Existence theory for a one-dimensional problem arising from the boundary layer analysis of radiative flows

We consider a simplified system of equations which models the transfer of energy with conductive, convective and radiative effects inside a convex region filled with a compressible fluid whose velocity field is known. The asymptotic analysis for positive but small distance from an optically thick medium leads to a one-dimensional system of differential equation which couples the temperature and the radiative intensity. We show that this system obeys a conservation law and this feature is explored in order to reduce the problem to a single one-dimension transport equation with anisotropic scattering. This equation admits a formulation in terms of integral operators in a suitable function space which allows us to establish the existence of a solution and infer its behavior far from the boundary. We also provide numerical simulations and comparison with the theoretical results which we have shown in order to validate our methodology.     

Existence theory and simulations for one-dimensional radiative flows

We consider the coupling of the radiative heat transfer equations and the energy equation for the temperature T of a compressible fluid within the finite segment [0, L]. Using the technique of upper and lower sequences associated to integro-parabolic equations, we establish the existence and uniqueness of a classical solution T, 0 ? Λ₋ ? T(x, t) ? Λ₊ < ∞ with corresponding radiative intensity I(x, Ω, ν, t). The boundary is considered to be semi-reflexive with reflection coefficient ρ, 0 ? ρ(μ) ? 1. The existence of the solution for the coupled system does not depend on any additional hypotheses besides that the total absorption coefficient is bounded and that the ratio between the coefficients of scattering and total absorption is uniformly bounded. As well we present numerical results for the coupled evolutive problem. Using the operational representation encountered in the course of establishing the existence theory, we derive vector Green’s functions for the transport equation which allow us to solve numerically the coupled system.     

A CFD model for particle dispersion in turbulent boundary layer flows

In Lagrangian particle dispersion modeling, the assumption that turbulence is isotropic everywhere yields erroneous predictions of particle deposition rates on walls, even in simple geometries. In this investigation, the stochastic particle tracking model in Fluent 6.2 is modified to include a better treatment of particle–turbulence interactions close to walls where anisotropic effects are significant. The fluid rms velocities in the boundary layer are computed using fits of DNS data obtained in channel flow. The new model is tested against correlations for particle removal rates in turbulent pipe flow and 90° bends. Comparison with experimental data is much better than with the default model. The model is also assessed against data of particle removal in the human mouth–throat geometry where the flow is decidedly three-dimensional. Here, the agreement with the data is reasonable, especially in view of the fact that the DNS fits used are those of channel flows, for lack of better alternatives. The CFD Best Practice Guidelines are followed to a large extent, in particular by using multiple grid resolutions and at least second order discretization schemes.     

A study of non-Boussinesq integral boundary layer analysis for an MTR research reactor

In the present work, a non-Boussinesq (variable physical properties) integral boundary layer analysis is accomplished. The model analyzes laminar free convection between nuclear fuel plates having large fuel plate length to gap between plate ratio. The coolant channels are undergoing to a uniform, symmetric, heat flux and varying fluid properties. In the present study the flow is assumed to be fully developed. This is a good assumption for channels with large fuel plate length to gap between plate ratios. To describe the velocity and temperature distributions of the coolant the non-Boussinesq approximation is introduced into the integral boundary layer equations of flow between parallel plates. The fuel plate temperature is related to the adjacent coolant fluid temperature by a principle in conduction heat transfer. Fluids considered here are air and water. The obtained results show that the present heat transfer problem encountered in nuclear research reactor such Tehran nuclear research reactor (TRR) is characterized by high temperature ratios and thereby rendering the commonly applied Boussinesq approximation invalid. As a result, the use of the Boussinesq approximation (constant fluid properties) for high temperature ratios is not suggested.     

An exact solution for the moving boiling boundary problem

An exact transient solution of the fluid velocity and temperature fields in a one-dimensional incompressible flow within a non-uniformly heated channel is presented. The first order partial differential equations for mass and energy conservation governing this problem are solved using Laplace transform technique. An analytical expression for the boiling boundary (BB) location as a function of time is derived from the temperature field solution when the saturation temperature is inserted. Results obtained reveal the interesting behavior of the temperature field and BB in space and time due to a step change in the fluid inlet mass flow rate.     

某厂址沿海大气边界层和大气扩散特征的数值模拟与分析

利用WRF数值模式和随机游动扩散模式对某厂址沿海地区的中小尺度风场和大气扩散特征进行了数值模拟研究与分析。结果表明,该地区受地形和滨海条件的影响,大气扩散输运总体受天气系统和海陆风环流影响,天气系统环流下风场在水平方向的空间变化不大,扩散烟流基本平直;海陆风环流下的风场随时间变化和空间摆动对当地扩散有重要意义。随机游动模拟方法较好地反映出当地大气扩散特征,特别是在复杂地形及中性层结作用下,放射性污染物易在迎风坡出现堆积现象。     

Application of the theory of random matrices to a reactor-noise problem

The stochastic equation corresponding to a nuclear reactor with random distribution of materials is written in a matrix form, in this way the probability distribution of reactivities is derived as the probability distribution of the higher eigenvalues of random matrices. The theoretical results are illustrated and validated with Monte Carlo simulations based on the diffusion equations and the matrix approach.     

A simple theory for the analysis of pulse trains from neutron counters

The theory of branching processes was applied to the analysis of neutron counting statistics in a previous note. A purely algebraic manipulation of the general formulae leads to a surprisingly simple structured explicit solution for the experimentally measurable quantities (moments of the probability generating function).In this note we show the essential points of this method on a practically important example.     

Solution of the one-dimensional time-dependent discrete ordinates problem in a slab by the spectral and LTSN methods

In this work, we present a new approach to solve the one-dimensional time-dependent discrete ordinates problem (S_N problem) in a slab. The main idea is based upon the application of the spectral method to the set of S_N time-dependent differential equations and solution of the resulting coupling equations by the LTS_N method. We report numerical simulations.     

Turbulent boundary layer control with a spanwise array of DBD plasma actuators

The turbulent boundary layer control on NACA 0012 airfoil with Mach number ranging from 0.3 to 0.5 by a spanwise array of dielectric barrier discharge(DBD)plasma actuators by hot-film sensor technology is investigated.Due to temperature change mainly caused through heat produced along with plasma will lead to measurement error of shear stress measured by hot-film sensor,the correction method that takes account of the change measured by another sensor is used and works well.In order to achieve the value of shear stress change,we combine computational fluid dynamics computation with experiment to calibrate the hot-film sensor.To test the stability of the hot-film sensor,seven repeated measurements of shear stress at Ma = 0.3 are conducted and show that confidence interval of hot-film sensor measurement is from-0.18 to 0.18 Pa and the root mean square is 0.11 Pa giving a relative error 0.5％over all Mach numbers in this experiment.The research on the turbulent boundary layer control with DBD plasma actuators demonstrates that the control makes shear stress increase by about 6％over the three Mach numbers,which is thought to be reliable through comparing it with the relative error 0.5％,and the value is hardly affected by burst frequency and excitation voltage.     

Effective boundary conditions in the theory of neutron diffusion

In this review, a method of determining effective boundary conditions (EBC) is described which guarantees the asymptotic agreement of the solution of the neutron diffusion equation with the solution of the corresponding kinetic equation. For monoenergetic neutrons, the EBC are considered for plane and cylindrical surfaces of black and gray bodies. Results are given for the EBC for the case of cylinders of arbitrary section.The authors discuss the simplest problem in the determination of EBC for neutrons that are slowed-down in a medium with heavy atoms and with an energy-independent cross section. The review gives also results obtained by various authors in the USSR and in other countries.     

Real time application of simultaneous estimation theory for parameters and state to one-dimensional heat conduction

This paper applies filtering theory of the parameters and states of a distributed system to one-dimensional heat conduction in order to obtain information on the real time application of nonlinear estimation theory. This involves a trial to study a simple and fast algorithm for the state estimation of power reactors limited to a small number of sensors by noisy observations. The authors estimated the heat transfer coefficients and the transient temperature profile in a copper rod simultaneously in real time by using a small computer, NOVA 3/12, where the parameter and state of the heat conduction-type P.D.E. could serve as a simplified alternative to the nuclear constant and power profile. The authors also examined the feasibility of a nonlinear filter provided for simultaneous estimation, considering unknown parameters as alternative state variables. The filter tested converged during the sampling period and generated reasonable estimates of the parameter and state from noisy observations with a small number of sensors and at a discrete number of times.     

Solution of a nonlinear diffusion type problem in doubly-connected domains of complicated boundary shape

Variable transformation and the conformal mapping methods are invoked when solving a nonlinear diffusion type problem in doubly-connected domains of complicated boundary shape. Results are presented for prisms with concentric, circular perforations. The results are in good agreement with numerical predictions obtained with a finite element code.     

Finite element analysis of a finite-strain plasticity problem

A finite-strain plasticity analysis was performed of an engraving process in a plastic rotating band during the firing of a gun projectile. The aim was to verify a nonlinear feature of the NIFDI/RB code: plastic large deformation analysis of nearly incompressible materials using a deformation theory of plasticity approach and a total Lagrangian scheme.     

Application of the finite-element method to a linear diffusion problem with reversible trapping and an eroding boundary

The finite-element technique (FEM) is applied to a mass diffusion problem in slab geometry with an eroding boundary and subject to reversible trapping, general extraneous source distribution and Dirichlet and Neumann boundary conditions. Numerical results show excellent agreement with those obtained by a generalized integral-transform technique (ITT). Computation time is significantly shorter than for the ITT solution and the FEM is able to solve the problem in regions where the ITT solution develops inaccuracies.