Development of a multiscale two-fluid approach with application to droplet dynamics

The present thesis introduces a novel numerical methodology for multiscale flows with application to complex droplet fragmentation cases. The proposed methodology concerns a compressible two-fluid model developed in OpenFOAM® and provides the flexibility of dealing with the multiscale character of flow fields: the interface scales greater than the grid size are resolved using the sharp interface (VOF) methodology, while the smaller ones, representing the diffused phase, are resolved by solving an additional transport equation of the generated surface area density (Σ) of the dispersed droplet cloud. The solver switches automatically between the sharp and the diffuse interface within the Eulerian-Eulerian framework in segregated and dispersed flow regions, respectively, by employing a dynamic interface sharpening based on a flow topology detection algorithm. Validation cases against a two-fluid shock tube and a rising bubble depict the accuracy of the numerical methodology to deal with highly compressible flows and fast changing interfaces. Initially, the functionality of the multiscale framework is demonstrated for high-speed droplet impact cases with Weber numbers above 105 and compared with new experimental data. At the investigated impact conditions, compressibility effects dominate the early stages of droplet splashing with shock waves to form and propagate inside the droplet and local Mach numbers up to 2.5 to be observed for the expelled surrounding gas outside the droplet. At the later stages of splashing, the dispersion of the dense cloud of fragments dominates and an insight into the fragments dynamics and the evolving sizes is presented. Subsequently, the droplet aerobreakup imposed by three different intensity shock waves, with Mach numbers of 1.21, 1.46 and 2.64, is investigated. The major features and physical mechanisms of breakup, including the incident shock wave dynamics and the vortices development, are accurately captured. Additionally, the dense mist development and the evolution of the underlying secondary droplets is examined under different post-shock conditions, based on the sub-grid scale modelling. Finally, the laser-induced fragmentation of a liquid droplet for different laser pulses that correspond to resulting droplet propulsion velocity values between 1.76m/s and 5.09m/s is investigated. Both the early- and later-time droplet dynamics are accurately captured and the influence of the laser energy on the droplet deformation and subsequent fragmentation is highlighted. The evolution of the produced fragments due to the rim breakup is quantified with respect to the different expansion rates and aerodynamic conditions

A Compressible Σ-Υ Two-Fluid Atomization Model with Dynamic Interface Sharpening based on Flow Topology Detection

Liquid fuel atomization is characterized by multi-scale flow features and the coexistence of different flow regimes which complicate the simulation of an atomizing spray under realistic operating conditions. The present work introduces an atomization model dealing with such multi-scale complexities. The proposed model is com-pressible, so it can capture the density variations that affect spray penetration and atomization mechanisms. It is developed within a multi-phase Eulerian-Eulerian framework that considers slip velocity effects between the phases and introduces an additional transport equation for the surface area (Σ); the latter aims to model the unre-solved sub-grid scale surface area variation. Moreover, a flow topology detection algorithm is applied in the flow field aiming to distinguish between different flow regimes; finally, the numerical algorithm applies appropriate closure relations for the interfacial source terms of the two-fluid model. The interfacial structures are also treated differently depending on the flow topology; a VOF method is applied in dense spray regions for resolving the interface fully and a non-sharp interface model is imposed in dilute spray regions, where sub-grid scale models are implemented for the modelling of relevant phenomena. The efficient coupling between the two-fluid model and the VOF method is examined via a standard interface capturing validation case of a rising bubble in a stagnant liquid. For the validation of the dynamic switching between different model formulations based on local topology and the numerical stability under the coexistence of various flow regimes, a Rayleigh-Taylor instability case is simulated and tested with the proposed model

Numerical investigation of high-speed droplet impact using a multiscale two-fluid approach

A single droplet impact onto solid surfaces remains a fundamental and challenging topic in both experimental and numerical studies with significant importance in a plethora of industrial applications, ranging from printing technologies to fuel injection in internal combustion engines. Under high-speed impact conditions, additional complexities arise as a result of the prompt droplet splashing and the subsequent violent fragmentation; thus, different flow regimes and a vast spectrum of sizes for the produced secondary flow structures coexist in the flow field. The present work introduces a numerical methodology to capture the multiscale processes involved with respect to local topological characteristics. The proposed methodology concerns a compressible Σ-Υ two-fluid model with dynamic interface sharpening based on an advanced flow topology detection algorithm. The model has been developed in OpenFOAM® and provides the flexibility of dealing with the multiscale character of droplet splashing, by switching between a sharp and a diffuse interface within the Eulerian-Eulerian framework in segregated and dispersed flow regions, respectively. An additional transport equation for the interface surface area density (Σ) introduces important information for the sub-grid scale phenomena, which is exploited in the dispersed flow regions to provide an insight into the extended cloud of secondary droplets after impact on the target. 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 velocity as high as 150m/s, which corresponds to a Weber number of ~7.6×10^5. At 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. The proposed numerical approach is found to capture relatively accurately the phenomena and provide significant information regarding the produced flow structure dimensions, which is not available from the experiment

Droplet aerobreakup under the shear-induced entrainment regime using a multiscale two-fluid approach

A droplet exposed to a high-speed gas flow is subject to a rapid and violent fragmentation, dominated by a widespread mist of multiscale structures that introduce significant complexities in numerical studies. The present work focuses on capturing all stages of the aerodynamic breakup of a waterlike droplet imposed by three different intensity shock waves, with Mach numbers of 1.21, 1.46, and 2.64, under the shear-induced entrainment regime. The numerical investigation is conducted within physically consistent and computationally efficient multiscale framework, using the Σ-Υ two-fluid model with dynamic local topology detection. Overall, the breakup of the deforming droplet and the subsequent dispersion of the produced mist show good agreement with available experimental studies in the literature. The major features and physical mechanisms of breakup, including the incident shock wave dynamics and the vortices development, are discussed, and verified against the experiments and the theory. While the experimental visualizations inside the dense mist are restricted by the capabilities of the diagnostic methods, the multiscale two-fluid approach provides insight into the mist dynamics and the distribution of the secondary droplets under different postshock conditions

Numerical modelling of droplet rim fragmentation by laser-pulse impact using a multiscale two-fluid approach

The present work examines the rim fragmentation of a millimeter-sized methyl-ethyl-ketone (MEK) droplet imposed by the impact of different millijoule nanosecond laser beams that correspond to droplet propulsion velocity values between 1.76 m/s and 5.09 m/s. The numerical investigation is conducted within a physically consistent and computationally efficient multiscale framework, using the Σ-Υ two-fluid model with dynamic local topology detection. Overall, the macroscopic droplet expansion and the obtained deforming shape show good agreement with the experimental observations. The influence of the laser beam energy on the droplet deformation and the evolution of the detached fragments from the rim is demonstrated. The physical mechanisms that determine the droplet expansion, including the expansion velocity and expansion rate, along with the effect of the surrounding air flow on the detached fragments, are addressed. Despite the visualization limitations inside the polydisperse cloud of fragments in the experimental results at higher laser energy, the evolution of fragments during the fragmentation process is quantified for the first time, and size distributions are obtained within the multiscale framework

A Σ-ϒ two-fluid model with dynamic local topology detection: Application to high-speed droplet impact

A numerical methodology resolving flow complexities arising from the coexistence of both multi-scale 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 velocity as high as 150 m/s, which corresponds to a Weber number of ∼7.6×105. Droplet splashing is followed by the formation of highly dispersed secondary cloud of droplets, with sizes ranging from 10−5 mm 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