Homogenized lattice Boltzmann model for simulating multi-phase flows in heterogeneous porous media

A homogenization approach for the simulation of multi-phase flows in heterogeneous porous media is presented. It is based on the lattice Boltzmann method and combines the grayscale with the multi-component Shan–Chen method. Thus, it mimics fluid–fluid and solid–fluid interactions also within pores that are smaller than the numerical discretization. The model is successfully tested for a broad variety of single- and two-phase flow problems. Additionally, its application to multi-scale and multi-phase flow problems in porous media is demonstrated using the electrolyte filling process of realistic 3D lithium-ion battery electrode microstructures as an example. The approach presented here shows advantages over comparable methods from literature. The interfacial tension and wetting conditions are independent and not affected by the homogenization. Moreover, all physical properties studied here are continuous even across interfaces of porous media. The method is consistent with the original multi-component Shan–Chen method (MCSC). It is as stable as the MCSC, easy to implement, and can be applied to many research fields, especially where multi-phase fluid flow occurs in heterogeneous and multi-scale porous media

Systematic Workflow for Efficient Identification of Local Representative Elementary Volumes Demonstrated with Lithium-Ion Battery Cathode Microstructures

The concept of a representative elementary volume (REV) is key for connecting results of pore-scale simulations with continuum properties of microstructures. Current approaches define REVs only based on their size as the smallest volume in a heterogeneous material independent of its location and under certain aspects representing the same material at the continuum scale. However, the determination of such REVs is computationally expensive and time-consuming, as many costly simulations are often needed. Therefore, presented here is an efficient, systematic, and predictive workflow for the identification of REVs. The main differences from former studies are: (1) An REV is reinterpreted as one specificsub-volume of minimal size at a certain location that reproduces the relevant continuum properties of the full microstructure. It is therefore called a local REV (lREV) here. (2) Besides comparably cheap geometrical and statistical analyses, no further simulations are needed. The minimum size of the sub-volume is estimated using the simple statistical properties of the full microstructure. Then, the location of the REV is identified solely by evaluating the structural properties of all possible candidates in a very fast, efficient, and systematic manner using a penalty function. The feasibility and correct functioning of the workflow were successfully tested and validated by simulating diffusive transport, advection, and electrochemical properties for an lREV. It is shown that the lREVs identified using this workflow can be significantly smaller than typical REVs. This can lead to significant speed-ups for any pore-scale simulations. The workflow can be applied to any type of heterogeneous material, even though it is showcased here using a lithium-ion battery cathode

Understanding Electrolyte Filling of Lithium‐Ion Battery Electrodes on the Pore Scale Using the Lattice Boltzmann Method

Electrolyte filling is a time-critical step during battery manufacturing that also affects battery performance. The underlying physical phenomena mainly occur on the pore scale and are hard to study experimentally. Therefore, here, the lattice Boltzmann method is used to study the filling of realistic 3D lithium-ion battery cathodes. Electrolyte flow through the nanoporous binder is modelled adequately. Besides process time, the influences of particle size, binder distribution, volume fraction and wetting behavior of active material and binder are investigated. Optimized filling conditions are discussed by pressure-saturation relationships. It is shown how the influencing factors affect the electrolyte saturation. The amount and distribution of entrapped residual gas are analyzed in detail. Both can adversely affect the battery performance. The results indicate how the filling process, the final electrolyte saturation, and also the battery performance can be optimized by adapting process parameters as well as electrode and electrolyte design

Understanding Electrolyte Filling of Lithium-Ion Battery Electrodes on the Pore Scale Using the Lattice Boltzmann Method

Electrolyte filling is a time-critical step during battery manufacturing that also affects battery performance. The underlying physical phenomena mainly occur on the pore scale and are hard to study experimentally. Therefore, here, the lattice Boltzmann method is used to study the filling of realistic 3D lithium-ion battery cathodes. Electrolyte flow through the nanoporous binder is modelled adequately. Besides process time, the influences of particle size, binder distribution, volume fraction and wetting behavior of active material and binder are investigated. Optimized filling conditions are discussed by pressure-saturation relationships. It is shown how the influencing factors affect the electrolyte saturation. The amount and distribution of entrapped residual gas are analyzed in detail. Both can adversely affect the battery performance. The results indicate how the filling process, the final electrolyte saturation, and also the battery performance can be optimized by adapting process parameters as well as electrode and electrolyte design

Multiphase flow in micro-thrusters: Using lattice Boltzmann modeling

Even though hundreds of CubeSats have been launched, few have launched with a micropropulsion module on board. Propulsion would allow for an extended lifetime and better mission capabilities, thus greatly increasing the attractiveness of CubeSats. TU Delft is working on a type of thruster suitable for CubeSats, called the Vaporizing Liquid Microthruster (VLM). For micro-propulsion it is viable to generate sufficient thrust by using an external heat source to vaporize a liquid and expanding the vapour via a nozzle. The usage of such micropropulsion modules is still inhibited by issues in the nozzle and heating chamber. One issue is the multiphase flow occurring inside the micronozzle, which lowers the thrust and specific impulse performance of the thruster as well as the stability due to the explosive boiling phenomena. Previous research indicates that the multiphase flow in the nozzle most likely occurs inside the heating chamber and flows into the nozzle. Little is known on how exactly this multiphase flow looks like, ranging from annular flow to dispersed droplets, nor on how it is generated within the chamber. It is indicated that the boiling may lead to large pressure oscillations inside the chamber, which contributes to the instability of the thruster. These pressure oscillations occur due to multichannel interactions from nucleate boiling in microchannels, as well as explosive boiling. In this thesis, the lattice Boltzmann method (LBM) is used to simulate the complex phase change multiphase flow occurring inside the microchannels of the vaporizing liquid micro-thruster. This method has recently gained a lot of attraction in simulating microscale fluid problems. Research shows that LBM applied to multiphase flows can be an order of magnitude faster than conversional Navier-Stokes solvers. This thesis utilizes the Bhatnagar–Gross–Krook (BGK) collision operator in combination with the pseudopotential method to simulate the multiphase flow. A modified Guo forcing scheme is used to ensure thermodynamic consistency. The water is modelled using the non-ideal Peng-Robinson equation of state. The thermal problem is solved using the double distribution function method, in combination with a semi-hybrid source term solved via a multiple relaxation time (MRT) collision operator. The phase change term is derived from the local balance of entropy, using the equation of state to calculate the latent heat. The open-source lattice Boltzmann method solver OpenLB is extended to be capable of simulating phase change flow. Verification tests are performed to show that the code extension is correctly implemented. The code was released to the OpenLB, making it the first open-source lattice Boltzmann method framework capable of simulation phase change flow. In the analysis of the tool developed, the pool boiling simulations showed how nucleation, bubble formation, and departure occurs. Correct behaviour are shown in the thermodynamic consistency, Laplace pressure and wall wettability. The effect of the spurious currents on the thermal solution are analysed in more depth than found in literature. The procedure for the multichannel simulation verification and validation is given, including a novel analysis method. The novel analysis method can estimate the multiphase flow type occurring inside real thrusters without any additional equipment required in a test setup. The required experiment data are the specific impulse values at various massflow rates, and the massflow rate at which multiphase flow starts to occur. The simulations are strongly limited by the BGK collision operator, which is apparent by the large spurious currents at high density ratio multiphase flow. The spurious currents can cause simulation instabilities, but are mitigated by using a thicker diffuse interface. This mitigation results in a larger metastable phase change region, which inhibits the nucleation process. Thus, nucleation inside the microchannels did not occur. However, using a MRT collision operator should reduce the spurious currents without needing to increase the diffuse interface thickness, allowing for nucleation to take place in the microchannels.Aerospace Engineerin

Lattice Boltzmann simulation in the context of battery systems

Simulations based on the Lattice Boltzmann method are a powerful and efficient tool for the investigation of mesoscopic processes that are hard to study experimentally. Such simulations have been used successfully to study redox flow batteries [1]. But they have rarely been used to study transport mechanisms in other battery systems [2,3]. In the present work, the wetting process during the electrolyte filling in the battery production is investigated by means of the flow of electrolyte through realistic three-dimensional porous battery electrodes. The electrode microstructures are generated using a sophisticated stochastic model [4] for the active material which is complemented by an additional binder phase. The focus of the study is on determining the capillary pressure-saturation relation during electrolyte intrusion and drainage. The main influencing factors investigated in the present work, are the porosity of the electrodes, the proportion of the binder phase as well as the wetting behavior of both the active material and the binder. Besides, also the effect of spatially non-resolved nanopores in the binder is studied using a homogenization approach. Lattice Boltzmann simulations with different multiphase flow methods, i.e. the Shan-Chen pseudopotential method [5] and the color gradient method [6], are conducted. Results from both methods are compared with each other. For validation purposes, they are also compared against results determined using the pore morphology method. The results from the present study are shown to agree well with results from the literature. They are especially useful for optimizing the electrolyte filling process which is a time-determining step in the battery production. [1] D. Zhang et al.; J. Power Sources, 447 (2020), pp. 227249 [2] T. Danner et al.; J. Power Sources, 324 (2016), pp. 646-656 [3] Z. Jiang et al.; J. Power Sources, 324 (2018), pp. 500-513 [4] J. Feinauer et al.; Comput. Mater. Sci., 109 (2015), pp. 137-146 [5] X. Shan et H. Chen; Phys. Rev. E, 47 (3) (1993), pp. 1815-1819 [6] J. Leclaire et al.; Phys. Rev. E, 95 (3) (2017), pp. 03330

Understanding Electrolyte Filling of Lithium-Ion Battery Electrodes on the Pore Scale

Filling electrodes with electrolyte is a time-critical battery manufacturing step that also affects the battery performance. Most of the physical phenomena during the filling occur on the pore scale and are hard to study experimentally. Therefore, in this work, computational approaches are used to study the filling process and the corresponding pore-scale phenomena. Using the lattice Boltzmann method (LBM), electrolyte flow in 3D lithium-ion battery cathodes with and without binder is simulated with high spatial resolution. The results are used to adjust and validate pore network models (PNM) which in comparison to LBM are computationally very efficient. The methodology proposed here is universal and can be generally applied to filling of other battery components or energy storage devices. The influence of a broad variety of structural and physico-chemical properties of the active material and binder as well as process parameters is studied. Pressure-saturation curves are determined and suggest a systematic entrapment of residual gas in the pores. A detailed analysis yields a strong interdependency of the amount, spatial distribution, and size distributions of the gas agglomerates. Moreover, it is shown how the residual gas can adversely affect the battery performance by reducing effective transport properties and electrochemically active surfaces. The results indicate how the filling process, the final degree of electrolyte saturation, and potentially also the battery performance can be optimized. The most favorable results are observed for electrodes with large pores and a good connectivity of the pore space as well as a strong wettability of the solid electrode components. Altogether, it is shown that both computational methods, i.e. LBM and PNM, yield a detailed insight into the influencing factors of filling processes on the pore scale and can be used to support the electrode, electrolyte, and process design. This work has been funded by European Union’s Horizon 2020 research and innovation programme within the research project DEFACTO under grant agreement No 875247. The simulations were carried out on the Hawk at the High Performance Computing Center Stuttgart (HLRS) under the grant LaBoRESys, and on JUSTUS 2 at the University Ulm under the grant INST 40/467-1 FUGG

Structurally resolved Lattice Boltzmann simulations of battery systems

Theoretical modeling and computational simulations are important approaches to gain a detailed insight into mesoscopic processes that are hard to study experimentally. Regarding lithium-sulfur batteries, several one-dimensional continuum models are published in the literature, which focus mainly on charge and discharge processes [1,2], e.g. the dissolution and precipitation of solid Li2S and S8 [3], as well as degradation mechanisms, such as the polysulfide shuttle. However, those models lack from dimension-related details such as the influence of the effect of the cell geometry and the electrolyte distribution as well as the electrolyte content [3,4]. Therefore, in our current research, a structurally resolved three-dimensional battery model is developed based on the Lattice Boltzmann method. The model will be applied to study the following aspects in the context of battery technology: (1) wetting processes during the electrolyte filling of realistic three-dimensional porous battery electrodes; (2) multi-species transport through the three-dimensional porous electrode; (3) chemical reactions such as dissolution and precipitation of species at the electrode surface. As part of the present poster, besides the methodological background, first interesting results as well as the future steps in model development will be presented. All in all, it is shown that the Lattice Boltzmann method is especially useful for understanding phenomena on the pore-scale of lithium-sulfur batteries and, thus, is a promising tool for the optimization of different aspects related to battery production, performance, and lifetime. [1] K. Kumaresan et al.; J. Electrochem. Soc., 155 (8) (2008), pp. A576 [2] M. Marinescu et al.; Phys. Chem. Chem. Phys., 18 (1) (2016), pp. 584-593 [3] T. Danner et A. Latz; Electrochim. Acta, 322 (2019), pp. 646-656 [4] T. Li et al.; Adv. Funct. Mater., 29 (32) (2019), pp. 1-5

Microstructure-Resolved Battery Simulation Using the Lattice Boltzmann Method

Lithium-ion batteries (LIB) and post-lithium-ion technologies such as metal-sulfur batteries (MSB) are promising for energy storage in mobile applications and e-mobility. While LIB are technically matured and currently lead in trade-offs considering cost and performance, the upcoming post-lithium-ion technologies show great potential with respect to higher energy densities at reduced costs. Beside the different technological readiness of LIB and MSB, the great difference is where current research activities for each technology are focused on. For MSB the investigations focus on more fundamental questions regarding chemical and electrochemical processes as well as degradation phenomena during battery operation. LIB technology is more mature and a significant part of the research already focuses on the optimization of the manufacturing process. However, improving both requires a detailed understanding of pore-scale phenomena in the battery microstructures and how these affect the cell level. Therefore, in our research, we developed a mesoscopic computational approach based on the lattice Boltzmann method (LBM) which can be used to study multi-physics issues in realistic and highly resolved battery microstructures. Using this method, for LIB the manufacturing step of electrolyte filling under the influence of structural and physico-chemical properties and their effect on electrolyte and gas distributions at the end of the filling was studied. In contrast, for MSB the new model was applied to study multi-species transport phenomena such as the polysulfide shuttle as well as chemical and electrochemical reactions including dissolution and precipitation. The results aid in both optimization and design of, e.g., battery microstructures to improve the filling process, cyclability and battery operation. It is also shown how residual gas from the filling, but also pore clogging by precipitates can adversely affect the battery performance. In this context, temporal varying diffusion pathways, reduced effective transport properties and passivated reaction surfaces are discussed and it is shown how they lead to capacity losses in both LIB and MSB. The present work shows the applicability of the LBM model for battery research. The model reproduces two-phase flow and complex diffusion and reaction dynamics. It can be used to study phenomena in LIB and MSB microstructures on the pore scale. Thus, the methodology proposed here is helpful for designing electrodes, electrolytes, and processes. It is universal and can be generally applied to other battery components or energy storage devices, too. This work has been funded by European Union’s Horizon 2020 research and innovation programme within the research project DEFACTO under grant agreement Nº875247. The simulations were carried out on the Hawk at the High Performance Computing Center Stuttgart (HLRS) under the grant LaBoRESys, and on JUSTUS 2 at the University Ulm under the grant INST 40/467-1 FUGG

Understanding Electrolyte Filling to Improve the Performance of Lithium-Ion Batteries: A Pore-Scale Study

The cell production of lithium-ion batteries is predicted to increase exponentially in the upcoming years. Therefore, the optimization of the cell manufacturing is key to reduce costs and also necessary to improve the battery performance. In this context, the filling of cells with liquid electrolyte has gained attention mainly from experimentalists. However, most of the experimental methods applied are complex and time-consuming, suffer from low spatial or temporal resolution, and can hardly resolve interdependencies of influencing factors. Thus, a comprehensive understanding especially of pore-scale phenomena during the filling process is still missing. In this study, mesoscopic computational approaches are used to investigate electrolyte filling and its effects on battery performance on the pore scale. Those are the lattice Boltzmann method (LBM) and pore network models (PNM). A common LBM approach is applied and combined with a recently developed homogenization approach to study flow in pores of different length scales simultaneously. Detailed simulations in realistic 3D reconstructions of lithium-ion battery cell components, such as different electrodes and separators, are conducted. The influence of a broad variety of structural and physico-chemical properties of the active material and binder as well as process parameters is studied. In this respect pressure-saturation curves are a characteristic property of porous media and relate the pressure difference needed for invasion to the amount of electrolyte in the pore space. Our intrusion simulations indicate a significant gas entrapment at the end of the filling process. Moreover, due the high structural resolution of LBM, detailed information about the spatial distribution of the gas in the pore space can be provided. This is analyzed in detail to show how the gas adversely affects the battery performance by reducing effective transport properties and electrochemically active surfaces. In addition, the pressure-saturation results are used to develop a new and efficient PNM approach which works on a strongly simplified basis regarding the pore geometry and the physics that are solved. It is based on a physically motivated geometrical shape correction and is shown to reproduce the LBM results quite well. The characteristic pressure levels are predicted correctly, while compared to LBM, the computational time needed is reduced from days to minutes. This study shows that both LBM and PNM are useful to understand the electrolyte filling process. Using the computationally demanding but very detailed LBM, results indicate how the filling process, the final degree of electrolyte saturation, and potentially also the battery performance can be optimized. Being only interested in the pressure-saturation behavior, the new PNM can give sufficient insight. It can also be used to efficiently scan parameter spaces to give first indications based on which more detailed simulations, such as LBM, can be conducted. Thus, each method has its specific strengths and their full potential can be achieved when being applied complementary. All in all, both methods are powerful tools in supporting electrode, electrolyte, and process design. This work has been funded by European Union’s Horizon 2020 research and innovation programme within the research project DEFACTO under grant agreement Nº875247. The simulations were carried out on the Hawk at the High Performance Computing Center Stuttgart (HLRS) under the grant LaBoRESys, and on JUSTUS 2 at the University Ulm under the grant INST 40/467-1 FUGG