dorsal/arxiv
View SchemaOn analogy between transition to turbulence in fluids and plasticity in solids
| Authors | Sergey Ananiev |
|---|---|
| Categories | |
| ArXiv ID | physics/0609055 |
| URL | https://arxiv.org/abs/physics/0609055 |
| Journal | Turbulence, Heat and Mass Transfer 5. K. Hanjalic, Y. Nagano and S. Jakirlic (Editors), 2006 |
Abstract
The subject of this work is the instability mechanism of simple shear flows, like Hagen-Poiseuille pipe flow, which is a long-standing problem in fluid mechanics [1,2]. A possible analogy with phenomenological theory of ideal plasticity in solids is explored. It allows an extension of the Navier-Stokes equations making the simple shear flows unstable. Following von Mises [4], the existence of maximal allowed shear stress or "yield stress" in fluid is assumed. After the actual stresses have reached this value, a new physical mechanism will be activated attempting to reduce them. This mechanism results in a pressure-like force, which has to be added to the Navier-Stokes equations. The yield stress itself is a material constant, which does not depend on the Reynolds number of particular flow. It will be shown how to estimate its value from experimental data. To demonstrate how the character of flow changes if the additional force is taken into account, an unsteady flow in a 2D nozzle is presented. The momentum source was introduced in the Navier-Stokes equations through the user-defined function's interface offered by Fluent [6]. The initial data and the results of simulation are summarized in appendix.
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"abstract": "The subject of this work is the instability mechanism of simple shear flows,\nlike Hagen-Poiseuille pipe flow, which is a long-standing problem in fluid\nmechanics [1,2]. A possible analogy with phenomenological theory of ideal\nplasticity in solids is explored. It allows an extension of the Navier-Stokes\nequations making the simple shear flows unstable. Following von Mises [4], the\nexistence of maximal allowed shear stress or \"yield stress\" in fluid is\nassumed. After the actual stresses have reached this value, a new physical\nmechanism will be activated attempting to reduce them. This mechanism results\nin a pressure-like force, which has to be added to the Navier-Stokes equations.\nThe yield stress itself is a material constant, which does not depend on the\nReynolds number of particular flow. It will be shown how to estimate its value\nfrom experimental data. To demonstrate how the character of flow changes if the\nadditional force is taken into account, an unsteady flow in a 2D nozzle is\npresented. The momentum source was introduced in the Navier-Stokes equations\nthrough the user-defined function\u0027s interface offered by Fluent [6]. The\ninitial data and the results of simulation are summarized in appendix.",
"arxiv_id": "physics/0609055",
"authors": [
"Sergey Ananiev"
],
"categories": [
"physics.flu-dyn"
],
"journal_ref": "Turbulence, Heat and Mass Transfer 5. K. Hanjalic, Y. Nagano and\n S. Jakirlic (Editors), 2006",
"title": "On analogy between transition to turbulence in fluids and plasticity in solids",
"url": "https://arxiv.org/abs/physics/0609055"
},
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