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At least 127 records · Page 7

Analysis of composite ablators using massively parallel computation

In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

Shia, David↗

Machine learning reveals factors that control ion mobility in anti-perovskite solid electrolytes

Solid-state batteries are projected to exhibit improved energy densities and safety compared to liquid-electrolyte-based systems. Consequently, the development of solid electrolytes that can conduct cations at rates comparable to that of liquid electrolytes is an active area of research. To facilitate this search it is desirable to understand the chemical and structural features that control ion transport through a crystalline lattice. Here, machine learning (ML) is used to identify features that influence ion mobility in solids, quantify the relative importance of those features, and demonstrate how the variation of individual features alters ion mobility. Adopting the anti-perovskite lattice as a model system, ML algorithms were trained to predict migration barriers from a data set containing hundreds of barriers calculated using density functional theory. In this study, more than 10 6 feature sets of non-redundant descriptors were evaluated for their ability to predict migration barriers. The present analysis correctly reiterates the importance of several features that are known to influence mobility – for example, anion polarizability – but also identifies others whose importance is not widely recognized. Lattice properties such as hopping distance and channel width exhibit the greatest influence on cation mobility. Individual conditional expectation analyses performed on these features shows that barriers decrease as hopping distance decreases and as channel width increases. The defect formation energy – which is commonly associated with the concentration of defects, but not with their mobility – is identified as an important feature for interstitial migration. In sum, this analysis aids in the design of optimal solid electrolytes by simplifying the multi-dimensional design space to a sub-set of properties that are the most important.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Technical Background and Validation Report on the Residential Water Inhalation Risk Calculator Presented in the Risk Assessment Information System

Indoor air quality (IAQ) is critical for human health. Poor IAQ is linked to respiratory issues, cardiovascular diseases, and cancer. Indoor pollutants are emitted by typical household items such as cleaning products, personal care items, building materials, and tap water - an understudied volatile organic compound (VOC) source. This document presents the Residential Water Inhalation Risk Calculator (RWIRC), which estimates daily VOC exposure concentrations from various household water uses, such as showering and dishwashing, to assess exposure risks for the most vulnerable occupant. Integrated into the Risk Assessment Information System (RAIS) and sponsored by the US Department of Energy (DOE), the calculator divides a house into three compartments: shower, bathroom, and other spaces, accounting for daily water usage patterns and calculating VOC concentrations. Exposure data generated using the calculator can assist health assessors in estimating excess lifetime cancer risk (ELCR) and hazard index (HI) from VOC inhalation. Unlike traditional exposure models that utilize Andelman’s constant, the RWIRC continuously assesses variability in VOC concentrations and environmental conditions using differential equations to track VOC concentrations and air exchange between compartments. The calculator also provides unique volatilization fractions for each chemical and appliance, enhancing accuracy of the exposure concentration estimation. The RWIRC is accessible online and allows users to customize parameters (i.e., number of bathrooms, water temperature, and exhaust fan conditions) and input VOC characteristics (i.e., tap water and ambient air concentrations). This document provides a step-by-step guide on implementing the calculator. It also provides comparisons with the ATSDR-SHOWER calculator, using eight VOCs with varying physicochemical properties to reveal differences in algorithms and output concentrations. Simulations also assess how bathroom door positions and exhaust fan usage affect VOC exposure. The calculator results can enhance EPA risk screening levels for inhalation exposure to VOCs from tap water, offering a sophisticated tool for assessing inhalation risks and improving public health protection.

54 ENVIRONMENTAL SCIENCES↗

Numerical study of finite-rate supersonic combustion using parabolized equations

A set of partial differential equations, describing the two-dimensional supersonic chemically-reacting flow of the hydrogen-air system, is formulated such that the equations are parabolic in the streamwise direction. A fully-implicit fully-coupled finite-difference algorithm is used to develop a computer code which solves the governing equations by marching in the streamwise direction. The combustion process is modeled by a two-step finite-rate chemistry whereas turbulence is simulated by an algebraic turbulence model. Results of two calculations of internal supersonic reacting flow show fairly good agreement with the results obtained by the more costly full Navier-Stokes procedure.

Chitsomboon, T.↗

Creating Aerosol Types Form CHemistry (CATCH): a New Algorithm to Extend the Link Between Remote Sensing and Models

Current remote sensing methods can identify aerosol types within an atmospheric column, presenting an opportunity to incrementally bridge the gap between remote sensing and models. Here a new algorithm was designed for Creating Aerosol Types from CHemistry (CATCH). CATCH-derived aerosol types—dusty mix, maritime, urban, smoke, and fresh smoke—are based on first-generation airborne High Spectral Resolution Lidar (HSRL-1) retrievals during the Ship-Aircraft Bio-Optical Research (SABOR) campaign, July/August 2014. CATCH is designed to derive aerosol types from model output of chemical composition. CATCH-derived aerosol types are determined by multivariate clustering of model-calculated variables that have been trained using retrievals of aerosol types from HSRL-1. CATCH-derived aerosol types (with the exception of smoke) compare well with HSRL-1 retrievals during SABOR with an average difference in aerosol optical depth (AOD) <0.03. Data analysis shows that episodic free tropospheric transport of smoke is underpredicted by the Goddard Earth Observing System- with Chemistry (GEOS-Chem) model. Spatial distributions of CATCH-derived aerosol types for the North American model domain during July/August 2014 show that aerosol type-specific AOD values occurred over representative locations: urban over areas with large population, maritime over oceans, smoke, and fresh smoke over typical biomass burning regions. This study demonstrates that model-generated information on aerosol chemical composition can be translated into aerosol types analogous to those retrieved from remote sensing methods. In the future, spaceborne HSRL-1 and CATCH can be used to gain insight into chemical composition of aerosol types, reducing uncertainties in estimates of aerosol radiative forcing.

K W Dawson↗

Autonomously Calibrating a Quadrupole Mass Spectrometer

A computer program autonomously manages the calibration of a quadrupole ion mass spectrometer intended for use in monitoring concentrations and changes in concentrations of organic chemicals in the cabin air of the International Space Station. The instrument parameters calibrated include the voltage on a channel electron multiplier, a discriminator threshold, and an ionizer current. Calibration is achieved by analyzing the mass spectrum obtained while sweeping the parameter ranges in a heuristic procedure, developed by mass spectrometer experts, that involves detection of changes in signal trends that humans can easily recognize but cannot necessarily be straightforwardly codified in an algorithm. The procedure includes calculation of signal-to-noise ratios, signal-increase rates, and background-noise-increase rates; finding signal peaks; and identifying peak patterns. The software provides for several recovery-from-error scenarios and error-handling schemes. The software detects trace amounts of contaminant gases in the mass spectrometer and notifies associated command- and-data-handling software to schedule a cleaning. Furthermore, the software autonomously analyzes the mass spectrum to determine whether the parameters of a radio-frequency ramp waveform are set properly so that the peaks of the mass spectrum are at expected locations.

Lee, Seungwon↗

Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation

Abstract An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near‐term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan distance is constrained by the quality of the ansatz, the AVQITE method iteratively expands the ansatz along the dynamical path to keep the McLachlan distance below a chosen threshold. This ensures the state is able to follow the quantum imaginary time evolution path in the system Hilbert space rather than in a restricted variational manifold set by a predefined fixed ansatz. AVQITE is used to prepare ground states of H 4 , H 2 O, and BeH 2 molecules, where it yields compact variational ansätze and ground state energies within chemical accuracy. Polynomial scaling of circuit depth with system size is shown through a set of AVQITE calculations of quantum spin models. Finally, quantum Lanczos calculations are demonstrated alongside AVQITE without additional quantum resource costs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

PeakDecoder enables machine learning-based metabolite annotation and accurate profiling in multidimensional mass spectrometry measurements

Multidimensional measurements using state-of-the-art separations and mass spectrometry provide advantages in untargeted metabolomics analyses for studying biological and environmental bio-chemical processes. However, the lack of rapid analytical methods and robust algorithms for these heterogeneous data has limited its application. Here, we develop and evaluate a sensitive and high-throughput analytical and computational workflow to enable accurate metabolite profiling. Our workflow combines liquid chromatography, ion mobility spectrometry and data-independent acquisition mass spectrometry with PeakDecoder, a machine learning-based algorithm that learns to distinguish true co-elution and co-mobility from raw data and calculates metabolite identification error rates. We apply PeakDecoder for metabolite profiling of various engineered strains of Aspergillus pseudoterreus, Aspergillus niger, Pseudomonas putida and Rhodosporidium toruloides. Results, validated manually and against selected reaction monitoring and gas-chromatography platforms, show that 2683 features could be confidently annotated and quantified across 116 microbial sample runs using a library built from 64 standards.

59 BASIC BIOLOGICAL SCIENCES↗

Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation

It is shown how the electronic equations of motion in extended Lagrangian Born–Oppenheimer molecular dynamics simulations can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born–Oppenheimer molecular dynamics. We note the low-rank approximation of the Jacobian is directly related to Broyden’s class of quasi-Newton algorithms and Jacobian-free Newton–Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Cloud-Resolved Simulations of Lightning NOx in an Observed Hector Thunderstorm

Cloud chemistry simulations are being performed for a "Hector" storm observed on 16 November 2005 during the SCOUT-03lACTIVE campaigns based in Darwin, Australia. The primary objective of these simulations is to estimate the average production of NO per lightning flash during the storm. The 3-D WRF-AqChem model is being used for these calculations. This modeling package contains the WRF nonhydrostatic cloud-resolving model, online gas- and aqueous-phase chemistry, and a lightning algorithm (Barth et al., 2007). Early morning soundings of temperature, water vapor and winds are used to initialize the model. Surface heating of the Tiwi Islands is simulated in the model to induce convection. Observations from the Egrett, Falcon, Geophysica, and Dornier aircraft in air undisturbed by the storm are used to construct composite initial condition chemical profiles. Convective transport in the model is tested using tracer species such as CO and O3. Lightning flashes observed by the LINET network are input to the model and a lightning placement scheme is used to inject the resulting NO into the simulated cloud. Various scenarios of NO production per flash are used for cloud-to-ground and intracloud flashes in a series of simulations for the storm. Resulting NO, mixing ratios from each simulation are compared with upper tropospheric anvil observations (from the Geophysica and Egrett aircraft) to determine the best fit with the mean NOx at anvil altitudes, the profile shape, and the frequency distribution of NOx values. We will compare the results for lightning NO production from this tropical thunderstorm with similar analyses conducted for several midlatitude and subtropical convective events.

Pickering, Kenneth↗

A Green's Function Approach to Simulate DNA Damage by the Indirect Effect

The DNA damage is of fundamental importance in the understanding of the effects of ionizing radiation. DNA is damaged by the direct effect of radiation (e.g. direct ionization) and by indirect effect (e.g. damage by.OH radicals created by the radiolysis of water). Despite years of research, many questions on the DNA damage by ionizing radiation remains. In the recent years, the Green's functions of the diffusion equation (GFDE) have been used extensively in biochemistry [1], notably to simulate biochemical networks in time and space [2]. In our future work on DNA damage, we wish to use an approach based on the GFDE to refine existing models on the indirect effect of ionizing radiation on DNA. To do so, we will use the code RITRACKS [3] developed at the NASA Johnson Space Center to simulate the radiation track structure and calculate the position of radiolytic species after irradiation. We have also recently developed an efficient Monte‐Carlo sampling algorithm for the GFDE of reversible reactions with an intermediate state [4], which can be modified and adapted to simulate DNA damage by free radicals. To do so, we will use the known reaction rate constants between radicals (OH, eaq, H,...) and the DNA bases, sugars and phosphates and use the sampling algorithms to simulate the diffusion of free radicals and chemical reactions with DNA. These techniques should help the understanding of the contribution of the indirect effect in the formation of DNA damage and double‐strand breaks.

Plante, Ianik↗

Data-Driven Prediction of Formation Mechanisms of Lithium Ethylene Monocarbonate with an Automated Reaction Network

Interfacial reactions are notoriously difficult to characterize, and robust prediction of the chemical evolution and associated functionality of the resulting surface film is one of the grand challenges of materials chemistry. The solid-electrolyte interphase (SEI), critical to Li-ion batteries (LIBs), exemplifies such a surface film, and despite decades of work, considerable controversy remains regarding the major components of the SEI as well as their formation mechanisms. Here we use a reaction network to investigate whether lithium ethylene monocarbonate (LEMC) or lithium ethylene dicarbonate (LEDC) is the major organic component of the LIB SEI. Our data-driven, automated methodology is based on a systematic generation of relevant species using a general fragmentation/recombination procedure which provides the basis for a vast thermodynamic reaction landscape, calculated with density functional theory. The shortest pathfinding algorithms are employed to explore the reaction landscape and obtain previously proposed formation mechanisms of LEMC as well as several new reaction pathways and intermediates. For example, we identify two novel LEMC formation mechanisms: one which involves LiH generation and another that involves breaking the (CH 2 )O-C(=O)OLi bond in LEDC. Most importantly, we find that all identified paths, which are also kinetically favorable under the explored conditions, require water as a reactant. This condition severely limits the amount of LEMC that can form, as compared with LEDC, a conclusion that has direct impact on the SEI formation in Li-ion energy storage systems. Finally, the data-driven framework presented here is generally applicable to any electrochemical system and expected to improve our understanding of surface passivation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An Overview of the Tropospheric Aerosol Radiative Forcing Observational Experiment

Aerosol effects on atmospheric radiation are a leading source of uncertainty in predicting future climate. As a result, the International Global Atmospheric Chemistry Program has established a Focus on Atmospheric Aerosols (IGAC/FAA) and endorsed a series of aerosol field campaigns. TARFOX, the second in the IGAC/FAA series, was designed to reduce this uncertainty by measuring aerosol properties and effects in the US eastern seaboard, where one of the world's major plumes of industrial haze moves from the continent over the Atlantic Ocean. TARFOX's objectives are to: 1. Make simultaneous measurements of: (a) aerosol effects on radiation fields, and (b) the chemical, physical, and optical properties of the aerosols causing those effects. 2. Perform a variety of closure studies by using overdetermined data sets to test the mutual consistency of measurements and calculations of a wide range of aerosol properties and effects. 3. Use the results of the closure studies to assess and reduce uncertainties in estimates of aerosol radiative forcing, as well as to guide future field programs. An important subset of the closure studies is tests and improvements of algorithms used to derive aerosol properties and radiative effects from satellite measurements. The TARFOX Intensive Field Period (IFP) was conducted July 10-31, 1996. It included coordinated measurements from four satellites (GOES-8, NOAA-14, ERS-2, LANDSAT), four aircraft (ER-2, C-130, C-131, and a modified Cessna), land sites, and ships. A variety of aerosol conditions was sampled, ranging from relatively clean behind frontal passages to moderately polluted with aerosol optical depths exceeding 0.5 at mid-visible wavelengths. The latter conditions included separate incidents of enhancements caused primarily by anthropogenic sources and another incident of enhancement apparently influenced by recent fog processing. Spatial gradients of aerosol optical thickness were sampled to aid in isolating aerosol effects from other radiative effects and to more tightly constrain closure tests, including those of satellite retrievals. This talk gives an overview of TARFOX goals, rationale, methods, and initial key findings.

Russell, P. B.↗

Additional support for the TDK/MABL computer program

An advanced version of the Two-Dimensional Kinetics (TDK) computer program was developed under contract and released to the propulsion community in early 1989. Exposure of the code to this community indicated a need for improvements in certain areas. In particular, the TDK code needed to be adapted to the special requirements imposed by the Space Transportation Main Engine (STME) development program. This engine utilizes injection of the gas generator exhaust into the primary nozzle by means of a set of slots. The subsequent mixing of this secondary stream with the primary stream with finite rate chemical reaction can have a major impact on the engine performance and the thermal protection of the nozzle wall. In attempting to calculate this reacting boundary layer problem, the Mass Addition Boundary Layer (MABL) module of TDK was found to be deficient in several respects. For example, when finite rate chemistry was used to determine gas properties, (MABL-K option) the program run times became excessive because extremely small step sizes were required to maintain numerical stability. A robust solution algorithm was required so that the MABL-K option could be viable as a rocket propulsion industry design tool. Solving this problem was a primary goal of the phase 1 work effort.

Nickerson, G. R.↗

Why HOC+ is detectable in interstellar clouds: the rate of the reaction between HOC+ and H2

The recent confirmation by Ziurys and Apponi of the detection of HOC+ toward Sgr B2 (OH), and their identification of the ion in Orion-KL and several other sources show that HOC+ is far more abundant than predicted by previous ion-molecule models. In these models, the reaction HOC(+) + H2 --> HCO(+) + H2 is assumed to rapidly destroy HOC+, based on the results of a prior calculation. We have recalculated the rate of this reaction as a function of temperature using a new ab initio potential surface and a phase space approach to the dynamics which includes tunneling. The newly calculated rate is small (< or = 1 x 10(-10) cm3 s-1) at temperatures under 100 K.

Non-NASA Center↗

Active Learning Accelerated Discovery of Stable Iridium Oxide Polymorphs for the Oxygen Evolution Reaction

The discovery of high-performing and stable materials for sustainable energy applications is a pressing goal in catalysis and materials science. Understanding the relationship between a material’s structure and functionality is an important step in the process, such that viable polymorphs for a given chemical composition need to be identified. Machine-learning-based surrogate models have the potential to accelerate the search for polymorphs that target specific applications. Herein, we report a readily generalizable active-learning (AL) accelerated algorithm for identification of electrochemically stable iridium oxide polymorphs of IrO 2 and IrO 3 . The search is coupled to a subsequent analysis of the electrochemical stability of the discovered structures for the acidic oxygen evolution reaction (OER). Structural candidates are generated by identifying all 956 structurally unique AB2 and AB3 prototypes in existing materials databases (more than 38000). Next, using an active learning approach, we find 196 IrO 2 polymorphs within the thermodynamic amorphous synthesizability limit and reaffirm the global stability of the rutile structure. We find 75 synthesizable IrO 3 polymorphs and report a previously unknown FeF 3 -type structure as the most stable, termed α-IrO 3 . To test the algorithms performance, we compare to a random search of the candidate space and report at least a 2-fold increase in the rate of discovery. Additionally, the AL approach can acquire the most stable polymorphs of IrO 2 and IrO 3 with fewer than 30 density functional theory optimizations. Analysis of the structural properties of the discovered polymorphs reveals that octahedral local coordination environments are preferred for nearly all low-energy structures. Subsequent Pourbaix Ir–H 2 O analysis shows that α-IrO3 is the globally stable solid phase under acidic OER conditions and supersedes the stability of rutile IrO 2 . Calculation of theoretical OER surface activities reveal ideal weaker binding of the OER intermediates on α-IrO 3 than on any other considered iridium oxide. We emphasize that the proposed AL algorithm can be easily generalized to search for any binary metal oxide structure with a defined stoichiometry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermal/Pyrolysis Gas Flow Analysis of Carbon Phenolic Material

Provided in this study are predicted in-depth temperature and pyrolysis gas pressure distributions for carbon phenolic materials that are externally heated with a laser source. Governing equations, numerical techniques and comparisons to measured temperature data are also presented. Surface thermochemical conditions were determined using the Aerotherm Chemical Equilibrium (ACE) program. Surface heating simulation used facility calibrated radiative and convective flux levels. Temperatures and pyrolysis gas pressures are predicted using an upgraded form of the SINDA/CMA program that was developed by NASA during the Solid Propulsion Integrity Program (SPIP). Multispecie mass balance, tracking of condensable vapors, high heat rate kinetics, real gas compressibility and reduced mixture viscosity's have been added to the algorithm. In general, surface and in-depth temperature comparisons are very good. Specie partial pressures calculations show that a saturated water-vapor mixture is the main contributor to peak in-depth total pressure. Further, for most of the cases studied, the water-vapor mixture is driven near the critical point and is believed to significantly increase the local heat capacity of the composite material. This phenomenon if not accounted for in analysis models may lead to an over prediction in temperature response in charring regions of the material.

Clayton, J. Louie↗

Application of a flux-split algorithm to chemically relaxing, hypervelocity blunt-body flows

Viscous, nonequilibrium, hypervelocity flow fields over two axisymmetric configurations are numerically simulated using a factored, implicit, flux-split algorithm. The governing gas-dynamic and species-continuity equations for laminar flow are presented. The gas-dynamics/nonequilibrium-chemistry coupling procedure is developed as part of the solution procedure and is described in detail. Numerical solutions are presented for hypervelocity flows over a hemisphere and over an axisymmetric aeroassisted orbital transfer vehicle using three different chemistry models. The gas models considered are those for an ideal gas, for a frozen gas, and for chemically relaxing air consisting of five species. The calculated results are compared with existing numerical solutions in the literature along the stagnation line of the hemisphere. The effects of free-stream Reynolds number on the nonequilibrium flow field are discussed.

Balakrishnan, A.↗