A mathematical model of turbulent drag reduction by high-molecular-weight polymeric additives in a shear flow
Drag reduction, or the mean velocity increase in a turbulent flow at a fixed pressure drop through the addition of tiny amounts (several parts per million) of high-molecular-weight polymers (Thoms effect), has been known already for more than 60 years. Long ago it was understood that this effect is...
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| Published in | Physics of fluids (1994) Vol. 20; no. 9 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Melville, NY
American Institute of Physics
01.09.2008
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1070-6631 1089-7666 |
| DOI | 10.1063/1.2979711 |
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| Abstract | Drag reduction, or the mean velocity increase in a turbulent flow at a fixed pressure drop through the addition of tiny amounts (several parts per million) of high-molecular-weight polymers (Thoms effect), has been known already for more than 60 years. Long ago it was understood that this effect is related to supramolecular structures formed in the flow. Recent experiments by Chu, Shaqfeh, and associates, where the motion of supramolecular structures was directly observed, made it possible to understand and quantify the dynamic interaction of the polymeric structures with the solvent (water) flow. These results lead to the construction of a mathematical model of the Thoms effect, based on the Kolmogorov (1942)–Prandtl (1945) semiempirical theory of shear flow turbulence. This is the subject of the present letter. |
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| AbstractList | Drag reduction, or the mean velocity increase in a turbulent flow at a fixed pressure drop through the addition of tiny amounts (several parts per million) of high-molecular-weight polymers (Thoms effect), has been known already for more than 60 years. Long ago it was understood that this effect is related to supramolecular structures formed in the flow. Recent experiments by Chu, Shaqfeh, and associates, where the motion of supramolecular structures was directly observed, made it possible to understand and quantify the dynamic interaction of the polymeric structures with the solvent (water) flow. These results lead to the construction of a mathematical model of the Thoms effect, based on the Kolmogorov (1942)–Prandtl (1945) semiempirical theory of shear flow turbulence. This is the subject of the present letter. |
| Author | Barenblatt, Grigory Isaakovich |
| Author_xml | – sequence: 1 givenname: Grigory Isaakovich surname: Barenblatt fullname: Barenblatt, Grigory Isaakovich organization: Department of Mathematics, University of California, Berkeley, California 94720, USA |
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| Cites_doi | 10.1007/978-94-011-3030-1_48 10.1016/j.jnnfm.2005.05.011 10.1021/ma062932e 10.1038/physci245095a0 10.1021/ma048077l 10.1007/BF00914344 |
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| Issue | 9 |
| Keywords | Modelling Turbulent flow Polymer solutions Drag reduction Shear flow Turbulence structure |
| Language | English |
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| References | Prandtl (c3) 1945 Teixeira, Babcock, Shaqfeh, Chu (c8) 2005; 38 Kudin, Barenblatt, Kalashnikov, Vlasov, Belokon (c6) 1973; 245 Chorin (c11) 1998; 14 Shaqfeh (c9) 2005; 130 Kolmogorov (c2) 1942; 6 Teixeira, Dambal, Richter, Shaqfeh, Chu (c7) 2007; 40 Barenblatt, Bulina, Zeldovich, Kalashnikov, Sholomovich (c4) 1965; 5 Barenblatt, Bulina, Kalashnikov, Kalinichenko (c5) 1966; 7 (2023062717585846900_c2a) 1942; 6 (2023062717585846900_c12) 2003 (2023062717585846900_c5b) 1966; 7 (2023062717585846900_c8) 2005; 38 Tikhomirov (2023062717585846900_c2b) 1991 (2023062717585846900_c10) 1996 (2023062717585846900_c3) 1945 (2023062717585846900_c6) 1973; 245 (2023062717585846900_c11) 1998; 14 (2023062717585846900_c1) 1971 (2023062717585846900_c4a) 1965; 5 (2023062717585846900_c4b) 1965; 5 (2023062717585846900_c5a) 1966; 7 (2023062717585846900_c7) 2007; 40 (2023062717585846900_c9) 2005; 130 |
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Kl. – volume: 38 start-page: 581 year: 2005 ident: 2023062717585846900_c8 article-title: Shear thinning and tumbling dynamics of single polymers in the flow-gradient plane publication-title: Macromolecules doi: 10.1021/ma048077l – volume: 5 start-page: 147 year: 1965 ident: 2023062717585846900_c4a article-title: On a possible mechanism of the influence of small additives of high-molecular-weight compounds on the turbulence publication-title: Prikl. Mekh. Tekh. Fiz. – volume: 7 start-page: 77 year: 1966 ident: 2023062717585846900_c5b article-title: On the structure of weak polymeric solutions, displaying the effect of turbulence damping publication-title: J. Appl. Mech. Tech. Phys. doi: 10.1007/BF00914344 – volume: 7 start-page: 108 year: 1966 ident: 2023062717585846900_c5a article-title: On the structure of weak polymeric solutions, displaying the effect of turbulence damping publication-title: Prikl. Mekh. Tekh. Fiz. |
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| SubjectTerms | Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) Physics Turbulence control Turbulence simulation and modeling Turbulent flows, convection, and heat transfer |
| Title | A mathematical model of turbulent drag reduction by high-molecular-weight polymeric additives in a shear flow |
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