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Rocket exhaust plume computer program improvement. Volume 1: Summary: Method of characteristics nozzle and plume programs

A summary is presented of the various documents that discuss and describe the computer programs and analysis techniques which are available for rocket nozzle and exhaust plume calculations. The basic method of characteristics program is discussed, along with such auxiliary programs as the plume impingement program, the plot program and the thermochemical properties program.

Ratliff, A. W.↗

Linear source method of characteristics in HELIOS2

The Studsvik Scandpower code HELIOS2 is a fast lattice transport code that has gained wide use for reactor fuel cycle analysis in commercial, regulatory, and research environments. It contains two transport solvers - Collision Probabilities (CP) and Method of Characteristics (MoC) - with a general geometry ability and generalized depletion for a variety of fuel types, experimental facilities, and isotope production applications. The HELIOS2 lattice code has been extended with the development of a linear source MoC option. The linear source equations are derived within the scope of the HELIOS2 general geometry and non-cyclic ray tracing. The implementation was tested for fine and coarse spatial mesh models of the 2D C5G7 MOX computational benchmark, which provides a pure and extreme test of a transport solver. The linear source yields at least comparable accuracy with reduced computational resource requirements relative to the flat-source approximation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Preliminary study on applying the method of characteristics to pebble-bed HTR - 18637

Neutron transport in high temperature pebble-bed gas-cooled reactor, which is a promising generation IV reactor candidate with cylindrical core, graphite moderator and spherical TRISO coated particles fuel, is of great interest. However, the stochastic method namely Monte Carlo faces with tremendous simulation of particles and the conventional two-step method featured by homogenization only can give the scalar flux. In this paper, method of characteristics is trying to be applied to pebble bed reactor because of its advantages in arbitrary geometry and the ability to obtain solution in neutronically large domains. Some challenges occur when it comes to HTR. First, the amount of calculation and the memory requirement are huge due to the large quantities of spherical fuel and stochastic distribution of pebbles. Second, the arrangement of characteristics and ray tracing process is more complex comparing to LWR with cuboid geometry because the stochastic distribution of the spherical assemblies and the longer neutron mean free path in pebble bed HTR. Third, the treatment of the multiscale sphere fuel need be detail studied to determine the subdivision of flat source region. At present, preliminary research on this subject is undergoing. This paper is concentrated on the modeling of the pebble-bed reactor core by constructive solid geometry (CSG) which allows complex spatial models to be built using boolean operations, characteristics arrangement and the treatment of boundary condition. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Method of characteristics design of a supersonic wind tunnel nozzle with square cross-section, supplement 3

Nozzle design codes developed earlier were modified and used in order to design a supersonic wind tunnel nozzle with square cross-sections. As part of the design process, a post-processing code that generates square nozzles from the output of the Sivells code was written. The method is based on the results of an axisymmetric method of characteristics code and an axisymmetric boundary layer code. These design codes are documented.

Schneider, Steven P.↗

A massively parallel method of characteristic neutral particle transport code for GPUs

Over the past 20 years, parallel computing has enabled computers to grow ever larger and more powerful while scientific applications have advanced in sophistication and resolution. This trend is being challenged, however, as the power consumption for conventional parallel computing architectures has risen to unsustainable levels and memory limitations have come to dominate compute performance. Heterogeneous computing platforms, such as Graphics Processing Units (GPUs), are an increasingly popular paradigm for solving these issues. This paper explores the applicability of GPUs for deterministic neutron transport. A 2D method of characteristics (MOC) code - OpenMOC - has been developed with solvers for both shared memory multi-core platforms as well as GPUs. The multi-threading and memory locality methodologies for the GPU solver are presented. Performance results for the 2D C5G7 benchmark demonstrate 25-35 x speedup for MOC on the GPU. The lessons learned from this case study will provide the basis for further exploration of MOC on GPUs as well as design decisions for hardware vendors exploring technologies for the next generation of machines for scientific computing. (authors)

97 MATHEMATICS AND COMPUTING↗

Variable Step Integration Coupled with the Method of Characteristics Solution for Water-Hammer Analysis, A Case Study

One-dimensional water-hammer modeling involves the solution of two coupled non-linear hyperbolic partial differential equations (PDEs). These equations result from applying the principles of conservation of mass and momentum to flow through a pipe, and usually the assumption that the speed at which pressure waves propagate through the pipe is constant. In order to solve these equations for the interested quantities (i.e. pressures and flow rates), they must first be converted to a system of ordinary differential equations (ODEs) by either approximating the spatial derivative terms with numerical techniques or using the Method of Characteristics (MOC). The MOC approach is ideal in that no numerical approximation errors are introduced in converting the original system of PDEs into an equivalent system of ODEs. Unfortunately this resulting system of ODEs is bound by a time step constraint so that when integrating the equations the solution can only be obtained at fixed time intervals. If the fluid system to be modeled also contains dynamic components (i.e. components that are best modeled by a system of ODEs), it may be necessary to take extremely small time steps during certain points of the model simulation in order to achieve stability and/or accuracy in the solution. Coupled together, the fixed time step constraint invoked by the MOC, and the occasional need for extremely small time steps in order to obtain stability and/or accuracy, can greatly increase simulation run times. As one solution to this problem, a method for combining variable step integration (VSI) algorithms with the MOC was developed for modeling water-hammer in systems with highly dynamic components. A case study is presented in which reverse flow through a dual-flapper check valve introduces a water-hammer event. The predicted pressure responses upstream of the check-valve are compared with test data.

Turpin, Jason B.↗

Large area polysilicon films with predetermined stress characteristics and method for producing same

Multi-layer assemblies of polysilicon thin films having predetermined stress characteristics and techniques for forming such assemblies are disclosed. In particular, a multi-layer assembly of polysilicon thin films may be produced that has a stress level of zero, or substantially so. The multi-layer assemblies comprise at least one constituent thin film having a tensile stress and at least one constituent thin film having a compressive stress. The thin films forming the multi-layer assemblies may be disposed immediately adjacent to one another without the use of intermediate layers between the thin films. Multi-layer assemblies exhibiting selectively determinable overall bending moments are also disclosed. Selective production of overall bending moments in microstructures enables manufacture of such structures with a wide array of geometrical configurations.

Heuer, Arthur H.↗

Nonstationary Gas Flow in Thin Pipes of Variable Cross Section

Characteristic methods for nonstationary flows have been published only for the special case of the isentropic flow up until the present, althought they are applicable in various places to more difficult questions too. This report derives the characteristic method for the flows which depend only on the position coordinates and time. At the same time the treatment of compression shocks is shown.

Guderley, G.↗

Limitations of the method of characteristics when applied to axisymmetric hypersonic nozzle design

A design study of axisymmetric hypersonic wind tunnel nozzles was initiated by NASA Langley Research Center with the objective of improving the flow quality of their ground test facilities. Nozzles for Mach 6 air, Mach 13.5 nitrogen, and Mach 17 nitrogen were designed using the Method of Characteristics/Boundary Layer (MOC/BL) approach and were analyzed with a Navier-Stokes solver. Results of the analysis agreed well with design for the Mach 6 case, but revealed oblique shock waves of increasing strength originating from near the inflection point of the Mach 13.5 and Mach 17 nozzles. The findings indicate that the MOC/BL design method has a fundamental limitation that occurs at some Mach number between 6 an 13.5. In order to define the limitation more exactly and attempt to discover the cause, a parametric study of hypersonic ideal air nozzles designed with the current MOC/BL method was done. Results of this study indicate that, while stagnations conditions have a moderate affect on the upper limit of the method, the method fails at Mach numbers above 8.0.

Edwards, Anne C.↗

The Blunt Plate In Hypersonic Flow

The sonic-wedge characteristics method has been used to obtain the shock shapes and surface pressure distributions on several blunt two-dimensional shapes in a hypersonic stream for several values of the ratio of specific heats. These shapes include the blunt slab at angle of attack and power profiles of the form yb = a)P, where 0 les than m less than 1, Yb and x are coordinates of the body surface, and a is a constant. These numerical results have been compared with the results of blast-wave theory, and methods of predicting the pressure distributions and shock shapes are proposed in each case. The effects of a free-stream conical-flow gradient on the pressure distribution on a blunt slab in hypersonic flow were investigated by the sonic-wedge characteristics method and were found to be sizable in many cases. Procedures which are satisfactory for reducing pressure data obtained in conical flows with small gradients are presented.

Baradell, Donald L.↗

The method of modular characteristic direction probabilities in MPACT

The method of characteristic direction probabilities (CDP) is based on a modular ray tracing technique which combines the benefits of the collision probability method (CPM) and the method of characteristics (MOC). This past year CDP was implemented in the transport code MPACT for 2-D and 3-D transport calculations. By only coupling the fine mesh regions passed by the characteristic rays in the particular direction, the scale of the probabilities matrix is much smaller compared to the CPM. At the same time, the CDP has the same capacity of dealing with the complicated geometries with the MOC, because the same modular ray tracing techniques are used. Results from the C5G7 benchmark problems are given for different cases to show the accuracy and efficiency of the CDP compared to MOC. For the cases examined, the CDP and MOC methods were seen to differ in k{sub eff} by about 1-20 pcm, and the computational efficiency of the CDP appears to be better than the MOC for some problems. However, in other problems, particularly when the CDP matrices have to be recomputed from changing cross sections, the CDP does not perform as well. This indicates an area of future work. (authors)

97 MATHEMATICS AND COMPUTING↗