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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 415 records · Page 23

On the synthesis of resonance lines in dynamical models of structured hot-star winds

We examine basic issues involved in synthesizing resonance-line profiles from 1-D, dynamical models of highly structured hot-star winds. Although these models exhibit extensive variations in density as well as velocity, the density scale length is still typically much greater than the Sobolev length. The line transfer is thus treated using a Sobolev approach, as generalized by Rybicki & Hummer (1978) to take proper account of the multiple Sobolev resonances arising from the nonmonotonic velocity field. The resulting reduced-lambda-matrix equation describing nonlocal coupling of the source function is solved by iteration, and line profiles are then derived from formal solution integration using this source function. Two more approximate methods that instead use either a stationary or a structured, local source function yield qualitatively similar line-profiles, but are found to violate photon conservation by 10% or more. The full results suggest that such models may indeed be able to reproduce naturally some of the qualitative properties long noted in observed UV line profiles, such as discrete absorption components in unsaturated lines, or the blue-edge variability in saturated lines. However, these particular models do not yet produce the black absorption troughs commonly observed in saturated lines, and it seems that this and other important discrepancies (e.g., in acceleration time scale of absorption components) may require development of more complete models that include rotation and other 2-D and/or 3-D effects.

Puls, J.↗

Mass loss at discrete velocities in Be stars: Evidence for non-radiatively driven wind

The temporal behavior of the high velocity, relatively narrow absorption components in C IV, Si III, IV observed in the pole-one Be stars psi Ori, 66 Oph, and HR 4009 and what these observations contribute toward our understanding of the Be phenomenon are discussed. Ground based and X-ray data on these stars are compared as well as their UV differences with similarly active Be stars with larger projected rotational velocities.

Peters, G. P.↗

On spectroscopy for a whole Abelian model

Postulated on the whole meaning a whole abelian gauge symmetry is being introduced. Various physical areas as complexity, statistical mechanics, quantum mechanics are partially supporting this approach where the whole is at origin. However, the reductionist crisis given by quark confinement definitely sustains this insight. It says that fundamental parts can not be seen isolatedely. Consequently, there is an experimental situation where the parts should be substituted by something more. This makes us to look for writing the wholeness principle under gauge theory. For this, one reinterprets the gauge parameter where instead of compensating fields it is organizing a systemic gauge symmetry. Now, it introduces a fields set {l_brace}A{sub {mu}I}{r_brace} rotating under a common gauge symmetry. Thus, given a fields collection {l_brace}A{sub {mu}I}{r_brace} as origin, the effort at this work is to investigate on its spectroscopy. Analyze for the abelian case the correspondent involved quanta. Understand that for a whole model diversity replaces elementarity. Derive the associated quantum numbers as spin, mass, charge, discrete symmetries in terms of such systemic symmetry. Observe how the particles diversity is manifested in terms of wholeness.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Comparison of broadband noise mechanisms, analyses, and experiments on helicopters, propellers, and wind turbines

Experimental data on broadband noise from airfoils are compared, together with analytical methods, in order to identify the mechanisms of noise emission. Rotor noise is categorized into discrete frequency, impulsive, and broadband components, the last having a continuous spectrum originating from a random source. The results of computer simulations of different rotor blade types which produce broadband noise were compared with experimental data and among themselves in terms of predictions of the spectra obtained. Consideration was given to the overall sound pressure level, unsteady turbulence forces, rotational forces, inflow turbulence, self-generated turbulence, and turbulence in the flow. Data are presented for a helicopter rotor and light aircraft propeller. The most significant source was found to be inflow turbulence induced lift fluctuations in helicopter rotors and boundary layer trailing edge noise on large wind energy conversion systems

George, A. R.↗

Analysis of mixed-mode crack propagation using the boundary integral method

Crack propagation in a rotating inner raceway of a high speed roller bearing is analyzed using the boundary integral equation method. The method consists of an edge crack in a plate under tension, upon which varying Hertzian stress fields are superimposed. A computer program for the boundary integral equation method was written using quadratic elements to determine the stress and displacement fields for discrete roller positions. Mode I and Mode II stress intensity factors and crack extension forces G sub 00 (energy release rate due to tensile opening mode) and G sub r0 (energy release rate due to shear displacement mode) were computed. These calculations permit determination of that crack growth angle for which the change in the crack extension forces is maximum. The crack driving force was found to be the alternating mixed-mode loading that occurs with each passage of the most heavily loaded roller. The crack is predicted to propagate in a step-like fashion alternating between radial and inclined segments, and this pattern was observed experimentally. The maximum changes DeltaG sub 00 and DeltaG sub r0 of the crack extension forces are found to be good measures of the crack propagation rate and direction.

Mendelson, A.↗

MOOSE framework enhancements for meshing reactor geometries

MOOSE is an open-source, parallel finite element framework designed to permit rapid development of robust multi-physics modeling capabilities. Under the DOE-NEAMS program, numerous solvers have been developed utilizing the open-source MOOSE framework for multiphysics reactor analysis. These solvers require input finite element meshes representing the discretized geometry. Typically, reactor analysts turn to licensed external tools for creation of reactor geometry meshes. Recently, enhancements have been added to the MOOSE framework to mesh common reactor geometries and improve MOOSE-based application user workflows. Support for hexagonal pins, assemblies, and cores has been added, and Cartesian support has been extended. Options for modeling static and rotating control drums within a hexagonal assembly are now available. Pin, assembly, and plane regions can be identified through automatically applied tags on the mesh called 'reporting IDs' for easier post- processing of physics results. An external open-source triangle routine has been leveraged within MOOSE to mesh core periphery zones. A set of reactor geometry builder routines further streamline the construction of hexagonal and Cartesian cores and include the ability to assign materials to regions during mesh generation. The new meshing routines are available through the MOOSE framework in the open-source 'Reactor' module, and the resulting directly within MOOSE-based applications or exported as Exodus II files for use in other finite element solvers. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The IUE Mega Campaign. Modulated Structure in the Wind of HD 64760 (B0.5 Ib)

We highlight systematic variability in the stellar wind of the early B type supergiant, HD 64760, whose UV line profiles were monitored for almost 16 days in 1995 January as part of the IUE 'MEGA Campaign.' The extensive coverage reveals a pattern of rapidly evolving discrete optical depth changes which typically migrate from approx. - 200 km/s to approx. -1500 km/s in less than 12 hr. These features coexist with more slowly evolving structures lasting several days. Time-series analysis of the Si(IV), Si(III), and N(V) profile variations presents a clear 1.2 day periodicity, which is a quarter of the estimated maximum rotation period of HD 64760. The line profile changes are consistent with an interpretation in terms of a set of corotating wind features which occult the stellar disk at least 3 times during the observing run. These data are combined with UV observations collected in 1993 March to argue in favor of rotationally modulated wind variations in HD 64760. The basic result of very regular, large-scale optical depth variations points to a 'clock' whose origin is on the stellar surface, rather than a mechanism that is entirely intrinsic to the stellar wind.

Prinja, Raman K.↗

Exploring the energy landscape of RBMs: reciprocal space insights into bosons, hierarchical learning and symmetry breaking

Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that hinders the development of a unified theory of AI learning. In this work, we address two central challenges: clarifying the connections between different deep generative models and deepening our understanding of their learning mechanisms. We focus on Restricted Boltzmann Machines (RBMs), a class of generative models known for their universal approximation capabilities for discrete distributions. By introducing a reciprocal space formulation for RBMs, we reveal a connection between these models, diffusion processes, and systems of coupled bosons. Our analysis shows that at initialization, the RBM operates at a saddle point, where the local curvature is determined by the singular values of the weight matrix, whose distribution follows the Marc̆enko-Pastur law and exhibits rotational symmetry. During training, this rotational symmetry is broken due to hierarchical learning, where different degrees of freedom progressively capture features at multiple levels of abstraction. This leads to a symmetry breaking in the energy landscape, reminiscent of Landau’s theory. This symmetry breaking in the energy landscape is characterized by the singular values and the weight matrix eigenvector matrix. We derive the corresponding free energy in a mean-field approximation. We show that in the limit of infinite size RBM, the reciprocal variables are Gaussian distributed. Our findings indicate that in this regime, there will be some modes for which the diffusion process will not converge to the Boltzmann distribution. To illustrate our results, we trained replicas of RBMs with different hidden layer sizes using the MNIST dataset. Our findings not only bridge the gap between disparate generative frameworks but also shed light on the fundamental processes underpinning learning in deep generative models.

97 MATHEMATICS AND COMPUTING↗

Simulations of Sea-Ice Dynamics Using the Material-Point Method

In recent years, the availability of large volumes of recorded ice motion derived from high-resolution SAR data has provided an amazingly detailed look at the deformation of the ice cover. The deformation is dominated by the appearance of linear kinematic features that have been associated with the presence of leads. These remarkable data put us in a position to begin detailed evaluation of current coupled mechanical and thermodynamic models of sea ice. This presentation will describe the material point method (MPM) for solving these model equations. MPM is a numerical method for continuum mechanics that combines the best aspects of Lagrangian and Eulerian discretizations. The material points provide a Lagrangian description of the ice that models convection naturally. Thus, properties such as ice thickness and compactness are computed in a Lagrangian frame and do not suffer from errors associated with Eulerian advection schemes, such as artificial diffusion, dispersion, or oscillations near discontinuities. This desirable property is illustrated by solving transport of ice in uniform, rotational and convergent velocity fields. Moreover, the ice geometry is represented by unconnected material points rather than a grid. This representation facilitates modeling the large deformations observed in the Arctic, as well as localized deformation along leads, and admits a sharp representation of the ice edge. MPM also easily allows the use of any ice constitutive model. The versatility of MPM is demonstrated by using two constitutive models for simulations of wind-driven ice. The first model is a standard viscous-plastic model with two thickness categories. The MPM solution to the viscous-plastic model agrees with previously published results using finite elements. The second model is a new elastic-decohesive model that explicitly represents leads. The model includes a mechanism to initiate leads, and to predict their orientation and width. The elastic-decohesion model can provide similar overall deformation as the viscous-plastic model; however, explicit regions of opening and shear are predicted. Furthermore, the efficiency of MPM with the elastic-decohesive model is competitive with the current best methods for sea ice dynamics. Simulations will also be presented for an area of the Beaufort Sea, where predictions can be validated against satellite observations of the Arctic.

Sulsky, D.↗

The Center for Momentum Transport and Flow Organization in Plasmas - Final Scientific Report

Overview of University of Colorado Efforts: The University of Colorado group has focused on two primary fronts during the grant period: development of a variety of multi-point diagnostic and/or imaging analysis techniques, and momentum-transport related experiments on a variety of devices (NSTX at PPPL, CSDX at UCSD, LAPD at UCLA, DIII-D at GA). Experimental work has taken advantage of several diagnostic instruments, including fast-framing cameras for imaging of electron density fluctuations (either directly or using injected gas puffs), ECEI for imaging of electron temperature fluctuations, and multi-tipped Langmuir and magnetic probes for corroborating measurements of Reynolds and Maxwell stresses. Mode Characterization in CSDX: We have performed a series of experiments at the CSDX linear device at UCSD, in collaboration with Center PI G. Tynan's group. The experiments included a detailed study of velocity estimation techniques, including direct comparisons between Langmuir probes and image-based velocimetry from fast-framing camera data. We used the camera data in a second set of studies to identify the spatial and spectral structure of coherent modes, which illuminates wave behavior to a level of detail previously unavailable, and enables direct comparison of dispersion curves to theoretical estimates. In another CSDX study, similar techniques were used to demonstrate a controlled transition from nonlinearly coupled discrete eigenmodes to fully developed broadband turbulence. The axial magnetic field was varied from 40-240 mT, which drove the transition. At low magnetic fields, the plasma is dominated by drift waves. As the magnetic field is increased, a strong potential gradient at the edge introduces an ExB shear-driven instability. At the transition, another mode with signatures of a rotation-induced Rayleigh–Taylor instability appears at the central plasma region. Concurrently, large axial velocities were found in the plasma core. For larger magnetic fields, all of the instabilities co-exist, leading to rich plasma dynamics and fully developed broadband turbulence. Edge-Turbulence and Flow Experiments in NSTX: A series of Gas Puff Imaging (GPI) observations on NSTX revealed a quasi-periodic oscillation in the plasma edge preceding the L-H transition in a limited set of neutral beam heated plasmas. These ~3 kHz flow oscillations exhibit both long wavelength and long correlation lengths, suggesting they are zonal-flow-like. The flow oscillations are strongly correlated with modulations of the level of edge turbulence, thus the system appears to undergo a predator--prey-type limit-cycle preceding the L-H transition. However, a clear trigger for the L-H transition was not observed. Reynolds stress profiles were obtained directly from image velocimetry for L-mode periods ELM-Precursor Studies in NSTX: A separate study based on NSTX-GPI data captured the two-dimensional evolution of edge-localized mode (ELM) precursors. Precursor events were observed preceding ELMs and ELM-induced H–L back-transitions in radio-frequency heated H-mode plasmas, and the growth of the precursor mode through the ELM filamentation was imaged in the plane perpendicular to the local B-field. Strong edge intensity modulations appeared to propagate in the electron diamagnetic direction while steadily drifting radially outwards. Intensity fluctuations were observed at frequencies around 20 kHz and wavenumbers of 0.05-0.2 cm -1 . Upon growing to a trigger point, precursor fluctuations were seen to form filamentary structures and move into the scrape-off layer (SOL) explosively with radial velocities peaking at 8 km/s. Once in the SOL, filaments reverse their propagation direction and travel in the ion diamagnetic direction. Edge intensity fluctuations were strongly correlated with magnetic signals from Mirnov coils, and toroidally distributed coils estimated toroidal mode numbers of n=5-10. Quantitatively similar precursors have been observed in ohmic H-mode plasmas as well, though significantly fewer events are seen in the ohmic cases and none were observed in the near-threshold NBI H-modes studied. Development of Velocimetry and Image Analysis Techniques: Along with the experiments listed above, the Colorado group has continued to explore various velocimetry techniques and their range of validity. We have developed a “linear optical flow” code, which calculates smooth velocity maps while accurately assessing local regions of high curl. This is critical for separating spatial scales of velocity behavior, and thus transport. This code has recently come on-line, and we are currently using it to revisit a number of older datasets. Additionally, we have worked on developing pattern-recognition techniques for imaging diagnostics, based on established digital image compression algorithms. This has the potential to open the analysis of turbulent plasma behavior beyond the well-trodden Fourier and wavelet approaches. Finally, we have extended several of these image-analysis routines to multiple other diagnostic sets, including GPI datasets in NSTX and ECEI imaging on DIII-D. In one study, correlation maps were used to measure the full 2-D mode structure of drift-wave level structures using ECEI for the first time. This enabled direct comparison to gyrokinetic simulations using the GEM code, from which is was determined that TEM modes were being measured in DIII-D.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A finite-element perturbation approach to fluid/rotor interaction in turbomachinery elements. I - Theory. II - Application

The vibrational characteristics of a rotor that is in contact with a fluid in an annular clearance gap are investigated. The disturbance under consideration involves the axis of rotation, and includes a virtual lateral eccentricity, together with a whirling motion around the housing centerline. The fluid reaction components arise from infinitesimally small deformations with varied magnitudes which are experienced by an assembly of finite elements in the rotor-to-housing gap. A perturbation model is presented in which the perturbation equations emerge from the flow-governing equations in their discrete finite-element form. It is concluded that restrictions on the rotor-to-housing gap geometry, or the manner in which the rotor virtual eccentricity occurs are practically nonexisting. This model is used to compute the rotordynamic coefficients of an annular seal. The rotordynamic behavior of a hydraulic seal with a clearance gap depth/length ratio of 0.01 is analyzed under a cylindrical type of rotor whirl and several running speeds.

Baskharone, E. A.↗

Infrared Spectroscopy of Matrix-Isolated Polycyclic Aromatic Compounds and their Ions: Polycyclic Aromatic Nitrogen Heterocycles - 6

The matrix-isolation technique has been employed to measure the mid-infrared spectra of several polycyclic aromatic nitrogen heterocycles in both neutral and cationic forms. The species studied include: 7,8 benzoquinoline (C13H9N); 2-azapyrene (C15H9N); 1- and 2-azabenz(a)anthracene (C17H11N); and 1-, 2-, and 4-azachrysene (also C17H11N). The experimentally measured band frequencies and intensities for each molecule are tabulated and compared with their theoretically calculated values computed using density functional theory at the B3LYP/4-31G level. The overall agreement between experiment and theory is quite good, in keeping with previous investigations involving the parent aromatic hydrocarbons. Several interesting spectroscopic trends are found to accompany nitrogen substitution into the aromatic framework of these compounds. First, for the neutral species, the nitrogen atom produces a significant increase in the total integrated infrared intensity across the 1600 - 1100/cm region and plays an essential role in the molecular vibration that underlies an uncharacteristically intense, discrete feature that is observed near 1400/cm in the spectra of 7,8 benzoquinoline, 1-azabenz(a)anthracene, and 4-azachrysene. The origin of this enhanced infrared activity and the nature of the new 1400/cm vibrational mode are explored. Finally, in contrast to the parent hydrocarbon species, these aromatic nitrogen heterocycles possess a significant permanent dipole moment. Consequently, these dipole moments and the rotational constants are reported for these species in their neutral and ionized forms.

Mattioda, A. L.↗

Finite-Temperature Quantum Matter with Rydberg or Molecule Synthetic Dimensions

Synthetic-dimension platforms offer unique pathways for engineering quantum matter. We compute the phase diagram of a many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as a synthetic dimension, where the particles are arranged in real space in optical microtrap arrays and interact via dipole-dipole exchange interaction. Using mean-field theory, we find three ordered phases—two are localized in the synthetic dimension, predicted as zero-temperature ground states, and one is a delocalized phase. We characterize them by identifying the spontaneously broken discrete symmetries of the Hamiltonian. We also compute the phase diagram as a function of temperature and interaction strength for both signs of the interaction. For system sizes with more than six synthetic sites and attractive interactions, we find that the thermal phase transitions can be first or second order, which leads to a tricritical point on the phase boundary. Furthermore, by examining the dependence of the tricritical point and other special points of the phase boundary on the synthetic dimension size, we shed light on the physics for thermodynamically large synthetic dimension.

74 ATOMIC AND MOLECULAR PHYSICS↗

Hybrid state vector methods for structural dynamic and aeroelastic boundary value problems

A computational technique is developed that is suitable for performing preliminary design aeroelastic and structural dynamic analyses of large aspect ratio lifting surfaces. The method proves to be quite general and can be adapted to solving various two point boundary value problems. The solution method, which is applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. A mixed variational formulation is presented that conveniently yields a useful form for these state vector differential equations. Solutions to these equations are obtained by employing an integrating matrix method. The application of an integrating matrix provides a discretization of the differential equations that only requires solutions of standard linear matrix systems. It is demonstrated that matrix partitioning can be used to reduce the order of the required solutions. Results are presented for several example problems in structural dynamics and aeroelasticity to verify the technique and to demonstrate its use. These problems examine various types of loading and boundary conditions and include aeroelastic analyses of lifting surfaces constructed from anisotropic composite materials.

Lehman, L. L.↗

Utah FORGE: 2024 Discrete Fracture Network Model Data

The Utah FORGE 2024 Discrete Fracture Network (DFN) Model dataset provides a set of files representing discrete fracture network modeling for the FORGE site near Milford, Utah. The dataset includes four distinct DFN model file sets, each corresponding to different time frames and modeling approaches in 2024. These models characterize both natural and induced fractures in the geothermal reservoir, which consists of crystalline granitic and metamorphic rock approximately 8,000 feet below the ground surface. The dataset includes a reference DFN model from February 2024 that incorporates planar fractures and well trajectories, as well as upscaled permeability, porosity, compressibility, and storage values on specified grids. Additionally, there are models based on new microseismic (MEQ) data from May and July 2024, including fracture planes fitted to the latest MEQ catalog datasets, tensile fractures from hydraulic stimulation, and an alternative connected DFN for modeling purposes. Coordinate data is provided in both global and local frames, with detailed instructions on the transformations used to align with principal stress orientations. The dataset also includes notes and calculation files for estimating fracture sizes and differences between various fracture sets. There are subfolders for Global Coordinates and Local Coordinates. To move from the global to the local coordinate frame, fractures and wells were a) rotated 20 degrees counterclockwise looking down about the global point (335376.400482041, 4263189.99998761, 250.093546450195) to better align with the principal stresses; and b) translated by (-335408.68, -4263010.9, 1150). Upscaled permeability values using the _XYZ suffix show directions with respect to the global XYZ coordinate frame, while those using the _IJK suffix are aligned with local coordinate frame.

15 GEOTHERMAL ENERGY↗

Sensitivity analysis for aeroacoustic and aeroelastic design of turbomachinery blades

A new method for computing the effect that small changes in the airfoil shape and cascade geometry have on the aeroacoustic and aeroelastic behavior of turbomachinery cascades is presented. The nonlinear unsteady flow is assumed to be composed of a nonlinear steady flow plus a small perturbation unsteady flow that is harmonic in time. First, the full potential equation is used to describe the behavior of the nonlinear mean (steady) flow through a two-dimensional cascade. The small disturbance unsteady flow through the cascade is described by the linearized Euler equations. Using rapid distortion theory, the unsteady velocity is split into a rotational part that contains the vorticity and an irrotational part described by a scalar potential. The unsteady vorticity transport is described analytically in terms of the drift and stream functions computed from the steady flow. Hence, the solution of the linearized Euler equations may be reduced to a single inhomogeneous equation for the unsteady potential. The steady flow and small disturbance unsteady flow equations are discretized using bilinear quadrilateral isoparametric finite elements. The nonlinear mean flow solution and streamline computational grid are computed simultaneously using Newton iteration. At each step of the Newton iteration, LU decomposition is used to solve the resulting set of linear equations. The unsteady flow problem is linear, and is also solved using LU decomposition. Next, a sensitivity analysis is performed to determine the effect small changes in cascade and airfoil geometry have on the mean and unsteady flow fields. The sensitivity analysis makes use of the nominal steady and unsteady flow LU decompositions so that no additional matrices need to be factored. Hence, the present method is computationally very efficient. To demonstrate how the sensitivity analysis may be used to redesign cascades, a compressor is redesigned for improved aeroelastic stability and two different fan exit guide vanes are redesigned for reduced downstream radiated noise. In addition, a framework detailing how the two-dimensional version of the method may be used to redesign three-dimensional geometries is presented.

Lorence, Christopher B.↗

Discrete and Continuum Plane-Hopper Flow Simulations with Experimental Validation Using X-Ray Imaging, Arch Profilometry and Wall Pressure Measurements

The flow of spherical glass beads, approximately cubic wood crumbles®, and wood microchips are investigated using a combination of discrete element modeling (DEM), finite element analysis (FEA), and physical experiments using a custom plane-flow hopper in which the flow is characterized using x-ray imaging, profilometry to measure arching geometry and pressure measurements at the wall. The purpose of this study is to investigate fundamental flow behavior, and for this purpose the simulations and physical tests are specially designed. During the physical tests and simulations, the hopper geometry begins as a V shape with the two opposing side walls touching at the bottom of the V. Basic tests are performed by first filling the hopper with material, and then rotating the opposing side walls inward about their common intersection axis to cause an approximately uniform stress condition throughout most of the hopper. The side walls then slide upward to effectively increase the size of the opening at the bottom of the hopper until the arch of material in the hopper breaks, and all of the material falls out of the hopper. More advanced tests are also performed in which the initial rotation of the walls is slightly reversed to decrease the pressure in the hopper, corresponding to “preshear” and “shear” conditions in standard shear tests. Shear tests of the materials are also performed using a Schulze automated ring shear tester with a standard size M shear cell, and the shear tests of the glass beads and wood crumbles® are also simulated using DEM to calibrate the DEM with the FEA. Reasonable agreement between predicted and measured flow behavior is obtained indicating that this type of physical tests and modeling shows promise for characterizing and predicting the flow behavior of compressible and anisotropic materials.

09 BIOMASS FUELS↗

Gas-kinetic unified algorithm for hypersonic flows covering various flow regimes solving Boltzmann model equation in nonequilibrium effect

Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗