First Grant Scheme: Boundary-layer transition on rotating bodies

背景：旋转盘边界层长期以来一直被用作后掠翼流动的模型，因为旋转盘和后掠翼的基本速度分布相似。然而，随着旋转弹丸、翼型、航空发动机和其他工业应用的不断发展，需要了解旋转的圆盘、球体和圆锥上边界层流动的层流-湍流转变的开始。例如，旋转的球体和圆锥在航空发动机和旋转的弹丸应用中用作鼻锥。在这里，鼻锥上边界层流动中的层流-湍流转变会导致阻力的显着增加。对于航空发动机应用，这会增加噪音和能量消耗，从而对燃油效率产生负面影响，而对于弹丸应用，这会对控制和精确瞄准产生负面影响。了解这种边界层流动的稳定性并制定保持层流流动的策略将导致对这些应用程序的设计进行修改，并实现显著的成本节约。此外，在电化学工业中用于在衬底上沉积光学和电子材料薄膜的化学气相沉积(CVD)反应器中存在旋转圆盘引起的流动。这样的反应器通过迫使含有反应分子的载气进入底物上来运行，底物保持在水平放置在流动中的盘状支撑物中。气体流动可以被认为是均匀的轴向入射到旋转圆盘上的流动，为了确保均匀沉积，靠近衬底的流动最好是层流的并且没有不稳定。研究：实验观察到细长圆锥和非细长圆锥上的过渡区是不同的。例如，对于在静止流体中旋转的具有细长半角的锥体，观察到一对反向旋转的Gortler型涡对。然而，当半角增加到30度以上时，结果清楚地表明涡对从对旋涡转变为同旋涡。众所周知，在旋转圆盘和非细长圆锥上观察到的涡旋实际上是归因于底层横流不稳定性的同向旋转涡旋，因此所观察到的细长圆锥不稳定源于一个内在不同的过程。假设了细长锥体存在粘性模式主导结构，从而导致了离心式Gortler不稳定性的发生。研究中将对这种不稳定性进行研究，重点放在上述旋转锥体的气动应用上。此外，尽管不可压缩边界层流动的常见假设对许多航空发动机应用是合理的，但它不适用于上述高速空气动力学和CVD应用。迄今为止在这种边界层上进行的研究虽然在理论上很重要，但必须被视为与这些应用有关的初步调查。因此，这项研究还旨在研究可压缩性和加热对这类物体的影响以及对机械设计的影响。

Background: The rotating-disk boundary layer has long been used as a model for swept-wing flow because of the similarity between the basic-flow velocity profiles of the disk and the swept wing. However, continuing developments in spinning projectiles, aerofoils, aeroengines and other industrial applications has led to the need to understand the onset of laminar-turbulent transition of the boundary-layer flows over rotating disks, spheres and cones as objects in their own right.For example, rotating spheres and cones are used as nose cones in aeroengine and spinning projectile applications. Here laminar-turbulent transition within the boundary-layer flow over the nose cones can lead to significant increases in drag. For aeroengine applications this has negative implications for the fuel efficiency through increased noise and energy dissipation, and for projectile applications this has negative implications for control and accurate targeting. Understanding the stability of such boundary-layer flows and developing strategies to maintain laminar flow will lead to modifications in the design of these applications and enable significant cost savings. Furthermore, flows arising from rotating disks are present in types of chemical vapour deposition (CVD) reactors used for depositing thin films of optical and electrical materials on substrates in the electrochemical industry. Such reactors operate by forcing a carrier gas containing the reactive molecules onto the substrate held within a disk-like support placed horizontally in the flow. The gas flow can be considered as a uniform axial flow incident on a rotating disk and it is desirable that the flow close to the substrate be laminar and free from instability to ensure uniform deposition.Research: Experimental observations have noted a distinction between the transition region on slender and non-slender cones. For example, for cones with slender half-angles rotating in still fluid, pairs of counter-rotating Gortler-type vortices are observed. However, as the half-angle is increased beyond 30degs, the results clearly show that the vortices change from pairs of counter-rotating vortices to co-rotating vortices. It is well known that the vortices observed on rotating disks and non-slender cones are in fact co-rotating vortices attributed to an underlying crossflow instability, and so the observed instability for slender cones stems from an inherently different process. The existence of a viscous-mode dominated structure for slender cones which leads to the onset of a centrifugal Gortler instability has been hypothesised. It is this instability that will be studied in the research, with particular emphasis placed on the aerodynamic applications of rotating cones mentioned above.In addition, although the common assumption of an incompressible boundary-layer flow is reasonable for many aeroengine applications, it is not for the high-speed aerodynamic and CVD applications mentioned above. The studies performed so far on such boundary layers, although important in a theoretical context, must be considered as preliminary investigations with regards these applications. This research therefore also aims to study the effects of compressibility and heating on such bodies and the implications for machinery design.