Stable numerical solutions of the reactor kinetics equations.
Solution of reactor kinetics equation numerically unconditionally stable for all values of reactivity or integration step size
REACTOR PHYSICS↗
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A Burst Mode, Ultrahigh Temperature UF4 Vapor Core Reactor Rankine Cycle Space Power System Concept
Static and dynamic neutronic analyses have been performed on an innovative burst mode (100's of MW output for a few thousand seconds) Ulvahigh Temperature Vapor Core Reactor (UTVR) space nuclear power system. The NVTR employs multiple, neutronically-coupled fissioning cores and operates on a direct, closed Rankine cycle using a disk Magnetohydrodynamic (MHD) generater for energy conversion. The UTVR includes two types of fissioning core regions: (1) the central Ultrahigh Temperature Vapor Core (UTVC) which contains a vapor mixture of highly enriched UF4 fuel and a metal fluoride working fluid and (2) the UF4 boiler column cores located in the BeO moderator/reflector region. The gaseous nature of the fuel the fact that the fuel is circulating, the multiple coupled fissioning cores, and the use of a two phase fissioning fuel lead to unique static and dynamic neutronic characteristics. Static neutronic analysis was conducted using two-dimensional S sub n, transport theory calculations and three-dimensional Monte Carlo transport theory calculations. Circulating-fuel, coupled-core point reactor kinetics equations were used for analyzing the dynamic behavior of the UTVR. In addition to including reactivity feedback phenomena associated with the individual fissioning cores, the effects of core-to-core neutronic and mass flow coupling between the UTVC and the surrounding boiler cores were also included in the dynamic model The dynamic analysis of the UTVR reveals the existence of some very effectlve inherent reactivity feedback effects that are capable of quickly stabilizing this system, within a few seconds, even when large positive reactivity insertions are imposed. If the UTVC vapor fuel density feedback is suppressed, the UTVR is still inherently stable because of the boiler core liquid-fuel volume feedback; in contrast, suppression of the vapor fuel density feedback in 'conventional" gas core cavity reactors causes them to become inherently unstable. Due to the strength of the negative reactivity feedback in the UTVR, it is found that external reactivity insertions alone are inadequate for bringing about significant power level changes during normal reactor operations. Additional methods of reactivity control such as variations in the gaseous fuel mass flow rate, are needed to achieve the desired power level oontrol.
Dugan, E. T.↗
Numerical solution of stiff systems of ordinary differential equations with applications to electronic circuits
Systems of ordinary differential equations in which the magnitudes of the eigenvalues (or time constants) vary greatly are commonly called stiff. Such systems of equations arise in nuclear reactor kinetics, the flow of chemically reacting gas, dynamics, control theory, circuit analysis and other fields. The research reported develops an A-stable numerical integration technique for solving stiff systems of ordinary differential equations. The method, which is called the generalized trapezoidal rule, is a modification of the trapezoidal rule. However, the method is computationally more efficient than the trapezoidal rule when the solution of the almost-discontinuous segments is being calculated.
Rosenbaum, J. S.↗
Projecting the Performance of a Continuous Bosch Carbon Dioxide Reduction System
Kinetic studies using a subscale reactor were used to develop power-law rate equations for the two primary reactions contributing to the Bosch carbon dioxide reduction process: the reverse water-gas shift reaction and the carbon monoxide hydrogenation reaction. An alloy catalyst in bead form was used in these studies, which investigated both the dependence on gas composition and the dependence on time as the beads gradually disintegrate during carbon formation. Bead disintegration impacts both the rates and the relative activities of the two primary reactions. Although the kinetic testing was conducted in a single-pass mode, the target Bosch application requires operation in a recycle mode to achieve high conversion. Further, the proposed design concept for a full-scale carbon dioxide reduction system would allow carbon to be removed continuously in contrast to previous Bosch processes that required replacement of expendable catalyst cartridges. The developed power-law kinetic rate equations were used in conjunction with a reactor model to project the operating conditions, performance, and sizing of a continuous Bosch system.
carbon dioxide reduction↗
An atmospheric pressure flow reactor: Gas phase kinetics and mechanism in tropospheric conditions without wall effects
A new type of gas phase flow reactor, designed to permit the study of gas phase reactions near 1 atm of pressure, is described. A general solution to the flow/diffusion/reaction equations describing reactor performance under pseudo-first-order kinetic conditions is presented along with a discussion of critical reactor parameters and reactor limitations. The results of numerical simulations of the reactions of ozone with monomethylhydrazine and hydrazine are discussed, and performance data from a prototype flow reactor are presented.
Koontz, Steven L.↗
Dynamic Response Testing in an Electrically Heated Reactor Test Facility
Non-nuclear testing can be a valuable tool in development of a space nuclear power or propulsion system. In a non-nuclear test bed, electric heaters are used to simulate the heat from nuclear fuel. Standard testing allows one to fully assess thermal, heat transfer, and stress related attributes of a given system, but fails to demonstrate the dynamic response that would be present in an integrated, fueled reactor system. The integration of thermal hydraulic hardware tests with simulated neutronic response provides a bridge between electrically heated testing and full nuclear testing. By implementing a neutronic response model to simulate the dynamic response that would be expected in a fueled reactor system, one can better understand system integration issues, characterize integrated system response times and response characteristics, and assess potential design improvements at a relatively small fiscal investment. Initial system dynamic response testing was demonstrated on the integrated SAFE-100a heat pipe cooled, electrically heated reactor and heat exchanger hardware, utilizing a one-group solution to the point kinetics equations to simulate the expected neutronic response of the system (Bragg-Sitton, 2005). The current paper applies the same testing methodology to a direct drive gas cooled reactor system, demonstrating the applicability of the testing methodology to any reactor type and demonstrating the variation in system response characteristics in different reactor concepts. In each testing application, core power transients were controlled by a point kinetics model with reactivity feedback based on core average temperature; the neutron generation time and the temperature feedback coefficient are provided as model inputs. Although both system designs utilize a fast spectrum reactor, the method of cooling the reactor differs significantly, leading to a variable system response that can be demonstrated and assessed in a non-nuclear test facility.
Bragg-Sitton, Shannon M.↗
LSENS, The NASA Lewis Kinetics and Sensitivity Analysis Code
A general chemical kinetics and sensitivity analysis code for complex, homogeneous, gas-phase reactions is described. The main features of the code, LSENS (the NASA Lewis kinetics and sensitivity analysis code), are its flexibility, efficiency and convenience in treating many different chemical reaction models. The models include: static system; steady, one-dimensional, inviscid flow; incident-shock initiated reaction in a shock tube; and a perfectly stirred reactor. In addition, equilibrium computations can be performed for several assigned states. An implicit numerical integration method (LSODE, the Livermore Solver for Ordinary Differential Equations), which works efficiently for the extremes of very fast and very slow reactions, is used to solve the "stiff" ordinary differential equation systems that arise in chemical kinetics. For static reactions, the code uses the decoupled direct method to calculate sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of dependent variables and/or the rate coefficient parameters. Solution methods for the equilibrium and post-shock conditions and for perfectly stirred reactor problems are either adapted from or based on the procedures built into the NASA code CEA (Chemical Equilibrium and Applications).
Radhakrishnan, K.↗
Improved Breathing Cartridge (IBC)
The Fire Cartridge (FC) is designed to work with the Emergency Mask (EM) to protect the crew by cleaning the inhaled air in a post fire environment. The Improved Breathing Cartridge (IBC) is designed as a next generation FC with the lessons learned from years of building and testing the FC design, as well as novel catalyst materials to improve the performance and robustness of the cartridge. The FC was designed with minimal margin to save on mass, while the IBC was sized to have over 100% excess catalyst to achieve the required conversion, and still reduce the production cost. Kinetic data taken from another project was used to size the catalyst bed from the standard plug flow reactor conversion equation. The cartridge has been 3D printed and will soon be filled with the required levels of media. Testing has not yet been performed to determine final performance.
Fire Response↗
Multiphysics Modeling of Electrode Dissolution under Hydrodynamic Conditions in Low Conductivity Water
Efficient plug-flow electrochemical reactors are characterized by their ability to effectively convert species with significant ionic strength and/or with the assistance of a well-behaved electrolyte. Because of the classic electroconductivity requirement, electrochemical reactors are not particularly attractive options for applications with low-conductivity conditions, especially for low-pressure feeds. However, these reactors can still find application in dedicated processes such as ultra-clean water conditioning and biological-coupled separation systems. Consequently, a multi-physics model was developed using COMSOL Multiphysics to characterize different reactor-design conditions based on the Tertiary Current Distribution which accounts for the effects of expected variations in electrolyte composition and ionic strength on the electrochemical process, as well as solution resistance and electrode kinetics. The modelling framework presented here employs single-phase laminar fluid flow, the Nernst-Planck equation, the water-based electroneutrality condition, and concentration-dependent overpotentials. This investigation particularly explores the electrolysis process of “anodic dissolution,” in which elemental species dissociate from the solid matrix of the electrode and enter the liquid phase of the electrolyte as soluble ions. The reactor configuration of interest has a rectangular parallel-electrode design and is operated galvanostatically. A series of parametric studies are carried out to inspect the response of the system when hydrodynamic, kinetic, and geometric conditions are changed. The parametric sweep resulted in variable effluent concentrations and system voltage, which reveal underlaying optimization patterns for electrode dissolution in low conductivity water.
Multiphysics↗
LSENS, a general chemical kinetics and sensitivity analysis code for gas-phase reactions: User's guide
A general chemical kinetics and sensitivity analysis code for complex, homogeneous, gas-phase reactions is described. The main features of the code, LSENS, are its flexibility, efficiency and convenience in treating many different chemical reaction models. The models include static system, steady, one-dimensional, inviscid flow, shock initiated reaction, and a perfectly stirred reactor. In addition, equilibrium computations can be performed for several assigned states. An implicit numerical integration method, which works efficiently for the extremes of very fast and very slow reaction, is used for solving the 'stiff' differential equation systems that arise in chemical kinetics. For static reactions, sensitivity coefficients of all dependent variables and their temporal derivatives with respect to the initial values of dependent variables and/or the rate coefficient parameters can be computed. This paper presents descriptions of the code and its usage, and includes several illustrative example problems.
Radhakrishnan, Krishnan↗
Effect of Porosity on Surface Catalytic Efficiency
This paper describes the effect of surface porosity of thermal protection materials on surface catalytic efficiency using test data taken from both arc-jet and side-arm reactor facilities. Relative surface porosity of the samples varied from 6% to 50%. Surface porosity was measured using a flow apparatus and Bernoulli equation. The surface catalytic efficiency of the materials was calculated using aerothermodynamic, and kinetic theories. The catalytic efficiency of the materials are compared at surface temperatures between room temperature and 2500 F. The data are presented in the form of graphs and tables.
Stewart, David A.↗
Flame stability in combusting turbulent jets
The paper develops a model for the stability of turbulent methane/air flames on the assumption that reaction kinetics is much more important than the fluid dynamics near blowout. Flame stability is predicted as a function of ambient atmospheric temperature and composition, initial preheat temperature, and the percentage of external product gas recirculation. A one-step reaction and a well-stirred reactor are used to equate the rate at which the mass is supplied to the flame to the rate at which the mass chemically reacts in the flame.
Nelson, H. F.↗
Model of ASTM Flammability Test in Microgravity: Iron Rods
There is extensive qualitative results from burning metallic materials in a NASA/ASTM flammability test system in normal gravity. However, this data was shown to be inconclusive for applications involving oxygen-enriched atmospheres under microgravity conditions by conducting tests using the 2.2-second Lewis Research Center (LeRC) Drop Tower. Data from neither type of test has been reduced to fundamental kinetic and dynamic systems parameters. This paper reports the initial model analysis for burning iron rods under microgravity conditions using data obtained at the LERC tower and modeling the burning system after ignition. Under the conditions of the test the burning mass regresses up the rod to be detached upon deceleration at the end of the drop. The model describes the burning system as a semi-batch, well-mixed reactor with product accumulation only. This model is consistent with the 2.0-second duration of the test. Transient temperature and pressure measurements are made on the chamber volume. The rod solid-liquid interface melting rate is obtained from film records. The model consists of a set of 17 non-linear, first-order differential equations which are solved using MATLAB. This analysis confirms that a first-order rate, in oxygen concentration, is consistent for the iron-oxygen kinetic reaction. An apparent activation energy of 246.8 kJ/mol is consistent for this model.
Steinberg, Theodore A↗
Investigation of the hydrochlorination of SiCl4
The hyrochlorination of SiC14 and m.g. silicon metal to produce SiHC13, was investigated. Reaction kinetic measurements were carried out to collect additional rate data at 525 C and 550 C. A theoretical study was carried out to provide a kinetic model and a rate equation for the hydrochlorination reaction. Results of this preliminary study show that the rate of formation of SiHC13 follows a pseudo first order kinetics. The rate constants were measured at three temperatures, 550 C, 500 C and 450 C, respectively. The activation energy was determined from the Arrhenius plot to give a value of 13.2 Kcal/mole. The design of a quartz reactor to measure reaction rates and equilibrium conversion of SiHC13 at reaction temperature up to 650 C was completed.
Mui, J. Y. P.↗
Updated Chemical Kinetics and Sensitivity Analysis Code
An updated version of the General Chemical Kinetics and Sensitivity Analysis (LSENS) computer code has become available. A prior version of LSENS was described in "Program Helps to Determine Chemical-Reaction Mechanisms" (LEW-15758), NASA Tech Briefs, Vol. 19, No. 5 (May 1995), page 66. To recapitulate: LSENS solves complex, homogeneous, gas-phase, chemical-kinetics problems (e.g., combustion of fuels) that are represented by sets of many coupled, nonlinear, first-order ordinary differential equations. LSENS has been designed for flexibility, convenience, and computational efficiency. The present version of LSENS incorporates mathematical models for (1) a static system; (2) steady, one-dimensional inviscid flow; (3) reaction behind an incident shock wave, including boundary layer correction; (4) a perfectly stirred reactor; and (5) a perfectly stirred reactor followed by a plug-flow reactor. In addition, LSENS can compute equilibrium properties for the following assigned states: enthalpy and pressure, temperature and pressure, internal energy and volume, and temperature and volume. For static and one-dimensional-flow problems, including those behind an incident shock wave and following a perfectly stirred reactor calculation, LSENS can compute sensitivity coefficients of dependent variables and their derivatives, with respect to the initial values of dependent variables and/or the rate-coefficient parameters of the chemical reactions.
Radhakrishnan, Krishnan↗
GCKP84--General Chemical Kinetics Code for Gas-Phase Flow and Batch Processes Including Heat Transfer Effects
A general chemical kinetics code is described for complex, homogeneous ideal gas reactions in any chemical system. The main features of the GCKP84 code are flexibility, convenience, and speed of computation for many different reaction conditions. The code, which replaces the GCKP code published previously, solves numerically the differential equations for complex reaction in a batch system or one dimensional inviscid flow. It also solves numerically the nonlinear algebraic equations describing the well stirred reactor. A new state of the art numerical integration method is used for greatly increased speed in handling systems of stiff differential equations. The theory and the computer program, including details of input preparation and a guide to using the code are given.
David A Bittker↗
A Computational Fluid Dynamic and Heat Transfer Model for Gaseous Core and Gas Cooled Space Power and Propulsion Reactors
A computational model based on the axisymmetric, thin-layer Navier-Stokes equations is developed to predict the convective, radiation and conductive heat transfer in high temperature space nuclear reactors. An implicit-explicit, finite volume, MacCormack method in conjunction with the Gauss-Seidel line iteration procedure is utilized to solve the thermal and fluid governing equations. Simulation of coolant and propellant flows in these reactors involves the subsonic and supersonic flows of hydrogen, helium and uranium tetrafluoride under variable boundary conditions. An enthalpy-rebalancing scheme is developed and implemented to enhance and accelerate the rate of convergence when a wall heat flux boundary condition is used. The model also incorporated the Baldwin and Lomax two-layer algebraic turbulence scheme for the calculation of the turbulent kinetic energy and eddy diffusivity of energy. The Rosseland diffusion approximation is used to simulate the radiative energy transfer in the optically thick environment of gas core reactors. The computational model is benchmarked with experimental data on flow separation angle and drag force acting on a suspended sphere in a cylindrical tube. The heat transfer is validated by comparing the computed results with the standard heat transfer correlations predictions. The model is used to simulate flow and heat transfer under a variety of design conditions. The effect of internal heat generation on the heat transfer in the gas core reactors is examined for a variety of power densities, 100 W/cc, 500 W/cc and 1000 W/cc. The maximum temperature, corresponding with the heat generation rates, are 2150 K, 2750 K and 3550 K, respectively. This analysis shows that the maximum temperature is strongly dependent on the value of heat generation rate. It also indicates that a heat generation rate higher than 1000 W/cc is necessary to maintain the gas temperature at about 3500 K, which is typical design temperature required to achieve high efficiency in the gas core reactors. The model is also used to predict the convective and radiation heat fluxes for the gas core reactors. The maximum value of heat flux occurs at the exit of the reactor core. Radiation heat flux increases with higher wall temperature. This behavior is due to the fact that the radiative heat flux is strongly dependent on wall temperature. This study also found that at temperature close to 3500 K the radiative heat flux is comparable with the convective heat flux in a uranium fluoride failed gas core reactor.
Anghaie, S.↗
Comprehensive investigation of HgCdTe metalorganic chemical vapor deposition
The principal objective of this experimental and theoretical research program was to explore the possibility of depositing high quality epitaxial CdTe and HgCdTe at very low pressures through metalorganic chemical vapor deposition (MOCVD). We explored two important aspects of this potential process: (1) the interaction of molecular flow transport and deposition in an MOCVD reactor with a commercial configuration, and (2) the kinetics of metal alkyl source gas adsorption, decomposition and desorption from the growing film surface using ultra high vacuum surface science reaction techniques. To explore the transport-reaction issue, we have developed a reaction engineering analysis of a multiple wafer-in-tube ultrahigh vacuum chemical vapor deposition (UHV/CVD) reactor which allows an estimate of wafer or substrate throughput for a reactor of fixed geometry and a given deposition chemistry with specified film thickness uniformity constraints. The model employs a description of ballistic transport and reaction based on the pseudo-steady approximation to the Boltzmann equation in the limit of pure molecular flow. The model representation takes the form of an integral equation for the flux of each reactant or intermediate species to the wafer surfaces. Expressions for the reactive sticking coefficients (RSC) for each species must be incorporated in the term which represents reemission from a wafer surface. The interactions of MOCVD precursors with Si and CdTe were investigated using temperature programmed desorption (TPD) in ultra high vacuum combined with Auger electron spectroscopy (AES). These studies revealed that diethyltellurium (DETe) and dimethylcadmium (DMCd) adsorb weakly on clean Si(100) and desorb upon heating without decomposing. These precursors adsorb both weakly and strongly on CdTe(111)A, with DMCd exhibiting the stronger interaction with the surface than DETe.
Raupp, Gregory B.↗