Asymptotic and numerical approaches to three-dimensional flows and their stability

三维流动的渐近数值方法及其稳定性

• 批准号: 2091877
• 金额: --
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2091877
• 关键词: Asymptotic; numerical; approaches; three; dimensional

For high-speed fluid flows over a relatively flat surface, can we predict the response downstream of a small scale three-dimensional structure/disturbance placed near the surface? For example, the injection into a high speed flow of a narrow jet of similar fluid through the surface, or a narrow region of "roughened" surface. The novelty in these cases is that to model these situations for high speed flow requires the re-inclusion of terms in the physically-derived governing equations that are traditionally ignored at larger length scales, similarly the flow structures produced near the surface can (in some cases) be beneficial to some applications (for example, by delaying flow separation locally). Although some attention has been applied to high-speed flow over periodic arrays of such structures in the past, here we tackle the more challenging problem of spatially isolated regions of disturbance. Direct numerical simulation of similar problems has been considered previously, but our approach is to investigate the computationally much less expensive boundary-layer/region formulation and its ability to predict the resulting flow response. The mathematical character of these equations is somewhat different from the traditional formulation, with algebraic decay away from a disturbance site into the free stream flow and some care/analysis is needed to achieve an accurate formulation of the resulting flow and its stability properties.The student will formulate and solve a reduced set of partial-differential equations that model these flows in the high-speed limit, analyse and classify the behaviour through asymptotic methods applied to computational results. The stability of the flow will be addressed by computation and analysis applied to (bi-global) eigenvalue problems.

对于在相对平坦的表面上高速流动的流体，我们能否预测靠近表面的小规模三维结构/扰动下游的响应？例如，通过表面或“粗糙”表面的狭窄区域注入类似流体的窄射流的高速流。这些情况的新颖之处在于，要对高速流动的这些情况进行建模，需要将物理导出的控制方程中的项重新包含在传统上在较大长度尺度上被忽略的项，类似地，在表面附近产生的流动结构可以（在某些情况下）情况）对某些应用有益（例如，通过局部延迟流动分离）。尽管过去已经对此类结构的周期性阵列上的高速流动进行了一些关注，但在这里我们解决了更具挑战性的空间隔离扰动区域的问题。以前已经考虑过类似问题的直接数值模拟，但我们的方法是研究计算成本低得多的边界层/区域公式及其预测所得流动响应的能力。这些方程的数学特征与传统的公式有些不同，代数衰减从扰动位置进入自由流，需要进行一些处理/分析才能获得结果流及其稳定性特性的准确公式。学生将制定并求解一组简化的偏微分方程，对高速极限下的这些流动进行建模，通过应用于计算结果的渐近方法对行为进行分析和分类。流动的稳定性将通过应用于（双全局）特征值问题的计算和分析来解决。