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Register a new userDrag enhancement in a dusty Kolmogorov flow
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Particles suspended in a fluid exert feedback forces that can significantly impact the flow, altering the turbulent drag and velocity fluctuations. We study flow modulation induced by particles heavier than the carrier fluid in the framework of an Eulerian two-way coupled model, where particles are represented by a continuum density transported by a compressible velocity field, exchanging momentum with the fluid phase. We implement the model in direct numerical simulations of the turbulent Kolmogorov flow, a simplified setting allowing for studying the momentum balance and the turbulent drag in the absence of boundaries. We show that the amplitude of the mean flow and the turbulence intensity are reduced by increasing particle mass loading with the consequent enhancement of the friction coefficient. Surprisingly, turbulence suppression is stronger for particles of smaller inertia. We understand such a result by mapping the equations for dusty flow, in the limit of vanishing inertia, to a Newtonian flow with an effective forcing reduced by the increase in fluid density due to the presence of particles. We also discuss the negative feedback produced by turbophoresis which mitigates the effects of particles, especially with larger inertia, on the turbulent flow.
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In a recent paper, Liu, Zhu and Wu (2015, {it J. Fluid Mech.} {bf 784}: 304) present a force theory for a body in a two-dimensional, viscous, compressible and steady flow. In this companion paper we do the same for three-dimensional flow. Using the fundamental solution of the linearized Navier-Stokes equations, we improve the force formula for incompressible flow originally derived by Goldstein in 1931 and summarized by Milne-Thomson in 1968, both being far from complete, to its perfect final form, which is further proved to be universally true from subsonic to supersonic flows. We call this result the textit{unified force theorem}, which states that the forces are always determined by the vector circulation $pGamma_phi$ of longitudinal velocity and the scalar inflow $Q_psi$ of transverse velocity. Since this theorem is not directly observable either experimentally or computationally, a testable version is also derived, which, however, holds only in the linear far field. We name this version the textit{testable unified force formula}. After that, a general principle to increase the lift-drag ratio is proposed.
Previous studies on nonspherical particle-fluid interaction were mostly confined to elongated fiber-like particles, which were observed to induce turbulence drag reduction. However, with the presence of tiny disk-like particles how wall turbulence is modulated and whether drag reduction occurs are still unknown. Motivated by those open questions, we performed two-way coupled direct numerical simulations of inertialess spheroids in turbulent channel flow by an Eulerian-Lagrangian approach. The additional stress accounts for the feedback from inertialess spheroids on the fluid phase. The results demonstrate that both rigid elongated fibers (prolate spheroids) and thin disks (oblate spheroids) can lead to significant turbulence modulations and drag reduction. However, the disk-induced drag reduction is less pronounced than that of rigid fibers with the same volume fraction. Typical features of drag-reduced flows by additives are observed in both flow statistics and turbulence coherent structures. Moreover, in contrast to one-way simulations, the two-way coupled results of spheroidal particles exhibit stronger preferential alignments and lower rotation rates. At the end we propose a drag reduction mechanism by inertialess spheroids and explain the different performance for drag reduction by fibers and disks. We find that the spheroidal particles weaken the quasistreamwise vortices through negative work and, therefore, the Reynolds shear stress is reduced. However, the mean shear stress generated by particles, which is shape-dependent, partly compensates for the reduction of Reynolds shear stress and thus affects the efficiency of drag reduction. The present study implies that tiny disk-like particles can be an alternative drag reduction agent in wall turbulence.
Efficiently predicting the flowfield and load in aerodynamic shape optimisation remains a highly challenging and relevant task. Deep learning methods have been of particular interest for such problems, due to their success for solving inverse problems in other fields. In the present study, U-net based deep neural network (DNN) models are trained with high-fidelity datasets to infer flow fields, and then employed as surrogate models to carry out the shape optimisation problem, i.e. to find a drag minimal profile with a fixed cross-section area subjected to a two-dimensional steady laminar flow. A level-set method as well as Bezier-curve method are used to parameterise the shape, while trained neural networks in conjunction with automatic differentiation are utilized to calculate the gradient flow in the optimisation framework. The optimised shapes and drag force values calculated from the flowfields predicted by DNN models agree well with reference data obtained via a Navier-Stokes solver and from the literature, which demonstrates that the DNN models are capable of predicting not only flowfield but also yield satisfactory aerodynamic forces. This is particularly promising as the DNNs were not specifically trained to infer aerodynamic forces. In conjunction with the fast runtime, the DNN-based optimisation framework shows promise for general aerodynamic design problems.
The upper bound of polymer drag reduction is identified as a unique transitional state between laminar and turbulent flow corresponding to the onset of the nonlinear breakdown of flow instabilities.
Unlike a helicopter, an insect can, in theory, use both lift and drag to stay aloft. Here we show that a dragonfly uses mostly drag to hover by employing asymmetric up and down strokes. Computations of a family of strokes further show that using drag can be as efficient as using lift at the low Reynolds number regime appropriate for insects.
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