The focus of the present work is an experimental study of the behaviour of semi-dilute, opaque fibre suspensions in fully developed cylindrical pipe flows. Measurements of the normal and turbulent shear stress components and the mean flow were acquired using phase-contrast magnetic resonance velocimetry. Two fibre types, namely, pulp fibre and nylon fibre, were considered in this work and are known to differ in elastic modulus. In total, three different mass concentrations and seven Reynolds numbers were tested to investigate the effects of fibre interactions during the transition from the plug flow to fully turbulent flow. It was found that in fully turbulent flows of nylon fibres, the normal, uzuz+, and shear, uzur+ (note that · is the temporal average, u is the fluctuating velocity, z is the axial or streamwise component, and r is the radial direction), turbulent stresses increased with Reynolds number regardless of the crowding number (a concentration measure). For pulp fibre, the turbulent stresses increased with Reynolds number when a fibre plug was present in the flow and were spatially similar in magnitude when no fibre plug was present. Pressure spectra revealed that the stiff, nylon fibre reduced the energy in the inertial-subrange with an increasing Reynolds and crowding number, whereas the less stiff pulp fibre effectively cuts the energy cascade prematurely when the network was fully dispersed.

The effect of grid resolution on a large eddy simulation (LES) of a wall-bounded turbulent flow is investigated. A channel flow simulation campaign involving a systematic variation of the streamwise (Îx) and spanwise (Îz) grid resolution is used for this purpose. The main friction-velocity-based Reynolds number investigated is 300. Near the walls, the grid cell size is determined by the frictional scaling, Îx+ and Îz+, and strongly anisotropic cells, with first Îy+ ⌠1, thus aiming for the wall-resolving LES. Results are compared to direct numerical simulations, and several quality measures are investigated, including the error in the predicted mean friction velocity and the error in cross-channel profiles of flow statistics. To reduce the total number of channel flow simulations, techniques from the framework of uncertainty quantification are employed. In particular, a generalized polynomial chaos expansion (gPCE) is used to create metamodels for the errors over the allowed parameter ranges. The differing behavior of the different quality measures is demonstrated and analyzed. It is shown that friction velocity and profiles of the velocity and Reynolds stress tensor are most sensitive to Îz+, while the error in the turbulent kinetic energy is mostly influenced by Îx+. Recommendations for grid resolution requirements are given, together with the quantification of the resulting predictive accuracy. The sensitivity of the results to the subgrid-scale (SGS) model and varying Reynolds number is also investigated. All simulations are carried out with second-order accurate finite-volume-based solver OpenFOAM. It is shown that the choice of numerical scheme for the convective term significantly influences the error portraits. It is emphasized that the proposed methodology, involving the gPCE, can be applied to other modeling approaches, i.e., other numerical methods and the choice of SGS model. 

This study investigates the application of machine learning, specifically Fourier neural operator (FNO) and convolutional neural network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our focus is on extending existing operator learning methods to handle additional inputs representing PDE parameters. The goal is to create a unified learning approach that accurately predicts short-term solutions and provides robust long-term statistics under diverse parameter conditions, facilitating computational cost savings and accelerating development in engineering simulations. We develop and compare parametric learning methods based on FNO and CNN, evaluating their effectiveness in learning parametric-dependent solution time-advancement operators for one-dimensional PDEs and realistic flame front evolution data obtained from direct numerical simulations of the Navier-Stokes equations.