Turbulence dramatically increases the drag in wall flows. Therefore, turbulent drag reduction is of great importance in air/water transportation. It is well known that the addition of a minute amount of flexible bead-spring-like polymers or rigid-rod-like fibers to turbulent wall flows can significantly reduce the drag, while the introduction of the same polymers to a laminar flow will increase the drag. Thus, the interaction between turbulence and polymers is conjectured to be the key reason for drag reduction. Experimental studies of this phenomenon are rare as they are expensive and time-consuming. Development of high-fidelity simulation techniques is hence of paramount importance for a detailed study of the drag reduction induced by elongated particles.
The objectives of this project are basically twofold. From the engineering side, we aim at developing a reliable simulation technology to study the physics of fiber-induced turbulent drag reduction. Two fields are interacting in this problem, i.e. the flow field and the particle dynamics field. The flow field is computed by the state-of-the-art direct numerical simulation (DNS) techniques. The particle dynamics
has been computed via the moment approximation method. This is an approximative yet computationally efficient approach. Its accuracy depends on the closure model used. So far, there has been no direct simulation approach, not requiring any closure model, for the two-way coupled simulations for weakly Brownian fibers which are the most relevant ones for drag reduction. In the course of this project, a direct two-way coupled stochastic (Monte-Carlo) simulation technology has been developed which is applicable to weakly Brownian fibers. The implementation is fully parallelized and can be run on high-performance computers. This allows one to study the fiber-induced turbulent drag reduction without interventions from the validity and accuracy of closure models.
For stronger Brownian motion a higher number of samples is needed in a Monte-Carlo simulation in order to obtain high quality solutions. At this point the mathematical perspective comes into play. One can reformulate the problem in terms of a Fokker-Planck equation, which leads to a high dimensional convection-diffusion PDE, in which some of the dimensions are curved. In particular, along Lagrangian paths in the flow the domain is a unit sphere. In order to treat the arising equations efficiently, adaptive techniques have been developed and proved to be high-performance, providing high-fidelity results at comparably low computational costs. In addition, the new techniques are of higher order, which allows to opt for a higher accuracy with moderate increase in computational time.