A method to determine local aerodynamic force coefficients from fiber-resolved 3D flow simulations around a staple fiber yarn

Even though air-jet weaving looms have become one of the most important weaving machines, the interactions between the air jets and fuzzy, flexible yarns are still not completely understood. Understanding these interactions is vital to improve the performance of these machines in terms of energy requirements and fabric quality. However, since experimental tests are expensive and time-consuming, there is a need for reliable numerical models and virtual prototyping. In the past decades, several methods have emerged where the yarn is modeled as a chain of beam-like elements. The aerodynamic forces on the yarn are typically represented by force coefficients. However, almost no representative data exist for force coefficients of staple fiber yarns subjected to relay nozzle flow in air-jet weaving, where apart from the inflow Reynolds number, the orientation of the yarn centerline with respect to the incoming flow is important. This paper presents a methodology to determine these local force coefficients applicable to relay nozzle flow using Computational Fluid Dynamics (CFD) simulations. A wool fiber yarn, used in air-jet weaving, is represented by the details of the fibers in a cubic flow domain. The overset technique enables the meshing of the fluid domain around the highly complex yarn geometry with additional contact treatment. The yarn is subjected to flow velocities ranging from 10 m/s to 175 m/s and orientations ranging from 0 degrees\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$0<^>{\circ }$\end{document} (axial flow) to 90 degrees\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$90<^>{\circ }$\end{document} (cross flow), which are conditions that typically occur in relay nozzle flow. Force coefficients in axial, transversal drag and lift direction, as well as an axial moment coefficient, are defined, and correlated as a function of flow Reynolds number and yarn inclination. This method can predict validated aerodynamic force coefficients for a general staple fiber yarn and goes beyond existing experimental approaches by accounting for the yarn orientation with respect to the incoming flow.