Session R36: Multiphase Flows: Computational Methods IV

Time Accurate Solutions of the Fokker-Planck Equation in Simple Shear

Existing efforts in simple shear flow have deemed solving the Fokker-Planck (FP) equation for fiber orientation kinetics using the centered differencing scheme (CDS) with an explicit time integration scheme (ETS) unstable, expensive, and inaccurate at high Peclet numbers (Pe). This work shows that conservative solutions may be obtained for the FP equation using this combination of schemes at a low computational cost. The FP equation is solved on unstructured cubed-sphere grids using the finite-volume method. The ETS is a two-stage second-order Runge-Kutta scheme. A modified Jeffery equation (Ferec et al. Rheol. Acta (2014) 53:445–456) is employed to solve for the time evolution of the orientation vector. The approach accounts for variable shape factor and rotational diffusion coefficient. Because an ETS is employed, the coupling of the fiber orientation probability density function with the shape factor and rotational diffusion coefficient does not require linearization. The solver is rigorously tested to show that the CDS does not require stabilization in the Pe interval considered. Solutions are obtained for non-dilute and semi concentrated suspensions up to Pe=100000. We will demonstrate that the solver aids the development of constitutive relations and closure models.   

Effect of Feedback Force on Self-Induced Perturbation Flow at Finite Volume Fraction

In Euler-Lagrange simulation in an unbounded domain, self-induced perturbation flow of an isolated particle is due to the application of a feedback force at the particle's location smoothed using a Gaussian function. This study aims to examine the impact of finite volume fraction and the feedback force on the self-induced perturbation velocity at the particle's location. Several physical parameters influence the self-induced perturbation velocity, including the Reynolds number based on the Gaussian width (Re_σ), the magnitude of feedback force components in the x and y directions (F_x and F_y) and averaged volume fraction (Φ₀). By investigating various combinations of these parameters, we explore the effect of increasing particle volume fraction on the self-induced correction, as well as the effect of an angled feedback force.    

Inferring multiscale bubble growth dynamics by deep neural operator learning

Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge in complex fluids. In this talk, we will present a composite deep neural network (a branch and a trunk network) for regressing nonlinear operators to predict multiscale bubble growth dynamics. We consider tiny bubbles of initial size from 100 nm to 10 μm modelled by the Rayleigh–Plesset equation in the deterministic continuum regime above 1 μm and the many-body dissipative particle dynamics method for bubbles below 1 μm in the stochastic microscale regime. We simulate the multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields, and collect simulation data of bubble growth for both deterministic continuum regime and stochastic microscale regime. Subsequently, we train the composite deep neural network based on mixed data to learn the governing operator of multiscale bubble growth dynamics. Results show that the trained neural operator can capture correct physics and make accurate predictions of bubble growth on-the-fly (within a fraction of a second) across four orders of magnitude difference in spatial scales and two orders of magnitude in temporal scales. We will demonstrate that the deep neural operator framework is general for learning nonlinear operators for diverse physical problems, including learning transient mechanical response of composites subject to a dynamic loading.   

Subgrid Scale Modeling of the Scalar Transport Equation in Multiphase Flows

In multi-phase systems with heat or mass transfer at large Peclet numbers, thin boundary layers form at the interface. These are potentially orders of magnitude smaller than the smallest hydrodynamic length scales, making a true DNS of the system infeasible. We present a subgrid-scale (SGS) model for the scalar transport equation which corrects transport for advective and diffusive fluxes near the interface from a DNS for the flow. This allows us to predict heat and mass transfer correctly even if the boundary layer is fully contained in a single cell layer around the interface. We demonstrate how a shallow neural network can be used to approximate a boundary layer profile, allowing the user to quickly develop a model for the boundary layer and integrate it into the overall framework. The modeling framework is integrated into an existing open-source multiphase flow solver with adaptive mesh resolution which computes the velocity field used in the scalar transport equation. We apply our SGS framework to a variety of problems including bubble dissolution, nucleate boiling, and liquid-liquid transfer in a gas-blown ladle. The method allows us to recover known scaling regimes with very coarse grids compared to what would be required with traditional methods.   

A statistical framework using LES to assess the effect of internal heating and natural convection on airborne transmission.

In confined spaces with standard ventilation, the natural convection resulting from heat sources, such as a human adult, a heated wall, or electronic equipment, may have a substantial impact on the airflow. The present work builds on a recently proposed statistical framework using high-fidelity large-eddy simulations and particle overloading. More specifically, we investigate the effect of heating on the mixing of contaminant concentration.

Several high-fidelity simulations were considered within a canonical room with over 20 million droplet nuclei of various sizes that were individually tracked. The heat sources consisted of volumetric heat sources, representing one or more adults/children in the room. In each simulation, the strength and positioning of the source were varied. Our statistically relevant results indicate that provided the flow is turbulent, the presence of heat sources or heated boundaries does not have a significant effect on the room averaged statistics, aligning with the well-mixed theory. However, these heat sources create localised regions of non-uniform mixing, emphasizing the importance of their spatial distribution for accurate guidelines in indoor airborne transmission scenarios. Furthermore, the research integrates the effects of natural convection with filtration to provide an easily-implementable correction factor to enhance the predictive capabilities of the well-mixed model.    

Artificial Neural Network Aided Vapor-Liquid Equilibrium Model for Multi-Component High-Pressure Transcritical Flows with Phase Change

With ever increasing demand for high performance combustors, increasing the chamber pressure is one often sought after option. This leads to the working conditions to overlap with the transcritical/ supercritical regime of the reactants. The CFD modeling of transcritical flows with phase change is very challenging. Such modeling can be achieved by using the first-principled vapor-liquid equilibrium (VLE) theory coupled with a real-fluid equation of state (EOS). However, two major problems exist with VLE calculations - robustness and speed. In order to tackle the second problem, in-situ adaptive tabulation (ISAT) has been used recently to provide significant computational speed-ups, but does not guarantee robustness. This work attempts to tackle both the issues by introducing a plug-and-play Artificial Neural Network (ANN) aided VLE model to couple with CFD.  Training is performed on Python and inference speeds are optimized using Open Neural Network Exchange (ONNX). The model is validated against the results generated by both direct VLE calculation as well as ISAT for a high-pressure shock-droplet interaction case. The extendability of the model is also shown by low-pressure shock-droplet interaction cases, validated by experimental results. Finally, the computational speeds and parallel scaling achieved by the method are presented.   

A Numerical Study of Coefficient-free Kinetic Evaporation Modeling in Liquid Hydrogen

Numerical modeling of liquid-vapor phase change has long presented a challenge due to the use of tuning coefficients. The commonly used Hertz-Knudsen-Schrage equation requires accommodation coefficients as necessary inputs but reported values span three orders of magnitude even for common fluids such as water. Data for cryogenic fluids are severely limited. Computational modeling of evaporation in liquid Hydrogen is critical to the development of long-term cryo-storage technologies for deep-space applications. Due to lack of data, the accommodation coefficient is commonly reduced to a non-physical tuning parameter to achieve numerical stability. To alleviate this, we use a Transition State Theory based analytical description of the accommodation coefficients to develop a new coefficient-free computational approach to model evaporation. This approach is used inside a CFD setup in Ansys Fluent to model quasi-steady-state evaporation, where a sharp interface is assumed. Mesh cells adjacent to the sharp interface are identified as the active region where User-Defined Functions are used to apply phase change-related mass, heat, and momentum sources. The source terms are computed using local thermophysical quantities and applied along the entire interface, resulting in non-uniform evaporation. The model is validated by comparison to evaporation rates from recently published cryo-neutron experiment datasets. The importance of drift velocity in the evaporation model is also studied.