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The development of processes to produce fullerenes and carbon nanotubes has largely been empirical. Fullerenes were first discovered in the soot produced by laser ablation of graphite [1]and then in the soot of electric arc evaporated carbon. Techniques and conditions for producing larger and larger quantities of fullerenes depended mainly on trial and error empirical variations of these processes, with attempts to scale them up by using larger electrodes and targets and higher power. Various concepts of how fullerenes and carbon nanotubes were formed were put forth, but very little was done based on chemical kinetics of the reactions. This was mainly due to the complex mixture of species and complex nature of conditions in the reactors. Temperatures in the reactors varied from several thousand degrees Kelvin down to near room temperature. There are hundreds of species possible, ranging from atomic carbon to large clusters of carbonaceous soot, and metallic catalyst atoms to metal clusters, to complexes of metals and carbon. Most of the chemical kinetics of the reactions and the thermodynamic properties of clusters and complexes have only been approximated. In addition, flow conditions in the reactors are transient or unsteady, and three dimensional, with steep spatial gradients of temperature and species concentrations. All these factors make computational simulations of reactors very complex and challenging. This article addresses the development of the chemical reaction involved in fullerene production and extends this to production of carbon nanotubes by the laser ablation/oven process and by the electric arc evaporation process. In addition, the high-pressure carbon monoxide (HiPco) process is discussed. The article is in several parts. The first one addresses the thermochemical aspects of modeling; and considers the development of chemical rate equations, estimates of reaction rates, and thermodynamic properties where they are available. The second part addresses modeling of the arc process for fullerene and carbon nanotube production using O-D, 1-D and 2-D fluid flow models. The third part addresses simulations of the pulsed laser ablation process using time-dependent techniques in 2-D, and a steady state 2-D simulation of a continuous laser ablation process. The fourth part addresses steady state modeling in O-D and 2-D of the HiPco process. In each of the simulations, there is a variety of simplifications that are made that enable one to concentrate on one aspect or another of the process. There are simplifications that can be made to the chemical reaction models , e.g. reduction in number of species by lumping some of them together in a representative species. Other simulations are carried out by eliminating the chemistry altogether in order to concentrate on the fluid dynamics. When solving problems with a large number of species in more than one spatial dimension, it is almost imperative that the problem be decoupled by solving for the fluid dynamics to find the fluid motion and temperature history of "particles" of fluid moving through a reactor. Then one can solve the chemical rate equations with complex chemistry following the temperature and pressure history. One difficulty is that often mixing with an ambient gas is involved. Therefore, one needs to take dilution and mixing into account. This changes the ratio of carbon species to background gas. Commercially available codes may have no provision for including dilution as part of the input. One must the write special solvers for including dilution in decoupled problems. The article addresses both ful1erene production and single-walled carbon nanotube (SWNT) production. There are at least two schemes or concepts of SWNT growth. This article will only address growth in the gas phase by carbon and catalyst cluster growth and SW T formation by the addition of carbon. There are other models that conceive of SWNT growth as a phase separation process from clusters me up carbon and metal catalyst, with the carbon precipitating from the cluster as it cools. We will not deal with that concept in this article. Further research is needed to determine the rates at which these composite clusters form, evaporate, and segregate.

The aerothermal environment is examined for two vehicle forebodies near the peak heating points of lunar and martian return-to-earth trajectories at several nominal entry velocities. The first vehicle forebody is that of a 70 deg aerobrake for entry into earth orbit; the second, a capsule of Apollo configuration for direct entry into the earth's atmosphere. The configurations and trajectories are considered likely candidates for such missions. Two-temperature, thermochemical nonequilibrium models are used in the flow field analyses. In addition to Park's empirical model for dissociation under conditions of thermal nonequilibrium, the Gordiets kinetic model for the homonuclear dissociation of N2 and O2 is also considered. Temperature and emission profiles indicate nonequilibrium effects in a 2 to 5 cm post shock region. Substantial portions of the shock layer flow appear to be in equilibrium. The shock layer over an aerobrake for return from the moon exhibits the largest extent of nonequilibrium effects of all considered missions. Differences between the Gordiets and Parks kinetic model were generally very small for the lunar return aerobrake case, the greatest difference of 6.1 percent occurring in the radiative heating levels.

A Navier-Stokes flowfield solution method (LAURA code) using finite-rate chemistry and two-temperature thermal nonequilibrium was used in combination with two nonequilibrium radiative heat transfer codes to calculate heating for the FIRE II vehicle. An axisymmetric model of the actual body shape was used. One radiative heating code (NEQAIR) was used in uncoupled fashion with the flowfield solver's energy equations, while the other code (LORAN) was used in both coupled and uncoupled variations. Several trajectory points ranging from highly nonequilibrium flow to near-equilibrium flow were used for a study of both convective and radiative heating over the vehicle. Considerable variation in radiative heating was seen at the extremes, while agreement was good in the intermediate trajectory points. Total heat transfer calculations gave good comparison until the peak heating trajectory points were encountered, and returned to good agreement for the last two equilibrium points.

A heating analysis for a 15.2 m diameter Lunar Transfer Vehicle (LTV) at 0 and 10.6 deg angle of attack for a nominal trajectory through the earth's atmosphere is described. The analysis utilizes the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) with thin-layer, Navier-Stokes, thermochemical nonequilibrium options. Radiative heating levels are calculated using the Langley Optimized RAdiative Nonequilibrium (LORAN) and the Non-EQuilibrium AIr Radiation (NEQAIR) codes. At peak heating, the shock layer is substantially in equilibrium. Comprehensive spatial and spectral grid convergence studies have been implemented to quantify grid effects on the convective and radiative heating levels. Axisymmetric tests including the coupled effects of radiative energy transfer show negligible change to the convective heating and a 20 percent reduction in the radiative heating.

A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.

A broad-spectrum version of the NEQAIR code was modified to account for self-absorption and applied to AFE flowfields calculated by the LAURA code with a variety of kinetic models. The resulting radiative fluxes were obtained in a decoupled fashion from the flowfield solver along the vehicle's stagnation streamline. The radiative flux obtained was broken down by causative process to study the radiative structure of the AFE's flowfield for the various kinetic models. In addition, the radiative fluxes for several points on a typical AFE trajectory were analyzed to examine how the radiative structure changes as the vehicle completes its aeropass. Only two radiative processes dominated the stagnation radiative flux, and the flow field conditions near the wal were found to exert considerable influence over the radiative flux to the wall.

The basic features of a Microwave Reflectometer Ionization Sensor (MRIS) as designed for utilization on the Aeroassist Flight Experiment are described. A parametric study of the effects of trajectory and unknowns in the thermochemical nonequilibrium models for translational and vibrational-electronic energy exchange rates, reaction rates, and the average electronic excitation level of atoms is performed to illustrate how the MRIS data may be employed for code validation. This study, implemented with program LAURA, shows a particular sensitivity of the onset and severity of an electron avalanche phenomena associated with changes in these physical models.

The total (convective and radiative) heating is calculated over the entire forebody heatshield of the Aeroassist Flight Experiment (AFE) vehicle. The convective heating is calculated using a three-dimensional Navier-Stokes code (LAURA) which includes both chemical and thermal nonequilibrium effects. The flowfield solution is then used to provide inputs to a nonequilibrium air radiation code (NEQAIR) to calculate the nonequilibrium radiative heating. Results are presented at two points on the current Baseline 5A trajectory corresponding to the start of the primary data taking period and peak heating.

A simplified method for the calculation of radiative heat transfer in hypersonic reentry flows where local thermal nonequilibrium (LTNE) conditions exist is presented. This method has been incorporated into the computer code RADMC (RADiation/Modified Corrections), which utilizes an approximate 'two-state' model of the electronic levels of atoms and molecules in the determination of the populations of the excited states for both LTNE and local thermal equilibrium (LTE) conditions for each of the relevant chemical species. The population data are used to calculate a correction factor to the radiative cross sections in an eight-step nongray radiative heat-transfer model. Results have been obtained for various points along the proposed trajectory of the Aeroassist Flight Experiment and the Fire II trajectory, and compared with results obtained for the same flowfields from the NEQAIR radiative heat-transfer code.

A series of detailed studies comparing various vibration dissociation coupling models, reaction systems and rates, and radiative heating models has been conducted for the nonequilibrium stagnation region of an AFE/AOTV vehicle. Atomic and molecular nonequilibrium radiation correction factors have been developed and applied to various absorption coefficient step models, and a modified vibration dissociation coupling model has been shown to yield good vibration/electronic temperature and concentration profiles. While results indicate sensitivity to the choice of vibration dissociation coupling model and to the nitrogen electron impact ionization rate, by proper combinations accurate flowfield and radiative heating results can be obtained. These results indicate that nonequilibrium effects significantly affect the flowfield and the radiative heat transfer. However, additional work is needed in ionization chemistry and absorption coefficient modeling.