A Note on the Iterative MRI Reconstruction from Nonuniform k-Space Data

In magnetic resonance imaging (MRI), methods that use a non-Cartesian grid in k-space are becoming increasingly important. In this paper, we use a recently proposed implicit discretisation scheme which generalises the standard approach based on gridding. While the latter succeeds for sufficiently uniform sampling sets and accurate estimated density compensation weights, the implicit method further improves the reconstruction quality when the sampling scheme or the weights are less regular. Both approaches can be solved efficiently with the nonequispaced FFT. Due to several new techniques for the storage of an involved sparse matrix, our examples include also the reconstruction of a large 3D data set. We present four case studies and report on efficient implementation of the related algorithms

An Empirical Wall Law for the Mean Velocity in an Adverse Pressure Gradient for RANS Turbulence Modelling

An empirical wall law for the mean velocity in an adverse pressure gradient is presented, with the ultimate goal of aiming at the improvement of RANS turbulence models and wall functions. For this purpose a large database of turbulent boundary-layer flows in adverse pressure gradients from wind tunnel experiments is considered, and the mean velocity in the inner layer is analysed. The log law in the mean velocity is found to be a robust feature. The extent of the log-law region is reduced in ratio to the boundary layer thickness with increasing strength of the pressure gradient. An extended wall law emerges above the log law, extending up to the outer edge of the inner layer. An empirical correlation to describe the reduction of the log-law region is proposed, depending on the pressure-gradient parameter and on the Reynolds number in inner viscous scaling, whose functional form is motivated by similarity and scaling arguments. Finally, there is a discussion of the conjecture of the existence of a wall law for the mean velocity, which is governed mainly by local parameters and whose leading order effects are the pressure gradient and the Reynolds number, but whose details can be perturbed by higher-order local and history effects

An Empirical Wall Law for the Mean Velocity in Adverse Pressure Gradients

An empirical wall law for the mean velocity in an adverse pressure gradient is presented, with the ultimate goal of aiming at the improvement of RANS turbulence models and wall functions. For this purpose a large database of turbulent boundary-layer flows in adverse pressure gradients from wind tunnel experiments is considered, and the mean velocity in the inner layer is analysed. The log law in the mean velocity is found to be a robust feature. The extent of the log-law region is reduced in ratio to the boundary layer thickness with increasing strength of the pressure gradient. An extended wall law emerges above the log law, extending up to the outer edge of the inner layer. An empirical correlation to describe the reduction of the log-law region is proposed, depending on the pressure-gradient parameter and on the Reynolds number in inner viscous scaling, whose functional form is motivated by similarity and scaling arguments. Finally, there is a discussion of the conjecture of the existence of a wall law for the mean velocity, which is governed mainly by local parameters and whose leading order effects are the pressure gradient and the Reynolds number, but whose details can be perturbed by higher-order local and history effects

Unique Compact Representation of Magnetic Fields using Truncated Solid Harmonic Expansions

Precise knowledge of magnetic fields is crucial in many medical imaging applications like magnetic resonance imaging or magnetic particle imaging (MPI) as they are the foundation of these imaging systems. For the investigation of the influence of field imperfections on imaging, a compact and unique representation of the magnetic fields using real solid spherical harmonics, which can be obtained by measuring a few points of the magnetic field only, is of great assistance. In this manuscript, we review real solid harmonic expansions as a general solution of Laplace's equation including an efficient calculation of their coefficients using spherical t-designs. We also provide a method to shift the reference point of an expansion by calculating the coefficients of the shifted expansion from the initial ones. These methods are used to obtain the magnetic fields of an MPI system. Here, the field-free-point of the spatial encoding field serves as unique expansion point. Lastly, we quantify the severity of the distortions of the static and dynamic fields in MPI by analyzing the expansion coefficients.Comment: 25 page

Experimental study of the inner layer of an adverse-pressure-gradient turbulent boundary layer

We present an analysis of the inner layer of adverse-pressure-gradient turbulent boundary layers at Reynolds numbers up te Re-theta=57000. The major aim is to determine the resilience of the log-law, the possible change of the log-law slope and the appearance of a square-root law above the log-law at significant adverse pressure gradients. The second objective is to characterise the total shear stress. The third aim is to provide a well-defined test case for the validation and improvement of numerical flow simulation methods. We designed and performed a new wind-tunnel experiment, in which the turbulent boundary layer flow of interest develops on the side wall of the wind-tunnel and then follows an accelerating ramp and a long flat plate at almost zero pressure gradient. Then the flow enters into the adverse pressure gradient section, first along a curved surface and then on a flat plate. We use a large-scale overview particle imaging velocimetry method for characterising the streamwise evolution of the flow over a streamwise distance of 15 boundary layer thicknesses. In the focus region, we use microscopic and Lagrangian particle tracking velocimetry to measure the mean velocity and the Reynolds stresses down to the viscous sublayer. Oil-film interferometry is used for the complementary direct measurement of the wall shear stress. In the adverse pressure gradient region we observe a composite form of the mean velocity profile with a thin log law region and a square-root law above up to 12% boundary layer thickness. We find lower values for the log-law slope coefficient than for zero pressure gradient boundary layers, but the reduction is within the uncertainties in the measurement and possible history effects. The total shear stress and the turbulent viscosity in the inner layer can be described by an analytical model whose parameters are the pressure gradient parameter and the acceleration parameter based on the streamwise gradient of the wall shear stress. Then we use a data base of adverse pressure gradient turbulent boundary layer flows at large Reynolds numbers from the literature. We find that the mean velocity profiles for different flows almost collapse provided that both the pressure gradient parameter and the wall shear stress gradient parameter are close to each other. Finally we describe and discuss the effects of the convex curvature and the relaxation of upstream curvature effects on a flat plate. The streamwise eddy-turnover distance indicates that the flow relaxes fast in the inner layer, whereas the turnover length is strongly increasing in the outer part of the boundary layer

Study of Richardson Number in flows with mean-streamline curvature

Flows with significant mean-streamline curvature effects are relevant in many applications, e.g., the curved wake flows above the flap of a high-lift system and vortical flows around deltawing type configurations. In such flows, mean-streamline curvature is known to cause considerable changes in the turbulence structure of shear layers. [1] More insight into a quantification of effects of curvature is important for devising modifications to RANS turbulence models