Finite difference method

Abstract: A model describing the propagation of a binary mixture at finite concentration in nonlinear liquid chromatography is discussed. This model consists of two mass balance equations, one for each solute. A finite difference method is used to derive numerical solutions of this set of nonlinear partial differential equation with boundary conditions corresponding to the elution of large concentration bands. These solutions describe the shape of the elution profiles of partially resolved compounds. Although the model used corresponds to ideal chromatography (constant equilibrium between the mobile and stationary phase, i.e., infinite column efficiency), it is possible to simulate the smoothing effect of a finite column efficiency by properly selecting the differential space element in the numerical integration. The numerical solutions appear to converge satisfactorily toward a stable solution of the system of equations provided the Courant-Friedrichs-Lewy (CFL) criterion is met in the choice of the integration parameters. The profiles obtained are very realistic and fare quite well with experimental results retrieved from the literature. Some of the results obtained are discussed in detail.

Abstract: The subsonic flow through highly loaded low-pressure turbines is simulated numerically using a high-order method. The configuration approximates cascade experiments that were conducted to investigate a reduction in turbine stage blade count, which can decrease both weight and mechanical complexity. At a nominal Reynolds number of 25 × 10 3 based upon axial chord and inlet conditions, massive separation occurs on the suction surface of each blade as a result of uncovered turning. Pulsed injection vortex generator jets were then used to help mitigate separation, thereby reducing wake losses. Computations were performed for both uncontrolled and controlled cases and reproduced the transitional flow occurring in the aft-blade and near-wake regions. The numerical method utilizes a centered compact finite difference scheme to represent spatial derivatives, which is used in conjunction with a low-pass Pade-type nondispersive filter operator to maintain stability. An implicit approximately factored time-marching algorithm is employed, and Newton-like subiterations are applied to achieve second-order temporal accuracy. Calculations were carried out on a massively parallel computing platform, using domain decomposition to distribute subzones on individual processors. A high-order overset grid approach preserved spatial accuracy in locally refined embedded regions. Features of the flowfields are elucidated, and simulations are compared with each other and with available experimental data. Relative to the uncontrolled case, it was found that pulsed injection maintained attached flow over an additional 15% of the blade chord, resulting in a 22% decrease of the wake total pressure loss coefficient.

Abstract: We report on recent advances in the modeling of magnetic losses in steel laminations used in electromagnetic devices. The integrated-lamination moving dynamic Preisach model, used to evaluate the dynamic magnetization loops under distorted unidirectional flux patterns, is described. The main goal is the comparison of two numerical procedures, using the finite element-finite difference technique and the finite element-fixed point technique, respectively, each properly taking into account the hysteresis characteristics by the Preisach theory. Moreover, attention is paid to the identification of the material parameters entering the moving dynamic Preisach model. Finally, the two techniques are validated by the comparison of numerical experiments and measurements on two different materials. Here, global as well as local quantities in the lamination structure are evaluated.