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Direct numerical simulations (DNS) of turbulent flows in an undulating channel.

机译：波动通道中湍流的直接数值模拟（DNS）。

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The combined problem posed by turbulence and viscoelasticity has been considered as the most difficult problem in physics even in 1990s. However, Direct Numerical Simulations (DNS) of Newtonian and non-Newtonian turbulent flows have become more popular with the increasing computer capabilities (high performance clusters of parallel supercomputers), the development of advanced viscoelastic models tailored for dilute polymer solutions, based on the kinetic theory, and accurate spectral methods with high efficiency. Based on an initial breakthrough from our research group in 1997, significant work has been conducted here and elsewhere in developing a theoretical understanding of the nature of polymer-induced drag reduction phenomena through DNS of viscoelastic turbulent channel flow in a straight channel flow geometry. However, no work has addressed so far the combined effect of turbulence, viscoelasticity and a moderately complex, non-planar flow geometry.; Turbulent flows over wall boundaries more complex than planar are of interest in many industrial and engineering problems, for example, heat exchanger designs, ocean flow simulations, pipeline transport, blood flow through arteries, etc. In particular, when the fluid is viscoelastic it is of interest to examine the effects of wall roughness on polymer drag reduction as we attempt to transfer laboratory test results to industrial flow applications. However, no numerical calculations have been performed so far to study the viscoelastic turbulent flows over rough surfaces, even idealized as wavy boundaries.; The first goal of the present work that we set and achieved was the development and validation of all necessary tools to perform high accuracy direct numerical simulations of viscoelastic turbulent flows within moderately complex flow geometries, such as a channel with a wavy wall. The second goal was to carefully validate the developed code against especially constructed limiting case solutions. The third was to test the new code extensively for Newtonian flows in a case of relatively high Reynolds number where experimental data and previous simulation results are available. The fourth was to develop and test the code performance in turbulent viscoelastic flows in a wavy channel in order to carefully understand the critical parameters for a successful simulation. In proceeding towards to completion of the last goal we have found necessary the development of a totally novel numerical representation that allows the preservation of a key characteristic in the viscoelastic flow simulations, that of the positive definiteness of an internal structural parameter of the viscoelastic simulations, the polymer conformation tensor.; More specifically, we first developed a new code based on an efficient implementation of spectral methods in non-orthogonal stretched coordinates in order to study the effects of complex flow boundaries acting on the flow behavior for both Newtonian and viscoelastic fluids. Second, the code has been validated against Newtonian laminar flow results. Detailed quantitative comparisons of the numerical and perturbation results have confirmed that the new code provides a very accurate spectral approximation for zero as well as non-zero Reynolds numbers. Third, large scale parallel computations involving DNS of Newtonian turbulent flows were performed at three different Reynolds numbers and for three different mesh resolutions. To achieve those results, a specially constructed initial guess velocity was used that was obtained through the intermediate use of a pseudoconformal transformation. DNS results obtained at the lowest friction Reynolds number (Retau =160) for two different mesh sizes allowed us to show the robustness of the code and convergence with mesh refinement.; Very large scale parallel computations, involving more than 200,000 CPU hours at the finest mesh resolution, executed at a high enough Reynolds number (Retau =310) in order to compare the simu
机译：由湍流和粘弹性构成的综合问题甚至在1990年代就被认为是物理学中最困难的问题。但是，随着计算机功能（并行超级计算机的高性能集群）的发展，基于稀薄聚合物溶液的量身定制的高级粘弹性模型的开发，牛顿和非牛顿湍流的直接数值模拟（DNS）变得越来越流行。理论和高效的精确光谱方法。基于我们研究小组在1997年取得的初步突破，在这里和其他地方已经进行了大量工作，以通过对直通道流几何中的粘弹性湍流通道的DNS理解聚合物引起的减阻现象的性质进行了理论理解。但是，到目前为止，还没有工作解决湍流，粘弹性和中等复杂的非平面流动几何形状的综合作用。在壁面边界上比平面更复杂的湍流在许多工业和工程问题中受到关注，例如，热交换器设计，洋流模拟，管道运输，通过动脉的血流等。特别是当流体是粘弹性时，我们试图将实验室测试结果转移到工业流应用中来研究壁粗糙度对聚合物减阻的影响。但是，到目前为止，还没有进行数值计算来研究粗糙表面上的粘弹性湍流，甚至理想化为波浪形边界。我们设定并实现的当前工作的首要目标是开发和验证所有必要的工具，以在中等复杂的流动几何体（例如带有波浪形壁的通道）内执行粘弹性湍流的高精度直接数值模拟。第二个目标是针对特别构造的限制案例解决方案仔细验证开发的代码。第三是在雷诺数相对较高的情况下，广泛地针对牛顿流测试新代码，在此情况下可获得实验数据和先前的模拟结果。第四是开发和测试波浪通道中湍流粘弹性流的代码性能，以便仔细了解成功进行仿真的关键参数。在完成最后一个目标的过程中，我们发现有必要开发一种全新的数值表示形式，该数值表示形式可以保留粘弹性模拟中的关键特性，即粘弹性模拟的内部结构参数的正定性，聚合物构象张量。更具体地说，我们首先基于在非正交拉伸坐标系中有效执行光谱方法的基础，开发了一种新代码，以研究复杂的流动边界对牛顿流体和粘弹性流体的流动行为的影响。其次，已针对牛顿层流结果对代码进行了验证。数值和摄动结果的详细定量比较已确认，新代码为零以及非零雷诺数提供了非常准确的频谱近似。第三，在三个不同的雷诺数和三个不同的网格分辨率下进行涉及牛顿湍流DNS的大规模并行计算。为了获得这些结果，使用了特殊构造的初始猜测速度，该速度是通过中间使用伪保形变换而获得的。在两个不同的网格尺寸下，以最低摩擦雷诺数（Retau = 160）获得的DNS结果使我们能够显示代码的鲁棒性和网格细化的收敛性。以足够高的雷诺数（Retau = 310）执行非常大规模的并行计算，在最佳的网格分辨率下涉及超过200,000 CPU小时，以比较simu

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