The Journal of Computational Multiphase Flows

An improved understanding of the breakup processes of two-phase flows is essential to effectively control the fuel atomization for future aircraft engines. A detailed insight into the phenomena of primary breakup is a major limitation in gaining this knowledge. Aircraft engines use airblast atomizers to provide the fuel atomization. The geometries of airblast atomizers are complex, the operating conditions are characterized by high Reynolds- and Weber numbers. Direct Numerical Simulations (DNS) of liquid breakup under realistic conditions and geometries are hardly possible. The embedded DNS (eDNS) concept aims to fill this gap. The concept consists of three steps: a geometry simplification, the generation of realistic boundary conditions for the DNS and the DNS of the breakup region. The realistic annular airblast atomizer geometry is simplified to a planar geometry. Inside this domain the eDNS is located. The eDNS domain requires the generation of boundary conditions. A zonal Large Eddy Simulation (LES) of the turbulent channel flow is performed prior to the DNS. The parameters are stored transiently on the “virtual” DNS inlet planes. These variables are then mapped to the DNS. The Volume of fluid (VOF) method is used to solve for the two-phase flow. DNS are performed for a shear-driven liquid wall film and for a generic planar prefilming airblast atomizer. As the Reynolds and Weber number for the first operating point (OP) are low (Re_air = 5,333/We_film = 1.9), the liquid wall film as well as the liquid sheet show no surface waves. For the second case with Re_air = 13,333 and We _film = 11.9, the surface appears more wrinkled and streamwise waves are transported along the wall for the shear-driven wall film. Instantaneous snapshots in 2–D and 3–D illustrate the qualitative behavior of the liquid sheet in time. Leaving the prefilmer trailing edge, the liquid sheet starts to oscillate in a sinusoidal fashion. This oscillation appears crucial for the onset of primary breakup. The qualitative characterization of the breakup for OP 1 and OP 2, yield to the distinction of the stretched ligament breakup for the former, and the torn-sheet breakup for the latter O P. The breakup time for OP 1 is longer than for OP 2. This study proves the applicability of the eDNS concept for investigating breakup processes as the transient nature of the phase interface behavior can be captured. The approach offers the potential of simulating realistic annular highly-swirled airblast atomizer geometries under realistic conditions.

We propose a method for DNS of particle motion in non-isothermal systems. The method uses a shared set of momentum and energy balance equations for the carrier-and the dispersed phases. Measures are taken to ensure that non-deformable entities (solid particles) behave like rigid bodies. Moreover, deformable entities (e.g. bubbles) as well as rarefaction effects can be accommodated. The predictions of the method agree well with the available data for isothermal solid particles motion in the presence of walls and other particles, natural convection around a stationary particle, solid particles motion accompanied with heat transfer effects and isothermal solid particles motion under rarefied conditions. The method is used to investigate the simultaneous effects of heat transfer and rarefaction on the motion of a solid catalyst particle in an enclosure, the interaction of a solid particle and a microbubble in a flotation cell and a case with more than 1000 particles.

Polyurethane foam is used for manufacturing different kinds of products, such as refrigerators, car dashboards or steering wheels. First, we developed a macro-scale simulation tool that is able to predict foam flow in such complex molds. Depending on the location within a product, final properties of polyurethane foams may vary significantly. These properties (e.g. thermal conductivity or impact strength) are strongly dependent on local foam structure. Modeling complex geometries like refrigerators completely on bubble scale is neither possible nor would it be efficient. The computational effort would be enormous. Therefore, we developed a micro-scale model describing bubble growth and the evolution of the foam microstructure in polyurethane foams considering a limited number of bubbles in a representative volume. Finally, we coupled our macro and micro-scale simulation approaches. For that purpose, we introduced tracer particles into our mold filling simulations. We are able to record information about density and temperature changes or varying flow conditions along particle trajectories. This information is then used to set up corresponding simulations on bubble scale. Through this coupling, a basis for studying the evolution of the local foam microstructure in complex geometries is provided.

Turbidity currents are submarine flows where the sediment fluid mixture (heavy current) drives along the sloping ocean floor displacing the surrounding clear fluid (light ambient). Under the influence of gravity, the suspended sediments drive the current and at the same time settle down on the ocean bed. The interplay of turbulent mixing and settling sediments leads to stable stratification of sediments in the turbidity current. In previous studies (Cantero et al. 2009b; Cantero et al., 2009a; Cantero et al., 2012a; Talling et al., 2007) it was observed that strong settling tendency (large sediment sizes) could cause complete turbulence suppression. In this study, we will analyse this process of complete turbulence suppression by means of direct numerical simulations (DNS) of turbidity currents. In wall bounded unstratified flows, it has been long established that turbulence is sustained by the process of auto-generation of near-wall hairpin like and quasi-streamwise turbulent vortical structures. It was also identified that auto-generation is possible only when the strength of the turbulent structures is greater than a threshold value (Zhou et. al., 1996). Through quadrant analysis of Reynolds stress events and visualization of turbulent vortical structures, we observe that stratification by sediments lead to damping and spatial re-distribution of turbulent vortical structures in the flow. We propose that complete turbulence suppression is brought about by a total shutdown in the auto-generation process of the existing turbulent structures in the flow. We also identify three parameters – Reynolds number (Re_τ), Richardson number (Ri_τ) and sediment settling velocity (V˜_z) that quantify the process of turbulence suppression. A criterion for complete turbulence suppression is also proposed which can be defined as a critical value for Ri_τV˜_z. This critical value is a function of Re_t and based on simulations, experiments and field observations it appears to have a logarithmic dependence on Re_τ (Cantero et al. 2012). DNS of turbidity currents driven by bi-disperse suspension of sediments is also carried out and compared with the results of mono-disperse suspensions.

In the present work, a high order realizable scheme for the Eulerian simulation of disperse phase flows on unstructured grids is developed and tested. In the Eulerian modeling framework two approaches are studied: the monokinetic (MK) [1] and the Gaussian closures [2, 3]. The former leads to a pressureless gas dynamics system (PGD). It accurately reproduces the physics of such flows at low Stokes number, but is challenging for numerics since the resulting system is weakly hyperbolic. The latter deals with higher Stokes numbers by accounting for particle trajectory crossings (PTC) [4]. Compared to the MK closure, the resulting system of equation is hyperbolic but has a more complex structure; realizability conditions are satisfied at the continuous level, which imply a precise framework for numerical methods. To achieve the goals of accuracy, robustness and realizability, the Discontinuous Galerkin method (DG) is a promising numerical approach [5, 6, 7, 8]. Based on the recent work of Zhang et al. [6], the DG method used is associated to a convex projection strategy, which respects the realizability constraints without affecting the accuracy. The main contribution of this work is to apply one of the latest developments in the field of numerical methods (DG) to physical models, taking into account the free transport and drag terms of the disperse phase flow, which are the building blocks for the Eulerian modeling based on moment methods. DG results are eventually compared qualitatively and quantitatively to the Lagrangian results and to the reference simulations provided by a second order structured MUSCL/HLL finite volume scheme [9, 3]. Through these comparisons, the DG method is shown to be competitive for the description of such flows.

This study focused on a bubble rising behavior in a molten glass because it is important to improve the efficiency of removal of bubbles from the molten glass. On the other hand, it is expected that some gas species which exists in a bubble are transferred into the molten glass through the bubble interface, i.e., the mass transfer, subsequently, it may cause a bubble contraction in the molten glass. In this paper, in order to understand the bubble rising behavior with its contraction caused by the mass transfer through the bubble interface in the very high viscous fluid such as the molten glass, a bubble contraction model has been developed. The direct numerical simulations based on the MARS (Multi-interface Advection and Reconstruction Solver) coupled with the mass transfer equation and the bubble contraction model regarding the mass transfer from the rising bubble in very high viscous fluid have been performed. Here, the working fluids were water vapor as the gas species and the molten glass as the very high viscous fluid. Also, the jump conditions at the bubble interface for the mass transfer were examined. Furthermore, the influence of the bubble contraction for the bubble rising compared to that in the water as a normal viscous fluid was investigated. From the result of the numerical simulations, it was found that the bubble rising behavior was strongly affected not only by the viscosity of the working fluid but also by the bubble contraction due to the mass transfer through the bubble interface.

Applicability of two kinds of computational-fluid-dynamics method adopting Cahn-Hilliard (CH) and Allen-Cahn (AC)-type diffuse-interface advection equations based on a phase-field model (PFM) is examined to simulation of motions of microscopic incompressible two-phase fluid on solid surface. A capillarity-driven gas-liquid motion in rectangular channel is simulated by use of a PFM method for solving Navier-Stokes (NS) equations and a CH equation, whereas an immiscible liquid-liquid flow in a microchannel with T-junction and square cross section is simulated by use of another PFM method proposed in this study, which adopts a lattice-Boltzmann method based on fictitious particles kinematics as numerical scheme for solving NS equations and an AC equation that is modified to improve volume-of-fluid conservation. The major findings are as follows: (1) effect of capillary force on the dynamic two-phase fluid system with a high density ratio is well predicted for cross-sectional aspect ratio of the channel = 1 and 2; (2) mono-dispersed slug flow pattern transition is reproduced in good agreement with experimental observations in terms of variation in length and interval of droplets as increasing their volumetric flow rates at a constant flow rate ratio = 1. These results prove that the PFM methods can be used for analyzing two-phase fluid motions in various microfluidic devices and micro fabrication processes.

Numerical simulations on confined bubble trains formed by cross-flowing streams are carried out with the numerical code THETIS which is based on the Volume of Fluid (VOF) method and has been developed for two phase flow studies and especially for a gas-liquid system. The surface tension force, which needs particular attention in order to determine the shape of the interface accurately, is computed using the Continuum Surface Force model (CSF). Through the coupling of a VOF-PLIC technique (Piecewise-Linear Interface Calculation) and a smoothing function of adjustable thickness, the Smooth Volume of Fluid technique (SVOF) is intended to capture accurately strong interface distortion, rupture or reconnection with large density and viscosity contrasts between phases. This approach is extended by using the regular VOF-PLIC technique, while applying a smoothing procedure affecting both physical characteristics averaging and surface tension modeling. The front-capturing strategy is extended to gas injection. We begin by introducing the main physical phenomena occurring during bubble formation in microfluidic systems. Then, an experimental study performed in a cylindrical T-junction for different wetting behaviors is presented. For the wetting configuration, Cartesian 2D numerical simulations concerning the gas-liquid bubble production performed in a T-junction with rectangular, planar cross sections are shown and compared with experimental measurements. Finally, the results obtained of bubble break-up mechanism, shape, transport and pressure drop along the channel will be presented, discussed and compared to some experimental and numerical outcomes given in the literature.

Numerical simulation of single bubble pool boiling process including transient thermal response of solid wall is performed using the ghost fluid method and the level set method for the sharp interface representation. The results show that non-physical initial condition in the numerical simulation deeply affects the process of bubble growth, and then multi-cycle simulation is necessary to eliminate its influence. It is shown by the present results that two nucleate criteria, i.e. constant waiting time and constant nucleate superheat, for determining the appearance time for the subsequent bubble lead to the same quasi-steady process of bubble growth if they are matched with each other. A periodically expanding and receding thermal “hollow” can be observed inside solid wall underneath the growing bubble. The recovery of the temperature on the nucleate site and the thermal boundary layer near the heating surface is influenced by transient heat conduction inside solid wall, which can affect evidently bubble thermal dynamics and heat transfer.

In this work we investigate the present capabilities of CFD for wall boiling. The computational model used combines the Euler/Euler two-phase flow description with heat flux partitioning. Very similar modelling was previously applied to boiling water under high pressure conditions relevant to nuclear power systems. Similar conditions in terms of the relevant non-dimensional numbers have been realized in the DEBORA tests using Dichlorodifluoromethane (R12) as the working fluid. This facilitated measurements of radial profiles for gas volume fraction, gas velocity, liquid temperature and bubble size.

Robust predictive capabilities of the modelling require that it is validated for a wide range of parameters. In previous studies (Krepper and Rzehak, 2011, 2013) it was shown that a careful calibration of correlations used in the wall boiling model is necessary to obtain agreement with the measured data. We here consider tests under a variety of conditions concerning liquid subcooling, flow rate and heat flux. It is investigated to which extent a set of calibrated model parameters suffices to cover at least a certain parameter range.

In the paper the potential of the application of a population balance model is demonstrated. The measured gas bubble size profiles show an increase of the bubble size with increased distance from the heated wall caused by bubble coalescence. Furthermore the model framework is shown to be able to describe a shift from wall peak to core peak in the radial gas volume fraction profiles with increasing inlet temperature respective decreasing subcooling temperature, which was observed in some test series.