M.T. de Vilhena

Determination of the exposure build-up factor in a slab using the LTSN method

Abstract In this paper an exposure build-up factor formulation is reported by solving the photon transport equation in a heterogeneous slab by the LTSN method, assuming the Klein-Nishina scattering kernel as the scattering differential cross section as well as the multigroup model in the wavelength variable. Numerical simulations and comparisons with available results in the literature are presented for different compositions containing water, iron and lead.

Existence Theory for Radiative Flows

We consider the coupling of radiative heat transfer equations and the energy equation for the temperature Tof a compressible fluid occupying a bounded convex region D with smooth boundary. Using the technique of upper and lower sequences associated with integro-parabolic equations, we establish the existence and uniqueness of a solution T, 0 ≤ Λ− ≤ T(x,t) ≤ Λ+ < ∞ with corresponding radiative intensity I(x,Ω,ν,t) where the total incident radiation satifies ∫S2 I(x,Ω,ν,t)dΩ = Sg B(ν,t)+Sb B(ν,Tb), and where Sb and Sg are positivity preserving linear operator, Tb is the external temperature of the boundary, and B is Plancks function. We also establish certain energy estimates for T.

An algebraic expression for the eddy diffusivities in the stable boundary layer: a description of near-source diffusion (*)

SummaryAn algebraic formulation to evaluate the eddy diffusivities for a turbulent Stable Boundary Layer (SBL) is described in this paper. The method is based on the local similarity and Taylors diffusion theory. The eddy diffusivities are functions of distance from the source and represent correctly the near-source diffusion in weak winds. The agreement with the eddy diffusivities available by an integral formulation indicates that the hypothesis of using an algebraic formulation as a surrogate for eddy diffusivities in the turbulent SBL is valid.

Existence Theory for the Solution of a Stationary Nonlinear Conductive‐Radiative Heat‐Transfer Problem in Three Space Dimensions

Abstract In this work we show that a stationary nonlinear coupled radiative‐conductive heat‐transfer problem in a convex bounded region with piecewise differentiable boundary in three dimensions under fairly general boundary conditions has a unique solution in a segment of a positive cone in a certain function space.

Improved Dancoff factors for cluster fuel bundles by the WIMSD code

Abstract The recently developed tracking routine PIJM, for computing improved two-dimensional first-flight collision matrices for the WIMSD code, has been modified to evaluate black Dancoff factors for cluster fuel bundles in unit cells with cylindrical outer boundaries. The routine, similar to the original PIJ but employing an efficient in-plane integration scheme of the Bickley functions appearing in those expressions, is first compared with the accurate Carlvik method in the calculation of Dancoff factors for regular lattices, both with and without a gap surrounding the fuel rods. Dancoff factors for the more general cases of CANDU37 and CANFLEX fuel bundles are next obtained and compared with Monte Carlo based calculations, illustrating the accuracy of the proposed scheme.

An analytical solution for the nonlinear energy spectrum equation by the decomposition method

We discuss the isotropic turbulence decay and solve the energy density spectrum (EDS) equation considering the inertial transfer energy and viscosity terms, using the Heisenberg parameterization. In the present approach, buoyant and shear terms are neglected and turbulence is assumed to be homogeneous and isotropic. The nonlinear integro-differential equation is solved by Adomians generic decomposition method, which yields an analytical recursive expression and upon truncation gives an approximate solution. We show the resulting EDS and the time-dependent decay of the intensity of the turbulent kinetic energy. Our results prove consistent the Heisenberg parameterization for the transfer term of the inertial energy. The analytical character of the solution permits a validation of the nonlinear details of the physical model.

Heuristic geometric “eigenvalue universality” in a one-dimensional neutron transport problem with anisotropic scattering

Abstract In the present work we propose a heuristic construction of a transport equation for neutrons with anisotropic scattering considering only the radial cylinder dimension. The eigenvalues of the solutions of the equation correspond to the positive values for the one dimensional case. The central idea of the procedure is the application of the SN method for the discretisation of the angular variable followed by the application of the zero order Hankel transformation. The basis the construction of the scattering terms in form of an integro-differential equation for stationary transport resides in the hypothesis that the eigenvalues that compose the elementary solutions are independent of geometry for a homogeneous medium. We compare the solutions for the cartesian one dimensional problem for an infinite cylinder with azimuthal symmetry and linear anisotropic scattering for two cases.

Deterministic calculation of grey Dancoff factors in cluster cells with cylindrical outer boundaries

Abstract In the present work, the WIMSD code routine PIJM is modified to compute deterministic Dancoff factors by the collision probability definition in general arrangements of partially absorbing fuel rods. Collision probabilities are calculated by an efficient integration scheme of the third-order Bickley functions, which considers each cell region separately. The effectiveness of the method is assessed by comparing grey Dancoff factors as calculated by PIJM, with those available in the literature by the Monte Carlo method, for the irregular geometry of the Canadian CANDU and CANFLEX assemblies. Dancoff factors at several different fuel pin positions are found in very good agreement with the literature results.

Simulating Boundaries for a Cascade-Like Flux Using a Fractal Scheme

The present work is an attempt to analyze a specific class of problems—fluxes with cascade like phenomenology and show how boundaries may be simulated by a fractal scheme approach. We start from a cascade transport equation, introduce the conception of an inclusive lacunarity and show how such a procedure reduces complex boundaries to a Cantor set construction rule C with lacunarity (N; d), i.e., a fractal scheme.

An Implicit Inversion Method for Estimating Boundary Conditions in Hydrologic Optics

An important topic in radiative process is the estimation of some characteristics of the media and/or other conditions of the problem.