Sharp-interface Simulations of Energetic Multiphase Flows with Large Density and Viscosity Ratios
Delft University of Technology（代尔夫特理工大学）；Maritime Research Institute Netherlands (MARIN)（荷兰海事研究所）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
Tzu-Yao Huang, Nicolas Valle, Artur K. Lidtke, Kelli Hendrickson, Gabriel D. Weymouth
备注：
Proceedings of 36th Symposium on Naval Hydrodynamics
Flows with high density ratios, such as wave breaking and air entrainment in maritime applications, remain challenging to simulate due to their energetic and strongly nonlinear nature. In such regimes, maintaining numerical robustness is difficult when using the commonly adopted velocity-based formulation. The Consistent Mass-Momentum (CMOM) transport framework improves numerical robustness by enforcing fundamental physical properties, most notably momentum conservation and semi-discrete energy-conserving. However, CMOM replaces the advection of a continuous velocity field with that of a discontinuous momentum field. When combined with sharp interface methods, this leads to severe momentum shocks, for which conventional shock-capturing schemes are ineffective. To reconcile physical fidelity with numerical robustness, this work proposes a Synchronized Donor-Region of Momentum fluxes (SynDRoM) that enforces monotonicity of the transported velocity field. The resulting algorithm effectively eliminates spurious velocity oscillations without sacrificing physical fidelity, as demonstrated through scalar transport and interfacial shear instability test cases. Beyond difficulties from large density ratio, improper estimation of viscosity in the vicinity of the interface can introduce numerical instabilities at finite time steps, thereby undermining overall robustness. To address this issue, a viscosity limiter based on the bounded kinetic viscosity concept is introduced and validated using a gravity-driven plane shear flow. Finally, a breaking wave simulation is performed to assess the combined performance of the proposed physics-preserving numerical schemes for multiphase flows.
This work investigates the effects of the choice of momentum diffusion operator on the evolution of multiphase fluid systems resolved with Meshless Lagrangian Methods (MLM). Specifically, the effects of a non-zero viscosity gradient at multiphase interfaces are explored. This work shows that both the typical Smoothed Particle Hydrodynamics (SPH) and Generalized Finite Difference (GFD) diffusion operators under-predict the shear divergence at multiphase interfaces. Furthermore, it was shown that larger viscosity ratios increase the significance of this behavior. A multiphase GFD scheme is propo…
This study presents a novel pressure-based methodology for the efficient numerical solution of a four-equation two-phase diffuse interface model. The proposed methodology has the potential to simulate low-Mach flows with mass transfer. In contrast to the classical conservative four-equation model formulation, the adopted set of equations features volume fraction, temperature, velocity and pressure as the primary variables. The model includes the effects of viscosity, surface tension, thermal conductivity and gravity, and has the ability to incorporate complex equations of state. Additionally, …
The predictions of resolvent analysis for turbulent channel flow are evaluated for a friction Reynolds number of Retau = 550. In addition to the standard resolvent operator with kinematic viscosity, a resolvent operator augmented with the Cess eddy viscosity is considered. Adding eddy viscosity significantly alters the low-rank behavior of the resolvent. Regardless of the wave speed selected, the eddy resolvent is low-rank for spanwise wavelengths of ly+ = 80 and ly/h = 3.5 in comparison to the standard resolvent whose low-rank behavior depends on the wave speed. The leading eddy modes have hi…
The computation of multiphase flows presents a subtle energetic equilibrium between potential (i.e., surface) and kinetic energies. The use of traditional interface-capturing schemes provides no control over such a dynamic balance. In the spirit of the wellknown symmetry-preserving and mimetic schemes, whose physics-compatible discretizations rely upon preserving the underlying mathematical structures of the space, we identify the corresponding structure and propose a new discretization strategy for curvature. The new scheme ensures conservation of mechanical energy (i.e., surface plus kinetic…
Speed of sound is a key parameter for the compressibility effects in multiphase flow. We present a new approach to do direct numerical simulations on the speed of sound in compressible two-phase flow, based on the stratified multiphase flow model (Chang & Liou, JCP 2007). In this method, each face is divided into gas-gas, gas-liquid, and liquid-liquid parts via reconstruction of volume fraction, and the corresponding fluxes are calculated by Riemann solvers. Viscosity and heat transfer models are included. The effects of frequency (below the natural frequency of bubbles), volume fraction, visc…
The seven-equation model is a compressible multiphase formulation that allows for phasic velocity and pressure disequilibrium. These equations are solved using a diffused interface method that models resolved multiphase flows. Novel extensions are proposed for including the effects of surface tension, viscosity, multi-species, and reactions. The allowed non-equilibrium of pressure in the seven-equation model provides numerical stability in strong shocks and allows for arbitrary and independent equations of states. A discrete equations method (DEM) models the fluxes. We show that even though st…
In the present study, the multiphase volume distribution problem, where there can be an arbitrary number of phases, is addressed using a consistent and conservative volume distribution algorithm. The proposed algorithm satisfies the summation constraint, the conservation constraint, and the \textit{consistency of reduction}. The first application of the volume distribution algorithm is to determine the Lagrange multipliers in multiphase Phase-Field models that enforce the mass conservation, and a multiphase conservative Allen-Cahn model that satisfies the \textit{consistency of reduction} is d…
We present a modification of a recently developed volume of fluid method for multiphase problems, so that it can be used in conjunction with a fractional step-method and fast Poisson solver, and validate it with standard benchmark problems. We then consider emulsions of two-fluid systems and study their rheology in a plane Couette flow in the limit of vanishing inertia. We examine the dependency of the effective viscosity on the volume-fraction (from 10% to 30%) and the Capillary number (from 0.1 to 0.4) for the case of density and viscosity ratio 1. We show that the effective viscosity decrea…
A large number of models which address the dynamics of particle-laden turbulent flows have been developed based on the assumption of local isotropy and use the Kolmogorov constant that correlates the spectral distribution of turbulent kinetic energy with the turbulent dissipation rate. Many turbulence models (Stochastic and LES models) use the Kolmogorov constant in the formulation. Compilation of a large number of experimental data for different flow configurations has revealed that the Kolmogorov constant is independent of Reynolds number in the limit of high Reynolds number (Sreenivasan, 19…
Response modes computed via linear resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models, or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In th…
Discontinuity-aware physics-informed neural network for phase-field method in three-phase flow with phase change
School of Interdisciplinary Science, Beijing Institute of Technology（北京理工大学交叉科学学院）；School of Mechatronical Engineering, Beijing Institute of Technology（北京理工大学机电学院）；IFP Energies nouvelles（法国石油研究院）；School of Aerospace Engineering, Beijing Institute of Technology（北京理工大学航天航空学院）；Beijing Institute of Technology (Zhuhai)（北京理工大学（珠海））
This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined Cartesian grids that adapt to the evolving interfaces and track regions of high vorticity. The algorithm combines the interface capturing level set method with a variable-coefficient incompressible Navier-Stokes solver that is demonstrated to stably resolve material contrast ratios of up to six orders of magnitude. The discretization approach ensures second-order pointwise accuracy for both velocity and pressure with several physical boundary treatments, …
Multiphase shear flows often show banded structures that affect the global behavior of complex fluids e.g. in microdevices. Here we investigate numerically the banding of emulsions, i.e. the formation of regions of high and low volume fraction, alternated in the vorticity direction and aligned with the flow (shear bands). These bands are associated with a decrease of the effective viscosity of the system. To understand the mechanism of banding experimentally observed we have performed interface resolved simulations of the two-fluid system. The experiments were perfomed starting with a random d…
We investigate the statistics of turbulence in emulsions of two-immiscible fluids of same density. We compute for the first time velocity increments between points conditioned to be located in the same phase or in different phases and examine their probability density functions (PDF) and the associated structure functions (SF). This enables us to demonstrate that the the presence of the interface reduces the skewness of the PDF at scales below the Kolmogorov-Hinze scale and therefore the magnitude of the energy flux towards the dissipative scales, which is quantified by the third-order SF. The…
Turbulent convection is thought to act as an effective viscosity ($ν_E$) in damping tidal flows in stars and giant planets. However, the efficiency of this mechanism has long been debated, particularly in the regime of fast tides, when the tidal frequency ($ω$) exceeds the turnover frequency of the dominant convective eddies ($ω_c$). We present the results of hydrodynamical simulations to study the interaction between tidal flows and convection in a small patch of a convection zone. These simulations build upon our prior work by simulating more turbulent convection in larger horizontal boxes, …
Microscopic multiphase flows have gained broad interest due to their capability to transfer processes into new operational windows and achieving significant process intensification. However, the hydrodynamic behavior of Taylor droplets is not yet entirely understood. In this work, we introduce a model to determine the excess velocity of Taylor droplets in square microchannels. This velocity difference between the droplet and the total superficial velocity of the flow has a direct influence on the droplet residence time and is linked to the pressure drop. Since the droplet does not occupy the e…
An asymmetry in the number density of left- and right-handed fermions is known to give rise to a new term in the induction equation that can result in a dynamo instability. At high temperatures, when a chiral asymmetry can survive for long enough, this chiral dynamo instability can amplify magnetic fields efficiently, which in turn drive turbulence via the Lorentz force. While it has been demonstrated in numerical simulations that this chiral magnetically driven turbulence exists and strongly affects the dynamics of the magnetic field, the details of this process remain unclear. The goal of th…
Slug flows are a typical intermittent two-phase flow pattern that can occur in submarine pipelines connecting the wells to the production facility and that is known to cause undesired consequences. In this context, computational fluid dynamics appears to be the tool of choice to understand their formation. However, few direct numerical simulations of slug flows are available in the literature, especially using meshless methods which are known to be capable of handling complex problems involving interfaces. In this work, a 2D study of the instability processes leading to the formation of interm…
