This work presents three simulation features developed in an existing mould filling simulation code for resin transfer moulding to address the processing issues encountered during manufacturing. They are gate control, venting, and dry spot formation. The first feature is achieved using numerical sensors, which simulate the sensors used in practice to control the process. This feature makes it possible to use the developed simulation code to design a control strategy to optimize mould filling time, or to reduce the injection pressure required. The second feature is developed to account for the presence of vents. With vent locations specified, simulation can be used to predict changes in the pressure distribution and mould filling pattern if the resin front is not directly connected to the vent. The third feature provides for the prediction of dry spot formation. The simulation code checks if air is trapped in the mould and keeps track of these trapped air pockets. It computes the Location, size and the pressure of all dry spots formed in the filling process. The combination of these features enhances the ability of the code as a design tool. The gate control and dry spot prediction features can be used in conjunction to guide the design of optimal processing conditions. Controlled resin injection as a strategy is an indispensable way to prevent dry spot formation, and reduce operation costs. Similarly, venting and dry spot prediction can be used to detect possible flaws and to correct them before a prototype mould is constructed.

In this paper “laminar-flow” and “plug-flow” models are presented for engineering photo-assisted chemical vapor deposition reactors. It is shown that the growth rate depends directly on the photodissociation rate, which in turn is proportional to the laser power and the precursor concentration. Dimensional analysis of the reactor conservation equations reveals that there are 5 key groups which characterize the process. These groups describe the dependence of the axial growth profile on the laser power, the laser beam width, the substrate to beam distance, the precursor concentration, and the axial dispersion in the reactor. The plug-flow model yields an analytical expression for the growth profile that can be used to design an illumination geometry for depositing uniformly thick films at high reactant utilization. Both models are in good agreement with experimental measurements of the photo-assisted CVD of cadmium telluride.

The time evolution of finite amplitude axisymmetric perturbations (Taylor cells) to the purely azimuthal. viscoelastic, cylindrical Couette flow was numerically simulated. Two time integration numerical methods were developed, both based on a pseudospectral spatial approximation of the variables, efficiently implemented using fast Poisson solvers and optimal filtering routines. The first method, applicable for finite Re numbers, is based on a time-splitting integration with the divergence-free condition enforced through an influence matrix technique. The second one, is based on a semi-implicit time integration of the constitutive equation with both the continuity and the momentum equations enforced as constraints. Stability results for an upper convected Maxwell fluid were obtained for the supercritical bifurcations, either steady or time-periodic, developed after the onset of instabilities in the primary flow. At small elasticity values, epsilon = De/Re, the time integration of finite amplitude disturbances confirms the stability of the single branch of steady Taylor cells. At intermediate epsilon values the rotating wave family of time-periodic solutions developed at the onset of instability is stable, whereas the standing wave is found to be unstable. At high epsilon, values, and in particular for the limit of creeping flow (epsilon = infinity), the present study shows that the rotating wave family is unstable and the standing (radial) wave is stable, in agreement with previous finite-element investigations. It is thus shown that spectral techniques provide a robust and computationally efficient method for the simulation of complex, non-linear, time-dependent viscoelastic flows.

A mathematical model has been developed which describes the transport phenomena and elementary reaction kinetics encountered during photoassisted organometallic vapor-phase epitaxy of cadmium telluride. Dimethylcadmium and dimethyltellurium in helium carrier gas are fed to a horizontal, square duct containing a substrate heated to 165 °C. The organometallic compounds are photodissociated in the gas by illumination with 248 nm photons from a continuous-wave laser. Average deposition rates predicted by the model agree to within 10% of those measured experimentally. The numerical simulations reveal that the growth rate is controlled by the photolysis rate of the organometallic compounds. This results in a linear dependence of the growth rate on dimethylcadmium pressure and laser power. The simulations further indicate that elemental tellurium deposits with cadmium telluride over a wide range of operating conditions. The elemental tellurium is avoided by operating below 20 Torr total pressure, by illuminating the gas directly above the substrate, and by feeding two–four times more dimethylcadmium than dimethyltellurium. Under these conditions, the flux of methyl radicals to the surface is sufficient to etch away the excess tellurium. The model has also been used to identify an illumination geometry suitable for obtaining uniformly thick CdTe films.

A reaction mechanism is presented for photo-assisted organometallic vapor-phase epitaxy (OMVPE) of cadmium telluride. Dimethylcadmium and dimethyltellurium are photodissociated in the gas into Cd and Te atoms and methyl radicals by 248 nm photons from a continuous-wave laser. The Te atoms and methyl radicals recombine to form Te2, TeCH3, and C2H6. The Cd atoms and Te species diffuse to the substrate, adsorb, and incorporate into the cadmium telluride film. The film stoichiometry is maintained by Cd sublimation when cadmium is in excess, and by methyl radical etching of Te when tellurium is in excess. This mechanism has been incorporated into a laminar-flow model of the photo-assisted OMVPE reactor. The model predicts that at low laser power and/or high flow rates, the growth rate is controlled by the dimethylcadmium photolysis rate. This yields a linear dependence of the growth rate on the laser power density and the dimethylcadmium pressure. These results are in good agreement with experiments. The model further predicts that elemental tellurium deposits with cadmium telluride over a broad range of operating conditions. Conditions which avoid tellurium deposition are described. In addition, a simple criterion is developed for determining when an excimer laser may be modeled as a continuous light source.

We have examined the effect of the carrier gas on the kinetics of cadmium telluride deposition from dimethylcadmium (DMCd) and dimethyltellurium (DMTe) in a hot-wall glass reactor. Upon switching the gas from hydrogen to helium, the methane/ethane product ratio decreases from 4.1/1.0 to 0.0/1.0, the growth rate falls by a factor of 3.3±0.3, and the film becomes substantially rougher. These results are explained by the following reaction mechanism: DMCd and DMTe adsorb on the CdTe surface, then decompose by desorbing methyl radicals. In hydrogen, the CH3 radicals react with H2 to form CH4, whereas in helium, the CH3 radicals recombine into C2H6. The growth rate decreases on switching from H2 to He because of the change in film morphology. Evidently, the rougher films produced in helium contain fewer or less active sites for adsorption and decomposition of the organometallic molecules.

A catalytic reaction mechanism is proposed for the organometallic vapor-phase epitaxy of cadmium telluride. Dimethylcadmium and diethyltellurium dissociatively adsorb onto exposed metal atoms on the cadmium telluride surface. The sticking probability is given by S = 1.5×10-4(1−θR), where θR is the methyl and ethyl coverage. Subsequently, methyl and ethyl radicals desorb at a rate given by rd = 1.5×109exp(-25 [kcal/mol]RT)θR(s-1). This mechanism is consistent with surface science studies of the adso rption and decomposition of organometallic molecules on semiconductor surfaces. A boundary-layer model incorporating the catalytic reaction is used to simulate the kinetics of cadmium telluride deposition in a horizontal, cold-wall reactor. The simulations show the same dependence of the growth rate on temperature as was observed by I.B. Bhat et al. [J. Electrochem. Soc. 134 (1987) 195] on sapphire substrates. The growth rate increases exponentially with temperature below 350°C, but remains constant above 400°C. At low temperatures, the reaction is controlled by the desorption of alkyl radicals. At high temperatures, the reaction is mainly controlled by the adsorption of organometallic molecules. The growth rate changes when different substrates are used in the experiments. This suggests that the kinetics of alkyl radical desorption are influenced by the cadmium telluride surface structure.

The performance of several numerical methods for hyperbolic equations is investigated. The various methods are tested on a system of quasilinear hyperbolic equations subject to nonperiodic boundary conditions: the one-dimensional approximation of the time-dependent viscoelastic fiber spinning problem.

The one-dimensional approximation to the time-dependent fiber spinning equations for an upper-convected Maxwell model is shown to consist of a set of four first-order quasilinear hyperbolic equations. The sign of the characteristics is shown to validate the customarily assigned boundary conditions for the time-dependent problem. A truncated set of three equations is presented which admits an analytic steady-state solution which exactly reproduces the Newtonian and high Deborah number viscoelastic limit behaviors. In the truncated set, the hyperbolic character of the equations is preserved and the previous results of a linear stability analysis at zero Reynolds number are well approximated. The normal forms of both the full and truncated fiber spinning equations are derived which are used to formulate stable numerical schemes in the companion paper [1].

The truncated time-dependent one-dimensional fiber spinning equations for an Upper Convected Maxwell model, presented in the previous paper [1], are approximated using various numerical methods. The eigenvalues and eigenfunctions of the linearized problem around the steady-state solution are calculated and compared against the analytical results for various values of Deborah and Reynolds numbers.