A Mean Flow Model for Polymer and Fiber Turbulent Drag Reduction
We present a one-parameter model that fits quantitatively the mean velocity profiles from experiments and numerical simulations of drag-reduced wall-bounded flows of dilute solutions of polymers and non-Brownian fibers in the low and modest drag reduction regime. The model is based on a viscous mech...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2005-12-01
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| Series: | Applied Rheology |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/arh-2005-0018 |
| _version_ | 1818726632822669312 |
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| author | Roy Anshuman Larson Ronald G. |
| author_facet | Roy Anshuman Larson Ronald G. |
| author_sort | Roy Anshuman |
| collection | DOAJ |
| description | We present a one-parameter model that fits quantitatively the mean velocity profiles from experiments and numerical simulations of drag-reduced wall-bounded flows of dilute solutions of polymers and non-Brownian fibers in the low and modest drag reduction regime. The model is based on a viscous mechanism of drag reduction, in which either extended polymers or non-Brownian fibers increase the extensional viscosity of the fluid and thereby suppress both small and large turbulent eddies and reduce momentum transfer to the wall, resulting in drag reduction. Our model provides a rheological interpretation of the upward parallel shift S+ in the mean velocity profile upon addition of polymer, observed by Virk. We show that Virk’s correlations for the dependence on polymer molecular weight and concentration of the onset wall shear stress and slope increment on the Prandtl-Karman plot can be translated to two dimensionless numbers, namely an onset Weissenberg number and an asymptotic Trouton ratio of maximum extensional viscosity to zero-shear viscosity. We believe that our model, while simple, captures the essential features of drag reduction that are universal to flexible polymers and fibers, and, unlike the Virk phenomenology, can easily be extended to flows with inhomogeneous polymer or fiber concentration fields. |
| first_indexed | 2024-12-17T22:01:18Z |
| format | Article |
| id | doaj.art-4fe25c5385ee4a5cacf85db381f8c4b2 |
| institution | Directory Open Access Journal |
| issn | 1617-8106 |
| language | English |
| last_indexed | 2024-12-17T22:01:18Z |
| publishDate | 2005-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Applied Rheology |
| spelling | doaj.art-4fe25c5385ee4a5cacf85db381f8c4b22022-12-21T21:30:59ZengDe GruyterApplied Rheology1617-81062005-12-0115637038910.1515/arh-2005-0018A Mean Flow Model for Polymer and Fiber Turbulent Drag ReductionRoy Anshuman0Larson Ronald G.1Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USADepartment of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USAWe present a one-parameter model that fits quantitatively the mean velocity profiles from experiments and numerical simulations of drag-reduced wall-bounded flows of dilute solutions of polymers and non-Brownian fibers in the low and modest drag reduction regime. The model is based on a viscous mechanism of drag reduction, in which either extended polymers or non-Brownian fibers increase the extensional viscosity of the fluid and thereby suppress both small and large turbulent eddies and reduce momentum transfer to the wall, resulting in drag reduction. Our model provides a rheological interpretation of the upward parallel shift S+ in the mean velocity profile upon addition of polymer, observed by Virk. We show that Virk’s correlations for the dependence on polymer molecular weight and concentration of the onset wall shear stress and slope increment on the Prandtl-Karman plot can be translated to two dimensionless numbers, namely an onset Weissenberg number and an asymptotic Trouton ratio of maximum extensional viscosity to zero-shear viscosity. We believe that our model, while simple, captures the essential features of drag reduction that are universal to flexible polymers and fibers, and, unlike the Virk phenomenology, can easily be extended to flows with inhomogeneous polymer or fiber concentration fields.https://doi.org/10.1515/arh-2005-0018drag reductionpolymerfibervirk phenomenologydirect numerical simulationturbulence |
| spellingShingle | Roy Anshuman Larson Ronald G. A Mean Flow Model for Polymer and Fiber Turbulent Drag Reduction Applied Rheology drag reduction polymer fiber virk phenomenology direct numerical simulation turbulence |
| title | A Mean Flow Model for Polymer and Fiber Turbulent Drag Reduction |
| title_full | A Mean Flow Model for Polymer and Fiber Turbulent Drag Reduction |
| title_fullStr | A Mean Flow Model for Polymer and Fiber Turbulent Drag Reduction |
| title_full_unstemmed | A Mean Flow Model for Polymer and Fiber Turbulent Drag Reduction |
| title_short | A Mean Flow Model for Polymer and Fiber Turbulent Drag Reduction |
| title_sort | mean flow model for polymer and fiber turbulent drag reduction |
| topic | drag reduction polymer fiber virk phenomenology direct numerical simulation turbulence |
| url | https://doi.org/10.1515/arh-2005-0018 |
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