NOTE: End date changed to 11/17/2024 per NSSC information (Ed., 10/12/23)

In the first year of the project, we will develop a computational fluid dynamics (CFD) approach for predicting dispersed gas-liquid flows. The CFD approach will be validated against the PBRE data from the PSI, specifically visual images of gas-liquid flows from videos, as well as corresponding pressure drop information across disparate flow regimes. First, a suitable 3D flow geometry will be constructed from the specifications of the PBRE. Then, interface-resolved simulations will be performed of gas-liquid flow through a packed bed. Using supercomputing resources at Purdue, we will perform large-scale simulations of gas-liquid flows across regimes (bubbly, slug, core-annular, stratified, etc.) at full and reduced gravity conditions. The gas-liquid interface dynamics, as we as the flow-wise pressure gradient, will be computed for different Reynolds numbers and gas volume fractions and compared to the PBRE datasets in the PSI.

Tracking the complex growing, merging, and rupturing gas-liquid interfaces in simulations is challenging. To address scale-up, two-fluid models, in which the gas and liquid phases are considered to be interpenetrating continua, have been proposed. Two-fluids models reduce computational cost by removing the need to track interfaces; however, they require calibration of parameters to become predictive. Specifically, a correlation for the interphase drag force must be developed. Previous work has shown that the dimensionless parameter space consists of the Suratman number (a modified gas Reynolds number with the velocity set by the ratio of surface tension to viscosity) and the ratio of the gas and liquid phases’ Reynolds numbers.

In second year of the project, we will calibrate two-fluid models, under the steady 1D flow assumption, by fitting the interphase drag coefficient to data from the PSI. In turn, two-fluid models will enable large-scale simulations, with unresolved pore-scale dynamics, towards scale up for packed-bed reactor properties. Specifically, two-fluid model simulations using the novel correlations learned from the PBRE datasets in the PSI will help determine the boundaries for flow regime transitions in the parameter space, leading to new regime diagrams, and specifically sharper transition boundaries between regimes, that address gaps in the current understanding.

While the flow physics alone is challenging to predict, such two-phase gas-liquid flows are often coupled with heat transfer and chemical reactions. In parallel, we propose to evaluate the feasibility of ground-based thermo-fluid experiments in a packed bed reactor against which to validate the extended models. In future work, correlations for heat transfer coefficients for gas-liquid flows in packed beds can be calibrated against novel ground-based experiments, which we will explore based on the design of the PBRE. Ultimately, the proposed research will provide tools for accurately modeling coupled thermal-fluid systems for both terrestrial and low-gravity applications.

Two-phase gas-liquid flows are ubiquitous in life support and thermal control systems for spacecraft, space stations, and proposed habitats on the Moon and Mars, as well as terrestrial applications involving distillation, purification and separation, and catalytic reactions to enhance heat and mass transfer in convective flows, among other examples. However, gas-liquid flows through packed bed reactors have not been fully understood. Predictive modeling of these flows is challenging---even for terrestrial applications---and the lack of predictive simulation tools prohibits effective scaling up of systems to sizes required for future missions. To this end, we propose a computational fluid dynamics (CFD) approach for simulating gas-liquid flows in porous media across regimes: from bubbly, slug, core-annular flow to fully-dispersed gas phase. The CFD approach will be validated against the PBRE data from the PSI and extended to flows with heat transfer.

Our major accomplishments during the award were the publication of 2 peer-reviewed articles in top journals. [See the Cumulative Bibliography.]

Understanding transport phenomena through porous media is essential for applications ranging from water treatment systems to heat pipes. In many of these systems, packed bed reactors (PBRs) are crucial components, and understanding and quantifying the pressure drop due to flow through the PBR is critical to effective operation. Prior works on the hydrodynamics of gas-liquid flow through a PBR under microgravity conditions have focused on characterizing the flow regime (into a bubble or pulse flow) and the corresponding pressure drops, without providing insight into the dynamics of the bubbles. Moreover, in the recent analysis of microgravity experiments on the International Space Station (ISS), Motil et al. noted that "one fundamental problem identified in the packed bed reactor experiment (PBRE) is that a minimum liquid superficial flux is needed to dislodge trapped bubbles in a porous medium". [Ed. Note: See REFERENCES below.] To better understand this fundamental problem and thus fill a knowledge gap in the literature, in our first peer-reviewed publication, we explored the bubble flow regime in-depth by investigating the influence of inertia, capillary, and buoyancy forces on a bubble's entrapment and displacement as it traverses the tortuous pore spaces of a PBR. We developed a workflow for generating the computational geometry of a PBR representative element volume (REV), and we performed simulations within this REV. To rationalize the dynamics of bubbles in PBRs at microgravity, we introduced two new dimensionless numbers that represent dynamic balances between capillary, inertial, and gravitational forces, as quantified through our computational fluid dynamics (CFD) simulations.

Motivated by the lack of fundamental studies on two-phase gas-liquid flow through a PBR under microgravity conditions, in our second peer-reviewed publication, we developed a data-driven methodology for calibrating a gas-liquid drag closure that can be used in CFD simulations. Recent experiments conducted by NASA measured the pressure drop due to gas-liquid flow through a PBR under microgravity conditions. Based on these experiments, we developed correlations for the interphase drag in a two-fluid model (TFM). Then, under the assumption of a 1D flow, we rewrote the TFM equations with the gas-liquid drag as the only unknown. We employed data-driven calculations to determine the drag, which we correlated (via composite fits) as a function of the liquid and gas Reynolds numbers based on the superficial velocities and the Suratman number. To demonstrate the use of these correlations, we performed 2D transient, multiphase CFD laminar flow simulations in ANSYS® Fluent employing an Euler-Euler formulation. These CFD simulations predicted a pressure gradient 25% of the experimental values reported in the PSI, highlighting the validity of the proposed approach based on the Euler-Euler simulation using the proposed drag law.

REFERENCES

Motil BJ, Ramé E, Salgi P, Taghavi M, Balakotaiah V. "Gas-liquid flows through porous media in microgravity: The International Space Station Packed Bed Reactor Experiment." AIChE J. 2021 Jan;67(1):e17031. https://doi.org/10.1002/aic.17031

NOTE: End date changed to 11/17/2024 per NSSC information (Ed., 10/12/23)

In the first year of the project, we will develop a computational fluid dynamics (CFD) approach for predicting dispersed gas-liquid flows. The CFD approach will be validated against the PBRE data from the PSI, specifically visual images of gas-liquid flows from videos, as well as corresponding pressure drop information across disparate flow regimes. First, a suitable 3D flow geometry will be constructed from the specifications of the PBRE. Then, interface-resolved simulations will be performed of gas-liquid flow through a packed bed. Using supercomputing resources at Purdue, we will perform large-scale simulations of gas-liquid flows across regimes (bubbly, slug, core-annular, stratified, etc.) at full and reduced gravity conditions. The gas-liquid interface dynamics, as we as the flow-wise pressure gradient, will be computed for different Reynolds numbers and gas volume fractions and compared to the PBRE datasets in the PSI.

Tracking the complex growing, merging, and rupturing gas-liquid interfaces in simulations is challenging. To address scale-up, two-fluid models, in which the gas and liquid phases are considered to be interpenetrating continua, have been proposed. Two-fluids models reduce computational cost by removing the need to track interfaces; however, they require calibration of parameters to become predictive. Specifically, a correlation for the interphase drag force must be developed. Previous work has shown that the dimensionless parameter space consists of the Suratman number (a modified gas Reynolds number with the velocity set by the ratio of surface tension to viscosity) and the ratio of the gas and liquid phases’ Reynolds numbers.

In second year of the project, we will calibrate two-fluid models, under the steady 1D flow assumption, by fitting the interphase drag coefficient to data from the PSI. In turn, two-fluid models will enable large-scale simulations, with unresolved pore-scale dynamics, towards scale up for packed-bed reactor properties. Specifically, two-fluid model simulations using the novel correlations learned from the PBRE datasets in the PSI will help determine the boundaries for flow regime transitions in the parameter space, leading to new regime diagrams, and specifically sharper transition boundaries between regimes, that address gaps in the current understanding.

While the flow physics alone is challenging to predict, such two-phase gas-liquid flows are often coupled with heat transfer and chemical reactions. In parallel, we propose to evaluate the feasibility of ground-based thermo-fluid experiments in a packed bed reactor against which to validate the extended models. In future work, correlations for heat transfer coefficients for gas-liquid flows in packed beds can be calibrated against novel ground-based experiments, which we will explore based on the design of the PBRE. Ultimately, the proposed research will provide tools for accurately modeling coupled thermal-fluid systems for both terrestrial and low-gravity applications.

Two-phase gas-liquid flows are ubiquitous in life support and thermal control systems for spacecraft, space stations, and proposed habitats on the Moon and Mars, as well as terrestrial applications involving distillation, purification and separation, and catalytic reactions to enhance heat and mass transfer in convective flows, among other examples. However, gas-liquid flows through packed bed reactors have not been fully understood. Predictive modeling of these flows is challenging---even for terrestrial applications---and the lack of predictive simulation tools prohibits effective scaling up of systems to sizes required for future missions. To this end, we propose a computational fluid dynamics (CFD) approach for simulating gas-liquid flows in porous media across regimes: from bubbly, slug, core-annular flow to fully-dispersed gas phase. The CFD approach will be validated against the PBRE data from the PSI and extended to flows with heat transfer.

In the current reporting period, we developed a data-driven methodology for the calibration of a gas-liquid drag closure that can be used in computational fluid dynamics (CFD) simulations based on NASA's Packed Bed Reactor Experiment (PBRE) dataset collected from experiments conducted aboard the International Space Station (ISS) and available in NASA's Physical Sciences Informatics (PSI) system. Specifically, we performed a data-driven calculation of the drag coefficient (fitting coefficient of our two-fluid model of the flow) to develop composite fits and obtain a novel correlation for the gas-liquid drag in microgravity conditions. The correlation gives the drag as a function of the liquid and gas Reynolds numbers (representing the relative importance of flow inertia to viscous forces) and the Suratman number (representing the relative importance of a combination of flow inertia and liquid surface tension to viscous forces).

In addition to theoretical efforts, computational fluid dynamics (CFD) has been widely used to study resolved two-phase flows through PBRs. Specifically, the two-fluid or "Euler-Euler" approach is used to predict pressure drop and liquid holdup within PBRs in common, commercially available CFD software, such as ANSYS Fluent. To highlight the utility of our proposed correlation, based on the NASA PBRE dataset, for the gas-liquid drag of multiphase flow through a porous medium, we performed 2D transient, multiphase CFD simulations at low Reynolds number (laminar flow regime) in ANSYS Fluent. We found a good agreement between the CFD simulations' predicted pressure drop based on the proposed correlation and the experimental data for prototypical PBR geometry and flow conditions similar to those of the PBRE ones.

This work has been submitted for review and publication. A preprint is available at https://arxiv.org/abs/2409.10674 , while the supporting data is available in the Purdue University Research Repository at https://purr.purdue.edu/publications/4565/1 . [See also the Bibliography.]

In the first year of the project, we will develop a computational fluid dynamics (CFD) approach for predicting dispersed gas-liquid flows. The CFD approach will be validated against the PBRE data from the PSI, specifically visual images of gas-liquid flows from videos, as well as corresponding pressure drop information across disparate flow regimes. First, a suitable 3D flow geometry will be constructed from the specifications of the PBRE. Then, interface-resolved simulations will be performed of gas-liquid flow through a packed bed. Using supercomputing resources at Purdue, we will perform large-scale simulations of gas-liquid flows across regimes (bubbly, slug, core-annular, stratified, etc.) at full and reduced gravity conditions. The gas-liquid interface dynamics, as we as the flow-wise pressure gradient, will be computed for different Reynolds numbers and gas volume fractions and compared to the PBRE datasets in the PSI.

Tracking the complex growing, merging, and rupturing gas-liquid interfaces in simulations is challenging. To address scale-up, two-fluid models, in which the gas and liquid phases are considered to be interpenetrating continua, have been proposed. Two-fluids models reduce computational cost by removing the need to track interfaces; however, they require calibration of parameters to become predictive. Specifically, a correlation for the interphase drag force must be developed. Previous work has shown that the dimensionless parameter space consists of the Suratman number (a modified gas Reynolds number with the velocity set by the ratio of surface tension to viscosity) and the ratio of the gas and liquid phases’ Reynolds numbers.

In second year of the project, we will calibrate two-fluid models, under the steady 1D flow assumption, by fitting the interphase drag coefficient to data from the PSI. In turn, two-fluid models will enable large-scale simulations, with unresolved pore-scale dynamics, towards scale up for packed-bed reactor properties. Specifically, two-fluid model simulations using the novel correlations learned from the PBRE datasets in the PSI will help determine the boundaries for flow regime transitions in the parameter space, leading to new regime diagrams, and specifically sharper transition boundaries between regimes, that address gaps in the current understanding.

While the flow physics alone is challenging to predict, such two-phase gas-liquid flows are often coupled with heat transfer and chemical reactions. In parallel, we propose to evaluate the feasibility of ground-based thermo-fluid experiments in a packed bed reactor against which to validate the extended models. Correlations for heat transfer coefficients for gas-liquid flows in packed beds can be calibrated against novel ground-based experiments, which we will explore based on the design of the PBRE. Ultimately, the proposed research will provide tools for accurately modeling coupled thermal-fluid systems for both terrestrial and low-gravity applications.

Two-phase gas-liquid flows are ubiquitous in life support and thermal control systems for spacecraft, space stations, and proposed habitats on the Moon and Mars, as well as terrestrial applications involving distillation, purification and separation, and catalytic reactions to enhance heat and mass transfer in convective flows, among other examples. However, gas-liquid flows through packed bed reactors have not been fully understood. Predictive modeling of these flows is challenging---even for terrestrial applications---and the lack of predictive simulation tools prohibits effective scaling up of systems to sizes required for future missions. To this end, we propose a computational fluid dynamics (CFD) approach for simulating gas-liquid flows in porous media across regimes: from bubbly, slug, core-annular flow to fully-dispersed gas phase. The CFD approach will be validated against the PBRE data from the PSI and extended to flows with heat transfer.

Our progress in the last year is based on the groundwork from Year 1. Specifically, in Year 1, we developed the workflow for generating a packing geometry and extracting a representative volume element (REV) from the larger packed bed geometry for performing interface-resolved using the ANSYS Fluent's solver. In Year 2, we performed a detailed Computational Fluid Dynamics (CFD) study to understand the physics behind the measurements made during the PBRE. Specifically, we simulated bubble flow through a PBR for different packing-particle-diameter-based Weber numbers and under different gravity conditions. We demonstrated different pore-scale mechanisms, such as capillary entrapment, buoyancy entrapment, and inertia-induced bubble displacement. Then, we performed a quantitative analysis by introducing a new dynamic length scale, dependent upon the evolving gas-liquid interfacial area, to understand the dynamic trade-offs between the inertia, capillary, and buoyancy forces on a bubble passing through a PBR. This analysis led us to define new dimensionless Weber-like numbers that delineate bubble entrapment from bubble displacement suitable for microgravity research. This work has been submitted for review for publication. A preprint is freely available at https://arxiv.org/abs/2308.08075 , while the supporting data is freely available in the Purdue University Research Repository at https://purr.purdue.edu/publications/4346/1. [Ed. Note: See Bibliography.]

Further, in Year 2, we laid down the groundwork for using the PBRE data from the PSI towards novel data-driven calibration of two-fluid (Euler-Euler) models for these gas-liquid flows.

In the first year of the project, we will develop a computational fluid dynamics (CFD) approach for predicting dispersed gas-liquid flows. The CFD approach will be validated against the PBRE data from the PSI, specifically visual images of gas-liquid flows from videos, as well corresponding pressure drop information across disparate flow regimes. First, a suitable 3D flow geometry will be constructed from the specifications of the PBRE. The interFOAM solver in OpenFOAM will be adapted for interface-resolved simulation of gas-liquid flow through a packed bed. Using supercomputing resources at Purdue, we will perform large-scale simulations of gas-liquid flows across regimes (bubbly, slug, core-annular, stratified, etc.) at full and reduced gravity conditions. The flow-wise pressure gradient will be computed for different Reynolds numbers and gas volume fractions and compared to the PBRE datasets in the PSI.

However, tracking the complex growing, merging, and rupturing gas-liquid interfaces in simulations is challenging. To address scale-up, two-fluid models, in which the gas and liquid phases are considered to be interpenetrating continua, have been proposed. Two-fluids models reduce computational cost by removing the need to track interfaces; however, they require calibration of parameters to become predictive. Specifically, a correlation for the interphase drag force must be developed. Using both fully resolved simulations and PBRE datasets, we will employ the physics-informed neural network (PINN) deep learning approach pioneered in 2019 to infer the parameters in the steady two-fluid model equations. The advantage of PINNs over other inverse methods is that PINNs work with limited measurements and noisy data. PINNs are not a "black box," as they build-in the underlying physical equations into the loss function to properly guide the learning process. Previous work has shown that the dimensionless parameter space consists of the Suratman number (a modified gas Reynolds number with the velocity set by the ratio of surface tension to viscosity) and the ratio of the gas and liquid phases’ Reynolds numbers. We will determine the boundaries for flow regime transitions in this 2D space using interface-resolved simulations and compare to the predictions of a two-fluid model calibrated via a PINN. This regime diagram is critical for design and scale-up of packed bed reactors.

While the flow physics alone is challenging to predict, such two-phase gas-liquid flows are often coupled with heat transfer and chemical reactions. In the second year of the project, we will consider flows coupled with heat transfer. Specifically, we will incorporate heat transfer into interFOAM and the two-fluid model. In parallel, we propose novel ground-based thermo-fluid experiments in a packed bed reactor against which to validate the extended models. Correlations for heat transfer coefficients for gas-liquid flows in packed beds will be calibrated (via PINNs) against these novel ground-based experiments, which we will perform based on the design of the PBRE. Ultimately, the proposed research will provide tools for accurately modeling coupled thermal-fluid systems for both terrestrial and low-gravity applications.

Two-phase gas-liquid flows are ubiquitous in life support and thermal control systems for spacecraft, space stations, and proposed habitats on the Moon and Mars, as well as terrestrial applications involving distillation, purification and separation, and catalytic reactions to enhance heat and mass transfer in convective flows, among other examples. However, gas-liquid flows through packed bed reactors have not been fully understood. Predictive modeling of these flows is challenging---even for terrestrial applications---and the lack of predictive simulation tools prohibits effective scaling up of systems to sizes required for future missions. To this end, we propose a computational fluid dynamics (CFD) approach for simulating gas-liquid flows in porous media across regimes: from bubbly, slug, core-annular flow to fully-dispersed gas phase. The CFD approach will be validated against the PBRE data from the PSI and extended to flows with heat transfer.

Our progress so far includes developing a workflow for generating a packing geometry using rigid body simulations in the open-source software Blender. Then, we extracted a representative volume element (REV or RVE) from the larger packed bed geometry that we generated in Blender. The idea is that this REV is more suitable for CFD analysis. The pore-space geometry was then meshed using a shrink-wrapping-based approach in order to generate bridges between adjacent spheres and avoid point-contacts. Next, VOF simulations were performed using ANSYS Fluent's solver. These fully-resolved simulations take into account the surface tension between the gas and liquid, as well as the contact angle between the liquid and the packing material. We simulated an example flow in the bubble regime by initializing the PBR flow domain with water and `patching in' a nitrogen bubble near the inlet of the geometry. We used a velocity inlet boundary condition for the water phase to push the bubble through the PBR, and observed its motion and deformation in our preliminary simulations so far.

In the first year of the project, we will develop a computational fluid dynamics (CFD) approach for predicting dispersed gas-liquid flows. The CFD approach will be validated against the PBRE data from the PSI, specifically visual images of gas-liquid flows from videos, as well corresponding pressure drop information across disparate flow regimes. First, a suitable 3D flow geometry will be constructed from the specifications of the PBRE. The interFOAM solver in OpenFOAM will be adapted for interface-resolved simulation of gas-liquid flow through a packed bed. Using supercomputing resources at Purdue, we will perform large-scale simulations of gas-liquid flows across regimes (bubbly, slug, core-annular, stratified, etc.) at full and reduced gravity conditions. The flow-wise pressure gradient will be computed for different Reynolds numbers and gas volume fractions and compared to the PBRE datasets in the PSI.

However, tracking the complex growing, merging, and rupturing gas-liquid interfaces in simulations is challenging. To address scale-up, two-fluid models, in which the gas and liquid phases are considered to be interpenetrating continua, have been proposed. Two-fluids models reduce computational cost by removing the need to track interfaces; however, they require calibration of parameters to become predictive. Specifically, a correlation for the interphase drag force must be developed. Using both fully resolved simulations and PBRE datasets, we will employ the physics-informed neural network (PINN) deep learning approach pioneered in 2019 to infer the parameters in the steady two-fluid model equations. The advantage of PINNs over other inverse methods is that PINNs work with limited measurements and noisy data. PINNs are not a "black box," as they build-in the underlying physical equations into the loss function to properly guide the learning process. Previous work has shown that the dimensionless parameter space consists of the Suratman number (a modified gas Reynolds number with the velocity set by the ratio of surface tension to viscosity) and the ratio of the gas and liquid phases’ Reynolds numbers. We will determine the boundaries for flow regime transitions in this 2D space using interface-resolved simulations and compare to the predictions of a two-fluid model calibrated via a PINN. This regime diagram is critical for design and scale-up of packed bed reactors.

While the flow physics alone is challenging to predict, such two-phase gas-liquid flows are often coupled with heat transfer and chemical reactions. In the second year of the project, we will consider flows coupled with heat transfer. Specifically, we will incorporate heat transfer into interFOAM and the two-fluid model. In parallel, we propose novel ground-based thermo-fluid experiments in a packed bed reactor against which to validate the extended models. Correlations for heat transfer coefficients for gas-liquid flows in packed beds will be calibrated (via PINNs) against these novel ground-based experiments, which we will perform based on the design of the PBRE. Ultimately, the proposed research will provide tools for accurately modeling coupled thermal-fluid systems for both terrestrial and low-gravity applications.