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At least 1,261 records · Page 70

Computational Aerodynamic Simulations of a 1484 ft/sec Tip Speed Quiet High-Speed Fan System Model for Acoustic Methods Assessment and Development

Computational Aerodynamic simulations of a 1484 ft/sec tip speed quiet high-speed fan system were performed at five different operating points on the fan operating line, in order to provide detailed internal flow field information for use with fan acoustic prediction methods presently being developed, assessed and validated. The fan system is a sub-scale, low-noise research fan/nacelle model that has undergone experimental testing in the 9- by 15-foot Low Speed Wind Tunnel at the NASA Glenn Research Center. Details of the fan geometry, the computational fluid dynamics methods, the computational grids, and various computational parameters relevant to the numerical simulations are discussed. Flow field results for three of the five operating points simulated are presented in order to provide a representative look at the computed solutions. Each of the five fan aerodynamic simulations involved the entire fan system, which includes a core duct and a bypass duct that merge upstream of the fan system nozzle. As a result, only fan rotational speed and the system bypass ratio, set by means of a translating nozzle plug, were adjusted in order to set the fan operating point, leading to operating points that lie on a fan operating line and making mass flow rate a fully dependent parameter. The resulting mass flow rates are in good agreement with measurement values. Computed blade row flow fields at all fan operating points are, in general, aerodynamically healthy. Rotor blade and fan exit guide vane flow characteristics are good, including incidence and deviation angles, chordwise static pressure distributions, blade surface boundary layers, secondary flow structures, and blade wakes. Examination of the computed flow fields reveals no excessive or critical boundary layer separations or related secondary-flow problems, with the exception of the hub boundary layer at the core duct entrance. At that location a significant flow separation is present. The region of local flow recirculation extends through a mixing plane, however, which for the particular mixing-plane model used is now known to exaggerate the recirculation. In any case, the flow separation has relatively little impact on the computed rotor and FEGV flow fields.

Tweedt, Daniel L.↗

All-Atom Molecular Dynamics Simulations of the Temperature Response of Densely Grafted Polyelectrolyte Brushes

Water acts a “good” solvent for most polyelectrolyte (PE) systems due to its high dielectric strength. Theoretical and experimental studies have highlighted some remarkably unconventional properties of strongly water-swollen PE brushes such as a reduction in brush height with increase in temperature. However, an understanding of the atomistic-scale response of the grafted PE chains as well as the local arrangement and organization of the brush-supported counterions and water molecules to changes in temperature is missing. Here, we conduct an all-atom molecular dynamics (MD) study to probe the influence of temperature on the “microstructure” of densely grafted, fully ionized polyacrylic acid (PAA) brushes. The atomistic insights obtained from our study shed light on prior experimental observations and elucidate the key role played by changes in hydrogen bonding network in dictating the hydrophilicity of the brushes. In addition to the temperature-mediated reduction in height of the PE brush layer, we study the influence of temperature on several properties of the brush-supported water molecules such as the number distribution and kinetics of water-water and water-PE hydrogen bonds (HBs), mass density, orientational tetrahedral order parameter, and the activation energy associated with the self-diffusion of water. The effect of temperature on the properties of the brush-trapped counterions is also quantified via changes in their solvation structure, counterion-water radial distribution function (RDF), and the translational mobility. Our findings unravel several hitherto unknown phenomena such as the enhanced propensity for attaining PE brush-induced “water-in-salt”-like scenarios at elevated temperatures, and an increase in the activation energy for the self-diffusion of water with increase in the degree of PE brush-induced nanoconfinement (from ‘bulk water’ to ‘sparsely grafted PE brushes’ to ‘densely grafted PE brushes’). Further, we anticipate that this work will be helpful in improving our predictive capabilities of the temperature response of water-swollen PE brushes, which would be instrumental for better design of several PE brush systems used in a multitude of applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multi-scale and multi-physics analysis, design optimization, and experimental validation of heat exchangers utilizing high performance, non-round tubes

Air-to-refrigerant heat exchangers (HXs) are fundamental components in HVAC&R systems, and considerable research has been dedicated designing continually smaller, lighter, and more efficient HX designs. In recent years, researchers have leveraged advancements in Computational Fluid Dynamics (CFD), Finite Element Analysis (FEA), and optimization algorithms to consider primary tube shape and topology optimization to design highly compact, high performance HXs for a multitude of applications. In this research, we present a computationally efficient, comprehensive, multi-scale, and multi-physics analysis and optimization method for air-to-refrigerant HXs featuring automated CFD and FEA simulations and approximation-assisted optimization. This methodology was utilized to design HXs with shape-optimized, non-round tubes which outperform current state-of-the-art tube-fin HXs without compromising structural integrity. The optimal HXs were shown to deliver similar thermal performance to the baseline HXs while also achieving more than 20% reductions in airside pressure drop and core envelope volume and more than 30% reduction in internal volume. Comprehensive experimental validation of the optimization methodology was conducted through the testing of two prototypes in a standardized wind tunnel facility under multiple operating conditions. For prototype #1 under dry evaporator conditions, the predicted heat load agreed within ± 10% of measured values and the predicted airside pressure drop agreed within ± 30%, while for dehumidifying conditions, the predicted sensible and latent heat loads agreed within ± 10% and ± 20% of the measured values, respectively. For prototype #2, the predicted condenser heat load agreed within ± 3.0% of measured values, and the predicted airside pressure drop agreed within ± 27%. The acceptable agreement between simulation and experimental results for the present application highlights the flexibility of the novel optimization methodology to design next generation HXs with improved performance and reduced volume, weight, and environmental impact.

42 ENGINEERING↗

Molecular Dynamics Simulations of Liquid and Polymer Electrolytes for Energy Storage Devices

Advancing beyond current lithium-ion technology is necessary in order to enable energy storage devices for electric airplanes. Electrolyte stability is a key limiting factor, yet the design of improved electrolytes remains a formidable challenge. Molecular dynamics (MD) simulations are a powerful tool for studying electrolytes, since they can be used to evaluate structural, thermodynamic, and transport properties, and can provide molecular-level detail often inaccessible to experimental techniques. Our computational materials groups at the NASA Ames Research Center has developed models and methods to accurately simulate both liquid and polymer electrolytes.We report the results from atomistic MD simulations of several electrolyte materials, with lithium salts dissolved in ionic liquids, dimethoxyethane (DME), and polyethylene oxide (PEO). For improved accuracy, we employ polarizable models, where each atom is given an environment-dependent atomic dipole. The simulations accurately predict bulk transport properties, including viscosity, diffusion, and ionic conductivity, in quantitative agreement with available experimental data. Moreover, the simulations provide important insights into the solvation structure of the lithium ions.We also report the results from coarse-grained MD simulations of polyanion electrolytes. In order to more efficiently capture the longer length- and time-scales of these systems, we employ a generic bead-spring model. These simulations provide important insight into how the polymer chain architecture and ionic interaction strengths affect the ionic aggregation behavior and cation dynamics. Despite the simplicity of the model, the simulations yield qualitative agreement with experimental data for similar systems.

Abbott, Lauren J.↗

Studies of Shuttle orbiter arrestment system

Scale model studies of the Shuttle Orbiter Arrestment System (AS) were completed with a 1/27.5-scale model at the NASA Langley Research Center. The purpose of these studies was to determine the proper configuration for a net arrestment system to bring the orbiter to a safe stop with minimal damage in the event of a runway overrun. Tests were conducted for runway on-centerline and off-centerline engagements at simulated speeds up to approximately 100 knots (full scale). The results of these tests defined the interaction of the net and the orbiter, the dynamics of off-centerline engagements, and the maximum number of vertical net straps that may become entangled with the nose gear. In addition to these tests, a test program with a 1/8-scale model was conducted by the arrestment system contractor, and the results are presented in the appendix.

Davis, Pamela A.↗

Power modeling of degraded PV systems: Case studies using a dynamically updated physical model (PV-Pro)

Power modeling, widely applied for health monitoring and power prediction, is crucial for the efficiency and reliability of Photovoltaic (PV) systems. The most common approach for power modeling uses a physical equivalent circuit model, with the core challenge being the estimation of model parameters. Traditional parameter estimation either relies on datasheet information, which does not reflect the system's current health status, especially for degraded PV systems, or requires additional I-V characterization, which is generally unavailable for large-scale PV systems. Thus, we build upon our previously developed tool, PV-Pro (originally proposed for degradation analysis), to enhance its application for power modeling of degraded PV systems. PV-Pro extracts model parameters from production data without requiring I-V characterization. This dynamic model, periodically updated, can closely capture the actual degradation status, enabling precise power modeling. PV-Pro is compared with popular power modeling techniques, including persistence, nominal physical, and various machine learning models. The results indicate that PV-Pro achieves outstanding power modeling performance, with an average nMAE of 1.4 % across four field-degraded PV systems, reducing error by 17.6 % compared to the best alternative technique. Furthermore, PV-Pro demonstrates robustness across different seasons and severities of degradation. The tool is available as a Python package at https://github.com/DuraMAT/pvpro.

14 SOLAR ENERGY↗

Editorial: Particulate Matter Emissions From Conventional and Reformulated Fuel Combustion: Advances in Experiments and Simulations

Particulate matter (PM or soot) emissions generated by combustion of conventional and reformulated fuels adversely impact the environment and human health (Bond et al., 2013; Landrigan et al., 2018; World Health Organization (WHO), 2016), generating public awareness and motivating efforts towards the mitigation of their harmful effects. Soot formation is one of the most complex phenomena in combustion, involving interactions between combustion chemistry, fluid mechanics, mass/heat transport, and particle dynamics, spanning different spatial and temporal scales. A fundamental understanding of soot formation process is thus necessary to achieve a strong reduction of PM emissions and design cleaner and more efficient combustion systems. This has motivated a longstanding and ongoing research activity aimed at improving our understanding of the physical and chemical processes involved in soot formation, well reviewed in these recent works (Wang and Chung, 2019; Michelsen et al., 2020; Martin et al., 2022). Despite the wide interest, the transition from gas-phase molecules to incipient soot particles is still elusive and the successive particle growth and oxidation processes are far from being fully understood, especially in conditions relevant to real-world applications. Recent advances in combustion PM emission diagnostic and computational capabilities helped in improving the predictability of fundamental chemical and aerosol models for practical applications, thus tackling some of the above-mentioned challenges. The aim of this research topic is to display the ongoing research efforts in addressing the existing gaps on particulate formation from various fuel sources and in conditions typical of practical combustion applications (e.g. flames, engines, pool fires), through both experimental and numerical approaches.

42 ENGINEERING↗

Energy efficiency in industrial drying: A hybrid ultrasonic system with a novel dynamic optimization framework

Drying processes are among the most energy-consuming operations in industrial and manufacturing settings, demanding strategic selection, design, and control for enhanced efficiency. Advancing drying technologies is critical for improving sustainability, lowering energy use, reducing carbon emissions, and minimizing waste. This study explores two innovative strategies aimed at transforming drying processes into sustainable, low-carbon systems by reducing energy consumption, minimizing waste, and maintaining a strong emphasis on preserving product quality. The first strategy showcases a sub-pilot scale hybrid ultrasonic-convective dryer for agrifood products. This technology, powered by electricity (process electrification), integrates non-thermal ultrasonic dehydration with convective heating and is presented as a sustainable and energy-efficient solution that enhances eco-friendly practices. The second strategy involves introducing and implementing a novel, multiobjective, mixed integer dynamic optimization technique to determine the optimal time-dependent process parameter values for the drying operation. This optimization technique yields operating conditions that are piecewise constant in time aiming to maximize the energy efficiency of the hybrid ultrasonic-convective dryer while ensuring strict adherence to product quality constraints. By adopting the hybrid ultrasonic-convective dryer, a notable 35% improvement in energy efficiency was achieved compared to conventional hot-air drying systems for drying apple slices. The proposed optimization framework further enhanced energy efficiency by nearly 14% over the most efficient process on the identical testbed, under static operating conditions. The reported enhancements have been experimentally validated. Regarding drying time (thereby improving production yield), the developed hybrid ultrasonic-convective dryer demonstrates as much as a 41% reduction in total processing time, which is further optimized by an additional 10% using our proposed optimization framework. The research outcomes have profound implications for the design and operation of drying systems, encompassing crucial aspects such as process electrification, cost-effectiveness, energy savings, time efficiency, product yield, product quality, and process automation.

Dynamic optimization↗

Improving Estimation of the Koopman Operator with Kolmogorov–Smirnov Indicator Functions

It has become common to perform kinetic analysis using approximate Koopman operators that transform high-dimensional timeseries of observables into ranked dynamical modes. The key to the practical success of the approach is the identification of a set of observables that form a good basis on which to expand the slow relaxation modes. Good observables are, however, difficult to identify a priori and suboptimal choices can lead to significant underestimations of characteristic time scales. Leveraging the representation of slow dynamics in terms of Hidden Markov Models (HMM), we propose a simple and computationally efficient clustering procedure to infer surrogate observables that form a good basis for slow modes. Here, we apply the approach to an analytically solvable model system as well as on three protein systems of different complexities. We consistently demonstrate that the inferred indicator functions can significantly improve the estimation of the leading eigenvalues of Koopman operators and correctly identify key states and transition time scales of stochastic systems, even when good observables are not known a priori.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Computational Aerodynamic Simulations of a 1215 ft/sec Tip Speed Transonic Fan System Model for Acoustic Methods Assessment and Development

Computational Aerodynamic simulations of a 1215 ft/sec tip speed transonic fan system were performed at five different operating points on the fan operating line, in order to provide detailed internal flow field information for use with fan acoustic prediction methods presently being developed, assessed and validated. The fan system is a sub-scale, low-noise research fan/nacelle model that has undergone extensive experimental testing in the 9- by 15-foot Low Speed Wind Tunnel at the NASA Glenn Research Center. Details of the fan geometry, the computational fluid dynamics methods, the computational grids, and various computational parameters relevant to the numerical simulations are discussed. Flow field results for three of the five operating points simulated are presented in order to provide a representative look at the computed solutions. Each of the five fan aerodynamic simulations involved the entire fan system, which for this model did not include a split flow path with core and bypass ducts. As a result, it was only necessary to adjust fan rotational speed in order to set the fan operating point, leading to operating points that lie on a fan operating line and making mass flow rate a fully dependent parameter. The resulting mass flow rates are in good agreement with measurement values. Computed blade row flow fields at all fan operating points are, in general, aerodynamically healthy. Rotor blade and fan exit guide vane flow characteristics are good, including incidence and deviation angles, chordwise static pressure distributions, blade surface boundary layers, secondary flow structures, and blade wakes. Examination of the flow fields at all operating conditions reveals no excessive boundary layer separations or related secondary-flow problems.

Tweedt, Daniel L.↗

Evidence for HCO(+) infall toward T Tauri?

High spectral and spatial resolution observations of the HCO(+) molecule toward the T Tau binary system obtained with the Owens Valley Millimeter Array reveal a broad emission line profile (V(sub LSR) = 7.2 km s(exp -1), Delta V = 2.0 km s(exp -1)) upon which a narrow, redshifted absorption feature (V(sub LSR) = 8.5 km s(exp -1), Delta V approximately equals 0.5 km s(exp -1)) is superposed. One possible interpretation of the absorption is that it rises from infall of molecular cloud envelope material onto the immediate circumbinary region, which would imply that large-scale dynamic accretion processes are still active well into the optically visible stages of star formation. Provided the mass is deposited at radii sufficiently close to the young stars, estimates of the accretion rates indicate that infall may add enough material to the system to account for the FU Orionis type flares recently observed in T Tau in approximately less than 100 yr.

Van Langevelde, Huib Jan↗

Integrated Testing Approaches for the NASA Ares I Crew Launch Vehicle

The Ares I crew launch vehicle is being developed by the U.S. National Aeronautics and Space Administration (NASA) to provide crew and cargo access to the International Space Station (ISS) and, together with the Ares V cargo launch vehicle, serves as a critical component of NASA's future human exploration of the Moon. During the preliminary design phase, NASA defined and began implementing plans for integrated ground and flight testing necessary to achieve the first human launch of Ares I. The individual Ares I flight hardware elements - including the first stage five segment booster (FSB), upper stage, and J-2X upper stage engine - will undergo extensive development, qualification, and certification testing prior to flight. Key integrated system tests include the upper stage Main Propulsion Test Article (MPTA), acceptance tests of the integrated upper stage and upper stage engine assembly, a full-scale integrated vehicle ground vibration test (IVGVT), aerodynamic testing to characterize vehicle performance, and integrated testing of the avionics and software components. The Ares I-X development flight test will provide flight data to validate engineering models for aerodynamic performance, stage separation, structural dynamic performance, and control system functionality. The Ares I-Y flight test will validate ascent performance of the first stage, stage separation functionality, validate the ability of the upper stage to manage cryogenic propellants to achieve upper stage engine start conditions, and a high-altitude demonstration of the launch abort system (LAS) following stage separation. The Orion 1 flight test will be conducted as a full, un-crewed, operational flight test through the entire ascent flight profile prior to the first crewed launch.

Taylor, James L.↗

Impact of climate change on water availability and its propagation through the Western U.S. power grid

Climate impact assessment for power systems has tended to focus on the effects of water availability on generation without explicitly considering how these impacts propagate through the interconnected grid to affect generation in other locations. We investigate the impact of projected water availability on the operations of the contemporary Western U.S. power grid, focusing specifically on regional interdependencies. Hydrologic simulations derived from three GCMs (CCSM4, INMCM4 and GFDL-CM3) and two radiative scenarios (RCP4.5 and RCP8.5) are used to force a large-scale, distributed water management model (MOSART-WM), which translates water availability into power generation constraints at hydropower plants and water-dependent thermo-electric plants. Power system dynamics are evaluated using the production cost model PLEXOS. We find that the inter-regional connections across the Western U.S. electricity infrastructure are key in managing drastic variations in regional water availability. Net generation in the Northwest and Northern California is substantially sensitive to local water availability. Generation from the Desert Southwest emerges as a critical resource to compensate for variations in water availability in those regions. Climate change impacts on Northwestern water availability therefore drive future changes in other regions’ generation and regional power flows. The large inter-annual hydrological variability of Northern California exacerbates grid stress arising from long-term changes in water availability in the Northwest. While the regional power flow directions seem insensitive to long-term variations in water availability, the analysis highlights the need to consider other compounding regional factors such as changes in Southern California net load or changes in regional fuel prices.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Characterization of wind conditions and impact on wind loading at an operational parabolic trough concentrating solar power plant using LiDAR observations

Wind loading is a major factor influencing the structural design costs of Concentrating Solar Power (CSP) collector systems, including heliostats and parabolic troughs. Traditionally, these designs have been based on wind-tunnel data, which often fail to accurately represent the dynamic effects experienced at full scale. This study presents a first-of-its-kind experimental characterization of wind conditions within an operational parabolic-trough CSP power plant focusing specifically on using lidar observations. The lidar observations give a unique opportunity to provide insights into wind flow conditions deep within the trough arrays. Our results suggest that (1) after being blocked by the first few rows, the wind speed above the troughs recovers to 73% of its inflow magnitude as it flows further over the trough field due to enhanced turbulent mixing and (2) due to the wind speed recovery, troughs in the interior field will likely experience higher shear-induced turning moments compared those at the front. The conclusions from this work stress the importance of better understanding the wind patterns and interior wind loads when designing solar collectors and highlights the need for more interior load measurements in the future field campaigns.

17 WIND ENERGY↗

Linking Pressure to Electrochemical Evolution in Solid-State Conversion Cathode Composites

Conversion-type cathodes, such as sulfur, FeS 2 , and FeF 3 , offer high theoretical capacities in solid-state lithium batteries but are hindered by substantial volume changes during cycling, leading to interfacial contact loss, crack formation, and microstructural degradation. Here, we investigate the relationships between electrochemical, mechanical, and structural evolution in solid-state electrode composites with these three active materials. Using real-time stack-pressure monitoring, synchrotron X-ray absorption spectroscopy, and electrokinetic modeling, we elucidate how stress evolution is linked to reversible and irreversible redox reactions. Nonlinear stack pressure evolution in cells with sulfur, FeS 2 , and FeF 3 electrode composites is found to arise from material-specific volume changes, the balance of volume change between the working and counter electrode, and the formation of distinct reaction intermediates. The three materials exhibit distinct stack pressure evolution, which is closely related to the different reaction processes in the materials, as demonstrated with X-ray absorption spectroscopy measurements. Through mesoscale modeling, we relate the experimental measurements to species evolution at the particle scale and track the dynamic coexistence of intermediate phases. Our findings highlight the importance of designing for volume changes of a given active material in solid-state battery systems.

batteries↗

Nanosecond carrier lifetimes in solution-processed enargite (Cu 3 AsS 4 ) thin films

Enargite (ENG) Cu 3 AsS 4 is a promising material for photovoltaic applications due to its constituent earth abundant elements of differing ionic radii, ideal predicted optoelectronic properties, and demonstrated use in a working thin-film solar cell. However, little is known about ENG's defect properties; such knowledge is necessary to assess its potential for future use in high-efficiency devices. One indicator of a material's quality is its photogenerated carrier lifetime, which can be related to its bulk defect properties. Here, we use a combination of time-resolved terahertz spectroscopy and time-resolved photoluminescence to assess carrier dynamics in ENG thin films processed from nanoparticle precursors. The Shockley–Read–Hall (SRH) lifetimes are on the multi-nanosecond scale, which exceed those reported in more mature systems and represent promising values for a candidate photovoltaic material. These results suggest that ENG is worthy of further research and development effort with an eye toward future photovoltaic applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Discoveries in Blast-Driven Turbulence of Astrophysical Relevance

The fluid mixing caused by variable-density instabilities is important in a wide variety of scenarios from ocean mixing and astrophysical phenomena to nuclear fusion techniques and atomic weapons. This thesis explores the mixing resulting from a specific instability known as the Blast Driven Instability (BDI). This work investigates the variable density mixing in an explosively driven environment due to the fluid instabilities at the material interfaces. Specifically, diverging Richtmyer-Meshkov (impulsive-acceleration environment) and Rayleigh-Taylor (variable-acceleration environment) instabilities (present in supernova and inertial confinement fusion) are studied using advanced high-speed diagnostics in carefully designed laboratory experiments. The BDI morphology is presented through a time development of Mie scattering images, and steps through the parameter space (varying density ratio and driver speed), highlighting the development of the structures that form during mixing. A scaling criterion is used to relate the two systems of vastly different spatiotemporal scales. Velocity fields in the BDI have been captured for the first time using the high temporal resolution PIV technique. Subsequent analysis of the dynamics of the instability from the velocity fields illustrates the distribution of kinetic energy, the transition to turbulence, and the characteristic growth of the instability are discussed. This study furthers understanding of how blast-driven instability pertains to supernova and inertial confinement fusion science. The morphology of the BDI has been characterized for the first time. This work steps through the parameter space covered in Mie scattering experiments, and how the different parameters contribute to development of structures and mixing. It also examines a scaling of the Atwood number for expanding predictive capabilities to other experimental conditions and simulations. The first collection of velocity fields acquired for the BDI are recorded, and subsequent analysis evaluating the distribution of kinetic energy throughout space and time for two density ratios from the overall parameter space, as well as the transition to turbulence, estimated from a Reynolds number calculated based on momentum mixing are all presented. This information is useful in advancing the development of models to predict physics of high energy density applications where experiments are not always readily available. This research has successfully demonstrated understanding for the time criteria defining regimes where the shock driven (Richtmyer-Meshkov instability) and the buoyancy driven (Rayleigh-Taylor instability) dominates through a parametric study of density variation (Atwood number) and driver speed (Mach number). All this furthers understanding of how the BDI pertains to SN and ICF.

79 ASTRONOMY AND ASTROPHYSICS↗

New Type of the Interface Evolution in the Richtmyer-Meshkov Instability

We performed systematic theoretical and numerical studies of the nonlinear large-scale coherent dynamics in the Richtmyer-Meshkov instability for fluids with contrast densities. Our simulations modeled the interface dynamics for compressible and viscous uids. For a two-fluid system we observed that in the nonlinear regime of the instability the bubble velocity decays and its surface attens, and the attening is accompanied by slight oscillations. We found the theoretical solution for the system of conservation laws, describing the principal influence of the density ratio on the motion of the nonlinear bubble. The solution has no adjustable parameters, and shows that the attening of the bubble front is a distinct property universal for all values of the density ratio. This property follows from the fact that the RM bubbles decelerate. The theoretical and numerical results validate each other, describe the new type of the bubble front evolution in RMI, and identify the bubble curvature as important and sensitive diagnostic parameter.

Abarzhi, S. I.↗