Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “diffusion equation”

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.

At least 1,657 records · Page 92

Investigation of inter-subject variation in ultrafine particle deposition across human nasal airways: A study involving children, adults, and the elderly

Occupational and environmental exposure to toxic nanoparticles, driven by the rapid expansion of nanotechnology, raises significant respiratory health concern. Numerous studies have explored airflow and particle dynamics in adult nasal airways, but understanding the impact of age-related anatomical changes in children and the elderly remains limited. This study systematically investigates age-related anatomical variations and associated influence on nasal airflow dynamics and ultrafine particle deposition characteristics. Using Computational Fluid-Particle Dynamics (CFPD) method, simulation was conducted under diverse inhalation conditions spanning a wide age range, including: two children (5 years old), two young adults (in their twenties), and two elderly (over 77 years old). Our results reveal distinctive variations across age groups in anatomical dimensions, which affect distribution of wall shear stress where the elderly and children display unique patterns distinct from the young adults. While total deposition efficiency differs significantly between children and adults, filtration efficiency in the subregion with most deposition, main respiratory, remains consistent. However, inter-subject differences are observed in the vestibular and olfactory regions,emphasizing nuanced impact of age-related anatomical variations. Overall and subregional empirical equations for deposition efficiency were developed by incorporating the combined diffusion parameter, Sc a Δ b , corroborating the use of geometrical characteristic parameters for each specific subject in predicting nasal deposition efficiency across age groups. Our findings contribute to predictive nanoparticle exposure analysis in nasal airways across different age groups, thereby enhancing respiratory healthcare for individuals across the life span.

60 APPLIED LIFE SCIENCES↗

Simulation and flow physics of a shocked and reshocked high-energy-density mixing layer

This work describes a computational investigation of multimode instability growth and multimaterial mixing induced by multiple shock waves in a high-energy-density (HED) environment, where pressures exceed 1 Mbar. The simulations are based on a series of experiments performed at the National Ignition Facility (NIF) and designed as an HED analogue of non-HED shock-tube studies of the Richtmyer–Meshkov instability and turbulent mixing. A three-dimensional computational modelling framework is presented. It treats many complications absent from canonical non-HED shock-tube flows, including distinct ion and free-electron internal energies, non-ideal equations of state, radiation transport and plasma-state mass diffusivities, viscosities and thermal conductivities. The simulations are tuned to the available NIF data, and traditional statistical quantities of turbulence are analysed. Integrated measures of turbulent kinetic energy and enstrophy both increase by over an order of magnitude due to reshock. Large contributions to enstrophy production during reshock are seen from both the baroclinic source and enstrophy–dilatation terms, highlighting the significance of fluid compressibility in the HED regime. Dimensional analysis reveals that Reynolds numbers and diffusive Péclet numbers in the HED flow are similar to those in a canonical non-HED analogue, but conductive Péclet numbers are much smaller in the HED flow due to efficient thermal conduction by free electrons. It is shown that the mechanism of electron thermal conduction significantly softens local spanwise gradients of both temperature and density, which causes a minor but non-negligible decrease in enstrophy production and small-scale mixing relative to a flow without this mechanism.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Vibrational hierarchy leads to dual-phonon transport in low thermal conductivity crystals

Many low-thermal-conductivity ( κ L ) crystals show intriguing temperature ( T ) dependence of κ L : κ L ∝ T -1 (crystal-like) at intermediate temperatures whereas weak T -dependence (glass-like) at high temperatures. It has been in debate whether thermal transport can still be described by phonons at the Ioffe-Regel limit. In this work, we propose that most phonons are still well defined for thermal transport, whereas they carry heat via dual channels: normal phonons described by the Boltzmann transport equation theory, and diffuson-like phonons described by the diffusion theory. Three physics-based criteria are incorporated into first-principles calculations to judge mode-by-mode between the two phonon channels. Case studies on La 2 Zr 2 O 7 and Tl 3 VSe 4 show that normal phonons dominate low temperatures while diffuson-like phonons dominate high temperatures. Our present dual-phonon theory enlightens the physics of hierarchical phonon transport as approaching the Ioffe-Regel limit and provides a numerical method that should be practically applicable to many materials with vibrational hierarchy.

42 ENGINEERING↗

A coarse-graining approach for molecular simulation that retains the dynamics of the all-atom reference system by implementing hydrodynamic interactions

We report on a new approach for deriving coarse-grained intermolecular forces that retains the frictional contribution that is often discarded by conventional coarse-graining methods. The approach is tested for water and an aqueous glucose solution, and the results from the new implementation for coarse-grained molecular dynamics simulation show remarkable agreement with the dynamics obtained from reference all-atom simulations. The agreement between the structural properties observed in the coarse-grained and all-atom simulations is also preserved. We discuss how this approach may be applied broadly to any existing coarse-graining method where the coarse-grained models are rigorously derived from all-atom reference systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of outer-cylinder rotation on the radially heated Taylor–Couette flow

A Taylor–Couette setup with radial heating is considered where a Boussinesq fluid is sheared in the annular region between two concentric, independently rotating cylinders maintained at different temperatures. Linear stability analysis is performed to determine the Taylor number for the onset of instability. Two radius ratios corresponding to wide and thin gaps with several rotation rate ratios are considered. The rotation of the outer cylinder is found to have a general stabilizing effect on the stability threshold as compared to pure inner-cylinder rotation, with a few exceptions. The radial heating sets up an axial flow which breaks the reflection symmetry of isothermal Taylor–Couette flow in the axial coordinate. This symmetry breaking separates linear stability thresholds, and we find the fastest growing modes with both positive and negative azimuthal numbers for different parameters. Another important finding of the current study is the discovery of unstable modes in the Rayleigh-stable regime. Furthermore, closed disconnected neutral curves (CDNCs) are observed for both wide and thin gaps which can separate from or merge into open neutral–stability curves. Alternatively, CDNCs can also morph into open neutral stability curves as the rotation rate ratio is changed. CDNCs are observed to be sensitive to changes in control parameters, and their appearance/disappearance is shown to induce discontinuous jumps in the critical Taylor number. Finally, for both wide and thin gaps, the fastest-growing modes found in the pure corotation case are shown to have their origins in the instability islands at smaller values of rotation rate ratios.

97 MATHEMATICS AND COMPUTING↗

Theory and modeling of molecular modes in the NMR relaxation of fluids

Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. Here, we recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker–Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole–dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé–Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The advancing wave front on a sloping channel covered by a rod canopy following an instantaneous dam break

The drag coefficient Cd for a rigid and uniformly distributed rod canopy covering a sloping channel following the instantaneous collapse of a dam was examined using flume experiments. The measurements included space x and time t high resolution images of the water surface h(x, t) for multiple channel bed slopes So and water depths behind the dam Ho along with drag estimates provided by sequential load cells. Using these data, an analysis of the Saint-Venant equation (SVE) for the front speed was conducted using the diffusive wave approximation. An inferred Cd=0.4 from the h(x, t) data near the advancing front region, also confirmed by load cell measurements, is much reduced relative to its independently measured steady-uniform flow case. This finding suggests that drag reduction mechanisms associated with transients and flow disturbances are more likely to play a dominant role when compared to conventional sheltering or blocking effects on Cd examined in uniform flow. The increased air volume entrained into the advancing wave front region as determined from an inflow–outflow volume balance partly explains the Cd reduction from unity.

Mechanics↗

Quantum Monte Carlo calculations of neutron matter with chiral three-body forces

Chiral effective field theory (EFT) enables a systematic description of low-energy hadronic interactions with controlled theoretical uncertainties. For strongly interacting systems, quantum Monte Carlo (QMC) methods provide some of the most accurate solutions, but they require as input local potentials. We have recently constructed local chiral nucleon-nucleon (NN) interactions up to next-to-next-to-leading order (N 2 LO). Chiral EFT naturally predicts consistent many-body forces. In this paper, we consider the leading chiral three-nucleon (3N) interactions in local form. These are included in auxiliary field diffusion Monte Carlo (AFDMC) simulations. We present results for the equation of state of neutron matter and for the energies and radii of neutron drops. Specifically, we study the regulator dependence at the Hartree-Fock level and in AFDMC and find that present local regulators lead to less repulsion from 3N forces compared to the usual nonlocal regulators.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Kinetics of the Formation of a Disordered Crystal Structure during High-Speed Solidification

A phase–field description is given for the kinetic transition in the structure of a binary ordering crystal growing from a supercooled liquid. The results are interpreted on the basis of the solution of the phasefield dynamics equation and the relaxation equation for the long-range order parameter at the diffuse crystal–liquid interface and in the bulk of the crystal. The critical temperatures for the variation of the growth rate and the long-range order parameter of a growing A{sub 50}B{sub 50} crystal are determined. A qualitative difference and analogies are found between the processes of nonequilibrium impurity trapping and the formation of a disordered structure of rapidly growing crystals. The results of the study are analyzed in comparison with the results of the theory of kinetic phase transitions [A.A. Chernov, Sov. Phys. JETP 26, 1182 (1967)] and the experimental data on the high-speed solidification of congruently melting samples [H. Hartmann et al., Europhys. Lett. 87, 40007 (2009)].

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Mechanism of Influence of Disperse Nanoparticles on Parameters of the Martensitic Transitions in Alloys with the Shape Memory Effect

Within the diffuse martensitic transition theory based on the thermodynamic and kinetic equations and relations, the mechanism of influence of disperse nanoparticles on the parameters of martensitic transitions in alloys with the shape memory effect (SME) is analyzed. The objects of the analysis are the TiNi alloy with the varied sizes of Ti{sub 3}Ni{sub 4} particle at their constant volume concentration, and the NiMnGaTb alloy with Tb precipitate particles with constant sizes and variation of volume concentration of the precipitates. Information about these alloys is available in the literature. The analysis has shown that, due to the coherent coupling of the Ti{sub 3}Ni{sub 4} particles with the substrate, the temperature width of the transition R–B19' depends on the particle sizes, which confirms the earlier established regularity of the local interior strain influence on this parameter. Concerning the NiMnGaTb alloy, the analysis has shown that, due to the presence of interior local strains associated with the Tb particles, the temperature width of the martensitic transformations increases linearly alongside the growth of the particle concentration in the alloy. The existence of the critical value of the particle concentration, above which the temperature width of the transition becomes indefinitely large, and the martensitic transformation in the alloy is blocked, is shown.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Mathematical simulation of heat and mass transfer in a cylindrical channel versus the tangential momentum accommodation coefficient

The process of heat and mass transfer in a long cylindrical channel has been considered in terms of the mirror–diffuse model of the Maxwell boundary condition. The Hazen–Williams equation is used as a basic equation of the process kinetics. A constant temperature gradient is maintained in the channel. The heat and mass fluxes through the cross section of the channel versus the tangential momentum accommodation coefficient have been calculated in a wide range of the Knudsen number. The heat flux profiles have been constructed. A comparison with relevant published data has been carried out.

42 ENGINEERING↗

Elastic Flow Modeling for Hydropower Digital Twins

This report details the elastic, unsteady, one-dimensional flow equations that are used to model flow through a penstock in a hydropower facility. The elastic flow model is accurate even in cases of fast transients, long penstock length, and high gravitation head. The compressibility of the water and elasticity of the pipe walls are explicitly accounted for in the developed models so that the water hammer phenomena can be accurately captured. The elastic flow model is coupled to a mechanistic turbine model to resolve the dynamic feedbacks between the elastic water column and the turbine rotation rate. A finite volume method is employed to solve the governing equations, and the method is shown to have low numerical diffusion in sharp gradient phenomena, such as those encountered when simulating water hammer. The method is applied to single dimensional linear advection benchmark problem and numerical results are compared with analytic results. This is followed on by an application to a full hydropower system with a coupled turbine. The elastic flow model results are compared against an inelastic model.

13 HYDRO ENERGY↗

Interior radiances in optically deep absorbing media. 3: Scattering from Haze L

The interior radiances are calculated within an optically deep absorbing medium scattering according to the Haze L phase function. The dependence on the solar zenith angle, the single scattering albedo, and the optical depth within the medium is calculated by the matrix operator method. The development of the asymptotic angular distribution of the radiance in the diffusion region is illustrated through a number of examples; it depends only on the single scattering albedo and on the phase function for single scattering. The exact values of the radiance in the diffusion region are compared with values calculated from the approximate equations proposed by Van de Hulst. The variation of the radiance near the lower boundary of an optically thick medium is illustrated with examples. The attenuation length is calculated for various single scattering albedos and compared with the corresponding values for Rayleigh scattering. The ratio of the upward to the downward flux is found to be remarkably constant within the medium. The heating rate is calculated and found to have a maximum value at an optical depth of two within a Haze L layer when the sun is at the zenith.

Kattawar, G. W.↗

Composition dependence of ion-transport coefficients in gas mixtures

Simple momentum-transfer theory for the composition dependence of ion mobilities and diffusion coefficients in gas mixtures at arbitrary field strengths is corrected and extended, and compared with a similar theory based on momentum and energy transfer, and with results based on direct solution of the Boltzmann equation by Kihara's method. Final equations are recommended for predicting composition dependences, given only results on ion mobilities and diffusion coefficients in the pure component gases.

Whealton, J. H.↗

Interior radiances in optically deep absorbing media. III Scattering from Haze L

The interior radiances are calculated within an optically deep absorbing medium scattering according to the Haze L phase function. The dependence on the solar zenith angle, the single scattering albedo, and the optical depth within the medium is calculated by the matrix operator method. The development of the asymptotic angular distribution of the radiance in the diffusion region is illustrated through a number of examples; it depends only on the single scattering albedo and on the phase function for single scattering. The exact values of the radiance in the diffusion region are compared with values calculated from the approximate equations proposed by Van de Hulst. The variation of the radiance near the lower boundary of an optically thick medium is illustrated with examples. The attenuation length is calculated for various single scattering albedos and compared with the corresponding values for Rayleigh scattering. The ratio of the upward to the downward flux is found to be remarkably constant within the medium.

Kattawar, G. W.↗

Turbulence in a gaseous hydrogen-liquid oxygen rocket combustion chamber

The intensity of turbulence and the Lagrangian correlation coefficient for a LOX-GH2 rocket combustion chamber was determined from experimental measurements of tracer gas diffusion. A combination of Taylor's turbulent diffusion theory and a numerical method for solving the conservation equations of fluid mechanics was used to calculate these quantities. Taylor's theory was extended to consider the inhomogeneity of the turbulence field in the axial direction of the combustion chamber, and an exponential function was used to represent the Lagrangian correlation coefficient. The results indicate that the value of the intensity of turbulence reaches a maximum of 14% at a location about 7" downstream from the injector. The Lagrangian correlation coefficient associated with this value is given by the above exponential expression where alpha = 10,000/sec.

Lebas, J.↗

Non-equilibrium radiation from viscous chemically reacting two-phase exhaust plumes

A knowledge of the structure of the rocket exhaust plumes is necessary to solve problems involving plume signatures, base heating, plume/surface interactions, etc. An algorithm is presented which treats the viscous flow of multiphase chemically reacting fluids in a two-dimensional or axisymmetric supersonic flow field. The gas-particle flow solution is fully coupled with the chemical kinetics calculated using an implicit scheme to calculate chemical production rates. Viscous effects include chemical species diffusion with the viscosity coefficient calculated using a two-equation turbulent kinetic energy model.

Penny, M. M.↗