Using direct numerical simulation (DNS) in combination with the volume of fluid method (VoF), we investigate the influence of the density ratio between the carrier and dispersed phase on emulsions, ...where the baseline simulation approximately corresponds to the ratio of water-in-gasoline emulsions. For this purpose, homogeneous isotropic turbulence (HIT) is generated using a linear forcing method, enhanced by a proportional–integral–derivative (PID) controller, ensuring a constant turbulent kinetic energy (TKE) for two-phase flows, where the TKE balance equation contains an additional term due to surface tension. Then, the forcing is stopped, and gravitational acceleration is activated. The proposed computational setup represents a unique and well-controlled configuration to study emulsification and segregation. We consider four different density ratios, which are applied in industrial processes, to investigate the influence of the density ratio on the statistically steady state of the emulsions, and their segregation under decaying turbulence and constant gravitational acceleration. At the statistically steady state, we hold the turbulence constant and study the effects of the density ratio ρd/ρc, on the interface area, the Sauter mean diameter (SMD), and the statistical droplet size distribution. We find that all are affected by the density ratio, and we observe a relation between the SMD and ρd/ρc. Furthermore, we assume a dependence of the critical Weber number on the density ratio. In the second part of our work, we study the segregation process. To this end, we consider the change in the center of mass of the disperse phase and the energy release, to analyze the dependence of segregation on the density difference Δρ/ρd. We show that segregation scales with the density difference and the droplet size, and a segregation time scale has been suggested that collapses the height of the center of mass for different density ratios.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
Mixing under high pressure conditions plays a central role in several engineering applications, such as direct-injection engines and liquid rocket engines. Numerical flow simulations have become a ...complementary tool to study the mixing process under these conditions but require complex thermodynamic modeling as well as validation with accurate experimental data. For this reason, we use experiments of supercritical single-phase jet mixing from the literature, where the mixing is quantified by the mixture speed of sound, as a reference for our work. We here focus on the thermodynamic modeling of multi-component flows under high pressure conditions and the analytical calculation of the mixture speed of sound. Our thermodynamic model is based on cubic equations of state extended for multi-components. Using an extension of OpenFOAM, we perform large-eddy simulations of hexane and pentane injections and compare our results with the experimentally measured mixture speed of sound at specific positions. The simulation results show the same characteristic trends, indicating that the mixing effects are well reproduced in the simulations. Additionally, the effect of the sub-grid scale modeling is assessed by comparing results using different models (Smagorinsky, Vreman, and Wall-Adapting Local Eddy-viscosity). The comprehensive simulation data presented here, in combination with the experimental data, provide a benchmark for numerical simulations of jet mixing in high pressure conditions.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
The characterisation of small-scale turbulence has been an active area of research for decades and this includes, particularly, the analysis of small-scale isotropy, as postulated by Kolmogorov. In ...particular, the question if the dissipation tensor is isotropic or not, and how it is related to the anisotropy of the Reynolds stresses is of particular interest for modelling purposes. While this subject has been extensively studied in the context of isothermal flows, the situation is more complicated in turbulent reacting flows because of heat release. Furthermore, the landscape of Computational Fluid Dynamics is characterised by a multitude of methods ranging from Reynolds-averaged to Large Eddy Simulation techniques, and they address different ranges of scales of the turbulence kinetic energy spectrum. Therefore, a multiscale analysis of the anisotropies of Reynolds stress, dissipation and sub-grid scale tensor has been performed by using a DNS database of statistically planar turbulent premixed flames. Results show that the coupling between dissipation tensor and Reynolds stress tensor is weaker compared to isothermal turbulent boundary layer flows. In particular, for low and moderate turbulence intensities, heat release induces pronounced anisotropies which affect not only fluctuation strengths but also the characteristic size of structures associated with different velocity components.
•Compressible simulations of near-wall collapses.•Rebound and pressure impact on the wall are captured.•Comprehensive study of the central mechanism for induced pressure peaks on the wall.•Highest ...grid resolution for 3D simulations of bubble collapses.•Grid study using six different grid resolutions and considering various stand-off distances.
We consider the collapse behavior of cavitation bubbles near walls under high ambient pressure conditions. Generic configurations with different stand-off distances are investigated by numerical simulation using a fully compressible two-phase flow solver including phase change. The results show that the stand-off distance has significant effects on collapse dynamics, micro-jet formation, rebound, and maximum wall pressure. A relation between cavitation induced material damage and corresponding collapse mechanisms is obtained from pressure-impact data at the wall. We analyze the resolution dependence of collapse and rebound and the observed maximum pressure distributions. The comparison of the results on six different grid resolutions shows that main collapse features are already captured on the coarsest resolution, while the peak pressures are strongly resolution dependent.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•Compressible Large-Eddy Simulation of cavitating nozzle flows featuring different cavitation regimes.•Cavitation dynamics and shedding mechanisms of cloud cavitation in a nozzle with constant ...cross-section.•Re-entrant jet and condensation shock initiated shedding.•Estimates for shock wave velocity and cavity growth velocity.•Detailed analysis of the re-entrant jet motion and velocity.
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Cloud cavitation is related to an intrinsic instability where clouds are shed periodically. The shedding process is initiated either by the motion of a liquid re-entrant jet or a condensation shock. Cloud cavitation in nozzles interacts with the flow field in the nozzle, the mass flow and the spray break-up, and causes erosion damage. For nozzle geometries cloud shedding and the associated processes have not yet been studied in detail.
In this paper, we investigate the process of cloud cavitation shedding, the re-entrant jet and condensation shocks in a scaled-up generic step nozzle with injection into gas using implicit Large-Eddy Simulations (LES). For modeling of the cavitating liquid we employ a barotropic equilibrium cavitation model, embedded in a homogeneous multi-component mixture model. Full compressibility of all components is taken into account to resolve the effects of collapsing vapor structures.
We carry out simulations of two operating points exhibiting different cavitation regimes. The time-resolved, three-dimensional simulation results cover several shedding cycles and provide deeper insight into the flow field. Our results show that at lower cavitation numbers, shedding is initiated by condensation shocks, which has not yet been reported for nozzle flows with a constant cross-section. We analyze the cavitation dynamics and the shedding cycles of both operating points. Based on our observations we propose modifications to established schematics of the cloud shedding process. Additionally, we analyze the near-wall upstream flow in and underneath the vapor sheet and possible driving mechanism behind the formation of the re-entrant jet.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
We study turbulent emulsions and the emulsification process in homogeneous isotropic turbulence (HIT) using direct numerical simulations (DNS) in combination with the volume of fluid method (VOF). ...For generating a turbulent flow field, we employ a linear forcing approach augmented by a proportional‐integral‐derivative (PID) controller, which ensures a constant turbulent kinetic energy for two phase flow scenarios and accelerates the emulsification process. For the simulations, the density ratio of dispersed and carrier phases is chosen to be similar to that of oil and water (0.9), representing a typical application. We vary the turbulence intensity and the surface tension coefficient. Thus, we modulate those parameters that directly affect the Hinze scale, which is expected to be the most stable maximum droplet diameter in emulsions in HIT. The considered configurations can be characterized with Taylor Reynolds numbers in the range of 100–140 and Weber numbers, evaluated with the velocity fluctuations and the integral length scale, of 4–70. Using the 3‐D simulation results, we study the emulsification process as well as the emulsions at a statistically stationary state. For the latter, droplet size distributions are evaluated and compared. We observe a Hinze scale similarity of the size distributions considering a fixed integral length scale, that is, similar Hinze scales obtained at different turbulence intensities or for different fluid properties result in similar distributions.
Turbulent emulsion.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
We numerically investigate the erosion potential of a cavitating liquid jet by means of high-resolution finite volume simulations. As thermodynamic model, we employ a barotropic equilibrium ...cavitation approach, embedded into a homogeneous mixture model. To resolve the effects of collapsing vapor structures and to estimate the erosion potential, full compressibility is considered. Two different operating points featuring different cavitation intensities are investigated and their erosion potential is estimated and compared. Different methods are used for this purpose, including collapse detection (Mihatsch et al., 2015), maximum pressure distribution on the wall, and a new method of generating numerical pit equivalents. The data of numerical pit equivalents is analyzed in detail and compared with experimental data from the literature. Furthermore, a comprehensive grid study for both operating points is presented.
•Numerical assessment of cavitation erosion.•Fully compressible simulations.•High-resolution simulations of a cavitating liquid jet.•Numerical counterparts to experimental erosion pits.•Detailed data on erosion pit formation.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The impact of a collapsing gas bubble above rigid, notched walls is considered. Such surface crevices and imperfections often function as bubble nucleation sites, and thus have a direct relation to ...cavitation-induced erosion and damage structures. A generic configuration is investigated numerically using a second-order accurate compressible multi-component flow solver in a two-dimensional axisymmetric coordinate system. Results show that the crevice geometry has a significant effect on the collapse dynamics, jet formation, subsequent wave dynamics and interactions. The wall-pressure distribution associated with erosion potential is a direct consequence of development and intensity of these flow phenomena.
We further elaborate on the generalized formulation for cubic equation of state proposed by Cismondi and Mollerup Fluid Phase Equilib. 232 (2005). With this formulation all well-known cubic equations ...of state can be described with a certain pair of values, which allows for a generic implementation of different equations of state. Based on this generalized formulation, we derive a complete thermodynamic model for computational fluid dynamics (CFD) simulations by providing the resulting correlations for all required thermodynamic properties. For the transport properties, we employ the Chung correlations. Our generic implementation includes the often used equations of state Soave-Redlich-Kwong and Peng-Robinson and the Redlich-Kwong-Peng-Robinson (RKPR) equation of state. The first two assume a universal compressibility factor and are therefore only suitable for fluids with a matching critical compressibility. The Redlich-Kwong-Peng-Robinson overcomes this limitation by considering the equation of state parameter as function of the critical compressibility. We compare the resulting thermodynamic modeling for the three equations of state for selected fluids with each other and CoolProp reference data. As supplementary material to this paper, we provide a Python tool called real gas thermodynamic python library (realtpl). This tool can be used to evaluate and compare the results for a wide range of different fluids. Additionally, we also provide the implementation of the generalized form in OpenFOAM.
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