dorsal/arxiv
View SchemaInstability of Taylor-Couette Flow between Concentric Rotating Cylinders
| Authors | Hua-Shu Dou, Boo Cheong Khoo, Koon Seng Yeo |
|---|---|
| Categories | |
| ArXiv ID | physics/0502069 |
| URL | https://arxiv.org/abs/physics/0502069 |
| Journal | Int.J.Thermal Sci.47:1422-1435,2008 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
The energy gradient theory is used to study the instability of Taylor-Couette flow between concentric rotating cylinders. This theory has been proposed in our previous works. In our previous studies, the energy gradient theory was demonstrated to be applicable for wall-bounded parallel flows. It was found that the critical value of the energy gradient parameter Kmax at turbulent transition is about 370-389 for wall-bounded parallel flows (which include plane Poiseuille flow, pipe Poiseuille flow and plane Couette flow) below which no turbulence occurs. In this paper, the detailed derivation for the calculation of the energy gradient parameter in the flow between concentric rotating cylinders is provided. The calculated results for the critical condition of primary instability (with semi-empirical treatment) are found to be in very good agreement with the experiments in the literature. A possible mechanism of spiral turbulence generation observed for counter-rotation of two cylinders can also be explained using the energy gradient theory. The energy gradient theory can serve to relate the condition of transition in Taylor-Couette flow to that in plane Couette flow. The latter reasonably becomes the limiting case of the former when the radii of cylinders tend to infinity. It is our contention that the energy gradient theory is possibly fairly universal for analysis of flow instability and turbulent transition, and is found valid for both pressure and shear driven flows in parallel and rotating flow configurations.
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"abstract": "The energy gradient theory is used to study the instability of Taylor-Couette\nflow between concentric rotating cylinders. This theory has been proposed in\nour previous works. In our previous studies, the energy gradient theory was\ndemonstrated to be applicable for wall-bounded parallel flows. It was found\nthat the critical value of the energy gradient parameter Kmax at turbulent\ntransition is about 370-389 for wall-bounded parallel flows (which include\nplane Poiseuille flow, pipe Poiseuille flow and plane Couette flow) below which\nno turbulence occurs. In this paper, the detailed derivation for the\ncalculation of the energy gradient parameter in the flow between concentric\nrotating cylinders is provided. The calculated results for the critical\ncondition of primary instability (with semi-empirical treatment) are found to\nbe in very good agreement with the experiments in the literature. A possible\nmechanism of spiral turbulence generation observed for counter-rotation of two\ncylinders can also be explained using the energy gradient theory. The energy\ngradient theory can serve to relate the condition of transition in\nTaylor-Couette flow to that in plane Couette flow. The latter reasonably\nbecomes the limiting case of the former when the radii of cylinders tend to\ninfinity. It is our contention that the energy gradient theory is possibly\nfairly universal for analysis of flow instability and turbulent transition, and\nis found valid for both pressure and shear driven flows in parallel and\nrotating flow configurations.",
"arxiv_id": "physics/0502069",
"authors": [
"Hua-Shu Dou",
"Boo Cheong Khoo",
"Koon Seng Yeo"
],
"categories": [
"physics.flu-dyn",
"astro-ph.HE"
],
"journal_ref": "Int.J.Thermal Sci.47:1422-1435,2008",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Instability of Taylor-Couette Flow between Concentric Rotating Cylinders",
"url": "https://arxiv.org/abs/physics/0502069"
},
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