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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.

The consequences of geometry alterations in a diesel injector caused by cavitation erosion are investigated with numerical simulations. The differences in the results between the nominal design geometry and the eroded one are analyzed for the internal injector flow and spray formation. The flow in the injector is modeled with a three-phase Eulerian approach using a compressible pressure-based multiphase flow solver. Cavitation is simulated with a nonequilibrium mass transfer rate model based on the simplified form of the Rayleigh–Plesset equation. Slip velocity between the liquid-vapor mixture and air is included in the model by solving two separate momentum conservation equations. The eroded injector is found to result in a loss in the rate of injection but also lower cavitation volume fraction inside the nozzle. The injected sprays are then simulated with a Lagrangian method considering as initial conditions the predicted flow characteristics at the exit of the nozzle. The results obtained show wider spray dispersion for the eroded injector and shorter spray tip penetration.

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.

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

Accurate wall-shear stress (WSS) in-vitro measurements within complex geometries such as the human aortic arch under pulsatile flow are still difficult to achieve, meanwhile such data are important for classifying impacts of prosthetic valves on aortic walls. Micro-cantilever beams can serve to sense the WSS in such flows for applications in in-vitro flow tester. However, within pulsatile flows and complex 3D curved geometries such as the aortic arch, the flexible sensor structures are subject to oscillating boundary layer thickness and profile shape, which may not have been taken into account in the calibration procedure. The fluid–structure interaction is sensitive to these changes, thus reflecting also the flow-induced deflection of the sensor tip which is actually the sensing signal. We develop herein a methodology for in-situ calibration of the response of the sensors directly in the complex geometry of the aortic arch, assisted by reference data from numerical simulations of the flow under the same boundary conditions. For this procedure, a quick exchange of the heart valve in the tester with a tubular insert is done to provide a smooth contour in the curved aorta model. Arrays of 500 μ m long micro-pillar WSS sensors in the aorta model are calibrated under physiological pulsatile flow and used then for mapping the WSS evolution in the arch induced by two different heart valve, showing their difference of impact. The developed methodology completes the in-house built in-vitro flow tester with a reliable WSS measurement technique and provides a unique hydrodynamic testing facility for heart valve prostheses and their impact on the WSS distal along the aortic walls.

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.

Understanding of plume direction and mixture quality in a combustion chamber is crucial to improve engine performance. While a variety of diagnostics using laser and x-ray facilities have been applied to identify plume direction, most applications require sophisticated experimental setup as well as troubleshooting for light attenuation or scattering issues. In this study, we acquire temporally and spatially resolved liquid volume fraction by three-dimensional tomographic reconstruction of ensemble-averaged extinction images to produce unique information on plume movement and growth in the midst of a multi-plume spray. Measurements were carried out in a constant-flow spray vessel coupled with high-speed Mie-scattering, diffused back-illumination extinction, and schlieren imaging. Four different fuels, a single component iso-octane, a multi-component surrogate with di-isobutylene, a multi-component fuel with olefinic molecular structure, and a 70% standardized gasoline 30% ethanol (e30) blend were injected using Engine Combustion Network (ECN) Spray G injector under ECN G2 (50 kPa absolute), G3 (100 kPa absolute), and G3HT (G3 with 393 K ambient temperature) conditions. Planar slices, available from the tomographically reconstructed extinction data, confirmed greater plume-to-plume interaction for the flash-boiling G2 iso-octane condition with an approximately 6° smaller plume direction angle relative to the injector axis, compared to the nozzle drill angle. The olefinic and e30 fuels, which have broader distillation curves, exhibited stronger plume growth and eventual complete spray plume collapse and longer time for evaporation. Using the 3D dataset, we show that factors that increase plume growth also create more interaction between plumes to ultimately reduce the plume direction angle.

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.

Spray and air–fuel mixing in gasoline direct-injection (GDI) engines play a crucial role in combustion and emission characteristics. While a variety of phenomenological spray models and computational fluid dynamics (CFD) simulations have been applied to identify air–fuel mixture distribution, most research efforts so far were concentrated on single axial-nozzle injectors and limited range of ambient conditions. Especially, the prediction of flash-boiling sprays in multi-hole injectors remains a great challenge due to the lack of understanding of the complicated two-phase flow dynamics. For the specific conditions, the question can arise concerning the capability of machine-learning algorithms to predict complex flash-boiling sprays. We developed a machine-learning algorithm, as a simple variant of linear regression, that is capable of predicting the spray 3D topology for various fuels and ambient conditions. A series of spray experiments were carried out in a constant-flow spray vessel coupled with high-speed diffused back-illumination extinction imaging to produce a data set for algorithm training. Nine different test fuels, including single component iso-octane (ic8) and multi-component EEE gasoline, that cover a wide range of fuel properties were injected using Engine Combustion Network (ECN) Spray G injector under ECN G2 (50 kPa absolute), G3 (100 kPa absolute), and G3HT (G3 with 393 K ambient temperature) conditions. Among the test fuels, ic8ib2 (ic8 80%, iso-butanol 20% v/v) and EEE gasoline were specified as target fuels for spray prediction by the machine-learning algorithm, thus they were not included in the training data. The macroscopic spray analysis based on projected liquid volume (PLV) and computed tomographic (CT) reconstruction showed that the spray prediction by the machine-learning algorithm showed excellent agreement with true values from the experimental data. The maximum differences in liquid penetration for ic8ib2 and EEE fuel were 3.6 mm (7.3% error) and 1.3 mm (2.32% error), respectively. The 3D spray predicted had a consistent trend to experimental data showing slight plume movement for ic8ib2 but complete spray collapsing for EEE gasoline fuel. The plume direction angle enabled by the CT data showed differences up to 2° compared to true values during the injection period. The quantitative validation results showed that the machine-learning algorithm is capable of predicting spray performance with nine input features (fuel properties and ambient conditions), and is actually superior to CFD performance for these same number of spray parameters.

Internally mixing twin-fluid Y-jet atomizers are widely used in coal fired thermal power plants for start-up, oil-fired thermal power plants and industrial boilers. The flow through internally mixing Y-jet atomizers is numerically modeled using the compressible Navier-Stokes equations; Wall Modeled Large Eddy Simulations (WMLES) is used to resolve the turbulence with Large Eddy Simulations whereas the Prandtl Mixing Length Model is used for modeling the subgrid scale structures, which are affected by geometric and operational parameters. Moreover, the Volume-of-Fluid (VOF) method is used to capture the development and fragmentation of the liquid-gas interface within the Y-jet atomizer. The numerical results are compared with correlations available in open literature for the pressure drop; further results are presented for the multiphase flow regime maps available for vertical pipes. The results show that the mixing point pressure is strongly dependent on the mixing port diameter to airport diameter ratio, specifically for gas to liquid mass flowrate ratio (GLR) in the range 0.1 < GLR < 0.4; the mixing port length moderately affects the mixing point pressure while the angle between mixing and liquid ports is found not to have an appreciable effect. Moreover, it is found that the vertical pipe multiphase flow regime maps in the literature could be applied to the flow through the mixing port of the twin-fluid Y-jet atomizer. The main flow regimes found under the studied operational conditions are annular and wispy annular flow.

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.

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.

The Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) has been coupled with Vapor-Liquid Equilibrium (VLE) calculations in a density-based solver of the Navier-Stokes equations to perform multicomponent two-phase simulations of Diesel injections at high-pressure conditions. 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 (REFPROP) library is utilised. PC-SAFT can handle flexibly the thermodynamic properties of multi-component mixtures for which the NIST (REFPROP) library supports only limited component combinations. Moreover, complex hydrocarbon mixtures can be modelled as a single pseudo-component knowing its number averaged molecular weight (MW) and hydrogen-to-carbon (HN/CN) ratio. Published molecular dynamic simulations have been utilised to demonstrate that the developed algorithm properly captures the VLE interface at high-pressure conditions. Several advection test cases and shock tube problems were performed to validate the numerical framework using analytical and exact solutions. Additionally, two-dimensional simulations of n-dodecane and Diesel injections into nitrogen are included to demonstrate the multidimensional, multispecies and multiphase capability of the numerical framework.

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.

We identify the physical mechanism through which newly developed quaternary ammonium salt (QAS) deposit control additives (DCAs) affect the rheological properties of cavitating turbulent flows, resulting in an increase in the volumetric efficiency of clean injectors fuelled with diesel or biodiesel fuels. Quaternary ammonium surfactants with appropriate counterions can be very effective in reducing the turbulent drag in aqueous solutions, however, less is known about the effect of such surfactants in oil-based solvents or in cavitating flow conditions. Small-angle neutron scattering (SANS) investigations show that in traditional DCA fuel compositions only reverse spherical micelles form, whereas reverse cylindrical micelles are detected by blending the fuel with the QAS additive. Moreover, experiments utilising X-ray micro computed tomography (micro-CT) in nozzle replicas, quantify that in cavitation regions the liquid fraction is increased in the presence of the QAS additive. Furthermore, high-flux X-ray phase contrast imaging (XPCI) measurements identify a flow stabilization effect in the region of vortex cavitation by the QAS additive. The effect of the formation of cylindrical micelles is reproduced with computational fluid dynamics (CFD) simulations by including viscoelastic characteristics for the flow. It is demonstrated that viscoelasticity can reduce turbulence and suppress cavitation, and subsequently increase the injector’s volumetric efficiency.

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.

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.

The present investigation, identifies the exact quantitative effects of fundamental parameters, on the detachment characteristics of isolated bubbles, emanating quasi-statically from submerged orifices into isothermal liquid pools. For this purpose, a Volume of Fluid (VOF) based interface capturing approach is further improved, for the conduction of axisymmetric and 3D numerical experiments on adiabatic bubble growth dynamics. The predictions of the model, are quantitatively validated against literature available experimental data, showing excellent agreement. Two series of numerical experiments are performed, quantitatively exploring the parametric effects of the liquid phase properties in five different gravity levels, and the effect of the gravity vector direction inclination angle, respectively. It is found that the bubble detachment characteristics, are more sensitive in the variation of the surface tension, liquid phase density and gravity, while the effect of liquid phase dynamic viscosity is generally minimal. From dimensionless analysis, two correlations are derived, which for the examined range of Eötvos numbers, are able to predict the equivalent bubble detachment diameter and the bubble detachment time, respectively. It is also found that the bubble detachment characteristics, reduce significantly as the gravity vector direction gradually deviates from being parallel to the bubble injection orifice, following a non-linear decrease.

The tendency of today’s fuel injection systems to reach injection pressures up to 3000 bar in order to meet forthcoming emission regulations may significantly increase liquid temperatures due to friction heating; this paper identifies numerically the importance of fuel pressurization, phase-change due to cavitation, wall heat transfer and needle valve motion on the fluid heating induced in high pressure Diesel fuel injectors. These parameters affect the nozzle discharge coefficient (Cd), fuel exit temperature, cavitation volume fraction and temperature distribution within the nozzle. Variable fuel properties, being a function of the local pressure and temperature are found necessary in order to simulate accurately the effects of depressurization and heating induced by friction forces. Comparison of CFD predictions against a 0-D thermodynamic model, indicates that although the mean exit temperature increase relative to the initial fuel temperature is proportional to (1 − Cd2) at fixed needle positions, it can significantly deviate from this value when the motion of the needle valve, controlling the opening and closing of the injection process, is taken into consideration. Increasing the inlet pressure from 2000 bar, which is the pressure utilized in today’s fuel systems to 3000 bar, results to significantly increased fluid temperatures above the boiling point of the Diesel fuel components and therefore regions of potential heterogeneous fuel boiling are identified.

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.

[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

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 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.

This paper discusses the implementation of an explicit density-based solver, that utilises the central-upwind schemes for the simulation of cavitating bubble dynamic flows. It is highlighted that, in conjunction with the Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) scheme they are of second order in spatial accuracy; essentially they are high-order extensions of the Lax–Friedrichs method and are linked to the Harten Lax and van Leer (HLL) solver family. Basic comparison with the predicted wave pattern of the central-upwind schemes is performed with the exact solution of the Riemann problem, for an equation of state used in cavitating flows, showing excellent agreement. Next, the solver is used to predict a fundamental bubble dynamics case, the Rayleigh collapse, in which results are in accordance to theory. Then several different bubble configurations were tested. The methodology is able to handle the large pressure and density ratios appearing in cavitating flows, giving similar predictions in the evolution of the bubble shape, as the reference.

The paper proposes a methodology within the Reynolds averaged Navier Stokes (RANS) solvers for cavitating flows capable of predicting the flow regions of bubble collapse and the potential aggressiveness to material damage. An aggressiveness index is introduced, called cavitation aggressiveness index (CAI) based on the total derivative of pressure which identifies surface areas exposed to bubble collapses, the index is tested in two known cases documented in the open literature and seems to identify regions of potential cavitation damage.

This paper discusses the implementation of an explicit density-based solver, based on the central-upwind schemes originally suggested by Kurganov, for the simulation of cavitating bubble dynamic flows. Explicit density based solvers are suited for highly dynamic, violent flows, involving large density ratios, as is rather common in cavitating flows. Moreover, the central-upwind schemes have the advantage of avoiding direct evaluation of the Jacobian matrix or estimation of the wave pattern emerging from Euler equations. Second order accuracy can be achieved with TVD MUSCL schemes. Basic comparison with the predicted wave pattern of the central-upwind schemes is performed with the exact solution of the Riemann problem showing an excellent agreement. Then several different bubble configurations were tested, similar to the work of Lauer et al. (2012). The central-upwind schemes prove to be able to handle the large pressure and density ratios appearing in cavitating flows, giving similar predictions in the evolution of the bubble shape.

In the current paper, indicative results of the flow simulation during the opening phase of a Diesel injector are presented. In order to capture the complex flow field and cavitation structures forming in the injector, Large Eddy Simulation has been employed, whereas compressibility of the liquid was included. For taking into account cavitation effects, a two phase homogenous mixture model was employed. The mass transfer rate of the mixture model was adjusted to limit as much as possible the occurrence of negative pressures. During the simulation, pressure peaks have been found in areas of vapour collapse, with magnitude beyond 4000bar, which is higher that the yield stress of common materials. The locations of such pressure peaks corresponds well with the actual erosion location as found from X ray scans.

This paper aims to compare the results of two commonly used methods for the simulation of cavitating flows; one is the two phase mass transfer approach and the other is a homogenous equilibrium model. Both methodologies are compared in a shock tube and a throttle flow, which resembles the constrictions in Diesel injector passages. The mass transfer rate in the two phase model plays the fundamental role in affecting how close to equilibrium the model is; by increasing the mass transfer the two phase model comes close to the homogenous equilibrium model.

Visualisation and Large Eddy Simulations (LES) of cavitation inside the apparatus previously developed by Franc (2011) for surface erosion acceleration tests and material response monitoring are presented. The experimental flow configuration is a steady-state closed loop flow circuit where pressurised water, flowing through a cylindrical feed nozzle, is forced to turn 90° and then, move radially between two flat plates towards the exit of the device. High speed images show that cavitation is forming at the round exit of the feed nozzle. The cavitation cloud then grows in the radial direction until it reaches a maximum distance where it collapses. Due to the complexity of the flow field, direct observation of the flow structures was not possible, however vortex shedding is inferred from relevant simulations performed for the same conditions. Despite the axisymmetric geometry utilized, instantaneous pictures of cavitation indicate variations in the circumferential direction. Image post-processing has been used to characterize in more detail the phenomenon. In particular, the mean cavitation appearance and the cavity length have been estimated, showing good correlation with the erosion zone. This also coincides with the locations of the maximum values of the standard deviation of cavitation presence. The dominant frequency of the ‘large-scale’ cavitation clouds has been estimated through FFT. Cloud collapse frequencies vary almost linearly between 200 and 2000 Hz as function of the cavitation number and the downstream pressure. It seems that the increase of the Reynolds number leads to a reduction of the collapse frequency; it is believed that this effect is due to the agglomeration of vortex cavities, which causes a decrease of the apparent frequency. The results presented here can be utilized for validation of relevant cavitation erosion models which are currently under development.

Predictive capability of RANS and LES models to calculate incipient cavitation of water in a step nozzle is assessed. The RANS models namely, Realizable k-?, SST k-? and Reynolds Stress Model did not predict any cavitation, due to the limitation of RANS models to predict the low pressure vortex cores. LES WALE model was able to predict the cavitation by capturing the shear layer instability and vortex shedding. The performance of a barotropic cavitation model and Rayleigh-Plesset-based cavitation models was compared using WALE model. Although the phase change formulation is different in these models, the predicted cavitation and flow field were not significantly different.

The present paper focuses on the simulation of the expansion and aspherical collapse of a laser-generated bubble subjected to an acceleration field and comparison of the results with instances from high-speed videos. The interaction of the liquid and gas is handled with the volume of fluid method. Compressibility effects have been included for each phase to predict the propagation of pressure waves. Initial conditions were estimated through the Rayleigh Plesset equation, based on the maximum bubble size and collapse time. The simulation predictions indicate that during the expansion the bubble shape is very close to spherical. On the other hand, during the collapse the bubble point closest to the bottom of the container develops a slightly higher collapse velocity than the rest of the bubble surface. Over time, this causes momentum focusing and leads to a positive feedback mechanism that amplifies the collapse locally. At the latest collapse stages, a jet is formed at the axis of symmetry, with opposite direction to the acceleration vector, reaching velocities of even 300 m/s. The simulation results agree with the observed bubble evolution and pattern from the experiments, obtained using high speed imaging, showing the collapse mechanism in great detail and clarity. (C) 2016 AIP Publishing LLC.

The present paper focuses on the simulation of the high-velocity impact of a projectile impacting on a water-jet, causing the onset, development and collapse of cavitation. The simulation of the fluid motion is carried out using an explicit, compressible, density-based solver developed by the authors using the OpenFOAM library. It employs a barotropic two-phase flow model that simulates the phase-change due to cavitation and considers the co-existence of non-condensable and immiscible air. The projectile is considered to be rigid while its motion through the computational domain is modelled through a direct-forcing Immersed Boundary Method. Model validation is performed against the experiments of Field et al. [Field, J., Camus, J. J., Tinguely, M., Obreschkow, D., Farhat, M., 2012. Cavitation in impacted drops and jets and the effect on erosion damage thresholds. Wear 290–291, 154–160. doi:10.1016/j.wear.2012.03.006. URL http://www.sciencedirect.com/science/article/pii/S0043164812000968 ], who visualised cavity formation and shock propagation in liquid impacts at high velocities. Simulations unveil the shock structures and capture the high-speed jetting forming at the impact location, in addition to the subsequent cavitation induction and vapour formation due to refraction waves. Moreover, model predictions provide quantitative information and a better insight on the flow physics that has not been identified from the reported experimental data, such as shock-wave propagation, vapour formation quantity and induced pressures. Furthermore, evidence of the Richtmyer-Meshkov instability developing on the liquid-air interface are predicted when sufficient dense grid resolution is utilised.

The present work investigates the complex phenomena associated with pressure/high temperature dodecane injection for the Engine Combustion Network (ECN) Spray-A case, employing more elaborate thermodynamic closures, to avoid well known deficiencies concerning density and speed of sound prediction using traditional cubic models. A tabulated thermodynamic approach is proposed here, based on log10(p)-T tables, providing very high accuracy across a large range of pressures, spanning from 0 to 2500 bar, with only a small number of interpolation points. The tabulation approach is directly extensible to any thermodynamic model, existing or to be developed in the future. Here NIST REFPROP properties are used, combined with PC-SAFT Vapor-Liquid-Equilibrium to identify the liquid in mixtures penetration, hence avoiding the use of an arbitrary threshold for mass fraction. Identified liquid and vapour penetration are compared against experimental data from the ECN database showing a good agreement, within approximately 3–8% for axial penetration of liquid, 2% for vapor axial penetration and within experimental uncertainty for radial distribution of mass fraction. Analysis of the vortex evolution indicates that driving mechanisms behind the jet break-up are vortex tilting/stretching, then baroclinic torque, leading to Rayleigh-Taylor instabilities, closely followed by vortex dilation and finally viscous effects.