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arXiv physics/0703135physics.flu-dyn
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流体混合中的源分布优化

Optimizing the Source Distribution in Fluid Mixing

Jean-Luc Thiffeault, G. A. Pavliotis

摘要:

一个被动标量平流的速度场,与非均匀的空间源,保持浓度不均匀。例如,标量可以是由热点和冷点组成的源的温度,使得平均温度恒定。哪个源分布在这个速度场中混合得最好?这个问题有一个直接而丰富的答案,与实际的混合问题有关。我们使用一个多尺度的措施,稳态增强混合和优化它的变分方法。然后,我们解决所产生的欧拉-拉格朗日方程的扰动均匀流和简单的细胞流。最佳源分布具有许多广泛的特征,正如预期的那样:它们避免了停滞点,有利于快速流动的区域,并且它们的轮廓对齐,使得流动将热点吹到冷点上,反之亦然。然而,详细的结构变化很大的扩散率和其他问题的参数。虽然这些都是模型问题,优化过程是足够简单,以适应更复杂的情况。

英文摘要:

A passive scalar is advected by a velocity field, with a nonuniform spatial source that maintains concentration inhomogeneities. For example, the scalar could be temperature with a source consisting of hot and cold spots, such that the mean temperature is constant. Which source distributions are best mixed by this velocity field? This question has a straightforward yet rich answer that is relevant to real mixing problems. We use a multiscale measure of steady-state enhancement to mixing and optimize it by a variational approach. We then solve the resulting Euler--Lagrange equation for a perturbed uniform flow and for simple cellular flows. The optimal source distributions have many broad features that are as expected: they avoid stagnation points, favor regions of fast flow, and their contours are aligned such that the flow blows hot spots onto cold and vice versa. However, the detailed structure varies widely with diffusivity and other problem parameters. Though these are model problems, the optimization procedure is simple enough to be adapted to more complex situations.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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