Session Q26: Multiphase Flows: Computational Methods II

Graph Neural Network Models of Multiphase Flow from Boundary Integral Methods

The suitability of graph convolutional neural networks for modeling multiphase flow through porous media is studied. The models are tasked with predicting interfacial velocity given fluid properties, such as capillary number, plus the location of fluid-fluid and fluid-solid particle interfaces as input. The networks are trained with data from high accuracy boundary integral simulations, a technique for simulating Newtonian flows at low Reynolds number, in which only the interface between fluid phases is meshed. The velocity at each collocation point is a function of all other points, so the adjacency matrix must be defined appropriately. When graph edges are weighted by inverse distance (within a cutoff), graph convolutional networks can encode the physics of multiphase flow interacting with solid obstacles, even without incorporating other physics-informed quantities, e.g., the curvature of the interface. Using graph convolutions with skip connections makes the use of very deep networks unnecessary. The performance of these optimized networks is compared to deep, densely connected neural networks and deep graph networks. The models developed in this work can accurately simulate interfacial flows two to three orders of magnitude faster than the original boundary integral simulations.   

Impact of the discretization on the stability of an RMT based Fully Eulerian FSI approach in 1D

Numerical simulation of fluid structure interaction (FSI) plays a critical role in analyzing a wide range of engineering applications, such as aircraft or medical device design. In the Fully Eulerian "one-continuum" approach to FSI, a single set of governing equations is solved in Eulerian form with variable properties and constitutive laws to model both the solid and fluid. A fixed non-conforming grid can be used along with an interface-capturing method, such as the level set method, to easily handle complex interface geometries and motions associated with large solid deformations. In this work, we investigate the impact of the discretization on the stability of a reference map technique (RMT) based Fully Eulerian FSI method in 1D. This approach utilizes the inverse motion map to track deformation of the solid and the fluid-solid boundary. We apply several discretization choices to the RMT based FSI equations and analyze the stability properties of the methods in the context of a 1D manufactured solution example involving a weakly compressible fluid and solid.   

Bypassing quadrature moment method instability via recurrent neural networks with application to cavitating bubble dispersions

Numerical models of disperse bubbly, cavitating flow require high-order moments of the dispersion statistics. The quadrature method of moments (QMOM) provide a framework for approximating these moments. QMOM carries a finite set of raw statistical moments and inverts them for an optimal quadrature rule as needed. However, moment-set realizability and moment-transport-equation instability can prohibit extending to arbitrarily high-order moments, thus limiting attainable accuracy. This limit is encountered when modeling a cavitating bubble population via conditional QMOM (CQMOM). For example, we show that even three-node CQMOM closure of the Rayleigh--Plesset equation is unstable (though two-node is stable). We treat this issue by dynamically altering the two-node quadrature rule via a long short-term memory recurrent neural network. The network is trained on Monte Carlo data and utilizes a novel loss function that penalizes both the error in the computed moments and unrealizable features in the projected moment set. This approach reduces the relative error of the high-order moments by about a factor of ten without numerical instabilities. Further improvement is seen when augmenting the quadrature rule with additional quadrature points.   

A volume-of-fluid (VOF) methodology for the prediction of cavitation phenomena

A sharp interface approach for modeling cavitation phenomena in incompressible viscous flows is presented. We utilize the incompressible Navier-Stokes equations with a modified Poisson equation to account for phase change taking place at the boundary. The phase change is modeled via a semi-implicit mass transfer term. We adopt a one-fluid formulation for the liquid-vapor two-phase flow and the interface is tracked using a modified volume-of-fluid (VOF) methodology. The modification to VOF is at the level of the advection step whereby the interface is advected with two velocity components, the first one originating from the incompressible flow field, and the second emerging as a result of phase change, whilst maintaining the sharpness of the interface. Details of the method and validation examples will be presented.   

Reconstructing Sub-Filter Shear Driven Instabilities for a Dual Scale Model with a Geometrically Transported Vortex Sheet

A method to predict sub-filter velocities in the presence of shear on a liquid-gas phase interface for use in a dual scale LES model is presented. The method reconstructs the sub-filter velocity field on a high resolution grid overlaid on the flow solver grid in a narrow band near the interface. A vortex sheet is applied at the interface location and transported by an unsplit geometric volume and surface area advection scheme with a Piecewise Linear Interface Construction (PLIC) representation of the material interface. At each step and desired location the shear-induced velocities can be calculated by integrating the vortex sheet and other relevant quantities over the liquid-gas surface. In an effort to keep computational cost low, the sub-grid velocity reconstruction is limited to a small number of cells near the phase interface necessary for geometric transport. The vortex sheet method is tested and compared against prior literature and a 3D implementation is discussed.   

A novel profile-preserving Phase-Field method to model multiphase flows

The Phase-Field methods, also known as the Diffuse-Interface methods, have been popularly used to model multiphase flows. The order parameters, governed by the Phase-Field equation, not only serve as phase indicators but also are related to computing the density of the fluid mixture and the surface tension force. After implementing the consistent and conservative volume distribution algorithm, a novel Phase-Field equation is developed, aiming to (i) conserve the mass of each phase, (ii) maintain the interface thickness, and (iii) preserve the equilibrium profile across phase interfaces. These properties are beneficial to avoid excessive numerical diffusion that keeps thickening the interfaces, to reduce distortion of the interfacial profile due to flow advection, and to improve the accuracy of computing the buoyancy and surface tension forces. Then, this novel Phase-Field equation is coupled to the flow dynamics consistently, and canonical problems are performed to demonstrate its effectiveness.   

Numerical modelling of bubble dynamics and growth in supersaturated water using a Front-Tracking method

Understanding and controlling bubble formation are of key importance for designing efficient electrochemical processes such as hydrogren production. In aqueous electrolytic solutions, bubble formation and the resulting void fraction have been found to be a function of the supersaturation. In addition, as the bubbles grow and rise, surface tension gradients along the interface are generated by species concentration gradients and/or surface active agents, which affect the bubbles dynamics (Marangoni stresses). In this study, we use the open-source platform OpenFOAM to solve the one-fluid formulation of the Navier-Stokes equations as well as the transport of dissolved gases in the aqueous solution and we present an interface-tracking method (Level Contour Reconstruction Method) to model two-phase flows. Benchmarks are used to show the accuracy of the method to simulate capillary driven flows as well as variable surface tension flows. 3D numerical simulations are then performed to study the effects of supersaturation of solutions on the bubble dynamics and its wake.   

FluTAS: a GPU-accelarated solver for multiphase flow applications

A numerical tool for GPU-accelerated simulations of fluid transport and multiphase flows is presented. Starting from the single-phase in-house solver CaNS-GPU (Costa et. al, Comput. Math. with Appl. 2021), the algebraic volume of fluid method MTHINC (Satoshi Ii et al., J. Comput. Phys. 2012) has been ported to GPU using OpenACC directives. Specific care has been paid to the parallelization of the Poisson solver where, optionally, to further reduce the communications among devices, an elliptic solver, based on a slab decomposition, has been included showing remarkable advantages in terms of the overall scalability. Next, to further expand the capabilities of the code, thermal effects have been ported in the accelerated version either in the Boussinesq approximation or in the more general low Mach framework. The entire code has been thoroughly tested first with canonical benchmarks of multiphase flows (e.g., Zalesak disk and three-dimensional rising bubble) and then employed in two more demanding configurations: bubbles in homogeneous isotropic turbulence and two-layer Rayleigh-Bernard convection. Both cases show remarkable potentials for simulations of multiphase flows on accelerated architectures.   

Breaching the capillary time-step constraint

The capillary time-step constraint is the dominant limitation on the applicable time-step for most simulations of interfacial flows with surface tension and, consequently, governs the execution time of these simulations. We propose a fully-coupled algorithm based on an algebraic Volume-of-Fluid (VOF) method, whereby the advection of the interface is solved together with the momentum and continuity equations of the interfacial flow in a single system of linearised equations. Surface tension is represented by an implicit formulation of the Continuum Surface Force (CSF) model, in which both the interface curvature and the gradient of the colour function are treated implicitly with respect to the colour function. Hence, this numerical framework features an implicit coupling of pressure, velocity and the VOF colour function in each governing equation. Results of representative test-cases are presented, which demonstrate that this new numerical framework makes it possible to apply time-steps larger than the capillary time-step constraint, as long as other relevant time-step constraints are respected.   

Self-induced velocity disturbance correction with consideration of weak-inertia and transient effects in Euler-Lagrange simulations

The velocity disturbance developing out of the transfer of momentum from a moving point-particle to the underlying fluid is known to limit the accuracy of the Euler-Lagrange (EL) simulation of particle-laden flows. In EL simulations, the fluid forces acting on each particle are estimated using reduced models, which require knowing the local undisturbed fluid velocity. This conceptual velocity can be recovered by substracting the particle's self-induced velocity disturbance from the local disturbed fluid velocity. In recent years, a variety of models have been proposed for its estimation, however they mostly rely upon steady Stokes flow solutions, augmented with semi-empirical corrections for inertial and transient effects. In this work, we propose a novel unified correction that intrinsically considers these effects for the recovery of the undisturbed fluid velocity. It is based on the solution to the linearised governing equations of the particle's self-induced flow disturbance, expressed as the linear combination of regularised fundamental singular solutions to the unsteady Stokes flow equations, and does not require the introduction of empirical or ad hoc parameters. The proposed correction is validated and compared to other published corrections with relevant test-cases.