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Uncertainty Analysis of Decomposing Polyurethane Foam

Sensitivity/uncertainty analyses are necessary to determine where to allocate resources for improved predictions in support of our nation's nuclear safety mission. Yet, sensitivity/uncertainty analyses are not commonly performed on complex combustion models because the calculations are time consuming, CPU intensive, nontrivial exercises that can lead to deceptive results. To illustrate these ideas, a variety of sensitivity/uncertainty analyses were used to determine the uncertainty associated with thermal decomposition of polyurethane foam exposed to high radiative flux boundary conditions. The polyurethane used in this study is a rigid closed-cell foam used as an encapsulant. Related polyurethane binders such as Estane are used in many energetic materials of interest to the JANNAF community. The complex, finite element foam decomposition model used in this study has 25 input parameters that include chemistry, polymer structure, and thermophysical properties. The response variable was selected as the steady-state decomposition front velocity calculated as the derivative of the decomposition front location versus time. An analytical mean value sensitivity/uncertainty (MV) analysis was used to determine the standard deviation by taking numerical derivatives of the response variable with respect to each of the 25 input parameters. Since the response variable is also a derivative, the standard deviation was essentially determined from a second derivative that was extremely sensitive to numerical noise. To minimize the numerical noise, 50-micrometer element dimensions and approximately 1-msec time steps were required to obtain stable uncertainty results. As an alternative method to determine the uncertainty and sensitivity in the decomposition front velocity, surrogate response surfaces were generated for use with a constrained Latin Hypercube Sampling (LHS) technique. Two surrogate response surfaces were investigated: 1) a linear surrogate response surface (LIN) and 2) a quadratic response surface (QUAD). The LHS techniques do not require derivatives of the response variable and are subsequently relatively insensitive to numerical noise. To compare the LIN and QUAD methods to the MV method, a direct LHS analysis (DLHS) was performed using the full grid and timestep resolved finite element model. The surrogate response models (LIN and QUAD) are shown to give acceptable values of the mean and standard deviation when compared to the fully converged DLHS model.

Hobbs, Michael L.

Implementation of a Message Passing Interface into a Cloud-Resolving Model for Massively Parallel Computing

The capability for massively parallel programming (MPP) using a message passing interface (MPI) has been implemented into a three-dimensional version of the Goddard Cumulus Ensemble (GCE) model. The design for the MPP with MPI uses the concept of maintaining similar code structure between the whole domain as well as the portions after decomposition. Hence the model follows the same integration for single and multiple tasks (CPUs). Also, it provides for minimal changes to the original code, so it is easily modified and/or managed by the model developers and users who have little knowledge of MPP. The entire model domain could be sliced into one- or two-dimensional decomposition with a halo regime, which is overlaid on partial domains. The halo regime requires that no data be fetched across tasks during the computational stage, but it must be updated before the next computational stage through data exchange via MPI. For reproducible purposes, transposing data among tasks is required for spectral transform (Fast Fourier Transform, FFT), which is used in the anelastic version of the model for solving the pressure equation. The performance of the MPI-implemented codes (i.e., the compressible and anelastic versions) was tested on three different computing platforms. The major results are: 1) both versions have speedups of about 99% up to 256 tasks but not for 512 tasks; 2) the anelastic version has better speedup and efficiency because it requires more computations than that of the compressible version; 3) equal or approximately-equal numbers of slices between the x- and y- directions provide the fastest integration due to fewer data exchanges; and 4) one-dimensional slices in the x-direction result in the slowest integration due to the need for more memory relocation for computation.

Juang, Hann-Ming Henry

Massively Parallel Dantzig-Wolfe Decomposition Applied to Traffic Flow Scheduling

Optimal scheduling of air traffic over the entire National Airspace System is a computationally difficult task. To speed computation, Dantzig-Wolfe decomposition is applied to a known linear integer programming approach for assigning delays to flights. The optimization model is proven to have the block-angular structure necessary for Dantzig-Wolfe decomposition. The subproblems for this decomposition are solved in parallel via independent computation threads. Experimental evidence suggests that as the number of subproblems/threads increases (and their respective sizes decrease), the solution quality, convergence, and runtime improve. A demonstration of this is provided by using one flight per subproblem, which is the finest possible decomposition. This results in thousands of subproblems and associated computation threads. This massively parallel approach is compared to one with few threads and to standard (non-decomposed) approaches in terms of solution quality and runtime. Since this method generally provides a non-integral (relaxed) solution to the original optimization problem, two heuristics are developed to generate an integral solution. Dantzig-Wolfe followed by these heuristics can provide a near-optimal (sometimes optimal) solution to the original problem hundreds of times faster than standard (non-decomposed) approaches. In addition, when massive decomposition is employed, the solution is shown to be more likely integral, which obviates the need for an integerization step. These results indicate that nationwide, real-time, high fidelity, optimal traffic flow scheduling is achievable for (at least) 3 hour planning horizons.

Rios, Joseph Lucio

An optimization model for energy generation and distribution in a dynamic facility

An analytical model is described using linear programming for the optimum generation and distribution of energy demands among competing energy resources and different economic criteria. The model, which will be used as a general engineering tool in the analysis of the Deep Space Network ground facility, considers several essential decisions for better design and operation. The decisions sought for the particular energy application include: the optimum time to build an assembly of elements, inclusion of a storage medium of some type, and the size or capacity of the elements that will minimize the total life-cycle cost over a given number of years. The model, which is structured in multiple time divisions, employ the decomposition principle for large-size matrices, the branch-and-bound method in mixed-integer programming, and the revised simplex technique for efficient and economic computer use.

Lansing, F. L.

Neurocomputing strategies in decomposition based structural design

The present paper explores the applicability of neurocomputing strategies in decomposition based structural optimization problems. It is shown that the modeling capability of a backpropagation neural network can be used to detect weak couplings in a system, and to effectively decompose it into smaller, more tractable, subsystems. When such partitioning of a design space is possible, parallel optimization can be performed in each subsystem, with a penalty term added to its objective function to account for constraint violations in all other subsystems. Dependencies among subsystems are represented in terms of global design variables, and a neural network is used to map the relations between these variables and all subsystem constraints. A vector quantization technique, referred to as a z-Network, can effectively be used for this purpose. The approach is illustrated with applications to minimum weight sizing of truss structures with multiple design constraints.

Szewczyk, Z.

Upward Flame Spread Over Thin Solids in Partial Gravity

The effects of partial-gravity, reduced pressure, and sample width on upward flame spread over a thin cellulose fuel were studied experimentally and the results were compared to a numerical flame spread simulation. Fuel samples 1-cm, 2-cm, and 4-cm wide were burned in air at reduced pressures of 0.2 to 0.4 atmospheres in simulated gravity environments of 0.1-G, 0.16-G (Lunar), and 0.38-G (Martian) onboard the NASA KC-135 aircraft and in normal-gravity tests. Observed steady flame propagation speeds and pyrolysis lengths were approximately proportional to the gravity level. Flames spread more quickly and were longer with the wider samples and the variations with gravity and pressure increased with sample width. A numerical simulation of upward flame spread was developed including three-dimensional Navier-Stokes equations, one-step Arrhenius kinetics for the gas phase flame and for the solid surface decomposition, and a fuel-surface radiative loss. The model provides detailed structure of flame temperatures, the flow field interactions with the flame, and the solid fuel mass disappearance. The simulation agrees with experimental flame spread rates and their dependence on gravity level but predicts a wider flammable region than found by experiment. Some unique three-dimensional flame features are demonstrated in the model results.

Feier, I. I.

Fluid-structural interactions using Navier-Stokes flow equations coupled with shell finite element structures

A computational procedure is presented to study fluid-structural interaction problems for three-dimensional aerospace structures. The flow is modeled using the three-dimensional unsteady Euler/Navier-Stokes equations and solved using the finite-difference approach. The three dimensional structure is modeled using shell/plate finite-element formulation. The two disciplines are coupled using a domain decomposition approach. Accurate procedures both in time and space are developed to combine the solutions from the flow equations with those of the structural equations. Time accuracy is maintained using aeroelastic configuration-adaptive moving grids that are computed every time step. The work done by aerodynamic forces due to structural deformations is preserved using consistent loads. The present procedure is validated by computing the aeroelastic response of a wing and comparing with experiment. Results are illustrated for a typical wing-body configuration.

Guruswamy, Guru P.

Quantum chemical calculation of the equilibrium structures of small metal atom clusters

A decomposition of the molecular energy is presented that is motivated by the atom superposition and electron delocalization physical model of chemical binding. The energy appears in physically transparent form consisting of a classical electrostatic interaction, a zero order two electron exchange interaction, a relaxation energy, and the atomic energies. Detailed formulae are derived in zero and first order of approximation. The formulation extends beyond first order to any chosen level of approximation leading, in principle, to the exact energy. The structure of this energy decomposition lends itself to the fullest utilization of the solutions to the atomic sub problems to simplify the calculation of the molecular energy. If nonlinear relaxation effects remain minor, the molecular energy calculation requires at most the calculation of two center, two electron integrals. This scheme thus affords the prospects of substantially reducing the computational effort required for the calculation of molecular energies.

Kahn, L. R.

Control of elastic robotic systems by nonlinear inversion and modal damping

Energy efficient, lightweight robot arms for space applications have considerable structural flexibility. For large and fast motions, both the nonlinear coupled dynamics and the elastic behavior of the robots must be considered in control system designs. This paper presents an approach to the control of a class of flexible robotic systems. A control law is derived which decouples the joint-angle motion from the flexible motion and asymptotically decomposes the elastic dynamics into two subsystems, representing the transverse vibrations of the elastic link in two orthogonal planes. This decomposition allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertainty in system parameters. Simulation results are presented to show that large, fast control of joint angles can be performed in spite of space vehicle motion and uncertainty in the payload.

Singh, S. N.

Thermostructural Analysis of Carbon Cloth Phenolic Material Tested at the Laser Hardened Material Evaluation Laboratory

RSRM nozzle liner components have been analyzed and tested to explore the occurrence of anomalous material performance known as pocketing erosion. Primary physical factors that contribute to pocketing seem to include the geometric permeability, which governs pore pressure magnitudes and hence load, and carbon fiber high temperature tensile strength, which defines a material limiting capability. The study reports on the results of a coupled thermostructural finite element analysis of Carbon Cloth Phenolic (CCP) material tested at the Laser Hardened Material Evaluation Laboratory (the LHMEL facility). Modeled test configurations will be limited to the special case of where temperature gradients are oriented perpendicular to the composite material ply angle. Analyses were conducted using a transient, one-dimensional flow/thermal finite element code that models pore pressure and temperature distributions and in an explicitly coupled formulation, passes this information to a 2-dimensional finite element structural model for determination of the stress/deformation behavior of the orthotropic fiber/matrix CCP. Pore pressures are generated by thermal decomposition of the phenolic resin which evolve as a multi-component gas phase which is partially trapped in the porous microstructure of the composite. The nature of resultant pressures are described by using the Darcy relationships which have been modified to permit a multi-specie mass and momentum balance including water vapor condensation. Solution to the conjugate flow/thermal equations were performed using the SINDA code. Of particular importance to this problem was the implementation of a char and deformation state dependent (geometric) permeability as describing a first order interaction between the flow/thermal and structural models. Material property models are used to characterize the solid phase mechanical stiffness and failure. Structural calculations were performed using the ABAQUS code. Iterations were made between the two codes involving the dependent variables temperature, pressure and across-ply strain level. Model results comparisons are made for three different surface heat rates and dependent variable sensitivities discussed for the various cases.

Clayton, J. Louie

Nonequilibrium shock wave structure, 1. Kinetics of nitric oxide formation and decomposition, 2

Theoretical and numerical aspects of molecular flow simulation focussed on the development of collision models for diatomic and triatomic gases undergoing rotational excitation and energy exchange. A laser absorption technique is proposed and analyzed as sufficiently sensitive for measuring rotational populations in a nonequilibrium shock wave. Also reported is a survey of available literature on NO chemical rate data in preparation for experiments on NO decompensation kinetics in atmospheric pollution.

Kruger, C. H.

Model-size reduction technique for the analysis of symmetric anisotropic structures

A two-step computational procedure is presented for reducing the size of the analysis model for an anisotropic symmetric structure to that of the corresponding orthotropic structure. The key elements of the procedure are: (1) decomposition of the stiffness matrix into the sum of an orthotropic and nonorthotropic (anisotropic) parts; and (2) successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique. The global approximation vectors are selected to be the solution corresponding to zero nonorthotropic matrix and its various-order derivatives with respect to an anisotropic tracing parameter (identifying the nonorthotropic material coefficients). The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic structure. The effectiveness of the proposed technique is demonstrated by means of numerical examples and its potential for solving other quasi-symmetric problems is discussed.

Noor, A. K.

Wing-Body Aeroelasticity Using Finite-Difference Fluid/Finite-Element Structural Equations on Parallel Computers

This paper presents a procedure for computing the aeroelasticity of wing-body configurations on multiple-instruction, multiple-data (MIMD) parallel computers. In this procedure, fluids are modeled using Euler equations discretized by a finite difference method, and structures are modeled using finite element equations. The procedure is designed in such a way that each discipline can be developed and maintained independently by using a domain decomposition approach. A parallel integration scheme is used to compute aeroelastic responses by solving the coupled fluid and structural equations concurrently while keeping modularity of each discipline. The present procedure is validated by computing the aeroelastic response of a wing and comparing with experiment. Aeroelastic computations are illustrated for a High Speed Civil Transport type wing-body configuration.

Byun, Chansup

Wing-Body Aeroelasticity on Parallel Computers

This article presents a procedure for computing the aeroelasticity of wing-body configurations on multiple-instruction, multiple-data parallel computers. In this procedure, fluids are modeled using Euler equations discretized by a finite difference method, and structures are modeled using finite element equations. The procedure is designed in such a way that each discipline can be developed and maintained independently by using a domain decomposition approach. A parallel integration scheme is used to compute aeroelastic responses by solving the coupled fluid and structural equations concurrently while keeping modularity of each discipline. The present procedure is validated by computing the aeroelastic response of a wing and comparing with experiment. Aeroelastic computations are illustrated for a high speed civil transport type wing-body configuration.

Guruswamy, Guru P.

Calculational and Experimental Investigations of the Pressure Effects on Radical - Radical Cross Combinations Reactions: C2H5 + C2H3

Pressure-dependent product yields have been experimentally determined for the cross-radical reaction C2H5 + C2H3. These results have been extended by calculations. It is shown that the chemically activated combination adduct, 1-C4H8*, is either stabilized by bimolecular collisions or subject to a variety of unimolecular reactions including cyclizations and decompositions. Therefore the "apparent" combination/disproportionation ratio exhibits a complex pressure dependence. The experimental studies were performed at 298 K and at selected pressures between about 4 Torr (0.5 kPa) and 760 Torr (101 kPa). Ethyl and vinyl radicals were simultaneously produced by 193 nm excimer laser photolysis of C2H5COC2H3 or photolysis of C2H3Br and C2H5COC2H5. Gas chromatograph/mass spectrometry/flame ionization detection (GC/MS/FID) were used to identify and quantify the final reaction products. The major combination reactions at pressures between 500 (66.5 kPa) and 760 Torr are (1c) C2H5 + C2H3 yields 1-butene, (2c) C2H5 + C2H5 yields n-butane, and (3c) C2H3 + C2H3 yields 1,3-butadiene. The major products of the disproportionation reactions are ethane, ethylene, and acetylene. At moderate and lower pressures, secondary products, including propene, propane, isobutene, 2-butene (cis and trans), 1-pentene, 1,4-pentadiene, and 1,5-hexadiene are also observed. Two isomers of C4H6, cyclobutene and/or 1,2-butadiene, were also among the likely products. The pressure-dependent yield of the cross-combination product, 1-butene, was compared to the yield of n-butane, the combination product of reaction (2c), which was found to be independent of pressure over the range of this study. The [ 1-C4H8]/[C4H10] ratio was reduced from approx.1.2 at 760 Torr (101 kPa) to approx.0.5 at 100 Torr (13.3 kPa) and approx.0.1 at pressures lower than about 5 Torr (approx.0.7 kPa). Electronic structure and RRKM calculations were used to simulate both unimolecular and bimolecular processes. The relative importance of C-C and C-H bond ruptures, cyclization, decyclization, and complex decompositions are discussed in terms of energetics and structural properties. The pressure dependence of the product yields were computed and dominant reaction paths in this chemically activated system were determined. Both modeling and experiment suggest that the observed pressure dependence of [1-C4H8]/[C4H10] is due to decomposition of the chemically activated combination adduct 1-C4H8* in which the weaker allylic C-C bond is broken: H2C=CHCH2CH3 yields C3H5 + CH3. This reaction occurs even at moderate pressures of approx.200 Torr (26 kPa) and becomes more significant at lower pressures. The additional products detected at lower pressures are formed from secondary radical-radical reactions involving allyl, methyl, ethyl, and vinyl radicals. The modeling studies have extended the predictions of product distributions to different temperatures (200-700 K) and a wider range of pressures (10(exp -3) - 10(exp 5) Torr). These calculations indicate that the high-pressure [1-C4H8]/[C4H10] yield ratio is 1.3 +/- 0.1.

Fahr, Askar

Perovskite oxides: Oxygen electrocatalysis and bulk structure

Perovskite type oxides were considered for use as oxygen reduction and generation electrocatalysts in alkaline electrolytes. Perovskite stability and electrocatalytic activity are studied along with possible relationships of the latter with the bulk solid state properties. A series of compounds of the type LaFe(x)Ni1(-x)O3 was used as a model system to gain information on the possible relationships between surface catalytic activity and bulk structure. Hydrogen peroxide decomposition rate constants were measured for these compounds. Ex situ Mossbauer effect spectroscopy (MES), and magnetic susceptibility measurements were used to study the solid state properties. X ray photoelectron spectroscopy (XPS) was used to examine the surface. MES has indicated the presence of a paramagnetic to magnetically ordered phase transition for values of x between 0.4 and 0.5. A correlation was found between the values of the MES isomer shift and the catalytic activity for peroxide decomposition. Thus, the catalytic activity can be correlated to the d-electron density for the transition metal cations.

Carbonio, R. E.

Perovskite-type oxides - Oxygen electrocatalysis and bulk structure

Perovskite type oxides were considered for use as oxygen reduction and generation electrocatalysts in alkaline electrolytes. Perovskite stability and electrocatalytic activity are studied along with possible relationships of the latter with the bulk solid state properties. A series of compounds of the type LaFe(x)Ni1(-x)O3 was used as a model system to gain information on the possible relationships between surface catalytic activity and bulk structure. Hydrogen peroxide decomposition rate constants were measured for these compounds. Ex situ Mossbauer effect spectroscopy (MES), and magnetic susceptibility measurements were used to study the solid state properties. X ray photoelectron spectroscopy (XPS) was used to examine the surface. MES has indicated the presence of a paramagnetic to magnetically ordered phase transition for values of x between 0.4 and 0.5. A correlation was found between the values of the MES isomer shift and the catalytic activity for peroxide decomposition. Thus, the catalytic activity can be correlated to the d-electron density for the transition metal cations.

Carbonio, R. E.

Parallel execution of a three-dimensional, chemically reacting, Navier-Stokes code on distributed-memory machines

This paper describes the parallel version of the three-dimensional, chemically reacting, computational fluid dynamics (CFD) code, SPARK. This work was performed on the Intel iPSC/860-based parallel computers. The SPARK code utilizes relatively simple explicit numerical algorithms, but models complex chemical reactions. The code solves the equations over a regular structured mesh so a simple dam decomposition is used to assign work to the individual processors. The explicit nature of the algorithm, combined with the computational intensity of the chemistry calculations, results in a very low communication-to-computation ratio when compared to typical CFD codes. The efficiency of the parallel code is examined and shown to be about 65 percent when the problem size is scaled with the number of processors. Two low-angle wall-jet injection cases are solved to demonstrate the capability of the parallel code for solving large problems efficiently.

Otto, John C.