Self-similar solution of the second kind for a convergent viscous gravity current
The axisymmetric flow of a very viscous fluid toward a central orifice is studied. In a recent paper, a self-similar solution for this problem has been found. The self-similarity is of the second kind and hence the flow remembers its initial condition only through a nondimensional constant which cha...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_08998213_v4_n6_p1148_Diez |
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todo:paper_08998213_v4_n6_p1148_Diez2023-10-03T15:44:05Z Self-similar solution of the second kind for a convergent viscous gravity current Diez, J.A. Gratton, R. Gratton, J. The axisymmetric flow of a very viscous fluid toward a central orifice is studied. In a recent paper, a self-similar solution for this problem has been found. The self-similarity is of the second kind and hence the flow remembers its initial condition only through a nondimensional constant which characterizes it. In this work this convergent flow is studied experimentally (using silicone oils) by measuring the front position and the height profile as a function of time. It is verified that the self-similar solution properly describes the flow within a certain interval of the cavity radius, where values are obtained for the similarity exponent δ in agreement (accounting for experimental errors) with the theoretical value 0.762... . The transition to the self-similar flow is also simulated numerically and numerical values are obtained for the time closure for different initial conditions. These simulations also show the theoretical self-similar flow after the cavity closure, which is very difficult to observe experimentally. © 1992 American Institute of Physics. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_08998213_v4_n6_p1148_Diez |
| institution |
Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
The axisymmetric flow of a very viscous fluid toward a central orifice is studied. In a recent paper, a self-similar solution for this problem has been found. The self-similarity is of the second kind and hence the flow remembers its initial condition only through a nondimensional constant which characterizes it. In this work this convergent flow is studied experimentally (using silicone oils) by measuring the front position and the height profile as a function of time. It is verified that the self-similar solution properly describes the flow within a certain interval of the cavity radius, where values are obtained for the similarity exponent δ in agreement (accounting for experimental errors) with the theoretical value 0.762... . The transition to the self-similar flow is also simulated numerically and numerical values are obtained for the time closure for different initial conditions. These simulations also show the theoretical self-similar flow after the cavity closure, which is very difficult to observe experimentally. © 1992 American Institute of Physics. |
| format |
JOUR |
| author |
Diez, J.A. Gratton, R. Gratton, J. |
| spellingShingle |
Diez, J.A. Gratton, R. Gratton, J. Self-similar solution of the second kind for a convergent viscous gravity current |
| author_facet |
Diez, J.A. Gratton, R. Gratton, J. |
| author_sort |
Diez, J.A. |
| title |
Self-similar solution of the second kind for a convergent viscous gravity current |
| title_short |
Self-similar solution of the second kind for a convergent viscous gravity current |
| title_full |
Self-similar solution of the second kind for a convergent viscous gravity current |
| title_fullStr |
Self-similar solution of the second kind for a convergent viscous gravity current |
| title_full_unstemmed |
Self-similar solution of the second kind for a convergent viscous gravity current |
| title_sort |
self-similar solution of the second kind for a convergent viscous gravity current |
| url |
http://hdl.handle.net/20.500.12110/paper_08998213_v4_n6_p1148_Diez |
| work_keys_str_mv |
AT diezja selfsimilarsolutionofthesecondkindforaconvergentviscousgravitycurrent AT grattonr selfsimilarsolutionofthesecondkindforaconvergentviscousgravitycurrent AT grattonj selfsimilarsolutionofthesecondkindforaconvergentviscousgravitycurrent |
| _version_ |
1807320856082251776 |