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NASA NTRS1990

Satellite formation in capillary jet breakup

Computations of finite-amplitude, spatially periodic wave growth on a cylindrical jet have been carried out using a boundary integral method. The initial wave growth is in agreement with Rayleigh's linear theory. When followed to completion these waves pinch off large drops separated by smaller satellite drops (spherules) that decrease in size with decreasing wavelength. The computed sizes of both drops and satellites agree with experiment. It is found that satellites will form for all unstable wave numbers. The small satellites that are computed at wave numbers near the critical wave number were not predicted by near-linear analysis but are observed in experimental photographs of jet breakup. Computation of the collapse of elongated satellites shows short waves propagating on their surfaces.

Mansour, Nagi N.↗

NASA NTRS1993

Micromechanics of crenulated fibers in carbon/carbon composites

The influence of crenulated noncircular fibers on the micromechanical stress states due to a transverse strain and to a temperature change in carbon/carbon composites is examined using the finite element method. Stresses at the interface of both fully bonded and fully disbonded fibers having two crenulation amplitudes and with two fiber volume fractions are presented. In each case, these interface stresses are compared to stresses at the interface of circular fibers which have the same degree of disbond and fiber volume fraction and are under the same loading conditions. For the disbonded cases, deformed meshes showing locations of fiber/matrix contact are also included. In addition to the interface stress states, selected composite properties are also computed and compared in each case examined. Interest in studying noncircular fibers stems from a desire to increase the transverse properties of carbon/carbon by introducing a mechanical interlocking between the fiber and the matrix. Results presented here indicate that this interlocking does in fact occur. Evidence from the interface stress data suggests, however, that any possible advantage of this interlocking may be outweighed by the disadvantage of stress concentrations which arise at the interface due to the crenulated geometry of the fibers.

Carapella, E. E.↗

NASA NTRS1991

A method for the geometrically nonlinear analysis of compressively loaded prismatic composite structures

A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite material.

Stoll, Frederick↗

NASA NTRS1985

Cellular interface morphologies in directional solidification. III - The effects of heat transfer and solid diffusivity

The shape and stability of two-dimensional finite-amplitude cellular interfaces arising during directional solidification are compared for several solidification models that account differently for latent heat released at the interface, unequal thermal conductivities of melt and solid, and solute diffusivity in the solid. Finite-element analysis and computer-implemented perturbation methods are used to analyze the families of steadily growing cellular forms that evolve from the planar state. In all models a secondary bifurcation between different families of finite-amplitude cells exists that halves the spatial wavelength of the stable interface. The quantitative location of this transition is very dependent on the details of the model. Large amounts of solute diffusion in the solid retard the growth of large-amplitude cells.

Ungar, Lyle H.↗

DOE OSTI2024

DK/Dπ scattering and an exotic virtual bound state at the SU(3) flavour symmetric point from lattice QCD

Abstract ElasticS-wave scattering of a charm meson with a light pseudoscalar meson inJ P = 0 + is investigated in the flavour$$ \overline{\textbf{3}} $$ 3 ¯ ,6and$$ \overline{\textbf{15}} $$ 15 ¯ sectors at the SU(3) f flavour point using lattice QCD, working on three volumes withm π ≈ 700 MeV. Large bases of interpolating operators are employed to extract finite-volume spectra, which are subsequently used with the Lüscher method to provide constraints on infinite-volume scattering amplitudes. Examining the singularities of the amplitudes, theS-wave amplitude in the flavour$$ \overline{\textbf{3}} $$ 3 ¯ sector is found to contain a deeply bound state, strongly coupled to elastic threshold, corresponding to the$$ {J}^P={0}^{+}\ {D}_{s0}^{\ast }(2317) $$ J P = 0 + D s 0 ∗ 2317 . In the exotic flavour6sector a virtual bound state is found at$$ \sqrt{s_{\textrm{pole}}} $$ s pole = 2510 – 2610 MeV, roughly 40 – 140 MeV below threshold, whereas the$$ \overline{\textbf{15}} $$ 15 ¯ channel shows weak repulsion.

Physics↗

DOE OSTI2023

Verifying Ray Tracing Amplitude Methods for Global Magnetospheric Modeling

Abstract Ray tracing is a commonly used method for modeling the propagation of electromagnetic waves in Earth's magnetosphere. To apply ray tracing results to global models of wave‐particle interaction such as energetic electron scattering, it is useful to map the discrete rays to a volume filling mesh. However, some methods have inherent losses of energy from the wave source, or do not account for the full range of wave properties within a sample volume. We have developed and tested a 3D magnetospheric ray tracing code “MESHRAY” which resolves these issues. MESHRAY uses the conservation of Poynting flux through ray triplets with finite volume to determine the local field amplitudes. Electromagnetic wave energy density from all ray data points is mapped to a mesh and verified against the wave source power for energy conservation varying time step length, number of rays, and total time steps. We find that the method is self‐consistent and numerically robust. We further investigate whether the neglect of phase information and superposition has a significant impact on the accuracy of mapping wave intensity to a mesh. We find excellent agreement between the analytic solution for waves emitted by a line source in a plane‐stratified medium and an equivalent ray tracing solution. When phase information is excluded, ray tracing reproduces an average amplitude spread over regions of coherent constructive and destructive interference. This may be an important consideration for interpolating ray tracing results of longer wavelength waves such as magnetosonic, electromagnetic ion cyclotron, or ULF waves.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1995

Category 5 problem solution using an unstructured finite volume algorithm

For the simulation of flows with complex geometries, unstructured finite volume methods have proven to be very popular, and simulations of a large number of flows have been done with good results using this approach. Since most of the simulations to date were done for steady flows, it is not clear that present unstructured finite volume algorithms can accurately track the unsteady propagation of acoustic waves in a computation. Therefore, there is a need to assess the accuracy of these methods for acoustic calculations. In this paper, we perform the numerical simulation of a very small amplitude acoustic wave incident on the non-uniform steady flow in a quasi- 1 D convergent-divergent nozzle using an unstructured finite volume algorithm with piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for the steady flow by running the simulation with a sequence of successively finer meshes. Then the unsteady numerical solution with the acoustic perturbation is presented.

Bui, Trong T.↗

DOE OSTI2025

Finite-volume quantization condition from the N/D representation

We propose a new model-independent method for determining hadronic resonances from lattice QCD. The formalism is derived from the general principles of unitarity and analyticity, as encoded in the N/D representation of a partial-wave two-body amplitude. The associated quantization condition relates the finite-volume spectrum to the infinite-volume numerator $\mathscr{N}$, used to reconstruct the scattering amplitude from dispersive relations. Unlike the original Lüscher condition, this new formalism is valid for energies coinciding with the left-hand cuts from arbitrary one- and multiparticle exchanges.

Dawid, Sebastian M. [Univ. of Washington, Seattle,↗

DOE OSTI2023

Acoustic Codes in 2D Spherical Coordinate

Finite-difference methods are widely used to simulate infrasound propagation in the atmosphere. Flexibility of finite-difference scheme allows implementation of highly heterogeneous media for sound propagation as well as complex source models for sound generation. While full 3-D finite-difference methods have been utilized for local infrasound propagation with pronounced topography, 2-D modeling approach has been preferred for regional and global propagation as full 3-D methods generally require enormous computational resources. Infrasound propagation is often simulated with a second-order finite difference scheme. This lowest-order finite-difference scheme is robust and straightforward to implement complex boundary conditions, but the solution includes large error with numerical dispersion and dissipation. This large numerical error may make the second-order finite-difference not optimal for long range infrasound propagation modeling as the numerical dispersion degrades the accuracy of the solution unacceptably. Here, we developed a high-order finite-difference solver for long-range infrasound simulation. The high-order scheme is particularly popular for linear wave modeling in aeroacoustics owing to its low-dispersive and low-dissipative behavior. We develop and evaluate a high-order finite difference scheme in 2-D axisymmetric coordinates. The axisymmetry allows to approximate 3-D spherical sound propagation and amplitude attenuation by a 2-D method. AC2Dr is developed to simulate infrasound propagation in realistic atmosphere, but can be used for linear acoustic waves in general materials with background flow. AC2Dr in an axisymmetric coordinates allows for spherical radiation of acoustic waves from compact sources.

Sjogreen, Bjorn↗

DOE OSTI2022

Reciprocal swimming at intermediate Reynolds number

In Stokes flow, Purcell's scallop theorem forbids objects with time-reversible (reciprocal) swimming strokes from moving. In the presence of inertia, this restriction is eased and reciprocally deforming bodies can swim. A number of recent works have investigated dimer models that swim reciprocally at intermediate Reynolds numbers Re≈1–1000. These show interesting results (e.g. switches of the swim direction as a function of inertia) but the results vary and seem to be case specific. Here, in this work, we introduce a general model and investigate the behaviour of an asymmetric spherical dimer of oscillating length for small-amplitude motion at intermediate Re. In our analysis we make the important distinction between particle and fluid inertia, both of which need to be considered separately. We asymptotically expand the Navier–Stokes equations in the small-amplitude limit to obtain a system of linear partial differential equations. Using a combination of numerical (finite element) and analytical (reciprocal theorem, method of reflections) methods we solve the system to obtain the dimer's swim speed and show that there are two mechanisms that give rise to motion: boundary conditions (an effective slip velocity) and Reynolds stresses. Each mechanism is driven by two classes of sphere–sphere interactions, between one sphere's motion and (1) the oscillating background flow induced by the other's motion, and (2) a geometric asymmetry induced by the other's presence. We can thus unify and explain behaviours observed in other works. Our results show how sensitive, counterintuitive and rich motility is in the parameter space of finite inertia of particles and fluid.

42 ENGINEERING↗

NASA NTRS1991

Special class of nonlinear damping models in flexible space structures

A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.

Hu, Anren↗

NASA NTRS1990

Numerical simulation of the control of the three-dimensional transition process in boundary layers

Surface heating techniques to control the three-dimensional laminar-turbulent transition process are numerically investigated for a water boundary layer. The Navier-Stokes and energy equations are solved using a fully implicit finite difference/spectral method. The spatially evolving boundary layer is simulated. Results of both passive and active methods of control are shown for small amplitude two-dimensional and three-dimensional disturbance waves. Control is also applied to the early stages of the secondary instability process using passive or active control techniques.

Kral, L. D.↗

NASA NTRS1992

A probabilistic approach to the evaluation of fatigue damage in a space propulsion system injector element

The fatigue damage of a space propulsion system component is computed using probabilistic structural analysis methods. The analysis takes into account the variations in static and dynamic loads, the uncertainty in structural damping, and the scatter in material fatigue resistance. The key elements of the probabilistic approach include: (1) a numerical engine model for describing the global component interface loads consistent with engine balance, (2) models for computing the local mode boundary conditions on the component, (3) a static structural analysis model that captures the strains at a damage critical location as a function of engine performance variables, (4) a finite element model for assessment of the random amplitude stress response due to random base and pressure excitations with uncertain power and correlation length, and (5) advanced first order reliability methods for computing the probabilities associated with the fatigue damage.

Rajagopal, K. R.↗

NASA NTRS1995

Application of essentially nonoscillatory methods to aeroacoustic flow problems

A finite-difference essentially nonoscillatory (ENO) method has been applied to several of the problems prescribed for the workshop sponsored jointly by the Institute for Computer Applications in Science and Engineering and by NASA Langley Research Center entitled 'Benchmark Problems in Computational Aeroacoustics'. The workshop focused on computational challenges specific to aeroacoustics. Among these are long-distance propagation of a short-wavelength disturbance, propagation of small-amplitude disturbances, and nonreflective boundary conditions. The shock capturing-capability inherent to the ENO method effectively eliminates oscillations near shock waves without the need to add and tune dissipation or filter terms. The method-of-lines approach allows the temporal and spatial operators to be chosen separately in accordance with the demands of a particular problem. The ENO method was robust and accurate for all problems in which the propagating wave was resolved with 8 or more points per wavelength. The finite-wave-model boundary condition, a local nonlinear acoustic boundary condition, performed well for the one-dimensional problems. The buffer-domain approach performed well for the two-dimensional test problem. The amplitude of nonphysical reflections were less than 1 percent of the exiting wave's amplitude.

Atkins, Harold L.↗

NASA NTRS1981

Linear/nonlinear behavior in unsteady transonic aerodynamics

The accurate calculation of the aerodynamic forces in unsteady transonic flow requires the solution of the nonlinear flow equations. The aeroelastician, on the other hand, seeks to treat his problems (flutter, for example) by means of linear equations whenever possible. He may do this, even when the underlying flow is nonlinear, if the perturbation forces are linear over some (perhaps small) range of unsteady amplitude of motion. This paper assesses the range of parameters over which linear behavior occurs. In particular calculations are made for an NACA 64A006 airfoil oscillating in pitch over a range of amplitudes, frequencies, and Mach numbers. The primary aerodynamic method used is the well known LTRAN2 code of Ballhaus and Goorjian that provides a finite-difference solution to the low frequency, small disturbance, two-dimensional potential flow equation. Comparisons are made with linear subsonic theory, local linearization, and, for steady flow, with the full potential equation code of Bauer, Garabedian, and Korn.

Dowell, E. H.↗

NASA NTRS1989

Finite element large-amplitude free and forced vibrations of rectangular thin composite plates

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite rectangular thin plates. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite rectangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, different boundary conditions, aspect ratios, lamination angles and number of plies are presented. The finite element results are compared with available approximate continuum solutions.

Chiang, C. K.↗

DOE OSTI2022

A novel post-processing method for progressive failure analysis of brittle composite compression

Finite element analysis of brittle materials in axial compression typically uses element deletion to allow continued global deformation post-element-failure. However, element deletion produces cyclic load-displacement curves that underestimate energy absorption and are not representative of a continuum system. Two key observations support the conclusion that results from an appropriately discretized model can be an adequate representation of a continuum system. Specifically, the frequency of the oscillations in the load-displacement curve is directly dependent upon element length in the loading direction, and the peak amplitudes of oscillations are mesh size independent. A method of post-processing the analysis results, by connecting the peak amplitudes of oscillations, is proposed and applied to a series of continuous carbon fiber composite crush tubes. The load-displacement curve, stable crushing load, and specific energy absorption of the post-processed results compare well to an experimental study of crush tubes with similar layups.

Materials Science↗

DOE OSTI2020

Finite-temperature coupled cluster: Efficient implementation and application to prototypical systems

In this work, we discuss the theory and implementation of the finite temperature coupled cluster singles and doubles (FT-CCSD) method including the equations necessary for an efficient implementation of response properties. Numerical aspects of the method including the truncation of the orbital space and integration of the amplitude equations are tested on some simple systems, and we provide some guidelines for applying the method in practice. The method is then applied to the 1D Hubbard model, the uniform electron gas (UEG) at warm, dense conditions, and some simple materials. The performance of model systems at high temperatures is encouraging: for the one-dimensional Hubbard model, FT-CCSD provides a qualitatively accurate description of finite-temperature correlation effects even at U = 8, and it allows for the computation of systematically improvable exchange–correlation energies of the warm, dense UEG over a wide range of conditions. We highlight the obstacles that remain in using the method for realistic ab initio calculations on materials

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗