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Flutter prediction at low mass density ratios, using modified and two dimensional strip analysis and kernel function methods
Herein this paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are benchmarked using a range of test cases and demonstrated using large-scale models of biomedical FSI. The numerical approach developed herein, which we refer to as an immersed Lagrangian-Eulerian (ILE) method, integrates aspects of partitioned and immersed FSI formulations by solving separate momentum equations for the fluid and solid subdomains, as in a partitioned formulation, while also using non-conforming discretizations of the dynamic fluid and structure regions, as in an immersed formulation. A simple Dirichlet-Neumann coupling scheme is used, in which the motion of the immersed solid is driven by fluid traction forces evaluated along the fluid-structure interface, and the motion of the fluid along that interface is constrained to match the solid velocity and thereby satisfy the no-slip condition. To develop a practical numerical method, we adopt a penalty approach that approximately imposes the no-slip condition along the fluid-structure interface. In the coupling strategy, a separate discretization of the fluid-structure interface is tethered to the volumetric solid mesh via stiff spring-like penalty forces. Our fluid-structure coupling scheme relies on an immersed interface method (IIM) for discrete geometries, which enables the accurate determination of both velocities and stresses along complex internal interfaces. Numerical methods for FSI can suffer from instabilities related to the added mass effect, but computational tests indicate that the methodology introduced here remains stable for selected test cases across a broad range of solid-fluid mass density ratios, including extremely small, nearly equal, equal, and large density ratios. Biomedical FSI demonstration cases include results obtained using this method to simulate the dynamics of a bileaflet mechanical heart valve in a pulse duplicator, and to model transport of blood clots in a patient-averaged anatomical model of the inferior vena cava.
Flutter characteristics of a cantilevered high aspect ratio wing with winglet were investigated. The configuration represented a current technology, twin engine airplane. Compressibility effects through transonic Mach numbers and a wide range of mass-density ratios were evaluated on a low speed and high speed model. Four flutter mechanisms were obtained from test, and analysis from various combinations of configuration parameters. It is shown that the coupling between wing tip vertical and chordwise motions have significant effect under some conditions. It is concluded that for the flutter model configurations studied, the winglet related flutter is amenable to the conventional flutter analysis techniques. The low speed model flutter and the high-speed model flutter results are described.
Flutter characteristics of a cantilevered high aspect ratio wing with winglet were investigated. The configuration represented a current technology, twin-engine airplane. A low-speed and high-speed model were used to evaluate compressibility effects through transonic Mach numbers and a wide range of mass-density ratios. Four flutter mechanisms were obtained in test, as well as analysis from various combinations of configuration parameters. The coupling between wing tip vertical and chordwise motions was shown to have significant effect under some conditions. It is concluded that for the flutter model configurations studied, the winglet related flutter was amenable to the conventional flutter analysis techniques.
Flutter characteristics of a cantilevered high aspect ratio wing with winglet were investigated. The configuration represented a current technology, twin-engine airplane. A low-speed and a high-speed model were used to evaluate compressibility effects through transonic Mach numbers and a wide range of mass-density ratios. Four flutter mechanisms were obtained in test, as well as analysis from various combinations of configuration parameters. The coupling between wing tip vertical and chordwise motions was shown to have significant effect under some conditions. It is concluded that, for the flutter model configurations studied, the winglet related flutter was amenable to the conventional flutter analysis techniques.
This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.
ABSTRACT The spatial distribution of mono-abundance populations (MAPs, selected in [Fe/H] and [Mg/Fe]) reflect the chemical and structural evolution in a galaxy and impose strong constraints on galaxy formation models. In this paper, we use APOGEE data to derive the intrinsic density distribution of MAPs in the Milky Way, after carefully considering the survey selection function. We find that a single exponential profile is not a sufficient description of the Milky Way’s disc. Both the individual MAPs and the integrated disc exhibit a broken radial density distribution; densities are relatively constant with radius in the inner Galaxy and rapidly decrease beyond the break radius. We fit the intrinsic density distribution as a function of radius and vertical height with a 2D density model that considers both a broken radial profile and radial variation of scale height (i.e. flaring). There is a large variety of structural parameters between different MAPs, indicative of strong structure evolution of the Milky Way. One surprising result is that high-α MAPs show the strongest flaring. The young, solar-abundance MAPs present the shortest scale height and least flaring, suggesting recent and ongoing star formation confined to the disc plane. Finally we derive the intrinsic density distribution and corresponding structural parameters of the chemically defined thin and thick discs. The chemical thick and thin discs have local surface mass densities of 5.62 ± 0.08 and 15.69 ± 0.32 M⊙pc−2, respectively, suggesting a massive thick disc with a local surface mass density ratio between thick to thin disc of 36 per cent.
A transonic model and a low-speed model were flutter tested in the Langley Transonic Dynamics Tunnel at Mach numbers up to 0.90. Transonic flutter boundaries were measured for 10 different model configurations, which included variations in wing fuel, nacelle pylon stiffness, and wingtip configuration. The winglet effects were evaluated by testing the transonic model, having a specific wing fuel and nacelle pylon stiffness, with each of three wingtips, a nonimal tip, a winglet, and a nominal tip ballasted to simulate the winglet mass. The addition of the winglet substantially reduced the flutter speed of the wing at transonic Mach numbers. The winglet effect was configuration-dependent and was primarily due to winglet aerodynamics rather than mass. Flutter analyses using modified strip-theory aerodynamics (experimentally weighted) correlated reasonably well with test results. The four transonic flutter mechanisms predicted by analysis were obtained experimentally. The analysis satisfactorily predicted the mass-density-ratio effects on subsonic flutter obtained using the low-speed model. Additional analyses were made to determine the flutter sensitivity to several parameters at transonic speeds.
Interstellar dust in the Magellanic Clouds, with a weak or nearly absent 2175 A extinction feature, may be of interest in studies of galaxies in early stages of chemical evolution. To this inquiry, we extend the graphite-silicate grain model, introduced by Mathis, Rumpl, and Nordsieck and developed by Draine and Lee (1984) from the Milky Way to the Magellanic Clouds. We find that the empirical extinction curves in the Large and Small Magellanic Clouds can be reproduced by adjusting only the relative abundances of graphite and silicate grains, while leaving all other model properties fixed to those appropriate for the Galactic extinction curve. Using the graphite-silicate models, we calculate the absorption and scattering optical depths, the mass-density ratio of interstellar dust to neutral hydrogen, and the Kramers-Kronig relation for all three galaxies. We also present a fitting function for the three extinction curves, valid not only over the observed range of wavelengths but also over the full range as predicted by the models. All the quantities we derived here are independent of the dust-to-gas ratios in the Milky Way and the Magellanic Clouds, and can be applied to other galaxies if they contain Galactic or Magellanic-type dust.
DebriSat is a planned laboratory ]based satellite hypervelocity impact experiment. The goal of the project is to characterize the orbital debris that would be generated by a hypervelocity collision involving a modern satellite in low Earth orbit (LEO). The DebriSat project will update and expand upon the information obtained in the 1992 Satellite Orbital Debris Characterization Impact Test (SOCIT), which characterized the breakup of a 1960 's US Navy Transit satellite. There are three phases to this project: the design and fabrication of an engineering model representing a modern, 50-cm/50-kg class LEO satellite known as DebriSat; conduction of a laboratory-based hypervelocity impact to catastrophically break up the satellite; and characterization of the properties of breakup fragments down to 2 mm in size. The data obtained, including fragment size, area ]to ]mass ratio, density, shape, material composition, optical properties, and radar cross ]section distributions, will be used to supplement the DoD fs and NASA fs satellite breakup models to better describe the breakup outcome of a modern satellite. Updated breakup models will improve mission planning, environmental models, and event response. The DebriSat project is sponsored by the Air Force fs Space and Missile Systems Center and the NASA Orbital Debris Program Office. The design and fabrication of DebriSat is led by University of Florida with subject matter experts f support from The Aerospace Corporation. The major milestones of the project include the complete fabrication of DebriSat by September 2013, the hypervelocity impact of DebriSat at the Air Force fs Arnold Engineering Development Complex in early 2014, and fragment characterization and data analyses in late 2014.
The goal of the DebriSat project is to characterize fragments generated by a hypervelocity collision involving a modern satellite in low Earth orbit (LEO). The DebriSat project will update and expand upon the information obtained in the 1992 Satellite Orbital Debris Characterization Impact Test (SOCIT), which characterized the breakup of a 1960 s US Navy Transit satellite. There are three phases to this project: the design and fabrication of DebriSat - an engineering model representing a modern, 60-cm/50-kg class LEO satellite; conduction of a laboratory-based hypervelocity impact to catastrophically break up the satellite; and characterization of the properties of breakup fragments down to 2 mm in size. The data obtained, including fragment size, area-to-mass ratio, density, shape, material composition, optical properties, and radar cross-section distributions, will be used to supplement the DoD s and NASA s satellite breakup models to better describe the breakup outcome of a modern satellite.
ABSTRACT This is the first paper in our series on the combined analysis of the Dynamics and stellar Population (DynPop) for the MaNGA survey in the final SDSS Data Release 17 (DR17). Here, we present a catalogue of dynamically determined quantities for over 10 000 nearby galaxies based on integral-field stellar kinematics from the MaNGA survey. The dynamical properties are extracted using the axisymmetric Jeans Anisotropic Modelling (JAM) method, which was previously shown to be the most accurate for this kind of study. We assess systematic uncertainties using eight dynamical models with different assumptions. We use two orientations of the velocity ellipsoid: either cylindrically aligned JAMcyl or spherically aligned JAMsph. We also make four assumptions for the models’ dark versus luminous matter distributions: (1) mass-follows-light, (2) free NFW dark halo, (3) cosmologically constrained NFW halo, (4) generalized NFW dark halo, i.e. with free inner slope. In this catalogue, we provide the quantities related to the mass distributions (e.g. the density slopes and enclosed mass within a sphere of a given radius for total mass, stellar mass, and dark matter mass components). We also provide the complete models which can be used to compute the full luminous and mass distribution of each galaxy. Additionally, we visually assess the qualities of the models to help with model selections. We estimate the observed scatter in the measured quantities which decreases as expected with improvements in quality. For the best data quality, we find a remarkable consistency of measured quantities between different models, highlighting the robustness of the results.
The gravitational interaction between two fragments of a split comet nucleus in the sun's gravitational field is studied by means of the n-body computer program of Schubart and Stumpff (1966). Patterns of interactions are found for combinations of the masses, mass ratios and densities of the parent nucleus and the fragment, directions of separation, and regions of separation for nucleus separations occurring at perihelion and at true anomalies of +90 deg and -90 deg. It has been found that solar gravitational effects become noticeable about 0.5 to 1 day after separation at perihelion, and about 1 to 2 days after separation at twice the perihelion distance. Mass ratios and bulk density do not appreciably affect the appearance of the calculated trajectories. The calculated patterns vary from zero to very high inclinations, from a prograde to a retrograde sense of motion, and from escape of the companion to its pursuance of periodic quasi-stable orbits around the principal nucleus, terminated in some cases by collision of the fragments.
The radial velocities of cluster members of two rich, large superclusters have been measured in order to probe the supercluster mass densities, and simple evolutionary models have been computed to place limits upon the mass density within each supercluster. These superclusters represent true physical associations of size of about 100 Mpc seen presently at an early stage of evolution. One supercluster is weakly bound, the other probably barely bound, but possibly marginally unbound. Gravity has noticeably slowed the Hubble expansion of both superclusters. Galaxy surface-density counts and the density enhancement of Abell clusters within each supercluster were used to derive the ratio of mass densities of the superclusters to the mean field mass density. The results strongly exclude a closed universe.
We present the first published method to convert data obtained by the Pioneer Venus Large Probe Neutral Mass Spectrometer (LNMS) into units of mixing ratio (ppm) and volume percent (v%) against CO 2 and N 2 , the dominant Venus atmospheric gases, including conversion to density (kg m −3 ). These unit conversions are key to unlocking the untapped potential of the data, which represents a significant challenge given the scant calibration data in the literature. Herein, we show that our data treatments and conversions yield mixing ratios and volume percent values for H 2 O, N 2 , and SO 2 that are within error to those reported for the gas chromatograph (LGC) on the Pioneer Venus Large Probe (PVLP). For the noble gases, we developed strategies to correct for instrument biases by treating the data as a relative scale and using PVLP and Venera-based measurements as calibration points. Together, these methods, conversions, calibrations, and comparisons afford novel unit conversions for the LNMS data and yield unified measures for Venus’ atmosphere from the LNMS and LGC on the PVLP. - Conversion into mixing ratio (ppm), volume percent (v%), and density (kg m −3 ). - Mixing ratios are expressed against CO 2 and N 2 . - LNMS and LGC measurements on the PVLP are consistent.
In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the consistency of mass and momentum transport are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the “optimal” coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the consistency of reduction of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Finally, numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios.
Long-lived indirect excitons (IXs) exhibit a rich phase diagram, including a Bose–Einstein condensate (BEC), a Wigner crystal, and other exotic phases. Recent experiments have hinted at a “classical” liquid of IXs above the BEC transition. To uncover the nature of this phase, we use a broad range of theoretical tools and find no evidence of a driving force toward classical condensation. Instead, we attribute the condensed phase to a quantum electron–hole liquid (EHL), first proposed by Keldysh for direct excitons. Taking into account the association of free carriers into bound excitons, we study the phase equilibrium between a gas of excitons, a gas of free carriers, and an EHL for a wide range of electron–hole separations, temperatures, densities, and mass ratios. Our results agree reasonably well with recent measurements of GaAs/AlGaAs coupled quantum wells.
Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.