28 research outputs found
A seven-equation diffused interface method for resolved multiphase flows
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 stiff
pressure- and velocity-relaxation solvers have been used, they are not needed
for the DEM because the non-conservative fluxes are accurately modeled. An
interface compression scheme controls the numerical diffusion of the interface,
and its effects on the solution are discussed. Test cases are used to validate
the computational method and demonstrate its applicability. They include
multiphase shock tubes, shock propagation through a material interface, a
surface-tension-driven oscillating droplet, an accelerating droplet in a
viscous medium, and shock-detonation interacting with a deforming droplet.
Simulation results are compared against exact solutions and experiments when
possible
An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics
Numerical simulation of bubble dynamics and cavitation is challenging; even
the seemingly simple problem of a collapsing spherical bubble is difficult to
compute accurately with a general, three-dimensional, compressible,
multicomponent flow solver. Difficulties arise due to both the physical model
and the numerical method chosen for its solution. We consider the 5-equation
model of Allaire et al. [1], the 5-equation model of Kapila et al. [2], and the
6-equation model of Saurel et al. [3] as candidate approaches for spherical
bubble dynamics, and both MUSCL and WENO interface-capturing methods are
implemented and compared. We demonstrate the inadequacy of the traditional
5-equation model of Allaire et al. [1] for spherical bubble collapse problems
and explain the corresponding advantages of the augmented model of Kapila et
al. [2] for representing this phenomenon. Quantitative comparisons between the
augmented 5-equation and 6-equation models for three-dimensional bubble
collapse problems demonstrate the versatility of pressure-disequilibrium
models. Lastly, the performance of pressure disequilibrium model for
representing a three-dimensional spherical bubble collapse for different bubble
interior/exterior pressure ratios is evaluated for different numerical methods.
Pathologies associated with each factor and their origins are identified and
discussed
Conditional moment methods for polydisperse cavitating flows
The dynamics of cavitation bubbles are important in many flows, but their
small sizes and high number densities often preclude direct numerical
simulation. We present a computational model that averages their effect on the
flow over larger spatiotemporal scales. The model is based on solving a
generalized population balance equation (PBE) for nonlinear bubble dynamics and
explicitly represents the evolving probability density of bubble radii and
radial velocities. Conditional quadrature-based moment methods (QBMMs) are
adapted to solve this PBE. A one-way-coupled bubble dynamics problem
demonstrates the efficacy of different QBMMs for the evolving bubble
statistics. Results show that enforcing hyperbolicity during moment inversion
(CHyQMOM) provides comparable model-form accuracy to the traditional
conditional method of moments and decreases computational costs by about ten
times for a broad range of test cases. The CHyQMOM-based computational model is
implemented in MFC, an open-source multi-phase and high-order-accurate flow
solver. We assess the effect of the model and its parameters on a two-way
coupled bubble screen flow problem.Comment: 19 pages, 9 figures, submitted to J. Comp. Phy
QBMMlib: A library of quadrature-based moment methods
QBMMlib is an open source Mathematica package of quadrature-based moment
methods and their algorithms. Such methods are commonly used to solve
fully-coupled disperse flow and combustion problems, though formulating and
closing the corresponding governing equations can be complex. QBMMlib aims to
make analyzing these techniques simple and more accessible. Its routines use
symbolic manipulation to formulate the moment transport equations for a
population balance equation and a prescribed dynamical system. However, the
resulting moment transport equations are unclosed. QBMMlib trades the moments
for a set of quadrature points and weights via an inversion algorithm, of which
several are available. Quadratures then closes the moment transport equations.
Embedded code snippets show how to use QBMMlib, with the algorithm
initialization and solution spanning just 13 total lines of code. Examples are
shown and analyzed for linear harmonic oscillator and bubble dynamics problems.Comment: Under review Software
MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver
MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock–bubble interaction, and bubble dynamics. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock–bubble, shock–droplet, and shock–water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas–liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock–bubble-vessel-wall and acoustic–bubble-net interactions are used to demonstrate the full capabilities of MFC
Fast Macroscopic Forcing Method
The macroscopic forcing method (MFM) of Mani and Park and similar methods for
obtaining turbulence closure operators, such as the Green's function-based
approach of Hamba, recover reduced solution operators from repeated direct
numerical simulations (DNS). MFM has been used to quantify RANS-like operators
for homogeneous isotropic turbulence and turbulent channel flows. Standard
algorithms for MFM force each coarse-scale degree of freedom (i.e., degree of
freedom in the RANS space) and conduct a corresponding fine-scale simulation
(i.e., DNS), which is expensive. We combine this method with an approach
recently proposed by Sch\"afer and Owhadi (2023) to recover elliptic integral
operators from a polylogarithmic number of matrix-vector products. The
resulting Fast MFM introduced in this work applies sparse reconstruction to
expose local features in the closure operator and reconstructs this
coarse-grained differential operator in only a few matrix-vector products and
correspondingly, a few MFM simulations. For flows with significant nonlocality,
the algorithm first "peels" long-range effects with dense matrix-vector
products to expose a local operator. We demonstrate the algorithm's performance
for scalar transport in a laminar channel flow and momentum transport in a
turbulent one. For these, we recover eddy diffusivity operators at 1% of the
cost of computing the exact operator via a brute-force approach for the laminar
channel flow problem and 13% for the turbulent one. We observe that we can
reconstruct these operators with an increase in accuracy by about a factor of
100 over randomized low-rank methods. We glean that for problems in which the
RANS space is reducible to one dimension, eddy diffusivity and eddy viscosity
operators can be reconstructed with reasonable accuracy using only a few
simulations, regardless of simulation resolution or degrees of freedom.Comment: 16 pages, 10 figures. S. H. Bryngelson and F. Sch\"afer contributed
equally to this wor
A Gaussian moment method and its augmentation via LSTM recurrent neural networks for the statistics of cavitating bubble populations
Phase-averaged dilute bubbly flow models require high-order statistical moments of the bubble population. The method of classes, which directly evolve bins of bubbles in the probability space, are accurate but computationally expensive. Moment-based methods based upon a Gaussian closure present an opportunity to accelerate this approach, particularly when the bubble size distributions are broad (polydisperse). For linear bubble dynamics a Gaussian closure is exact, but for bubbles undergoing large and nonlinear oscillations, it results in a large error from misrepresented higher-order moments. Long short-term memory recurrent neural networks, trained on Monte Carlo truth data, are proposed to improve these model predictions. The networks are used to correct the low-order moment evolution equations and improve prediction of higher-order moments based upon the low-order ones. Results show that the networks can reduce model errors to less than 1% of their unaugmented values