J.M.C. Pereira

Variable Order Modeling of Diffusive-convective Effects on the Oscillatory Flow Past a Sphere

This work advances our understanding of the drag force acting on a particle due to the oscillatory flow of a viscous fluid with finite Reynolds and Strouhal numbers. The drag force is is determined using the novel concept of variable order (VO) calculus, where the order of derivative can vary with the parameters and variables, according to the dynamics of the flow. Using the VO formulation we determine: (i) The region of validity of Tchens equation for oscillatory flow, (ii) the region where the order of the derivative is fractional but constant, and (iii) the region where the strong non-linearity of the flow requires a variable order derivative to account for the increased complexity of the flow.

Adaptive mesh finite-volume calculation of 2D lid-cavity corner vortices

Abstract An anisotropic refinement criterion suitable for Finite-Volume methods is presented and Navier–Stokes solutions are reported for the lid-driven cavity flow configuration at Re = 1000 with adaptive anisotropic meshes (h-refinement). The a posteriori error estimation criterion is based on the assessment of the goodness-of-fit of the least squares regression used to perform the variables profile reconstruction and it is capable of detecting both large-scale and small-scale flow phenomena. The criterion allowed to capture in detail the large-scale flow structure and also the sequence of creeping flow small sharp corner’s [1] eddies, up to the fourth corner vortex in addition to the primary cavity vortex. The smallest corner vortex detected is O ( 10 - 16 ) smaller in velocity magnitude compared with the cavity primary recirculation flow.

Uncertainty quantification in the catalytic partial oxidation of methane

This work focuses on uncertainty quantification of eight random parameters required as input for 1D modelling of methane catalytic partial oxidation within a highly dense foam reactor. Parameters related to geometrical properties, reactor thermophysics and catalyst loading are taken as uncertain. A widely applied 1D heterogeneous mathematical model that accounts for proper transport and surface chemistry steps is considered for the evaluation of deterministic samples. The non-intrusive spectral projection approach based on polynomial chaos expansion is applied to determine the stochastic temperature and species profiles along the reactor axial direction as well as their ensemble mean and error bars with a confidence interval of 95%. Probability density functions of relevant variables in specific reactor sections are also analysed. A different contribution is noticed from each random input to the total uncertainty range. Porosity, specific surface area and catalyst loading appear as the major sources of uncertainty to bulk gas and surface temperature and species molar profiles. Porosity and the mean pore diameter have an important impact on the pressure drop along the whole reactor as expected. It is also concluded that any trace of uncertainty in the eight input random variables can be almost dissipated near the catalyst outlet section for a long-enough catalyst, mainly due to the approximation to thermodynamic equilibrium.

Computational Method for Calculating the Effective Permittivity of Complex Mixtures

Abstract This work presents a computational method for the calculation of the effective complex permittivity of a heterogeneous material using its microscopic properties and structure. The new method to calculate the effective properties aims to guarantee that the electric energy stored and dissipated by the heterogeneous material is the same. The analysis of a bi-phase mixture with periodic cubic sample was tested to check the homogenization of the material. An iterative procedure that corrects the initial permittivity yields an electric field distribution of the effective material that is in good agreement with the electric field of the real mixture.

Variable order modeling of diffusive-convective effects in the oscillatory flow past a sphere

Abstract This work advances our understanding of the drag force acting on a particle due to the oscillatory flow of a viscous fluid at finite Reynolds and Strouhal numbers. The drag force is is determined by using the novel concept of Variable-Order (VO) Calculus, where the order of derivative can vary with the parameters and variables according to the dynamics of the flow. With the VO formulation we determine: (i) the region of validity of Tchens equation for oscillatory flow, (ii) the region where the order of the derivative is fractional, but constant and (iii) the region where the strong non-linearity of the flow requires a variable order derivative to account for the increased complexity of the flow.