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At least 955 records · Page 53

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NASA NTRS1987

The terminal area simulation system. Volume 1: Theoretical formulation

A three-dimensional numerical cloud model was developed for the general purpose of studying convective phenomena. The model utilizes a time splitting integration procedure in the numerical solution of the compressible nonhydrostatic primitive equations. Turbulence closure is achieved by a conventional first-order diagnostic approximation. Open lateral boundaries are incorporated which minimize wave reflection and which do not induce domain-wide mass trends. Microphysical processes are governed by prognostic equations for potential temperature water vapor, cloud droplets, ice crystals, rain, snow, and hail. Microphysical interactions are computed by numerous Orville-type parameterizations. A diagnostic surface boundary layer is parameterized assuming Monin-Obukhov similarity theory. The governing equation set is approximated on a staggered three-dimensional grid with quadratic-conservative central space differencing. Time differencing is approximated by the second-order Adams-Bashforth method. The vertical grid spacing may be either linear or stretched. The model domain may translate along with a convective cell, even at variable speeds.

Proctor, F. H.↗

NASA NTRSDate not supplied

Numerical Simulation of Lean Blowout of Alternative Fuels in 7-element Lean Direct Injector

This research presents the result of numerically simulating 7-element swirl-venturi Lean Direct Injector (SV-LDI) lean blowout (LBO) experiments conducted at NASA Glenn Research Center in May of 2019. After simulating a cold flow case to confirm the pressure drop agrees well with the experiment, additional cases with two different fuels (an average jet fuel and a Gevo alcohol-to-jet fuel) from the National Jet Fuels Combustion Program (NJFCP) were computed to numerically determine the LBO condition. The procedure to approach the LBO follows the method used in the experiment where the air mass flow rate is gradually increased while the fuel supply is maintained. Transient history of global heat release rate as a function of air flow rate is presented, as well as temperature contours at different conditions to give a visual representation of the flame state. The Open National Combustion Code (OpenNCC) used in this research adopted reduced HyChem (Hybrid Chemistry) models along with k-LES turbulence model and a Lagrangian spray model that takes into account droplet internal temperature distribution affected by the shear force on the droplet surface. The transport equations and chemical reaction terms are integrated together to enhance conservation of chemical species that are especially important in the near LBO conditions. After showing the computed range of LBO agrees well with the experimental measurements, time averaged solutions of both fuels at their initial condition and at their limiting condition just before LBO are compared in detail to facilitate the understanding of LBO mechanism.

combustion↗

NASA NTRS2012

Theory of a Traveling Wave Feed for a Planar Slot Array Antenna

Planar arrays of waveguide-fed slots have been employed in many radar and remote sensing applications. Such arrays are designed in the standing wave configuration because of high efficiency. Traveling wave arrays can produce greater bandwidth at the expense of efficiency due to power loss in the load or loads. Traveling wave planar slot arrays may be designed with a long feed waveguide consisting of centered-inclined coupling slots. The feed waveguide is terminated in a matched load, and the element spacing in the feed waveguide is chosen to produce a beam squinted from the broadside. The traveling wave planar slot array consists of a long feed waveguide containing resonant-centered inclined coupling slots in the broad wall, coupling power into an array of stacked radiating waveguides orthogonal to it. The radiating waveguides consist of longitudinal offset radiating slots in a standing wave configuration. For the traveling wave feed of a planar slot array, one has to design the tilt angle and length of each coupling slot such that the amplitude and phase of excitation of each radiating waveguide are close to the desired values. The coupling slot spacing is chosen for an appropriate beam squint. Scattering matrix parameters of resonant coupling slots are used in the design process to produce appropriate excitations of radiating waveguides with constraints placed only on amplitudes. Since the radiating slots in each radiating waveguide are designed to produce a certain total admittance, the scattering (S) matrix of each coupling slot is reduced to a 2x2 matrix. Elements of each 2x2 S-matrix and the amount of coupling into the corresponding radiating waveguide are expressed in terms of the element S11. S matrices are converted into transmission (T) matrices, and the T matrices are multiplied to cascade the coupling slots and waveguide sections, starting from the load end and proceeding towards the source. While the use of non-resonant coupling slots may provide an additional degree of freedom in the design, resonant coupling slots simplify the design process. The amplitude of the wave going to the load is set at unity. The S11 parameter, r of the coupling slot closest to the load, is assigned an arbitrary value. A larger value of r will reduce the power dissipated in the load while increasing the reflection coefficient at the input port. It is now possible to obtain the excitation of the radiating waveguide closest to the load and the coefficients of the wave incident and reflected at the input port of this coupling slot. The next coupling slot parameter, r , is chosen to realize the excitation of that radiating waveguide. One continues this process moving towards the source, until all the coupling slot parameters r and hence the S11 parameter of the 4-port coupler, r, are known for each coupling slot. The goal is to produce the desired array aperture distribution in the feed direction. From an interpolation of the computed moment method data for the slot parameters, all the coupling slot tilt angles and lengths are obtained. From the excitations of the radiating waveguides computed from the coupling values, radiating slot parameters may be obtained so as to attain the desired total normalized slot admittances. This process yields the radiating slot parameters, offsets, and lengths. The design is repeated by choosing different values of r for the last coupling slot until the percentage of power dissipated in the load and the input reflection coefficient values are satisfactory. Numerical results computed for the radiation pattern, the tilt angles and lengths of coupling slots, and excitation phases of the radiating waveguides, are presented for an array with uniform amplitude excitation. The design process has been validated using computer simulations. This design procedure is valid for non-uniform amplitude excitations as well.

Rengarajan, Sembiam↗

DOE OSTI2020

Efficient Fourier transforms for transverse momentum dependent distributions

Hadron production at low transverse momenta in semi-inclusive deep inelastic scattering can be described by transverse momentum dependent (TMD) factorization. This formalism has also been widely used to study the Drell-Yan process and back-to-back hadron pair production in $e^+e^-$ collisions. These processes are the main ones for extractions of TMD parton distribution functions and TMD fragmentation functions, which encode important information about nucleon structure and hadronization. One of the most widely used TMD factorization formalism in phenomenology formulates TMD observables in coordinate $b_\perp$-space, the conjugate space of the transverse momentum. The Fourier transform from $b_\perp$-space back into transverse momentum space is sufficiently complicated due to oscillatory integrands that it requires a careful and computationally intensive numerical treatment in order to avoid potentially large numerical errors. Within the TMD formalism, the azimuthal angular dependence is analytically integrated and the two-dimensional $b_\perp$ integration reduces to a one-dimensional integration over the magnitude $b_\perp$. In this paper we develop a fast numerical Hankel transform algorithm for such a $b_\perp$-integration that improves the numerical accuracy of TMD calculations in all standard processes. Libraries for this algorithm are implemented in Python 2.7 and 3, C++, as well as FORTRAN77. All packages are made available open source.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A modified model parametrization algorithm for solving a special type of heat and mass transfer systems

A new method for solving nonlinear heat and mass transfer design tasks was considered. Systems using the Number of Transfer Units (NTU) method are a special type of mathematical model of heat and mass exchangers. It was observed, that the NTU models in a form of differential-algebraic equations (DAEs) cannot be directly solved with higher values of NTU. The requirements for consistent initial conditions, as well as numerical limitations of DAEs solvers, result, that the solution to the considered design problems that cannot be obtained by a classical direct shooting procedure. To overcome the presented difficulties, the αDAE model optimization algorithm was adjusted for solving NTU-based models. The new approach consists of 3 main steps: 1) task discretization by a multiple-shooting approach, 2) design an appropriate function $f_{NTU}$(α) to effectively influence the variability of the state variables described by dynamical relations, 3) the iterative numerical optimization algorithm for the new parametrized system. Moreover, computations can be performed by a chosen numerical optimization approach, which can be communicated with an available outer procedure for solving differential-algebraic equations. The presented algorithm was implemented and applied to solve the design task with the NTU model of a counter-flow exchanger. Here, the new approach was used to modify the system dynamics to influence the difficulty of the considered problem. Finally, the presented method enabled failure-free numerical computations for the higher values of the NTU parameter.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Towards developing robust algorithms for solving partial differential equations on MIMD machines

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Saltz, J. H.↗

NASA NTRS1988

Towards developing robust algorithms for solving partial differential equations on MIMD machines

Saltz, Joel H.↗

NASA NTRS1994

The ozone depletion potentials on halocarbons: Their dependence of calculation assumptions

The concept of Ozone Depletion Potential (ODP) is widely used in the evaluation of numerous halocarbons and of their replacement effects on ozone, but the methods, assumptions and conditions used in ODP calculations have not been analyzed adequately. In this paper a model study of effects on ozone of the instantaneous releases of various amounts of CH3CCl3 and of CHF2Cl (HCFC-22) for several compositions of the background atmosphere are presented, aimed at understanding connections of ODP values with the assumptions used in their calculations. To facilitate the ODP computation in numerous versions for the long time periods after their releases, the above rather short-lived gases and the one-dimensional radiative photochemical model of the global annually averaged atmospheric layer up to 50 km height are used. The variation of released gas global mass from 1 Mt to 1 Gt leads to ODP value increase with its stabilization close to the upper bound of this range in the contemporary atmosphere. The same variations are analyzed for conditions of the CFC-free atmosphere of 1960's and for the anthropogenically loaded atmosphere in the 21st century according to the known IPCC 'business as usual' scenario. Recommendations for proper ways of ODP calculations are proposed for practically important cases.

Karol, Igor L.↗

NASA NTRS1984

Airfoil computation at high angles of attack, inviscid and viscous phenomena

An implicit central difference code is used to calculate two dimensional inviscid and thin-layer Navier-Stokes solutions for flow about an NACA0012 airfoil at high angles of attack. Among the issues addressed are whether separation can occur in an inviscid calculation and what the causes would be of such separation. Examples are shown of inviscid shocked flow with and without separation and shock-free flow with separation. An Euler solution with self-induced oscillation and separation driven by a strong shock is contrasted with a shock-free solution whose separation is caused by numerical error. Computed solutions to the Euler equations are compared to those of the potential equations. Comparisons are also made between experimental data from wind tunnel tests and viscous calculations at similar conditions.

Barton, J. T.↗

NASA NTRS1992

Computational structures technology and UVA Center for CST

Rapid advances in computer hardware have had a profound effect on various engineering and mechanics disciplines, including the materials, structures, and dynamics disciplines. A new technology, computational structures technology (CST), has recently emerged as an insightful blend between material modeling, structural and dynamic analysis and synthesis on the one hand, and other disciplines such as computer science, numerical analysis, and approximation theory, on the other hand. CST is an outgrowth of finite element methods developed over the last three decades. The focus of this presentation is on some aspects of CST which can impact future airframes and propulsion systems, as well as on the newly established University of Virginia (UVA) Center for CST. The background and goals for CST are described along with the motivations for developing CST, and a brief discussion is made on computational material modeling. We look at the future in terms of technical needs, computing environment, and research directions. The newly established UVA Center for CST is described. One of the research projects of the Center is described, and a brief summary of the presentation is given.

Noor, Ahmed K.↗

NASA NTRS1972

The selection of approximating functions for tabulated numerical data

A computer program was developed that selects, from a list of candidate functions, the approximating functions and associated coefficients which result in the best curve fit of a given set of numerical data. The advantages of the approach used here are: (1) Multivariable approximations can be performed. (2) Flexibility with respect to the type of approximations used is available. (3) The program is designed to choose the best terms to be used in the approximation from an arbitrary list of possible terms so that little knowledge of the proper approximating form is required. (4) Recursion relations are used in determining the coefficients of the approximating functions, which reduces the computer execution time of the program.

Ingram, H. L.↗

NASA NTRS1989

The numerical solution of the Navier-Stokes equations for 3-dimensional, unsteady, incompressible flows by compact schemes

The present numerical method for the solution of unsteady, incompressible three-dimensional flow Navier-Stokes equations using velocity-vorticity variables and irregular Cartesian grids proceeds by solving: (1) equations of Cauchy-Riemann type for the velocity; and (2) transport-diffusion equations for the vorticity, whose solenoidal vorticity components are generated by a Poisson equation for an appropriate scalar potential. Iterations are used to solve the finite difference equations, facilitating the use of vector and parallel-computing methods; numerical experiments have verified the method's second-order spatial and temporal accuracy.

Gatski, T. B.↗

NASA NTRS1995

"Recognizing Numerical Constants"

The advent of inexpensive, high performance computer and new efficient algorithms have made possible the automatic recognition of numerically computed constants. In other words, techniques now exist for determining, within certain limits, whether a computed real or complex number can be written as a simple expression involving the classical constants of mathematics. In this presentation, some of the recently discovered techniques for constant recognition, notably integer relation detection algorithms, will be presented. As an application of these methods, the author's recent work in recognizing "Euler sums" will be described in some detail.

Bailey, David H.↗

DOE OSTI2025

Hybrid quantum simulations with qubits and qumodes on trapped-ion platforms

We explore the feasibility of gate-based hybrid quantum computing using both discrete (qubit) and continuous (qumode) variables on trapped-ion platforms. Trapped-ion systems have demonstrated record one- and two-qubit gate fidelities and long qubit coherence times, while qumodes, which can be represented by the collective vibrational modes of the ion chain, have remained relatively unex- plored for their use in computing. Using numerical simulations, we show that high-fidelity hybrid gates and measurement operations can be achieved for existing trapped-ion quantum platforms. As an exemplary application, we consider quantum simulations of the Jaynes-Cummings-Hubbard model, which is given by a one-dimensional chain of interacting spin and boson degrees of free- dom. Using classical simulations, we study its real-time evolution and develop a suitable variational quantum algorithm for ground state preparation. Furthermore, our results motivate further studies of hybrid quantum computing in this context, which may lead to direct applications in condensed matter and fundamental particle and nuclear physics.

Lower-dimensional field theories↗

DOE OSTI2021

A scalable algorithm for the optimization of neural network architectures

In this work, we propose a new scalable method to optimize the architecture of an artificial neural network. The proposed algorithm, called Greedy Search for Neural Network Architecture, aims to determine a neural network with minimal number of layers that is at least as performant as neural networks of the same structure identified by other hyperparameter search algorithms in terms of accuracy and computational cost. Numerical results performed on benchmark datasets show that, for these datasets, our method outperforms state-of-the-art hyperparameter optimization algorithms in terms of attainable predictive performance by the selected neural network architecture, and time-to-solution for the hyperparameter optimization to complete.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1981

Computer prediction of dual reflector antenna radiation properties

A program for calculating radiation patterns for reflector antennas with either smooth analytic surfaces or with surfaces composed of a number of panels. Techniques based on the geometrical optics (GO) approach were used in tracing rays over the following regions: from a feed antenna to the first reflector surface (subreflector); from this reflector to a larger reflector surface (main reflector); and from the main reflector to a mathematical plane (aperture plane) in front of the main reflector. The equations of GO were also used to calculate the reflected field components for each ray making use of the feed radiation pattern and the parameters defining the surfaces of the two reflectors. These resulting fields form an aperture distribution which is integrated numerically to compute the radiation pattern for a specified set of angles.

Christodoulou, C.↗

NASA NTRS1993

The combustion program at CTR

Understanding and modeling of turbulent combustion are key problems in the computation of numerous practical systems. Because of the lack of analytical theories in this field and of the difficulty of performing precise experiments, direct numerical simulation (DNS) appears to be one of the most attractive tools to use in addressing this problem. The general objective of DNS of reacting flows is to improve our knowledge of turbulent combustion but also to use this information for turbulent combustion models. For the foreseeable future, numerical simulation of the full three-dimensional governing partial differential equations with variable density and transport properties as well as complex chemistry will remain intractable; thus, various levels of simplification will remain necessary. On one hand, the requirement to simplify is not necessarily a handicap: numerical simulations allow the researcher a degree of control in isolating specific physical phenomena that is inaccessible in experiments. CTR has pursued an intensive research program in the field of DNS for turbulent reacting flows since 1987. DNS of reacting flows is quite different from DNS of non-reacting flows: without reaction, the equations to solve are clearly the five conservation equations of the Navier Stokes system for compressible situations (four for incompressible cases), and the limitation of the approach is the Reynolds number (or in other words the number of points in the computation). For reacting flows, the choice of the equations, the species (each species will require one additional conservation equation), the chemical scheme, and the configuration itself is more complex.

Poinsot, Thierry J.↗

NASA NTRS2011

Measurement of CPAS Main Parachute Rate of Descent

The Crew Exploration Vehicle Parachute Assembly System (CPAS) is being designed to land the Orion Crew Module (CM) at a safe rate of descent at splashdown. Flight test performance must be measured to a high degree of accuracy to ensure this requirement is met with the most efficient design possible. Although the design includes three CPAS Main parachutes, the requirement is that the system must not exceed 33 ft/s under two Main parachutes, should one of the Main parachutes fail. Therefore, several tests were conducted with clusters of two Mains. All of the steady-state rate of descent data are normalized to standard sea level conditions and checked against the limit. As the Orion design gains weight, the system is approaching this limit to within measurement precision. Parachute "breathing," cluster interactions, and atmospheric anomalies can cause the rate of descent to vary widely and lead to challenges in characterizing parachute terminal performance. An early test had contradictory rate of descent results from optical trajectory and Differential Global Positioning Systems (DGPS). A thorough analysis of the data sources and error propagation was conducted to determine the uncertainty in the trajectory. It was discovered that the Time Space Position Information (TSPI) from the optical tracking provided accurate position data. However, the velocity from TPSI must be computed via numerical differentiation, which is prone to large error. DGPS obtains position through pseudo-range calculations from multiple satellites and velocity through Doppler shift of the carrier frequency. Because the velocity from DGPS is a direct measurement, it is more accurate than TSPI velocity. To remedy the situation, a commercial off-the-shelf product that combines GPS and an Inertial Measurement Unit (IMU) was purchased to significantly improve rate of descent measurements. This had the added benefit of solving GPS dropouts during aircraft extraction. Statistical probability distributions for CPAS Main parachute rate of descent and drag coefficient were computed and plotted. Using test data, a terminal rate of descent at splashdown can be estimated as a function of canopy loading.

Ray, Eric S.↗