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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Arrangement of vortex lattices

A new method is developed for solving the lifting-surface equation for thin wings. The solution requires the downwash equation to be in the form of Cauchy integrals which can be interpreted as a vortex lattice with the positions of the vortices and control points dictated by the finite sum used to approximate the integrals involved. Lan's continuous loading method is employed for the chordwise integral since it properly accounts for the leading-edge singularity, Cauchy singularity, and Kutta condition. Unlike Lan, the spanwise loading is also continuous and the Cauchy singularity in the spanwise integral is also properly accounted for by using the midpoint trapezoidal rule and the theory of Chebyshev polynomials. This technique yields the exact classical solution to Prandtl's lifting-line equation.The solution to the lifting-surface equation for rectangular wings was found to compare well with other continuous loading methods, but with much smaller computational times, and to converge faster than other vortex lattice methods.

Dejarnette, F. R.↗
DOE OSTI2020

Learning compact physics‐aware delayed photocurrent models using dynamic mode decomposition

Abstract Radiation‐induced photocurrent in semiconductor devices can be simulated using complex physics‐based models, which are accurate, but computationally expensive. This presents a challenge for implementing device characteristics in high‐level circuit simulations where it is computationally infeasible to evaluate detailed models for multiple individual circuit elements. In this work we demonstrate a procedure for learning compact delayed photocurrent models that are efficient enough to implement in large‐scale circuit simulations, but remain faithful to the underlying physics. Our approach utilizes dynamic mode decomposition (DMD), a system identification technique for learning reduced‐order discrete‐time dynamical systems from time series data based on singular value decomposition. To obtain physics‐aware device models, we simulate the excess carrier density induced by radiation pulses by solving numerically the ambipolar diffusion equation, then use the simulated internal state as training data for the DMD algorithm. Our results show that the significantly reduced‐order delayed photocurrent models obtained via this method accurately approximate the dynamics of the internal excess carrier density—which can be used to calculate the induced current at the device boundaries—while remaining compact enough to incorporate into larger circuit simulations.

Hanson, Joshua↗
NASA NTRS1973

Nearly spherical constant-power detonation waves as driven by focused radiation.

Analysis is made of the flow within a 3-D spark created in a gas absorbing energy from a steady conical beam of radiation (typically obtained from an array of lasers) with nearly spherical symmetry. First-order deviations are represented by series of Legendre polynomials of the polar angle. Self-similarity is demonstrated. For harmonics 1 to 5 radial profiles of velocity components, density and pressure are presented. The linear perturbation scheme exhibits a singularity at the focus. This reflects the existence of a 'forbidden zone', as is shown by a study of the full non-linear flow equations.

George, Y. H.↗
NASA NTRS1976

The Boeing plastic analysis capability for engines

The current BOPACE program is described as a nonlinear stress analysis program, which is based on a family of isoparametric finite elements. The theoretical, user, programmer, preprocessing aspects are discussed, and example problems are included. New features in the current program version include substructuring, an out-of-core Gauss wavefront equation solver, multipoint constraints, combined material and geometric nonlinearities, automatic calculation of inertia effects, provision for distributed as well as concentrated mechanical loads, follower forces, singular crack-tip elements, the SAIL automatic generation capability, and expanded user control over input quantity definition, output selection, and program execution. BOPACE is written in FORTRAN 4 and is currently available for both the IBM 360/370 and the UNIVAC 1108 machines.

Vos, R. G.↗
NASA NTRS1979

Boundary layer thermal stresses in angle-ply composite laminates

Boundary-layer thermal stress singularities and distributions of angle-ply composite laminates under uniform thermal loading are investigated through a system of sixth-order governing partial differential equations developed with the aid of the anisotropic elasticity field equations and Lekhnitskii's complex stress functions. Results are presented for cases of various angle-ply graphite/epoxy laminates, and it is shown that the boundary-layer thickness depends on the degree of anisotropy of each individual lamina, thermomechanical properties of each ply, and the relative thickness of adjacent layers.

Wang, S. S.↗
NASA NTRS1986

A generalization of the method of harmonic balance

A procedure is provided for generalizing the method of harmonic balance to obtain higher-order approximations to the periodic solutions of differential equations for two systems, one a conservative system and the other nonconservative. The procedure is currently being applied to investigate the possible solution behaviors of singular, nonlinear oscillators, where the usual perturbation methods do not work.

Mickens, R. E.↗
NASA NTRS1995

Accurate ab Initio Quartic Force Fields, Vibrational Frequencies, and Heats of Formation for FCN, FNC, ClCN, and ClNC

The XCN and XNC (X = F, Cl) isomers have been investigated using the CCSD(T) method in conjunction with correlation consistent basis sets. Equilibrium geometries, harmonic frequencies, anharmonic constants, fundamental frequencies, and heats of formation have been evaluated. Agreement with experiment for the fundamental frequencies is very good, even for nu(sub 2), for CICN, which is subject to a strong Fermi resonance with 2nu(sub 3). It is also shown that a second-order perturbation theory approach to solving the nuclear Schroedinger equation gives results in excellent agreement with essentially exact variational calculations. This is true even for nu(sub 2) of ClCN, provided that near-singular terms are eliminated from the perturbation theory formulas and the appropriate Fermi interaction energy matrix is then diagonalized. A band at 615/cm, tentatively assigned as the Cl-N stretch in ClNC in matrix isolation experiments, is shown not to be due to ClNC. Accurate atomization energies are determined and are used to evaluate accurate heats of formation (3.1 +/- 1.5, 33.2 +/- 1.5, 72.6 +/- 1.5, and 75.9 +/- 1.5 kcal/mol for FCN, ClCN, FNC, and ClNC, respectively). It is expected that the theoretical heats of formation for FCN, FNC, and ClNC are the most accurate available.

Lee, Timothy J.↗
NASA NTRS1991

On the nonlinear development of the most unstable Goertler vortex mode

The nonlinear development of the most unstable Gortler vortex mode in boundary layer flows over curved walls is investigated. The most unstable Gortler mode is confined to a viscous wall layer of thickness O(G -1/5) and has spanwise wavelength O(G 11/5); it is, of course, most relevant to flow situations where the Gortler number G is much greater than 1. The nonlinear equations covering the evolution of this mode over an O(G -3/5) streamwise lengthscale are derived and are found to be of a fully nonparallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall (1988) for the numerical solution of the nonlinear Gortler equations valid for O(1) Gortler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion, whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flowfield as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer.

Denier, James P.↗
NASA NTRS1993

On the nonlinear development of the most unstable Goertler vortex mode TLSP - Final report

The nonlinear development of the most unstable Goertler vortex mode in boundary layer flows over curved walls is investigated. The most unstable Goertler mode is confined to a viscous wall layer of thickness O(G -1/5) and has spanwise wavelength O(G 11/5); it is, of course, most relevant to flow situations where the Goertler number G is much greater than 1. The nonlinear equations covering the evolution of this mode over an O(G -3/5) streamwise lengthscale are derived and are found to be of a fully nonparallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall (1988) for the numerical solution of the nonlinear Goertler equations valid for O(1) Goertler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion, whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flowfield as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer.

Denier, James P.↗
NASA NTRS1993

On nonlinear Tollmien-Schlichting/vortex interaction in three-dimensional boundary layers

The instability of an incompressible three-dimensional boundary layer (that is, one with cross-flow) is considered theoretically and computationally in the context of vortex/wave interactions. Specifically the work centers on two low amplitude, lower-branch Tollmien-Schlichting waves which mutually interact to induce a weak longitudinal vortex flow; the vortex motion, in turn, gives rise to significant wave-modulation via wall-shear forcing. The characteristic Reynolds number is taken as a large parameter and, as a consequence, the waves' and the vortex motion are governed primarily by triple-deck theory. The nonlinear interaction is captured by a viscous partial-differential system for the vortex coupled with a pair of amplitude equations for each wave pressure. Three distinct possibilities were found to emerge for the nonlinear behavior of the flow solution downstream - an algebraic finite-distance singularity, far downstream saturation or far-downstream wave-decay (leaving pure vortex flow) - depending on the input conditions, the wave angles, and the size of the cross-flow.

Davis, Dominic A. R.↗
NASA NTRS1993

The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows

We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing Eulerian schemes in its use of operator-splitting and artificial viscosity, except that we solve the Lagrangian equations of motion with a predictor-corrector and then remap onto a fixed Eulerian grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector Lagrangian-remap code has great flexibility for application to a variety of astrophysical problems.

Lufkin, Eric A.↗
NASA NTRS1995

The history of re-connection and the concept of the solar wind plasma with relatively small electrical conductivity

Petschek's 're-connection' model, aspiring to be universal, treated as a boundary problem meets unresolvable difficulties connected with impossibility to specify correctly boundary and initial conditions. This problem was incorrectly formulated. Hence, ineradicable logarithmic singularities occurred on the boundary surfaces. Attempts to eliminate them by incorporating the finite electrical conductivity are incorrect. This should lead to the change in the equation type, boundary condition type and in consequence to the change in solutions. Besides, the slow mode shocks cannot be driven by small internal source. As an alternative a new plasma concept is suggested. The state of fully ionized plasma in space depends completely on the entropy of the plasma heating source and on the process in which plasma is involved. The presumptive source of the solar wind creation - the induction electric field of the solar origin - has very low entropy. The state of plasma should be very far from the thermodynamic equilibrium. Debye's screening is not complete. The excitation of the powerful resonant self-consistent electric fields in plasma provides low electric conductivity. The MHD problems should be treated in frameworks of dissipative theories.

Chertkov, A. D.↗
DOE OSTI2024

An unstructured body-of-revolution electromagnetic particle-in-cell algorithm with radial perfectly matched layers and dual polarizations

A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code, utilizes a set of field scalings and a coordinate mapping, reducing the Maxwell field problem in a cylindrical system to a Cartesian finite element Maxwell solver in the meridian plane. The latter obviates the cylindrical coordinate singularity in the symmetry axis. The choice of an unstructured finite element discretization enhances the geometrical flexibility of the BORPIC++ solver compared to the more traditional finite difference solvers. Symmetries in Maxwell’s equations are explored to decompose the problem into two dual polarization states with isomorphic representations that enable code reuse. The particle-in-cell scatter and gather steps preserve charge conservation at the discrete level. Our previous algorithm (BORPIC+) discretized the E and B field components of TE Φ and TM Φ polarizations on the finite element (primal) mesh. Here, we employ a new field-update scheme. Using the same finite element (primal) mesh, this scheme advances two sets of field components independently: (1) E and B of TE Φ polarized fields, (E z , E ρ , B Φ ) and (2) D and H of TM Φ polarized fields, (D Φ , H z , H ρ ). Since these field updates are not explicitly coupled, the new field solver obviates the coordinate singularity, which otherwise arises at the cylindrical symmetric axis, ρ = 0 when defining the discrete Hodge matrices (generalized finite element mass matrices). Here, a cylindrical perfectly matched layer is implemented as a boundary condition in the radial direction to simulate open space problems, with periodic boundary conditions in the axial direction. We investigate effects of charged particles moving next to the cylindrical perfectly matched layer. We model azimuthal currents arising from rotational motion of charged rings, which produce TMΦ polarized fields. Several numerical examples are provided to illustrate the first application of the algorithm.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1955

On the Kernel function of the integral equation relating the lift and downwash distributions of oscillating finite wings in subsonic flow

This report treats the Kernel function of an integral equation that relates a known prescribed downwash distribution to an unknown lift distribution for a harmonically oscillating finite wing in compressible subsonic flow. The Kernel function is reduced to a form that can be accurately evaluated by separating the Kernel function into two parts: a part in which the singularities are isolated and analytically expressed and a nonsingular part which may be tabulated. The form of the Kernel function for the sonic case (Mach number 1) is treated separately. In addition, results for the special cases of Mach number of 0 (incompressible case) and frequency of 0 (steady case) are given. The derivation of the integral equation which involves this Kernel function is reproduced as an appendix. Another appendix gives the reduction of the form of the Kernel function obtained herein for the three-dimensional case to a known result of Possio for two-dimensional flow. A third appendix contains some remarks on the evaluation of the Kernel function, and a fourth appendix presents an alternate form of expression for the Kernel function.

Watkins, Charles E↗
NASA NTRS1988

Dynamic structural correlation via nonlinear programming techniques

A solution to the correlation between structural dynamic test results and finite element analyses of the same components is presented in this paper. Basically, the method can be categorized as a Levenberg-Marquardt type Gauss-Newton method which requires only the differences between FE modal analyses and test results and their first derivatives with respect to preassigned design variables. With proper variable normalization and equation scaling, the method has been made numerically better-conditioned and the inclusion of the Levenberg-Marquardt technique overcomes any remaining difficulty encountered in inverting singular or near-singular matrices. An important feature is that each iteration requires only one function evaluation along with the associated design sensitivity analysis and so the procedure is computationally efficient.

Ting, T.↗
DOE OSTI2024

Electron– K -phonon interaction in twisted bilayer graphene

We develop an analytic theory to describe the interaction between electrons and K phonons and study its influence on superconductivity in the bare bands of twisted bilayer graphene (TBG). We find that, due to symmetry and the two-center approximation, only one optical K phonon (160meV) of graphene is responsible for the intervalley electron-phonon interaction. Here, this phonon has recently been found in angular-resolved photoemission spectroscopy to be responsible for replicas of the TBG flat bands. By projecting the interaction to the TBG flat bands, we perform the full symmetry analysis of the phonon-mediated attractive interaction and pairing channels in the Chern basis, and show that several channels are guaranteed to have gapless order parameters. From the linearized gap equations, we find that the highest T c pairing induced by this phonon is a singlet gapped s-wave inter-Chern-band order parameter, followed closely by a gapless nematic d-wave intra-Chern-band order parameter. We justify these results analytically, using the topological heavy-fermion mapping of TBG which has allowed us to obtain an analytic form of a phonon-mediated attractive interaction and to analytically solve the linearized and T = 0 gap equations. For the intra-Chern-band channel, the nematic state with nodes is shown to be stabilized in the chiral flat-band limit. While the flat-band Coulomb interaction can be screened sufficiently enough—around the Van Hove singularities—to allow for electron-phonon based superconductivity, it is unlikely that this effect can be maintained in the lower density of states excitation bands around the correlated insulator states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗