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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
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NASA NTRS2009

Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.

Nielsen, Eric J.↗
NASA NTRS2010

Adaptive Numerical Algorithms in Space Weather Modeling

Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different physics in different domains. A multi-physics system can be modeled by a software framework comprising of several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solar wind Roe Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamics (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical schemes. Depending on the application, we find that different time stepping methods are optimal. Several of the time integration schemes exploit the block-based granularity of the grid structure. The framework and the adaptive algorithms enable physics based space weather modeling and even forecasting.

Toth, Gabor↗
NASA NTRS2010

Environmental Impact Specification for Direct Space Weathering of Kuiper Belt and Oort Cloud Objects

The Direct Space Weathering Project of NASA's Outer Planets Research Program addresses specification of the plasma and energetic particle environments for irradiation and surface chemical processing of icy bodies in the outer solar system and the local interstellar medium. Knowledge of the radiation environments is being expanded by ongoing penetration of the twin Voyager spacecraft into the heliosheath boundary region of the outer heliosphere and expected emergence within the next decade into the very local interstellar medium. The Voyager measurements are being supplemented by remote sensing from Earth orbit of energetic neutral atom emission from this boundary region by NASA's Interstellar Boundary Explorer (IBEX). Although the Voyagers long ago passed the region of the Classical Kuiper Belt, the New Horizons spacecraft will encounter Pluto in 2015 and thereafter explore one or more KBOs, meanwhile providing updated measurements of the heliospheric radiation environment in this region. Modeling of ion transport within the heliosphere allows specification of time-integrated irradiation effects while the combination of Voyager and IBEX data supports projection of the in-situ measurements into interstellar space beyond the heliosheath. Transformation of model ion flux distributions into surface sputtering and volume ionization profiles provides a multi-layer perspective for space weathering impact on the affected icy bodies and may account for some aspects of color and compositional diversity. Other important related factors may include surface erosion and gardening by meteoritic impacts and surface renewal by cryovolcanism. Chemical products of space weathering may contribute to energy resources for the latter.

Cooper, John F.↗
NASA NTRS2011

GPM Mission Overview

The Global Precipitation Measurement (GPM) Mission is an international satellite mission to unify and advance precipitation measurements from a constellation of research and operational sensors to provide "next-generation" precipitation products. Relative to current global rainfall products, GPM data products will be characterized by: (1) more accurate instantaneous precipitation measurements (especially for light rain and cold-season solid/snow precipitation), (2) more frequent sampling by an expanded constellation of microwave radiometers that include operational humidity sounders over land, (3) inter-calibrated microwave brightness temperatures from constellation radiometers within a unified framework, and (4) physical-based precipitation retrievals from constellation radiometers using a common a priori cloud hydrometeor database derived from GPM Core sensor measurements. The cornerstone of the GPM mission is the deployment of a Core Observatory in a unique 65 degree non-Sun-synchronous orbit to serve as a physics observatory and a calibration reference to improve precipitation measurements by a constellation of dedicated and operational passive microwave sensors. The Core Observatory will carry a KulKa-band Dual-frequency Precipitation Radar (DPR) and a multi-channel (10-183 GHz) GPM Microwave Radiometer (GMI). The combined use ofDPR and GMI measurements will place greater constraints on possible solutions to radiometer retrievals to improve the accuracy and consistency of precipitation retrievals from all constellation radiometers. As a science mission with integrated application goals, GPM is designed to (1) advance precipitation measurement capability from space through combined use of active and passive microwave sensors, (2) advance the knowledge of the global water/energy cycle and freshwater availability through better description of the space-time variability of global precipitation, and (3) improve weather, climate, and hydrological prediction capabilities through more accurate and frequent measurements of instantaneous precipitation rates and time-integrated rainfall accumulation. An overview of the GPM mission concept and science activities in the United States, together with an update on international collaborations in radiometer intercalibration and ground validation, will be presented.

Hou, Arthur Y.↗
NASA NTRS2012

Stagnation Point Radiative Heating Relations for Venus Entry

Improved analytic expressions for calculating the stagnation point radiative heating during entry into the atmosphere of Venus have been developed. These analytic expressions can be incorporated into entry trajectory simulation codes. Together with analytical expressions for convective heating at the stagnation point, the time-integrated total heat load at the stagnation point is used in determining the thickness of protective material required, and hence the mass of the fore body heatshield of uniform thickness.

Tauber, Michael E.↗
NASA NTRS2012

Effect of Inductive Coil Geometry on the Operating Characteristics of a Pulsed Inductive Plasma Accelerator

Operational characteristics of two separate inductive thrusters with coils of different cone angles are explored through thrust stand measurements and time-integrated, un- filtered photography. Trends in impulse bit measurements indicate that, in the present experimental configuration, the thruster with the inductive coil possessing a smaller cone angle produced larger values of thrust, in apparent contradiction to results of a previous thruster acceleration model. Areas of greater light intensity in photographs of thruster operation are assumed to qualitatively represent locations of increased current density. Light intensity is generally greater in images of the thruster with the smaller cone angle when compared to those of the thruster with the larger half cone angle for the same operating conditions. The intensity generally decreases in both thrusters for decreasing mass ow rate and capacitor voltage. The location of brightest light intensity shifts upstream for decreasing mass ow rate of propellant and downstream for decreasing applied voltage. Recognizing that there typically exists an optimum ratio of applied electric field to gas pressure with respect to breakdown efficiency, this result may indicate that the optimum ratio was not achieved uniformly over the coil face, leading to non-uniform and incomplete current sheet formation in violation of the model assumption of immediate formation where all the injected propellant is contained in a magnetically-impermeable current sheet.

Hallock, Ashley K.↗
NASA NTRS2012

Derivation of a New Smoke Emissions Inventory using Remote Sensing, and Its Implications for Near Real-Time Air Quality Applications

A new emissions inventory of particulate matter (PM) is being derived mainly from remote sensing data using fire radiative power (FRP) and aerosol optical depth (AOD) retrievals from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument, as well as wind data from the Modern Era Retrospective-Analysis for Research and Applications (MERRA) reanalysis dataset, which spans the satellite era. This product is generated using a coefficient of emission, C(sub e), that has been produced on a 1x1 degree global grid such that, when it is multiplied with satellite measurements of FRP or its time-integrated equivalent fire radiative energy (FRE) retrieved over a given area and time period, the corresponding PM emissions are estimated. This methodology of using C(sub e) to derive PM emissions is relatively new and advantageous for near real-time air quality applications compared to current methods based on post-fire burned area that may not provide emissions in a timely manner. Furthermore, by using FRP to characterize a fire s output, it will represent better accuracy than the use of raw fire pixel counts, since fires in individual pixels can differ in size and strength by orders of magnitude, resulting in similar differences in emission rates. Here we will show examples of this effect and how this new emission inventory can properly account for the differing emission rates from fires of varying strengths. We also describe the characteristics of the new emissions inventory, and propose the process chain of incorporating it into models for air quality applications.

Ellison, Luke↗
NASA NTRS2013

Inductive Pulsed Plasma Thruster Development and Testing at NASA-MSFC

THE inductive pulsed plasma thruster (IPPT) is an electrodeless space propulsion device where a capacitor is charged to an initial voltage and then discharged producing a high current pulse through a coil. The field produced by this pulse ionizes propellant, inductively driving current in a plasma located near the face of the coil. Once the plasma is formed it can be accelerated and expelled at a high exhaust velocity by the electromagnetic Lorentz body force arising from the interaction of the induced plasma current and the magnetic field produced by the current in the coil. In the present work, we present a summary of the IPPT research and development conducted at NASA's Marshall Space Flight Center (MSFC). As a higher-power, still relatively low readiness level system, there are many issues associated with the eventual deployment and use of the IPPT as a primary propulsion system on spacecraft that remain to be addressed. The present program aimed to fabricate and test hardware to explore how these issues could be addressed. The following specific areas were addressed within the program and will be discussed within this paper. a) Conical theta-pinch IPPT geometry thruster configuration. b) Repetition-rate multi-kW thruster pulsing. c) Long-lifetime pulsed gas valve. d) Fast pulsed gas valve driver and controller. e) High-voltage, repetitive capacitor charging power processing unit. During the course of testing, a number of specific tests were conducted, including several that, to our knowledge, have either never been previously conducted (such as multi-KW repetition-rate operation) or have not been performed since the early 1990s (direct IPPT thrust measurements).2 Conical theta-pinch IPPT thrust stand measurements are presented in Fig. 1 while various time-integrated and time

Polzin, Kurt A.↗
NASA NTRS2012

SGR J1550-5418 Bursts Detected with the Fermi Gamma-Ray Burst Monitor during Its Most Prolific Activity

We have performed detailed temporal and time-integrated spectral analysis of 286 bursts from SGR J1550-5418 detected with the Fermi Gamma-ray Burst Monitor (GBM) in 2009 January, resulting in the largest uniform sample of temporal and spectral properties of SGR J1550-5418 bursts. We have used the combination of broadband and high time-resolution data provided with GBM to perform statistical studies for the source properties.We determine the durations, emission times, duty cycles, and rise times for all bursts, and find that they are typical of SGR bursts. We explore various models in our spectral analysis, and conclude that the spectra of SGR J15505418 bursts in the 8-200 keV band are equally well described by optically thin thermal bremsstrahlung (OTTB), a power law (PL) with an exponential cutoff (Comptonized model), and two blackbody (BB) functions (BB+BB). In the spectral fits with the Comptonized model, we find a mean PL index of -0.92, close to the OTTB index of -1. We show that there is an anti-correlation between the Comptonized E(sub peak) and the burst fluence and average flux. For the BB+BBfits, we find that the fluences and emission areas of the two BB functions are correlated. The low-temperature BB has an emission area comparable to the neutron star surface area, independent of the temperature, while the high temperature BB has a much smaller area and shows an anti-correlation between emission area and temperature.We compare the properties of these bursts with bursts observed from other SGR sources during extreme activations, and discuss the implications of our results in the context of magnetar burst models.

bursts↗
NASA NTRS2014

Global Top-Down Smoke-Aerosol Emissions Estimation Using Satellite Fire Radiative Power Measurements

Fire emissions estimates have long been based on bottom-up approaches that are not only complex, but also fraught with compounding uncertainties. We present the development of a global gridded (1 deg ×1 deg) emission coefficients (Ce) product for smoke total particulate matter (TPM) based on a top-down approach using coincident measurements of fire radiative power (FRP) and aerosol optical thickness (AOT) from the Moderate-resolution Imaging Spectroradiometer (MODIS) sensors aboard the Terra and Aqua satellites. This new Fire Energetics and Emissions Research version 1.0 (FEER.v1) Ce product has now been released to the community and can be obtained from http://feer.gsfc. nasa.gov/, along with the corresponding 1-to-1 mapping of their quality assurance (QA) flags that will enable the Ce values to be filtered by quality for use in various applications. The regional averages of Ce values for different ecosystem types were found to be in the ranges of 16-21/gMJ−1 for savanna and grasslands, 15-32/gMJ−1 for tropical forest, 9-12/gMJ−1 for North American boreal forest, and 18- 26/MJ−1 for Russian boreal forest, croplands and natural vegetation. The FEER.v1 Ce product was multiplied by time-integrated FRP data to calculate regional smoke TPM emissions, which were compared with equivalent emissions products from three existing inventories. FEER.v1 showed higher and more reasonable smoke TPM estimates than two other emissions inventories that are based on bottom-up approaches and already reported in the literature to be too low, but portrayed an overall reasonable agreement with another top-down approach. This suggests that top-down approaches may hold better promise and need to be further developed to accelerate the reduction of uncertainty associated with fire emissions estimation in air-quality and climate research and applications. Results of the analysis of FEER.v1 data for 2004-2011 show that 65-85 Tg yr−1 of TPM is emitted globally from open biomass burning, with a generally decreasing trend over this short time period. The FEER.v1 Ce product is the first global gridded product in the family of "emission factors", that is based essentially on satellite measurements, and requires only direct satellite FRP measurements of an actively burning fire anywhere to evaluate its emission rate in near-real time, which is essential for operational activities, such as the monitoring and forecasting of smoke emission impacts on air quality.

biomass burning↗
NASA NTRS2014

Visualizing Flutter Mechanism as Traveling Wave Through Animation of Simulation Results for the Semi-Span Super-Sonic Transport Wind-Tunnel Model

It has long been recognized that frequency and phasing of structural modes in the presence of airflow play a fundamental role in the occurrence of flutter. Animation of simulation results for the long, slender Semi-Span Super-Sonic Transport (S4T) wind-tunnel model demonstrates that, for the case of mass-ballasted nacelles, the flutter mode can be described as a traveling wave propagating downstream. Such a characterization provides certain insights, such as (1) describing the means by which energy is transferred from the airflow to the structure, (2) identifying airspeed as an upper limit for speed of wave propagation, (3) providing an interpretation for a companion mode that coalesces in frequency with the flutter mode but becomes very well damped, (4) providing an explanation for bursts of response to uniform turbulence, and (5) providing an explanation for loss of low frequency (lead) phase margin with increases in dynamic pressure (at constant Mach number) for feedback systems that use sensors located upstream from active control surfaces. Results from simulation animation, simplified modeling, and wind-tunnel testing are presented for comparison. The simulation animation was generated using double time-integration in Simulink of vertical accelerometer signals distributed over wing and fuselage, along with time histories for actuated control surfaces. Crossing points for a zero-elevation reference plane were tracked along a network of lines connecting the accelerometer locations. Accelerometer signals were used in preference to modal displacement state variables in anticipation that the technique could be used to animate motion of the actual wind-tunnel model using data acquired during testing. Double integration of wind-tunnel accelerometer signals introduced severe drift even with removal of both position and rate biases such that the technique does not currently work. Using wind-tunnel data to drive a Kalman filter based upon fitting coefficients to analytical mode shapes might provide a better means to animate the wind tunnel data.

Christhilf, David M.↗
NASA NTRS2014

Assessment of Reduced-Kinetics Mechanisms for Combustion of Jet Fuel in CFD Applications

A computational effort was undertaken to analyze the details of fluid flow in Lean-Direct Injection (LDI) combustors for next-generation LDI design. The National Combustor Code (NCC) was used to perform reacting flow computations on single-element LDI injector configurations. The feasibility of using a reduced chemical-kinetics approach, which optimizes the reaction rates and species to model the emissions characteristics typical of lean-burning gas-turbine combustors, was assessed. The assessments were performed with Reynolds- Averaged Navier-Stokes (RANS) and Time-Filtered Navier Stokes (TFNS) time-integration, with a Lagrangian spray model with the NCC code. The NCC predictions for EINOx and combustor exit temperature were compared with experimental data for two different single-element LDI injector configurations, with 60deg and 45deg axially swept swirler vanes. The effects of turbulence-chemistry interaction on the predicted flow in a typical LDI combustor were studied with detailed comparisons of NCC TFNS with experimental data.

Ajmani, Kumud↗
NASA NTRS2015

Lead Isotopes in Olivine-Phyric Shergottite Tissint: Implications for the Geochemical Evolution of the Shergottite Source Mantle

Geochemically-depleted shergottites are basaltic rocks derived from a martian mantle source reservoir. Geochemical evolution of the martian mantle has been investigated mainly based on the Rb-Sr, Sm-Nd, and Lu-Hf isotope systematics of the shergottites [1]. Although potentially informative, U-Th- Pb isotope systematics have been limited because of difficulties in interpreting the analyses of depleted meteorite samples that are more susceptible to the effects of near-surface processes and terrestrial contamination. This study conducts a 5-step sequential acid leaching experiment of the first witnessed fall of the geochemically-depleted olivinephyric shergottite Tissint to minimize the effect of low temperature distrubence. Trace element analyses of the Tissint acid residue (mostly pyroxene) indicate that Pb isotope compositions of the residue do not contain either a martian surface or terrestrial component, but represent the Tissint magma source [2]. The residue has relatively unradiogenic initial Pb isotopic compositions (e.g., 206Pb/204Pb = 10.8136) that fall within the Pb isotope space of other geochemically-depleted shergottites. An initial μ-value (238U/204Pb = 1.5) of Tissint at the time of crystallization (472 Ma [3]) is similar to a time-integrated mu- value (1.72 at 472 Ma) of the Tissint source mantle calculated based on the two-stage mantle evolution model [1]. On the other hand, the other geochemically-depleted shergottites (e.g., QUE 94201 [4]) have initial μ-values of their parental magmas distinctly lower than those of their modeled source mantle. These results suggest that only Tissint potentially reflects the geochemical signature of the shergottite mantle source that originated from cumulates of the martian magma ocean

Moriwaki, R.↗
NASA NTRS2017

Changing Seasonality of Panarctic Tundra Vegetation in Relationship to Climatic Variables

Potential climate drivers of Arctic tundra vegetation productivity are investigated to understand recent greening and browning trends documented by maximum normalized difference vegetation index (NDVI) (MaxNDVI) and time-integrated NDVI (TI-NDVI) for 19822015. Over this period, summer sea ice has continued to decline while oceanic heat content has increased. The increases in summer warmth index (SWI) and NDVI have not been uniform over the satellite record. SWI increased from 1982 to the mid-1990s and remained relatively flat from 1998 onwards until a recent upturn. While MaxNDVI displays positive trends from 19822015, TI-NDVI increased from 1982 until 2001 and has declined since. The data for the first and second halves of the record were analyzed and compared spatially for changing trends with a focus on the growing season. Negative trends for MaxNDVI and TI-NDVI were more common during 19992015 compared to 19821998.

sea ice↗
NASA NTRS2017

Photospheric Emission in the Joint GBM and Konus Prompt Spectra of GRB 120323A

GRB 120323A is a very intense short gamma-ray burst (GRB) detected simultaneously during its prompt gamma-ray emission phase with the Gamma-Ray Burst Monitor (GBM) on board the Fermi Gamma-Ray Space Telescope and the Konus experiment on board the Wind satellite. GBM and Konus operate in the kiloelectronvolt - megaelectronvolt regime; however, the GBM range is broader toward both the low and the high parts of the gamma-ray spectrum. Analyses of such bright events provide a unique opportunity to check the consistency of the data analysis as well as cross-calibrate the two instruments. We performed time-integrated and coarse time-resolved spectral analysis of GRB 120323A prompt emission. We conclude that the analyses of GBM and Konus data are only consistent when using a double-hump spectral shape for both data sets; in contrast, the single hump of the empirical Band function, traditionally used to fit GRB prompt emission spectra, leads to significant discrepancies between GBM and Konus analysis results. Our two-hump model is a combination of a thermal-like and a non-thermal component. We interpret the first component as a natural manifestation of the jet photospheric emission.

Guiriec, S.↗
NASA NTRS2017

Robust Acoustic Objective Functions and Sensitivities in Adjoint-Based Design Optimizations

The multidisciplinary design of aircraft typically includes considerations of performance, weight, fuel burn, and noise, among other factors. An objective function is applied to each of these considerations in order to weight the influence of trade-offs between different designs. Higher-order optimization exercises have utilized an adjoint approach to reach an optimal set of objective functions, such as maximum lift and reduced drag. Taking advantage of the adjoint approach significantly reduces the computational time required to find an optimal configuration. Including acoustics in the set of objective functions during an adjoint-based design optimization requires the sensitivity of the acoustic objective function. This document will present an approach for defining the sensitivity of several acoustic metrics and operations that can fill the role of the acoustic objective function. This includes time-integrated metrics such as effective perceived noise level (EPNL) and frequency-integrated metrics such as overall sound pressure level (OASPL). A demonstration case, validation, and details on the implementation in the second generation Aircraft NOise Prediction Program (ANOPP2) are also shown.

Lopes, Leonard V.↗
NASA NTRS2021

Climate Drivers of Arctic Tundra Variability and Change Using an Indicators Framework

This study applies an indicators framework to investigate climate drivers of tundra vegetation trends and variability over the 1982–2019 period. Previously known indicators relevant for tundra productivity (summer warmth index (SWI), coastal spring sea-ice (SI) area, coastal summer open-water (OW)) and three additional indicators (continentality, summer precipitation, and the Arctic Dipole (AD): second mode of sea level pressure variability) are analyzed with maximum annual Normalized Difference Vegetation Index (MaxNDVI) and the sum of summer bi-weekly (time-integrated) NDVI (TI-NDVI) from the Advanced Very High Resolution Radiometer time-series. Climatological mean, trends, and correlations between variables are presented. Changes in SI continue to drive variations in the other indicators. As spring SI has decreased, summer OW, summer warmth, MaxNDVI, and TI-NDVI have increased. However, the initial very strong upward trends in previous studies for MaxNDVI and TI-NDVI are weakening and becoming spatially and temporally more variable as the ice retreats from the coastal areas. TI-NDVI has declined over the last decade particularly over High Arctic regions and southwest Alaska. The continentality index (CI) (maximum minus minimum monthly temperatures) is decreasing across the tundra, more so over North America than Eurasia. The relationship has weakened between SI and SWI and TI-NDVI, as the maritime influence of OW has increased along with total precipitation. The winter AD is correlated in Eurasia with spring SI, summer OW, MaxNDVI, TI-NDVI, the CI and total summer precipitation. This winter connection to tundra emphasizes the role of SI in driving the summer indicators. The winter (DJF) AD drives SI variations which in turn shape summer OW, the atmospheric SWI and NDVI anomalies. The winter and spring indicators represent potential predictors of tundra vegetation productivity a season or two in advance of the growing season.

Uma S. Bhatt↗
NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗