Results for “Time-integration” — Page 8

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↗

NASA NTRSDate not supplied

On the Integration of Loudness Over Time for the Prediction of Single-Event Annoyance

Loudness is the quality of human perception that is most related to acoustic intensity and energy, however there is no agreed-upon way of integrating loudness over time for the prediction of noise-induced annoyance. Most noise metrics used today for aircraft certification and regulation employ the “Equal-Energy Hypothesis” (EEH) and sum the acoustical energy of one or more noise events over time to create a single metric value that represents the entire exposure. Using the EEH creates a natural tradeoff between the peak energy and the duration of a single noise event, the “hypothesis” being that this tradeoff optimally predicts annoyance in a wide variety of situations. This work proposes a strategy for integrating a loudness-like time series which is flexible in two ways: First, it includes a parameter b ∈ [0,1]. When b = 0, the metric will return the peak of the time series. At b = .5, the metric will behave in accordance with the EEH. At b = 1, the metric will penalize the duration of the sound more than the EEH would. Second, transformations are given so that the strategy can be computed from, or generate quantities in units analogous to, decibels (or phon), physical units (acoustic pressure/power), or perceptually-scaled units (sone). This approach is demonstrated on a dataset of annoyance responses to single events of UAV and road vehicle noise that is fit with an augmented linear regression. Analyses based on this integration of A-weighted level and the output of the “Zwicker” loudness model yield similar results: that subjects may have been slightly more sensitive to the durations of the events than the EEH would suppose, but that the EEH cannot be disproven using these data. The time-integrated metrics outperform both time-averaged and centile-based metrics.

Psychoacoustics↗

NASA NTRSDate not supplied

Wall-Modeled Large Eddy Simulations of Transonic Buffet Over a Supercritical Airfoil

A series of scale-resolving simulations of flow over the ONERA OAT15A airfoil have been performed at an angle of attack of 3.5◦, just past the onset of buffet. The focus of this study is to document the sensitivity of the wall-modeled large eddy simulation (WMLES) methodology for curvilinear structured overset grids within the Launch, Ascent, and Vehicle Aerodynamics (LAVA) framework to mesh spacing, mesh distribution, and domain size. A secondary purpose of the study is to compare the results from WMLES to unsteady Reynolds-averaged Navier Stokes (URANS) simulations and hybrid RANS-LES (HRLES) within the same LAVA solver framework. The study provides a unique perspective regarding comparisons between different turbulence modeling approaches, time-integration methods, and computational performance since many of the same numerical routines are used for all three types of simulations. The results are compared with experiments and previous numerical studies of the same geometry and flow conditions.

TTT↗

NASA NTRSDate not supplied

On the Integration of Loudness Over Time for the Prediction of Single-Event Annoyance

Loudness is the quality of human perception that is most related to acoustic intensity and energy, however there is no agreed-upon way of integrating loudness over time for the prediction of noise-induced annoyance. Most noise metrics used today for aircraft certification and regulation employ the “Equal-Energy Hypothesis” (EEH) and sum the acoustical energy of one or more noise events over time to create a single metric value that represents the entire exposure. Using the EEH creates a natural tradeoff between the peak energy and the duration of a single noise event, the “hypothesis” being that this tradeoff optimally predicts annoyance in a wide variety of situations. This work proposes a strategy for integrating a loudness-like time series which is flexible in two ways: First, it includes a parameter b ∈ [0,1]. When b = 0, the metric will return the peak of the time series. At b = .5, the metric will behave in accordance with the EEH. At b = 1, the metric will penalize the duration of the sound more than the EEH would. Second, transformations are given so that the strategy can be computed from, or generate quantities in units analogous to, decibels (or phon), physical units (acoustic pressure/power), or perceptually-scaled units (sone). This approach is demonstrated on a dataset of annoyance responses to single events of UAV and road vehicle noise that is fit with an augmented linear regression. Analyses based on this integration of A-weighted level and the output of the “Zwicker” loudness model yield similar results: that subjects may have been slightly more sensitive to the durations of the events than the EEH would suppose, but that the EEH cannot be disproven using these data. The time-integrated metrics outperform both time-averaged and centile-based metrics.

Psychoacoustics↗

NASA NTRS2024

Discounting Water for Optimal Carbon Gain as a Basis of Stomatal Closure

The exchange of carbon dioxide and water vapor between terrestrial ecosystems and the atmosphere is regulated by stomata (small pores in the leaves of plants). Unsurprisingly, environmental factors controlling the opening and closure of stomata has been sought as early as 1800. One approach, popularized in the early 1970s, is a stomatal optimization framework. This framework is based on the hypothesis that plants optimize carbon gain subject to water loss or water availability constraints. This constraint optimization problem was solved in various forms assuming instantaneous adjustments of stomatal aperture to maximize a reward function with no future foresight or legacy effects. Holtzman et al. (2024, https://doi.org/10.1029/2023av001113) offers a novel approach that can diagnose the effective timescale over which the reward function maximization must be time-integrated. The developed method thus optimizes an integrated carbon gain function but adjusted by a discount factor subject to water availability in the root zone. The discount factor considers how the plant values carbon gain to save water and its timescale can be inferred from observations because the model is analytically tractable. The results suggest that the most important climate factor that determines this discount timescale is multi-annual mean of the longest dry period during the growing season. The findings highlight how local climate traits influence the spatial variation in ecosystem-level water use strategies. This sets the stage for expanding such a framework to cases where multiple constraints act in concert while operating at distinct time scales.

stomata↗