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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.

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.

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.

Numerical predictions of the fuel heating and cavitation erosion location indicators occurring during the opening and closing periods of the needle valve inside a five-hole common rail Diesel fuel injector are presented. These have been obtained using an explicit density-based solver of the compressible Navier-Stokes (NS) and energy conservation equations; the flow solver is combined with two thermodynamic closure models for the liquid, vapour and vapour-liquid equilibrium (VLE) property variation as function of pressure and temperature. The first is based on tabulated data for a 4-component Diesel fuel surrogate, derived from the Perturbed-Chain, Statistical Associating Fluid Theory (PC-SAFT) Equation of State (EoS), allowing for the variation of the physical and transport properties of the fuel with the local pressure and temperature to be quantified. The second thermodynamic closure is based on the widely used barotropic Equation of State (EoS) approximation between density and pressure only and neglects viscous heating. The Wall Adapting Local Eddy viscosity (WALE) LES model was used to resolve sub-grid scale turbulence while a cell-based mesh deformation Arbitrary Lagrangian–Eulerian (ALE) formulation is used for modelling the injector's needle valve movement. Model predictions are found in close agreement against 0-D estimates of the temporal variation of the fuel temperature difference between the feed and hole exit during the injection period. Two mechanisms affecting the temperature distribution within the fuel injector have been revealed and quantified. The first is ought to wall friction-induced heating, which may result to local liquid temperature increase up to fuel's boiling point while superheated vapour is formed. At the same time, liquid expansion due to the depressurisation of the injected fuel results to liquid cooling relative to the fuel's feed temperature; this is occurring at the central part of the injection orifice. The spatial and temporal temperature and pressure gradients induce significant variations in the fuel density and viscosity, which in turn, affect the formed coherent vortical flow structures. It is found, in particular, that these affect the locations of cavitation formation and collapse, that may lead to erosion of the surfaces of the needle valve, sac volume and injection holes. Model predictions are compared against corresponding X-ray surface erosion images obtained from injector durability tests, showing good agreement.

An investigation of the fuel heating, vapor formation, and cavitation erosion location patterns inside a five-hole common rail diesel fuel injector, occurring during the early opening period of the needle valve (from 2 μm to 80 μm), discharging at pressures of up to 450 MPa, is presented. Numerical simulations were performed using the explicit density-based solver of the compressible Navier–Stokes (NS) and energy conservation equations. The flow solver was combined with tabulated property data for a four-component diesel fuel surrogate, derived from the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS), which allowed for a significant amount of the fuel’s physical and transport properties to be quantified. The Wall Adapting Local Eddy viscosity (WALE) Large Eddy Simulation (LES) model was used to resolve sub-grid scale turbulence, while a cell-based mesh deformation arbitrary Lagrangian–Eulerian (ALE) formulation was used for modelling the injector’s needle valve movement. Friction-induced heating was found to increase significantly when decreasing the pressure. At the same time, the Joule–Thomson cooling effect was calculated for up to 25 degrees K for the local fuel temperature drop relative to the fuel’s feed temperature. The extreme injection pressures induced fuel jet velocities in the order of 1100 m/s, affecting the formation of coherent vortical flow structures into the nozzle’s sac volume.

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 present work examines numerically the breakup of water droplets exposed to gas flows at Mach numbers Ma>1, which resemble the ambient conditions encountered in the injection systems of scramjet (supersonic combustion ramjet) engines. A CFD model is utilized which solves the compressible Navier-Stokes equations, the energy equation, the mass conservation in volume fraction form (volume of fluid method) along with two equations of state to model the density variations of the two phases. In addition, a coupled VOF/Lagrange model is employed to capture the appearance of micro-droplets, which are smaller than the smallest grid cell. As a first step, a 2-dimensional planar simulation (water column) is performed at conditions of Ma=1.47 in order to validate the numerical model; its results are compared against published experimental and numerical data. Good agreement is observed for the temporal evolution of droplet shape, the streamwise deformation, the leading-edge displacement as well as the shock wave reflection. Subsequently, the validated model is utilized to perform a 3-D simulation at Ma=1.23, which corresponds to the conditions of previous experimental studies, and its results are compared against the experimental data as well as the results from previous numerical studies, showing good agreement. Furthermore, surface instabilities are observed at the droplet surface initiated by interfacial instabilities due to the shearing effect and the interaction with the shock-wave, pertaining to Kelvin-Helmholtz and Rayleigh-Taylor instabilities, despite the stabilising contribution of surface tension; viscosity effects are found to play an insignificant role.

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

Cavitation induction is of high interest for a wide range of applications, from hydraulic machines to bioengineering applications. Numerous experimental and numerical studies have aimed to unveil the dynamics of cavitation to enhance the performance and lower the impact of erosion on machinery but also to employ its mechanics in advanced noninvasive medical procedures. The current work provides a comprehensive review of the methodologies that have been developed in the framework of computational fluid dynamics in order to study cavitating flows, highlighting the link of the application with the utilized approach. The methods are presented and assessed according to the class of physical problems addressed, which, in turn, are classified into problems of single-bubble dynamics, bubble cluster dynamics, and cavitating flows at engineering scales.

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.

Positive displacement pumps are an integral part of many applications, ranging from fuel systems in the transportation sector and the petrochemical industry to precise flow-metering devices used in the biomedical field. A common characteristic of such devices is the varying shape and volume of the geometry enclosing the transferred liquid. This fact renders modeling and investigation of their operation rather difficult. In this chapter, different methods that can be employed to tackle such issues will be discussed. Furthermore, indicative examples of a high-pressure fuel pump and a gear pump will be discussed along with thermodynamic phenomena that take place, such as compression heating. Furthermore, factors that affect the performance and cavitation formation in such devices will be demonstrated.

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.

The Perturbed-Chain, Statistical Associating Fluid Theory equation of state is utilised to model the effect of pressure and temperature on the density, volatility and viscosity of four Diesel surrogates; these calculated properties are then compared to the properties of several Diesel fuels. Perturbed-Chain, Statistical Associating Fluid Theory calculations are performed using different sources for the pure component parameters. One source utilises literature values obtained from fitting vapour pressure and saturated liquid density data or from correlations based on these parameters. The second source utilises a group contribution method based on the chemical structure of each compound. Both modelling methods deliver similar estimations for surrogate density and volatility that are in close agreement with experimental results obtained at ambient pressure. Surrogate viscosity is calculated using the entropy scaling model with a new mixing rule for calculating mixture model parameters. The closest match of the surrogates to Diesel fuel properties provides mean deviations of 1.7% in density, 2.9% in volatility and 8.3% in viscosity. The Perturbed-Chain, Statistical Associating Fluid Theory results are compared to calculations using the Peng–Robinson equation of state; the greater performance of the Perturbed-Chain, Statistical Associating Fluid Theory approach for calculating fluid properties is demonstrated. Finally, an eight-component surrogate, with properties at high pressure and temperature predicted with the group contribution Perturbed-Chain, Statistical Associating Fluid Theory method, yields the best match for Diesel properties with a combined mean absolute deviation of 7.1% from experimental data found in the literature for conditions up to 373°K and 500 MPa. These results demonstrate the predictive capability of a state-of-the-art equation of state for Diesel fuels at extreme engine operating conditions.

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.

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.

Real industrial examples have been used to evaluate the viability of several cavitation erosion risk indicators (ERIs). Industry standard endurance tests resulted in non-critical cavitation erosion of a shoe and shoe-guide assembly in a high-pressure fuel pump. A design modification was made which eliminated the erosion. Transient CFD simulations of the two designs were run. The distribution and intensity of the resulting ERIs were evaluated against photographic evidence of erosion taken after endurance testing. Details of the component dynamics and the resulting cavitation formation and collapse are presented, along with an analysis of the ERIs for their potential usefulness. Of the 10 ERIs studied, two were found to be particularly good indicators, one of which is newly derived for this research. It is now anticipated that using these ERIs to guide product design and development will save considerable time and cost.

Pressure (left) and velocity contours (right) combined with the iso-lines of gas volume fraction of 0.5 (gas-liquid interface is denoted by dash line) and tissue volume fraction of 0.5 (gas-tissue interface is denoted by solid line) at 4 instances during the penetration of the liquid jet into the soft tissue are shown.

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 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 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 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.