Defect and Diffusion Forum Vol. 396

Abstract: This work presents an analytical solution for the transient three-dimensional advection-diffusion equation to simulate the dispersion of pollutants in the atmosphere. The solution of the advection-diffusion equation is obtained analytically using a combination of the methods of separation of variables and GILTT. The main advantage is that the presented solution avoids a numerical inversion carried out in previous works of the literature, being by this way a totally analytical solution, less than a summation truncation. Initial numerical simulations and statistical comparisons using data from the Copenhagen experiment are presented and prove the good performance of the model.

Abstract: This paper presents results of the test of methods for numerical inversion of the Laplace Transform for solving the one-dimensional advection-diffusion equation, which describes solute transport processes, focusing on the contaminant transport in a porous medium. The performance of Stehfest and Power Series Expansion methods is analyzed, for diffusion-dominated and advection-dominated transport problems under linear flow condition. Numerical results are compared to the analytical solution by means of the absolute error. Based on these results, we concluded that both methods, Stehfest and Power Series Expansion, are recommended only for diffusion-dominated cases.

Abstract: A modelling system was utilised to simulate the movement and behaviour of oil slicks for two types of hydrocarbons, a diesel and another residual, considering hydrodynamic variations. Susceptible areas to oil touching were found in adjacent regions of two vessel manoeuvring zones, in two types of zones, one in a marine coastal and another in an estuarine environment. The evaporation rates were calculated for an estimate of the mass losses. For the maritime zone, the oil particles reached the vicinity of the beaches in approximately 4 to 8 hours after the beginning of the spill simulations, while for the estuary in approximately 1 hour. For the scenarios with diesel oil, mass losses oscillated between 13 to 16% in the estuarine region, and between 23 and 29% in the marine coastal zones. The evaporation rates for scenarios with residual oil, between 2 and 5%, were considerably lower than for diesel (15 and 22%), especially for spills simulated in the estuarine region, where the oil particles reached the lagoon banks after 1 hour. Mass losses by evaporation were more intense in marine coastal areas than for oil spills simulated in estuarine regions, possibly due to the more intense hydrodynamic conditions and the longer time that the oil needs to reach the coast. The fluctuations of observed environmental conditions justify the need for a robust number of simulations for reducing the uncertainties related to the oceanographic and meteorological variability that affect oil spill movement.

Abstract: The global transportation of fossil fuels occurs mainly by sea and grows annually, along with the risks to the marine ecosystems, especially in the vicinity of navigation routes. Numerical simulations able to reproduce realistic oil spill scenarios can be utilised for planning risk mitigation actions. This study is based on simulating the behaviour and weathering rates recorded during the first 24 h after an oil spill that occurred in an estuarine region. The numerical system used is the ECOS (Easy Coupling Oil System) oil spill model coupled to the three-dimensional hydrodynamic model Telemac-3D. The hydrodynamic results were analysed considering wind velocity fields and currents, which are the dominant forces in the displacement and behaviour of the oil. The reproducibility of the oil leak was confirmed by comparing the results of the simulations with the official environmental emergency report of the accident. The strong correlation between the simulation and the report showcases the capacity of the simulation methodology to reproduce real case scenarios of oil spills.

Abstract: Thermal mechanism analysis of heat exchange between a gas phase flow and the internal region of a particulate is still a subject of interest among researchers, mainly due to its complexity and lack of a simplified (in terms of computational effort) solution. Main goal of present work is to develop a simplified model capable of predict internal particle temperature, as a function of its surface temperature and flow conditions, in a fluidized bed, transporting spherical particles. Proposed model was implemented in C++ programming language and an algorithm was developed to solve two energy equations, for gas and particulate phases, and an algebraic equation to determine internal particle temperature. As a result, predicted particle temperature decreases while gas temperature rises. At approximate 12 m, both temperatures reach the equilibrium at 755 K which remains unaltered up to the riser outlet section. Energy balance verification, between inlet and outlet riser sections, showed that proposed model and balance calculated temperatures agree with a difference of 1.804E−11 kW on the outlet. In terms of internal particle temperature, results showed that it remains higher than surface temperature from riser entrance up to approximated 32.8 m. After this point it reaches surface temperature, which already is in equilibrium with the gas phase temperature.

Abstract: In the present work it is investigated the performance of an algorithm that associates Differential Evolution and Constructal Design for geometrical optimization of a heat transfer problem. It is considered the intrusion of a cooled Double T-shaped cavity into a rectangular conducting solid wall with internal heat generation. The main purpose here is to evaluate the algorithm capability to reproduce the effect of geometric ratios over the dimensionless maximum excess of temperature (performance indicator of the heat transfer problem), as well as, the influence of Differential Evolution (DE) parameters over the optimization analysis. The definition of search space for each degree of freedom and problem constraints is performed with Constructal Design, while the Differential Evolution algorithm is used in the optimization process. Here parameters as mutation operator (M), crossover constant (CR), differential amplification factor (F), Population Size (PS) and Generations number (G) are evaluated. A theoretical recommendation about the suitable parameters set for the optimization algorithm for this kind of heat transfer problem is proposed. Results indicated that the crossover constant (CR) and amplification factor (F) are important parameters for suitable prediction of the effect of degrees of freedom over thermal performance. Moreover, when CR = 0.7 and F = 1.5 results obtained with the algorithm are more robust for the achievement of the best shapes and requires lower number of iterations (IT = PS × G) for reproduction of effect of geometric variables over performance.

Abstract: In the present work it is performed a study on the geometric evaluation of a pair of elliptical tubes subjected to external flow with forced convection by means of numerical approach. The objectives are the maximization of Nusselt number (Nu_D) and the minimization of drag coefficient (C_D). The degrees of freedom for the pair of tubes arrangement are: the ratio between the transverse pitch and characteristic length of tubes (S_T/D), where D = (A)^1/2, the ratio of the main and secondary axes of the elliptical tube (a/b) and the angle of incidence of the flow on the pair of tubes (α). The simulations were carried out considering two-dimensional forced convective flows, in the laminar regime and incompressible conditions. For all configurations, Reynolds and Prandtl numbers are constant, Re_D = 100 and Pr = 0.71. The Finite Volume Method (FVM) is used to solve conservation equations of mass, momentum and energy. The software Gmsh is used for creation of the geometries and generation of the meshes. Results showed that the degrees of freedom affected the fluid dynamic and thermal performance of the forced convective flow. According to the objectives outlined in this study, the best performance for the maximization of heat transfer was obtained when α = 0o, a/b = 1⁄2 and S_T/D = 3.5. In the case of the fluid dynamics study, the optimal result for C_D minimization occurred when α = 0o, a/b = 2.0 and S_T/D = 4.0. Thus, the optimal geometry will depend on the indicator performance where the problem is evaluated.

Abstract: In this work, a numerical study of a flow with heat transfer by mixed convection are carried out. The objective is the geometric evaluation through the application of the Construtal Design and the exhaustive search method. The behavior of a lid-driven cavity with stable stratification subjected to an incompressible, laminar and two-dimensional flow is investigated. The cavity has two rectangular fins inserted in the lower surface. The problem is subject to three constrains: three geometric constraints: the area of the cavity, two fin areas. The investigated geometry has three degrees of freedom: the ratio between height and cavity length (H/L) and the ratio between height and length of each fin (H₁/L₁ and H₂/L₂). The effect of the fin geometry over spatial-averaged Nusselt (Nu_H) is investigated for Reynolds number (Re_H) = 400 and Richardson (Ri) = 0.1. The conservation equations of mass, momentum and energy are tackled with Finite Volume Method (FVM) through the use of commercial software FLUENT. The results showed that the lower H₂/L₂ ratios resulted in higher Nu_H values. An increase in Nu_H value of approximately 49% between the worst and the best geometrical configuration was found, thus highlighting the importance of geometric evaluation on this kind of problem. It is concluded that for the problem addressed the best behavior is obtained when the fins have a small insertion into the cavity, thus avoiding the restriction of the main vortex flow. The results found highlight the importance of the geometric evaluation for the purpose of theoretical recommendation on the geometric configurations that lead to the best thermal performance.

Abstract: This article presents the results of flows in "T" shaped duct bifurcations. The problem is to find the resistance to flow in three-dimensional (3D) structures with different homothetic relationships between sizes (diameters and lengths) of parent and daughter ducts. The method used is the Constructal Design, which is based on the Constructal Theory. The minimization of the global resistance to flow, subjected to geometric constraints of volume and area occupied by the ducts, is the key to search for optimum configurations. The flows investigated were three-dimensional, laminar, incompressible, in steady state, with uniform and constant properties. The results obtained numerically were verified via comparison with analytical results available in the literature. In this work, ranges of length and ratio of diameterss from 0.5 to 1 and 0.1 to 1, respectively, were investigated, for Reynolds numbers equal to 10² and 10³. The main results indicate that the T-shaped structure with impermeable walls, agree with Hess-Murray's law.

Abstract: . The increased occurrence of floods in the city of Rio do Sul (SC), even with the creation of dams to contain floods, show that non-structural measures can be good alternatives to reduce losses in the region. Numerical flood modeling has been widely used to anticipate risks and assist in decisionmaking. One of the numerical models that is being used to simulate floods is TELEMAC-2D, which is able to simulate the hydrodynamics of open channels by solving the shallow water equations in a domain discretized by an unstructured finite element mesh. We used the TELEMAC-2D model tosimulate the dynamics of the rivers of the region of Rio do Sul throughout the year of 2013, period during which a flood with large proportions occurred in September. Fluviometric data avaliable from the National Water Agency and high resolution (1 m) topographic data provided by government agen-cies of Santa Catarina were used in the simulation. The results show that the model performed well in simulating the maximum flood extension occurred in September, however, the simulations were underestimated for most of the time, indicating that calibrations in the model can still be performed.