based solver, whereas thermodynamic equilibrium is adopted in the density-based solver. Tabulated data for the variation of the fluid thermodynamic properties have been derived by the Helmholtz Equation of State (EoS) in a modelling approach universal for both the sub- and supercritical states. This approach has been comparatively assessed in the sub-critical regime against the bubble-dynamics-based model including different EoS for the liquid/vapour phases and against a different tabulated approach based on the NIST dataset for supercritical injection. In terms of flow physics, more severe flow expansion in the diverging part of the nozzle has been detected for subcritical pressures, leading to supersonic flow velocities and significant cooling of the fluid mixture. Complementary Detached Eddy Simulations (DES) have provided detailed insight on the complex expansion phenomena and flow instabilities manifesting on the divergent part of the nozzle for subcritical-injection conditions. The comparison of the numerical predictions against available experimental data and analytical solutions demonstrates the suitability of the employed methodologies in describing the evolution of the cryogenic oxygen flow expansion and phase-change.

This paper presents a three-phase fully compressible model applied along with an immersed boundary model for predicting cavitation occurring in a two dimensional gear pump in the presence of non-condensable gas (NCG). Combination of these models is capable of overcoming numerical challenges such as modelling the contact between the gears and simulating the effect of NCG in cavitation. The model accounting for the effect of NCG also has broader applicability, since gas dissolved in liquids can come out of the solution when exposed to low pressures; this plays a significant role in the pump performance and cavitation erosion. Here the simulation results are presented for the gear pump at different operating conditions including the contact between gear, gear RPM and % of NCG; their effects on performance and cavitation is demonstrated. The results suggest that modelling the contact between the gears play a role in the cavitation prediction inside the gear pump. An increase in cavitation is observed when the contact is modelled even for the small pressure difference considered between the inlet and outlet. An increase in the RPM of the gears also results in increased cavitation within the pump, whereas an increase in the percentage of NCG content by a small amount can reduce the cavitation to a greater extent. This reduction is due to the expansion of the gas at a lower pressure which recovers the pressure and prevents or delays the phase-change process of the working fluid. The fluctuations in the outflow rate is also found to increase when the gears are in contact and also with increasing gas content.

High-flux synchrotron radiation has been employed in a time-resolved manner to characterize the distinct topology features and dynamics of different cavitation regimes arising in a throttle orifice with an abrupt flow-entry contraction. Radiographs obtained though both x-ray phase-contrast and absorption imaging have been captured at 67 890 frames per second. The flow lies in the turbulent regime (Re = 35 500), while moderate (CN = 2.0) to well-established (CN = 6.0) cavitation conditions were examined encompassing the cloud and vortical cavitation regimes with pertinent transient features, such as cloud-cavity shedding. X-ray phase-contrast imaging, exploiting the shift in the x-ray wave phase during interactions with matter, offers sharp-refractive index gradients in the interface region. Hence, it is suitable for capturing fine morphological fluctuations of transient cavitation structures. Nevertheless, the technique cannot provide information on the quantity of vapor within the orifice. Such data have been obtained utilizing absorption imaging, where beam attenuation is not associated with scattering and refraction events, and hence can be explicitly correlated with the projected vapor thickness in line-of-sight measurements. A combination of the two methods is proposed as it has been found that it is capable of quantifying the vapor content arising in the complex nozzle flow while also faithfully illustrating the dynamics of the highly transient cavitation features.

The atomization mechanism of the gas-liquid multiphase flow through an internally mixing twin-fluid Y-jet atomizer has been studied by examining both the internal and external flow patterns. Superheated steam and light fuel oil (LFO) are used as working fluids. The flow is numerically modeled using the compressible Navier-Stokes equations; the hybrid large eddy simulation approach through wall-modeled large eddy simulations (WMLES) is used to resolve the turbulence with the large eddy simulations, whereas the Prandtl mixing length model is used for modeling the subgrid-scale structures, which are affected by operational parameters. A volume-of-fluid to discrete phase model (VOF-to-DPM) transition mechanism is utilized along with dynamic solution-adaptive mesh refinement to predict the initial development and fragmentation of the gas-liquid interface through VOF formulations on a sufficiently fine mesh, while DPM is used to predict the dispersed part of the spray on the coarser grid. Two operational parameters, namely, gas-to-liquid mass flow rate ratio (GLR) and liquid-to-gas momentum ratio, are compared; the latter is found to be an appropriate operational parameter to describe both the internal flow and atomization characteristics. It is confirmed that the variation in the flow patterns within the mixing port of the atomizer coincides with the variation of the spatial distribution of the spray drops.

Abstract A high-speed flow visualisation set-up comprising of combined diffuse backlight illumination (DBI) and schlieren imaging has been developed to illustrate the highly transient, two-phase flow arising in a real-size optical fuel injector. The different illumination nature of the two techniques, diffuse and parallel light respectively, allows for the capturing of refractive-index gradients due to the presence of both interfaces and density gradients within the orifice. Hence, the onset of cavitation and secondary-flow motion within the sac and injector hole can be concurrently visualised. Experiments were conducted utilising a diesel injector fitted with a single-hole transparent tip (ECN spray D) at injection pressures of 700–900 bar and ambient pressures in the range of 1–20 bar. High-speed DBI images obtained at 100,000 fps revealed that the orifice, due to its tapered layout, is mildly cavitating with relatively constant cavity sheets arising mainly in regions of manufacturing imperfections. Nevertheless, schlieren images obtained at the same frame rate demonstrated that a multitude of vortices with short lifetimes arise at different scales in the sac and nozzle regions during the entire duration of the injection cycle but the vortices do not necessarily result in phase change. The magnitude and exact location of coherent vortical structures have a measurable influence on the dynamics of the spray emerging downstream the injector outlet, leading to distinct differences in the variation of its cone angle depending on the injection and ambient pressures examined. Graphic abstract

A methodology for modelling cavitating flows using a high-order Adaptive Mesh Refinement (AMR) approach based on the Discontinuous Galerkin method (DG) is presented. The AMR implementation used features on-the-fly adaptive mesh refinement for unstructured hybrid meshes. The specific implementation has been developed for the resolution of complex multi-scale phenomena where high accuracy p-adaptive discretisations are combined with an h-adaptive data structure. This approach accommodates the fine spatial resolution for the interface discontinuities and the shock waves observed in compressible cavitating flows. The Tait equation of state is used for the modelling of the liquid phase while an isentropic path is assumed for the liquid/vapour mixture. Second order spatial and a third order non-oscillatory temporal discretisation are used for the integration of the mass and momentum conservation equations, in order to resolve the flow structures responsible for the formation of cavitation bubbles and the resulting compression waves. Assessment of the developed methodology is performed for the one-dimensional advancement of a compressible liquid-vapour interface and the symmetric collapse of a spherical vapour bubble. Following, results obtained with the developed multi-scale modelling AMR approach has revealed a complex bubble collapse mechanism near a rigid wall, providing evidence of processes that have been unknown before due to reduced resolution and dissipative nature of past simulations. The impinging jet accompanying the collapse of a bubble near a wall, was found to induce vortical structures, which result to the formation of a secondary cavitation of a wall-attached bubble at the vicinity of the impingement jet shear layer. At the final stages of the initial bubble collapse, the impinging jet was found to penetrate the centre-line of the wall bubble inducing its partial collapse. This secondary collapse results to a rich spatial structure of shock waves, interacting with the secondary bubbles. Moreover, the calculated pressure level are found to be much higher than those reported from previous methodologies.

A numerical methodology resolving flow complexities arising from the coexistence of both multiscale processes and flow regimes is presented. The methodology employs the compressible Navier-Stokes equations of two interpenetrating fluid media using the two-fluid formulation; this allows for compressibility and slip velocity effects to be considered. On-the-fly criteria switching between a sharp and a diffuse interface within the Eulerian-Eulerian framework along with dynamic interface sharpening is developed, based on an advanced local flow topology detection algorithm. The sharp interface regimes with dimensions larger than the grid size are resolved using the VOF method. For the dispersed flow regime, the methodology incorporates an additional transport equation for the surface-mass fraction (Σ-ϒ) for estimating the interface surface area between the two phases. To depict the advantages of the proposed multiscale two-fluid approach, a high-speed water droplet impact case has been examined and evaluated against new experimental data; these refer to a millimetre size droplet impacting a solid dry smooth surface at a velocity as high as 150 m/s, which corresponds to a Weber number of 7.6 × 10 5 . Droplet splashing is followed by the formation of highly dispersed secondary cloud of droplets, with sizes ranging from 10 μm close to the wall to less than 1 μm forming at the later stages of droplet fragmentation. Additionally, under the investigated impact conditions, compressibility effects dominate the early stages of droplet splashing. A strong shock wave forms and propagates inside the droplet, where transonic Mach numbers occur; local Mach numbers up to 2.5 are observed for the expelled surrounding gas outside the droplet. Relative velocities between the two fluids are also significant; local values on the tip of the injected water film up to 5 times higher than the initial impact velocity are observed. The proposed numerical approach is found to capture relatively accurately the flow phenomena and provide additional information regarding the produced flow structure dimensions, which is not available from the experiment.

Cavitating flow dynamics are investigated in an axisymmetric converging–diverging Venturi nozzle. Computational Fluid Dynamics (CFD) results are compared with those from previous experiments. New analysis performed on the quantitative results from both datasets reveals a coherent trend and shows that the simulations and experiments agree well. The CFD results have confirmed the interpretation of the high-speed images of the Venturi flow, which indicated that there are two vapor shedding mechanisms that exist under different running conditions: re-entrant jet and condensation shock. Moreover, they provide further details of the flow mechanisms that cannot be extracted from the experiments. For the first time with this cavitating Venturi nozzle, the re-entrant jet shedding mechanism is reliably achieved in CFD simulations. The condensation shock shedding mechanism is also confirmed, and details of the process are presented. These CFD results compare well with the experimental shadowgraphs, space–time plots, and time-averaged reconstructed computed tomography slices of vapor fraction.

The impact of liquid droplets on solid surfaces at conditions inducing cavitation inside their volume has rarely been addressed in the literature. A review is conducted on relevant studies, aiming to highlight the differences from non-cavitating impact cases. Focus is placed on the numerical models suitable for the simulation of droplet impact at such conditions. Further insight is given from the development of a purpose-built compressible two-phase flow solver that incorporates a phase-change model suitable for cavitation formation and collapse; thermodynamic closure is based on a barotropic Equation of State (EoS) representing the density and speed of sound of the co-existing liquid, gas and vapour phases as well as liquid-vapour mixture. To overcome the known problem of spurious oscillations occurring at the phase boundaries due to the rapid change in the acoustic impedance, a new hybrid numerical flux discretization scheme is proposed, based on approximate Riemann solvers; this is found to offer numerical stability and has allowed for simulations of cavitation formation during drop impact to be presented for the first time. Following a thorough justification of the validity of the model assumptions adopted for the cases of interest, numerical simulations are firstly compared against the Riemann problem, for which the exact solution has been derived for two materials with the same velocity and pressure fields. The model is validated against the single experimental data set available in the literature for a 2-D planar drop impact case. The results are found in good agreement against these data that depict the evolution of both the shock wave generated upon impact and the rarefaction waves, which are also captured reasonably well. Moreover, the location of cavitation formation inside the drop and the areas of possible erosion sites that may develop on the solid surface, are also well captured by the model. Following model validation, numerical experiments have examined the effect of impact conditions on the process, utilizing both planar and 2-D axisymmetric simulations. It is found that the absence of air between the drop and the wall at the initial configuration can generate cavitation regimes closer to the wall surface, which significantly increase the pressures induced on the solid wall surface, even for much lower impact velocities. A summary highlighting the open questions still remaining on the subject is given at the end.

The effect of viscoelastic additives on the topology and dynamics of the two-phase flow arising within an axisymmetric orifice with a flow path constriction along its main axis has been investigated employing high-flux synchrotron radiation. X-ray Phase Contrast Imaging (XPCI) has been conducted to visualise the cavitating flow of different types of diesel fuel within the orifice. An additised blend containing Quaternary Ammonium Salt (QAS) additives with a concentration of 500 ppm has been comparatively examined against a pure (base) diesel compound. A high-flux, 12 keV X-ray beam has been utilised to obtain time resolved radiographs depicting the vapour extent within the orifice from two views (side and top) with reference to its main axis. Different test cases have been examined for both fuel types and for a range of flow conditions characterised by Reynolds number of 35500 and cavitation numbers (CN) lying in the range 3.0–7.7. It has been established that the behaviour of viscoelastic micelles in the regions of shear flow is not consistent depending on the cavitation regimes encountered. Namely, viscoelastic effects enhance vortical (string) cavitation, whereas hinder cloud cavitation. Furthermore, the use of additised fuel has been demonstrated to suppress the level of turbulence within the orifice.

Viscous oils flowing in the geometrically-complex hydraulic circuits of earth-moving machines are associated with extensive friction losses, thus reducing the fuel efficiency of the vehicles and increasing emissions. The present investigation examines the performance effectiveness of different hydraulic oils, in terms of secondary-flow suppression and pressure-drop reduction. The flow of two non-Newtonian oil compounds, containing poly(alkylmethacrylate) (PMA) and poly(ethylene-co-propylene) (OCP) polymers, respectively, have been comparatively investigated against a base, monograde liquid through Particle Image Velocimetry. An 180° curved-tube layout and a check-valve replica have been selected as representative examples of the hydraulic components comprising the hydraulic circuit. The flow conditions prevailing in the experimental cases are characterized by Reynolds-number values in the range 76–1385. Precursor viscosity measurements with shear rate along with a theoretical analysis conducted using the FENE and PTT models have verified the influence of viscoelasticity and/or shear-thinning on the liquid flow behavior. PIV results have demonstrated that viscoelastic effects setting in due to the OCP additives tend to reduce the magnitude of the secondary flow pattern, commonly known as a Dean-vortex system, arising in the curved geometry by as much as 15% on average compared to the base liquid. A similar flow behavior was also demonstrated in the valve replica layout with reference to the geometry-induced coherent vortical motion in the constriction region, where a vorticity decrease up to 38% was observed for the OCP sample. On the contrary, the flow behavior of the primarily shear-thinning PMA oil was found to be comparable to that of the base oil, hence not presenting significant flow-enhancement characteristics.

In this work, we report high-pressure, high-temperature (HPHT) mixture density and T-p isopleth (bubble (BP) and dew (DP) point) data for hexadecane (HXD) + N2 and heptamethylnonane (HMN) + N2 mixtures from ~323 to 523 K and pressures to ~100 MPa. Isothermal, mixture density data for both mixtures are measured in the single–phase region from the BP pressure to ~135 MPa and with ~14–90 mol% N2. A HPHT variable-volume, windowed view cell is used for both density and phase behavior measurements using the synthetic method. Mixture densities are correlated with the modified Tait equation and isothermal BP/DP data are correlated with an Antoine-type equation to allow for reliable interpolation of the data sets. Mixture densities and BP/DP pressures are modeled with the PC-SAFT equation coupled with pure component parameters calculated with two different group contribution methods. Although fairly reasonable predictions of liquid mixture densities are obtained when the binary interaction parameter, kij, is set to zero for both HXD + N2 and HMN + N2 mixtures, a value of kij equal to at least 0.119 is needed for both systems to obtain reasonable predictions of isothermal p-x behavior.

The determination of the critical Weg number separating the different breakup regimes has been extensively studied in several experimental and numerical works, while empirical and semi-analytical approaches have been proposed to relate the critical Weg number with the Ohl number. Nevertheless, under certain conditions, the Reg number and the density ratio ε may become important. The present work provides a simple but reliable enough methodology to determine the critical Weg number as a function of the aforementioned parameters in an effort to fill this gap in knowledge. It considers the main forces acting on the droplet (aerodynamic, surface tension and viscous) and provides a general criterion for breakup to occur but also for the transition among the different breakup regimes. In this light, the present work proposes the introduction of a new set of parameters named as Weg,eff and Cal monitored in a new breakup plane. This plane provides a direct relation between gas inertia and liquid viscosity forces, while the secondary effects of Reg number and density ratio have been embedded inside the effective Weg number (Weg,eff)

The head-to-head impact of diesel-fuel droplets on a polished spherical brass target has been investigated experimentally. High-speed imaging was employed to visualize the impact process for wall surface temperatures and Weber and Reynolds numbers in the ranges of 140-340 °C, 30-850, and 210-1135, respectively. The thermohydrodynamic outcome regimes occurring for the aforementioned ranges of parameters were mapped on a We-T diagram. Seven clearly distinguishable postimpact outcome regimes were identified, which are conventionally called the coating, splash, rebound, breakup-rebound, splash-breakup-coating, breakup-coating, and splash-breakup-rebound regimes. In addition, the effects of the Weber number and surface temperature on the wettability dynamics were examined; the temporal variations of the dynamic contact angle, dimensionless spreading diameter, and liquid film thickness forming on the solid particle were measured and are reported.

A numerical study is presented, evaluating in a comparative manner the capability of various mass-transfer rate models to predict the evolution of flashing flow in various geometrical configurations. The examined models comprise phase-change mechanisms based on the kinetic theory of gases (Hertz–Knudsen equation), thermodynamic-equilibrium conditions (HEM), bubble-dynamics considerations using the Zwart-Gerber-Belamri model (ZGB), as well as semi-empirical correlations calibrated specifically for flash boiling (HRM). Benchmark geometrical layouts, i.e a converging-diverging nozzle, an abruptly contracting (throttle) nozzle and a highly-pressurized pipe, for which experimental data are available in the literature have been employed for the validation of the numerical predictions. Consideration on additional aspects associated with phase-change processes, such as the distribution of activated nucleation sites, as well as the deviation from thermodynamic-equilibrium conditions have also been taken into account. The numerical results have demonstrated that the onset of flashing flow in all cases is associated with the occurrence of compressible flow phenomena, such as flow choking at the constriction location and expansion downstream, accompanied by the formation of shockwaves. Phase-change models based on the kinetic theory of gases produced more accurate predictions for all the cases investigated, while the validity of the HRM and ZGB models was found to be situational. Furthermore, it has been established that the inter-dependence between intrinsic physical factors associated with flash boiling, such as the nucleation-site density and the phase-change rate, has a significant, yet not clearly distinguishable influence on the two-phase flow characteristics.

The development and collapse of cloud cavitation and its link to surface erosion within a transparent test single-orifice nozzle operating with a closed Diesel fuel hydraulic circuit, has been characterized using high-speed imaging. Data have been obtained for a range of cavitation and Reynolds numbers under fixed lift positions. Post processing of a large number of images acquired with short exposure time (1 μs) allowed the elucidation of the distinct flow phenomena associated with the highly transient two-phase flow. At the inlet of the flow orifice, the vapour cloud was found to occupy the largest part of the nozzle hole cross-section. Coherent vortical structures of a hairpin shape have been detected to onset at the closure region of this vapour cloud and shed downstream in a fully transient manner. The effect of the operating parameters on the temporal and spatial characteristics with regards to the emergence and collapse of the hairpin vortices has been quantified. It has been established that the cavitation-vortex shedding was taking place in a periodical manner, characterized by a Strouhal number.

This study 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, coupled with a dynamic local grid refinement technique in order to minimize the computational cost. Phase-change phenomena, as well as catalytic cracking surface reactions (2-lump scheme) are taken into account. In this paper, the numerical model is extended to investigate the droplet-particle collision process in three dimensions. In order to save computational resources, only half of the droplet is investigated, by imposing symmetry conditions. Firstly, single droplet-catalyst collisions are simulated and compared against the corresponding ones provided by 2D axisymmetric simulations and afterwards, the model is applied for the characterization of the collision dynamics between a single droplet and a particle cluster, i.e. a realistic 3D particle configuration. As the droplet flows through the space between the catalytic particles, important phenomena are observed, such as a) drop levitation due to the formed vapour layer and b) a thin liquid sheet formation, both of which affect the rate of gasoline production, as well as predictions for liquid pore blocking mechanism; a phenomenon frequently observed industrially. Results indicate that gasoline production decreases when the collision target is a particle cluster, instead of same number (as many as in the cluster) single catalysts, as the corresponding contact area decreases.

The aerodynamic droplet breakup under the influence of heating and evaporation is studied numerically by solving the Navier-Stokes, energy and transport of species conservation equations; the VOF methodology is utilized in order to capture the liquid-air interphase. The conditions examined refer to an n-decane droplet with Weber numbers in the range 15–90 and gas phase temperatures in the range 600–1000 K at atmospheric pressure. To assess the effect of heating, the same cases are also examined under isothermal conditions and assuming constant physical properties of the liquid and surrounding air. Under non-isothermal conditions, the surface tension coefficient decreases due to the droplet heat-up and promotes breakup. This is more evident for the cases of lower Weber number and higher gas phase temperature. The present results are also compared against previously published ones for a more volatile n-heptane droplet and reveal that fuels with a lower volatility are more prone to breakup. A 0-D model accounting for the temporal variation of the heat/mass transfer numbers is proposed, able to predict with sufficient accuracy the thermal behavior of the deformed droplet.

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.

The present work investigates the formation and development of cavitation of a multicomponent Diesel fuel surrogate discharging from a high-pressure fuel injector operating in the range of injection pressures from 60MPa to 450MPa. The compressible form of the Navier-Stokes equations is numerically solved with a density-based solver employing the homogeneous mixture model for accounting the presence of liquid and vapour phases, while turbulence is resolved using a Large Eddy Simulation approximation. Simulations are performed on a tapered heavy-duty Diesel engine injector at a nominal fully-open needle valve lift of 350 μ m. To account for the effect of extreme fuel pressurisation, two approaches have been followed: (i) a barotropic evolution of density as function of pressure, where thermal effects are not considered and (ii) the inclusion of wall friction-induced and pressurisation thermal effects by solving the energy conservation equation. The PC-SAFT equation of state is utilised to derive thermodynamic property tables for an eight-component surrogate based on a grade no.2 Diesel emissions-certification fuel as function of pressure, temperature, and fuel vapour volume fraction. Moreover, the preferential cavitation of the fuel components within the injector's hole is predicted by Vapour-Liquid Equilibrium calculations; lighter fuel components are found to cavitate to a greater extent than heavier ones. Results indicate a significant increase of temperature with increasing pressures due to friction-induced heating, leading to a significant increase in the mean vapour pressure of the fuel and an increase of the mass of fuel cavitating, but at the same time to an unprecedented decrease of cavitation volume inside the fuel injector with increasing injection pressure. This has been attributed to the shift of the pressure drop from the feed to the back pressure inside the injection hole orifice as fuel discharges; as injection pressure increases, so does the pressure inside the orifice, confining the location of cavitation formation to a smaller volume attached to the upper part of orifice, thus restricting cavitation growth.

Immiscible heavy fuel-water (W/HFO) emulsion droplets inside combustion chambers are subjected to explosive boiling and fragmentation due to the different boiling point between the water and the surrounding host fuel. These processes, termed as either puffing or micro-explosion, are investigated with the aid of a CFD model that solves the Navier-Stokes and energy conservation equations alongside with three sets of VoF transport equations resolving the formed interfaces. The model is applied in 2-D axisymmetric configuration and it is valid up to the time instant of HFO droplet initiation of disintegration, referred to as breakup time. Model predictions are obtained for a wide range of pressure, temperature, water droplet surface depth and Weber number; these are then used to calibrate the parameters of a fitting model estimating the initiation breakup time of the W/HFO droplet emulsion with a single embedded water droplet. The model assumes that the breakup time can be split in two distinct temporal stages. The first one is defined by the time needed for the embedded water droplet to heat up and reach a predefined superheat temperature and a vapor bubble to form; while the succeeding stage accounts for the time period of vapor bubble growth, leading eventually to emulsion droplet break up. It is found that the fitting parameters are ±10% accurate in the examined range of We

The 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 interface. 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 (= ρu2Do/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 particle. 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.

The present paper focuses on erosion development due to cavitation inside Diesel injectors. Two similar injector designs are discussed both in terms of numerical simulation and experimental results from X-ray CT scans. In order to capture the complex flow field and cavitation structures forming in the injector, Large Eddy Simulation along with a two phase homogenous mixture model were employed and compressibility of the liquid was included as well. During the simulation, pressure peaks have been found in areas of vapour collapse, with magnitude beyond 4000 bar, which is higher than the yield stress of common materials employed in the manufacturing of such injectors. The locations of such pressure peaks correspond well with the actual erosion locations as found from X-ray scans. The present work is the first to correlate pressure peaks due to vapour collapse with erosion development in industrial injectors with moving needle including comparison with experiments.

A creative low-cost and compact mechanical device that mimics the rapid closure of the pistol shrimp claw was used to conduct electrochemical experiments, in order to study the effects of hydrodynamic cavitation on the corrosion of aluminum and steel samples. Current–time curves show significant changes associated with local variations in dissolved O2 concentration, cavitation-induced erosion, and changes in the nature of the surface corrosion products.

The present work examines the aerodynamic breakup of four liquid droplets in tandem formation at Diesel engine conditions using the Volume of Fluid (VOF) method. The examined Weber (We) numbers range from 15 up to 64 and the non-dimensional distances between the droplet centres (L/D0) vary from 1.25 up to 20. Focus is given on the breakup process of the third droplet of the row, which is regarded as a “representative chain droplet”; its development is compared against that of an isolated droplet at the same flow conditions. It is found that for small distances and depending on the We number, the obtained shapes and breakup modes between the droplets are different, with the representative chain droplet experiencing a new breakup mode in the multi-mode regime, termed as “shuttlecock”. This is characterized by an oblique peripheral stretching of the droplet caused by the acting of pressure forces at an off-centre region. Moreover, the drag coefficient and liquid surface area of the representative chain droplet are lower than the corresponding ones of the isolated droplet, while the breakup initiation time is longer and the minimum We number required for breakup (critical We) is higher; correlations are provided to quantify the effect of droplet distance on the aforementioned quantities. Generally, the droplet proximity becomes important for L/D0 Finally, the predicted drag coefficient is utilised in a simplified 0-D model that is capable of estimating the temporal evolution of droplet velocity of the representative chain droplet. &nbsp

The impact of a laser pulse onto a liquid metal droplet is numerically investigated by utilising a weakly compressible single phase model; the thermodynamic closure is achieved by the Tait equation of state (EoS) for the liquid metal. The smoothed particle hydrodynamics (SPH) method, which has been employed in the arbitrary Lagrangian Eulerian (ALE) framework, offers numerical efficiency, compared to grid related discretization methods. The latter would require modelling not only of the liquid metal phase, but also of the vacuum, which would necessitate special numerical schemes, suitable for high density ratios. In addition, SPH-ALE allows for the easy deformation handling of the droplet, compared to interface tracking methods where strong mesh deformation and most likely degenerate cells occur. Then, the laser-induced deformation of the droplet is simulated and cavitation formation is predicted. The ablation pattern due to the emitted shock wave and the two low pressure lobes created in the middle of the droplet because of the rarefaction waves are demonstrated. The liquid metal droplet is subject to material rupture, when the shock wave, the rarefaction wave and the free surface interact. Similar patterns regarding the wave dynamics and the hollow structure have been also noticed in prior experimental studies.

The aim of this paper is to present a fully compressible three-phase (liquid, vapour and air) model and its application to the simulation of in-nozzle cavitation effects on liquid atomization. The model employs a combination of homogeneous equilibrium barotropic cavitation model with an implicit sharp interface capturing VoF approximation. The numerical predictions are validated against the experimental results obtained for injection of water into the air from a step-nozzle, which is designed to produce asymmetric cavitation along its two sides. Simulations are performed for three injection pressures, corresponding to three different cavitation regimes, referred to as cavitation inception, developing cavitation and hydraulic-flip. Model validation is achieved by qualitative comparison of the cavitation, spray pattern and spray cone angles. The flow turbulence in this study is resolved using the Large Eddy Simulation approach. The simulation results indicate that the major parameters that influence the primary atomization are cavitation, liquid turbulence and, to a smaller extent, the Rayleigh-Taylor and Kelvin-Helmholtz aerodynamic instabilities developing on the liquid/air interface. Moreover, the simulations performed indicate that periodic entrainment of air into the nozzle occurs at intermediate cavitation numbers, corresponding to developing cavitation (as opposed to incipient and fully-developed cavitation regimes); this transient effect causes a periodic shedding of the cavitation and air clouds and contributes to improved primary atomization. Finally, the cone angle of the spray is found to increase with increased injection pressure but drops drastically when hydraulic-flip occurs, in agreement with the relevant experiments.

The present paper focuses on the simulation of the growth and collapse of a bubble in the vicinity of a wall. Both liquid and gas phases are assumed compressible, and their interaction is handled with the volume-of-fluid method. The main interest is to quantify the influence of the induced shear stress and pressure pulse in the vicinity of the wall for a variety of bubble sizes and bubble–wall distances. The results are validated against prior experimental results, such as the measurements of the bubble size, induced pressure field, and shear stress on the wall. The simulation predictions indicate that the wall in the vicinity of the bubble is subjected both to high shear stresses and large pressure pulses because of the growth and collapse of the bubble. In fact, pressure levels of 100 bar or more and shear stresses up to 25 kPa have been found at localized spots on the wall surface, at the region around the bubble. Moreover, the simulations are capable of providing additional insight to the experimental investigation, as the inherent limitations of the latter are avoided. The present work may be considered as a preliminary investigation in optimizing bubble energy and wall generation distance for ultrasound cleaning applications.

A numerical framework for modelling micro-scale multiphase flows with sharp interfaces has been developed. The suggested methodology is targeting the efficient and yet rigorous simulation of complex interface motion at capillary dominated flows (low capillary number). Such flows are encountered in various configurations ranging from micro-devices to naturally occurring porous media. The methodology uses as a basis the Volume-of-Fluid (VoF) method combined with additional sharpening smoothing and filtering algorithms for the interface capturing. These algorithms help the minimisation of the parasitic currents present in flow simulations, when viscous forces and surface tension dominate inertial forces, like in porous media. The framework is implemented within a finite volume code (OpenFOAM) using a limited Multidimensional Universal Limiter with Explicit Solution (MULES) implicit formulation, which allows larger time steps at low capillary numbers to be utilised. In addition, an adaptive interface compression scheme is introduced for the first time in order to allow for a dynamic estimation of the compressive velocity only at the areas of interest and thus has the advantage of avoiding the use of a-priori defined parameters. The adaptive method is found to increase the numerical accuracy and to reduce the sensitivity of the methodology to tuning parameters. The accuracy and stability of the proposed model is verified against five different benchmark test cases. Moreover, numerical results are compared against analytical solutions as well as available experimental data, which reveal improved solutions relative to the standard VoF solver.

The collapse of a cavitation bubble near a rigid boundary induces a high-speed transient jet accelerating liquid onto the boundary. The shear flow produced by this event has many applications, examples of which are surface cleaning, cell membrane poration and enhanced cooling. Yet the magnitude and spatio-temporal distribution of the wall shear stress are not well understood, neither experimentally nor by simulations. Here we solve the flow in the boundary layer using an axisymmetric compressible volume-of-fluid solver from the OpenFOAM framework and discuss the resulting wall shear stress generated for a non-dimensional distance, $\unicode[STIX]{x1D6FE}=1.0$ ($\unicode[STIX]{x1D6FE}=h/R_{max}$, where $h$ is the distance of the initial bubble centre to the boundary, and $R_{max}$ is the maximum spherical equivalent radius of the bubble). The calculation of the wall shear stress is found to be reliable once the flow region with constant shear rate in the boundary layer is determined. Very high wall shear stresses of 100 kPa are found during the early spreading of the jet, followed by complex flows composed of annular stagnation rings and secondary vortices. Although the simulated bubble dynamics agrees very well with experiments, we obtain only qualitative agreement with experiments due to inherent experimental challenges.

The present paper describes a numerical framework to simulate transcritical and supercritical flows utilising the compressible form of the Navier–Stokes equations coupled with the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS); both conservative and quasi-conservative formulations have been tested. This molecular model is an alternative to cubic EoS which show low accuracy computing the thermodynamic properties of hydrocarbons at temperatures typical for high pressure injection systems. Liquid density, compressibility, speed of sound, vapour pressures and density derivatives are calculated with more precision when compared to cubic EoS. Advection test cases and shock tube problems are included to show the overall performance of the developed framework employing both formulations. Additionally, two-dimensional simulations of nitrogen and dodecane jets are presented to demonstrate the multidimensional capability of the developed model.

A numerical framework has been developed to simulate supercritical Diesel injection using a compressible density-based solver of the Navier-Stokes equations along with the conservative formulation of the energy equation. Multi-component fuel-air mixing is simulated by considering a diffused interface approximation. The thermodynamic properties are predicted using the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) real-fluid equation of state (EoS). This molecular-based EoS requires three empirically determined but well-known parameters to model the properties of a specific component, and thus, there is no need for extensive model calibration, as is typically the case when the NIST library is utilised. Moreover, PC-SAFT can handle flexibly the thermodynamic properties of multi-component mixtures, which is an advantage compared to the NIST library, where only limited component combinations are supported. This has allowed for the properties of Diesel fuel to be modelled as surrogates comprising four, five, eight and nine components. The proposed numerical approach improves the overall computational time and overcomes the previously observed spurious pressure oscillations associated with the utilization of conservative schemes. In the absence of experimental data, advection test cases and shock tube problems are included to validate the developed framework. Finally, two-dimensional simulations of planar jets of n-dodecane and a four component Diesel surrogate are included to demonstrate the capability of the developed methodology to predict supercritical Diesel fuel mixing into air.

The present work examines numerically the aerodynamic breakup of Diesel and heavy fuel oil (HFO) droplets in ambient pressures ranging from atmospheric up to those encountered in Diesel engines. The numerical model solves the Navier-Stokes equations coupled with the Volume of Fluid (VOF) methodology along with an adaptive local grid refinement technique to enhance the resolution near the high deformable interface. Simulations are performed both in 2D axisymmetric and 3D computational domains. The capabilities of the model are evaluated by comparing its results against published experimental data for Diesel fuel droplets at small Ohnesorge numbers (OhWe) numbers ranging from 14 up to 264, and liquid to air density ratios (ε) from 79 up to 695. These conditions correspond to the bag, multimode and sheet-thinning breakup regimes. Following model validation for Diesel droplets, the breakup mechanism of HFO droplets is investigated for the same range of We numbers, two relatively large Oh numbers (0.96 and 1.53) and two density ratios (30 and 72); these conditions are representative for Diesel engines operating with HFO. The simulations reveal the effect of Oh number and density ratio on the breakup mode, drop deformation, liquid surface area and drag coefficient. Finally, a correlation is proposed for the prediction of the breakup initiation time as function of the non-dimensional numbers We, Re, ε and Oh.

Snapping shrimps use a special shaped claw to generate a cavitating high speed water jet. Cavitation formed in this way, may be used for hunting/stunning prey and communication. The present work is a novel computational effort to provide insight on the mechanisms of cavitation formation during the claw closure. The geometry of the claw used here is a simplified claw model, based on prior experimental work. Techniques, such as Immersed Boundary and Homogenous Equilibrium Model (HEM), are employed to describe the claw motion and cavitating flow field respectively. The simulation methodology has been validated against prior experimental work and is applied here for claw closure at realistic conditions. Simulations show that during claw closure, a high velocity jet forms, inducing vortex roll-up around it. If the closure speed is high enough, the intensity of the swirling motion is enough to produce strong depressurization in the vortex core, leading to the formation of a cavitation ring. The cavitation ring moves along the jet axis and, soon after its formation, collapses and rebounds, producing high pressure pulses.

[EN] Abstract The present study investigates numerically the aerodynamic breakup of Diesel droplets for a wide range of ambient pressures encountered in engineering applications relevant to oil burners and internal combustion engines. The numerical model solves the Navier-Stokes equations coupled with the Volume of Fluid (VOF) methodology utilized for capturing the interface between the liquid and the surrounding gas. An adaptive local grid refinement technique is used to increase the accuracy of the numerical results around the interface. The Weber (We) numbers examined are in the range of 14 to 279 which correspond to bag, multimode and sheet-thinning breakup regimes. Model results are initially compared against published experimental data and show a good agreement in predicting the drop deformation and the different breakup modes. The predicted breakup initiation times for all cases lie within the theoretical limits given by empirical correlations based on the We number. Following the model validation, the effect of density ratio on the breakup process is examined by varying the gas density (or equivalently the ambient pressure), while the We number is kept almost constant equal to 270; ambient gas pressure varies from 1 up to 146bar and the corresponding density ratios (ε) range from 700 down to 5. Results indicate that the predicted breakup mode of sheet-thinning remains unchanged for changing the density ratio. Useful information about the instantaneous drag coefficient (Cd) and surface area as functions of the selected non-dimensional time is given. It is shown that the density ratio is affecting the drag coefficient, in agreement with previous numerical studies., Financial support from the MSCA-ITN-ETN of the European Union’s H2020 programme, under REA grant agreement n. 675676 is acknowledged.

The operation of a high-pressure, piston-plunger fuel pump oriented for use in the common rail circuit of modern diesel engines for providing fuel to the injectors is investigated in this study from a numerical perspective. Both the suction and pressurization phases of the pump stroke were simulated with the overall flow time being in the order of 12 × 10−3 s. The topology of the cavitating flow within the pump configuration was captured through the use of an equation of state implemented in the framework of a barotropic, homogeneous equilibrium model. Cavitation was found to set in within the pressure chamber as early as 0.2 × 10−3 s in the operating cycle, while the minimum liquid volume fraction detected was in the order of 60% during the second period of the valve opening. Increase in the in-cylinder pressure during the final stages of the pumping stroke leads to the collapse of the previously arisen cavitation structures and three layout locations, namely, the piston edge, the valve and valve-seat region and the outlet orifice, were identified as vulnerable to cavitation-induced erosion through the use of cavitation aggressiveness indicators.

Experiments and numerical simulations of cavitating flow inside a single-orifice nozzle are presented. The orifice is part of a closed flow circuit, with diesel fuel as the working fluid, designed to replicate the main flow pattern observed in high-pressure diesel injector nozzles. The focus of the present investigation is on cavitation structures appearing inside the orifice, their interaction with turbulence and the induced material erosion. Experimental investigations include high-speed shadowgraphy visualization, X-ray micro-computed tomography (micro-CT) of time-averaged volumetric cavitation distribution inside the orifice as well as pressure and flow rate measurements. The highly transient flow features that are taking place, such as cavity shedding, collapse and vortex cavitation (also known as ‘string cavitation’), have become evident from high-speed images. Additionally, micro-CT enabled the reconstruction of the orifice surface, which provided locations of cavitation erosion sites developed after sufficient operation time. The measurements are used to validate the presented numerical model, which is based on the numerical solution of the Navier–Stokes equation, taking into account compressibility of both the liquid and liquid–vapour mixture. Phase change is accounted for with a newly developed mass transfer rate model, capable of accurately predicting the collapse of vaporous structures. Turbulence is modelled using detached eddy simulation and unsteady features such as cavitating vortices and cavity shedding are observed and discussed. The numerical results show agreement within validation uncertainty with the obtained measurements.

The aim of this article is to assess the impact of turbulence and cavitation models on the prediction of diesel injector nozzle flow. Two nozzles are examined, an enlarged one, operating at incipient cavitation, and an industrial injector tip, operating at developed cavitation. The turbulence model employed includes the re-normalization group k–ε, realizable k–ε and k–ω shear stress transport Reynolds-averaged Navier–Stokes models; linear pressure–strain Reynolds stress model and the wall adapting local eddy viscosity large eddy simulation model. The results indicate that all Reynolds-averaged Navier–Stokes and the Reynolds stress turbulence models have failed to predict cavitation inception due to their limitation to resolve adequately the low pressure existing inside vortex cores, which is responsible for cavitation development in this particular flow configuration. Moreover, Reynolds-averaged Navier–Stokes models failed to predict unsteady cavitation phenomena in the industrial injector. However, the wall adapting local eddy viscosity large eddy simulation model was able to predict incipient and developed cavitation, while also capturing the shear layer instability, vortex shedding and cavitating vortex formation. Furthermore, the performance of two cavitation methodologies is discussed within the large eddy simulation framework. In particular, a barotropic model and a mixture model based on the asymptotic Rayleigh–Plesset equation of bubble dynamics have been tested. The results indicate that although the solved equations and phase change formulation are different in these models, the predicted cavitation and flow field were very similar at incipient cavitation conditions. At developed cavitation conditions, standard cavitation models may predict unrealistically high liquid tension, so modifications may be essential. It is also concluded that accurate turbulence representation is crucial for cavitation in nozzle flows.

The 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 modelled 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.

[EN] The present investigation illustrates the temporally-resolved, phase-contrast visualization of the cavitating flow within an enlarged injector replica conducted at the ANL Advanced Photon Source. The flow was captured through side-view, x-ray radiographies at 67890 frames per second with an exposure time of 347ns. The orifice employed for the experiments has an internal diameter of 1.5mm and length equal to 5mm. A parametric investigation was conducted considering various combinations of the Reynolds and cavitation numbers, which designate the extent of in-nozzle cavitation. Proper post-processing of the obtained radiographies enabled the extraction of information regarding the shape and dynamical behaviour of cavitating strings. The average string extent along with its standard deviation was calculated for the entire range of conditions examined (Re=18000-36000, CN=1.6-7.7). Furthermore, the effect of the prevailing flow conditions on quantities indicative of the string dynamic behaviour such as the breakup frequency and lifetime was characterized and the local velocity field in the string region was obtained., The research leading to these results has received funding from the MSCA-ITN-ETN of the EU H2020 programme, under REA grant agreement n. 642536. This research used resources of the Advanced Photon Source, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) by Argonne National Laboratory under Contract No. 53697.

[EN] A numerical framework has been developed to simulate the mixing of supercritical and transcritical fluids using an equation of state based on statistical associating fluid theory. In a Diesel engine the liquid fuel is injected into supercritical air. After the injection, the Diesel is heated over its critical temperature reaching a supercritical state. Modelling real-fluid effects is critical in order to properly characterize the air/fuel mixing in the combustion chamber. By using the PC-SAFT EoS (Perturbed Chain Statistical Association Fluid Theory Equation of State) real fluids effects can be taken into account in a CFD simulation. The PC-SAFT EoS shows best results than cubic EoS computing liquid density, compressibility, speed of sound, vapor pressures and density derivatives. Unlike cubic EoS, this model accounts for the shape and size of the molecules. Gas, liquid, supercritical and vapor-liquid equilibrium states can be simulated. PT FLASH (Isothermal Multiphase Flash Calculation) is applied to compute the phase diagram used by the code. Shock tube problems were conducted in a wide range of pressures and densities using n-dodecane to show the capability of the developed algorithm. The results were compared with the solution of an exact Riemann solver which has the PC-SAFT EoS implemented showing a high degree of agreement. In addition, a two-dimensional simulation of supercritical nitrogen jet mixing was carried out to check the multidimensional capability of the code., This project has received funding from the European Union Horizon 2020 Research and Innovation programme. Grant Agreement No 675528

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.

The formation of a liquid jet into air induced by the growth of a laser-generated bubble inside a needle-free device is numerically investigated by employing the compressible Navier–Stokes equations. The three co-existing phases (liquid, vapour and air) are assumed to be in thermal equilibrium. A transport equation for the gas mass fraction is solved in order to simulate the non-condensable gas. The homogeneous equilibrium model is used in order to account for the phase change process between liquid and vapour. Thermodynamic closure for all three phases is achieved by a barotropic Equation of State. Two-dimensional axisymmetric simulations are performed for a needle-free device for which experimental data are available and used for the validation of the developed model. The influence of the initial bubble pressure and the meniscus geometry on the jet velocity is examined by two different sets of studies. Based on the latter, a new meniscus design similar to shaped-charge jets is proposed, which offers a more focused and higher velocity jet compared to the conventional shape of the hemispherical gas–liquid interface. Preliminary calculations show that the developed jet can penetrate the skin and thus, such configurations can contribute towards a new needle-free design.

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 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.

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

The present paper focuses on the numerical simulation of the interaction of laser-generated bubbles with a free surface, including comparison of the results with instances from high-speed videos of the experiment. The Volume Of Fluid method was employed for tracking liquid and gas phases while compressibility effects were introduced with appropriate equations of state for each phase. Initial conditions of the bubble pressure were estimated through the traditional Rayleigh Plesset equation. The simulated bubble expands in a non-spherically symmetric way due to the interference of the free surface, obtaining an oval shape at the maximum size. During collapse, a jet with mushroom cap is formed at the axis of symmetry with the same direction as the gravity vector, which splits the initial bubble to an agglomeration of toroidal structures. Overall, the simulation results are in agreement with the experimental images, both quantitatively and qualitatively, while pressure waves are predicted both during the expansion and the collapse of the bubble. Minor discrepancies in the jet velocity and collapse rate are found and are attributed to the thermodynamic closure of the gas inside the bubble. Published by AIP Publishing.