Fourier Transformation method for solving integral equation in the 2.5D problem of electric sounding

The paper discusses a method for solving an integral equation for calculating a three-dimensional electric field in a medium with a two-dimensional geometry based on the Fourier transform. The results of the numerical solution of the transformed integral equation and the original integral equation for the medium with the surface relief are compared. The original equation was solved using parallelization technologies on a system with shared memory. A significant performance improvement based on the transformed equations, including in comparison with the parallel version of the program for the original integral equation, is shown.

A new Fourier transformation method for SAXS of polymer lamellar crystals

The interface distribution function is composed mainly of the self-interference item of the first interface F11, the interference term of the first and the second interfaces F12, and the interference term of the first and the third interfaces F13.

Potential of Workshop Measurement Positioning System to Measure Oscillation Frequencies of Rigid Structures

A workshop measuring and positioning system (wMPS) is a large three-dimensional (3D) coordinate-measurement system based on optoelectronic scanning. It is capable of large-range coverage, high measurement accuracy and frequency, and multi-task synchronous measurement. Existing geodetic instruments cannot measure the intrinsic parameters of strong rigid structures. Thus, this study conducted experiments to explore the feasibility of the wMPS to measure the intrinsic parameters of rigid structures. A test bed was established using a reverse-engineering method to simulate the oscillation frequency of the structure. Displacement data, which changed with the time series through the fast Fourier transformation method, were analyzed to determine the feasibility and range of the wMPS in measuring intrinsic parameters of the structure. The experimental results demonstrated that the wMPS can measure the vibrational frequency up to 9 Hz with a 3-mm amplitude and up to 4 Hz with a 30-mm amplitude.

Influence of Flow Coefficient on the Unsteady Impeller Loading Induced by the Impeller-Diffuser Interaction

Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulation has been conducted to investigate how flow coefficient affects unsteady impeller loading. Simulations have been carried out at three flow coefficients — near stall, design, and near choke conditions — for a radial gap of 1.04. For computational efficiency, the unsteady simulation has been conducted for two impeller and diffuser passages via Fourier Transformation method. Both steady and unsteady simulations have been validated against experimental data. The unsteady loading (the difference between the maximum and minimum loadings) is the largest at the near stall condition; second largest at the near choke condition; and smallest at the design condition. Flow coefficient effects on the unsteady impeller loading are mostly due to the variations in pressure fluctuations on the pressure side of the impeller blade. Relative to the design condition, the near stall condition shows lower minimum loading and the near choke condition shows higher maximum loading. Thus, both off design conditions result in higher unsteady loading than the design condition. Such differences stem from the variations in the pitch-wise static pressure at the diffuser vane inlet caused by the flow incidence onto the diffuser vanes.

On the Impact of Simulation Approaches on the Predicted Aerodynamic Damping of a Low Pressure Steam Turbine Rotor

The determination of the aerodynamic damping is a major task in predicting flutter stability and therefore safety margins for turbine operation. Throughout the current work the energy method is employed to predict the aerodynamic damping for a last stage rotor blade numerically. The focus is put on the prediction of the aerodynamic damping with different traveling wave mode representations and on the influence of the blade fixation at the root. The Fourier transformation-method, the influence-coefficients-method and a direct traveling wave mode calculation are employed. The investigated rotor geometry was taken from the open literature, a root was designed and an iterative process was installed to determine the cold blade geometry. It became apparent, that the influence-coefficients-method is capable of predicting the overall stability curve computationally efficient, whereas the Fourier-transformation-method showed advantages in the identification of the least stable point for a finer mesh. Nevertheless, all methods predicted a potential flutter risk for the current operating point. The influence of the additional blade root with a completely fixed support on the aerodynamic damping is minor.

Fast Fourier Transformation method for computing the permeability of periodic porous media

A Fourier-based method is adopted to determine the permeability of periodic porous media made up of a rigid skeleton saturated by viscous fluid. The flow, induced by a prescribed macroscopic gradient of pressure, adopts the Stokes equations with incorporating a condition of adherence at the surface of the solid. The permeability is determined by solving a linear problem on a unit cell for which we determine the local velocity fields due to a prescribed gradient of pressure. The method uses the Fourier Transformation and exact expressions of the periodic Green tensor in the Fourier space. It is shown that the resolution of the problem requires an introducing of undetermined forces acting within the solid phase.

FFT simulations and multi-coated inclusion model for macroscopic conductivity of 2D suspensions of compound inclusions

Article introduces the Fast-Fourier transformation method (FFT) and an approximation method to calculate the conductivity of compound-inclusion composites in two-dimensional space. The approximation compares favorably with the numerical results for a number of periodic and random models over a range of volume proportions of phases, but divers at large volume proportions of the included phases when the interactions between the inclusions are more pronounced.