Adjoint Complement to the Universal Momentum Law of the Wall
Adjoint Complement to the Universal Momentum Law of the Wall
复制标题
墙的普遍动量定律的伴随补集
DOI：
10.1007/s10494-021-00286-7
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
T. Rung
中科院分区：
文献类型：
--
作者：
N. Kühl;P. M. Müller;T. Rung
本文致力于对流体动力学动量边界层的普遍壁定律（LoW）的伴随补充。后者通常是在常应力假设下从一个强烈简化的单向剪切流得出的。我们首先推导出伴随同伴的简化动量方程，同时区分两种策略。使用混合长度参数，我们证明了冻结湍流策略和低一致（差分）的方法提供了几乎相同的伴随动量方程，不同的只是在一个单一的标量系数控制在对数区域的倾斜度。此外，可以看出，一个伴随的LoW可以推导出类似于其原始对应在许多方面。该策略也是兼容的壁函数假设突出的RANS型两方程湍流模型，地面上的混合长度假设。作为一个直接的后果，经常采用的假设，即所有的原始流属性代数尺度与摩擦速度，它表明，一个简单的代数表达式提供了一个一致的封闭的伴随动量方程的对数层。这种代数伴随封闭也可以作为一个近似更一般的伴随流优化研究使用标准的一个或两个方程Boussinesq粘度模型的原始流量。从建议的代数封闭得到的结果进行了验证，对原始/伴随LoW配方，低和高Re设置。本文中的应用是指内部和外部工程流的二维和三维形状优化。相关结果表明，所提出的伴随代数湍流闭合加速优化过程，并提供了改进的最优值相比，冻结湍流方法在没有计算盈余。
The paper is devoted to an adjoint complement to the universal Law of the Wall (LoW) for fluid dynamic momentum boundary layers. The latter typically follows from a strongly simplified, unidirectional shear flow under a constant stress assumption. We first derive the adjoint companion of the simplified momentum equation, while distinguishing between two strategies. Using mixing-length arguments, we demonstrate that the frozen turbulence strategy and a LoW-consistent (differentiated) approach provide virtually the same adjoint momentum equations, that differ only in a single scalar coefficient controlling the inclination in the logarithmic region. Moreover, it is seen that an adjoint LoW can be derived which resembles its primal counterpart in many aspects. The strategy is also compatible with wall-function assumptions for prominent RANS-type two-equation turbulence models, which ground on the mixing-length hypothesis. As a direct consequence of the frequently employed assumption that all primal flow properties algebraically scale with the friction velocity, it is demonstrated that a simple algebraic expression provides a consistent closure of the adjoint momentum equation in the logarithmic layer. This algebraic adjoint closure might also serve as an approximation for more general adjoint flow optimization studies using standard one- or two-equation Boussinesq-viscosity models for the primal flow. Results obtained from the suggested algebraic closure are verified against the primal/adjoint LoW formulations for both, low- and high-Re settings. Applications included in this paper refer to two- and three-dimensional shape optimizations of internal and external engineering flows. Related results indicate that the proposed adjoint algebraic turbulence closure accelerates the optimization process and provides improved optima at no computational surplus in comparison to the frozen turbulence approach.
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发表时间：
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期刊：
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影响因子：
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