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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 NTRS1960

Performance of Several Method-of-Characteristics Exhaust Nozzles

Nozzle performance data were obtained with three "method-of-characteristics" nozzles and a 150 conical nozzle at pressure ratios up to 130. Each basic configuration was cut off and tested at expansion ratios of 25, 20, 15, and 10. Unheated dry air was used at nozzle inlet pressures up to 22,000 pounds per square foot absolute. Nozzle thrust data were extrapolated to infinite pressure ratio (zero discharge pressure). As much as 1-percent increase in thrust with no increase in nozzle surface area (weight), can be obtained by using a method-of-characteristics, nozzle instead of a 15 conical nozzle when operating with a nozzle expansion ratio of 25 and nozzle pressure ratios from 200 to infinity. Conversely, for the same thrust, reductions in nozzle divergent surface area in the order of 25 percent are possible. The thrust performance of the method-of-characteristics nozzle was not as good as that of the 150 conical nozzle when operating at pressure ratios considerably below design (below 100 for the expansion ratio 25 nozzles). Theoretical and measured nozzle momentum coefficients agreed within about 0.6 percent. This is the order of accuracy of both the measured and theoretical values.

Farley, John M.↗
NASA NTRS2001

An Implicit Characteristic Based Method for Electromagnetics

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

Beggs, John H.↗
DOE OSTI2013

High order spatial expansion for the method of characteristics applied to 3-D geometries

The method of characteristics is an efficient and flexible technique to solve the neutron transport equation and has been extensively used in two-dimensional calculations because it permits to deal with complex geometries. However, because of a very fast increase in storage requirements and number of floating operations, its direct application to three-dimensional routine transport calculations it is not still possible. In this work we introduce and analyze several modifications aimed to reduce memory requirements and to diminish the computing burden. We explore high-order spatial approximation, the use of intermediary trajectory-dependent flux expansions and the possibility of dynamic trajectory reconstruction from local tracking for typed subdomains. (authors)

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1981

Determination of two-stroke engine exhaust noise by the method of characteristics

A computational technique was developed for the method of characteristics solution of a one-dimensional flow in a duct as applied to the wave action in an engine exhaust system. By using the method, it was possible to compute the unsteady flow in both straight pipe and tuned expansion chamber exhaust systems as matched to the flow from the cylinder of a small two-stroke engine. The radiated exhaust noise was then determined by assuming monopole radiation from the tailpipe outlet. Very good agreement with experiment on an operation engine was achieved in the calculation of both the third octave radiated noise and the associated pressure cycles at several locations in the different exhaust systems. Of particular interest is the significance of nonlinear behavior which results in wave steepening and shock wave formation. The method computes the precise paths on the x-t plane of a finite number of C(sub +), C(sub -) and P characteristics, thereby obtaining high accuracy in determining the tailpipe outlet velocity and the radiated noise.

Jones, A. D.↗
DOE OSTI2023

Adaptive Angular Quadrature Scheme for a backwards-in-time Method of Characteristics Solution to the Radiative Transfer Equation [Slides]

Radiative transfer/radiation transport are important problems to solve in astrophysics and high energy density physics. Various methods exist to solve radiation transport, such as Monte Carlo (MC), Discrete Ordinates (S N ), Method of Characteristics (MOC), and the spherical harmonics (P N ) method. Method of Characteristics requires “launching” of rays in discrete directions. Unresolved details of angular mesh create ray effects and can miss sources in the domain. Ray effects can lead to unphysical “stepping” in solution and incorrect energy deposition. Adaptive quadrature schemes can be used to detect and mitigate these effects. The Method of Characteristics (MOC) is a common method for solving hyperbolic PDEs in radiation transport and supersonic flow problems. Generally in MOC for radiation transport, virtual particles are tracked from birth to the end of a timestep. This requires interpolation to go from final location to cell averaged or corner values of angular intensity. Backwards-in-Time (BIT) particle tracking avoids this by prescribing the final position of the virtual particle at the cell nodes/corners. Angular intensities are computed at time k + 1 by launching ray back to previous timestep(s), or t = 0. Scheme allows solution to be computed as the characteristic ray is traced backwards in time.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1972

Solution of non-isoenergetic supersonic flows by method of characteristics, volume 3

The calculation of supersonic flow fields by the method of characteristics. The theoretical approach to the solution of these flow fields and a computer program to implement the numerical solution of the flow equations are discussed. This versatile program has a flexible set of boundary conditions enabling the calculation of nozzles, plumes and many other complex flow fields. A complete derivation of the equations of motion for reacting gas systems is presented. An important consequence of this derivation is that, for the reaction assumptions which were made, the thermochemistry was shown to be uncoupled from the flow solution and as such could be solved separately. The methods of characteristics equations are shown to be formally the same for ideal, frozen, and equilibrium reacting gas mixtures.

Prozan, R. J.↗
NASA NTRS1991

Characteristics-based methods applied to infinite Prandtl number thermal convection in the hard turbulent regime

Characteristics-based methods for the advection-diffusion equation are presented and directly applied to study thermal convection with extremely large Rayleigh number (Ra). It is shown that the operator-splitting method for advection-diffusion problems is very accurate for determining the advected field at extremely high Peclet number (Pe). The technique presented is considered to have great potential for solving advection-dominated problems, while the Langrangian method is more accurate for lower Pe. It is noted that the accuracy of these characteristics-based methods strongly depends on the quality of interpolation. The computational time for the operator-splitting method grows with the number of time steps employed. The Langrangian method was used for simulations of convection at very high Ra, up to 3 x 10 to the 9th, and time-dependent, thermal convection solutions were obtained for infinite Prandtl number.

Malevsky, A. V.↗
DOE OSTI2013

Synergism of the method of characteristics and CAD technology for neutron transport calculation

The method of characteristics (MOC) is a very popular methodology in neutron transport calculation and numerical simulation in recent decades for its unique advantages. One of the key problems determining whether the MOC can be applied in complicated and highly heterogeneous geometry is how to combine an effective geometry processing method with MOC. Most of the existing MOC codes describe the geometry by lines and arcs with extensive input data, such as circles, ellipses, regular polygons and combination of them. Thus they have difficulty in geometry modeling, background meshing and ray tracing for complicated geometry domains. In this study, a new idea making use of a CAD solid modeler MCAM which is a CAD/Image-based Automatic Modeling Program for Neutronics and Radiation Transport developed by FDS Team in China was introduced for geometry modeling and ray tracing of particle transport to remove these geometrical limitations mentioned above. The diamond-difference scheme was applied to MOC to reduce the spatial discretization error of the flat flux approximation in theory. Based on MCAM and MOC, a new MOC code was developed and integrated into SuperMC system, which is a Super Multi-function Computational system for neutronics and radiation simulation. The numerical testing results demonstrated the feasibility and effectiveness of the new idea for geometry treatment in SuperMC. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1978

Calculation of the flow field in supersonic mixed-compression inlets at angle of attack using the three-dimensional method of characteristics with discrete shock wave fitting

The influence of molecular transport is included in the computation by treating viscous and thermal diffusion terms in the governing partial differential equations as correction terms in the method of characteristics scheme. The development of a production type computer program is reported which is capable of calculating the flow field in a variety of axisymmetric mixed-compression aircraft inlets. The results agreed well with those produced by the two-dimensional method characteristics when axisymmetric flow fields are computed. For three-dimensional flow fields, the results agree well with experimental data except in regions of high viscous interaction and boundary layer removal.

Vadyak, J.↗
DOE OSTI2019

The Subray Method of Characteristics

The MPACT code is being jointly developed by the University of Michigan and Oak Ridge National Laboratory. It uses the 2-D/1-D method to solve neutron transport problems for reactors. The 2-D/1-D method decomposes the problem into a stack of 2-D planes and uses a high-fidelity transport method to resolve all heterogeneity in each plane. These planes are then coupled axially, using a lower-order solver. With this scheme, three-dimensional (3-D) solutions to the transport equation can be obtained at a much lower cost. The 2-D/1-D method assumes that the materials are axially homogeneous for each 2-D plane. Violation of this assumption requires homogenization, which can significantly reduce the accuracy of the calculation. This work proposes the subray method of characteristics (subray MOC) as a solution to this problem. Subray MOC is a subgrid method that allows local heterogeneities to be directly resolved by method of characteristics while treating the rest of the 2-D plane as axially uniform. This improves the accuracy in the neighborhood of the heterogeneity while minimizing the increase in run time. The method was applied to variations of the C5G7 benchmark problems and compared with a previously developed subgrid method called the subplane collision probabilities (SCP) method. Comparisons were made among results obtained using subray MOC, the SCP method, and no subgrid method. Subray MOC consistently performed best, reducing maximum 3-D power distribution errors from as high as 30% to 2% or less. Moreover, it consistently outperformed the SCP method with run times that were shorter than the reference calculations.

2-D/1-D method↗
DOE OSTI2013

Proteus-MOC: A 3D deterministic solver incorporating 2D method of characteristics

A new transport solution methodology was developed by combining the two-dimensional method of characteristics with the discontinuous Galerkin method for the treatment of the axial variable. The method, which can be applied to arbitrary extruded geometries, was implemented in PROTEUS-MOC and includes parallelization in group, angle, plane, and space using a top level GMRES linear algebra solver. Verification tests were performed to show accuracy and stability of the method with the increased number of angular directions and mesh elements. Good scalability with parallelism in angle and axial planes is displayed. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Second-order method of characteristics through local cell refinement

A new approach to the method of characteristics is developed for 2D unstructured triangular mesh that is locally second order accurate with respect to mesh cell size. The second order accuracy is obtained through a local cell refinement and flux reconstruction process. Numerical examples are provided to demonstrate the theoretical error prediction for simple test problems. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Quantifying hydrate solidification front advancing using method of characteristics

Here, we develop a one-dimensional analytical solution based on the method of characteristics to explore hydrate formation from gas injection into brine-saturated sediments within the hydrate stability zone. Our solution includes fully coupled multiphase and multicomponent flow and the associated advective transport in a homogeneous system. Our solution shows that hydrate saturation is controlled by the initial thermodynamic state of the system and changed by the gas fractional flow. Hydrate saturation in gas-rich systems can be estimated by 1 – cl 0 /cl e when Darcy flow dominates, where cl 0 is the initial mass fraction of salt in brine, and cl e is the mass fraction of salt in brine at three-phase (gas, liquid, and hydrate) equilibrium. Hydrate saturation is constant, gas saturation and gas flux decrease, and liquid saturation and liquid flux increase with the distance from the gas inlet to the hydrate solidification front. The total gas and liquid flux is constant from the gas inlet to the hydrate solidification front and decreases abruptly at the hydrate solidification front due to gas inclusion into the hydrate phase. The advancing velocity of the hydrate solidification front decreases with hydrate saturation at a fixed gas inflow rate. This analytical solution illuminates how hydrate is formed by gas injection (methane, CO 2 , ethane, propane) at both the laboratory and field scales.

58 GEOSCIENCES↗