Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session L10: Multiphase Flows: Modeling and Theory II |
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Chair: Shankar Subramaniam, Iowa State University Room: Georgia World Congress Center B215 |
Monday, November 19, 2018 4:05PM - 4:18PM |
L10.00001: Extending current mathematical formulations of multiphase flow to regions of strong inhomogeneity Shankar Subramaniam, S. Balachandar In particle-laden flows, sprays and bubbly flows, it is commonplace to encounter steep gradients in the average number density and volume fraction at material fronts where the multiphase flow penetrates into the continuous carrier phase. The growth of instabilities at the boundary is of critical importance in many applications and is tied to the growth of fluctuations at the interface. This problem violates the standard separation of scales assumption that underlies current multiphase flow theories. This talk examines the adequacy of three commonly used mathematical formulations—ensemble-averaging, volume-averaging and spatial filtering—to capture this important phenomenon. Extensions to current formulations that are needed to relax the scale separation assumption and properly represent this phenomenon will be presented. Connections to flows involving the clustering of dispersed phase entities, which are also characterized by fluctuations in number and volume fraction, will be established. These new formulations have the capability to represent the full range of multiphase flow phenomena. Implications for existing theories, models and simulations will be highlighted. |
Monday, November 19, 2018 4:18PM - 4:31PM |
L10.00002: General Definition of Particle-fluid-particle Stress in Multiphase Flows Duan Zhong Zhang, Georges Akiki, Marianne M Francois Particle-particle interactions result in a stress in a dense system. For systems containing small amount of viscous liquids, the particle interaction becomes particle-fluid-particle interaction through the liquid bridges between particles. In this case we have clear definition of the particle-fluid-particle stress which appears in the momentum equation for the particle phase. As the liquid amount increases, the liquid bridges cannot be clearly identified, while there is no reason for the particle-fluid-particle stress to disappear from the momentum equation. In this presentation, we start from the ensemble averaging method to show that the stress can be defined using particle forces conditionally averaged on the nearest neighbor. These forces are not necessary interaction forces between particles, but statistical correlations given the nearest pair. The assumption of pair interaction is not necessary; therefore, this definition is valid for finite volume fractions. The stress is defined as an integral over the space surrounding a particle. The use of the nearest neighbor quantities ensures convergence of the integral. |
Monday, November 19, 2018 4:31PM - 4:44PM |
L10.00003: Particle-Fluid-Particle Stress in Multiphase Flows Georges Akiki, Marianne M Francois, Duan Zhong Zhang Multiphase flows with particles modeled using an Euler-Euler formulation often neglect the stress coming from the particle-fluid-particle (PFP) interactions. Consider an array of particles moving in otherwise quiescent inviscid fluid. For a potential uniform flow over a single sphere, the forces are zero due to symmetry, implying that the presence of the fluid has no effect on the particles. In reality, the PFP interactions will break this symmetry which leads to a non-zero force. This force is represented by a stress gradient term in the momentum equation which to our best knowledge has never been quantified and modeled. In this presentation, we discuss the definition and calculation of this stress. We first present the calculation of the stress in the potential flow limit. For finite Reynolds numbers, the stress can be approximately calculated using the Pairwise Interaction Point Particle (PIEP) model (Akiki et al. JFM 2017) valid up to a moderate volume fractions of 0.2. To calculate the stress, we need to compute the average forces acting on particles conditional on the nearest particle location and then integrate over the relative pair locations over the space. The use of quantities conditional on the nearest particles ensures the convergence of the integral. |
Monday, November 19, 2018 4:44PM - 4:57PM |
L10.00004: 3D computational investigation of plug motion and film deposition in straight and Y-shaped tubes with pre-wetted walls Cory Hoi, Ashish Pathak, Mehdi Raessi Liquid plug flow through tubes and the associated liquid film deposition play an important role in several applications, including medical procedures (e.g., surfactant replacement therapy), coating industry, chemical processing, etc. Previous studies have developed empirical and theoretical correlations predicting the thickness of the film deposited by the plug for relatively small capillary numbers. We present 3D CFD simulations of plug motion in straight and Y-shaped tubes with pre-wetted walls for a range of capillary numbers. The pre-existing film is differentiated from the deposited film by using a passive scalar that tags the liquid plug allowing for accurate quantification of transient film deposition. We study the temporal and spatial variation of the deposited film thickness, and show its dependency on pre-existing film thickness and interplay between gravity and plug inertia. Additionally, we present 3D simulations of plug splitting in Y-shaped tubes at various roll angles, where one daughter tube is gravitationally favored. The plug splitting is quantified as a plug split ratio. We also discuss the 3D orientation of the liquid plug in the bifurcation zone. |
Monday, November 19, 2018 4:57PM - 5:10PM |
L10.00005: Numerical simulation of wax deposition in crude-oil flows in a pipeline Mirco Magnini, Omar K Matar Crude oils are complex mixtures of hydrocarbons including high molecular weight paraffin waxes. When a “waxy” crude oil flows through a cold pipeline whose temperature is below the wax appearance temperature, e.g. in subsea transportation systems, heavy paraffins separate and deposit on the pipe walls. The available prediction methods for wax deposition are essentially empirical, in particular in terms of the description of the fouling removal due to the coupling between the deposit layer and the bulk flow. We present a numerical model to simulate fouling deposition, based on the solution of the Navier-Stokes and energy equations for the oil-fouling mixture using a Volume-Of-Fluid method. Additional transport equations for the waxy and non-waxy components within each phase are solved simultaneously. The wax deposition process is described using a chemical equilibrium model based on the Gibbs free energy. The numerical framework is validated by comparison with experimental wax deposition data from the literature. The model is suitable for parametric studies of the wax deposition process and can be developed further to incorporate the effect of wax inhibitors. |
Monday, November 19, 2018 5:10PM - 5:23PM |
L10.00006: Spontaneous structure formation in polymer blends: implications for reactor design Pavan Inguva, Lachlan R Mason, Richard V Craster, Omar K Matar When engineering new materials for energy storage and membrane applications, material scientists must learn to design and create novel porous structures. A physical understanding of the relevant continuous manufacturing techniques is difficult to capture, particularly as micro-scale structure formation can be disrupted by the presence of macro-scale flows. Comprehensive modelling of such systems remains a challenge due to length scale disparity: any included transport models must be solved at the unit-operation scale, while simultaneously capturing structure formation at the level of the product material. Here, we simulate spontaneous structure formation within flowing polymer blends. Detailed pattern formation is modelled via a coupling of the Navier–Stokes and multi-component Cahn–Hilliard equations. To cascade physical information across scales, we consider a moving frame formation in which characteristic time-dependent shear fields are sampled from accompanying reactor-scale flow simulations. This approach enables a closed-loop design whereby macro-scale design parameters, including reactor geometry, can be tuned such that micro-scale properties are optimised for each target application. |
Monday, November 19, 2018 5:23PM - 5:36PM |
L10.00007: Travelling-wave spatially periodic forcing of asymmetric binary mixtures Lennon O Naraigh We study travelling-wave spatially periodic solutions of a forced Cahn-Hilliard equation. This is a model for phase separation of a binary mixture, subject to external forcing. We look at arbitrary values of the mean mixture concentration, corresponding to asymmetric mixtures (previous studies have only considered the symmetric case). We characterize in depth one particular solution which consists of an oscillation around the mean concentration level, using a range of techniques, both numerical and analytical. We determine the stability of this solution to small-amplitude perturbations. Next, we use methods developed elsewhere in the context of shallow-water waves to uncover a (possibly infinite) family of multiple-spike solutions for the concentration profile, which linear stability analysis demonstrates to be unstable. Throughout the work, we perform thorough parametric studies to outline for which parameter values the different solution types occur. |
Monday, November 19, 2018 5:36PM - 5:49PM |
L10.00008: Modeling the speed of jet induced by a shock wave Xiao Bai, Xiaolong Deng When a shock wave impacts on a curved interface between two fluids, the disturbance will grow as described by Richtmyer-Meshkov instability (RMI). If the shock runs from a heavy fluid to a light fluid, the interface shape may be reversed and a jet could be generated. Although numerical simulations could give more details, as shown in our earlier work on single-mode RMI (Bai, Deng & Jiang, Shock Waves 2018), people often wants a simple analytical model to predict the interface movement. In the current work, under the situation of a planar shock wave impacting a spherical cap interface, we try to use analytical and numerical methods to model the speed of jet and so provide a tool to predict the maximum jet speed. Through theoretical analysis, the formula of interfacial velocity between liquid-gas interface is achieved and applied to the modeling of jet speed. Then numerical simulations with a cut-cell based sharp-interface method (Chang, Deng & Theofanous, JCP 2013) are performed to validate the formula and identify the related parameters. The analytical formula of interfacial velocity and the result model of maximum jet speed could be used to estimate the interfacial behavior in similar situations. |
Monday, November 19, 2018 5:49PM - 6:02PM |
L10.00009: Numerical study of surfactant dynamics during emulsification in a T-junction microchannel Antoine Riaud, Hao Zhang, Kai Wang, Guangsheng Luo Microchannel emulsification requires large amounts of surfactant to prevent coalescence and improve emulsions lifetime. However, most numerical studies have considered surfactant-free mixtures as models for droplet formation in microchannels, without taking into account the distribution of surfactant on the droplet surface. In this presentation, we develop an extended lattice-Boltzmann model to investigate the effects of nonuniform surfactant coverage on the microfluidic flow pattern. This numerical study, supported by micro-particle image velocimetry experiments, reveals the likelihood of uneven distribution of surfactant during the droplet formation and the appearance of a stagnant cap. The Marangoni effect affects the droplet breakup by increasing the shear rate. According to our results, surfactant-free and surfactant-rich droplet formation processes are qualitatively different, such that both the capillary number and the Damköhler number should be considered when modeling the droplet generation in microfluidic devices. |
Monday, November 19, 2018 6:02PM - 6:15PM |
L10.00010: An Analysis of the Droplet Splitting Ratio in Asymmetric T-junction Reza Sadr, Way Lee Cheng, Arum Han There is an increasing interest in splitting droplets into two smaller, unequal, droplets as a major functional feature in a variety of microfluidic applications. In this work, the dynamics of droplet breakups in an asymmetric microchannel T-junctions system is investigated. Finite volume simulations were conducted in ANSYS Fluent for the splitting of water micro-droplet in oil within an asymmetric T-junction to examine the breakup dynamics. The evolution of droplets during breakup was examined. The splitting ratio for asymmetric breakup is presented under different flow conditions. In particular, the focus is with the breakup with permanent obstruction and the unstable breakup regimes. More often, the splitting ratio is often larger than the pressure gradient ratio and only in certain circumstances it is equal to the pressure gradient ratio. The splitting ratio may increase to up to twice of the pressure gradient ratio of the T-junction as Capillary number decreases for breakup in the unstable breakup regime. For the case of the splitting ratio follows the pressure gradient ratio, breakup is in the permanent obstruction regime. Additional factors affecting the breakup process such as the cross-section area and the interfacial properties are also examined. |
Monday, November 19, 2018 6:15PM - 6:28PM |
L10.00011: Dissolution or Growth of a Liquid Drop Embedded in a Continuous Phase of Another Liquid via a Phase-Field Ternary Mixture Model based on the NRTL (Non-Random Two Liquid) equation. Roberto Mauri, Andrea Lamorgese We simulate the diffusion-driven dissolution or growth of a single-component drop embedded in a continuous phase of a binary liquid (or viceversa). Our theoretical approach follows a phase field model of partially miscible ternary liquid mixtures, which is based on a regular solution assumption together with a Cahn-Hilliard representation of the nonlocal components of the Gibbs free energy of mixing. In addition, the excess free energy is modeled with either a Flory-Huggins or an NRTL model equation. Based on 2D simulation results, we show that for a single-component drop embedded in a continuous phase of a binary liquid (which is highly miscible with either one component of the continuous phase but immiscible with the other) the size of the drop can either shrink to zero or reach a stationary value, depending on whether the global composition of the mixture is within the one-phase region or the unstable range of the phase diagram. Similar results are obtained in the case of an isolated two-component drop embedded in a continuous phase of a single-component liquid. Finally, we show that the results obtained using the two excess free energy models are virtually identical to each other. |
Monday, November 19, 2018 6:28PM - 6:41PM |
L10.00012: Sparse identification of particle-laden turbulence closures Sarah Beetham, Jesse S Capecelatro In this talk, we present a sparse identification methodology for model closure of the multiphase Reynolds Average Navier—Stokes (RANS) equations, with specific emphasis on collisional fluid-particle flows. Sparse identification of multiphase RANS closures (SIMR) employs linear regression with a mixed penalty term. The penalty acts to ensure sparsity of the resultant model and bounded coefficients, thereby encouraging robust model selection. The outcome is a compact, algebraic RANS model, which is easily incorporated into existing CFD solvers and allows direct inferences about underlying physics to be drawn. We first demonstrate the SIMR methodology on single-phase homogeneous shear turbulence, and show improvement over existing turbulence models. We then demonstrate the method on highly-resolved data obtained from Eulerian-Lagrangian simulations of fully-developed cluster-induced turbulence (CIT), where fluctuations in particle concentration generate and sustain the carrier-phase turbulence. The numerical data is used as the training basis of the sparse identification regression to infer improved closure models for the Reynolds Stress Equations. |
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