Unified Framework for Modeling Swirl Dominated Helical Motions
Unified Framework for Modeling Swirl Dominated Helical Motions
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DOI：
10.2514/6.2014-3677
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发表时间：
2014-07
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通讯作者：
J. Majdalani
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作者：
J. Majdalani
在这篇文章中，涡流占主导地位的运动的基本特征进行了检查的上下文中的外部和内部流，单细胞和双细胞涡，以及单向和多向配置。我们的报道开始与单细胞的朗肯，兰姆-奥森，和Burgers-Rott解决方案，演变成两个细胞的沙利文和郭涡，然后过渡到家庭的多方向运动在圆锥形和圆柱形的限制气旋室。在这个过程中，一个明智的重整化的变量使我们能够重铸的适度选择模型的问题，成为一个自相似的，普遍的形式，主要取决于一个埃克曼，离旋参数。这是通过重新调整外部涡流的峰值切向速度和核心半径来实现的，核心半径是从旋转轴到最大涡流点的距离。对于内部涡流，重整化是基于平均切向喷射速度和特征腔室半径。通过提供一个基本的修正郭的两个细胞的运动，直接和解与传统的模型是实现，这包括透视郭的强烈相似性沙利文的漩涡，一个属性，代表在实现温度诱导浮力和曲率为基础的旋转之间的普朗特-布拉德肖类比的能力。此外，通过提供一个微妙的修正的Bloor-Ingham涡，锥形旋流器的精确解是可能的。其次是一个新的扩展匹配渐近，粘性层分析的壁有界的气旋流场。因此，我们的工作最终在一个通用的，一致有效的粘性近似，这是适用于特殊类的双向涡的上下文中出现的右圆柱形涡流燃烧冷壁室（VCCWC），原型推力室，是众所周知的推进社区的介绍。随后的讨论包括相互补充的螺旋轮廓的复杂的层状，线性Beltramian和非线性Beltramian类型的集合。我们的粘性分析也延伸到一个广义的贝尔特拉米公式，可以同化一个可变的端壁喷射模式。在一开始，几个无量纲参数来自第一原理，并通过猜测，缩放，或合理化的传统的类似物进行比较。这些措施包括一个修改后的形式的涡流数，保持配置独立，和独特的形式的涡流雷诺数，包括涡流的影响，有限的腔室长度，和切向喷射模式在入口处。在识别出涡流模式的共性后，如涡流速度的复合结构及其强制、自由和过渡涡流层的包容性，将上述模型的基本特征表示为无量纲参数的函数，然后进行简要描述。这些包括核心和壁边界层，最大的漩涡和径向速度，横流沿着地幔界面，地幔定位，流动逆转模式的多样性，有效粘度等。最后，Holzapfel的修订Richardson数的不可压缩和可压缩流动条件下，探讨其连接到Cotel的标准涡核湍流和再层化。
In this article, the fundamental characteristics of swirl dominated motions are examined in the context of both external and internal flows, single and two-cell vortices, as well as unidirectional and multidirectional configurations. Our coverage begins with the single cell Rankine, Lamb-Oseen, and Burgers-Rott solutions, evolves into the two-cell vortices by Sullivan and Kuo, and then transitions into the family of multidirectional motions in both conically and cylindrically confined cyclonic chambers. In the process, a judicious renormalization of variables enables us to recast the modest selection of models in question into a selfsimilar, universal form that is mainly dependent on an Ekman-like, off-swirl parameter. This is achieved by rescaling external vortices by their peak tangential velocity and core radius, which is the distance from the axis of rotation to the point of maximum swirl. For internal vortices, the renormalization is based on the average tangential injection speed and characteristic chamber radius. By providing a basic correction to Kuo’s two-cell motion, straightforward reconciliation with traditional models is attained, and this includes the ability to bring into perspective Kuo’s strong similarity with Sullivan’s vortex, a property that stands in fulfilment of the Prandtl-Bradshaw analogy between temperature-induced buoyancy and curvature-based rotation. Furthermore, by providing a subtle correction to the Bloor-Ingham vortex, an exact solution for conical cyclones is made possible. This is followed by a novel extension to the matched-asymptotic, viscous layer analysis of wall-bounded cyclonic flowfields. Our work thus culminates in the presentation of a generic, uniformly valid viscous approximation, which is applicable to the special class of bidirectional vortices that arise in the context of a right-cylindrical Vortex Combustion Cold-Wall Chamber (VCCWC), a prototypical thrust chamber that is well known in the propulsion community. The ensuing discussion encompasses mutually complementary sets of helical profiles of the complex lamellar, linear Beltramian, and nonlinear Beltramian types. Our viscous analysis also extends to a generalized Beltramian formulation that can assimilate a variable endwall injection pattern. At the outset, several dimensionless parameters are derived from first principles and compared to traditional analogues that are conjectured via guesswork, scaling, or rationalization. These include a modified form of the swirl number that remains configuration-independent, and unique forms of the vortex Reynolds number that incorporate the effects of swirl, finite chamber length, and tangential injection patterns at entry. After identifying commonalities in vortex patterns, such as the composite structure of the swirl velocity and its containment of forced, free, and transitional vortex layers, the fundamental features of the aforementioned models are expressed as a function of dimensionless parameters and then briefly described. These include the core and wall boundary layers, maximum swirl and radial velocities, crossflow along the mantle interface, mantle positioning, multiplicity of flow reversal modes, effective viscosity, etc. Finally, Holzapfel’s revision of the Richardson number is explored under both incompressible and compressible flow conditions in view of its connection to Cotel’s criterion on vortex core turbulence and relaminarization.