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This study aims to analyse the non-linear losses of a porous media (stack) composed by parallel plates and inserted in a resonator tube in oscillatory flows by proposing numerical correlations between pressure gradient and velocity.

The numerical correlations origin from computational fluid dynamics simulations, conducted at the microscopic scale, in which three fluid channels representing the porous media are taken into account. More specifically, for a specific frequency and stack porosity, the oscillating pressure input is varied, and the velocity and the pressure-drop are post-processed in the frequency domain (Fast Fourier Transform analysis).

It emerges that the viscous component of pressure drop follows a quadratic trend with respect to velocity inside the stack, while the inertial component is linear also at high-velocity regimes. Furthermore, the non-linear coefficient b of the correlation ax + bx² (related to the Forchheimer coefficient) is discovered to be dependent on frequency. The largest value of the b is found at low frequencies as the fluid particle displacement is comparable to the stack length. Furthermore, the lower the porosity the higher the Forchheimer term because the velocity gradients at the stack geometrical discontinuities are more pronounced.

The main novelty of this work is that, for the first time, non-linear losses of a parallel plate stack are investigated from a macroscopic point of view and summarised into a non-linear correlation, similar to the steady-state and well-known Darcy–Forchheimer law. The main difference is that it considers the frequency dependence of both Darcy and Forchheimer terms. The results can be used to enhance the analysis and design of thermoacoustic devices, which use the kind of stacks studied in the present work.

Performing accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various manufacturing steps, e.g. heat treatment or cutting techniques, the magnetic material properties can strongly vary locally, and the assumption of homogenized global material parameters is no longer feasible. This paper aims to present the general methodology and two different solution strategies for determining the local magnetic material properties using reference and simulation data.

The general methodology combines methods based on measurement, numerical simulation and solving an inverse problem. Therefore, a sensor-actuator system is used to characterize electrical steel sheets locally. Based on the measurement data and results from the finite element simulation, the inverse problem is solved with two different solution strategies. The first one is a quasi Newton method (QNM) using Broyden's update formula to approximate the Jacobian and the second is an adjoint method. For comparison of both methods regarding convergence and efficiency, an artificial example with a linear material model is considered.

The QNM and the adjoint method show similar convergence behavior for two different cutting-edge effects. Furthermore, considering a priori information improved the convergence rate. However, no impact on the stability and the remaining error is observed.

The presented methodology enables a fast and simple determination of the local magnetic material properties of electrical steel sheets without the need for a large number of samples or special preparation procedures.