On the Weissenberg effect of turbulence

Within the framework of the Navier–Stokes equations, the Weissenberg effect of turbulence is investigated. We begin with our investigation on the elastic effect of homogeneous turbulent shear flow. First, in the sense of Truesdell (Physics of Fluids, 1964) on the natural time of materials, we derive...

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Main Authors: Yu-Ning Huang, Wei-Dong Su, Cun-Biao Lee
Format: Article
Language:English
Published: Elsevier 2019-07-01
Series:Theoretical and Applied Mechanics Letters
Online Access:http://www.sciencedirect.com/science/article/pii/S2095034919300418
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spelling doaj-22b7cfbf00864f1e83243dce7a900e852020-11-25T01:25:39ZengElsevierTheoretical and Applied Mechanics Letters2095-03492019-07-0194236245On the Weissenberg effect of turbulenceYu-Ning Huang0Wei-Dong Su1Cun-Biao Lee2Corresponding author; State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, ChinaState Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, ChinaState Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, ChinaWithin the framework of the Navier–Stokes equations, the Weissenberg effect of turbulence is investigated. We begin with our investigation on the elastic effect of homogeneous turbulent shear flow. First, in the sense of Truesdell (Physics of Fluids, 1964) on the natural time of materials, we derive the natural time of turbulence, and use it together with the natural viscosity of turbulence derived in the article of Huang et al. (Journal of Turbulence, 2003) to define the natural Weissenberg number of turbulence as a measure of the elastic effect of homogeneous turbulence. Second, we define a primary Weissenberg number of turbulence, which in laminar flow reduces to the Weissenberg number widely applied in rheology to characterize the elasticity of visco-elastic fluids. Our analysis based on the experimental results of Tavoularis and Karnik (Journal of Fluid Mechanics, 1989) indicates that the larger is the Weissenberg number of turbulence, the more elastic becomes the turbulent flow concerned. Furthermore, we put forth a general Weissenberg number of turbulence, which includes the primary Weissenberg number of turbulence as a special case, to measure the overall elastic effects of turbulence. Besides, it is shown that the general Weissenberg number can also be used to characterize the elastic effects of non-Newtonian fluids in laminar flow. Keywords: Normal stress difference, Natural time of turbulence, Weissenberg number of turbulence, Elastic effect, Non-Newtonian fluidhttp://www.sciencedirect.com/science/article/pii/S2095034919300418
collection DOAJ
language English
format Article
sources DOAJ
author Yu-Ning Huang
Wei-Dong Su
Cun-Biao Lee
spellingShingle Yu-Ning Huang
Wei-Dong Su
Cun-Biao Lee
On the Weissenberg effect of turbulence
Theoretical and Applied Mechanics Letters
author_facet Yu-Ning Huang
Wei-Dong Su
Cun-Biao Lee
author_sort Yu-Ning Huang
title On the Weissenberg effect of turbulence
title_short On the Weissenberg effect of turbulence
title_full On the Weissenberg effect of turbulence
title_fullStr On the Weissenberg effect of turbulence
title_full_unstemmed On the Weissenberg effect of turbulence
title_sort on the weissenberg effect of turbulence
publisher Elsevier
series Theoretical and Applied Mechanics Letters
issn 2095-0349
publishDate 2019-07-01
description Within the framework of the Navier–Stokes equations, the Weissenberg effect of turbulence is investigated. We begin with our investigation on the elastic effect of homogeneous turbulent shear flow. First, in the sense of Truesdell (Physics of Fluids, 1964) on the natural time of materials, we derive the natural time of turbulence, and use it together with the natural viscosity of turbulence derived in the article of Huang et al. (Journal of Turbulence, 2003) to define the natural Weissenberg number of turbulence as a measure of the elastic effect of homogeneous turbulence. Second, we define a primary Weissenberg number of turbulence, which in laminar flow reduces to the Weissenberg number widely applied in rheology to characterize the elasticity of visco-elastic fluids. Our analysis based on the experimental results of Tavoularis and Karnik (Journal of Fluid Mechanics, 1989) indicates that the larger is the Weissenberg number of turbulence, the more elastic becomes the turbulent flow concerned. Furthermore, we put forth a general Weissenberg number of turbulence, which includes the primary Weissenberg number of turbulence as a special case, to measure the overall elastic effects of turbulence. Besides, it is shown that the general Weissenberg number can also be used to characterize the elastic effects of non-Newtonian fluids in laminar flow. Keywords: Normal stress difference, Natural time of turbulence, Weissenberg number of turbulence, Elastic effect, Non-Newtonian fluid
url http://www.sciencedirect.com/science/article/pii/S2095034919300418
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