A thermodynamic analysis of forced convection through porous media using pore scale modeling

The flow thorough porous media is analyzed from a thermodynamic perspective, with a particular focus on the entropy generation inside the porous media, using a pore scale modeling approach. A single representative elementary volume was utilized to reduce the CPU time. Periodic boundary conditions were employed for the vertical boundaries, by re-injecting the velocity and temperature profiles from the outlet to the inlet and iterating. The entropy generation was determined for both circular and square cross-sectional configurations, and the effects of different Reynolds numbers, assuming Darcy and Forchheimer regimes, were also taken into account. Three porosities were evaluated and discussed for each cross-sectional configuration, and streamlines, isothermal lines and the local entropy generation rate contours were determined and compared. The local entropy generation rate contours indicated that the highest entropy generation regions were close to the inlet for low Reynolds flows and near the central cylinder for high Reynolds flows. Increasing Reynolds number from 100 to 200 reveals disturbances in the dimensionless volume averaged entropy generation rate trend that may be due to a change in the fluid flow regime. According to Bejan number evaluation for both cross-section configurations, it is demonstrated that is mainly provoked by the heat transfer irreversibility. A performance evaluation criterion parameter was calculated for different case-studies. By this parameter, conditions for obtaining the least entropy generation and the highest Nusselt number could be achieved simultaneously. Indeed, this parameter utilizes both the first and the second laws of thermodynamics to present the best case-study. According to the performance evaluation criterion, it is indicated that the square cross-section configuration with o=0.64 exhibits better thermal performance for low Reynolds number flows. A comparison between the equal porosity cases for two different cross-sectional configurations indicated that the square cross-section demonstrated a higher performance evaluation criterion than the circular cross-section, for a variety of different Reynolds numbers

Numerical Algorithms for a Variational Problem of the Spatial Segregation of Reaction-Diffusion Systems

In this paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support, which are governed by a minimization problem. We use quantitative properties of both solutions and free boundaries to derive our scheme. Furthermore, the proof of convergence of the numerical method is given in some particular cases. We also apply our numerical simulations for the spatial segregation limit of diffusive Lotka-Volterra models in presence of high competition and inhomogeneous Dirichlet boundary conditions. We discuss numerical implementations of the resulting approach and present computational tests

A Method for Geometry Optimization in a Simple Model of Two-Dimensional Heat Transfer

This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations and involving a one-dimensional cooling element represented by a contour on which interface boundary conditions are specified. The problem consists in finding an optimal shape of the cooling element which will ensure that the solution in a given region is close (in the least squares sense) to some prescribed target distribution. We formulate this problem as PDE-constrained optimization and the locally optimal contour shapes are found using a gradient-based descent algorithm in which the Sobolev shape gradients are obtained using methods of the shape-differential calculus. The main novelty of this work is an accurate and efficient approach to the evaluation of the shape gradients based on a boundary-integral formulation which exploits certain analytical properties of the solution and does not require grids adapted to the contour. This approach is thoroughly validated and optimization results obtained in different test problems exhibit nontrivial shapes of the computed optimal contours.Comment: Accepted for publication in "SIAM Journal on Scientific Computing" (31 pages, 9 figures

An optimal adiabatic-to-diabatic transformation of the 1 2A[prime] and 2 2A[prime] states of H3

Molecular reaction dynamics in the adiabatic representation is complicated by the existence of conical intersections and the associated geometric phase effect. The first-derivative coupling vector between the corresponding electronically adiabatic states can, in general, be decomposed into longitudinal (removable) and transverse (nonremovable) parts. At intersection geometries, the longitudinal part is singular, whereas the transverse part is not. In a two-electronic-state Born–Huang expansion, an adiabatic-to-diabatic transformation completely eliminates the contribution of the longitudinal part to the nuclear motion Schrödinger equation, leaving however the transverse part contribution. We report here the results of an accurate calculation of this transverse part for the 1 2A[prime] and 2 2A[prime] electronic states of H3 obtained by solving a three-dimensional Poisson equation over the entire domain [sans-serif U] of internal nuclear configuration space [script Q] of importance to reactive scattering. In addition to requiring a knowledge of the first-derivative coupling vector everywhere in [sans-serif U], the solution depends on an arbitrary choice of boundary conditions. These have been picked so as to minimize the average value over [sans-serif U] of the magnitude of the transverse part, resulting in an optimal diabatization angle. The dynamical importance of the transverse term in the diabatic nuclear motion Schrödinger equation is discussed on the basis of its magnitude not only in the vicinity of the conical intersection, but also over all of the energetically accessible regions of the full [sans-serif U] domain. We also present and discuss the diabatic potential energy surfaces obtained by this optimal diabatization procedure

Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow

The present work provides an optimal control strategy, based on the nonlinear Navier–Stokes equations, aimed at hampering the rapid growth of unsteady finite-amplitude perturbations in a Blasius boundary-layer flow. A variational procedure is used to find the blowing and suction control law at the wall providing the maximum damping of the energy of a given perturbation at a given target time, with the final aim of leading the flow back to the laminar state. Two optimally growing finite-amplitude initial perturbations capable of leading very rapidly to transition have been used to initialize the flow. The nonlinear control procedure has been found able to drive such perturbations back to the laminar state, provided that the target time of the minimization and the region in which the blowing and suction is applied have been suitably chosen. On the other hand, an equivalent control procedure based on the linearized Navier–Stokes equations has been found much less effective, being not able to lead the flow to the laminar state when finite-amplitude disturbances are considered. Regions of strong sensitivity to blowing and suction have been also identified for the given initial perturbations: when the control is actuated in such regions, laminarization is also observed for a shorter extent of the actuation region. The nonlinear optimal blowing and suction law consists of alternating wall-normal velocity perturbations, which appear to modify the core flow structures by means of two distinct mechanisms: (i) a wall-normal velocity compensation at small times; (ii) a rotation-counterbalancing effect al larger times. Similar control laws have been observed for different target times, values of the cost parameter, and streamwise extents of the blowing and suction zone, meaning that these two mechanisms are robust features of the optimal control strategy, provided that the nonlinear effects are taken into account