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NASA NTRS2005

Boundary-Layer Receptivity and Integrated Transition Prediction

The adjoint parabold stability equations (PSE) formulation is used to calculate the boundary layer receptivity to localized surface roughness and suction for compressible boundary layers. Receptivity efficiency functions predicted by the adjoint PSE approach agree well with results based on other nonparallel methods including linearized Navier-Stokes equations for both Tollmien-Schlichting waves and crossflow instability in swept wing boundary layers. The receptivity efficiency function can be regarded as the Green's function to the disturbance amplitude evolution in a nonparallel (growing) boundary layer. Given the Fourier transformed geometry factor distribution along the chordwise direction, the linear disturbance amplitude evolution for a finite size, distributed nonuniformity can be computed by evaluating the integral effects of both disturbance generation and linear amplification. The synergistic approach via the linear adjoint PSE for receptivity and nonlinear PSE for disturbance evolution downstream of the leading edge forms the basis for an integrated transition prediction tool. Eventually, such physics-based, high fidelity prediction methods could simulate the transition process from the disturbance generation through the nonlinear breakdown in a holistic manner.

Chang, Chau-Lyan↗

DOE OSTI2020

Solving Coupled Cluster Equations by the Newton Krylov Method

We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster amplitude. The multiplication of the Jacobian with a vector, which is required in each step of a Krylov iterative method such as the Generalized Minimum Residual (GMRES) method, is carried out through a finite difference approximation, and requires an additional residual evaluation. The overall cost of the method is determined by the sum of the inner Krylov and outer Newton iterations. We discuss the termination criterion used for the inner iteration and show how to apply pre-conditioners to accelerate convergence. We will also examine the use of regularization technique to improve the stability of convergence and compare the method with the widely used direct inversion of iterative subspace (DIIS) methods through numerical examples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1989

Composite structure dynamics and space applicability

Guided wave modes in cladded or uncladded fiber-reinforced composite plates and tubes have been analyzed using a stiffness method in which the displacement variation through the thickness is approximated by polynomial interpolation functions. This allows for an arbitrary number of laminations and fiber orientations different from lamina to lamina. It is shown that dispersive behavior of guided modes depends significantly on the cladding, number of laminae, and interfaces between the adjacent laminae. A hybrid modeling technique is described in which an inner region containing cracks (or other defects) is discretized by finite elements, and the field in the exterior region is represented in terms of modes that are found using the stiffness method described above. It is found that the reflected and transmitted amplitudes of modes vary significantly with the size of a transverse or longitudinal (delamination) crack and frequency. We have also studied the impact response of a unidirectional fiber-reinforced plate. Received signals at the epicentral and other locations are shown. Strong longitudinal anisotropy of the graphite/epoxy plate causes the signal to be considerably different from that in an isotropic plate.

Datta, Subhendu K.↗

NASA NTRS1989

An integrated methodology for optimizing structural composite damping

A method is presented for tailoring plate and shell composite structures for optimal forced damped dynamic response. The damping of specific vibration modes is optimized with respect to dynamic performance criteria including placement of natural frequencies and minimization of resonance amplitudes. The structural composite damping is synthesized from the properties of the constituent materials, laminate parameters, and structural geometry based on a specialty finite element. Application studies include the optimization of laminated composite beams and composite shells with fiber volume ratios and ply angles as design variables. The results illustrate the significance of damping tailoring to the dynamic performance of composite structures, and the effectiveness of the method in optimizing the structural dynamic response.

Saravanos, D. A.↗

NASA NTRS1990

An integrated methodology for optimizing the passive damping of composite structures

Saravanos, D. A.↗

DOE OSTI2021

Caravel: A C++ framework for the computation of multi-loop amplitudes with numerical unitarity

We present the first public version of Caravel, a C++17 framework for the computation of multi-loop scattering amplitudes in quantum field theory, based on the numerical unitarity method. Caravel is composed of modules for the D-dimensional decomposition of integrands of scattering amplitudes into master and surface terms, the computation of tree-level amplitudes in floating point or finite-field arithmetic, the numerical computation of one- and two-loop amplitudes in QCD and Einstein gravity, and functional reconstruction tools. Here, we provide programs that showcase Caravel's main functionalities and allow to compute selected one- and two-loop amplitudes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Two- and three-meson scattering amplitudes with physical quark masses from lattice QCD

We study systems of two and three mesons composed of pions and kaons at maximal isospin using four CLS ensembles with 𝑎 ≈ 0.063 fm, including one with approximately physical quark masses. Using the stochastic Laplacian-Heaviside method, we determine the energy spectrum of these systems including many levels in different momentum frames and irreducible representations. Using the relativistic two- and three-body finite-volume formalism, we constrain the two- and three-meson K matrices, including not only the leading 𝑠 wave, but also 𝑝 and 𝑑 waves. By solving the three-body integral equations, we determine, for the first time, the physical-point scattering amplitudes for 3⁢𝜋 + , 3⁢𝐾 + , 𝜋 + ⁢𝜋 + ⁢𝐾 + , and 𝐾 + ⁢𝐾 + ⁢𝜋 + systems. These are determined for total angular momentum 𝐽 𝑃 = 0 − , 1 + , and 2 − . We also obtain accurate results for 2⁢𝜋 + , 𝜋 + ⁢𝐾 + , and 2⁢𝐾 + phase shifts. We compare our results to chiral perturbation theory and to phenomenological fits.

FOS: Physical sciences↗

NASA NTRS1991

Effect of leading-edge geometry on boundary-layer receptivity to freestream sound

The receptivity to freestream sound of the laminar boundary layer over a semi-infinite flat plate with an elliptic leading edge is simulated numerically. The incompressible flow past the flat plate is computed by solving the full Navier-Stokes equations in general curvilinear coordinates. A finite-difference method which is second-order accurate in space and time is used. Spatial and temporal developments of the Tollmien-Schlichting wave in the boundary layer, due to small-amplitude time-harmonic oscillations of the freestream velocity that closely simulate a sound wave travelling parallel to the plate, are observed. The effect of leading-edge curvature is studied by varying the aspect ratio of the ellipse. The boundary layer over the flat plate with a sharper leading edge is found to be less receptive. The relative contribution of the discontinuity in curvature at the ellipse-flat-plate juncture to receptivity is investigated by smoothing the juncture with a polynomial. Continuous curvature leads to less receptivity. A new geometry of the leading edge, a modified super ellipse, which provides continuous curvature at the juncture with the flat plate, is used to study the effect of continuous curvature and inherent pressure gradient on receptivity.

Lin, Nay↗

NASA NTRS2001

Calculation of the Scattering Amplitude Without Partial Wave Expansion

Two developments in the direct calculation of the angular differential scattering amplitude have been implemented: (a) The integral expansion of the scattering amplitude is simplified by analytically integration over the azimuthal angle. (b) The resulting integral as a function of scattering angle is calculated by using the numerically generated wave function from a finite element method calculation. Results for electron-hydrogen scattering in the static approximation will be shown to be as accurate as a partial wave expansion with as many l's as is necessary for convergence at the incident energy being calculated.

Shertzer, J.↗

NASA NTRS2002

Calculation of Scattering Amplitude Without Partial Analysis: Inclusion of Exchange - II

There was a method for calculating the whole scattering amplitude, f(Omega(sub k)), directly. The idea was to calculate the complete wave function Psi numerically, and use it in an integral expression for f, which can be reduced to a 2 dimensional quadrature. The original application was for e-H scattering without exchange. There the Schrodinger reduces a 2-d partial differential equation (pde), which was solved using the finite element method (FEM). Here we extend the method to the exchange approximation. The S.E. can be reduced to a pair of coupled pde's, which are again solved by the FEM. The formal expression for f(Omega(sub k)) consists two integrals, f+/- = f(sub d) +/- f(sub e); f(sub d) is formally the same integral as the no-exchange f. We have also succeeded in reducing f(sub e) to a 2-d integral. Results will be presented at the meeting.

Temkin, Aaron↗

DOE OSTI2022

From force chains to nonclassical nonlinear dynamics in cemented granular materials

In this letter, we present evidence for a mechanism responsible for the nonclassical nonlinear dynamics observed in many cemented granular materials that are generally classified as mesoscopic nonlinear elastic materials. We demonstrate numerically that force chains are created within the complex grain-pore network of these materials when subjected to dynamic loading. The interface properties between grains along with the sharp and localized increase of the stress occurring at the grain-grain contacts leads to a reversible decrease of the elastic properties at macroscopic scale and peculiar effects on the propagation of elastic waves when grain boundary properties are appropriately considered. These effects are observed for relatively small amplitudes of the elastic waves, i.e., within tens of microstrain, and relatively large wavelengths, i.e., orders of magnitude larger than the material constituents. The mechanics are investigated numerically using the hybrid finite-discrete-element method and match those observed experimentally using nonlinear resonant ultrasound spectroscopy.

36 MATERIALS SCIENCE↗

NASA NTRS1992

Axially symmetric pulse propagation in semi-infinite hollow cylinders

The effects of dispersion and end conditions on axially symmetric pulse propagation in semiinfinite tubes are investigated. Numerical modeling of the dynamic response is accomplished using a stable and efficient finite element and wave propagation based method. This method yields the dispersive and modal data required to express displacements in a frequency domain modal expansion. Boundary conditions are applied to the tube end to obtain mode amplitudes. A fast Fourier transform is then used to get the time response. The specific end conditions considered are intended to give some insight into how the tube would behave as a member of a jointed truss structure.

Kohl, T.↗

NASA NTRS1973

Computational fracture mechanics

Numerical procedures for accurate determination of elastic stress intensity factors for the general two-dimensional crack problem are reviewed. The elastic perfectly plastic state of crack tip deformation is studied by a finite element procedure. Elastic-plastic fields in the immediate vicinity of a crack tip are determined numerically by finite element procedures based on asymptotic studies of crack tip singularities in plastic materials. The small-scale yielding problem is modeled, and expressions for crack tip opening displacement, shear singularity amplitude, and plastic zone extent are derived. A finite element solution to the large-scale yielding of a circumferentially cracked round tension bar is obtained. The three-dimensional aspects of flawed structures and numerical methods of treating them are studied. Ductile fracture mechanisms, in particular crack tip fracture on the microscale, are discussed.

Rice, J. R.↗

NASA NTRS1978

The role of rotor impedance in the vibration analysis of rotorcraft, part 4

A method for a strongly idealized case of vertical excitation and for rolling and pitching moment excitation of a four bladed hingeless rotor on an up-focussing flexible mount is developed. The aeroelastic rotor impedances are computed directly with a finite blade element method that includes aerodynamics. The rotor impedance matrix for three or more blades is determined from the root moment impedance for a single blade by a simple multiblade transformation rule. Force and moment amplitudes transferred from the rotor to support are found to be critically dependent on the support dynamics.

Hohenemser, K. H.↗

NASA NTRS1978

The role of rotor impedance in the vibration analysis of rotorcraft

In an improved method which retains the advantage of separate treatment of rotor and airframe, the rotor impedance is used to correct the input to the airframe. This improved method is illustrated for a strongly idealized case of vertical excitation and then for rolling and pitching moment excitation of a four bladed hingeless rotor on an up-focussing flexible mount. Contrary to the usual approach that represents aeroelastic blade motions by a series of normal blade modes in vacuum, the aeroelastic rotor impedances are computed directly with a finite blade element method that includes aerodynamics. The rotor impedance matrix for three or more blades is determined from the root moment impedance for a single blade by a simple multiblade transformation rule. Force and moment amplitudes transferred from the rotor to the support are found to be critically dependent on the support dynamics.

Hohenemser, K. H.↗

NASA NTRS1983

Reduction methods for nonlinear steady-state thermal analysis

Hybrid analysis techniques and a problem adaptive computational algorithm are presented for predicting the nonlinear steady state temperature distribution in structures and solids. In the proposed techniques, the structure is discretized by using the finite element method. The vector of nodal temperatures is then expressed as a linear combination of a small number of global temperature modes (or basis vectors), and the Bubnov Galerkin technique is used to compute the amplitudes of the global modes. The global temperature modes (or basis vectors) are chosen to include the various order derivatives of the nodal temperature vector with respect to preselected path parameter(s). The potential of the proposed reduction methods for solution of large scale, nonlinear thermal problems is discussed and the effectiveness of the methods is demonstrated by means of numerical examples, including steady state conduction, convection, and radiation modes of heat transfer.

Noor, A. K.↗

NASA NTRS1984

Coding schemes for improving MST radar performance, part 7.1A

The performance of an mesosphere-stratosphere-troposphere (MST) radar can be characterized by its system sensitivity and its range resolution. The former enables Doppler velocities to be determined even in the presence of very weak structures; the latter permits study of the fine structure within a turbulent region. Coding of transmitted signals has as its aim an increase in the effective radar sensitivity or range resolution without an increase in the peak transmitted power. This is accomplished by spreading the power in the frequency domain, giving better range resolution, without reducing the pulse width. Two basic techniques are used to accomplish this frequency dispersion: (1) using a type of pseudorandom code for the phase or amplitude within a single pulse, or within a finite sequence of pulses; (2) to code the frequency of the transmitted signal in some way. The various possibilities are discussed and are compared with the pulse-coding methods.

Bowhill, S. A.↗

NASA NTRS1973

Response of panels to turbulence-induced, surface-pressure fluctuations and resulting acoustic radiation to the flow field.

The response of finite rectangular panels, excited by turbulent boundary layers and the resulting acoustical radiation into the flow field is studied. The method of normal modes and the technique of spectral analysis are used to compute the power spectra of the panel amplitude and strain response. Computed results are compared with the corresponding response measurements for panels exposed to attached and separated flows at supersonic speeds and attached flow at subsonic speeds. The thin plate and the convected wave equations are coupled through the boundary condition on the panel to give a formula for the radiation pressure power spectra. A formula for the acoustical damping ratio of the panel is obtained through the principle of virtual work.-

Chyu, W. J.↗