Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Point Kinetics Equations”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

136 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Simulations of classical three-body thermalization in one dimension

One-dimensional systems, such as nanowires or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of pointlike particles, typically the dominant process for reaching thermal equilibrium in higher-dimensional systems, cannot thermalize a 1D system. We study how dilute classical 1D gases thermalize through three-body collisions. We consider a system of identical classical point particles with pairwise repulsive inverse power-law potential V ij ∝ 1/|x i –x j | n or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute a collision kernel and use it in the Boltzmann equation to evolve a perturbed thermal state with temperature T toward equilibrium. We explain the shape of the kernel and its dependence on the system parameters. Additionally, we implement molecular dynamics simulations of a many-body gas and show agreement with the Boltzmann evolution in the low-density limit. For the inverse power-law potential, the rate of thermalization is proportional to ρ 2 ⁢T$\frac{1}{2}$ – $\frac{1}{n}$, where ρ is the number density. Furthermore, the corresponding proportionality constant decreases with increasing n.

1-dimensional systems↗
NASA NTRS1989

On the Nature of Navier-stokes Turbulence

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, largest Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The solutions, separate exponentially with time, having a positive Liapunov exponent. Thus the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number is reduced. Several qualitatively different flows are noted. These are, fully chaotic, complex period, weakly chaotic, simple periodic, and fixed-point. Of these, only the fully chaotic flows are classified as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, is both time-dependent and aperiodic. Turbulent solutions are obtained in which energy cascades from large to small-scale motions. In general, the spectral energy transfer takes place between wavenumber bands that are considerably separated. The special transfer can occur either as a result of nonlinear turbulence self-interaction or by interaction of turbulence with mean gradients. Turbulent systems are compared with those studied in kinetic theory. The two types of systems are fundamentally different (continuous and dissipative as opposed to discrete and conservative), but there are similarities. For instance, both are nonlinear and show sensitive dependence on initial conditions. Also, the turbulent and molecular stress tensors are identical if the macroscopic velocities for the turbulent stress are replaced by molecular velocities.

Deissler, Robert G.↗
DOE OSTI2024

Data‐driven variational method for discrepancy modeling: Dynamics with small‐strain nonlinear elasticity and viscoelasticity

Abstract The effective inclusion of a priori knowledge when embedding known data in physics‐based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics‐constrained data‐driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first‐principles theory and sensor‐based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy‐informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data‐embedding term serves as residual‐based least‐squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here.

Masud, Arif↗
NASA NTRS2023

The Gamma-Ray Pulsar Phenomenology in View of 3D Kinetic Global Magnetosphere Models

We develop kinetic plasma models of pulsar magnetospheres with magnetic-field-line-dependent plasma injection that reveal the importance of various magnetosphere regions in regulating the gamma-ray emission. We set different particle injection rates for the so-called open, closed, and separatrix zones. Moderate particle injection rates in open and closed zones ensure a global field structure close to the force-free one, while the dissipation occurs mainly in and around the equatorial current sheet. The particles injected in the separatrix zone affect the particle populations that enter the equatorial current sheet region and, therefore, the corresponding accelerating electric fields, particle energies, the spectral cutoff energy, and gamma-ray efficiency. The separatrix zone models reproduce the recently discovered fundamental plane of gamma-ray pulsars consistent with curvature radiation emission, the gamma-ray light-curve shapes, and the radio-lag vs. peak-separation correlation reported in the Fermi second pulsar catalog. The model beaming factors indicate that the pulsar total gamma-ray luminosities listed in the Fermi catalogs are overestimations of the actual ones. We find that the radiation reaction limited regime starts ceasing to govern the high-energy emission for spin-down powers less than 1034 erg/s. Our results also indicate that toward high magnetic inclination angles, the "Y point" around the rotational equator migrates well inside the light cylinder sparking additional peaks in the gamma-ray pulse profiles. We find that an equivalent enhanced particle injection beyond the Y point strengthens these features making the model gamma-ray light curves inconsistent with those observed.

Neutron stars↗
NASA NTRS2013

Propellant-Flow-Actuated Rocket Engine Igniter

A rocket engine igniter has been created that uses a pneumatically driven hammer that, by specialized geometry, is induced into an oscillatory state that can be used to either repeatedly impact a piezoelectric crystal with sufficient force to generate a spark capable of initiating combustion, or can be used with any other system capable of generating a spark from direct oscillatory motion. This innovation uses the energy of flowing gaseous propellant, which by means of pressure differentials and kinetic motion, causes a hammer object to oscillate. The concept works by mass flows being induced through orifices on both sides of a cylindrical tube with one or more vent paths. As the mass flow enters the chamber, the pressure differential is caused because the hammer object is supplied with flow on one side and the other side is opened with access to the vent path. The object then crosses the vent opening and begins to slow because the pressure differential across the ball reverses due to the geometry in the tube. Eventually, the object stops because of the increasing pressure differential on the object until all of the kinetic energy has been transferred to the gas via compression. This is the point where the object reverses direction because of the pressure differential. This behavior excites a piezoelectric crystal via direct impact from the hammer object. The hammer strikes a piezoelectric crystal, then reverses direction, and the resultant high voltage created from the crystal is transferred via an electrode to a spark gap in the ignition zone, thereby providing a spark to ignite the engine. Magnets, or other retention methods, might be employed to favorably position the hammer object prior to start, but are not necessary to maintain the oscillatory behavior. Various manifestations of the igniter have been developed and tested to improve device efficiency, and some improved designs are capable of operation at gas flow rates of a fraction of a gram per second (0.001 lb/s) and pressure drops on the order of 30 to 50 kilopascal (a few psi). An analytical model has been created and tested in conjunction with a precisely calibrated reference model. The analytical model accurately captures the overall behavior of this innovation. The model is a simple "volume-orifice" concept, with each chamber considered a single temperature and pressure "node" connected to adjacent nodes, or to vent paths through flow control orifices. Mass and energy balances are applied to each node, with gas flow predicted using simple compressible flow equations.

Wollen, Mark↗
NASA NTRS1995

Modeling and simulation of a turbulent far wake

Work continued on two projects which had been started during previous years. Both projects involve calculations of the subsonic, turbulent far wake of a two-dimensional object at a Reynolds number of 1000 (based on wake momentum thickness). This flow was used as a test case for direct comparison of various turbulence models and a direct numerical simulations (DNS) of this flow were undertaken. In the turbulence model comparison studies, for any particular model tested, a unique self-similar solution was obtained far enough downstream, regardless of inlet conditions. Furthermore, different turbulence models led to different far-wake equilibrium solutions. No turbulence model could correctly predict all features of the turbulent far wake. For example, the spreading rate and turbulent shear stresses were underpredicted by all the standard models (both two-equation and full Reynolds stress models). In cases where a more correct spreading rate was achieved, it was at the expense of the turbulent kinetic energy, which was overpredicted. In general, the Algebraic Dissipation Rate Model of Gatski and Speziale, 1992, when added to any of the standard models, improved the results dramatically. Also, full Reynolds stress closure models did a much better job at predicting the shapes of both the mean and turbulence profiles, but the spreading rate was not significantly improved over that predicted by the simpler two-equation models. There are two main conclusions from these studies: First, in a comparison such as this, it is not enough to compare just one parameter, like the spreading rate. A good prediction for one parameter does not necessarily imply good predictions for all parameters in a flow. Second, since no turbulence model could correctly predict the turbulent far wake, much of the important physics of turbulent free shear flows is apparently lost by the assumptions inherent in today's methods of turbulence modeling; turbulence models must be improved. Direct simulations of this flow were begun last year in order to provide a data base through which some of the deficiencies of the existing turbulence models could be identified. Quantities such as the pressure-strain correlation, turbulent diffusion, and the dissipation rate tensor can be easily calculated from the DNS results, whereas these quantities are nearly impossible to measure experimentally. Improvements to existing turbulence models (and development of new models) require knowledge about flow quantities such as these. During this summer, diagnostics codes were written which will calculate the parameters mentioned above, along with other single-point and multi-point statistics. The DNS calculations are still in progress at the time of this writing. When these calculations are complete, the diagnostics codes will be applied so that the results can aid turbulence modelers. In addition, the results will show whether or not there exists a universal equilibrium turbulent far wake, independent of initial conditions.

Cimbala, John M.↗
DOE OSTI2024

Theoretical modeling of hepatitis C acute infection in liver-humanized mice support pre-clinical assessment of candidate viruses for controlled-human-infection studies

Designing and carrying out a controlled human infection (CHI) model for hepatitis C virus (HCV) is critical for vaccine development. However, key considerations for a CHI model protocol include understanding of the earliest viral-host kinetic events during the acute phase and susceptibility of the viral isolate under consideration for use in the CHI model to antiviral treatment before any infections in human volunteers can take place. Humanized mouse models lack adaptive immune responses but provide a unique opportunity to obtain quantitative understanding of early HCV kinetics and develop mathematical models to further understand viral and innate immune response dynamics during acute HCV infection. We show that the models reproduce the measured HCV kinetics in humanized mice, which are consistent with early acute HCV-host dynamics in immunocompetent chimpanzees. Our findings suggest that humanized mice are well-suited to support development of a CHI model. In-silico and in-vivo modeling estimates provide a starting point to characterize candidate viruses for testing in CHI model studies.

Agent-based modeling↗
NASA NTRS2014

Comparitive Study of High-Order Positivity-Preserving WENO Schemes

In gas dynamics and magnetohydrodynamics flows, physically, the density ρ and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order Weighted Essentially Non-Oscillatory (WENO) schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative ρ may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more di cult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium ow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case as well as for the case consisting of two species and one reaction.. This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

Schemes↗
DOE OSTI2025

Complex Dependence of Calcite Crack Kinetics on Salinity: The Role of DLVO and Hydration Forces

Abstract Subcritical crack growth (SCG) plays an important role in many geological processes such as delayed earth rupture and rock weathering. The complex dependency of SCG on the in‐crack fluid chemistry, however, is still poorly understood. In this study, we utilize the newly developed surface force‐based fracture theory (SFFT) to elucidate the relative contributions of surface forces and solute transport to the crack growth kinetics of calcite in NaCl solutions. Expanding on Barenblatt's cohesive crack model, SFFT introduces an effective stress intensity at the crack tip that encompasses all the relevant intermolecular forces across the crack in addition to the external far‐field stresses. The nonlinear system of equations portraying the crack opening profile, the solute distribution in a propagating crack, and the crack growth velocity are numerically solved via an implicit scheme. After carefully calibrating the model for calcite‐water systems, the SFFT is used to predict the SCG response of calcite at different NaCl concentrations, based on various hypotheses. These predictions are then compared to existing SCG data from the literature. We demonstrate that the experimentally observed variation of SCG rate with NaCl concentration cannot be explained solely by DLVO forces (electrostatic and Van der Waals interactions). This can be remediated by introducing an exponentially decaying hydration force with a nonlinear, nonmonotonic dependence on NaCl concentration. Furthermore, we demonstrate that accounting for both diffusive and advective transport of ions is important in explaining the absence of a stage‐II SCG response for calcite in electrolyte solutions. Plain Language Summary Subcritical crack growth (SCG) refers to the slow propagation of cracks in materials under a stress below the threshold for catastrophic failure. SCG is a key process in many geological events, for example, delayed earth ruptures and rock weathering. New initiatives such as underground CO 2 and H 2 storage in carbonate reservoirs further call for better understanding of SCG in carbonate minerals subjected to varying fluid chemistry. This study examines the SCG of calcite, a key mineral found in carbonate rocks, intergranular cement in sandstones, and filling material in mineral veins and faults, determining their deformation and strength. A mathematical model is developed to describe how the crack opens and propagates, how solutes (like salts) distribute within the crack, and how the crack surfaces interact with each other. We used the model to predict calcite SCG in water at different salt concentrations and compared it with experimental data. Our results revealed that the hydration force is the dominating factor in determining the complex, non‐linear dependency of SCG on salinity. We also found that both the movement of ions by diffusion and by bulk water flow are crucial for explaining the SCG rates, especially when the cracks grow quickly. Key Points Surface Force‐Based Fracture Theory predicts the complex subcritical crack growth patterns of calcite crystals immersed in NaCl solutions Results highlight the dominant role of hydration forces in altering the fracture behavior of calcite compared to VdW and electric double‐layer forces Advective solute transport explains the absence of stages‐II and ‐III subcritical crack growth responses in solid‐liquid systems

DLVO↗
NASA NTRS2013

Comparative Study on High-Order Positivity-preserving WENO Schemes

In gas dynamics and magnetohydrodynamics flows, physically, the density and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order WENO schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more difficult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium flow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case (LeVeque & Yee 1990) as well as for the case consisting of two species and one reaction (Wang et al. 2012). For further information concerning this issue see (LeVeque & Yee 1990; Griffiths et al. 1992; Lafon & Yee 1996; Yee et al. 2012). This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

WENO↗