Ali Mani

Data-driven closure modeling for transport partial differential equations requires training data that are accurate, affordable, diverse, and directly tailored to the target closure fields. We develop the Generalized Forcing Method (GFM), a data-generation framework for training linear transport closure models. GFM generates such data by running simulations with a zero initial condition and an extra body force that is constructed compatibly with the reduced dynamics. This framework leads to implicit GFM (iGFM), which prescribes resolved trajectories, and explicit GFM (eGFM), which constructs a basis of admissible forcings. We apply eGFM to three linear transport closure problems: homogeneous shear flows, spatially inhomogeneous flows, and homogeneous shear flows with random coefficients. The results show that eGFM can identify accurate and stable reduced models when the reduced variables and model form are consistent with the underlying closure relation.

Data-driven closure modeling for transport partial differential equations requires training data that are accurate, affordable, diverse, and directly tailored to the target closure fields. We develop the Generalized Forcing Method (GFM), a data-generation framework for training linear transport closure models. GFM generates such data by running simulations with a zero initial condition and an extra body force that is constructed compatibly with the reduced dynamics. This framework leads to implicit GFM (iGFM), which prescribes resolved trajectories, and explicit GFM (eGFM), which constructs a basis of admissible forcings. We apply eGFM to three linear transport closure problems: homogeneous shear flows, spatially inhomogeneous flows, and homogeneous shear flows with random coefficients. The results show that eGFM can identify accurate and stable reduced models when the reduced variables and model form are consistent with the underlying closure relation.

We study isotropic turbulence decay in the context of the k-epsilon model, which solves the dissipation and kinetic energy equations. In modeling the dissipation equation, the coefficient C_epsilon2, suggested by Hanjalic and Launder [Journal of Fluid Mechanics, 1972] [1], is related to the temporal decay power-law by n = 1/(C_epsilon2 -1 )) and is assumed to be a constant value. In this work, we perform high-fidelity numerical simulations to examine the mathematical terms responsible for the decay of isotropic turbulence, considering both scenarios of forced and decaying turbulence. Our data suggest that the instantaneous C_epsilon2 not only depends on the instantaneous Reynolds number but is also sensitive to the history of energy injection in turbulence. We attribute these observations to the finite time required for the cascade from energetic to dissipative scales. Considering data from both decaying and growing forced turbulence, we develop an evolution equation for C_epsilon2 with Reynolds-dependent coefficients. We demonstrate that this model accurately captures the time evolution of dissipation and kinetic energy over a wide range of Reynolds numbers under a wide range of forced and decay scenarios.

We study isotropic turbulence decay in the context of the k-epsilon model, which solves the dissipation and kinetic energy equations. In modeling the dissipation equation, the coefficient C_epsilon2, suggested by Hanjalic and Launder [Journal of Fluid Mechanics, 1972] [1], is related to the temporal decay power-law by n = 1/(C_epsilon2 -1 )) and is assumed to be a constant value. In this work, we perform high-fidelity numerical simulations to examine the mathematical terms responsible for the decay of isotropic turbulence, considering both scenarios of forced and decaying turbulence. Our data suggest that the instantaneous C_epsilon2 not only depends on the instantaneous Reynolds number but is also sensitive to the history of energy injection in turbulence. We attribute these observations to the finite time required for the cascade from energetic to dissipative scales. Considering data from both decaying and growing forced turbulence, we develop an evolution equation for C_epsilon2 with Reynolds-dependent coefficients. We demonstrate that this model accurately captures the time evolution of dissipation and kinetic energy over a wide range of Reynolds numbers under a wide range of forced and decay scenarios.

This archive contains the reproduction data, reduced models, plotting scripts, and precomputed figures for the paper “Generalized Forcing Method: Generation of Diverse Data for Training Linear Transport PDE Closure Models.” The archive includes five model-evaluation cases: two homogeneous parallel-flow cases, two inhomogeneous-flow cases, and one homogeneous random-flow case. The provided scripts evaluate the reduced models against the included test solutions and reproduce the RMSE convergence plots and eGFM dataset-summary plots reported in the manuscript. The release is intended for figure reproduction and model-evaluation verification. It does not include the full simulation code or the model-fitting code.

This archive contains the reproduction data, reduced models, plotting scripts, and precomputed figures for the paper “Generalized Forcing Method: Generation of Diverse Data for Training Linear Transport PDE Closure Models.” The archive includes five model-evaluation cases: two homogeneous parallel-flow cases, two inhomogeneous-flow cases, and one homogeneous random-flow case. The provided scripts evaluate the reduced models against the included test solutions and reproduce the RMSE convergence plots and eGFM dataset-summary plots reported in the manuscript. The release is intended for figure reproduction and model-evaluation verification. It does not include the full simulation code or the model-fitting code.

In this work, an LES model with finite-rate phase change and subgrid spray based on a high-resolution numerical scheme for multiphase multi-component simulations which satisfies interface equilibrium and phase immiscibility conditions is proposed. The multiphase model is based on a robust implementation of the four-equation multiphase model which assumes a strict subgrid equilibrium of pressure, temperature, and velocity. Critically, the equilibrium assumptions of the four-equation model provide large computational savings compared to modeling the full non-equilibrium multiphase system. To obtain predictive capabilities with these restrictive equilibrium assumptions, a new phase-confined form of the Eulerian $Σ$ spray model is proposed to predict subgrid interfacial surface area while avoiding unphysical leakage across interfaces. Additionally, an improved finite rate phase change model which is thermodynamically bounded by the equilibration of the Gibbs-free energy is coupled with the $Σ$ equation to model complex phase change regimes. The full modeling framework is validated using the Engine Combustion Network (ECN) Spray A case in non-evaporating and evaporating conditions and shows excellent agreement with experimental measurements.

In this work, an LES model with finite-rate phase change and subgrid spray based on a high-resolution numerical scheme for multiphase multi-component simulations which satisfies interface equilibrium and phase immiscibility conditions is proposed. The multiphase model is based on a robust implementation of the four-equation multiphase model which assumes a strict subgrid equilibrium of pressure, temperature, and velocity. Critically, the equilibrium assumptions of the four-equation model provide large computational savings compared to modeling the full non-equilibrium multiphase system. To obtain predictive capabilities with these restrictive equilibrium assumptions, a new phase-confined form of the Eulerian $Σ$ spray model is proposed to predict subgrid interfacial surface area while avoiding unphysical leakage across interfaces. Additionally, an improved finite rate phase change model which is thermodynamically bounded by the equilibration of the Gibbs-free energy is coupled with the $Σ$ equation to model complex phase change regimes. The full modeling framework is validated using the Engine Combustion Network (ECN) Spray A case in non-evaporating and evaporating conditions and shows excellent agreement with experimental measurements.

Microporous electrodes (pores <2 nm in width) can confine molecules into uniquely packed, charged volumes that exhibit characteristics different from molecules from a bulk solution interacting with an electrode surface. By using surface and electrochemical characterizations, we show the confinement of organic molecules in micropores can shift their redox potentials beyond the classical Nernstian regime, with a shift as large as 252 mV. We identify an excess contribution to the electrochemical potentials of ions that leads to the thermodynamic limit for these shifts and use continuum-scale simulations from a modified Donnan model to confirm this limit and derive deviations from it. Density functional theory simulations confirm that micropore confinement can change the mechanism of charge transfer. We find trends in behavior in micropore environments for organic and metalorganic molecules in aqueous solutions based on their electrophilicity, charge, core molecules, and molecular functionalizations (i.e., side chains). Finally, using micropore confinement on the high and low potential sides of an enclosed secondary battery to increase the open circuit voltage, we demonstrate an increase in average discharge cell voltage of 39% and a corresponding increase in discharge energy density of 36% by replacing macroporous electrodes with microporous electrodes.

This work seeks to understand the importance of nonlocality in modeling scalar transport in turbulent Rayleigh-Taylor instability (RTI) at different Atwood numbers. We apply the Macroscopic Forcing Method to determine moments of the eddy diffusivity from high-fidelity numerical simulations of RTI. We additionally present a framework for incorporating nonlocality for modeling RTI at different Atwood numbers. We find that nonlocality is important for modeling RT and appears to increase in importance with Atwood number.

Water is a critical resource for development of other resources. The assessment of available water resources and demand of water for various purposes is of utmost important without which it is difficult to prepare any developmental plan. Guntur channel is selected as study area to determine the availability of canal water and estimate water demand of all sectors of water use in a command area i.e., agricultural water demand of all crops grown in command, domestic water demand and livestock demand were also estimated. The highest irrigation intensity was noticed during the year 2011-12 as 90.62%. Total Agricultural irrigated water demand was highest in year 2011-12 as 96.2 MCM. Three scenarios were proposed in order to check the canal water supply is adequate to meet the demands of different sectors of water use. In existing scenario highest amount of deficit flows (-19.00, -44.93, -76.97 and -21.56) were observed during the year 2013-14 to 2016-17. If the drinking water demand of Guntur Municipality was met from the other source, then there is possibility of commanding entire area by practicing water management technologies.

Multiphase flows are ubiquitous in both nature and engineering. Over the past two to three decades, substantial progress has been made in developing numerical methods for simulating these complex flows. Yet, significant challenges persist in accurately capturing intricate interfacial dynamics and the multi-scale interactions inherent to multiphase systems. This review focuses on several key numerical approaches that have proven particularly relevant from both practical and theoretical perspectives. In particular, we discuss Volume-Of-Fluid techniques, level set methods, diffuse interface models, and front tracking methods, along with immersed boundary strategies designed for particle-laden flows. We also examine multi-fluid Eulerian frameworks, population balance models for reactive processes, and sub-grid scale techniques for handling unresolved dynamics. Furthermore, emerging hybrid strategies that integrate conventional numerical methods with data-driven machine learning techniques are highlighted as promising directions. In conclusion, while current methodologies offer valuable insights into multiphase flow behavior, continued interdisciplinary efforts are essential to enhance predictive accuracy, computational efficiency, and the overall applicability of these simulations to real-world challenges.

The importance of nonlocality is assessed in modeling mean scalar transport for turbulent Rayleigh-Taylor (RT) mixing at different Atwood numbers. Building on the two-dimensional incompressible work of Lavacot et al. (2024, JFM), the present work extends the Macroscopic Forcing Method (MFM) to variable density problems in three-dimensional space to measure moments of the generalized eddy diffusivity kernel in RT mixing for increasing Atwood numbers (A=0.05, 0.3, 0.5, 0.8). It is found that as A increases: 1) the eddy diffusivity moments become asymmetric, and 2) the higher-order eddy diffusivity moments become larger relative to the leading-order diffusivity, indicating that nonlocality becomes more important at higher A. There is a particularly strong temporal nonlocality at higher $A$, suggesting stronger history effects. The implications of these findings for closure modeling for finite-Atwood RT are discussed.

Microporous electrodes (pores &lt;2 nm in width) can confine molecules into uniquely packed, charged volumes that exhibit characteristics different from molecules from a bulk solution interacting with an electrode surface. By using surface and electrochemical characterizations, we show the confinement of organic molecules in micropores can shift their redox potentials beyond the classical Nernstian regime, with a shift as large as 252 mV. We identify an excess contribution to the electrochemical potentials of ions that leads to the thermodynamic limit for these shifts and use continuum-scale simulations from a modified Donnan model to confirm this limit and derive deviations from it. Density functional theory simulations confirm that micropore confinement can change the mechanism of charge transfer. We find trends in behavior in micropore environments for organic and metalorganic molecules in aqueous solutions based on their electrophilicity, charge, core molecules, and molecular functionalizations (i.e. side chains). Finally, using micropore confinement on the high and low potential sides of an enclosed secondary battery to increase the open circuit voltage, we demonstrate an increase in average discharge cell voltage of 39% and a corresponding increase in discharge energy density of 36% by replacing macroporous electrodes with microporous electrodes.

Simulation of superhydrophobic surfaces (SHS) commonly utilizes a slip length boundary condition, relating slip velocity to wall-normal velocity gradient. In the Stokes flow limit, this effect can be shown to only depend on local velocity gradients at the wall; at finite Reynolds numbers, we find that nonlocal effects emerge. We investigate both scalar and momentum transport using the macroscopic forcing method to construct nonlocal eddy diffusivity, eddy viscosity, and slip kernels for turbulent channel flow over pattern-resolved SHS. The importance of nonlocality in these operators is assessed using the Reynolds-averaged representations for mean scalar and velocity fields.

A mass-conserving contact line treatment for second-order conservative phase field methods is presented and applied to the conservative diffuse interface (CDI) model. The treatment centers on a no-flux boundary condition for the phase field along with a slip boundary condition for the velocity that is based on the generalized Navier boundary condition (GNBC). Since the CDI model is a second-order partial differential equation, it does not permit a second (contact angle) boundary condition, in contrast to the popular fourth-order Cahn-Hilliard model. As such, we use one-sided stencils and extrapolations from the interior of the domain to compute phase-field-related quantities on and near the wall. Additionally, we propose novel modifications to the GNBC on the continuous and discrete levels that reduce spurious slip velocity when the contact angle achieves its equilibrium value. The proposed treatment is validated with the equilibrium drop and two-phase Couette flow test cases.

This report contains a compilation of key results and findings from the ACT project “Determining Exact RANS Operators with the Macroscopic Forcing Method.” The Macroscopic Forcing Method (MFM), a numerical tool for determining closure operators, is used to measure eddy diffusivity moments in Rayleigh-Taylor (RT) instability. It is first applied to low-Atwood 2D RT instability; that work is then extended to 3D RT at different finite Atwood numbers. It is found that nonlocality is important for modeling the mean scalar transport closure operator in RT mixing. Additionally, work is done to improve the statistical convergence of MFM for chaotic problems like RT mixing.

A general approach for transforming phase field equations into generalized curvilinear coordinates is proposed in this work. The proposed transformation can be applied to isotropic, non-isotropic, and curvilinear grids without adding any ambiguity in determining the phase field parameters. Moreover, it accurately adapts the interface thickness to the local grid-size for a general curvilinear grid without creating oscillations. Three canonical verification tests are presented on four grids with varying skewness levels. The classic advection and drop in shear tests are extended to curvilinear grids and show that the original phase field on Cartesian grids and the proposed curvilinear form have an identical order of convergence. Additionally, the proposed method is shown to provide grid-independent convergence on a two-way coupled compressible Rayleigh-Taylor instability. These simulations illustrate the robustness and accuracy of the proposed method for handling complex interfacial structures on generalized curvilinear grids.

This study aims to quantify how turbulence in a channel flow mixes momentum in the mean sense. We applied the macroscopic forcing method (Mani &amp; Park, Phys. Rev. Fluids , 2021, 054607) to direct numerical simulation (DNS) of a turbulent channel flow at $Re_\tau =180$ using two different forcing strategies that are designed to separately assess the anisotropy and non-locality of momentum mixing. In the first strategy, the leading term of the Kramers–Moyal expansion of the eddy viscosity is quantified, revealing all 81 tensorial coefficients that essentially characterise the local-limit eddy viscosity. The results indicate the following: (1) the eddy viscosity has significant anisotropy, (2) Reynolds stresses are generated by both the mean strain rate and mean rotation rate tensors associated with the momentum field and (3) the local-limit eddy viscosity generates asymmetric Reynolds stress tensors. In the second strategy, the eddy viscosity is quantified as an integration kernel revealing the non-local influence of the mean momentum gradient at each wall-normal coordinate on all nine components of the Reynolds stresses over the channel width. Our results indicate that while the shear component of the Reynolds stress is reasonably reproduced by the local mean gradients, other components of the Reynolds stress are highly non-local. These results provide an understanding of anisotropy and non-locality requirements for closure modelling of momentum transport in attached wall-bounded turbulent flows.

Superhydrophobic surfaces (SHS) are textured hydrophobic surfaces which have the ability to trap air pockets when immersed in water. This can result in significant drag reduction, due to substantially lower viscosity of air resulting in substantial effective slip velocity at the interface. Past studies of both laminar and turbulent flows model this slip velocity in terms of a homogenized Navier slip boundary condition with a slip length relating the wall slip velocity to the wall-normal velocity gradient. In this work, we seek to understand the effects of superhydrophobic surfaces in the context of mean scalar and momentum mixing. We use the macroscopic forcing method (Mani and Park, 2021) to compute the generalized eddy viscosity and slip length operators of a turbulent channel over SHS, implemented as both a pattern-resolved boundary condition and homogenized slip length boundary condition, for several pattern sizes and geometries. We present key differences in the mixing behavior of both boundary conditions through quantification of their near-wall eddy viscosity. Analysis of transport in turbulent flow over pattern-resolved surfaces reveals substantial nonlocality in the measured homogenized slip length for both scalar and momentum mixing when the Reynolds and Peclet numbers based on pattern size are finite. We present several metrics to quantify this nonlocality and observe possible trends relating to Reynolds number, texture size, and pattern geometry. The importance of nonlocality in the slip length operator and in the eddy diffusivity operator is demonstrated by examining the impact on Reynolds-averaged solutions for the mean scalar and velocity fields.

We specifically focus on the terms responsible for decay of the Reynolds stresses which can be isolated and evaluated separately from other terms in a canonical setup of homogeneous turbulence. We show that by using anisotropic forcing of the momentum equation we can access states of turbulence traditionally not probed in a triply-periodic domain. We then consider a variety of model forms for which these data allow us to perform a robust selection of model coefficients and select an optimal model that extends to cubic terms when expressed in terms of the principal coordinate Reynolds stresses.

Reynolds-averaged Navier---Stokes (RANS) closure operators are generally nonlocal and anisotropic, for example in wall-bounded turbulence. We introduce a computationally efficient approach to obtain these operators, using an adjoint formulation. We then quantify the streamwise and wall-normal nonlocal eddy viscosity in turbulent channel flow, which can be used to guide closure modeling.

Models for solving the Reynolds-averaged Navier-Stokes equations are popular tools for predicting complex turbulent flows due to their computational affordability and ability to provide or estimate quantities of engineering interest. However, results depend on a proper treatment of unclosed terms, which require progress in the development and assessment of model forms. In this study, we consider the Reynolds stress transport equations as a framework for second-moment turbulence closure modeling. We specifically focus on the terms responsible for decay of the Reynolds stresses, which can be isolated and evaluated separately from other terms in a canonical setup of homogeneous turbulence. We show that by using anisotropic forcing of the momentum equation, we can access states of turbulence traditionally not probed in a triply-periodic domain. The resulting data span a wide range of anisotropic turbulent behavior in a more comprehensive manner than extant literature. We then consider a variety of model forms for which these data allow us to perform a robust selection of model coefficients and select an optimal model that extends to cubic terms when expressed in terms of the principal coordinate Reynolds stresses. Performance of the selected decay model is then examined relative to the simulation data and popular models from the literature, demonstrating the superior accuracy of the developed model and, in turn, the efficacy of this framework for model selection and tuning.

Electroreduction of CO and CO 2 offer a pathway toward renewable-powered synthesis of hydrocarbon chemicals and fuels. Both the composition and the structure of cathodic catalyst microenvironments in gas diffusion electrodes play a dominant role in determining the product composition and efficiency metrics. Porous and hydrophilic copper environments are known to produce multi-carbon species and exhibit large active surface areas, but recent investigations have shown that the inclusion of sporadically-distributed porous hydrophobic regions creates additional pathways for the delivery of gaseous reactants, thereby mitigating transport limitations seen in pure Cu catalysts. As the design space for catalysts has grown to include a wide variety of material and geometric parameters, accurate PDE-based modeling and simulation of such systems has become necessary to understand and optimize the coupled reaction and transport processes that determine cell performance. High fidelity models, however, pose immense computational challenges. Physical and chemical processes occur over a wide variety of spatiotemporal scales, ranging from pore-scale reaction and transport to device-scale gradients in species concentrations. Additionally, the spatial orientation of these features necessitates modeling in multiple dimensions, and transport occurs simultaneously through two phases located within randomly-intermixed porous regions. As a result of all these factors, numerical simulation of high fidelity models is prohibitively expensive. In this work, we develop, numerically simulate, and validate a predictive model that efficiently incorporates a wide range of physical and chemical processes occurring in catalyst microenvironments with intermixed hydrophobic and hydrophilic regions. We employ homogenization as a means of model reduction, constructing a medium fidelity model that captures both microenvironment geometric scales and full device scales in 3D. Our model, coupled with the appropriate numerical methods for treatment of stiff and multi-dimensional problems, permits low-cost exploration of the high-dimensional parameter space associated with recently developed catalysts, offering quantitative insight into the optimal design of microenvironments for CO and CO 2 electroreduction. This work is supported by the United States Department of Energy under grant DE-SC0021633.

Low Stokes number particles at dilute concentrations in turbulent flows can reasonably be approximated as passive scalars. The added presence of a drift velocity due to buoyancy or gravity when considering the transport of such passive scalars can reduce the turbulent dispersion of the scalar via a diminution of the eddy diffusivity. In this work, we propose a model to describe this decay and use a recently developed technique to accurately and efficiently measure the eddy diffusivity using Eulerian fields and quantities. We then show a correspondence between this method and standard Lagrangian definitions of diffusivity and collect data across a range of drift velocities and Reynolds numbers. The proposed model agrees with data from these direct numerical simulations, offers some improvement to previous models in describing other computational and experimental data and satisfies theoretical constraints that are independent of Reynolds number.

Carbon monoxide electrolysis has the potential to unlock new routes to sustainable C 2+ chemicals. Improvements to CO reduction (COR) gas diffusion electrodes (GDEs) are critical for advancing CO electrolysis cells, but a comprehensive understanding of COR GDEs remains elusive because of the complex interplay of physical and chemical processes under operating conditions and the difficulty of experimentally probing the heterogeneous environment of a GDE. In this study, we build a model for COR GDEs that includes fully coupled gas and ion transport and competing electrokinetic reactions. The transport and electrokinetic equations are solved in two dimensions to calculate critical COR figures of merit across multiple operating parameters including current density, flow rate, pressure, temperature, and electrochemically active surface area (ECSA). We validate our model by showing agreement with experimental data for steady-state CO electrolysis at various pressures and flow rates and then apply it to see how the figures of merit depend on the operating parameters over a wide range of values. We demonstrate that increasing the cell pressure above ambient and augmenting the ECSA of the catalyst are two effective strategies to improve cathode performance.

The importance of non-locality of mean scalar transport in two-dimensional Rayleigh–Taylor Instability (RTI) is investigated. The macroscopic forcing method is utilized to measure spatio-temporal moments of the eddy diffusivity kernel representing passive scalar transport in the ensemble averaged fields. Presented in this work are several studies assessing the importance of the higher-order moments of the eddy diffusivity, which contain information about non-locality, in models for RTI. First, it is demonstrated through a comparison of leading-order models that a purely local eddy diffusivity is insufficient to capture the mean field evolution of the mass fraction in RTI. Therefore, higher-order moments of the eddy diffusivity operator are not negligible. Models are then constructed by utilizing the measured higher-order moments. It is demonstrated that an explicit operator based on the Kramers–Moyal expansion of the eddy diffusivity kernel is insufficient. An implicit operator construction that matches the measured moments is shown to offer improvements relative to the local model in a converging fashion.

The Poisson-Nernst-Planck-Stokes equations capture the chaotic dynamics of electroconvection accurately, but direct numerical simulation of electroconvection is prohibitively expensive. Furthermore, prediction of the mean fields via application of Reynolds averaging leads to a closure problem. In this work, we combine the macroscopic forcing method, a numerical technique for measurement of closure operators in Reynolds-averaged equations, with high-fidelity experimental data in order to determine a leading order closure for chaotic electroconvection. Simulations of the Reynolds-averaged equations using the leading order closure accurately predict experimental polarization curves.

The rapid growth and plummeting cost of solar energy have spurred growing interest in using CO₂ electrolysis to produce chemicals and fuels as an alternative to conventional petrochemical processes. High-temperature (>800 °C) solid oxide electrolyzers that convert CO₂ into CO and O₂ have recently become commercially available. Low-temperature electrolysis cells offer the prospect of more convenient and flexible operation, which is critical for utilizing intermittent solar energy, and provide access to more valuable C²⁺ products such as ethylene, ethanol, and propanol. Over the past 10 years, research in this area has yielded substantial progress in both fundamental understanding of the requisite electrocatalytic reactions and design of prototype devices. Leveraging insights from fuel cells and membrane water electrolyzers, researchers have developed electrolysis cells with gas diffusion electrodes (GDE) that have demonstrated high CO₂ electrolysis current densities (>100 mA cm^–2) as well as promising selectivity and stability. Despite these advances, the energy efficiency (electrical energy-to-product) and carbon efficiency (CO₂-to-product) of low-temperature CO₂ electrolysis remain far too low for large-scale deployment. A preponderance of evidence indicates that the principal source of efficiency losses is the rapid and thermodynamically favorable reaction of CO₂ with hydroxide (OH^–) to form carbonate (CO₃^2–). Carbonate formation imposes steady-state electrolysis conditions that result in large voltage and CO₂ losses for all known (photo)electrochemical CO₂ cells. While much current research remains focused on CO₂ reduction catalyst design, this largely overlooked CO₃^2– problem presents a fundamental scientific barrier to creating a viable electrochemical option for converting solar energy into chemicals and fuels. The project pursues an integrated, multi-PI research effort that establishes a fundamental science of CO₃^2– management. PI Kanan and Co-PI Mani’s contribution to the project is to evaluate strategies to mitigate the CO₃^2– problem by changing the properties of the electrolyte and the environment in which CO₂ reduction catalysis takes place. Experimental studies showed that electrolytes composed of a high concentration of both CO₃^2– and HCO₃^–, which serve as moderately alkaline buffers, improved the cell voltage by compared to all-HCO₃^– electrolytes, but these buffered systems still show substantial CO₂ uptake that reduces pH over time. Computational studies developed a homogenized model of a CO₂ reduction catalyst layer that permits a low-cost exploration of the high-dimensional parameter space associated with catalyst layers on gas diffusion electrodes. The model was validated by accurately reproducing experimental data for the related but simpler reaction of CO reduction and then used to probe the effects of catalyst layer architecture on CO₂ reduction. Minimizing the size of catalyst and hydrophobic domains in the catalyst layer is predicted to mitigate CO₃^2– formation and thereby enable prolonged operation at elevated pH. In support of the CO₂ electrolysis studies, a new method for rapidly prototyping electrochemical cells was developed and validated. The method uses a combination of 3D printing and electroless plating to generate conductive cell components for evaluating new cell designs. The carbonate problem encompasses mass transport processes and acid-base reactions that are relevant to many other electrochemical systems. Investigation of strategies to address the carbonate problem led to an additional line of inquiry into the physicochemical phenomena that determine the efficiency of electrochemical acid-base production, which has numerous applications in the broader field of carbon management. New strategies for using the supporting electrolyte to inhibit H⁺/OH^– recombination in electrochemical acid-base production were evaluated, leading to the development of a novel acid-base producing system that eliminates the need for ion exchange membranes and exhibits promising efficiency and current densities for scalable applications.

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.

Prior studies have shown that the eddy diffusivities governing mean passive scalar transport can be nonlocal in space and time. However, nonlocal eddy diffusivities are often cost prohibitive to compute and difficult to implement in reduced-order models. This work proposes a systematic and cost-effective approach for quantifying and modeling nonlocal eddy diffusivities.

Wireless passive sensors, being battery-free and simple, are suitable for disposable use across various applications, from tracking food and monitoring the environment to clinical diagnostics. However, their utilization is hampered by the complexity of existing readout techniques and the absence of memory functionality within the sensor. Here, we present a reader technique that can automatically lock to the sensor value wirelessly through inductive coupling, significantly reducing the reader complexity. By integrating a high-frequency audio link and wireless powering, we demonstrate a battery-free and flexible reader. We integrated this reader for wireless temperature logging, which logs temperature data based on the irreversible geometric change of low-melting-point metal during phase transitions, resulting in non-volatile resistance change. As a whole, these results establish the feasibility of a simplistic reader and a passive non-volatile thermistor sensor, opening up new possibilities for disposable and ubiquitous temperature monitoring as well as a range of other applications.