当前位置: X-MOL 学术Flow Turbulence Combust. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Adjoint Complement to the Universal Momentum Law of the Wall
Flow, Turbulence and Combustion ( IF 2.4 ) Pub Date : 2021-08-18 , DOI: 10.1007/s10494-021-00286-7
Niklas Kühl 1 , Peter M. Müller 1 , Thomas Rung 1
Affiliation  

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.



中文翻译:

墙的普遍动量定律的伴随补

该论文致力于对流体动力动量边界层的普遍壁垒定律 (LoW) 进行伴随补充。后者通常来自在恒定应力假设下的高度简化的单向剪切流。我们首先推导出简化动量方程的伴随同伴,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(微分)方法提供了几乎相同的伴随动量方程,不同之处仅在于控制对数区域倾角的单个标量系数。此外,可以看出可以推导出一个伴随的 LoW,它在许多方面都类似于它的原始对应物。该策略还与基于混合长度假设的突出 RANS 型两方程湍流模型的壁函数假设兼容。作为经常采用的假设的直接结果,即所有原始流动特性都随摩擦速度代数缩放,证明了简单的代数表达式提供了对数层中伴随动量方程的一致闭包。这种代数伴随闭包也可以作为使用标准一或二方程 Boussinesq 粘度模型的原始流的更一般伴随流优化研究的近似值。针对低 Re 和高 Re 设置的原始/伴随低公式验证从建议的代数闭合获得的结果。本文中包含的应用是指内部和外部工程流程的二维和三维形状优化。相关结果表明,与冻结湍流方法相比,所提出的伴随代数湍流闭合加速了优化过程,并在没有计算剩余的情况下提供了改进的优化。

更新日期:2021-08-19
down
wechat
bug