Moving Boundary Formulation Research Articles

Mathematical modeling and transient thermal-hydraulic analysis of boiling water reactors

This paper presents the development and practical application of a dynamic mathematical model for the simulation of the transient thermal-hydraulic analysis of Boiling Water Reactors (BWRs). In the development of the mathematical model, the reactor core thermal-hydraulic model for the coolant flow along the fuel pin channel is based on the moving boundary concept. Some results from the transient analysis are examined to evaluate the thermal-hydraulic performance of the mathematical model using moving boundaries. These analyses show that the predictions of the mathematical model based on the moving boundary formulation provide a suitable analytical tool for the transient thermal-hydraulic analysis of BWRs.

Thermal-hydraulic transient analysis of light water reactors using moving boundaries

This paper examines the applicability of a mathematical dynamic model developed here for the simulation of the thermal-hydraulic transient analysis for light water reactors (LWRs). The thermal-hydraulic dynamic modeling of the fuel pin and adjacent coolant channel in LWRs is based on the moving boundary concept. The fuel pin model (FUELPIN) with moving boundaries is developed to accommodate the core thermal-hydraulic model, with detailed thermal conduction in fuel elements. Some results from transient calculations are examined for the first application of the thermal-hydraulic model and the fuel pin model with moving boundaries in a boiling water reactor (BWR). An accurate minimum departure from nucleate boiling ratio (MDNBR) and its axial MDNBR boundary versus time within the fuel channel are predicted during transients. Transient analysis using a known thermal-hydraulic code, COBRA and FUELPIN linked with a PWR systems analysis code show that the thermal margin gains more by a transient MDNBR approach than the traditional quasi-steady methodology for a pressurized water reactor (PWR). The studies of the overall nuclear reactor system show that moving boundary formulation provides an efficient and suitable tool for thermal transient analysis of LWRs.

Modeling of nucleation and growth of voids in silicon

During Si crystal growth, nucleation and growth of voids and vacancy-type dislocation loops under Si vacancy supersaturation conditions have been modeled. From nucleation barrier calculations, it is shown that voids can be nucleated, but not dislocation loops. The homogeneous nucleation rate of voids has been calculated for different temperatures by assuming different enthalpy of Si vacancy formation. The void growth process has been calculated using a moving boundary formulation. Matching the results of void nucleation and growth simulations and taking into account the competition between the two processes, limited time available, and the crystal cooling rate, it is shown that the experimentally observed void density and size data can be explained if the Si vacancy formation enthalpy is in the range of 2.8–3.4 eV and the void nucleation temperature is in the range of 970–1060 °C.

A moving-boundary formulation for modeling time-dependent two-phase flows

A mathematical model describing the transient interactions in one-dimensional two-phase flows with heat transfer is presented. A moving-boundary refrigerant model is used to predict the position of the two-phase/vapor interface. A boundary immobilization technique is used to predict the temperature profile along the heat-exchanger wall. Typical results of an evaporator model, in terms of interface position and discharge superheat, are presented for inlet flow disturbances. The model is then used in an overall heat-pump simulation to predict cyclic performance. The results compare favorably to those obtained with a high-fidelity spatially dependent heat-pump model, but require significantly less computational effort.

An application of membrane theory to tip morphogenesis in Acetabularia

Focusing our attention on the cell wall and the plasmalemma (i.e. the cell membrane), we seek to show that the initiation of the regenerative, growing tip in the unicellular marine alga Acetabularia mediterranea, can be predicted using the techniques of thin-shell and elasticity theory. We build upon and extend the work of Goodwin & Trainor (1985, J. theor. Biol. 117, 79-106), Trainor & Goodwin (1986, Physica D. 21D, 137-145) and Brière & Goodwin (1988, J. theor. Biol. 131, 461-475) where the attention was focused on the calcium-regulated strain and stress fields of the cortical cytoplasm. Finally, we attempt to model the subsequent tip growth using a moving-boundary formulation, with cytosolic free calcium concentration and turgor pressure being the two variables responsible for the growth.

Combustion of a finite quatity of gas released in the atmosphere

Low Mach number and large activation energy asymptotic approximations are used to derive a model for the thermal behaviour of a finite planar, cylindrically or spherically symmetric fuel region released in an unconfined oxidant environment. A single one-step exothermic reaction is taken to occur. The induction stage has been studied in a previous paper [1] where it was shown that ignition occurs provided the fuel region exceeds a critical size. Below this size diffusive dilution starves the reaction too quickly for ignition to be possible. In this paper combustion of the system following ignition is studied. The analysis is equally valid whether ignition arises through self-heating or whether it is brought about by some other means such as a spark. Deflagration flames are formed which quickly consume the locally lean species at any point. A criterion is identified for any diffusion flame to exist after the passage of deflagration flames. A non-linear moving boundary formulation is developed to describe the progress and eventual collapse of such diffusion flames as the remaining fuel is consumed. The linearised version of these equations gives an upper limit for the time in which all combustion ceases.

Mathematical modelling of rate-limiting mechanisms of pyritic oxidation in overburden dumps

The mining of valuable minerals often leads to major environmental pollution problems especially when pyritic material is associated with the orebody being mined. In this thesis mathematical equations are formulated which describe a dual region model of pyritic oxidation within a waste rock dump, where it is assumed that oxygen transport is the rate-limiting step in the oxidation process, and that oxygen transport to reaction sites occurs in two stages; bulk diffusion of oxygen from the atmosphere, at the top surface of the dump, through the pore space of the dump to particles within the dump, and then diffusional transport of oxygen from the surface of particles to oxidation sites within the particles. A moving boundary (shrinking-core) formulation, describing transport and reaction processes within a single particle of the dump, is solved by a new analytic series solution technique involving a change of coordinates leading to a non-linear partial differential equation with fixed boundaries. Based on this analysis a pseudo-steady state assumption is made with respect to diffusion within the particles giving a simplified system of equations for the dump model. The system of equations is solved both in an approximate analytic way and numerically. An approximate analytic result is obtained by solving a planar moving boundary formulation which in turn comes from approximation of the position of the moving reaction front within the particles of the dump. The position of the planar front within -vthe dump is given by a transcendental equation which is shown to I collapse on the (time)2 classical planar moving boundary result when the particle size tends to zero. A combined Crank-Nicolson and Backward Euler discretisation of the system of equations is adopted for the numerical scheme. The approximate and numerical solutions