DNS of Microfiber-Induced Drag Reduction Using a Two-Way Coupled Lagrangian Moment Approximation Method
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RESEARCH PAPER
DNS of Microfiber‑Induced Drag Reduction Using a Two‑Way Coupled Lagrangian Moment Approximation Method Amin Moosaie1 Received: 6 July 2020 / Accepted: 11 August 2020 © Shiraz University 2020
Abstract A two-way coupled Lagrangian moment approximation method for the simulation of Brownian fiber suspensions in turbulence is proposed. The flow equations are solved in an Eulerian manner. The influence of fibers on the fluid flow is taken into account by a non-Newtonian stress tensor. The fiber conformation and stresses are computed in a Lagrangian manner using the moment approximation method. The new method is used to simulate turbulent drag reduction in a plane channel. The results are compared with those of a direct Monte–Carlo solution of the Fokker–Planck equation, and a very good agreement is established. In comparison with the Newtonian flow case, the logarithmic region of the mean velocity profile shows a shift toward higher velocities, and velocity fluctuations in the streamwise direction are amplified, whereas the spanwise and wall-normal velocity fluctuations are attenuated, and the viscous sublayer is thickened. Small discrepancies between the results of the presented method and the reference data are conjectured to be mostly a consequence of the errors associated with the closure modeling, as also observed in previous Eulerian simulations. Keywords Turbulent drag reduction · Brownian fiber suspensions · Direct numerical simulation · Lagrangian particle tracking · Moment approximation method
1 Introduction A minute amount of rigid fibers can cause dramatic drag reduction when added to turbulent wall-bounded flows. Moreover, suspensions of prolate spheroidal particles (fibers) in Newtonian fluids are of technical interest in various pulp and polymer processing industries such as paper making and manufacturing of fiber-reinforced composite materials. Under certain assumptions, addition of fibers to a Newtonian carrier fluid makes to fluid to exhibit non-Newtonian features and it reveals anisotropic properties. In addition to this, when the fibers show rotary Brownian motion, which often takes place for small fibers, then the elasticity of the fluid comes into play and we observe a viscoelastic behavior, which intensifies by increasing the strength of the Brownian motion. Because of these diverse areas of application, developing numerical methods to simulate fiber suspension flows * Amin Moosaie [email protected] 1
Turbulence Research Laboratory, Department of Mechanical Engineering, Yasouj University, Yasouj 75914‑353, Iran
is of paramount importance, especially when it comes to turbulent drag reduction applications, due to the inherent complexity of turbulence. In order to simulate such flows, a rheological theory is required which provides the governing equations. Such theories have been developed in a number of publications, as reviewed below. Jeffery (1922) analytically solved the creeping flow about an ellipsoidal particle and proposed an ordinary differential equation that governs
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