In this paper, a validation and uncertainty quantification (VUQ) framework for the Eulerian-Eulerian two-fluid-model based multiphase-computational fluid dynamics solver (MCFD) is formulated. The framework aims to answer the question: how to evaluate if a MCFD solver adequately represents the underlying physics of a multiphase system of interest? The proposed framework is based on total data-model integration (TDMI) approach that uses Bayesian method to inversely quantify the uncertainty of the solver predictions with the support of multiple experimental datasets. The framework consists of six steps with state-of-the-art statistical methods, including: 1). Solver evaluation and data collection; 2). Surrogate model construction; 3). Sensitivity Analysis; 4). Parameter selection; 5). Uncertainty quantification with Bayesian inference; and 6). Validation metrics calculation. Those steps are formulated in a modular manner and using non-intrusive methods. Such features ensure the applicability of the flexible framework to different scenarios and modeling of multiphase flow and boiling heat transfer, as well as the extensibility of the framework to support VUQ of different MCFD solvers.
The paper describes capabilities of numerical simulation of liquid flows with solid and/or gas admixtures in centrifugal pumps using modern commercial CFD software packages, with the purpose to predict performance curves of the pumps treating such media. In particular, the approaches and multiphase flow models available in the package CFX-5 are described; their advantages and disadvantages are analyzed.
This paper is the second part of a two-part series, which introduces and demonstrates a Validation and Uncertainty Quantification (VUQ) framework that serves two major purposes: i). quantify the uncertainties of the closure relation parameters and predictions of the Multiphase Computational Fluid Dynamics (MCFD) solver; ii). evaluate the agreement between the solver predictions and the experimental measurements. The framework, with the corresponding theory and method, are outlined in the first part paper. In this paper, the workflow of the framework is implemented and demonstrated for two rele…
In this paper a fully Eulerian solver for the study of multiphase flows for simulating the propagation of surface gravity waves over submerged bodies is presented. We solve the incompressible Navier-Stokes equations coupled with the volume of fluid technique for the modeling of the liquid phases with the interface, an immersed body method for the solid bodies and an iterative strong-coupling procedure for the fluid-structure interaction. The flow incompressibility is enforced via the solution of a Poisson equation which, owing to the density jump across the interfaces of the liquid phases, has…
Classical Computational Fluid Dynamics (CFD) of long-time processes with strongly separated time scales is computationally extremely demanding if not impossible. Consequently, the state-of-the-art description of such systems is not capable of real-time simulations or online process monitoring. In order to bridge this gap, we propose a new method suitable to decouple slow from fast degrees of freedom in many cases. Based on the recurrence statistics of unsteady flow fields, we deduce a recurrence process which enables the generic representation of pseudo-periodic motion at high spatial and temp…
We introduce an Eulerian approach for problems involving one or more soft solids immersed in a fluid, which permits mechanical interactions between all phases. The reference map variable is exploited to simulate finite-deformation constitutive relations in the solid(s) on the same fixed grid as the fluid phase, which greatly simplifies the coupling between phases. Our coupling procedure, a key contribution in the current work, is shown to be computationally faster and more stable than an earlier approach, and admits the ability to simulate both fluid--solid and solid--solid interaction between…
The two-fluid model based Multiphase Computational Fluid Dynamics (MCFD) has been considered as one of the most promising tools to investigate two-phase flow and boiling system for engineering purposes. The MCFD solver requires closure relations to make the conservation equations solvable. The wall boiling closure relations, for example, provide predictions on wall superheat and heat partitioning. The accuracy of these closure relations significantly influences the predictive capability of the solver. In this paper, a study of validation and uncertainty quantification (VUQ) for the wall boilin…
Thus far, Computational Fluid Dynamics (CFD) simulations fail to predict the electrostatic charging of particle-gas flows reliably. The lack of a predictive tool leads to powder operations prone to deposits and discharges, making chemical plants unsustainable and prime candidates for explosions. This paper reviews the rapid progress of numerical models in recent years, their limitations, and outlines future research. In particular, the discussion includes CFD models for the physics and chemistry of particle electrification. The condenser model is most popular today in CFD simulations of powder…
The aim of the present paper is to introduce and to discuss inconsistencies errors that may arise when Eulerian and Lagrangian models are coupled for the simulations of turbulent poly-dispersed two-phase flows. In these hydrid models, two turbulence models are in fact implicitely used at the same time and it is essential to check that they are consistent, in spite of their apparent different formulations. This issue appears in particular in the case of very-small particles, or tracer-limit particles, and it is shown that coupling inconsistent turbulence models (Eulerian and Lagrangian) can res…
Thus far, Computational Fluid Dynamics (CFD) simulations fail to reliably predict the electrostatic charging of powder during pneumatic conveying. The lack of a predictive tool is one reason for unwanted discharges and growing deposits that make a plant a prime candidate for an explosion. This paper reviews the numerical models' state-of-the-art, limitations, and progress in recent years. In particular, the discussion includes the condenser model, which is up to today most popular in CFD simulations of powder flow electrification but fails to predict most of its features. New experiments led t…
In this paper, we develop a machine learning-based Bayesian approach to inversely quantify and reduce the uncertainties of the two-fluid model-based multiphase computational fluid dynamics (MCFD) for bubbly flow simulations. The proposed approach is supported by high-resolution two-phase flow measurement techniques, including double-sensor conductivity probes, high-speed imaging, and particle image velocimetry. Local distribution of key physical quantities of interest (QoIs), including void fraction and phasic velocities, are obtained to support the modular Bayesian inference. In the process, …
Idaho National Laboratory（爱达荷国家实验室）；Massachusetts Institute of Technology（麻省理工学院）；North Carolina State University（北卡罗来纳州立大学）
Multiphase flow phenomena have been widely observed in the industrial applications, yet it remains a challenging unsolved problem. Three-dimensional computational fluid dynamics (CFD) approaches resolve of the flow fields on finer spatial and temporal scales, which can complement dedicated experimental study. However, closures must be introduced to reflect the underlying physics in multiphase flow. Among them, the interfacial forces, including drag, lift, turbulent-dispersion and wall-lubrication forces, play an important role in bubble distribution and migration in liquid-vapor two-phase flow…
The volume of fluid (VOF) method is a popular approach for multiphase flow modeling. The open-source computational fluid dynamics (CFD) software, OpenFOAM, implements a variety of VOF-based solvers and provides users a wide range of turbulence models. Since isothermal multiphase flows under the VOF framework belong to the variable-density incompressible flow category, the isothermal VOF-based solvers in OpenFOAM fail to use the correct turbulence models. varRhoTurbVOF is designed to solve this issue and with the hope to replace all the corresponding existing solvers in the future. With the obj…
An adpative integration technique for time advancement of particle motion in the context of coupled computational fluid dynamics (CFD) - discrete element method (DEM) simulations is presented in this work. CFD-DEM models provide an accurate description of multiphase physical systems where a granular phase exists in an underlying continuous medium. The time integration of the granular phase in these simulations present unique computational challenges due to large variations in time scales associated with particle collisions. The algorithm presented in this work uses a local time stepping approa…
DNS of compressible multiphase flows through the Eulerian approach
Scuola Normale Superiore di Pisa（比萨高等师范学院）；Istituto Nazionale di Vulcanologia e Geofisica（意大利火山学与地球物理研究所）；Istituto Nazionale di Geofisica e Vulcanologia（意大利地球物理与火山学研究所）
An open-sourced multiphase Darcy-Brinkman approach is proposed to simulate two-phase flow in hybrid systems containing both solid-free regions and porous matrices. This micro-continuum model is rooted in elementary physics and volume averaging principles, where a unique set of partial differential equations is used to represent flow in both regions and scales. The crux of the proposed model is that it tends asymptotically towards the Navier-Stokes volume-of-fluid approach in solid-free regions and towards the multiphase Darcy equations in porous regions. Unlike existing multiscale multiphase s…
Direct numerical simulation of a compressible multiphase flow through the fast Eulerian approach
Scuola Normale Superiore di Pisa（比萨高等师范学院）；Istituto Nazionale di Vulcanologia e Geofisica（火山学与地球物理学国家研究所）；Istituto Nazionale di Geofisica e Vulcanologia（地球物理学与火山学国家研究所）
A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and Nichols (1981, J. Comput. Phys., 39, 201)), which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney-Riv…
In this paper we employ two implementations of the fictitious domain (FD) method to simulate water-entry and water-exit problems and demonstrate their ability to simulate practical marine engineering problems. In FD methods, the fluid momentum equation is extended within the solid domain using an additional body force that constrains the structure velocity to be that of a rigid body. Using this formulation, a single set of equations is solved over the entire computational domain. The constraint force is calculated in two distinct ways: one using an Eulerian-Lagrangian framework of the immersed…
Imperial College London（伦敦帝国理工学院）；BP Plc（英国石油公司）；Florida State University（佛罗里达州立大学）；Newcastle University（纽卡斯尔大学）
The modelling of multiphase flow in a pipe presents a significant challenge for high-resolution computational fluid dynamics (CFD) models due to the high aspect ratio (length over diameter) of the domain. In subsea applications, the pipe length can be several hundreds of kilometres versus a pipe diameter of just a few inches. In this paper, we present a new AI-based non-intrusive reduced-order model within a domain decomposition framework (AI-DDNIROM) which is capable of making predictions for domains significantly larger than the domain used in training. This is achieved by using domain decom…
A series of benchmarks based on the physical situation of "phase inversion" between two immiscible liquids is presented. These benchmarks aim at progressing toward the direct numerical simulation of two-phase flows. Several CFD codes developed in French laboratories and using either Volume-of-Fluid or Level-Set interface tracking methods are used to provide physical solutions of the benchmarks, convergence studies and code comparisons. Two typical configurations are retained, with integral scale Reynolds numbers of 13.700 and 433.000, respectively. The physics of the problem are probed through…
In this work, model closures of the multiphase Reynolds-Average Navier-Stokes (RANS) equations are developed for homogeneous, fully-developed gas--particle flows. To date, the majority of RANS closures are based on extensions of single-phase turbulence models, which fail to capture complex two-phase flow dynamics across dilute and dense regimes, especially when two-way coupling between the phases is important. In the present study, particles settle under gravity in an unbounded viscous fluid. At sufficient mass loadings, interphase momentum exchange between the phases results in the spontaneou…
Liquid spreading in gas-liquid concurrent trickle-bed reactors is simulated using an Eulerian twofluid CFD approach. In order to propose a model that describes exhaustively all interaction forces acting on each fluid phase with an emphasis on dispersion mechanisms, a discussion of closure laws available in the literature is proposed. Liquid dispersion is recognized to result from two main mechanisms: capillary and mechanical (Attou and Ferschneider, 2000; Lappalainen et al., 2009- The proposed model is then implemented in two trickle-bed configurations matching with two experimental set ups: I…
In this paper, a three-dimensional numerical solver is developed for suspensions of rigid and soft particles and droplets in viscoelastic and elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow for the first time three-dimensional simulations of inertial and turbulent EVP fluids with a large number particles and droplets. This is achieved by combining fast and highly scalable methods such as an FFT-based pressure solver, with the evolution equation for non-Newtonian (including elastoviscoplastic) stresses. In this flexible computational framework, the fluid can be mod…
Over the past few years much progress has been made in Computational Fluid Dynamics (CFD) in its ability to accurately simulate the hydrodynamics associated with a deep-V monohull planing craft. This work has focused on not only predicting the hydrodynamic forces and moments, but also the complex multiphase free-surface flow field generated by a deep-V monohull planing boat at high Froude numbers. One of these state of the art CFD codes is Numerical Flow Analysis (NFA). NFA provides turnkey capabilities to model breaking waves around a ship, including both plunging and spilling breaking waves,…
An understanding of the hydrodynamics of multiphase processes is essential for their design and operation. Multiphase computational fluid dynamics (CFD) simulations enable researchers to gain insight which is inaccessible experimentally. The model frequently used to simulate these processes is the two-fluid (Euler-Euler) model where fluids are treated as inter-penetrating continua. It is formulated for the multiphase flow regime where one phase is dispersed within another and enables simulation on experimentally relevant scales. Phase fractions are used to describe the composition of the mixtu…
In this work, we discuss some points relevant for stochastic modelling of one- and two-phase turbulent flows. In the framework of stochastic modelling, also referred to PDF approach, we propose a new Langevin model including all viscosity effects and thus that is consistent with viscous Navier-Stokes equations. In the second part of the work, we show how to develop a second-order unconditionally stable numerical scheme for the stochastic equations proposed. Accuracy and consistency of the numerical scheme is demonstrated analytically. In the last part of the work, we study the fluid flow in a …
We propose a numerical methodology for the numerical simulation of distinct, interacting physical processes described by a combination of compressible, inert and reactive forms of the Euler equations, multiphase equations and elastoplastic equations. These systems of equations are usually solved by coupling finite element and CFD models. Here we solve them simultaneously, by recasting all the equations in the same, hyperbolic form and solving them on the same grid with the same finite-volume numerical schemes. The proposed compressible, multiphase, hydrodynamic formulation can employ a hierarc…
We present a robust immersed boundary (IB) method for high density ratio multiphase flows that is capable of modeling complex wave-structure interaction (WSI) problems arising in marine and coastal engineering applications. The IB/WSI methodology is enabled by combining the distributed Lagrange multiplier (DLM) method of Sharma and Patankar (J Comp Phys, 2005) with a robust level set method based multiphase flow solver. The fluid solver integrates the conservative form of the variable-coefficient incompressible Navier-Stokes equations using a hybrid preconditioner and ensures consistent transp…
In multiphase flow phenomena, bubbles and droplets are advected, deformed, break up into smaller ones, and coalesce with each other. A primary challenge of classical computational fluid dynamics (CFD) methods for such flows is to effectively describe a transition zone between phases across which physical properties vary steeply but continuously. Based on the van der Waals theory, Allen-Cahn phase field method describes the face-to-face existence of two fluids with a free-energy functional of mass density or molar concentration, without imposing topological constraints on interface as phase bou…
In this paper we study the motion of a fluid with several dispersed particles whose concentration is very small (smaller than $10^{-3}$), with possible applications to problems coming from geophysics, meteorology, and oceanography. We consider a very dilute suspension of heavy particles in a quasi-incompressible fluid (low Mach number). In our case the Stokes number is small and --as pointed out in the theory of multiphase turbulence-- we can use an Eulerian model instead of a Lagrangian one. The assumption of low concentration allows us to disregard particle--particle interactions, but we tak…
