J. Michael Doster

Semi-analytical modelling and simulation of the evolution and flow of Ohmically-heated non-ideal plasmas in electrothermal guns

In this paper, the Ohmic power input to the discharge capillary is recovered and used to analyse the basic processes involved in electrothermal (ET) plasma devices operated in an ablation-controlled-arc regime. Such an interplay between theory and experiment is necessary to reduce the number of reasons which might be responsible for the reported discrepancies between theory and experiment, as well as to illuminate the subject of ablation controlled arcs. A consistent methodology for determining detailed composition and thermodynamic functions of the non-ideal plasma generated in such devices is presented and used in the present computations. Different non-ideality effects, due to Debye-Huckel corrections in the Gibbs free energy, which have been ignored in prior publications, have been taken into account. A semi-analytical model for an ET plasma source with non-ideal effects is described and incorporated into a comprehensive computer code to simulate plasma evolution and flow in the discharge capillary. The model is one-dimensional, time dependent and uses the recovered Ohmic power input in the source term of the energy equation. The developed code has been used to investigate the ablation process and has shown the inappropriateness of a widely used ablation model. Code predictions for different plasma parameters are presented, discussed, and compared to available experimental data.

A simple formulation and solution strategy of the Saha equation for ideal and nonideal plasmas

A simple formulation and solution strategy for the Saha equation is introduced. The formulation discriminates between the cases in which either the pressure or the number density of heavy particles is known. This discrimination allows the method to be generalized to include all problems of practical interest, as well as to clarify ambiguities found in other formulations in the literature. The present method overcomes restrictions imposed on other competitive techniques and takes into account all possible formulae for nonideality corrections. In most practical cases the solution of the nonlinear set of the Saha equations is reduced to the simple problem of solving a single transcendental equation.

On the average electron–ion momentum transport cross-section in ideal and non-ideal plasmas

Abstract The energy-averaged electron–ion (e–i) momentum transport cross-section has been derived analytically and computed numerically. The result shows inaccuracy of the computations and fitting formula given by other authors.

Energy-averaged electron–ion momentum transport cross section in the Born Approximation and Debye–Hückel potential: Comparison with the cut-off theory

Abstract An exact analytical expression for the energy-averaged electron–ion momentum transport cross section in the Born approximation and Debye–Huckel exponentially screened potential has been derived and compared with the formulae given by other authors. A quantitative comparison between cut-off theory and quantum mechanical perturbation theory has been presented. Based on results from the Born approximation and Spitzers formula, a new approximate formula for the quantum Coulomb logarithm has been derived and shown to be more accurate than previous expressions.

Thermal performance of batch boiling water targets for 18F production.

Batch boiling targets are commonly used in cyclotrons to produce Fluorine-18 by proton bombardment of Oxygen-18 enriched water. Computational models have been developed to predict the thermal performance of bottom-pressurized batch boiling production targets. The models have been validated with experimental test data from the Duke University Medical Cyclotron and the Wisconsin Medical Cyclotron. Good agreement has been observed between experimental measurements and model predictions of average target vapor fraction as a function of beam current and energy.

A sensitivity study of the effects of evaporation/condensation accommodation coefficients on transient heat pipe modeling

Abstract The dynamic behavior of liquid metal heat pipe models is strongly influenced by the choice of evaporation and condensation modeling techniques. Classic kinetic theory descriptions of the evaporation and condensation processes are often inadequate for real situations; empirical accommodation coefficients are commonly utilized to reflect nonideal mass transfer rates. The complex geometries and flow fields found in proposed heat pipe systems cause considerable deviation from the classical models. The THROHPUT code, which has been described in previous works, was developed to model transient liquid metal heat pipe behavior from frozen startup conditions to steady state full power operation. It is used here to evaluate the sensitivity of transient liquid metal heat pipe models to the choice of evaporation and condensation accommodation coefficients. Comparisons are made with experimental liquid metal heat pipe data. It is found that heat pipe behavior can be predicted with the proper choice of the accommodation coefficients. However, the common assumption of spatially constant accommodation coefficients is found to be a limiting factor in the model.

Application of mixture drift flux equations to vertical separating flows

The one-dimensional drift flux model is widely used in the thermal-hydraulic simulation of nuclear power systems, particularly in simulator and control system modeling where faster-than-real-time solutions are necessary. During normal implementation, however, this model does not correctly simulate buoyancy-driven flows and countercurrent flow of liquid and vapor in vertical, stagnant channels. In this paper, a technique is introduced that overcomes this limitation without using special component models, modifications of the equations of motion, or modifications in constitutive relations.

Stability of one-dimensional natural-circulation flows

Natural circulation is important for the long-term cooling of light water reactors in off-normal conditions, and it is therefore important to understand the numerical behavior of reactor safety codes used to simulate flows under those conditions. While the methods and models in these codes have been studied in some detail, the impact of the weight force term on the numerical behavior has been largely ignored. The dynamic and numerical stability of the one-dimensional, single-phase-flow equations are examined for natural-circulation problems. It is shown that the presence of the weight force in the momentum equation results in a minimum value of the frictional loss coefficient for the equations to be stable. It is further shown that the numerical solution is unstable unless this dynamic stability limit is satisfied. The stability limits developed are verified by numerical solution of the single-phase-flow equations under natural-circulation conditions.

Optimization of Thermal-Hydraulic Reactor System for SMRs via Data Assimilation and Uncertainty Quantification

Abstract This paper discusses the utilization of an uncertainty quantification methodology for nuclear power plant thermal-hydraulic transient predictions, with a focus on small modular reactors characterized by the integral pressurized water reactor design, to determine the value of completing experiments in reducing uncertainty. To accomplish this via the improvement of the prediction of key system attributes, e.g., minimum departure from nucleate boiling ratio, a thermal-hydraulic simulator is used to complete data assimilation for input parameters to the simulator employing experimental data generated by the virtual reactor. The mathematical approach that is used to complete this analysis depends upon whether the system responses, i.e., sensor signals, and the system attributes are or are not linearly dependent upon the parameters. For a transient producing mildly nonlinear response sensitivities, a Bayesian-type approach was used to obtain the a posteriori distributions of the parameters assuming Gaussian distributions for the input parameters and responses. For a transient producing highly nonlinear response sensitivities, the Markov chain Monte Carlo method was utilized based upon Bayes’ theorem to estimate the a posteriori distributions of the parameters. To evaluate the value of completing experiments, an optimization problem was formulated and solved. The optimization addressed both the experiments to complete and the modifications to be made to the nuclear power plant made possible by using the increased margins resulting from data assimilation. The decision variables of the experiment optimization problem include the selection of sensor types and locations and experiment type imposing realistic constraints. The decision variables of the nuclear power plant modification optimization problem include various design specifications, e.g., power rating, steam generator size, and reactor coolant pump size, with the objective of minimizing cost as constrained by required margins to accommodate the uncertainty. Since the magnitude of the uncertainty is dependent upon the experiments via data assimilation, the nuclear power plant optimization problem is treated as a suboptimization problem within the experiment optimization problem. The experiment optimization problem objective is to maximize the net savings, defined as the savings in nuclear power plant cost due to the modified design specifications minus the cost of the experiments. Both the experiment and the nuclear power plant optimization problems were solved using the simulated annealing method.

Wide-Beam X-Ray Source Target Thermal Management Simulation Using Inner Jet Cooling

A wide-beam area X-ray source has been proposed as a practical replacement for synchrotron sources in clinical DEI applications. Due to a wide X-ray illumination area, a decrease in X-ray flux is expected and thus high electron beam currents up to 3A are considered. To ensure the target performance without deterioration, melting, cracking, or even evaporation, an active cooling system is required for the target block in order to remove the heat and allow for sufficient scanning time. In this study, jet cooling of the target back is investigated for a prototype proof-of-principle target. The prototype target was simulated with the transient k- ɛ turbulence multiphysics model in ANSYS CFX. The simulations were conducted at a heat flux of 1.8 × 10 7  W/ m 2 , consistent with values anticipated for a full scale target. The simulation results show that the target temperature exceeds the copper melting point in 2 seconds at inlet velocities below 2 m/s. Also, critical heat flux calculations show that a 1.5 m/s inlet velocity at atmospheric pressure is a lower limit for prevention of target burnout using water as a coolant. Inlet velocities in excess of 2 m/s allows for steady-state operation while satisfying all thermal design constraints.