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 small spherical 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.

中文翻译：

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尘土飞扬的Kolmogorov气流中的阻力增强

悬浮在流体中的颗粒会产生反馈力，该反馈力会显着影响流量，从而改变湍流阻力和速度波动。我们研究了在欧拉双向耦合模型的框架中由比载液重的球形小颗粒引起的流动调节，其中颗粒由可压缩速度场传输的连续体密度表示，与流体相交换动量。我们在湍流Kolmogorov流动的直接数值模拟中实现了该模型，该简化的设置允许在没有边界的情况下研究动量平衡和湍流阻力。我们表明，通过增加颗粒质量负荷可以降低平均流量的振幅和湍流强度，从而提高摩擦系数。出奇，对于较小惯性的粒子，湍流抑制作用更强。我们通过将消失的惯性极限中的尘埃流方程映射到牛顿流来理解这样的结果，该有效力由于颗粒的存在而导致流体密度的增加而降低了有效强迫。我们还将讨论由涡轮电泳产生的负反馈，该负反馈减轻了颗粒（尤其是具有较大惯性的颗粒）对湍流的影响。