Institute of Fluid Mechanics and Heat Transfer, Vienna University of Technology, Resselgasse 3, 1040 Wien, Austria
Institute of Fluid Mechanics and Heat Transfer, Vienna University of Technology, Resselgasse 3, 1040 Wien, Austria.
Philos Trans A Math Phys Eng Sci. 2014 Jul 28;372(2020). doi: 10.1098/rsta.2013.0343.
Thin aerofoils are prone to localized flow separation at their leading edge if subjected to moderate angles of attack α. Although 'laminar separation bubbles' at first do not significantly alter the aerofoil performance, they tend to 'burst' if α is increased further or if perturbations acting upon the flow reach a certain intensity. This then either leads to global flow separation (stall) or triggers the laminar-turbulent transition process within the boundary layer flow. This paper addresses the asymptotic analysis of the early stages of the latter phenomenon in the limit as the characteristic Reynolds number [Formula: see text], commonly referred to as marginal separation theory. A new approach based on the adjoint operator method is presented that enables the fundamental similarity laws of marginal separation theory to be derived and the analysis to be extended to higher order. Special emphasis is placed on the breakdown of the flow description, i.e. the formation of finite-time singularities (a manifestation of the bursting process), and on its resolution being based on asymptotic arguments. The passage to the subsequent triple-deck stage is described in detail, which is a prerequisite for carrying out a future numerical treatment of this stage in a proper way. Moreover, a composite asymptotic model is developed in order for the inherent ill-posedness of the Cauchy problems associated with the current flow description to be resolved.
薄翼型在中等攻角α下，前缘容易发生局部流动分离。尽管最初的“层流分离气泡”不会显著改变翼型性能，但如果α进一步增加或作用于流动的扰动达到一定强度，它们往往会“破裂”。这会导致全局流动分离（失速）或触发边界层流内的层流-湍流转变过程。本文研究了后者现象在特征雷诺数[Formula: see text]极限下的早期渐近分析，通常称为边缘分离理论。提出了一种基于伴随算子方法的新方法，该方法能够推导出边缘分离理论的基本相似律，并将分析扩展到更高阶。特别强调了流动描述的崩溃，即有限时间奇点的形成（破裂过程的表现），以及基于渐近论证来解决该问题。详细描述了随后的三层阶段的过渡，这是以后以适当的方式对该阶段进行数值处理的前提。此外，还开发了一种组合渐近模型，以解决与当前流动描述相关的柯西问题固有的不适定性。
