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首页> 外文会议>AIAA/ASME/SAE/ASEE joint propulsion conference exhibit >On the Viscous Bidirectional Vortex with Arbitrary End wall Injection
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On the Viscous Bidirectional Vortex with Arbitrary End wall Injection

机译：任意端壁注入的粘性双向涡流

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This work extends the inviscid framework developed by the authors for the purpose of modeling swirl-dominated cyclonic motions in straight cylindrical chambers with arbitrarily specified endwall velocities (Akiki, G. and Majdalani, J., "On the Bidirectional Vortex with Arbitrary Endwall Velocity," AIAA Paper 2010-6652, July 2010). This framework emerges directly from the Bragg-Hawthorne streamfunction equation and leads to an exact Euler solution that is capable of reproducing the flow in a bidirectional vortex chamber under a variety of user-prescribed inlet and outlet conditions. However, being derived in a frictionless environment, it leads to a characteristic singularity along the axis of rotation that affects both tangential velocity and pressure. The unbounded behavior of some properties about the centerline may be linked to the presence of a forced vortex in the core region that cannot be captured in a viscosity-free setting. The present study will overcome this deficiency by first transforming the tangential momentum equation with viscous diffusion to a form that is more germane to the core boundary layer region. Then using the tools of matched asymptotic expansions, a stretched radial coordinate is introduced to the extent of producing an inner velocity approximation that can be smoothly matched to the outer, inviscid flowfield. The latter manifests itself in an essentially free vortex that remains nearly invariant in the axial direction. By superimposing the inner and outer solutions asymptotically, a singularity-free representation is obtained for the swirl velocity, vorticity, and pressure. In the process, our analysis reveals a new dimensionless parameter, the generalized vortex Reynolds number; this group parameter incorporates the viscous Reynolds number, swirl number, aspect ratio, and imposed velocity pattern. We also find that vorticity originating from the viscous core markedly exceeds the vorticity introduced at the boundary as a result of fluid injection. Finally, all properties are discussed and compared to their inviscid counterparts.
机译：这项工作扩展了作者开发的无粘性框架，目的是为具有任意指定端壁速度的直圆柱室内的旋流主导的旋风运动建模（Akiki，G。和Majdalani，J。，“关于具有任意端壁速度的双向涡流， “ AIAA文件2010-6652，2010年7月）。该框架直接从Bragg-Hawthorne流函数方程产生，并产生一个精确的Euler解决方案，该解决方案能够在各种用户指定的入口和出口条件下在双向涡流室内重现流量。但是，在无摩擦的环境中导出时，会导致沿旋转轴的特征奇异性，从而影响切向速度和切向力。围绕中心线的某些属性的无限制行为可能与在核心区域中存在强制涡旋有关，而在无粘度设置中无法捕获这种强制涡旋。本研究将通过首先将具有粘性扩散的切向动量方程式转换为与核心边界层区域更紧密相关的形式，来克服这一缺陷。然后，使用匹配的渐近展开工具，将拉伸的径向坐标引入到生成内部速度近似值的程度，该速度可以平滑地匹配到外部无粘性流场。后者以基本自由的涡流表现出来，该涡流在轴向上几乎保持不变。通过渐近地叠加内部和外部解，可以得到旋流速度，涡度和压力的无奇异表示。在这个过程中，我们的分析揭示了一个新的无量纲参数，即广义涡旋雷诺数。该组参数包含粘性雷诺数，旋涡数，纵横比和施加的速度模式。我们还发现，由于流体注入的缘故，源自粘性芯的涡旋明显超过了在边界处引入的涡旋。最后，讨论了所有属性并将其与无粘性对应项进行比较。

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