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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.

Past experimental studies have shown that the needle valve of high-pressure diesel injectors undergoes lateral movement and deformation, while the continuous increase in injection pressure enlarges the gap of the needle valve assembly. Two different analytical models, considering or omitting this change are presented here, linking the geometries of the needle valve assembly with the magnitude of needle valve tip lateral movement. It is found that the physical dimensions of the needle valve assembly and the injection pressure have a significant impact on the radial displacement of the needle. For example, for nominal clearances between the needle guidance and the needle valve of about 1–3 μm, the magnitude of the radial movement of the needle tip could reach tens of microns. The model that takes into account the variation of the gap between the needle guide and needle valve is found to give predictions closer to the experimental results.

In diesel engines, double-layer multi-holes nozzles contribute significantly in making spray injection uniform in both the circumferential and axial directions; they further ensure that minimal or no interactions are encountered among the spray jets emerging from the nozzle holes and positively affect fuel atomisation and enhance mixing during engine operation. In this study, the variation in internal flow characteristics and spray patterns from the upper and the lower layer nozzle holes were investigated experimentally and computationally. A double-layer 8-hole heavy-duty diesel engine injector nozzle was utilised for the characterisation of hole-to-hole variation on spray formation. The actual nozzle geometry was derived from X-ray scans obtained at the third generation X-ray imaging and biomedical beamline station in SSRF, revealing all geometrical differences between the individual injection holes. The momentum fluxes from each holes were obtained together with spray tip penetration under non-evaporating conditions. These data were used to validate the computational fluid dynamics (CFD) model suitable to describe the relevant flow processes. Initially, an Eulerian-Eulerian two-phase flow model was utilised to predict the internal nozzle flow under cavitating conditions. This model was weakly coupled with a Lagrangian spray model predicted the subsequent atomisation and penetration of all individual spray plumes. The results show that cavitation development within the upper layer holes is more intense than those formed within the lower layer nozzle holes; this is leading to higher injection rates from the lower layer nozzle holes that they also exhibit less cycle-to-cycle variations in the observed spray patterns.

Highly branched alkanes exhibit enhanced free volume relative to their straight chain analogues, leading to the increased solubility of sparingly soluble gases, such as N2, as well as lower hydroca...

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.

Soot prediction for diesel engines is a very important aspect of internal combustion engine emissions research, especially nowadays with very strict emission norms. Computational Fluid Dynamics (CFD) is often used in this research and optimisation of CFD models in terms of a trade-off between accuracy and computational efficiency is essential. This is especially true in the industrial environment where good predictivity is necessary for engine optimisation, but computational power is limited. To investigate soot emissions for Diesel engines, in this work CFD is coupled with chemistry tabulation framework and semi-empirical soot model. The Flamelet Generated Manifold (FGM) combustion model precomputes chemistry using detailed calculations of the 0D homogeneous reactor and then stores the species mass fractions in the table, based on six look-up variables: pressure, temperature, mixture fraction, mixture fraction variance, progress variable and progress variable variance. Data is then retrieved during online CFD simulation, enabling fast execution times while keeping the accuracy of the direct chemistry calculation. In this work, the theory behind the model is discussed as well as implementation in commercial CFD code. Also, soot modelling in the framework of tabulated chemistry is investigated: mathematical model and implementation of the kinetic soot model on the tabulation side is described, and 0D simulation results are used for verification. Then, the model is validated using reallife engine geometry under different operating conditions, *Corresponding Author: Mijo Tvrdojevic: Mijosoft, Croatia ; Email: mijo@mijosoft.net Milan Vujanovic: Zagreb University, Croatia Peter Priesching: AVL List GmbH, Austria Ferry A. Tap, Anton Starikov, Dmitry Goryntsev: AVL Dacolt BV, Netherlands Manolis Gavaises: City University, United Kingdom of Great Britain and Northern Ireland where better agreement with experimental measurements is achieved, compared to the standard implementation of the kinetic soot model on the CFD side.

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

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

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.

Vortex ring structures occur in light or hoarse cough configurations. These instances consist of short impulses of exhaled air resulting to a self-contained structure that can travel large distances. The present study is the first implementation of the second order Fully Lagrangian Approach (FLA) for three-dimensional realistic flow-fields obtained by means of Computational Fluid Dynamics (CFD) and provides a method to calculate the occurrence and the intensity of caustic formations. The carrier phase flow field is resolved by means of second order accurate Direct Numerical Simulation (DNS) based on a Finite Difference approach for the momentum equations, while a spectral approach is followed for the Poisson equation using Fast Fourier Transform (FFT). The effect of the undulations of the carrier phase velocity due to large scale vortical structures and turbulence is investigated. The evaluation of the higher order derivatives needed by the second order FLA is achieved by prefabricated least squares second order interpolations in the three dimensions. The method allows for the simulation of the clustering of droplets and droplet nuclei exhaled in ambient air in conditions akin to light cough. Given the ambiguous conditions of vortex-ring formation during cough instances, three different formation numbers n = UT /D are assumed, i.e. underdeveloped (n = 2), ideal (n = 3.7) and over-developed VRs (n = 6). The formation of clusters results in the spatial variance of the airborne viral load. This un-mixing of exhumed aerosols is related to the formation of localised high viral load distributions that can be linked to super-spreading events.

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.

The development of reference correlations for viscous fluids is predicated on the availability of accurate viscosity data, especially at high pressure, high temperature (HPHT) conditions. The rolling ball viscometer (RBV) is a facile technique for obtaining such HPHT viscosity data. A new, universal RBV calibration methodology is described and applied over a broad T-p region and for a wide range of viscosities. The new calibration equation is used to obtain viscosities for n-hexadecane (HXD), 2,2,4,4,6,8,8-heptamethylnonane (HMN), and 2,6,10,15,19,23-hexamethyltetracosane (squalane) from 298 – 530 K and pressures to 250 MPa. The available literature data base for HMN is expanded to 520 K and 175 MPa and for squalane to 525 K and 250 MPa. The combined expanded uncertainties are 0.6% and 2.5% for the densities and viscosities, respectively, each with a coverage factor, k = 2. The reliability of the viscosity data is validated by comparison of HXD and squalane viscosities to accepted reference correlations and HMN viscosities to available literature data. The necessity of this new calibration approach is confirmed by the large deviations observed between HXD, HMN, and squalane viscosities determined using the new, universal RBV calibration equation and viscosities determined using a quadratic polynomial calibration equation. HXD, HMN, and squalane densities are predicted with the Perturbed Chain Statistical Associating Fluid Theory using pure component parameters calculated with a previously reported group contribution (GC) method. HXD, HMN, and squalane viscosities are compared to Free Volume Theory (FVT) predictions using FVT parameters calculated from a literature correlation for nalkanes. Although the FVT predictions for HXD, a normal alkane, result in an average absolute percent deviation (∆AAD) of 3.8%, predictions for HMN and squalane, two branched alkanes, are four to 13 times larger. The fit of the FVT model for the branched alkanes is dramatically improved if the FVT parameters are allowed to vary with temperature.

Rail pressures of modern diesel fuel injection systems have increased significantly over recent years, greatly improving atomisation of the main fuel injection event and air utilisation of the combustion process. Continued improvement in controlling the process of introducing fuel into the cylinder has led to focussing on fluid phenomena related to transient response. High-speed microscopy has been employed to visualise the detailed fluid dynamics around the near nozzle region of an automotive diesel fuel injector, during the opening, closing and post injection events. Complementary computational fluid dynamic (CFD) simulations have been undertaken to elucidate the interaction of the liquid and gas phases during these highly transient events, including an assessment of close-coupled injections. Microscopic imaging shows the development of a plug flow in the initial stages of injection, with rapid transition into a primary breakup regime, transitioning to a finely atomised spray and subsequent vaporisation of the fuel. During closuring of the injector the spray collapses, with evidence of swirling breakup structures together with unstable ligaments of fuel breaking into large slow-moving droplets. This leads to sub-optimal combustion in the developing flame fronts established by the earlier, more fully-developed spray. The simulation results predict these observed phenomena, including injector surface wetting as a result of large slow-moving droplets and post-injection discharge of liquid fuel. This work suggests that post-injection discharges of fuel play a part in the mechanism of the initial formation, and subsequent accumulation of deposits on the exterior surface of the injector. For multiple injections, opening events are influenced by the dynamics of the previous injection closure; these phenomena have been investigated within the simulations.

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

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

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.

This chapter is devoted to X-ray measurement techniques that are suitable for cavitating flows, the physics behind the interaction of X-rays with matter, and how the findings can be interpreted to provide information on (1) the topology and dynamics of the two-phase flow in a qualitative manner in order to illustrate the shape evolution of the arising vapor structures characteristic of different cavitation regimes and (2) the actual extent of vapor forming in terms of quantitative void fraction data. The experimental infrastructure necessary for the generation of X-ray beams with diverse characteristics (photon flux, energy, spectrum, and direction) and relevant instrumentation to extract physical information, as well as the flow configurations with reference to cavitating flows that have been investigated so far in the literature, are discussed in detail. X-ray diagnostics that have been proposed as applicable to cavitation studies can be broadly categorized as X-ray absorption (densitometry), X-ray phase contrast imaging, X-ray computed tomography, and X-ray fluorescence spectroscopy.

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.

Recently, Rokni et al. [1,2] developed entropy-scaling based pseudo-component techniques to predict the viscosity and thermal conductivity of hydrocarbon mixtures and fuels up to high temperature and pressure conditions using only two calculated or measured mixture properties (number average molecular weight and hydrogen-to-carbon ratio). The models are accurate for many hydrocarbon mixtures that do not contain branched compounds (7 and 2% mean absolute percent deviation (MAPD) for viscosity and thermal conductivity, respectively, on average). However, predictions for some hydrocarbon mixtures and fuels containing iso-alkanes are often less accurate (16 and 19% MAPD for viscosity and thermal conductivity, respectively, on average). To improve predictions, it was proposed by Rokni et al. [1,2] to fit one model parameter using an experimental reference viscosity or thermal conductivity data point, which may not be ideal if experimental reference data are not available. In order to make these models more practical, this study fits empirical correlations for the model parameters, so that accurate predictions can be made without fitting model parameters. The correlations enable viscosity and thermal conductivity predictions for a wide range of hydrocarbon mixtures and fuels, including those containing branched alkanes, and no longer require input of any experimental reference viscosity or thermal conductivity data. The correlations are temperature (fit to data from 288 to 550 K) and pressure (fit to data from 1 to 4,400 bar) dependent and are functions of average molecular weight, hydrogen-to-carbon ratio, iso-alkane and two-ring saturate concentrations. Viscosity and thermal conductivity predictions were found to improve to within 5 and 2% average MAPD, respectively, relative to experimental data for the hydrocarbon mixtures and fuels considered in this study.

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.

Internal combustion (IC) engines operating on fossil fuel oil provide about 25% of the world's power (about 3000 out of 13,000 million tons oil equivalent per year-see Figure 1), and in doing so, they produce about 10% of the world's greenhouse gas (GHG) emissions (Figure 2). Reducing fuel consumption and emissions has been the goal of engine researchers and manufacturers for years, as can be seen in the two decades of ground-breaking peer-reviewed articles published in this International Journal of Engine Research (IJER). Indeed, major advances have been made, making today's IC engine a technological marvel. However, recently, the reputation of IC engines has been dealt a severe blow by emission scandals that threaten the ability of this technology to make significant and further contributions to the reduction of transportation sector emissions. In response, there have been proposals to replace vehicle IC engines with electric-drives with the intended goals of further reducing fuel consumption and emissions, and to decrease vehicle GHG emissions

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

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

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